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'rofessor R.T. Crawford
LIBRARY
BESEAECHES
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EVOLUTION OF THE STELLAR SYSTEMS
VOLUME I
ON THE UNIVERSALITY OK THE RAW fl*' GRAVITATION AND ON THE
ORBITS AND GENERAL CHARACTERISTICS OK BINARY STARS
T. J. J. SEE, A.M., PH.D., (BEBLIK)
ASTROXOMEK AT THE LOWELL OBxKKV AToKY IX ClI AK<1E OF A SURVEY OF THE SoUTHEKX Hr.AVKNH
F0« THE Dl»COVE*T AJ<D MK.AHl KKMKNT OF NEW DOUBLE STAKM AND NEBULAE;
FELLOW OF THE ROYAL AMTKOMUIK-AI. SIM-IKTY; MITOLIEU DEB
A8TKOXOMISCHEM GE8ELL8CHAFT, ETC., ETC.
is;..;
THE NICHOLS PRESS — THO8. P. NICHOLS
rOBLISBBBt
LTNN, MASS., D. 8. A.
R. FKIKI.I AXDKB A Sous, Buu.15
ASTRONOMY LIBRARY
S45
DEDICATED
TO
DR. BENJAMIN Armour GOULD,
THE ARQELANDER OF THE SOUTHERN HEAVENS,
IN TKHTIMONV or A HICH AI-PKWIATIOX or Lirr.-ix»x« SRRVK KM
CONSECRATED TO THE ADVANCEMENT or
AMERICAN SCIENCE.
CONTENTS.
INTRODUCTION, . »-•
CHAPTER I.
Ox TH« DKVXLOPMKXT or DOUBLK-STAH AUTBOXOMY, AXD ox THK MATHEMATICAL THKOHIIW or
THE MOTIONS or BINARY STAB*.
S 1. Historical Sketch of Double-Star Astronomy from Hertchel to Iturnham. 1 1-16
{ 2. Laplace's Demonstration of the Law of Gravitation in the Planetary Sy*lem, . 1 .". 1 s
S3. Investigation of the Laic of Attraction in the Stellar Systems, . 18-21
{4. Analytical Solution of Bertram?* Problem Hated on that Developed by Durban* ;
Solution of Halphen 21-29
1 5. Theory of the Determination, by Meant *f a Single Spectroscopic Observation, of
the Absolute Dimensions, Parallaxes and Mattes of Stellar Systems whose
Orbits are Known from Mirrometriral Measurement, . 30-36
J6. Rigorous Method for Testing the Universality of the Law of Gravitation, 36-38
1 7. On the Theoretical Possibility of Determining the Distances of Star-Clusters and
of the Milky Way, and of Investigating the Structure of the Heavens by
Actual Measurement, . . 38-41
|8. Historical Sketch of the Different Methods for Determining Orbits of Double
Stars, «-"
$9. Kowaltky's Method, . ' ' '
Modification Proposed by Glasenapp, ' ' '
|10. Graphical Method of Klinkerfuet, .
Graphical Method of Finding the Apparent Orbit of a Double Star, .
§11. Formulae for the Improvement of Elements, . :'"'"
§ 12. A General Method for Facilitating the Solution of Kepler's Equation by Mechanical
Means, . . ... . '•" ' '
VI
CONTENTS.
CHAPTER II.
ON THE ORBITS OF FORTY BINARY STARS.
Introductory Remarks, ......
PAGES
65 66
1.
Abbreviations of the Names of Observers,
.£3062
66-67
67 71
2.
77 Cassiopeae = .£60,
72 77
3.
y Andromedae BC = O238,
77 80
4.
5.
a Cants Majoris = Sirius •= A.G.C.\, .
9 ^rws (9 Puppis) — B 101,
81-86
86 88
6.
£ Cawcri AB — .£1196, ....
88-94
7
.£3121, .... ...
94 97
8.
taLeonis — .£1356,
97-102
9
(f Ursae Majoris — O.£208, .....
102 105
10,
$ Ursae Majoris — .£1523,
105 111
11.
O.£234,
112 114
12.
0.£235,
114 117
13,
y Centauri = H25370, ......
117 120
14.
y Virninls = .£1670,
120 129
15.
1f>.
42 Comae Berenices = .£1728, ....
0.£269,
130-134
134 136
17.
18
25 Canum Venatifomim = .£1768,
a Centauri, ........
. . . . . 137-140
140 149
19
0.£285,
149 151
9,0
( Bob'tis — .£1888,
152 157
21.
fl?
j; Coronae Borealis = 2 1937, ....
^ Hootis — 21938,
157-163
163 168
?3
0^298,
168 171
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
y Coronae Borealis = .£1967, ....
tScorpii = .£1998,
o- Coronae Borealis = .£2032, . . ...
{ Herculis = .£2084, ... . .
)8416 = Lac. 7215,
.£2173, .
ft1 Herculis BC = A.C. 7,
r Ophiuchi = 22262,
70 Ophiuchi = .£2272, . . .
99 Herculis = A.C. 15, .
171-175
176-180
180-185
186-192
192-194
194-198
198-202
. 202-206
207-221
221-223
< <.\ M \ i -. vii
34. tSayittarii, . I
85. y Coronae Auttralu - //, 5084, . 226 229
36. ftDetphini - 0151. . ... . 220-232
37. 4 ^7ManV - .12729, . . . 232-234
38. lEyuuM AH - O2&3&, . . . . . . 235-237
39. K Peyati - 0989, . . 237-240
40. 85 Peyui « 0733, 240-242
CHAPTER III.
KIM I r- or RUKABCHKS OH THE (>KBITH OK FoRTV Hl.SAKY ST.\K-, WITH (iKNKKAI.
CoXaiDMUTIOXH KKKfKiTIMi THE STKI.LAK STKTEMH.
fl. JBffMUfe of the OrinU of Forty Binary Stan, . . 243 245
. /. Velocity of tht ComjMtHion in tk« Line of Siyht for the Kjiork 1896.50, 246-247
J3. Investigation of a Pottiole Kelation of the Orbit-I'ltine* of Itiuary Syttemt to the
Plane of the Milky Way, . ... . 247-249
§4. Iligk Krrtntririiie* a Fundamental Law of Katun, . . 249-253
|5. Relative Matte* of the CtWjftmmti in Stellar Syttemt, ..... 253-256
{6. Exceptional Character of the Planetary System, . 257-258
"Z-'«w des pkcnomcnes les -phis remarquables du systcme du mondc cst celui de tons
les mouvements de rotation et de revolution des planetes et des satellites dans le sens de
la rotation du soleil et a pen pres dans le plan de son equateur. Un phcnomcne aussi
remarquable n'cst point reject du hazard; il indique une cause generale qui a determine
tous ces mouvements. ...» * *
" Un autre phcnomene cgalement remarquable du systeme solaire est le peu d°ex-
ccntricite des orbes des planetes et des satellites, tandis que ceux des cometes sont ires
allonges. ...» * •
"£>uellc cst cette cause primitive? J'exposerai sur ccla, dans la note qui termine
cet ouvrage (Systeme du Monde) une hypothese, qui me parait resuller avec une grandc
•vraisemblance des phenomenes precedents, mats que je presente avec la defiance que doit
inspircr tout ce qui n'est point un rcsultat de I 'observation ou de calcul."
LAPLACE.
INTRODUCTION.
< >M hundred \ear- ago L.vi'l.ACK published an outline of the nebular
|I\|MI||M •-!-. \\hirh has >inee been continued mid develojietl by tlie labors of
a-.tioiioiw.T8. His physical explanation of the evolution of the planets and
satellite.*, under the gradual operation of the lawH of nature, was the logical
outcome of his profound study of the mechanism of our system, and rested
mainly on the common direction of motion and the small eccentricities and
mutual inclinations of the orbits. From the concurrence of such remarkable
phenomena in a great numl>er of Ixxlies the author of the Mfcanique Cflextt was
led to conccixc that at a remote epoch in the past, the matter now constituting
the plaiu-ts and satellites was expanded into a vast rotating fiery nebula, which
slowh contracted with the radiation of its heat into surrounding space. Accord-
ing to the mechanical principle of the conservation of areas, the contraction accel-
erated the rotation and thereby increased the oblateness; when the centrifugal
force at the equator Iwcatne equal to the force of gravity the particles ceased
to tall towards the centre, and the nebula shed successive rings or zones of
vapor from its equatorial |H-riphery. The condensation of the several rings
thus abandoned by the contracting mass eventually gave rise to the Ixxlies of
the planetary system.
I. MM. .MI <.l,Mi\.,l that the comets, unlike the planets and satellites. ha\e
every degree of inclination and very high eccentricities, and hence he concluded
that they were originally foreign to the solar -y-t.'m: accordingly, in the nebular
hyixithesis, the comets are regarded as small nebulae which have been drawn
to tin- -mi in its secular motion among the fixed stars.
The alnive hypothesis, based on sound dynamical principles and worked
out in detail by the philo-ophic judgement and imaginative geniii- "I" I. MM. MI.
merited and iccci\cd the attention of -iih-eqin-nt natural philosopher-.
Owing to the brief duration of human hi-lory compared to the inmien-e |
required for appreciable cosmogonic changes, probably the e\olniion of the
heavenly bodie- can n. \. t I.e observed, but mu-t be inferred from n cmiipara-
2i INTRODUCTION.
tive study of existing phenomena; and hence the sublime discovery of the
essential process involved in the formation of the planetary system would
necessarily mark an epoch in the history of science. The boldness and pro-
found physical insight with which LAPLACE attacked this problem have justly
ranked his effort among the greatest achievements of the human intellect. The
germ of the general theory of evolution, which has so powerfully influenced
the thought of the nineteenth century, may be traced to the recondite specula-
tions of this great geometer.
The strikingly analagous cosmogonic views advanced by KANT in the
Naturgeschichte und Theorie des Ilimmels preceded those of LAPLACE by forty-
one years, and hence some priority is claimed for the great metaphysician of
Konigsberg; but since the real vitality of the nebular hypothesis springs from
LAPLACE, whose scientific eminence gave it authority commensurate with the
development of Physical Astronomy in the eighteenth century, this great cos-
mogonic speculation is justly dated from the publication of the Systime du
Monde in 1796.
SIR WILLIAM HERSCHEL'S observations on the different types of stars and
nebulae led him to consider them of different ages, and to compare the heavenly
bodies in such various stages of development to the mixture of growth and
decay presented by the trees of an aged forest. The combination of HERSCIIEL'S
studies on actual phenomena of the heavens with LAPLACE'S dynamical specula-
tions relative to the solar system gave the nebular hypothesis both an observational
and a theoretical basis, and hence it soon became an integral part of scientific
philosophy. SIR JOHN HERSCHEL'S survey of the entire heavens supplied new
and important observations relative to the appearances of the stars and nebulae,
and confirmed the general validity of the nebular hypothesis. When, however,
LORD ROSSE'S great Reflector resolved certain clusters previously classed as
nebulae, the question naturally arose whether with sufficient power all nebulae
might not be resolved into discrete stars. Fortunately, the invention of the
Spectroscope about I860, and HUGGINS'S application of it to the heavenly
bodies, showed that many of the nebulae are masses of glowing gas gradually
condensing into stars, and, so far as possible, realized the postulates laid
down by LAPLACE. JOULE'S discovery of the mechanical equivalent of heat
and HKI.MIKM.TZ'S application of the resulting laws of thermodynamics to
the heat of the sun, established the contraction of the solar nebula, while
the subsequent researches of LANE, NEWCOMB, KELVIN and DARWIN have
shown the theoretical possibility of most of the development outlined in the
Systhne du Monde.
i\ I i:«-i.i ( I i"\. ;t
Notwithstanding the general continuation nf tin- e— eiitial part- "I I . M-I.ACK'S
-peculation, some doubt still remains whether the planets ami satellites separated
:i- rinir- or a- lumpv in:i--«--. ami \\hcthcr ring- of anything like regularity could
e\er condense inin single bodies. The mo-t recent investigations of this
<|iu--tion indieate that in-lead »{' separating as rings or xones which afterward*
(••>ndeii-eil, the planet- and satellites, like the double stars, assumed originally
the farm of lumpy or globular ma— e-.
In the time "t I.\i-i \< i it was -uppo-cd that the figures of equilibrium of
rotating ma--e- of llnid. whose particles attract one another according to the
Newtonian law. are of necessity surfaces of revolution about the axis of
rotation, and then-fore that a separation could take place only in the form of
a ring or /one. lint the investigations of JACOHI showed that a homogeneous
ma-- of llnid in the form of an ellipsoid of three unequal axes rotating iihnut
its shortest axis could be maintained in equilibrium by the pressure and
attraction of it- part-: the figure of such a mass is no longer one of revo-
lution, although it i- -till symmetrical with respect to the axis of rotation.
l'->i\< \I:K'S recent investigation of the stability of the equilibrium of the
Jacobian ellip-oid -bowed that when the ohlateness has heeonu* about two-fifths
the equilibrium in this form becomes tin-table, and another figure in developed;
the body assumes the form of a pear or an hour-glass with two unequal bulbs,
and finally breaks up into two comparable, though unequal, massea. Starting
from an entirely different point of view, DAUWIV made an indc|>endent and
almost simultaneous investigation of the form assumed by the mass after the
•laeohian ellipsoid becomes unstable. Taking two separate masses of fluid
revolving as a rigid -\-i.-m in -neb close proximity that the tidal dixtortionH of
figure cause them to coalesce, he determined the resulting figure of equilibrium.
and found a dumb-bell form corresponding very closely to the Apioid discovered
l>\ I'"i\< \i:i. Though both of these investigations relate to homogeneous
ma— e-. and tln-relon- are m. I -tricilv ap|.li.-;ili|f to ill,- eases uhidi .-in-i- in
nature, yet they agree entirely in proving the existence <>!' iin-ymmctrical form-
"I equilibrium; and a comparison of these figures with the drawing- of double
nebulae made by Sin .Foiis I Ii ix m;i. |,-a\i-s no doubt that the process of
separation into unequal but comparable masses indicated by these recondite
mathematical researches is abundantly illustrated in the evolution of double
-tar- from double nebulae. If tin- proce— ha- played such a prominent part in
the geiie-i- of the stellar systems, it is highly probable that the plain t- and
satellite- originated in a similar manner, not withstanding the abnormally rapid
increase in density toward- the centres of the -..lar nebula implied by the
separation of such inconsiderable ma— c-.
INTRODUCTION.
When NEWTON established the law of universal gravitation he also discovered
the true cause of the tides of the sea, and outlined some of the principal phenomena
which follow from the perturbing action of the sun and moon upon the waters
which cover the terrestrial spheroid. After the lapse of more than a century
LAPLACE attacked this problem from the dynamical point of view, and developed
his celebrated analytical theory of oceanic tides, which has been generally
adopted in the subsequent researches of astronomers. About two centuries
after NEWTON established the cause of the tides, DARWIN was led to consider
not only the tides in the mass of fluid spread over the earth's surface, but also
those which arise in the body of the globe, owing to its imperfect rigidity.
He inquired whether the earth's mass might not be a fluid of great viscosity,
and proceeded to develop the theory of bodily tides, and to discuss the bear-
ing of these researches on the cosmogonic history of the earth and moon.
When the investigation was subsequently extended to other pails of our system,
it was found that while LAPLACE'S hypothesis as a whole remained unshaken,
some appreciable modifications were rendered necessary, especially in the case of
the earth and moon, where the relatively large mass-ratio of the component
bodies sensibly increased the efficiency of tidal friction. It seemed clear that
in the development of the lunar-terrestrial system, the action of tidal friction
had been of paramount importance, but that elsewhere the effects had been
much less considerable, owing chiefly to the small masses of the attendant
bodies.
AVhen we reflect that the planetary system is made up of a great number
of very small bodies revolving in almost circular orbits about large central
masses, and is therefore different from all other known systems in the heavens,
although other systems like it may exist unobserved, it is remarkable that
previous investigators have almost invariably approached the problems of
Cosmogony from the point of view of the planets and satellites, and that no
considerable attempt has been made to inquire into the development of the
great number of systems observed among the fixed stars. The short period
of time which has elapsed since the explorations of the Telescope have made
known the general state of the heavens, with the impossibility of observing any
considerable changes, except in the case of double stars, may perhaps account
for the natural tendency to focus all effort upon the development of the planets
and satellites. But the peculiar character of our system, compared to other
known systems in space, renders this procedure incapable of giving us any
general law of nature. It is only from a study of the systems of the universe
ivn: ....... [ON. ft
:ii 1:11-1- tliat we tuny IM.JM in throw light upon the general problem- of
1 "".v> aiming tln->< -\-i<-m- tin- binary -tans arc eminently suited for
-iidi an investigation.
In the present work we propose t» inve-tigate the evolution of tlie stellar
-\-tcni8. The problem i- difficult and the observations arc incomplete, and
henee in this arduous undertaking we may l>eg the indulgence of astronomers
for Midi imperfection- a- I In- di-cus-ion of the subject will necessarily exhibit.
The present volume i- devoted mainly to the facts as made known by the
lalHir- of double-star ol>-er\ers since the time of Sill WlI.I.IAM III i:-< ur.i.: the
more ihcorctical ini|uiry into the Secular Effects of Tidal Friction and the IVo-
oi CosniogoiM i~ reserrw! for Mbtaqoenl trattmenl
It would seem that the inicroinetrical uu-a-nn-- discussed in this work
i -taMi-li for the first time, on a secure observational basis, the general sha|>e of
the real orbits of double stars. It follows from the results here brought to light
that the most probable eccentricity among double stars is over 0.45, and since this
nu-an value i- deduced from the consideration of forty orbits, which future
observations will not alter materially, we see that such high eccentricities are
rliarartei i-tie of the stellar systems. In the solar system the mean eccentricity
tor the great planets and their satellites does not surpass (UKkSO, and hence
we see that the average eccentricity among double stars is about twelve tiuu*
thai found in our own system. The great number of binary stars and the
practical certainty that the projHTtics deduced from forty of the best orbits
now available will be confirmed by the stellar systems in general, justifies us
in raiding this remarkable induction, relative to the eccentricities, to the dignity
of a fundamental law of nature. The binary stars arc therefore distinguished
from the planet- and satellites by two striking characteristics:
1. The orbit* <in' In't/fily eccentric.
2. The stars of a »ystem are comparable, and freqw ////// nlmn.fl ,</n>ilt in
•MM.
The first of these remarkable properties is traced mainly to the condition
stated in the second; high eccentricities probably did not belong to these
systems originally, but have been devtloi>cd by the secular action of tidal friction,
which is a physical cause affecting all cosmical systems.
In developing the theory of gravitation mathematicians have very generally
.i"iiin.-.l that the attracting masses are rigid solids, and hence it has IH-CII
too\erlook the fact that nearly all the bodies of the visible universe are really
fluid. The stars and nebulae are self-luminous masses of a gaseous, liquid or
0 INTRODUCTION.
semi-solid nature, and hence it is apparent that in such systems enormous bodily
tides will necessarily arise from the mutual gravitation of the particles. Tides
are cosmic phenomena as universal as gravitation itself; and since tidal friction
will operate in every system of fluid bodies which is endowed with a relative
motion of its parts, we see that the general agency of bodily tides gives rise
to most important secular changes in the figures and motions of the heavenly
bodies. The tidal alterations of figure, which modify the attraction on neighboring
bodies, will become especially marked in the case of double stars and double
nebulae, where two large fluid masses in comparative proximity are subjected to
their mutual gravitation; and hence if the bodies of such a system be rotating
as well as revolving the secular working of tidal friction becomes an agency of
great and indeed of paramount importance. The general theory of all the secular
changes which follow from the double tidal action arising in a binary system
remains to be developed, but meanwhile the work of DARWIN in connection
with the extension which I have given his researches, makes known some of
the more important effects.
From our previous investigations it seems exceedingly probable that the
great eccentricities now observed among double stars have arisen from the
action of tidal friction during immense ages; that the elongation of the real
orbits, so unmistakably indicated by the apparent ellipses described by the stars,
is the visible trace of a physical cause which has been working for millions of
years. It appears that the orbits were originally nearly circular, and that under
the working of the tides in the bodies of the stars they have been gradually
expanded and rendered more and more eccentric.
Some simple considerations will enable us to see how these general results
arise from the secular action of tidal friction. Suppose the two stars of a system
to be spheroidal fluid masses of small viscosity, and let us assume, conformably
to the motions observed in the solar system and to those which would result
from the division of a double nebula, that the two bodies are rotating about
axes nearly perpendicular to the plane of orbital motion, and in the same
direction as the revolution about the common centre of gravity; also let the
angular velocity of rotation considerably surpass that of orbital revolution.
Then, as the fluid is viscous, the tides raised in either mass by the attraction
of the other will lag, and hence the major axes of the tidal ellipsoids will point
in advance of the tide-raising bodies, and the tidal elevations will exercise on
them tangential disturbing forces which tend to accelerate the instantaneous
velocities and thereby increase the mean distance. The reaction of the revolving
bodies upon the tidal protuberances will retard the axial rotations; for the
IN i I;..IM « I i«'\. 7
moment of momentum <>(' the whole -\-tem i- eon-taut, and the moment of
m.'im niimi of axial rotation |o-t !.\ tin- -tar- mn-t l>e just equal to the gain
in moment of momentum of orbital motion. Thn- llie rotations of the stars are
diminished, while tlu- mean distance i- conv-| dingly increased.
But the tangential di-turhing force i- foiind in vary inversely as the seventh
l»'\\cr of tin- di-tanee. and hence \vln-n tin- orhit is eccentrie the accelerating
foree at |>ena-tn>ii i- \ery inm-h greater than at apnstron. The result is tliat
at jH-riastron tin di-tnrhing force increases the apastron distance hy an abnor-
mally large aiiK.unt, while at apastron it increases the |>eriastron distance hy a
\.-r\ -mall amount. Thn- while the ellipse is being gradually expanded, the
apa-trun i- driven away -o rapidly compared to the slight recession of the
peria-tmn that the orhit grows more and more eccentric. When the axial
rotation- are -ntlieieiitly red need hy the transfer of axial to orhital moment of
nioni'-ntnm thi- change of the system will finally cease; under conditions different
from those mentioned alnive the eccentricity and major axis may decrease, and
\arioiis other change- take place.
The can-e- here liriellv sketched ap|H-ar to l>e suflicient to account for the
de\e|opni«-nt of donlile >tar-, and the tidal theory might therefore I>e regarded
a- -ati-l'aetor\ ; yet if the explanation l>c deemed incomplete it is cany to adduce
eon^ideration- which exclude other conceivable hypotheses. Let us imagine the
./•-axi- to represent the region of eccentricity, and divide this line into convenient
parts, making the intervals, say, 0.1; then we may erect ordinates denoting the
number of orbits falling in a given region, and thus illustrate the distribution
of orbits as regards the eccentricity. The irregular line which results from
connecting the point- determined by a finite number of orbits would become a
smooth curve if the number were indefinitely increased. In case of the double
-tars we obtain what is essentially a probability curve with the maximum near
o.l.'i: the slojKj on either side appears to be somewhat gradual, but the curve
vanishe- at /ero and unity.
If we make a similar representation for the orbits of comets, we shall find
a very high maximum at the eccentricity unity; in this case both sloi>es are
extraordinarily steep, though jierhaps the curve descends with less rapidity on
the -id. toward- the origin, on account of the considerable numl>cr of periodic
comets which have been gradually accumulated by the |M-rturbing action of the
planet-. The corres|M>nding curve for the planet- and -atellite- ha- a high
maximum near U.ICJSK; arid while both slope- are -teep. that on the side from
the origin i> the more gradual by virtue of the somewhat unusual eccentricities
of Hyperion, the Moon and Mercury.
8 rSTEODUCT ICXN .
If we inquire into the physical meaning of these illustrations, it is easy to
see that the distribution of the cometary orbits about the parabolic eccentricity
indicates, as LATLACE first pointed out, that the comets have been drawn to
our system from the regions of the fixed stars. The curve for the planets and
satellites proves merely that the eccentricities were originally small, and that,
under the minimized effects of tidal friction resulting from such inconsiderable
masses, they have never been much increased. The curve for the orbits of
double stars is of such a nature that we cannot, as in the case of comets, assign
to these systems a fortuitous origin; for in this event the eccentricities would
surpass, equal or approximate unity, and the periods of revolution, if finite, would
be of immense duration; nor could any cause be assigned for the reduction of
the eccentricity and period if it be admitted that anything which might properly
be called a system could arise from the approach of separate stars. On the
other hand the stellar orbits have no close analogy with those of the planets
and satellites, for they are densest in the region of mean elliptic eccentricity,
and thus almost equally removed from the two extremes presented in the solar
system. They were therefore of this mean form originally, or have been made
so by a cause which has left a distinct impress upon the nature of the systems.
The secular alteration in the figure of equilibrium of a greatly expanded mass
like a double nebula would of necessity be very gradual, and hence it follows
that the mass cut oft' under the increased centrifugal force incident to slowly
accelerated rotation would begin to revolve in an orbit of comparatively small
eccentricity. Indeed, were the initial eccentricity considerable the two nebulae
would come into grazing collision at periastron, and in consequence of the
resistance encountered the system would rapidly degenerate into a single mass.
When at length the bodies are separated, each mass will contract and gain
correspondingly in velocity of axial rotation, and tidal friction will begin expand-
ing and elongating the orbit; nothing but this secular process would be adequate
to develop the mean eccentricities observed in the immensity of space. If then
tidal friction be sufficient to account for the elongation of the real orbits of
double stars, we shall be justified in concluding that it is the true cause of the
phenomenon. Accordingly, it does not seem probable that the conclusions reached
in the Inaugural Dissertation which I presented to the Faculty of the University
of Berlin will be materially altered, but some of the many problems connected
with the general theory of tides still need additional elucidation. If we shall
be able to explain the origin and development of double stars, the abundance
of such systems will raise a presumption that the agencies and processes involved
are more or less general throughout the universe, and no inconsiderable light
l\ I K"I'I I I I"N.
will IM- thrown II|MIII tlit- h\\^ i>! < '.i-in-i^'in . |'.\ extending our researches to
tin- various classes of nebulae and clu-ier*. additional knowledge will be gained,
and in the course of time it will IK- po-.-ihle to approach tin- general problem
of cosmicid evolution.
For more thun two eciitiiric- Celestial Mechanics lias l>een occupied with
the fonfirinntion of lli«- Newtonian law, and with the development of theories
for the |nvei-e determination of tin- figures and motions of the heavenly l>-"li, -.
In tin- writing of Ni \\ i"\ an. I I. \ri.\cK the attracting masses are essentially
solid spheroid> eo\eivd by a Hnid in ei|iiilil)rium. The theories of iln- orbital
motion* and perturbations of the planets, ami of the li^urt- and rotations of
these bodie- ali. .in their eentres of gravity, are treated mainly from the point
of view of rigid dynamies, and little aeeount is taken of the fuel that so far as
known the heavenly l>odies are masses of viseous lluid. The work of PAKWIX
mi tin- prcec-.>ion of a viseous spheroid and on the secular effects of lx»dily
tidal friction marks an e|>och in the history of Celestial Mechanics, which will
eventually become a science of the equilibrium and motion of fluids, and must
take account of not only the attractions due to undisturbed figures, hut also the
fon-o ari-inir from tidal deformation, with the resulting secular changes in the
motion* of the heavenly bodies.
Physical Astronomy has been devoted heretofore to first approximations
under the law of universal gravitation, in particular, to the development of
methods for tracing the exact paths of the heavenly bodies through past ami
future centuries; the theories thus developed are applicable to all |>criods of
; ded history and are justly considered the most imposing monuments yet
reared by the human intellect. But the ultimate aim of Astronomy is not only
\]'lain and to predict phenomena which the course of time will make known
to ob-er\i i •-. but al>o to determine the secular effects of cumulative causes, and,
ipproachinjr the primitive condition of the universe, to discover the origin
and to trace the evolutionary hi.-tory of the stars. As the slow processes of
< ..-mi.-al development are fon-\er withheld from the direct vision of the astronomer,
and can be discovered only by the investigation of the continued effect* of laws
and causes now at work in the heavens, the solution of this sublime problem
will be an achievement not unworthy of the human mind.
HAWLKY HOUSE,
\\ • \ . . . •
.i/.../ •;. •
CHAPTER I.
ON THE DEVEI.O -MI s r "i Dot HI.K-SI\I. ASTRONOMY, ANM> ON THE MATIIK
M\IK \i Tni"i:ii- ..i mi MOTIONS OK BINAKY STAKS.
!J 1. //i.tforirttl N/v/r/i of Double-Star Astronomy from Herschel to Bumham.
THK su-rire-tivc relation of certain prominent stars, in contrast with the irreg-
ular manner in whieh the innltitiule are strewn over the surface of the celestial
>phciv. presented to the minds of the ancients the api>caranee of arrangement
or cla*>itieation; the more or less obvious constellations thus invented for
bright and widely-separated objects were of various sizes, and frequently of
an arbitrary character. The condensation of the stars into natural groups,
Mich as the /*/• ' '"//<" RerenicrM, and the clouds in the Milky Way, must
have attracted tally attention, but no one attempted a philosophical inquiry
into tin- cause of such arrangement until MITCHELL took up the question in
1707, and showed from the theory of probability that a real physical connection
was strongly indicated. Further considerations' of a similar character led
him to predict in advance of observation that compound stars would IM- found
revolving about their common centres of gravity. LAMHEUT had surmised
tin- existence of possible stellar systems in 1761, and GIORDANO BKUNO,
(\--IM. and M \t pKKTfis had advanced even earlier conjectures of the same
kind. The argument for physical connection of closely associated stars, based
on the theory of probability, has >ince been greatly extended \>\ WILLIAM
STRUVE, and a practical vcritieation of theory is furnished by the evidence of
orbital motion in about 500 out of the 5000 interesting double stars catalogued
by modern observers.
The designation double-star (SwrXovs) was first employed by I'TOI.I MV in
di-eribing the appearance of v Sni/iffni-ii. Tin- lir>t object of the kind e\i-r
di-eovered with the TcleseojH- \\a- probably £ 1'rnae Majoris, which ap|>< an d
double to KICCIOLI about the middle of the seventeenth century. The quad-
ruple system d Orionis was detected by Hi I..IIINS in 16.">(5. and the wide pair
yArieli* by HOOKE some eight year- later. While observing a comet at
Pondicherry, India, in December. !<;>'.'. Fvim.i: KHJIAUD separated tin- com-
12 HISTORICAL, SKETCH OF DOUBLE-STAR ASTRONOMY
ponents of a Centauri, and thus secured the first record of a star, which has
proved to be binary. The duplicity of y Virginia was accidentally discovered
by BRADLEY and POUND in 1718, and subsequently re-discovered by CASSINI
and MESSIER, while observing occupations, with a view of finding evidence of
an atmosphere surrounding the moon.
aGeminorum was resolved in 1719, 61 Cygni in 1753, and ft Cygni in 1755;
but although these sporadic discoveries had been made, no systematic search
for double stars was attempted until 1777, when CHRISTIAN MAYER, of Mann-
heim, began to collect a list of these remarkable objects. Having reached the
conclusion that faint stars near larger ones are essentially revolving planets,
he searched the heavens attentively with an eight-feet mural circle, by BIRD,
and discovered in all some seventy-two pairs, including y Andromedae, £ Cancri,
a Hermits, e Lyrae and ft Cygni. Unfortunately, the wide objects within the
reach of such a telescope seldom have any appreciable relative motion, and
hence the stars discovered by MAYER give very little evidence of the physical
connection which he expected.
The real history of double-star discovery and measurement, dates from the
explorations begun by SIR WILLIAM HERSCHEL in 1779. This indefatigable
observer sought to grapple with the unsolved problem of stellar parallax, which
had engaged the attention of astronomers since the time of COPERNICUS.
Rejecting the methods recommended by GALILEO, FLAMSTEED and BRADLEY,
he proposed one of his own, depending on the measurement of position-angles
of two stars of unequal magnitudes from opposite sides of the earth's orbit.
HERSCHEL supposed the double stars to be mere groups of perspective, and
hence he hoped to detect the relative parallax due to the orbital motion of the
earth. He resolved to examine every star in the heavens with the utmost
attention under a very high power; the superiority of his telescope gave him
an advantage over previous observers; and moreover, his improved optical
appliances were supplemented by great energy and boundless enthusiasm.
During the interval from 1779 to 1784 he made an extensive catalogue of
double stars, some of which he hoped would ultimately prove to be suitable
for measurement of parallax. In 1782 he communicated to the Royal Society
a catalogue of 209 double stars, 227 of which were new, and followed it three
years later by a second catalogue containing 434 such objects. For the next fifteen
years the attention of the great observer was devoted to, among other things,
the measurement of these pairs, with a view of finding those best adapted to
parallax determination. Slight changes were observed from the first, but in
most cases the shifting of the relative positions of the objects was attributed
n:«-M in i:-« in i T«> in i:\ii \\i. 13
cither to the pro|x»r motion- ,,| the stars, or to the* secular motion of the sun
in -pace. The motion- \\ -low that it took the observations of mnny
\.;irs to prove eoncln-h. -Iv tliat cert:, in double stars are moving in regular
orbits. This unexpected and a-toni-hing result was finally announced by
HK.ICSI IIEI. in IN'-, and demonstrated during the following year by his clal>o-
rate memoir* on binar\ -tar-. Tin--.- in\. -libations supplied the first satisfac-
tory evidence that -omc of tin- double stars constitute genuine stellar systems
maintained l.\ the action of nniver.-al gravitation. HKUSCIIKI/S celebrated papers
dealt with the motion- of -uch object- a- $ Ursae Mtijoris, HlOpltiucki, y Virginia,
' • '/iifiortim, yCoronae Bortali*, ( HoMix, r) Caxxioptae, £ IlerciUi*, p.* UoMix;
and in some cases aligned rough estimates of the periods of revolution. The
interest in an announcement which opened up fields of inquiry of the widest
-i "l>c, was fully commensurate with the inherent importance of the discovery;
and yet, notwithstanding the splendor of the achievement, double stars were
little observed during the first twenty years of this century.
>n: JOHN HKKS< IIKI. began some preliminary work on double stars in 18U5,
and was SIM.II joined by Sin JAMKS SOUTH. During the next ten years these
t\\.. ..l.-ci -vcrs piiblisheil several series of observations made either conjointly or
-eparately; and when Sn: JOHX IlKKsriiKi. made his survey of the Southern
Hemisphere, over 2000 pairs were discovered and roughly measured. The con-
scientious records which he has left us in the Results of his observations at
the Cape of Good Hope, as well as the catalogues since published, and his
elegant researches on the orbits of double stars, ensure to him a distinguished
place among those astronomers who have tailored to advance our knowledge
of binary systems.
I'll, -y-tematic survey of the part of the heavens between the north |M>|C
and fifteen degrees -oiith declination, executed by WILLIAM STKUVE lictwccii
the years 1824 and 18M, will long remain the most important contribution to
double-star A-trouomy ever made by one man. The instrument used was the
Dorpat IMMnch refract. .r by Flt.u MIOKKI:; the r.-nli- fnrni.-hed the material
of the Menswrae Micrometricae which includes careful observation- of .'U12 double
and multiple star-, be-ide- records of his previous work with smaller instruments.
The labors of WILLIAM STKUVE abolished HKISSCIIKI.'S cumin rsomo method of
referring position-angle- t<> the .|iiadi-ant-. and reduced double-star A-ti-»n..my
to a -cientilic l.a-i- liy reckoning the angle continnoii-ly from (P to IMJO0. Out
of thi- e\tcn-ivc work grew other reform-, -iieli a- the -upcrior da— ili< ation
and arrangement of the re-nlt-, and in thi- way STIM \i laid tin- foundation- of
the subsequent development of the s,-j,.|icc.
14 HISTORICAL SKETCH OF DOUBLE-STAR ASTRONOMY
Among the other observers who contributed to this branch of Astronomy
prior to 1850, we may mention especially MADLER, BESSEL, and DAWES. The
measures of DAWES take high rank for quality and serve as an example of
what may be done by private observers with limited appliances. Other deceased
observers especially deserving of mention for important contributions to the
records of double-star Astronomy are SECCHI, KAISER, KNOTT, ENGLEMANN,
JEDRZEJEWICZ, and, above all, BARON DEMBOWSKI.
Though the last-mentioned observer worked privately and with a small
instrument, his measures are more extensive and perhaps more accurate than
those of any other observer either living or dead. Covering the period from
1854 to 1878, the work included measures of all the pairs in the Mensurae
Micrometricae accessible to his 7-inch glass, besides numerous observations of
pairs more recently discovered by himself, OTTO STRUVE, BURNHAM and ALVAN
CLARK. The twenty thousand precise measures executed by this great astronomer
were collected after his death, edited by OTTO STRUVE and SCHIAPARELLI, and
published in two large quarto volumes by the Academia dei Lyncei of Rome.
Beginning prior to 1840 and extending over the next fifty years, the double-
star work of the illustrious OTTO STRUVE furnishes by far the longest and most
homogeneous set of observations yet made by any astronomer. Besides records
of the numerous stars discovered by himself and by his father, OTTO STRUVE'S
work includes reliable data for the most important stars discovered by other
previous and contemporary observers. Many of his own stars are close and have
proved to be comparatively rapid, and hence will soon yield satisfactory orbits.
Among living observers the names of OTTO STRUVE, HALL, DUNER,
SCIIIAPARELLI, TARRANT, BIGOURDAN, MAW, GLASENAPP, TEHBUTT, STONE,
COMSTOCK, KNORRE, SEABROKE, DOBERCK, PERROTIN, HOUGH, and BURNHAM
will be familiar to the reader. Each has contributed important material for the
study of the stellar systems, but the work of STRUVE, HALL, SCIIIAPARELLI,
and BURNHAM is especially important to the computer, as covering a long series
of years and thus supplying homogeneous material for the determination of the
orbits of revolving binaries.
Prior to 1870 it had been gent-rally held by such authorities as DAWES
that the subject of double stars was practically exhausted by the discoveries of
the HERSCHELS and the systematic surveys of the STRUVES. As the latter had
swept over all the brighter stars in the northern heavens, including about 140,000
objects, we may refer with a certain pleasure to the epoch-making discoveries
since made by BURNHAM, who has detected nearly 1300 important pairs which
had escaped all previous observers. BURNHAM'S stars are either very close or
FHOM III IX III I Tl> lU'ltMl \M. 1/5
the companion is very faint, and their high importance lies in their rapid orliitnl
in-.tion. This characteristic of l»i I:MI \M'> -tars has already enabled us to
deduce a number of ino-i intcre-ting orbit-. It is probable that during tin-
next half century hi- -tars will yield moiv good orbits than all the other stars
previously discovered put together. When we rcincinl>er that the aim of tin-
observer is to determine tin- paths of the -tar- with a view of throwing light
upon the character "I" tin- -tellar sy-tcin-. it is clear that the measurement ol
these close objects, which will yield a large mtml>er «»f orbits within a reasonable
time, is the iim-t piv— ing duty of the observer of the future. Many distinguished
observers have dexotcd their attention to the sidereal studies begun by the
HKI:-< HI i - and developed by the STRUVKS, but none have labored more devotedly
or achieved more splendid discoveries than the illustrious HIUNIIAM.
^ •_'. Ltij»f(ire''n Demonstration of the Law of Gravitation
in the Planetary System.
SUPPOSE we denote by X and Y the forces which act on a planet, resolved
along the coordinate axes, and directed towards the origin at the centre of the
-nn ; let the plane of the orbit IK- taken as the plane of TIJ. Then we have,
as the equations of motion,
& + X-° > &+r-n' (I)
If we multiply the first equation by — y, and the second by a?, and add
the re-lilts, we find
Hut i- the double areal velocity, and by KKIM.KH'S law tin-
area- de-eribed by the radins-veet«»r of the planet are proportional to the time.
Therefore we have
*Y-yX-0, (3)
or the forces A' and }' an- related as the coordinates .r and y ; which indicates
that the attractive force is directed to the origin of coordinates. Therefore we
conclude that the force which retains the planets in their orbit* is directed to
the centre of the -nil.
We may in«w inve-tigate the law of this force- at dillerent di-tam-e-. On
multiplying the lirst of (1) by dx, and the second b\ <l>/. adding and inte-
gratinir. we ha\.-
ta. (4)
16 LAPLACE'S DEMONSTRATION OF THE LAW -OK UUAVITATIOX
If we denote the double areal velocity by c, we shall have
and hence the last equation gives
g££$+*/<™- "»>-«. - TO
In polar coordinates,
x = rcosf? ; y = r sin y ; r = *J x- + y'2 ,
and we find
dx* + dy* = r*dv*+di* ; xdy - ydx = iadi>.
If we now denote by F the central force which acts on the planet, we
shall have
A' == Fcosv ; Y = F sin u ; F — -^J x*-\- Y'2-
Hence we get
XJx + Ydy = F cos v (cosvdr— r sinw/r) + F sin v (sin vdr-\-r cos udii) = Fdr.
Therefore
and we find
cdr
dv = - = . (7)
— 2 — a
If the force F were a known function of r, we might find v by the pro-
cess of quadrature. But since the force is unknown, although the species of
curve it causes the planets to describe is known, we may differentiate equation
(0), and obtain
dr*
F = C* - °* * rtdv* > (8)
r8 2 dr
K KIT, Kit found from observation that the planets and comets respectively
move in ellipses and parabolas, which are conic sections. The polar equation
of a conic may be written
1 1 + e cos (i>— o>)
whence we find
dr e sin (v — to)
a(l—e*)
If we reduce the second member b\ (J)),
we shall easily find
'//J
IN TIIK I'l.VM T\i:V swri M. 17
,/r» •«-«•» CO*1 («•-•)
!-«
and hence we get
. 2 .2
rfr ai*(l-e*) t*'
Thus equation (S) U'comcs
>'- ; , , ' L- 02)
Therefore we conclude that the force which causes the planets and comet M
to move in eonic sections nlnmt the BUD varies inversely as the square of the
distance from the sun's centre. Such is the demonstration by which LAPLACK
was led to the law of universal gravitation ; it rests solely on phenomena, and
i-. in.l. I'.'inl. ni of any hypothesis. The original demonstration by NKWTON was
I mi ^«-< (metrical methods, and is given in the Principia, Lib. I., Sec. III.,
IV.. p. XI.
The laws of KKPLER made use of in these demonstrations are taken an
fundamental facts discovered from observation ; but planetary observations in
the time of KKPLKU were not sufficiently exact to ensure entire rigor in these
laws, and ln-sides no account was taken of the mutual gravitation of the
planets. Hence it will l>e seen that the accuracy of the laws of K I.IM i i:. even
in the time of NEWTON, could be maintained only within given limits.
It i- never i»i.>ilde to realize the conditions of undisturlM'd motion assumed
by Ki ri.i.i:. and hence the problem presented to astronomers can IK- solved
only by succr--i\i- approximations. A-- inning that the fact- embodied in KKP-
I.ER'K laws are strictly true, NEWTON'S reasoning shows that the law of gravi-
tation is mathematically exact ; if on the other hand we a--nme the accuracy
of the law of NEWTON, we are led directly to the laws of K i I-I.KR as phe-
nomena which would ari-e under the operation of gravitation. The laws of
Kr.n.Ki: are seii-ihly correct, ami on the adinis.-ihle supposition that they are
entirely rigoroii>,* astronomers have applied the law of gravitation to the <li--
turln-d motion- of the planets, with a view of explaining observed inequalities.
and of discovering from theory other perturbations which have Ix-on
• The thinl Imw b here ipppoxd to bp roirectnl for th« plamHary mmmru aeiHeettd by KKPL
18 INVESTIGATION OF THE LAW OP ATTRACTION
quently verified by observation. This development of the planetary theories
has occupied the attention of astronomers for over two centuries, and in every
case where doubt has arisen the accuracy of the Newtonian law has been
verified.
The range of possible inaccuracy has been gradually narrowed, until at
present the data of Astronomy show that if the law of nature departs at all from
that given by NEWTON, the deviation must be extremely slight. Indeed, the law
of gravitation, taken in connection with its simplicity, is so thoroughly estab-
lished as to authorize the belief that it is rigorously the law of nature. Its
brilliant confirmation and extension since the time of NEWTON, especially by
LAPLACE, leaves but few, and generally insignificant, motions yet unexplained;
and since we know that the slightest deviation from the law of inverse squares
would become very perceptible in the motions of the perihelia of the orbits of
the planets and the periplaneta of the orbits of the satellites, and no such
outstanding phenomena have been disclosed by observation, except in the case of
the perihelion of the orbit of Mercury, which may be explained in a different
manner, it is hardly possible to doubt that the few anomalous phenomena yet
remaining will finally be explained in perfect accord with the law of NEWTON.
The . strongest proof of the rigor of this law is to be found in the fact
that it accounts for both the regular and the irregular motions of the heavenly
bodies, and in the hands of LAPLACE and his successors has become a means
of discovery as real as observation itself.
A law which explains satisfactorily the figures, the secular variations, and
the delicate long-period inequalities of the planets, and above all the numerous
perturbations to which the moon is subjected, certainly has a strong claim to
be regarded as a fundamental law of nature, and is incontestibly the sublimest
discovery yet achieved in any science.
§ 3. Investigation of the Law of Attraction in the Stellar Systems.
The labors of NEWTON and LAPLACE on the mechanism of the solar system
established the law of gravitation with all the rigor which modern observations
could demand; but neither of these two great geometers attempted to apply
this law to other systems existing in space. The close of the career of LAPLACE,
just a century after that of NEWTOX, marks an epoch in the verification of the
Newtonian law, since in this year SAVAKY devised the first method for deter-
mining the orbits of double stars; he justly based his theory on the principle
i\ mi. -TKU \i: -v-n M-. 11)
<>| Lrra\ nation which the author <>(' tin \f nt'qve CSfew/' liacl recently tested
\sith such thoroughness for I lu« ivirion- about tin- sun traversed by the planets
Mini comet-. Tlie method de\ eloped b\ > \\.MM ha- In-eii improved niul rendered
more practical by the lal>or- of -iib-eniient geometers, niul consequently at the
pi-< -flit time there i- no considerable body uf phenomena which ap|x>ar to IK*
irreconcilable with the law of NI\SI<>\. Indeed, when proj>cr allowance is made
for the large Imt inevitalile error- of our micrometrical measures, all modern
oltscrvations of hinai \ -tar- ma\ be explained either by the theory of two Ixidie-
revolving under tin- law of gravitation, or by the action of unseen liodics |H'rtiirl>in^
the rrirular elliptical motion. This accordance of observation with theory, while
it iiu-rca-e- enormously the probability of the Newtonian law, docs not furni-h
an independent criterion; and therefore it is desirable to ascertain the most
general form of the expressions which will cause a particle to deseril>c a conic,
-<> ili.ii \\e may determine whether any other law can explain the phenomena.
In the case of double stars, microinctrical measures enable us to study only the
apparent orbits, which are projections of the real orbits ujxm the plane tangent
to the celestial sphere. The apparent orbits are ellipses, ami therefore we may
(••include that the real orbits arc also conic** of the same s|>ecics. When the
orbit i- projected the centre of the real ellipse will fall UJMHI the centre of the
apparent ellipse, but the |H)sitions of the projected foci are not determinate
unless the j)osition of the real ellipse is known. Astronomers are accustomed
to assume that Newtonian gravitation is the attractive force, and as this requires
that the principal star shall l>c in the focus of the real ellipse, it then In-comes
ea-\ t» deduce the corrcsjioiuling node, inclination and other elements. It is
ob-ervcd that the principal star is not in the centre of the ellipse, and therefore
\\e infer that the force does not vary directly as the distance. But since the
area- -\\ept over by the radius vector are projK>rtional to the times, we may
conclude that the force i- central; and since tin- apparent motion of 42 Coimr
Jiemiice* is rectilinear, it is clear that the orbit is a plane curve, or conic
-cct ion. As other force- be-ide- gravitation could cause a particle to clescril>e
a c.inic. HKI:TI:AM> pn>|>o-ed the following problem to the Paris Academy of
S-ieiice-: " Kiiim'iiiii flint n mull rinl {Hirticle under the. fiction of a central font
'//'/•'/ i-iftfg a COlli'-. it i.-- i-i I/HI r«l fit fiinl tin /<///•/»/'/// <//' ////X fnrif."*
Hefon- prcM-nting the solutions developed by I >.\i:it<>r\ ami II.\U»IIKX, we
shall iri\f an e\pn-ition of the geometrical method by which Niui"\ tn-ated
tin- -ame problem.
In the S-holinm to I'mpo-ition \\'I1. Liln-r I, of the /'rim //</</. \I\VTOX
•Comfit* Kr»d**, April 0, 1887.
I'd
INVESTIGATION OF THE LAW OF ATTRACTION
derived the general expression for the force which will cause a particle to
describe a conic section, the centre of force occupying any internal point. The
demonstration given by NEWTON depends upon several preceding propositions;
a more direct but similar solution of the same problem has been published by
PKOFESSOR GLAISIIER in the Monthly Notices, Vol. XXXIX.
This investigation is as follows: Let C be the centre of the ellipse,
P any point occupied by the particle, Q the point occupied by the particle at the
next instant, PZ the tangent at P, PG the diameter through P, CD the semi-
conjugate diameter to PG, O the centre of attraction, QS a right line parallel
Fig. 1.
to OP, OZ and G Y perpendiculars on the tangent from O and C, PF the
perpendicular on CD from P, QT the perpendicular from Q on ()!*, Qi< and
OM perpciidicnlm-s on /'/'' from Q and O, x the intersection of Qr with Ol\
I the intersection of OM with CP; and R the required force tending to O.
Then we shall have
where // denotes the areal velocity.
OP"
Q8_
'.' T
(1)
IX Till ITBLJ M: §T8T1 M- 21
By the similar triangles o /' ami /M/o.
/•i/
"I-
By conic Kection*,
Cf*
r, .o»" CP*'
And from the figuo .
/•• PP Pi CP I'M
»*/• /•/•' »/••
Therefore by (3) and (4) we find
. 6t. c/'./'/' tip'
In the limit C/r — f^r , and hence (2), (.'{) und (5) give
VT« 2C7/« //M/V
TF ' U/V '
Substituting in (1), we obtain
/«' PP/OP\* Wfl'PV . h' /CK\V.
R » -=- . - I - 1 «- ( - 1 • OP — — ) op, (-T)
OP' (7/A/M// aV\PluJ aW\07J
which ih the required law of force.
§ 4. Aiifilf/fit-fil KoltUioti of HrrtruiuFx I'ruMt'in /tam-it OH Unit
It, rrfojied In/ DaftotUS ; No/M/iVw* of llal/iln-n.
The cHjuations of acceleration are,
-R* = -Boott ; - -B - -*»intf, (1)
where K is the attractive force, at unit distance. Multiplying the first by — y
and the second by x, and adding, we get
On integrating we obtain
<l dr
ANALYTICAL SOLUTION OF BERTRAND'g PROBLEM
In polar coordinates this equation becomes
* -j- = h = double areal velocity.
Let us now put u = ? and then
'
u sin 0 + cos 0 -777- ,
cosfl dx dO dO
~^T ' dt = —tf- -~df-
By equation (4) this becomes
Tt
(7)
From (7) and (1) we get
where the centre of force is at the origin.
This equation is perfectly general for the determination of R when the
equation of the path is known. To get the central force, 72, which will cause
a particle to describe any given path, we find the value of (*+?£} for that
/2 \ ** J
path, and multiply it by ~. Therefore, to find the law of R, when the path
is a conic section, we have the general equation,
ox' + 2bxy + cif + 2dx + 2fy = y. (0)
Putting r == -, aiui transforming to polar coordinates, we have
« co82tf 2/> sin e cos 6 c sin30 2d cos 6 2f sin 6
n* u* ~tf~ ~^T ~H~ = 'J'
from which we obtain
/ sinfi + d cos 6 . 1 , — 3-: - _ _
—j- f->((/2+c.7)sin3tf + 2(fd+/i;/)sm()cos6+(d*+ag)cos20' (10)
This equation reduces to the form
a = Asin6 + HcosO+ ^ C siu26 + D cos20 + //, (11)
where
/
C = n aff--ey
9 ff* V
BASKI) OX THAT l>i \ I I • -ri I • n\ l>\i:ii"i \. "£\
From (11) we derive
-A Bin*- BOOB*- C«- />'- (T, .„•.•<* * /Jom'.'tf)'- '-'//( C sin »|+/>co»2tf)
(0 sin 2*4-0 oo. *
Therefore by (8) we get
*' -- u
' r1 v '
Thin IK the general expression for K whatever IK- the constants u, h, c, il,
f and v-
Since by (11) we have
« - A sin * - H <x*0 - V Cain 2* + b c^'0 + // ,
we may write (l.'J)
A : " i3 7T~
V?" /
\\hirh is another general expression for /?.
When the conic is an ellipse with the origin at the centre, equation (!»)
takes the form rt-r" + of = ar, and from (l.'l) or (14) we find after rediietion
AV
R — — . (!"•)
M
The force varies directly as r, which is the well-known law.
When the centre of force is on the .r-axis between the centre and one of
foci at a dManee HI from the centre, equation (0) l>ceomes
cf — a (e—
and we find from
Jt-S'[(—+.ffn-g-iT>- °6)
Since a — c + m* is always negative, the force at unit distance is a maxi-
mum in the direction of the apsidr- ami is a minimum when * = We
h:ivr from (14), in this case,
R = a(g_^_w (17)
This • A invasion can ivadily IK- Iran-formed into < |M.
24 ANALYTICAL SOLUTION OF BERTRAXD's PROBLEM
When the origin is at one of the foci (13) or (14) gives
(18)
which is the Newtonian law.
This is also deducible from (1(>) by putting in- = c a.
When the centre of force is on the *-axis between one of the foci and
the nearest apse, at a distance n from the centre, we obtain from (13)
Since <t — c -f w3 is always positive, the force at unit distance is a maxi-
mum when 0 = anti ., niinimnm at the apsides. From (14) it is easy
to obtain
which may be transformed into (19).
When the centre of force is on the minor axis at a distance /!• from the
centre, equation (13) gives
,, ?j? _ (ac)v*
^' (21)
Since a — c — A>a is always negative the force at unit distance is a maximum
when 6 == 0, and a minimum when & = In this case we obtain from (14)
When the centre of force is within the ellipse, at a distance p from the
//-axis, and q from the »-axis, we get from (13)
R _. _
r3 \2pq sin6cos6+(a—c—ri2+2J*) co
which becomes (19) when q = 0, and (21) when p = 0. We also obtain from
(14)
R __ _ AVcV _
(ac — ap'—cq'—ctjy—apx)' '
which becomes (20) when q = 0, and (22) when p = 0.
I.KNKI .»n i. 10 11 \i mi x
The t'.ii U.HII- values <>f A* an- n-al ami |.«.-in\, . ntui n |.r. -mi all the lawn
with tin- <»lt-tr\t.l mntiiin- i>f binary stars.
It may IK- inttn-tinjr |i> i»>t<- that when the centre of force is at out- of
tlu* apsides or at one cm! »l' tin- minor axis, our general formulae (l.'i) and (14)
•rixe iiuleteriuiuate result-. In ilii- case we take the e<|uatioii of the ellipse
with the origin at the end of one of the axes, and calculate It by (H). When
the centre of foree i- ai tin- apse, we obtain after reduction
When the eentre of foree is at the end of the minor nxin, we fiml
If. *f- (26)
In lx)th of these ciMex the origin is taken in the jjositive direetion from
the eentre of the ellipse; if the other ends of the axes IK- ehosen the si^nn of
I •_'"> ( and (2G) will IK- reversal.
When c = a in (25) or (20) the conic become* a circle, and the expression
reduces to the well-known law
*-8-^. (27)
The expression for the force at external jxiints may IK- derived in a manner
entirely similar to that for points within.
Solution of
L.I /// IK- the maw of the central l>ody, and R an unknown function of x
and y. Then \\r have the equation.-
R is to be determined by the condition that the «>r!>it of the particle i- a
conic section. l.« i
g.«»fg.y;A. -mur,
where u \» an unknown function of x and y.
• TlMEBAXD't Mtcamlgut Ctffwte, Tona 1, Cap. I. whin UM original MlaUon baa been MMilnl
26
ANALYTICAL, SOLUTION OF BERTKAXI)'s PROBLKM
From (28) and (29) we obtain
dx' di/'
-j- = ux ; -£- = uy
(30)
By this equation we have
(31)
We now proceed to find the differential equation which is common to all
conies. The general equation of a conic has the form,
+ 2Bx>j + Cy3 + 2Fx + 2Gy + H = 0 ,
(32)
ill which there are five arbitrary constants. Taking x as the independent vari-
able and differentiating five times in succession we have, in LAGRANGE'S notation,
Cyy'
C (?/.'/"+.'/-)
CW+-W)
+ B(xy'+y) + Ax + Gi/'+F = 0
+ B(xifJr'2!J') + A + Gy" = 0
+B(x!/"i+3!/f) +G,/"> =0
+B(x,j* + ±u>") + Gytv = 0
(U!/v + Wit v + 10 ff "</'") + B(xU" + 5^) + G yv =0
(33)
We now have to eliminate the five constants in (32) and (33). We notice
that the last three equations of (33) are homogeneous, containing only the three
constants C, B and G, and we can eliminate them by equating to zero the
determinant
//"
A=
+4 //"
(34)
By elementary principles of Determinants equation (34) reduces to
A =
0
ylll yiV
10/" %lv }/
•V iff'11 !f
(35)
Expanding (35) and returning to the differential notation, we have
40 -
'
(36)
This is the general differential equation of a conic section. We now
rf2// dbii
calculate ^ • • ^js from the relations expressed in (29), (30) and (31).
We have
dy _ y'
dx x"
ItKVKI "I'l I' ll\ II \l nil \
•JT
if x'uy — y'tuf
~ '
or
Since the !'"iv.
Then-fort1 we il»-i i\ e
(37)
mitral. \ty the law of area*. (y/y — y'x) i« constant.
(f'y-y'f) ('" J -
- 3«V*+ 15
..V-A
(38)
+ dj" (105KW-16.M-") + 45«W* - I05.i«r»~] .
(it
j
these values in (>'tt>) and reducing, we ohtain
«/*(/ „ dii d*u . „ /</"\f , '/"
9«» , k - ! r 4- 401 1 — On* j- .
»//* rf/ <//* \<//y rf/
M = IP"**, in which »o is a function of x and y, (.'ii>) rednccN to
»-*«
(40)
When we n-nieinlH-r that
and
ami that </• i> a "function of x and y, we gt-t
«IT . ' , • '
,t,
. > r^W\
' f^tf 7 V r'y ' '''/ /
28
ANALYTICAL SOLUTION OP BERTRAMS PRO HI.
Substituting these values in (40), we obtain
0 =
+ AJ-'-
+ Sx'i/'*
#*,„
<l'_L
— ^. +
. r
--- (x- +11 —
" Ox <
i -u, r<> ( f)'2"; _L <?a"t ~\ dv
>Jw *"• \2w y— - +x—
L \ &r dxdy &v
_L
+y
> (-12)
This equation holds true whatever be the value of t, and hence when t = 0,
in which case x, y, at, tj' may be any four quantities mutually independent of
one another. Then (42) gives the following equations
(43)
(44)
o • l(' - o • w o • rw o
* ~ ' Ifif ''
'dw
()xdy)
We obtain from (43), when we denote the arbitrary constants by «, ft, c,
f, g, //,
•w = <ix* + 'Ibj-y + <-,f + 2/r + 2>/t/ + h .
Forming the differentials and substituting in (44), we obtain
('if- ".'/) *y + ('/- bg) <f + (/*- « A) f + (f<j - IK) >, = 0 .
(by-rf)xy + (<uj-l,f)x* + (f,j-bh)x + (y*-ch) y = 0 .
Since these equations hold true for all values of x and //, we find
«.'/ - ''f = 0 , l<j - ,-f = o .
/2 - ah = 0 , ,f - eh = 0 , f,j - bh = 0 .
From (48) we have
fh(ay-bf) = 0 , yk(by-cf) = 0.
(45)
(46)
(47)
(48)
(49)
Then, if none of the quantities /, c/, h vanishes, (47) follows from (48),
and it is sufficient to verify the latter.
We may write (45) in the form
w = Ji\_(fx+yy+hY-(f'-ah')xt-(yt-ch-)y1-2(fy-bh-)x!/],
(50)
1.1 \ I I iil'l H ll\ II M.I-IIKN.
which, in consequence of ( I*). '••
,,(/*+»+»)". (51)
Therefore, sim. " " . ««• huve by (2!»)
which !H nn »\|n.— i..n for the force twilight. When /* — 0. (4H) leads to
f = 0 and g = 0. In tliiH cam- we have
* - as* + 2Ar./ + ry« , (S3)
from which we get
R •
This in another cxprctwion f«ir the force, whatever IK- the constant <i. li and c.
When /= 0, (47) and (48) give ay == by == ak == A/I == », //' = *•*, from
which a = 6.
In this cane we get from (.W)
.-JBJS. ,»,
•
which gives the twine result an (S2), when/=0.
Thus there are two lawn of force, ami only two, which answer the question;
luil the f.u<«- A', ami It* contain Ixrth the nulius vector r, ami the jMilar angU-
= ton-1''
X
If the forces depeml u|*in r alone, as is natural to snpix.se, we should have
in #„ f=g — 0; and in #„ a == c and // == <>. Then we find
The finrt of th.-.- law- i- • -xelmhil l»v oliM-r\aliMii: the Mi-.iml i- the law
of Newtonian gi-:i\it:itimi.
30 THEORY OF THE SPEG'TROSCOPIC DETERMINATION
§ 5. Theory of the Determination, by Means of a Single Spectroscopic
Observation, of the Absolute Dimensions, Parallaxes and
Masses of Stellar Systems whose Orbits are Known
from Micrometrical Measurement*
i *
Recent researches on the orbits of double stars have led me to develop
the suggestion, first thrown out by Fox TALBOT in 1871f and since somewhat
varied by others,J for determining the absolute dimensions, parallaxes and masses
of stellar systems by spectroscopic observation of the relative motion of the
companion in the line of sight. A simple and general theory of this motion may
be derived from the application of the hodograph of the ellipse, and hence we
shall now investigate the nature of this curve.
Let x, y be the coordinates of a point in the ellipse; xf'y1 those of the
corresponding point in the hodograph; then we shall have
x' - dx «' - Ay m
" d7 - At'
Suppose M to be attracting the mass in the focus of the ellipse; and let r
and 6 be the polar coordinates of the particle moving in the orbit, and we
have
A*x MX M A*y My M
By the principle of the conservation of areas resulting from central forces,
we have the equation
r* -j- = double areal velocity = C ,
or
and hence
d*x M A6 d*y M
If we integrate we obtain
* Axtronomische Nachrichten, No. 3314.
t Report of Hritigh Association, 1871, Part II. p. 34; CI.KRKE'S "System of the Stars," p. 201, and "History
of Astronomy during the 19th Century," third edition, p. 4(!7.
: I; \MI: M i. M. ff.. March, 1800; WII.SINO, A. N., 319H; also a papor on the determination of orhits from
spectroscopie observation of the velocity-components in the line of sight, by LRII.M AN-Fii.nfc«, A. Jf.,
• •I III) I'M: U.I.AXKS OF STKI.I.Al:
w lu-re « ami b are thi- arbitral \ eon-iani- of integration. Hut since
we find
<Lr
8111 0 mi
i/
---
0080 —
I'. mean- of equation (1) We have
, y' + l> =-
and on s<|iiarin<r and adding we obtain
I/-
IV
which shows that tin- hodograph of the i-llipsc is a circ-li* of nidius
Tin- f<dlowing gi-onictrical |>r«">l' will rcndiT tin- application somewhat more
intelligible.
Flg.2.
In the figure let /'/>A !>«• tin- ellipse d.-M-riln-d I »v the particle p\ PA
l>«inir tlie major :i\i-. and /•' and /•' the two foci. L, I r T IM- the tangent to
the ellip-e at j>. and let the perpendicular from the focn* njMin the tangeiil IK-
di-iioti-<l by FQ. Then 1>\ definition the radin- vector of the point in the
hcxlogmph i- paralh-1 t<i the tangent /< T and proportional to the velocity at
32 THEORY OF THE SPECTROSCOPIC DETERMINATION
the point jp. It is well known from the law of the conservation of areas that
this velocity is always inversely as the perpendicular FQ, or directly propor-
tional to the length of F'Q1. But the locus of Q or ty is known to be the
auxiliary circle described upon the major axis as a diameter. Therefore we see
that the hodograph is of the same form as the locus of Q', but since the point
p' in the hodograph is on a radius vector parallel to pT, its situation relative
to the focus F will always be 90° in advance of Q.
The shape and situation of the hodograph relative to the ellipse is shown
in the figure. Thus, when p is in periastron the point of the hodograph is in
the direction perpendicular to the major axis, and at a distance proportional to
F'Q', which is then equal to F'P; and similarly for other points of the orbit.
For the sake of clearness we have made the hodograph in the figure of the
same size as the auxiliary circle of the ellipse, but if the radius vector in the
hodograph is to represent the velocity in the ellipse the scale of the hodograph
ought in reality to be greatly reduced.
If the orbit of a double star is given we may at once construct the form
of the hodograph, the position relative to the ellipse being the same as in the
preceding figure. Moreover if the velocity of the companion about the central
star is known in absolute units for any point of the orbit, we may determine
the velocity for any other point by means of the hodograph. For the magnitude
of the velocity will be the length of the radius vector of the hodograph which
is parallel to the tangent of the orbit at the point in question, and can easily
be computed or measured graphically directly from the diagram.
When the elements of a binary are known, we may determine the com-
ponent of the velocity in the line of sight as follows: Suppose p to be the radius
vector of the point in the hodograph, and w to be the angle made by the radius
vector p with the ascending node, and therefore identical with the angle made
by the tangent to the orbit with the line of nodes; and let i be the inclination
of the plane of the orbit to the plane tangent to the' celestial sphere. Then
we evidently have, as the component towards the earth,
K = p sin ta sin / . (7)
The angle i is an element of the star's orbit and is known; the angle <a
can be computed from the theory of the ellipse, or can be determined directly
from the diagram; and when p is known in absolute units the component in
the line of sight is perfectly determined.
We shall now show how to compute <a and p for any given orbit. The
OF TIIK
..i -11:11
radius vector of the Mar / ;m«l the true :iin»m:il\ r must Ix- computed bv the
usual prut •« •-.-. in, I th. -n we lin.l the radius vector with respect to the other focus
t> - 2a - r;
and we have the angle y by means of the equation
r aiu r
Silly —
f>
The angle Ji IM t\\« u the radii veetore* drawn to the two foci in evidently
equal to r — y, and In-nee
It is also eawy to see that <j, the angle made by the tangent with the latus
rectum of the ellipHc, is given by
i - - i*-
When the value of ., is determined, it is clear that
(10)
so that we easily find the angle of the radius vector p from the ascending node.
We may compute the length of thi- i.nlin- \.cidi- in ilu- h<N|«igniph in the
following manner. L«-l tin- nuliu- <.f tin- cin-l. I., <|, n<,i.-«l li\ «. it- v.-ilue In-ing
34 THEORY OF THE SPECTROSCOPIC DETERMINATION
supposed known in absolute units; the linear eccentricity will be cuj, and we
shall have
«2 = p2 + «ae2 — 2p ae cos qr ;
on solving for p we find
p = « [e cosqr+ Vl — e2 sin2g;] . (12)
Thus when a, the radius of the hodograph, is known in absolute units, we
are enabled by means of (11) and (12) to predict the motion in the line of
sight for any instant whatever.
Now suppose we determine the relative motion of the companion in the
line of sight by means of a modern Spectrograph such as that at Potsdam;
this will give us results freed from the effect of the proper motion of the system
in space, as well as the secular motion of the sun and the orbital motion of
the earth. Then by equation (7) we have
(13)
.
sm<D sin i
in which K is furnished by spectroscopic measurement, and o> and i are found
from the orbit deduced from micrometrical measures.
A single observation therefore gives us the absolute velocity in the orbit,
and this fixes the scale of the hodograph. For since we have
p = « [e cosqp + Vl — e2sin2gt] ,
and e and g> are known, we may determine the radius of the hodograph by
[e cosqr>+ Vl— e'
(14)
Having determined K by observation, we get the absolute value of p by
(13) and of a by (14), and we may then predict the value of K in absolute
units for any time whatever. In practice it will be desirable to measure the
motion in the line of sight when the function K is a maximum, in order that
an error in K may have a minimum effect upon the radius of the hodograph.
"When a is thus determined in absolute units, the problem arises to find the
absolute dimensions of the system, the masses of the stars, and their distance
from the earth. Suppose we choose two epochs separated by a convenient
interval of time, say a year or a fractional part of a year, when the companion
is near apastron, and the velocity changes slowly. We shall denote the radii
vectores by i\ and r2, and the interval of time by t2 — /,. The length of the
included elliptic arc can be expressed rigorously only by means of an elliptic
• »K THK I'AI.'VM V\l- "I -Mil \l: -Y-TKM-. 35
integral, but as the evaluation of tin- integral would !H« inconvenient in practice
and for :i short an- unnece— arilv exact. we shall determine the length of tin-
arc by mechanical quadrature. Thn- we have
arc
- J fAi - f(tt-tt)
where p is the average velocity of the interval, cattily deduced from the hodo-
graph. If the iuicnal i- short compared to the time of revolution, so that tin-
arc may IK- put equal to it« sine, we shall have approximately
or
r +r -
•in (»,-»,)'
Now r, and r, are known true anomalies, and r, and r, are given in units
of the major axit* by the |iolar equation
a 1 4-
Hence, with r, and r, thua cxpreHHcd numerically, we find
_ .
(r.+r,) •§»(.•,-*,)•
Here the interval /, — /, must be cxpretwed in the name units a» p, pref-
erably in kilonu-tn-> prr second. The length of the major semi-axis of the orbit
i- tliu- found in kilometre*, and the absolute diniennionH of the system are
determined.
The parallax of the system is eijual to the major semi-axis of the orbit in
seconds of arc divided by the major semi-axis in astronomical units; or the
di-tanee of the system from the earth is equal to the major semi-axis in astro-
nomical units divided by the sine of the anirle subtended by the major scmi-
axis in second- of arc-; thus
» (16)
Sinei
If '/, - »/. denote the combined ma«« of the -\-ti-m. M-\-m the combined
mass of the -mi ami earth. '/ the major -emi-a\i- of the orbit of the companion.
and /' the periotl of revolution. R the distance of the earth from the sun, and
db RIGOROUS METHOD FOR TESTING
T the length of the sidereal year, we have, by the well known extension of
KEPLER'S law:
M, + Mt = J . ^ (M+m) . (17)
If as usual we put M-\-m =1, 72 = 1, and T = 1, and express <i and
P in these units, we find
Jf.+ Jf, = j£, (18)
where the mass of the system will be expressed in units of the combined mass
of the sun and earth. The mass of the system is thus determined absolutely.
In conclusion it seems proper to add that this investigation was stimulated
by an elegant proof of MR. F. R. MOULTON, that the aberrational orbit of a
fixed star is the hodograph of the ellipse in which the earth moves, and there-
fore a circle. The idea brought out in MR. MOULTON'S proof caused me to
revert to the motion of binaries in the line of sight, and hence no small part
of the credit is due to him for the interesting application of SIR W. R. HAM-
ILTON'S hodograph given above.
§ 6. Rigorous Method for Testing the Universality of the
Law of Gravitation*
It remains to consider how we may use the foregoing results to test the
law of NEWTON. It is evident that the law of gravitation can be tested by
comparing the observed with the theoretical motion of the companion in the
line of sight. We may choose a system whose orbit is accurately known and
whose stars are suitable for exact spectroscopic measurement of the component
K; we then determine from one or more observations at a suitable epoch the
absolute dimensions of the orbit, as explained in the preceding theory, and
predict the motion in the line of sight for other parts of the orbit, perhaps for
a whole revolution. If we then determine by spectroscopic measurement the
vnltie of the component K independent of any theory, and find that the theo-
retical results are confirmed by actual observations, we may consider the result,
a direct observational proof that the force which retains the companion in its
orbit is Newtonian gravitation.
For we know from micrometrical measures that the areas described by the
radius vector of the companion are proportional to the time, and therefore that
* Axtronomische Nachrlchten No. :!:!I4.
rXIVKRSAI.il V OK Till I v u OF GRAVITATION. !{"
the force is central; and the ob-.i-r\ation- ..I I'J formic Iterenut*, whose motion
|I:I|'|M-N- to l» in the I'Lin. <>! \i-ion. indicate thut tin- orbit is a plane curve.
'I'ln- motion being in a pl;.m- ami tin lone U m- central, we mn-t I..- nble to
show that the principal -tar i- in tin- focus of the real ellipse. Thin can IM-
•lone if we can show b\ -\» « trox-opic observations that the inclination and node
reuniting from the theory of gravitation account jn-rfectly for the motion in t In-
line of Might.
We therefore assume the law of gravitation in deriving the elements of the
orbit and in predicting the motion in the line of sight, as heretofore explained;
*j>ectroscopie observation will enable us to test the results of theory experi-
mentally. If the theoretical results are confirmed by observation throughout a
revolution — thus showing that the node and inclination are identical with those
resulting from the theory of gravitation — we may regard the observations as
giving a direct and incontestible proof of the validity of the law of NEWTON
in the stellar systems.
If we desire to ascertain whether any other inclination and node — in other
words, any other law of force — could give rise at every |>oint of the orbit to
a relative motion in the line of sight identical with that resulting from the law
of gravitation, we may proceed as follows: Snp|H)se that some other inclina-
tion and node and orbital velocity be possible; they will differ by unknown
ipiantities from those values resulting from the theory of gravitation, and we
shall have the relation
p .sini' sin. =» p'sin(i-fy) sin(«+8) .
By expanding and reducing we find
p = p {coey oosi+cosy cotm sinS + siny cot i coufi+siny sin 8 coti cot*} .
Hut we ob-«-r\r that w is a variable angle de|>ending on the position of
the body in the orbit; and since a> = 0, or at = w would render the cotangent
infinite, and p is known to be finite for every point, (the two bodies never
come into contact but are always separated by a certain distance), it follows
that those terms depending on cot <a must vanish, or 8 = 0, and the line of
nodes becomes the same as that resulting from the t henry of gravitation. Our
expression thus takes the form
p = p'(cO8y+siny COtl) •• p' A .
where A' is a constant.
Therefore, if the inclination differs by y from the value given by the theory
of gravitation, it will follow that the velocity at every point of the real orbit
THEORETICAL POSSIBILITY OF DETERMINING
must be multiplied by a constant factor. But since no alteration of the incli-
nation can change the radius vector at the line of nodes, it follows that at
these points the orbital velocities would necessarily be the same however the
inclination might vary. And since we have seen that the line of nodes is
identical with that given by the theory of gravitation, we conclude that the
velocities in the orbits could not differ throughout by a constant ratio. Hence
it is evident that cosy-j- siny coU' = 1, or y = 0, and the inclination is
identical with that resulting from the theory of gravitation. It follows there-
fore that no other conceivable law of attraction could produce the same relative
motion in the line of sight as the law of inverse squares. Consequently if
observation shall give for every point a relative motion in the line of sight
which accords with theory, we may confidently conclude that Newtonian gravi-
tation is the force which retains the stars in their orbits.
§ 7. On the Theoretical Possibility of Determining the Distances of Star-
Clusters and of the Milky Way, and of Investigating the Structure
of the Heavens by Actual Measurement.*
The practical problem of measuring the parallaxes of the fixed stars is
one of the greatest of modern Astronomy, and has been solved heretofore very
imperfectly. The quantity to be deduced is so very small that accidental and
systematic errors often wholly obscure the element desired, and render the
probable errors of most of our parallaxes painfully large compared to the minute
quantities sought. Moreover, the method of relative parallax, which is the only
one in general use, aside from its theoretical inaccuracy, is encumbered with
many practical difficulties, the chief of which is in finding suitable comparison
stars; and hence not a few astronomers have practically abandoned hope of
determining the distances of the fixed stars with any considerable degree of
precision. None have felt these difficulties more keenly than those astronomers
who have attempted investigations requiring exact knowledge of the masses
and dimensions of the stellar systems. At the present time the only parallaxes
of binaries which lay claim to any considerable precision are those of a Centaur i
(0".75), a Canis Majoris (0".38), 70 Ophiuchi (0".162), and r, Cassiopeae
(0".154). To this list we might perhaps add a few spectroscopic binaries
whose parallaxes have been investigated, but even then the number of systems
'Astronomische Nachrichten, No. 3323.
TIIK |il-T\N<K- "I -I \l>< I I -IKi:- \\|. .IK THK MILKY WAY. 30
would ivmain very small, and altogether in-nlHeicnt to sup|K>rt any sound gen-
« rali/atii'ii respecting tin- ma— e- and dimensions of binary stars as a class.
If we consider single, in-tcad of double stars, it will IK' evident that while
a much larger number have IM-CH measured for parallax, and in a good many
rases reliable values have been derived, yet in the majority of instances the
divergence of results obtained by different observers, may fairly IK- taken to
indicate that our .knowledge of stellar parallax is still very limited; and owing
to the small dimensions of the earth's orbit, very little hoj>e has IH-CII enter-
tained of material improvement in time to come.
The met IKK! which we have devclo|>ed in section 5 is full of promise for the
ease of binary stars. Tins method is theoretically applicable to any pair where
the component have an angular separation of 0".l, and a single application of
the s|>eetrograph at a suitable c|>och gives us the absolute dimensions, mass
and parallax of the system.
As 0".l is about the present limit of exact micrometrical or heliometrical
measurement, and as this angle would correspond to the parallax of a fixed star
at the distance of 36 light-years (eight times the distance of a (Jrntaur!) we
see that all smaller parallaxes determined by method- heretofore in use must
-sarily remain very uncertain. On the other hand the spcctroscopic method
will apply satisfactorily to much more distant systems — to pairs which have
an angular separation of O.I, and where an observer by the ordinary
method would find that our sun had a parallax of this amount. This is equiv-
alent to using the major semi-axis of the stellar orbit for a base line instead
of the mean distance of the earth from the sun; and thus the parallaxes deduced
by the s|>ectroscopic method might be as much smaller than 0".l as the major
axis of the stellar orbit is larger than that of the earth, provided of course
that the combined mass of the stars is great enough to give a relative motion
of the companion in the line of sight which can be measured with the desired
precision.
Thus, by the usual method tin- parallax of a Cmtanri would be just mea«-
urable at the distance of .% light-years, and would amount to 0".l ; and as the
major semi-axis of the orbit would there subtend an angle of 2".2, the spcctro-
scopic method could be applied at 22 times that distance, or when the system
is removed from us by about 800 light-years. Of course we can never hope
to measure the distance of a system so remote by tin- ordinary method, since
at the distance of 800 light-years the parallax would amount to only 0".0045.
If tin- ma-s and dimensions of the -\-ti-iu be larger than those of aCentauri,
the spectroscopic method would enable us to measure a parallax correspondingly
40 THEORETICAL POSSIBILITY OF DETERMINING
smaller. While at present little is known of the magnitude of binary systems,
it seems probable that in some cases at least the masses and dimensions will
much surpass those of a Centouri. It is therefore probable that it will occa-
sionally be possible to determine the distances of systems removed from us by
several thousand light-years.
The present state of Astronomy does not permit us to make a confident
assertion with regard to the distances of the clusters or of the Milky Way,
but it seems exceedingly probable that both are very remote. In each of these
species of stellar aggregation there exists a considerable but unknown number
of binary stars which can be detected with our present optical means. Thus,
BURNHAM has searched for double stars in several of the great northern clus-
ters, such as Praesepe, the Pleiades and the great clusters in Perseus, Hercules, &c.
(Publications of Lick Obs., vol. II. pp. 211-216), and discovered a number of
pairs which promise to be physically connected. He observes that interesting
stars are apparently more frequent in wide clusters like the Pleiades, Praesejte,
and the great cluster in Perseus, than in the more compact clusters like that
in Hercules. Yet he has discovered an important pair in this dense globular'
cluster, and SIR JOHN HERSCIIEL has likewise detected double stars of special
interest in several of the great clusters of the southern hemisphere. It is not to
be doubted that many more such objects will be detected when the clusters gen-
erally are critically examined under the powers of our great modern refractors.
When the orbits of these binaries have been found by exact micrometrical
measurement, the spectroscopic method will eventually afford the means for
determining their immense distances, not by probable assumptions but by exact
computation. It is evident therefore that if we are ever to determine the dis-
tances of clusters from the earth — and no sound ideas of the nature of these
masses of stars can be formed until such determination is made — we must first
search the clusters critically for binary stars, and determine their orbits by
micrometrical measurement. If, when the orbit is known, it shall appear that
the binary has the same proper motion as the adjacent stars of the group, there
will be a strong presumption that the system forms a part of the cluster. If
the pair be also of about the same magnitude as its neighbors, and of the same
color and spectral type, we may conclude with practical certainty that the
binary is intimately connected with the mass of stars in which it is projected.
Determination of the parallax of the binary will therefore give the distance
of the cluster from the earth, and supply all desired information as to the
dimensions of the cluster, the brilliancy of its stars, their mutual distances, &c.
If in like manner any group of stars in the Milky "Way could be carefully
THE IMSTANTK8 OF M Vi:-« I I -II i:- VXD OF THK MII.KV WAY. 41
searched I'm- binary ~\ -i.-m-. iind -»t\n- intimate connection of n pair with nci^li-
iMtiini; -tar- shown t«> »-\i-t. a determination of its orbit and an application of
the s|>ectroseopic method would lead to a knowledge of tin- distance of dial
part of the Milky Way. l'»\ > \icnding the same process to all parts of the
<i:il:i\y it will !>• p<i--ililc in tin- course of time to ascertain the nature of that
immense aggregation of stars, ami throw light upon the construction of the
heavens. While the sj»ectroscopic method applies only to hinary -tar-, it in
evident that their great abtindanee and univerMal distribution in space will some
ilay give a mean*) for determining with precision and certainty the actual
structure of the sidereal universe.
We must not expect that the immense possibilities here outlined will
be practically realized at once, or even in the near future, yet giant refractors
like the 40-inch Yerkes Telesco|>e will give such (tower for separating
close double stare and for supplying a great amount of light for the spcc-
troscopic study of faint objects, that an application of these ideas may not be
found ini|N>ssible in the course of the coming century. If there lie ipectroaoopic
or photographic difficulties, the progress of spectroscopic Astronomy during
the last thirty years justifies the belief that such obstacles will not continue
to be insurmountable. The great philosophic interest attaching to the foregoing
method for investigating the structure of the visible universe by exact 8|>ectro-
scopic measurement, instead of by the doubtful processes of ganging employed
by 1 1 1 ix IIM and STKUVK, appears to be a sufficient justification for considering
what is at present only a theoretical possibility. The history of Astronomy
shows that it is not always the theories that can IH> realixed in a decade or
even in a century which in the long run exercise the most important influence
on the development of science.
///>/'//•/.•(// S(,,fch of t/ie Dijf'rrenl Mrlhttd* for I>ftenniiiin»j
Orbit* of I>»Me. Stars.
!t is assumed that the law of gravitation governs the motions of double
stars, and therefore that the orbits are ellipses with the principal stars in
the foci. From the nature of conic sections the centre of the real ellipse
will be projected into the centre of the apparent ellipse. But in general the
foci of the real ellipse will not fall u|>on the foci of the apparent ellipse. If,
however, a line be drawn from the centre of the apparent ellipse to the princi-
pal star and prolonged in either direction until it intersects the curve, the
result will define the projection of the real major axis. The diameter of the
42 HISTORICAL SKETCH OF THE DIFFERENT METHODS
ellipse conjugate to this line will be the projection of the minor .axis. Thus:
It is easy to fix the positions of the real major and minor axes as seen in the
apparent orbit. Since all parts of the major axis are shortened in the same
ratio, the eccentricity of the real orbit may be deduced from the apparent
orbit, by dividing the distance from the centre to the principal star by the
major semi-axis as seen in projection. The end of this axis which is nearest
the principal star will be the periastron; that farthest away, the apastron; -the
dates corresponding to the passage of the companion through these points will
give the epochs of periastron and apastron passage respectively. It is evident
that only one diameter of the real ellipse will suffer no shortening, owing to
projection, and this is the diameter parallel to the line of nodes. If from
points on the apparent ellipse perpendiculars be drawn to this diameter, and
then increased in the ratio of cosi to 1, we shall get points of the real orbit
whose projections give points on the apparent orbit.
The observations of a double star are expressed in polar coordinates, p and 0,
which give the angular separation of the components in seconds of the arc
of a great circle, and the position-angle of the companion with respect to
the meridian. The companion is thus referred to the principal star regarded
as fixed, and hence the observations give the means of finding only the relative
orbit of one star about the other. The absolute orbit of either star about the
centre of gravity of the system has a form similar to that of the relative orbit,
but the linear dimensions are reduced in the ratio of M^ or Ml to M1 -j- M* >
where Ml and M% are the masses of the stars. The absolute orbits of the
stars have the same shape, but are reversed in relative position. The centre
of gravity of a pair of stars can be determined only by the criterion that the
centre of gravity of a system moves uniformly in a right line; and as most of
the systems have too little motion to define this point with any considerable
degree of precision, owing to the imperfect state of our absolute positions as
determined by the meridian circle, it is in general impossible to define the
absolute orbits or relative masses of the stars. With few exceptions, therefore,
astronomers have contented themselves heretofore with determining the relative
orbit of one body about the other.
The first method for determining the orbit of a double star was proposed
by SAVARY in 1827 ( Connaissance des Temps, 1830). This method is closely
analogous to those used for planets and comets, in so far as it rests on the
treatment of four complete observations for the definition of the seven elements.
The problem is solved by elaborate geometrical constructions, such as charac-
terize work in pure mathematics rather than the practical processes which must
FOR DKTBBMIMM "i.mtx OP DofRI.K STARS. 43
be invoked by the working computer. >\\ MM'- principal equation is based
on tin- difference between tin -. i t..i- ami triangle, the an»a derived from the
time being equated with an expression in\ul\ing the product* of the semi-axes
and eeeentrie angles of tin appai-mi ellipse. The method is thus ill adapted
to the determination of an -prl.it from Mich positions as are furnished by the
measures of double star-.
KNCKK recast the method of SAVARY, from the j»oiiit of view of a practi-
eal eomputer, and dedueed formulae similar to those used by astronomers in
their work on planets and comets. Rejecting the equations depending on
conjugate diameters, so much employed by the French geometer, he based his
formulae on recognized astronomical processes and develojK-d tables to facili-
tate their application. As SAVARY had applied his method to £ Ur*n< Mujori*,
KNCKK was led to illustrate his computations on the equally well-known system
of 70 Opfiinchi (Berliner Aslronomincfieti Jahrbuch, 1(332).
SIR JOHN HKKSCIIKI, took up the problem al>out 1830, and sought to
improve the processes by a graphical method which enabled him to make
list; of all the observational material, and to eliminate the grosser errors of tin-
individual observations. He was convinced that in order to obtain orbits of a
-;»ti-l'actory character, it would be necessary to correct the angles by an inter-
polating curve, one axis representing the time, the other the angle, and that
the distances must be rejected altogether, except for the determination of the
major axis. He proceeds by successive approximations to deduce normal places
for- the angles, and by gradual improvement of his graphical results render-
them consistent with an ellipse, and finally obtains a satisfactory apparent orbit.
The elements are then deduced by formulae not very different from those
employed by SAVARY. The method is illustrated by applications to y Virginia,
a Geminorum, <r Coronae Borealis, £ Ur*ae Majoris, and 70 Ophim-hi (Memoir*,
Royal Astronomical Society, Vol. V).
While the process of interpolation invented by HKKSCIIKL has been exten-
sively employed, and in some cases is very useful, I am satisfied that in general
it is better to plot the observations directly and to make a trial ellipse the
interpolating curve. This enables us to use both angles and distances and
secures all the advantage of judgement which HERSCIIKL considered so essen-
tial. It often happens that the length of the radius vector changes with extreme
rapidity, and as the areas are constant this will imply very great and unequal
changes in the angular motion; when the angular velocity of the radius vector
is so variable in different parts of the apparent ellipse the course of the inter-
polating curve becomes altogether uncertain. Under these conditions it is much
44 METHODS FOB DETERMINING ORBITS OF DOUBLE STARS.
better to use the observations directly. It is also recognized that modern
measures of distance should be allowed an equal or nearly equal weight in
the determination of orbits.
After SAVARY, ENCKE and HERSCHEL had given such an impetus to the
study of sidereal systems, the work was carried forward by MADLER and
VILLARCEAU, both of whom published a number of orbits with some minor
improvements in the processes of computation.
KLINKERFUES took up the subject about 1856, and in the course of work
on several orbits developed very elegant formulae and more practical methods
than any which had been used before. His analytical method is marked by rigor
and generality, but in the present state of double-star Astronomy is not so
practicable as the graphical method treated in section 10.
THIELE, some years later, devised an elegant graphical method which
has many good points, and is much admired by those who are inclined to
determine all the elements geometrically. It will be found in the Astronomische
Navhrichten, Band LII.*
Among the more recent investigations those of PROFESSOR KOWALSKY are
remarkable for their extreme elegance and great generality. This method,
depending on the general equation of a conic, is all that can be desired from
a mathematical point of view, and as simplified by GLASENAPP has been exten-
sively used by several computers. The original exposition of the method
will be found in the Proceedings of the Imperial University of Kasan for
1873; the valuable modification introduced by GLASENAPP is given in the
Monthly Notices, Vol. XLIX, p. 278.
Other recent investigations which are worthy of special notice include
those of SEELIGER (Inaugural Dissertation of SCHORR, Munich, 1889), and of
ZWIERS (AstronomiscJie Nachrichten, No. 3336).
It is singular that nearly all the methods given above have been developed
from the point of view of analysis rather than of practical Astronomy. BURN-
HAM has recently rendered double-star Astronomy a conspicuous service by
reviving the method of representing observations first employed by WILLIAM
STRUVE (Mensurae Micrometricae, last plate). This consists in plotting the
points as determined by the micrometer, and in finding from the places thus
laid down the apparent ellipse which best satisfies the observations. "VVe have
used a modification of this method throughout the present work, and have dis-
cussed it in connection with the graphical method of KLINKERFUES, which
supplies the process for deriving the elements from the apparent orbit.
•It is also explained by PBOFESSOB II ALL in The Astronomical Journal, No. 324.
K«l\\ \l -K->'- Ml IIIOll. 4ft
We shall now give an r\|»<'-iii<»n of the elegant method of KOWALKKY,
which seems likely to IK- I lie tun- that will ultimately be adopted by astronomer*.
The general equation of the ellipse with the origin at any |M»int, here taken
at the principal -tar. i-
F - «x« + <>kjry + by* + 2yt + 2fy + r - 0 ; (1,
which may l>e reduced to the form
Ax* + 2Hxy + Hy* + 2fix + 2Fy + I - 0 . ('.')
This equation contain- five unknown constants, and hence five values of
x and ij will enable us to determine the constants of the ellipse. Kach obser-
vation given one equation by means of the relations
win -iv the avaxis i- directed to the north-|K)int. And hence five observations at
cliH.Tent e|M>eh8 will give a determination of the apparent orbit. In practice it is
found that a larger numlxr of observations is desirable, and if the observa-
tions are sufficiently good, the best results will generally !><• obtained by a
least-square adjustment of the residuals.
When the apparent ellipse is determined, the problem arises to express tin-
elements of the real orbit in terms of the constants which fix the apparent
orbit.
It is evident that projection does not alter the diameter coinciding with
the line of nodes, and this enables us to pass from the apparent to the real
orbit. The real orbit is evidently the curve determined by the intersection of
the orbit-plane with the elliptical cylinder whose right section is the apparent
orbit. In the apparent orbit tin- axis of x is directed to the north-|K>int, hut
in passing to the real orbit we shall direct (lie new a\i> of x to the a«ccndini;
node, while tin new a\i< of y will be taken in the plane of tin- real orbit, and
the origin ivtain.-.l at the principal star. Calling the n<-\\ -\-leni of coordinates
.r.'/.:, it i- evident that we shall have
f m, l' COt Q — t/ Kill fi COS I + S1 »lll Q Mil •
y « f> Mil Q + y1 cusQcos/ - i' c<* Q MM •' '•'*>
* — + ft sin i + c* «w i .
;
46 KOWALSKY'S METHOD
If we put z' = 0, we shall have the coordinates of a point in the plane of
the real orbit. Thus our expressions are simplified, and become equations for
turning the axis of x through the angle ft, and that of y through the angle i.
If we put
.r = .r' cos Q — i/' sill ft cos / , // = .r' sin SI + .'/' cos Q cos i ,
in (2), we shall obtain the equation of the intersection of the plane x' y' with
the elliptical cylinder, which is the equation of the real ellipse. Thus we have,
on omitting the accents,
A (x cos ft —y sin ft cos i)2
+ 2H(x cos SI —y sin Q cos i) (x sin ft +y cos ft cos f)
+ B (3- sin ft +y cos Q cost)2 + 2 G (x cos ft —y sin ft cos i)
+ 2F(r sin £ + // cos ft cos i) + 1 = 0 .
The equation of the real ellipse referred to its centre is
a-2 ?/"
^ + P = 1- . <«>
If we shift the origin to the focus, we must increase x by ae, and the
equation becomes
, y*
+ -1-0. (6)
when referred to the principal star.
Now suppose X to be the angle from the node to the periastron, measured
in the plane of the real orbit; then if we turn the axis of x back to the line of
nodes, the new coordinates are
x cos A + y sin A ; — x sinA 4- ?/ cos A .
By means of these values of x and y, equation (6) becomes
(x COB X + y sin A + aef . ( — * sinA + y COsA)2 1 ^^
the origin is taken at the focus and the axis of x is directed to the node.
Now this equation is necessarily identical with (4), which also represents
the true ellipse referred to the same axes. Hence, when multiplied by a con-
stant factor e the coefficients of the variables must equal the corresponding
ones in the equation deduced from the apparent orbit, so that (7) and (4) give
I'M: HI TKKMINIMi IXH'BI.K-STAK OHHITS. 47
— (^«in*Q +/?coa' JJ-//siu2Q)co«'/.
74-£,)«n2A - (-^sin2Q + /f8iu28+2//co82Q)ros«. (10)
•> O oosQ + /'sin Q . (11)
(12)
• (e«-l) - +1 .
This last equation gives
t — — •: . and - —
l-f1 a p
Also, since
we have
Now (11) and (12) give
rsinA— -^(Fco«Q-« 8infl)OM< ; ecosA— -/' (F sin Q -I- (i cos
Multiplying (11) by (12) and reducing, we find
If we subtract (9) from (8), we get
/coe'A-sin'A co8fA-8in«A\
From (10) we have
-,8in2A - (-A 8in
/'
and hence
-0.
and the difference of the squares of r cos X ami • -in X gives another value
of Equating these two values of p««2A, and solving for cos'i,
we find
(F'-B) 8in'Q+(^-^) co.«Q-f-(^v;-//) 8in2Q 16
-(^;-//> 8iu2Q
48 KOWALSKY'S METHOD.
The forms of the numerator and denominator show that if we put
cos'2i=-, and hence tan2/ = _2> we 8i,all get
tan2 1 = - ' v _ 2 .
The first member of (9) gives
/sin2 A cos2A\ e2 1
and therefore we obtain
e'2 1
-jSin2A — -5 = (.4 sin2 ft + K cos2 ft -//sin 2 ft) cos2 i.
By squaring (12) we find
e'2
-j sin2A = (/>'* cos2 ft + G* sin2 ft —FG sin 2ft) cos2* .
I1
Therefore we have
- == [(^2-#)cos2ft+(G2-.4)sin2ft-(/Y;-//)sin2ft]cos2i. (16)
Comparing this with (15), we find -^ =•- P; and hence
2_ + tej£» = F, + (J, _ (A + /{) (17)
Now since
l
-5 = P = (F*-lf) sin2 ft + (G'2-A) cos2 ft + ( FG - H ) sin2Q ,
f
we easily find
>2
—, = F*+G* - (A + ll) — (F'2-I!) cos2ft + (G^—A) cos2ft + 2 (FG-H) sin2ft . (18)
Hence (17) gives
= (F*-G*+A-/i) cos2Q-2(F(,'-// ) sin2ft . (19)
If we multij)ly this equation by .sin 2ft, and (14) by cos 2ft, and subtract
the last result from the first, we get
sin 2ft = -2 (AY;-//).
i>i i i KMIMM. i>«,i i-.i i --i \i; OUHITS. I'.'
If we use 008 28 ami sin 20, nml add the produets, we have
tan* i'
•T-C082Q - F'-d'+A-B.
r
Therefore we finally obtain tin- following net of equations:
^£-'sin2Q - -I(FG-H),
I'
t
0sinA — —
These formulae enable us to find 8,i',y>, X, f, » ; we may then find r at
any e|x>ch by the formula
tao(»+X) • Un^O)' and JP by tan \ S • ^ -f tan J .• .
\\ a find 3/ by KKPLKK'S equation
M - ^-«»8inA'.
And Kinee Mt— 3/1 = « (/, — /,), we see that
t - M,
ami
l'i:"M--"i: <•! \-I\\PI- li:i- |.|-. .(» ,~,-(l a -iui|.I.- iihtii'"! !-r cnscs in \\hi.ii
good drawings of the apparent orbits have been made, but it in not dc-in-d
to adjust the results by tin- imthod of Leant Squares, owing to the uncertainty
of the data furnished by observation. In the present state of double-star
A-tronomy this method i- \cr\ pr:ict'u-:il>lc. and can be advantageously em-
ployed in the determination of orbits.
In the equation (2)
21/J-y + fly1 + '2Hr + 1V,j + 1 - 0 ,
we put y = 0, and then find the roots of
1 - 0.
50 GRAPHICAL METHOD OF KLINKERFUES
This may be written
2G 1
a-2 + - — * + -7 = 0 , or (x— x^) (x—x^) = x* — (^i+a-j) x + x^ = 0 ,
A A
where a;, and x% are the roots of the equation, or the abscissae of the points of
the orbit on the a>axis.
Hence, by the theory of equations, we have
1
Also
2G
A =
x,xa
or G -
'
A 2
In like manner, putting x = 0, we find
By* + 2Fy + 1 = 0 , or K = — ;
Hence when the coordinates of the intersections of the orbit with the
axes of x and y are known directly from the apparent orbit, we have the
four constants A, B, F, G.
And the other constant is given by
Ax1 + Bif + 2Gx
In finding H we must take a point (x, y) such that the product x . y has
a large value. It may be desirable to take the mean of several values of //.
When all the constants A, £, F, G, II, have been derived, we find the
elements by equations (20) and (21).
§ 10. Graphical Method of Klinkerfues.
Suppose a and ft to denote the lengths of the real major and minor semi-
axes when projected on the plane tangent to the celestial sphere, and A and
B to be their position-angles. Then we readily find
«2 cos3 (^-Q)4- «" sina(^ - ft) sec 1 = « . fl )
/33cosa(.B-Q) + /3»8ins(«- Q) sec2/ = V1 • \
FOR DETKRMIMM I >« >! 1:1 I -- I \ i: . >KIUTS. fil
it is evident tliat tin- -inn of these equation* in the square of the
chord between the vertices of the major and minor axes; and the square
"I tin same chord is given by
Therefore we have
<x»(A-Q)co»(B-Q) + sin(^-Q) sin(//-Q) aec'i - 0; (2)
and hence
coe'i - tan(^-O) Un(Q-fl) . (3)
This equation determines the inclination when the nodi- is known, as the
anirle- .1 and li arc taken directly from the apparent orbit.
If we divide tin- -econd of equations (1) by the first, we get
*V tP»* (B- 8) + »»n* (B- Q) geo« i
^j? "" co6«(^-ft) + 8in'(^-a)8ec*i;
and on substituting for sec'*' it« value, we find
8in2(/?-Q)
" ~'
In this equation a and /3 art« given directly by the apparent orbit, and as
e is known, we have also the ratio -,-!-«*. Therefore the only unknown
quantity is 20, which we may determine in the following manner. Since the
left member of (4) is the square of a real quantity, the right member must IK-
essentially positive, and we may put
?
and -nice
, 8in2(^-Q) + «in2(g-a)
sin 2(^-Q) -8in2(/f-ft»
we get
- sec 2{ tan (.<-/?) . (6)
The angle £ is known from its tangent, and hence we easily find Q.
In (U) it is to be observed that cos'i is necessarily positive and smaller
than unity, and hence we have to choose between two values of a differing
by 180°. As it is thus impossible t<> di-tin^ui-h between the ascending and
de-ceiiding node, we may arbitrarily take the a-eending imde I., twt. n u and
180°, and find » by nu-an- »l' ( :: i
cos'i - t*a(A-Q) tan(ft-/
52 GRAPHICAL METHOD OF KLIXKERFUES
The angular distance from the node to the periastron is denoted by TT —
= X, and is given by the equation
tan (A — Q ) = cos i tan A ,
or by using (3) we obtain*
tan' A --
-
If u denote the argument of the latitude, we have
n = v + \ = v + TT — SI , and tan u = sec i tan (6— Q) ,
where 9 is the observed position-angle at the given epoch. The latitude I is
given by sin I = sin i sin u.
From the apparent radius vector p, we may find the corresponding true
*
radius vector by
r = p sec I .
The major semi-axis is then found by the polar equation
a = r(1^°S") . " , (8)
If we take the apastron as the point in question, I will be given by
sml = sini sin A ;
and since p is taken directly from the diagram of the apparent orbit, we easily
find r. Then, since v = 180°, we have
p seel
TT7- (9)
To find the time of revolution we take two observations which are widely
separated in time, and find the intervening change in the mean anomaly; or
we may find from the diagram the part of the area swept over during this
interval compared to the whole area of the apparent ellipse. If #, and 02 be
the two angles of position, and MJ and i^ the corresponding arguments of the
latitude, we shall have
tan «j = sec i tan (Ol— SI) ,
taint, = sect tan (02— Q) »
and then
"i = «i — A ; vi. = "2 — A ;
whence the mean anomalies are easily found. Instead of computing the change
of the mean anomaly, it is generally preferable to measure up the area swept
• .4 — JJ and X must lie In the same or in opposite quadrants. Throughout this work % is taken in the
direction of the motion.
K>K HI TKIIMIMM. l»«il III I --I \|: MIMIITM. .'VJ
over by the radius vector during the interval, and determine the i>criod by
the law of art-at*.
Su 1 1| •<•-.«• that /, and I. IMJ the dates of two widely-separated observations;
then the double area swept over by the radius veetor will be
Putting a', b' for the major and minor semi-axes of the apparent ellipse,
it is evident that the time of revolution will lie given by
Tt (10)
In ease the period is computed from the change in the mean anomalies,
we have
.V.-.V,
M
The j>eriastron passage is given by T — /, - -? , or it may lie found from
the prineiple of areas, in the same manner as the period. Thus, sinee the«
double areal velocity is known, we simply determine the double area included
between a given radius veetor and the |>criastron, and ascertain the intervening
time. This interval is to be added to or subtracted from the time of observa-
tion, according as the date chosen is before or after the epoch of |>criastron
pa-saga
To find the node by graphical construction we draw from the centre of the
ellipse lines whose position-angles are "2.A and 2//; then, parallels to these at
distance- related as a*/3* to 6*a*. Connect the intersection of the parallel lines
with the centre, and this will give a line whose position-angle is 28. This
construction is easily deduced from (4), and in practice will be found extremely
exact. The graphical method is highly practicable, and in the present state of
double-star Astronomy is the one which should generally be preferred. The
pOMible inaccuracies of the method arc greatly inferior to the uncertainty still
attaching to the best orbits. The principal difficulty experienced by computers
consists in the finding of a satisfactory apparent orbit.
GRAPHICAL METHOD OF KLIXKKKKfKS
^2 B
1878
\
\
The apparent orbit of 20 Persei = /3524 is shown above. We find by the figure e = 0.738,
'— = 0.194 ; A = 20°.5 ; B = 137°.3 ; & = 142°.2 ; i = 67°.9 ;
\ = 103M ; n = -9°.0 ; P = 40.0 years ; a = 0".290 ; T = 1884.40.
To obtain the apparent orbit it is best to make use of both angles and
distances. If the precession has a sensible eifect upon the position angles, it is
desirable to refer the observations to a common epoch by applying the formula.
J6 = n sin« sec 8 (t — 10) .
(12)
M. n.,i 1.1 i --i \i; ,,1:1,1 , ,.
*
where n = 20'.04967, and t, is the date of observation, / the e]>och adopted.
We then combine the individual measures of the best observers into suitable
annual means, and plot the resulting positions on a convenient scale. The
approximate normal places thus defined arc subject to two conditions:
(1) That the areas swept over by the radius vector shall l»e proportional
to the times;
(2) That the apparent ellipse which satisfies the law of areas shall eon-
form also to the observed distances.
The ellip.-e which -ati-tic* thoe conditions must !H' found by trial. Fine
planimeter measurement renders the approximation comparatively rapid, and
when a satisfactory ellipse has been obtained we derive the elements and com-
pare the computed with the observed places.
Af«*
We first determine «-, then compute the ratio a,« . and find the -node by
graphical construction; it is then easy to find i, X, /', T, and a, as explained in
the foregoing method. If further refinement of the elements l>e desired, re-
course must IK- had to differential formulae.
It is to be remarked, however, that the assumption of constant areal velocity
is equivalent to postulating the absence of unseen bodies or other disturbing
influences, and as this is not yet fully established, the orbits which test repre-
sent the angular motion are not necessarily correct, as may be seen in the case
of 70 Ophiitchi. If it is necessary to violate the distances in a conspicuous man-
ner in order to preserve the law of the areas, the result must be looked upon
with suspicion. In the present state of double-star Astronomy most of our
orbits must be regarded as tentative, but when they shall finally l>e improved
there is no doubt that, if the motion is really undisturbed, l>»tli angles and
ili-tanees will IK; well represented.
If it is ill -in d to compute p and 0 from the elements, we may employ the
formulae
The element X is counted from the node between 0° and 180°, in the di-
rection of the motion ; in case of retrograde motion the formula for 6 become*
tan (8-0) — tan (X+r) coal .
56
GRAPHICAL METHOD OF FUNDING THE APPARENT ORBIT
Graphical Method of Finding the Apparent Orbit of a Double Star.
It is frequently desirable to project the apparent orbit of a double star
from the elements; this interesting and useful result may be effected in a
Fig. 5.
very simple manner. In order to make the process more intelligible we shall
apply it to a particular case, and" for this purpose we select the orbit of
9
OF A DOUBLE STAR FROM THE ELEMENTS. *>T
The elements required lor this purpose art- the following:
Koceiitru-ity. 0 «• 0.700 ±0.02
Mkjor semi-axis, a — 0*.lM>4'.»
N..II-. a - 9fi°.c
Inclination, i — 77*.72
Node to periMtron, X - 75°. 28
We lay down on stiitaiMe drawing pa|>cr two lines which intersect each
other at right anirle-, ;m<l thus mark the four quadrants of position-angle. The
intersection of these lino will !>«• the centre of the real orbit and also the
centre of the apparent <>ri>it. The line of nodes in then drawn through the
centre, having a petition-angle of 95° .5. In like manner we lay down the line
whose position-angle is ft -|- X = 170° .78, and this will IK- the major axis of
the real ellipse.
\\ c now adopt a convenient scale, which will give a length on the draw-
ing paper of 10 or 12 inches for the major axis.
With close stars 0".l may represent one or two inches of the scale, so
that the work can be done with the highest degree of accuracy. From the
centre the length of the major semi-axis (0".G540) is laid down on the line
just drawn, and the distance of the foci of the ellipse from the centre will l>c
ae (0".6549 x 0.70). The ellipse is then drawn in the usual manner.
We now lay off point- on the line of nodes at equal distances from the
centre of the ellipse, and through these points draw lines a a', A//, r</, tld' etc.,
perpendicular to the line of nodes. The lengths of these lines on either side
are found in seconds of arc by the scale used, and then multiplied by the
cosine of the inclination (cos 77° .72 = 0.214) ; the resulting values are marked
on the corresponding lines at a', &', c', d', e7, f, etc., on both sides of the line
of nodes.
The points thus determined will lie on the arc of the true ellipse as seen
from the Earth, and when we pass the curve through them, we have the a|>-
parent orbit of the double star.
To find the ]K>sition of the star in the apparent ellipse, we multiply the
distance of the focus of the real ellipse from the line of nodes by the cosine
of the inclination, and thus find the j>omt J, which will In- tin- p<>-iti..n of the
central star in the projected orbit. A line O*'/*, drawn from the centre
through this point to intersect the arc of the apparent ellipse, gives the posi-
tion-angle of the real major axis, and the position of the real i>eria«tron.
Having thus obtained the position <»1 the central star in the apparent orbit,
it only remains to draw through tin- principal star lines parallel to those inter-
58 FORMULAE FOR THE IMPROVEMENT OF
secting at the centre and marking the four quadrants, which may now be erased.
In the figure the lines which mark the four quadrants are somewhat heavier
than the rest, so that they are easily recognized.
Thus a very simple process of projection enables us to trace the outline
of the apparent orbit of any star when the required elements are given;
and from the observed positions it is possible to see at a glance whether the
apparent orbit represents the observations satisfactorily. It only remains to
add that in the case of retrograde motion, the angle X (which should always
be counted in the direction of motion, while the ascending node should be
taken -between 0° and 180°) must for purposes of graphical representation be
taken as negative, and the position-angle of the major axis of the real ellipse be-
comes Q — X, whereas for direct motion the angle is 8 -|- X, as in the case of
9 Argus.
§ 11. Formulae for the Improvement of Elements.
The foregoing graphical method, when judiciously applied, will give elements
having all the accuracy which can be desired in the present state of double-
star Astronomy. But as some improvement of a very refined character will
ultimately be possible, we shall present the differential formulae which may
be employed to effect these slight variations of the elements.
The formulae for finding the position-angle 6 from the elements are
M = n(t-T) = E-e"s\nE,
tan J v = Zf tan J E ,
\l — e
tan (*'+X) cost = tan (6— JJ) .
Since 0 is a function of the six elements, Si, *', X, e, T, n, we have
When the variations of the .elements are finite, but small, we have the
•approximate formula,
6. - 6, = JO = AJSl + BJi + CJ\ + DJe + GJT + HJn ,
where A, JB, C, D, G and //, denote the partial differential coefficients.
From the equations which enable us to compute 0 we obtain these coef-
I.I.I Ml NT- <>l I>"1 HI I -I \l - .V.I
ficicnt- I'V |i:irlial diHVrrmialion with iv-prei tit tin- »c\cral elements. Thus
we find
I - +1;
C - •
/ 2UnjA' lITi sec'i #«n*\
D [ i ' •
\(l-«)vl— •* Nl— « 1— eootiA /
G •
"
l -o 1-00MJT
Tin- formulae usually employed by astronomers for effecting thr differential
corrections of the elemeiitH thus take the fonu
+ Hi<1* - I9i " ° .
t1n -.19, = 0 ,
Jirln - .I6V =. 0 .
There are six quantities to be deduced from thin gyittem of iH|uatioiiH ; a
by the method of Least Squares will jfeiH-rally ensuiv the l>est result h.
In tin- above form of the equations it is tacitly assumed that the residuals in
angle represent absolute displacements of the companion in space, regardless of
its distance from the central star, which is evidently inexact. The ini]>ortaiic.c
of a given error in angle increases in proportion to the length of the radius
vector, and as the distance of the companion is generally very unequal in
different parts of the apparent orbit, the formulae should be so modified as to
render the absolute displacements of the observed positions a minimum. This
improvement can IK- effected as follows. We shall assume that the major axis
»:ui IH IM -t determined from the apparent orbit, which serves as an intcr|>o-
lating curve analogous to that recommended by SIK JOHN* HEKWIIKI., and hence
this element need not IK- regarded as variable. It is, therefore, required to
compute the slight variations for the other six elements.
Let us suppose that the value of p corresponding to the position-angle 0.
is p.; this value may IH- computed or measured graphically from the diagram.
Let the corrected angle and distance IK- 0C and pe respectively. Then it is eaay
to see that the displacement of a point on the apparent orbit due to the correction
of the elements will be given by
' "
60 A GENERAL METHOD FOR FACILITATING THE SOLUTION
In case the length of the radius vector in the apparent orbit is practically
constant, the last term of the radical becomes insensible, and the displace-
ment in space at a given distance is proportional to the displacement in angle.
But as many of the orbits are very eccentric and highly inclined, and the
radius vector therefore changes rapidly, the best result can be obtained
only by the use of the complete residuals expressed above. In computing
these values numerically we may express (pa — pc) in degrees by the
formula 2 (^rpj «"°.3 ; and since (60 — 9C) is already given in degrees, we
must express the coefficient as an abstract number in units of the major semi-
axis, in order to give the displacements in angle weight proportional to the
length of the radius vector.
Since the second term of the resulting expression under the radical sign
will often be very small, it will frequently be sufficient to use the first term
only; or in other words, to assign the residuals in angle weights proportional
to the lengths of the radii vectores.
This method of improving the elements will be found very much shorter
than that involved in the process of correcting both angles and distances by
separate differential formulae, and will lead to the same results without loss of
accuracy.
§ 12. A General Method for Facilitating the Solution of Kepler's Equation by
Mechanical Means.*
The standard works on planetary motion, such as GAUSS' Theoria Motus,
OPPOLZER'S Bahnbestimmung, and WATSON'S Theoretical Astronomy, give
methods for solving KEPLER'S Equation which are very satisfactory when the
eccentricity of the orbit is small, and also when this element is large, as in
the case of most of the periodic comets. When the eccentricity is small, an
expansion in series, usually by LAGRANGE'S Theorem, enables us to find the
eccentric anomaly with the desired facility. The series frequently employed
has the form
e" sinM+e" =sm2M+
•Monthly Notices, June, 1895; also Note in Monthly Notices for December, 1895.
OK M I'M I:'-. I ...I VIK'N 1l\ Ml I II \\ II \l Ml V\8. <J1
'\'» the approximate valiir /•,'„. obtained from a few terms of this series,
we appK ;i i "i n i-ti'iii resulting from thr expansion by TAYMW'S Theorem:
i
E - K, + ?£ dM. + . . . .
Tin- equation of KKIM.KI; gives
or
» - 1 -«cosAt;
and since
we find two terms of the series to be
*- * + r^F
Successive applications of this formula will n-ndily yield the true value of
the ecxH'iitric anomaly. But when the eccentricity in considerable the expansion
in Herien fails to converge with the desired rapidity. On the other hand, when
llu- orbits differ but little from paraliolaM, the solution can readily IK- found by
means of *|n-<-ial talih-s, such as those given by (t AUKS, WATSON and Oi'i'oi./KH.
It i> \«-i\ remarkable that among the many solutions of KKIM. Kit's Kqiiation
discovertnl by mathematicians there is not one, so far as I am aware, which
has come into general use among astronomers that is applicable to ellipses of
all |tossihlc eccentricities.
The method to which I desire to direct attention is a modification of the
graphical method originally invented by .1. «I. WATKHSTOX (^f^nlillly
'-."><>, p. lii'.l). and subsequently re<liscovere<l by Dntois (
'-rirlifi;,, no. lint). The method was afterwards discussed by KLIXKKH-
i i i - in lii> Tln'ii-'li.tcln .IstriHioiHi'i', p. 17; but so far as I am aware* it never
came into practical use until employed in the investigations embodied in this
work.
Suppose we construct, on a convenient scale, a srini-circiimferrnee of the
curve of sines, y = sin./-. In practice it i- ilr-iral»le to use millimetre pajn-r,
ami a convenient M-ale is obtained by taking one degree of the arc as li\«-
millimetres, so that the scale may easily IM- read to OM. The origin of the
are i- taken at the origin of coordinates; and as the M-ale along the axis of
abscissae extends from 0° to 180°, it will have a length of '.HI centimetres.
In the figure let O.\/ repn-eiit the mean anomalx. and -II|I|><>M- from M
•JTonttly .VoHcM, December. 1M5.
62
A GENERAL METHOD FOR FACILITATING THE SOLUTION
we draw a right line making an angle V with the axis of abscissae, the angle
V being defined by the equation
tan ¥ = -
e
Let the abscissa of the point C, determined by the intersection of the right
line MC with the sine curve, be denoted by E. Then we evidently have
OE - ME = O M .
(Y)
M
C
K
\
x
\
v
\
90°
IX
Fig. 6
Thus, denoting the arc OE by E, and observing that e sin >F = cos 'F, we
find that e sin <F -. - ME, the radius in the case of sin V being such that sin ¥
is always equal to sin E.
Hence we get
OE - ME = OM ,
or
E — e sin E = M,
which is the Equation of KEPLER.
Therefore we conclude that if for an orbit of given eccentricity we con-
struct a triangle CME (in practice this may be made of cardboard) and apply
the vertex M of the triangle to the successive mean anomalies, tin- base coin-
ciding with the a>axis, the intersection of the hypothenuse with the curve of
sines will give at once abscissae which are the corresponding eccentric anom-
alies. Any actual diagram such as we have described will be subject to slight
inaccuracies of construction, owing to the transcendental nature of the sines,
and hence we cannot obtain solutions of absolute precision. But it is entirely
possible to get approximate solutions exact to OM, and this work can be done
with the greatest rapidity. It is merely necessary to slide the base of the
"K KI I-I.KK'S K/iATiov in MIMIXMI \i MI \\-. »'..",
triangle along the a>axis, placing tin \.rt< \ .)/ at the points corrcs|>oiiding U>
tin- (iirfiTi-nt value* «>f tin- mean anomalv. and reading off the corrcs|iondilig
eccentric anomalies.
Thin triangle device i* rendered (Krasible by virtue of the fact that f is
constant in unf- ; and we may observe that in case of elliptic orbit** the
angle F can vary only from 45° in the case of a paralxda to (K)° in the case of a
circle. Thin method in therefore directly applicable to ellipses of every jiossihlc
eccentricity, and the accuracy of the solution i* always substantially the -aim-.
In the COM*. of parabolic motion, however, the method fail*. -incc when V = 45°
the hvpothenuse 3/C is tangent to the sine curve at the origin. But for f<\
the by pot hcnuse JVC intersects the curve y = sin a;, and the intersection will IK-
well delined e\eept when e approaches unity and M i- very ninall. In such
cases it is best to use the Special Tables or the Theory of I>arulN>lic M-.ii.ui.
Solution* - \a< t to OM an- often sufficient in the present state of double-star
observation, and we readily see how great is the practical value of this method
in comparing a long series of observations with a given set of elements. One
hundred approximate solutions of KEIM.KK'S Equation, accurate to OM, may IK*
obtained by this method in less than half an hour; while if 6 KM between ".-'!•">
and 0.8o probably a skilled computer could not obtain the same results by the
ordinary method in less than a day. Thus the time and lalxu- required for
this work is much diminished, and it is clear that the chances of large error
are corre8|K>ndingly reduced.
If a curve of sine* were engraved on a metallic plate it would IK* an easy
matter to devise a movable protractor which could be set at any angle; such
a piece of apparatu* \v»uld serve -for every possible elliptic orbit, and would
last for an indefinite time. Considering the immense lal>or devolving UJMHI
astronomers in the computation of the motion of the heavenly bodies, it would
seem that such a labor-saving device might IK- advantageously employed in
the offices of the a-tronomical cphemerides. However, as several astronomers
have pivpaivd tables for facilitating the solution of KI.PI.I i:'* Equation in the
case of orbits which are not very eccentric, such an apparatus would IK- useful
elm-llv in work on the more eccentric asteroids, the double stars, and the |H'riodic
comet*. Iii dealing with the motions of these ln>dics the labor saved would
be very considerable, and we might ho]>c that the apparatus here suggested
would come into actual use. But in case this instrument of precision could not
be successfully manufactured, owing to its limited commercial use, it is etty
for a working astronomer to construct a curve of sines on millimetre pu|>cr.
64 SOLUTION OF KEPLER'S EQUATION.
This can be mounted on a suitable wooden board, and a triangle of cardboard
will give the solutions of KEPLER'S Equation for any given orbit.
Thus, while the graphical method, originally proposed by WATERSTON,
afterwards independently discovered by DUBOIS, and subsequently discussed by
KLINKERFUES, was suggested many years ago, it does not appear that it has
yet come into general use; and therefore it deserves the careful attention of
astronomers. It is worthy of remark that a method of such great practical
importance should rest in comparative oblivion during half a century, at a time
when astronomers were constantly working on the motions of periodic comets
and double stars; but it is probable that neither WATERSTON nor DUBOIS recog-
nized the great generality and high value of the method in practical work.
Since writing the paper which I communicated to the Royal Astronomical Society
in June, 1895, I have had occasion to make great use of the method in revis-
ing the orbits of double stars, and have found it not only the easiest and most
rapid process yet invented, but one altogether so satisfactory that we may pre-
dict its universal adoption by astronomers. The simplicity and generality of
the method and the rapidity and accuracy with which solutions can be obtained,
invite the inference that in the nature of the case the method is probably ulti-
mate, and is not likely to be improved upon in any future age.
While this method is of special importance in dealing with the motions
of double stars, owing to the wide range of their eccentricities, it will evidently
be almost, if not quite, equally important in the case of periodic comets and the
asteroids. But in dealing with comets and planets, where we desire very exact
solutions of KEPLER'S Equation, it will be necessary to correct the approximate
values by the formula
' 1-ecosV
where M0, E^ are the approximate values of the mean and eccentric anomalies.
A second correction will ensure all the accuracy desirable in planetary and
cometary ephemerides.*
•Among the other means for solving KEPI.KIS'S Equation we mention especially the tables of AHTKAND
(ENOI.EMANN, Leipzig); DOHKKCK, A.N., Bd. 130; ami a graphical method by Mi«. H. 0. I'I.ITMMKII, Monthly
Notices, March, 1896.
CHAPTER II.
OX TIIK OlMIlT- OK FOKTY BlN'AKY STAHS.
IntroiliK-litry Iti-nutrk*.
TIIK present chapter is occupied with detailed researches on the motion*
«»!' tin- forty stars whose orbits can be best determined at this epoch. The
mad-rial presented for each star has Wen collected from all available sources
:iinl is very complete. It is highly improbable that any important records have
l>. « ii overlooked, and since we have drawn the material almost wholly from
original sources, future investigators will have little need to repeat the labor
involved in collecting observations of these stars prior to 1895.
In some cases we have not used all of the available measures, either localise
tin- observations appeared to l>e defective, or because good observations were
obtained too late to be incorporated in the discussions, which were not changed
unless the elements adopted were found to be inconsistent with the new mate-
rial. In the main, our choice of observations has been guided by the assump-
tion that it is ]>ossible to find an orbit which is consistent with undisturbed
elliptical motion. The observations have justified a violation of this principle
only in the case of 70 Ophiuc/ii, which presented anomalies too large to IK-
attributed to errors of observation. If the course of time should show that other
stars also are perturbed, it will become apparent that we have not always made
the best choice of the material now available.
In the determination of these orbits a numlier of distinguished astronomers
have contributed their observations in advance of publication. They have not
only sent manuscript copies of valuable measures, but have ofleivd their work
with a gcncrositv which merits my mo>t grateful acknowledgement. Among
those to whom we return thanks are: M. <>. Hi«.<>i IM> AN. National Observatory,
Paris; PROF*. G. C. COMSTOCK and A. S. I 'MM. \Va-hburn Observatory,
Madison; PROF. S. DE GLASEXAIT, Director of the Observatory, Imperial
Tniversity, St. Petersburg; PROF. G. W. Houciir, Director of the I >earl>orii
Observatory, Evanston, III.; \'\:<n. V. K\«H:I:I-. Koval Observatory, Berlin;
T. LEWIS, ESQ., Koyal Observatorv. < ,i, ,-nwich; M. W. MAW, ESQ., Private
6(5 ABBREVIATIONS OF THE NAMES OF OBSERVERS.
Observatory, London; PROF. G. V. SCHIAPARELLI, Director of the Royal
Observatory, Milan; PROF. W. SCHUR, Director of tbe Royal Observatory,
Gottingen; JOHN TEBBUTT, ESQ., Private Observatory, Windsor, N. S. Wales;
DR. H. C. WILSON, Goodsell Observatory, Northfield, Minn.
I have also had the constant cooperation of PROFESSORS BURNHAM and
BARNARD, who have made valuable suggestions in addition to contributing
important observations, some of which were secured expressly for this work.
In the investigation of the individual orbits my friends MR. GEO. K. LAWTON,
MR. ERIC DOOLITTLE, and MR. F. R. MOULTON have at different times
rendered valuable assistance in the execution of a large part of the com-
putations. Without such assistance, uniformly characterized by both zeal and
enthusiasm, it would have been impossible to have completed the determination
of so many orbits in so short a time. To these gentlemen I acknowledge my
deep and lasting obligations. Besides aiding me in the preparation of Chapter I,
MR. MOULTON has assisted in arranging the manuscript for the printer, and
in reading the proofs, and thus not only expedited the work but also ensured
greater accuracy than otherwise would have been possible.
While no effort has been spared to ensure exactness in the computations
and in the drawings, it can scarcely be hoped that in dealing with so great a
mass of material all errors have been avoided. There is reason, however, to
believe that such errors as may exist in the work will have no appreciable
effect upon the final results.
A number of the orbits embodied in this Chapter have been published in
the Astronomical Journal, the Astronomische Nachrichtfn, and the Monthly
Notices of the Royal Astronomical Society; references to these sources will be
found in the appropriate places.
Abbreviations of the Names of Observers.
A.C. = Alvan Clark. llrw. = Brlinnow. Dur. = Durham Observers.
A.G.C. = Alvan G. Clark. Cal. = Callandreau. Ek. = Eneke.
Adh. = Adolph. Cin. = Cincinnati Obsrncis. Kl. - Kiln v.
Au. = Auwers. Col. = Collins. KM. •• Knglemann.
/3. = Iturnham. Com. = Comstoek. i'Vr. = Ferrari.
liar. = Barnard. Cop. = Copelaml. Kl. = Flainmarion.
]ie. = Itessel. Da. = Dawes. Fli. = Flint.
l?h. = llrulins. Dav. = Davidson. Fit. = Fletcher,
llig. = Bigourdan. Dem. = DemW-ski. Fi>. = Fiierster.
Bo. = Bond. Dk. = Doberfk. Fr. = Franz.
Ilii. = Horgen. Du. = Dune'r. Ga. = Guile.
^ 9062,
U7
Gia. - Giaoomelli.
Ma. - Main.
O00* ^ DOOCIII.
Gl. - Gledhill.
Ma. - Madler.
Sea - T. J. J. SM.
Qhi • CHiMnapp.
Go. — Goldeny.
H,. - W. Hemrhel.
H, - J. F. W. H.-rx, l,,-l.
Hi. - Hind.
Mao. - Macl«r.
Maw - M. W. Maw.
M -. Mill.-r.
M • - Mitchell.
Ml. - Moulton.
Sel. - Sellon.
Sh. — Schur.
81. - Selander.
Sin. =. Smith.
So. - South.
HI. - Hall.
\.'W. — Newroinb.
Sr. = Searle.
Ha *m Hough.
Hoi. - Holden.
- Nubile.
I'.-i. ~ Peiroa.
St =- O. Stone.
T. - Teblmtt
Hv. — Harvard Obwr
PIT. — Perrotin.
Tar. — Tarnuit.
Ja. — Jacob.
Jtd. •• Jedrzejewicz.
Jo. — Jones,
IVt. - Peters.
Ph. - Philpot
PI. — Pluinnier.
Tj. — Tietjen.
Vo. B Vojjel.
Wdo. - Waldo.
Ka. - Kaiser.
Po. - Powell.
Wh. = Wifhiiian.
Kn. — Knott.
l»r. - Pritdiett
Ws. = J. M. Wilson.
Knr. = K nor re.
Kad. = Kadrliffe Olmervers.
H.C.W. = II. C. Wilson.
Kit. = Kikstner.
HUH. — Hussell.
W. & S. = Wilson & Seabmke.
Ix-y. *m Leyton Observers.
I. in. = Lindstedt
2. = W. Strove.
IIS.- H. Strove.
Well. = Welliiiaiin.
Winn. =* \\ iiiin-i ki-.
LOT. *m Lovett.
02. = o. strove.
Wlk. = WinWk.
Ls. = Lewis.
Lu. => Luther.
— Leavenworth.
Sch. = Schiaparelli.
Scl. — Schloter.
Sea. — Seabroke.
Wr. = Wrottesley.
Y. «» Young.
a = 0» 1- ; 8 = +57° KI'.
6.9, TellowUh ; 7.5, bliitnh white.
IHtcorrrrd liy Sir Wiltinm Ilrrtrhrt. Ainjunt 25, 17K2.
OBSKRVATIOXS.
I7S2.6I
it
319?4
ft
9
1
Obtenren
Herwhcl
t
1842.80
8.
207^3
P-
0^87
H
1
Madler
1783.05
319.1
1
Herschel
1843.58
208.7
0.92
3
Madler
1K23.81
36.7
1.25 ±
1
St nive
1843.80
210.0
0.94
1
Daww
1831.71
1833.71
85.7
. :..,
2
3
Strove/
Strove
1844.49
1H46.42
213.7
220.3
0.85
0.97
5
2
Midler
O. Strove
IK.-t5.OG
1836.61
140.4
0.41
0.47
5
5
Strove
IVI-
1847.53
1>IK.22
IM-
225.1
229.7
1.12
1.14
1.16
5
1
Madler
O. Strove
1840.32
180.5
,,,.:.
4
O. Strove
1849.19
232.5
1.09
3
O. Strove
1840.78
180.9
0.8 ±
.". '_'
Da we*
1850.04
233.9
1.17
3
O. Strove
1841
t
Madler
1850.71
232.3
1.31
3
Midler
184]
2
Dawes
1850.93
235.2
—
1
Dawea
.i'3062.
t
6,
Po
n
Observers
t
e.
Po
71
Observers
o
IT
O
ff
1851.16
235.7
1.35
2
O. Struve
1871.57
283.8
1.39
7
Dembowski
1851.18
236.9
1.10
8
Madler
1871.00
284.0
1.0
1
Gledhill
1851.75
234.5
1.27
2
MMler
1872.63
285.7
1.47
6
Dembowski
1852.49
238.4
1.23
3
0. Stnive
1872.80
286.3
1.45
1
W. & S.
1854.11
243.5
1.48
4
O. Struve
1873.63
287.6
1.45
9
Dembowski
1854.32
244.3
1.28
3
Dawes
1873.80
297.8
0.91
1
Leyton Obs.
1854.99
249.9
Sep.
0
Dembowski
1873.82
287.8
1.45
1
W. & S.
1855.05
242.7
1.38
3
O. Struve
1873.84
288.0
1.55
2
Gledhill
1855.80
249.4
1.3
8
Dembowski
1874.64
289.8
1.40
0
Dembowski
1855.91
247.9
1.33
3
Morton
1874.72
299.1
1.08
1
Leytou Obs.
1850.57
245.5
1.41
1
Winnecke
1874.80
291.2
1.37
1
W. & S.
1850.02
250.6
1.2
4
Dembowski
1874.91
291.1
1.35
2
Gledhill
1850.00
247.8
1.40
2
O. Struve
1875.07
292.2
1.47
0
Dembowski
1850.80
248.8
1.43
1
Madler
1875.69
292.9
1.49
5
Duner
1857.:?7
250.4
1.50
3
O. Struve
1876.74
293.3
1.61
1
0. Struve
1857.00
253.4
1.25
3
Secchi
1876.67
294.5
1.46
5
Dembowski
1857.71
252.2
1.2
4
Dembowski
1876.87
294.5
1.00
3-2
Doberck
1858.54
252.4
1.2
2
Dembowski
1876.93
298.8?
1.44
1
W. & S.
1859.10
255.3
1.40
3
O. Struve
1876.99
294.5
1.40
5-4
Plummet1
1801.79
265.2
1.21
2
Mildler
1877.61
295.8
1.46
4
Dembowski
1802.18
201.7
1.54
2
O. Struve
1877.74
297.3
1.49
4
Doberck
1802.79
203.0
1.40
11
Dembowski
1878.60
299.1
1.51
4
Dembowski
1802.8.3
200.1
1.29
2
Madler
1878.90
302.3
1.39
5
Doberck
1803.80
200.0
1.43
9
Dembowski
1879.45
301.9
1.50
8
Hall
1803.86
205.6
1.40
1
Dawes
1879.77
303.2
1.33
5
Doberck
1804.73
268.7
1.40
7
Dembowski
1880.60
304.5
1.50
0
Burnham
1805.70
271.2
1.35
0
Dembowski
1880.88
304.3
1.55
4
Doberck
1805.71
1805.71
269.9
271.9
1.43
1.14
3
2-3
Knott
Leyton Obs.
1881.14
1881.60
301.0
307.8
1.44
1.60
3-2
3
Jedrzejewicz
Iturnham
1800.20
270.4
1.47
2
O. Struve
1881.81
306.5
1.97
2-1
Bigourdatt
1806.64
270.3
1.46
3
Leyton Obs.
1881.83
305.5
1.40
4
Hall
1806.72
275.5
1.13
3
Harvard
1800.74
273.4
1.44
5
Dembowski
1882.11
304.9
1.29
7
Jedrzejewicz
1806.97
270.0
1.34
1
Secchi
1882.70
312.3
1.62
1
O. Struve
1882.82
308.1
1.52
4-3
Doberck
1867.74
275.2
1.41
7
Dembowski
1883.00
309.8
1.69
9
Englemann
1808.67
277.5
1.38
4
Dembowski
1883.94
312.8
1.44
3
Hall
1868.75
1808.98
268.3
276.5
1.00
1.59
3-1
2
Leyton Obs.
O. Struve
1884.47
311.7
1.26
2
Seabroke
1869.75
279.9
1.48
0
Dembowski
1885.80
316.1
1.46
5
Hall
1870.18
279.2
1.48
2
0. Stmve
1880.20
315.2
1.43
3-2
Seabroke
1870.44
281.0
1.5
1
Gledhill
1880.92
314.6
1.46
5
Hall
1870.64
280.6
1.63
-
Leyton Obs.
1887.06
315.5
1.36
0-3
Schiaparelli
1870.67
282.2
1.43
7
Dembowski
1887.10
310.7
1.50
3
Tarrant
t
9.
P.
•
OfaMnren
(
9.
P.
M
Obwnreni
e
9
0
J
817.7
1.40
1
S-hia|>arvlli
18«r.
323.7
1.62
1
.li'lll--
1-XV
319.4 .
1.36
4
Hall
1892.9!)
328.5
1.47
•
Srliiapairlli
>96
319.5
1.46
••
Schiapaivlli
'.57
'H6
321.1
323.0
i:.
3
i
Itiiniliani
Hall
1893.83
IVI::.;M;
327.8
330.9
1.58
1.45
•
•>
('(im.Ht... k
Srliiaparrlli
1889.94
320.5
1
Seabr.'k.
1894.28
33O.6
1.70
3-2
I'.iiroiinlaii
•76
321.8
.f.i
1
Iti^niinlan
1894.64
331.99
1.86
1
(iliutcnapp
1>'Ht.79
325.2
:.
Hall
1S1NI.93
323.5
1
Sdiiaiiun-lli
1895.10
151.2
1.58
1
lhi\ iil-nii
1895.14
330.3
i.r.i
7-6
r>ii;i>iiiilati
1891.48
1
A±
1
-,
1895.15
327.4
1.16
3
llllll^ll
lv'1.95
::
17
^
Sdiiaparelli
1895.18
331.9
1.46
2-1
( 'niu>t<>rk
18'X'.71
329.1
41
3
Comstock
1895.73
334.3
1.53
4
S«>«
..-.I'
2
Collins
1895.74
334.5
1.41)
>2
Moultuii
When Hi i:-< MM. discovered this pair he measured the angle and repeated
his observation the following year, without finding any sensible change.* Be-
ginning with 1823, STRUVE followed the star for ten years; and from the
nu ;i-uri"- tliii^ M-rurril lie discovered that the system is a binary in rapid orbital
motion. Since Sn:i YK'S time the star has been carefully measured by many of
tin- best observers, so that there is abundant materiaJ upon which to base an
orbit which seems likely to be substantially correct.
Having collected all the published observations of 2 3<)62 from original
sources, I have formed for each year a mean position which is the arithmetical
mean of the mean results obtained severally by the best observers. In accor-
dance with the experience of Sna VK, OTTO STKUVK, DEMHowsKl, and BUHX-
IIAM the>e yi-arlv mean- may be held to furnish the most trustworthy basis lot-
tin- clement- of an orbit. The following is a table of the orbits hitherto pul>-
lishcil for this star:
p
T
t
a
a
<
1
Authority
Soarre
•I..'.
1 If. S3
lOS.i; i
11 •-••HI
KU .11.-,
102.943
• ;• i
. .11
M
1835.508
0.4496
0.57
U.41.-.1
113
0.4472
1.255
1 II..
1 :t!<»
L27
1.270
:.-.•>:
i; ii
38.6
39.15
35.53
20.97
32.2
135.46
I. "
•IV. 1
92.1
Mftdler. 1840
er, IM;
V.MI FII-S. 1^1. :
Srliur. I MIT
Di,i»-r.-k.is;:
Doberck,lK7!>
Dorp. Obs. IX, 180
I >i.- F
\ \ ]i.:;<; [tsc,7,|, ].•-
\ \ VI.M;
A.N.V'.'77
By tin- method of KI.INKIIMI K- we lind the following element-:
P - 104.61 years fl = 47 i:>
T — 1X36.26 i - 43
t - 0.4.',<i
• = l'.3;iV M - +3*. 441
'.
70
v 30G2.
Apparent orbit:
Length of major axis = 2".526
Length of minor axis = 1".984
Angle of major axis = 45°.7
Angle of periastron = 138°.4
Distance of star from centre = 0".446
It will be seen that these elements are very similar to those derived by
VON Fuss in 1867. The following comparison of the computed and observed
places shows that the above elements are highly satisfactory, and that the true
elements of this remarkable binary will hardly differ sensibly from the values
here obtained.
COMPARISON OF COMPUTED WITH OBSERVED PLACES.
t
6.
&
p
pe
e,-e.
Po— PC
n
Observers
1782.65
319.4
315.7
' ff
1.44
o
+ 3.7
It
2
Herschel
1823.81
36.7
45.3
1.25 ±
1.16
-8.6
+ 0.09
1
Struve
1831.71
85.7
85.1
0.82
0.72
+ 0.6
+ 0.10
2
Strnve
1833.73
108.6
105.3
0.56
0.61
+ 3.3
-0.05
3
Struve
1835.66
132.6
130.5
0.41
0.55
+ 2.1
-0.14
5
Strnve
1836.61
146.4
143.8
0.47
0.55
+2.6
-0.08
5
Struve
1840.55
186.7
188.8
0.72
0.71
-2.1
+ 0.01
7-6
CLi'4; Dawes 3 2
1841.72
193.5
197.6
0.92
0.79
-4.1
+ 0.13
9
MMlei-7; Dawes 2
1842.80
207.3
204.7
0.87
0.86
+ 2.6
+ 0.01
1
Madler
1843.69
209.3
209.5
0.93
0.91
-0.2
+ 0.02
4
Madler 3 ; Dawes 1
1844.49
213.7
213.6
0.85
0.96
+ 0.1
-0.11
5
Mtidler
1846.42
220.3
222.2
0.97
1.07
-1.9
-0.10
2
O. Struve
1847.53
225.1
226.1
1.12
1.11
-1.0
+ 0.01
5
Miidler
1848.54
229.2
229.7
1.15
1.16
-0.5
-0.01
3
OZ 2 ; Dawes 1
1849.19
232.5
231.9
1.09
1.18
+ 0.6
-0.09
3
O. Struve
1850.56
233.8
236.1
1.24
1.23
-2.3
+ 0.01
7-6
O2 3 ; Miidler 3 ; Dawes 1-0
1851.36
235.7
238.3
1.26
1.25
-2.6
+ 0.01
12
fti- 2; Madler 8; Madler 2
1852.49
238.4
241.6
1.23
1.29
-3.2
-0.06
3
0. Struve
1854.47
245.9
246.7
1.38
1.33
-0.8
+ 0.05
13-7
O2 4 ; Dawes 3 ; Dembowski 6-0
1855.58
246.6
249.4
1.34
1.35
-2.8
-0.01
14
Oi'3 ; Dembowski 8 ; Mo. 3
1856.69
249.1
251.5
1.31
1.37
-2.4
—0.06
rr
t
Dembowski 4; OZ2; Madler 1
1857.56
251.6
254.0
1.32
1.38
-2.4
-0.06
10
O2 it ; Seabroke 3 ; Dembowski 4
1858.54
252.4
256.3
1.2
1.39
-3.9
-0.19
2
Dembowski
1859.16
255.3
257.3
1.46
1.40
-2.0
+ 0.06
3
O. Struve
1861.79
265.2
263.4
1.21
1.42
+ 1.8
-0.21
2
Madler
1862.60
263.8
265.2
1.43
1.43
-1.4
0.00
15
ttl'2; Dembowski 11 ; Mildler 2
1863.83
265.8
267.7
1.41
1.43
-1.9
-0.02
10
Dembowski'.); Dawes 1
1864.73
268.7
269.7
1.40
1.43
-1.0
-0.03
7
Dembowski
1865.70
270.5
271.8
1.39
1.44
-1.3
-0.05
9
Dembowski (1 ; Knott 3
1866.60
271.3
273.6
1.42
1.44
-2.3
-0.02
8
Oi'2; Dembowski 5; Sea. 1
1867.74
275.2
276.1
1.41
1.44
-0.9
-0.03
7
Dembowski
1868.82
277.0
278.2
1.48
1.44
-1.2
+0.04
6
Dembowski 4 ; 0—2
1869.75
279.9
280.6
1.48
1.44
-0.7
+ 0.04
6
Dembowski
1870.43
280.8
281.5
1.47
1.44
-0.7
+0.03
10
02 2 ; Gledliill 1 ; Dembowski 7
1871.58
283.9
283.8
1.49
1.45
+ 0.1
+ 0.04
8
Dembowski 7 ; Gledhill 1
1872.71
286.0
286.1
1.46
1.44
-0.1
+ 0.02
7
Dembowski 6; W. & S. 1
1873.76
287.8
288.3
1.48
1.44
-0.5
+0.04
12
Dembowski 9; W. & S. 1 ; G1.2
1874.80
290.7
290.4
1.37
1.44
+0.3
-0.07
9
Dembowski 6; W. & S. 1 ; 01. 2
1875.68
292.5
292.2
1.48
1,1!
+0.::
+0.04
11
Dembowski 6 ; Dune'r 5
180
ISJ4 •
270
187'. •
71
1
•.
(•
ft
f
, (,
P.-f,
•
olmwYwm
o
9
•
•
1871
i :.i
\ 1 1
—0.1
+<>.i>7
!.: 11
181
296.5
1 is
1 II
+ 0.3
+ O.IU
8
DtMiilxiwski 4 ; Dolwrck 4
ii.-,
111
-H'.:t
+ 0.i '1
9
Deiulxiwski 4 ; lX»U'ivk 5
iv
11
1 II
-0
13
Hall 8; |t..l,..,,k 5
1^0.74
:•'! 1
88
13
4-1.9
+o.oy
10
ft 6 ; lX>berck 4
1.59
310.2
.00
18
+ <>.'.»
+ 0.17
12-10
Jed. 3-2; 03; 1%. 2- 1 ; Hull 4
J.46
11
.43
+ 0.4
-0.02
11-10
Jed. 7; lX>berck 4-3
-:.77
::il .:
.48
+ :i.<\
+0.13
12
Kn^li'inuim 9; II. ill.'!
-1.47
811.7
31O3
•_••;
.4:t
+ 1.5
-0.17
2
Seal>roke
188
::ir. 1
812.9
.48
.43
+3.2
+0.02
5
Hall
ISM'. .'...
::il •.'
::i» I
II
13
-HI.5
+0.01
8-7
Seul.rokc-3 2; Hall .'.
L8tt
::i:: 1
310.4
.48
I.:
-2.3
0.00
96
Sr Iii;i|i;in-lli (> .". ; T.u i ant 3
I88f
:;i;.-.
II
13
-f-1.4
-0.02
11
Sch. 1 ; Hull 4 ; S.-h. C>
.:•-•! :.
18
II
+ 0.6
-0.01
8
/i.'f; Hall 4; Sval>rok<- 1
.T_>:». i
.48
.44
+ 1.2
-0.01
8
Hall 5; Schiaparelli 1
11.71
324.8
18
.44
+ 1.1
+0.04
8
See 1 ; Sdiia|>urelli 2
.r>ii
.44
-0.5
+0.08
8
Com. 3; Col. 2; Jo. 1 ; Mi. 2
,M
.44
+ 0.1
+0.07
4
Comstot'k 2 ; Schiajan-lli 2
i I*'.
.70
.45
+ 1.0
+ 0.35
4-2
<;'.!•-. -n. »|.|. Ill; r.|'4iilinl:ill 3 2
L89
35S.1
.44
.45
+ 0.2
-0.01
16-14
Big. 7-6 ; 1 lo. 03 j Com. 2- 1 ; See 4
Hl-IIRMKKIH.
t
9< PC (
It
Pt
•
O
9
.-HI
334.8
.45
1908 JQ
346.8
1.46
lvi;.50
336.8 1
.45
I'.M-:: :.n
::i.vs
1.46
lM«.W..'iO
338.8
.45
1904.50
350.8
1.46
1899.50
340.K 1
.45
1<H 15.50
352.8
1.46
liMM).50
342.8 1
.46
1906.50
354.8
1.46
1901.50
344.8 1
.46
It will be seen that there are occasional systematic errors both in the
angles and in the distances, and in some cases these deviations appear to be
rather IIHHV i \itii-i\f tlian \vi- .should expect in the work of the liest observers;
Init the star has some peculiar difficulties. « -|u< ially as regards the distance,
and on the whole tin- m.-asures arc fairl\ accordant for so close an object.
This star dc-cnr- tin- careful attention of i.l.-crvers, as the next •_'<> \.-ai--
will give the material which will make the orbit exact to a \ci-y hi^li <lt ••_•
It may be (minted out that the -v>i.ni has a considerable proper inotinn in
-pace, in a+0".34<), in 84-0".(>2(); and therefore the chances are that it ha-
a -.-n-ilil,. parallax. If the parallax could be determined it would give us the
al>-olnte dimcn-ions of the system and the combined mass of the components
— two clement* of the highest interest in the study of the stellar sv-tem-.
72
rj CASSIOPEAK = 2 (50.
Discovered
a = Oh 42"'. 9 ; 8 = +57°
4, yellow ; 7, purple.
by Sir William Herschel, ^
18'.
iiif/itst 1
7, 1779.
OBSERVATIONS.
t
00
Po
n
Observers t
60
Po
n
Observers
0
t
1779.81
70 ±
11.09
1
Herschel
ISSO.lrf
106.8
7*96
15-14
Miidler
1780.52
11.46
1
Herschel
1850.61
105.5
8.32
2
Johnson
1850.72
106.5
8.01
6-7
Miidler
1782.45
62.1
—
1
Herschel
1850.84
105.6
8.16
5
Jacob
1803.11
70.8
—
1
Herschel
1851.45
106.6
8.17
7-6
Fletcher
1814.10
78.5
9.70
1
Bessel
1851.76
107.7
7.72
3
Miidler
1851.84
108.0
8.04
3
0. Struve
1820.16
81.1
10.68
5
Struve
1851.89
106.9
8.12
4
Miller
1827.21
85.6
10.2
1
Strove
1851.89
106.4
8.04
3
Jacob
1830.75
86.2
10.07
5
Bessel
1852.61
108.5
7.65
7-8
Miidler
1853.39
108.4
7.57
5
Miidler
1831.75
88.7
9.69
1
Herschel
1853.51
109.2
7.98
7
Jacob
1832.05
87.6
9.78
5
Struve
1853.90
110.1
7.52
3
Miidler
1832.87
88.7
9.74
2
Dawes
1853.92
109.4
—
6
Powell
1834.76
89.6
9.80
1
Bessel
1854.00
109.6
7.SI1
1
Dawes
1835.26
91.2
9.52
3
Struve
1854.56
112.0
7.97
4
O. Struve
1854.80
110.6
7.60
2
.Miidler
1836.46
1836.74
91.1
92.1
10.83
9.39
2-1
4
Miidler
Struve
1854.91
1854.94
111.9
111.5
7.80
7
6
Dembowski
Powell
1840.14
95.8
8.98
37-29 obe
. Kaiser
1854.95
110.0
8.12
2
Morton
1841.34
98.1
9.21
3
O. Struve
1855.24
110.9
7.95
3
Winnecke
1841.57
98.3
9.50
4
Miidler
1855.52
111.0
7.60
4-3
Miidler
1841.80
95.7
9.33
1
Dawes
1855.79
110.2
7.89
2
Secchi
1842.41
98.3
8.76
2-1
Miidler
1855.93
112.5
7.63
9-4
Powell
1842.65
96.4
9.09
7
Sclil liter
1855.94
113.2
7.57
4
Demlxnv.ski
1843.07
98.4
8.97
3
Schlflter
1855.96
112.4
7.80
3
Morton
1844.56
100.1
8.48
6-5
Miidler
1856.07
112.4
7.57
4
Jacob
1845.44
101.1
8.44
8
Miidler
1856.51
112.9
7.22
2-1
M lid lei-
1845.86
97.2
8.85
1
Jacob
1856.55
117.3
8.34
3
Luther
1846.41
100.5
8.89
2
Jacob
1856.86
L14.6
7.:;::
4
Dcmbow.ski
1846.66
102.5
8.57
12
Miidler
1857.0(1
111'.!)
7.49
3
Jacob
1846.72
101.5
8.71
2
Jacob
1S57.22
114.1
7.57
2
O. Struve
1S.-.7.23
114.5
7.09
5
Miidler
1847.34
102.7
8.28
6-7
Miidler
1857.87
115.8
7.14
4
Dembowski
1847.40
101.8
8.48
5
O. Struve
1848.12
102.5
8.60
2-1
Jacob
1 S5S.06
115.1
7.42
3
Jacob
1858.19
115.9
7.12
4
Miidler
1849.66
105.0
8.26
4
0. Struve
1858.62
115.8
7.24
3
Dembowski
>/ < V88IOPEAK = 2M50.
i
9.
*
II
Ml i •••*••
vmwrrrr*
I
0.
P.
H
9
o
9
1859.27
11. '..7
6.96
2-1
Mft.ll.-r
1872.01
—
6.0 ±
I
S-alir.ikr
1859.72
116.6
7.02
• i
1 '..«•«• 11
1872.18
140.8
5.94
• >
O. Struve
1859.94
117.0
7.08
•>
M..rt..n
1872.50
140.5
6.02
7
Dntidr
isc-o.iw
119.8
7.17
<2
•IIVI-
1872.63
139.1
5.97
6
Dmbowski
1860.97
118.3
6.99
7-6
IV.w.-ll
1872.65
137.8
6.10
1
Knott
1 Mil. 58
119.8
7.37
5
A u were
1872.77
144.0
5.94
1
Main
1861.70
117.9
7.08
5
M4.11t-r
1872.86
124.4
6.32
—
Ley tun < Hw.
1861.82
118.2
6.44
6
Main
1873.06
142.3
1
\V. & S.
1861.95
120.6
6.7
3-2
Powell
1873.53
144.6
5.68
3
O. Strove
1862.71
120.6
6.85
8
Midler
1873.IU;
140.7
5.97
7
DiMiiliowKki
1S62.86
121.3
7.00
12
DoinlMiw.Hki
1873.68
143.7
6.WI
•i
(iledliill
1862.88
120.4
7.15
1 .i-\ 1 1 -1 1 i >lm.
1873.83
144.7
6.33
1
\V. & S.
1863.80
123.4
6.87
9
Deiubuwiiki
1873.86
141.2
5.66
1
1 .-•> t "ii ( MM.
1873.98
143.6
—
6
Noliile
1K(U.OO
123.1
6.65
4-3
Powell
1864.80
125.0
6.76
9
I>i'inl«iw >ki
1874.22
144.9
5.82
1
l»uin;r
1X«;5.59
125.5
6.52
6
bghnm
1874.63
1874.90
143.1
146.0
5.83
5.8
t
1
Dw&bowikJ
W. A S.
i N...-..62
126.4
6.67
8
iK'iiiUiwski
IN-.. V69
125.7
6.75
3
Knott
1875.15
14S.6
5.58
•i
O. Strove
1865.7B
123.9
6.43
2-1
Ley ton Oba.
1875.51
146.7
5.77
10
1 MIIH'T
US
132.6
6.44
n
O. Strove
1875.66
146.5
5.67
7
Donbowski
89
.'1.7
6.38
8
I^eyton < )\m.
1875.78
146.1
5.78
1
Main
23.9
r..i.r.
1
</
Searlo
1875.94
147.7
—
•i
U.|«-i.-k
72
28.5
6.58
7
IX-nilxiwuki
1876.61
149.3
5.59
t
D0mbowikJ
1866.84
26.0
—
1
Winl«K-k
1876.79
4'.».1
5. IS
6
I'llllllllHT
1866.86
27.7
6.79
4
Secchi
1876.86
49.3
4.72
1
1 ..-\ Ii in < >!M.
1867.15
130.1
li..Vl
1
Bowie
1877.19
52.8
5.44
1
O. Strove
Is.;;, c.-,
130.0
6.31
1
Main
1877.6!)
51 .5
5.48
6
Dcinbon >ki
1867.74
130.4
6.48
•
<
Dpinbowski
1877.76
50.4
5.77
5
U.U-r.-k
1868.37
131.8
6.38
5
Ihin^r
^53
132.9
3
(). Struve
1878.19
154.6
5.25
•>
< t. Strove
1868.67
132.1
1
iVinliowHki
1878.58
153.7
5.42
I
iN'inlMiwHki
1868.90
124.3
r..i'l
1
t on < >l » .
1878.83
1878.90
153.9
155.1
5.51
5.28
1
5
(tohlney
iVilierck
1869.67
132.4
6.12
1
M:iin
1869.72
124.8
1
Leyton Olm.
1879.20
154.7
5.16
••
0. Struve
1869.75
134.0
6.20
6
iN-inlxiwski
1879.01
156.8
5.35
7
Hall
1869.93
135.2
6.16
4
Dun^r
1879.80
158.3
5.21
3
]X>licn-k
1879.96
161.9
5.60
5
Franz
IN 7<».07
133.4
6.39
5-4
Powell
l>7" IN
6.28
2
O. Strove
1880.14
159.9
5.32
7
Jeclr/ejewirz
18X0.1
r..ir,
7
I»i-iul«iw-ki
1880.60
161.1
5.26
••
l»..l«-n-k
I870.n
• ;].-.n.iii
1881.10
164.1
5.32
2-1
Ifc.U-n-k
IN;I in
BJO
:• l
P. .well
1881.14
:.ln
3-2
Jadrzejewirz
IN71.65
, M,
6
I>«-nilN.\vski
1881.16
102.0
BJ6
3
0. Strove
18T1
•_•
<;i.-.n,iii
1881.72
ir.l •
B 1>
•»
PriU-hctt
1*71.93
• ;.••.
1
\V AS.
1881.90
4
Hall
74
T) CASSIOPEAE = 2 GO.
t
fc
Po
R
Observers
t
ft,
Po
n
Observers
0
it
O
If
1882.15
165.5
5.08
3
Jedrzejewicz
1890.79
188.4
5.07
5
Hall
1882.70
166.8
5.28
1
O. Struve
1882.76
166.3
5.11
6-5
Doberck
1891.48
191.7
5.02
5-4
See
1882.87
165.7
5.15
6
Englemann
1891.74
191.8
4.79
4-3
Maw
1883.94
168.8
5.12
3
Hall
1892.77
194.1
4.92
3
Corns! <>rk
1885.23
172.8
5.27
1
Seabroke
1892.85
197.3
4.90
2
Collins
1885.81
173.4
5.06
5
Hall
1892.95
197.4
4.75
1
Jones
1886.07
176.3
4.92
5
Englemann
1893.84
196.0
4.88
1
Comstock
1886.20
176.6
4.78
3-2
Seabroke
1893.97
198.2
5.12
1
Lovett
1886.95
175.3
4.99
5
Hall
1886.97
178.6
4.71
7
Tarrant
1894.05
201.6
4.89
1
Comstock
1887.35
180.6
4.6
1
Smith
1894.1
200.2
496
1
Maw
1888.48
1888.54
181.3
183.9
4.69
" 4.83
2
5
Seabroke
Maw
1895.16
1895.17
204.8
203.8
4.97
5.01
3
3
Hough
Comstock
1888.97
183.2
4.88
4
Hall
1895.29
203.4
4.84
3
See
1889.10
185!9
4.64
3
Seabroke
1895.73
204.3
4.78
2
See
1889.86
185.4
4.98
4
Hall
1895.73
205.9
4.74
2
Moulton
At the date of discovery Sm WILLIAM HEUSCHEL found the distance* of
the component to be 11".()9, and estimated the angle at 70°. At the epoch
1780.52 he found the distance 11".46, but made no measure of the angle of
position until 1782.45, when it proved to be 62°.07. HEKSCHEL observed the
angle to be 70°.8, in 1803, but made no measure of the distance. The earliest
observation of both angle and distance is a rough measure by BESSEL, in 1814;
and although his angle is nearly correct, it is evident from the subsequent
work of STKUVE that the distance is much too small. Since the time of
STHUVE r) Cassiopeae has been followed by nearly all of the best observers; so
that we have good material upon which to base an investigation of the orbit.
Although the observations of 17 Cassiopeae do not suffice to fix all the
elements so well as might be desired, yet it appears that the range of uncer-
tainty is comparatively unimportant, except in the case of the periodic time, which
may possibly differ several years from the value here derived. Some of the
orbits found for 77 Caasiopeae by previous computers are indicated in the fol-
lowing Table of Elements.
p
r
e
a
SI
i
1
Authority
Source
176.37
222.435
195.235
167.4
208.1
190.50
1896.0
1924.78
1909.24
1901.25
1904.0
1908.9
1906.12
0.77083
0.6268
0.5763
0.6244
0.622
0.500
0.547
10.335
10.68
9.83
8.639
8.702
8.45
8.20J7
25.55
50.80
39.95
33.33
41.02
47.1
43.0
57.98
68.5
53.83
48.3
52.09
47.6
46.08
243.65
245.9
223.33
229.45
288.1
214.2
222.02
Powell
DlllK'r
Doberck
GrUber
Coit
Lewis
See
M.N., vol. XXI, p. 66
Mes. Micro., p. !(>(>
A.N. 2091
A.N. 21 1 1
M.N.,vol.XLlI,p.359
M.N.,vol. LV,p.20
A.J. 343
* Astronomical Journal, 343; and Astronomical Journal, 355.
\Vc find tin- following element- for this celebrated binary :
/' - 1U.-..7G years Q - 46M
T - I'." .' - 4.V.W
• - <'.:.! l-j x - 217e.H"
a - SMT-'N „ » + 1°8:W99
Apparent nrliii :
I..-i.-ili of major axis « 1.V.80
tli of minor axis = 1O*.'_'4
lo of major axis = fwV.H
Angle of ]M<riantrou = L'W-fl
Distance of star from centre = 3".80
The table of computed and observed places -li..u - that these eleinentH are
highly -aii-lactorv. Hut the rapid orbital motion near |>eriastron will make it
possible to effect a slight improveineiit in alxxit ten years.
The parallax of the system recently determined by DH. HKHMAXN S. DAVIS
of Columbia College seems to be entitled to great weight; and yet the value
is so large that with these elements the mass is only O.KK5 that of the sun.
Tin- di>tanee of the system is 4(>4540 times the distance of the earth from the
MIII, and the semi-major axis of the orbit is 18.54 astronomical units. This
mass is very small for the size of the system, and if the parallax of " . I.'! be
continued, say, by Ileliomcter measures, our idea* of the nature of the stellar
systems will have to be considerably modified. The parallax of 0".la4 found by
OTTO STKUVE in 18a<}, from measures with the micrometer, gives a distance for the
system of 1339400 astronomical units. The semi major axis comes out .">:[.:>:> times
the distance of the earth from the sun, and the combined mass proves to IK* :!!"',
The companion i> at pn-sciit. near the line of nodes, and its relative motion
in the line of M^ht i> near its maximum value. Tin- brightness and width of
this pair is such as to justify an application of the spcrtniscopie method for
determining parallax developed in !| ."», ( 'hapter I.
lu this connection we may point out the great importanee of the determi-
nation of the parallaxes of </»uf>/- rather than of .-•//////. -tars. The parallaxes
of single >tars are of comparatively little interest, since they give us only the
di-tance ami hence the velocity perpendicular to the line of vision, and the
radiation compared to that of the sun. On the other hand, the parallaxes of
double stars whose orbits are known give us, besides these data, the absolute
dimensions of the orbits and the combined masses of the components — two
elements of the highest importance in the study of the systems of the universe,
is remarkable for the great angular distance of the com|K>ncnts,
76
CASSIOPEAE = I 60.
and for the rapid proper motion of the system. Both of these circumstances
support the belief that the star is comparatively near to us in space, and ren-
der it certain that the parallax is sensible.
In 1881 MR. LUDWIG STRUVE discussed the relative motion of the com-
ponents about the common center of gravity of the system; and from his inves-
tigation it follows that ^- = 0-268, or the masses of the two stars, according
to OTTO STRUVE'S parallax, are respectively 2.00 and 1.06 times the combined
mass of the sun and earth. The companion is therefore more massive than the
sun and moves in an ellipse nearly twice the size of the orbit of Neptune; but
the eccentricity is so large that in periastron the companion would come con-
siderably within the orbit of the outer planet, while at apastron it would recede
to more than three times that distance.
COMPARISON OF COMPUTED WITH OBSERVED PLACES.
t
do
6c
Po
PC
00— 6c
PO—PC
n
Observers
1779.81
70 ±
O
57.2
11.09
11.33
+ 12.8±
-0.24
1
Herschel
1780.52
57.6
11.46
11.36
—
+ 0.10
1
Herschel
1782.45
62.1
58.7
—
11.42
+ 3.4
—
1
Ilrrschel
1803.11
70.8
70.3
—
11.41
+ 0.5
—
1
Herschel
1814.10
78.5
76.7
9.70
11.00
+ 1.8
-1.30
1
]5essel
1820.16
81.1
80.5
10.68
10.67
+ 0.6
+0.01
5
Struve
1827.21
85.6
85.4
10.2
10.21
+ 0.2
-0.01
1
Struve
1830.75
86.2
87.9
10.07
9.94
- 1.7
+ 0.13
5
Uessol
1831.75
88.7
88.6
9.69
9.87
+ 0.1
-0.18
1
Herschel
1832.46
88.1
89.1
9.76
9.82
- 1.0
-0.06
7
—. 5 ; Dawes 2
1835.26
91.2
91.4
9.52
9.58
- 0.2
-0.06
3
Struve
1836.74
92.1
92.6
9.39
9.44
- 0.5
-0.05
4
Struve
1841.57
97.4
96.9
9.35
9.02
+ 0.5
+ 0.33
8
02.3; Miicller4; Dawes 1
1842.41
98.3
97.8
8.76
8.91
+ 0.5
-0.15
2-1
Miidler
1844.56
100.1
99.7
8.48
8.73
+ 0.4
-0.25
6-5
Mildler
1845.65
99.2
100.7
8.64
8.62
- 1.5
+0.02
9
MadlerS ; Jacob 1
184G.60
101.5
101.7
8.72
8.51
- 0.2
+0.21
16
Miidler 12 ; Jacob 4
1847.37
102.3
102.5
8.38
8.44
- 0.2
-0.06
11-12
Miidler 6-7; O2. 5
1848.12
102.5
103.4
8.60
8.37
- 0.9
+ 0.23
2-1
Jacob
1849.06
105.0
105.0
8.26
8.25
± 0.0
+ 0.01
4
0. Struve
1850.87
106.4
106.4
8.04
8.12
± 0.0
-0.08
26
Madler21; Jacob 5
1851.80
107.8
107.5
7.88
8.00
+ 0.3
-0.12
6
Miidler3; U2.::
1852.61
108.5
108.5
7.65
7.91
± 0.0
-0.25
7-8
Miidler
1853.68
109.3
109.8
7.69
7.81
- 0.5
-0.12
21-15
Mil. 8; Ja.7; Po. 6-0
1 S.V4.7G
111.5
111.2
7.79
7.69
+ 0.3
+ 0.10
18
<>2. 4; Mii.2; Dein.7 [Mo.:!
1865.81
111.9
112.5
7.70
7.59
- 0.6
+0.11
22-10
Mii.4-3;Sn-.2; I'o.'.l 1; I>rui.l;
1856.48
113.4
113.8
7.37
7.48
- 0.4
-0.11
10-9
Ja.4; Mii. 2-1; Dem. -I
1857.84
lll.l
114.8
7.32
7.40
- 0.7
-0.08
14
.la..'!; 0^.2; Mii. 5; Dem. 4
1858.29
115.6
116.4
7.26
7.30
- 0.8
-0.01
10
Ja. 3; Mii. 4; Dem. 3
1859.60
116.4
118.3
7.02
7.14
- 1.9
-0.12
10-7
Ma. 2-1; Po. 6-4; Mo. 2
1860.68
119.8
119.4
7.17
7.09
+ 0.4
+ 0.08
2
( ). Stvuve
1861.82
119.2
121.4
6.89
6.95
— 2.L'
-0.06
8-7
M -idler fi; Powell 3-2
1862.78
120.9
122.9
6.92
6.87
- 2.0
+ 0.05
20
Miidler 8; Dembowski 12
1863.80
123.4
124.7
i;.s:
6.76
- 1.3
+0.12
9
Dembowski
y \\mtOMKDAE BC = 01' \
4 t
1
9.
••
P*
*
»•-»«
•
,,.„,•,,
12 1.1
r. -
,.,,,
- 1.7
+0.02
13-12
l'owelU-3; Dentbowski9
135.9
1.7 >
,.,.:.
- 1.9
4-0.08
17
KM. 6; IK-MI. 8; Ku.3
IM • •
I."'.,
8.61
+ (•.•_•
4-0.18
13
tti".2; Dem. 7; Sec. 4
IM',7 II
i.;i.-j
,. . .
- 0.9
+•0.18
8
Sr.irli- 1 ; IK-Mttwwski 7
.; ;:i
- 0.6
+0.06
12
Du. 5; (>2.:t; Item. 4
L84 l.M
• • •
8 Lfl
8.17
- I."
+0.01
10
|)<-iiiliii»ski l'i ; Iliini-i 1
1870.41
843
- 1.4
+0.10
17-16
l'o.S-4; <U*.2; Item. 7} Ol. 3
1871.48
- i,;
—0.05
10-9
l'o.2-l; Item. 6; O1.2
I in
:-.••••
140.7
8.01
, „.
- 1 •_•
+0.05
19
O.1.2; Du.7; ltem.fi; Kn.4
181
li.;::
6.00
± o.o
+0.14
19-13
W.& S. 2-1 ;0^'.3 ; Item.7 ; Ul.2 ;
1874
L875J4
Ill 7
n; .1
1 1:,..-,
147.6
6.67
5.78
— 0.8
- 0.2
+0.03
—0.05
g
21-19
Du.l ; Dem.7 ; W.& S.I [N«.6-0
O^.2; Du. 10; Item. 7; Dk. 2-0
is?.
1 1 •.'•.'
160.3
5.64
— 1.0
-0.11
13
Deinbowski'; I'ltiiniucrfi
1871
l.M n
163.6
.-.'._•
- 1.6
+0.06
11
1 vmli. i\\ >k i 6 ; Dol>crck 5
l.M •_'
1.V..1
6.61
- 0.9
-0.11
11
Item. 5; C.,1, 1.1; Dk. .*.
Is.
L08.0
157.4
5.44
+ 1.6
-0.05
15
Hall 7; Dol>crck3; Frunz5
188
'• ' •
I.Vi-j
.-, 1 1
4- 1.3
-0.12
12
Jolrzejcwic/. 7 ; Dolicivk 5
1^1 n;
I.'.-.' N
If.'.M
:.•-•:•
+ 0.7
-OJ5
11-9
Dk. 1; Je«l. 3-2; l*r. 2; III. 4
L8fl
166.3
5.11
6.30
+ 0.5
-0.19
15-11 .I.-.I.; :;; l>k.«; .'•: F.n.r.
L88
5.12
SM
- 0.1
-0.12
3
Hull
18X
173.1
178.8
5.16
:,. i :
+ 0.3
-0.01
6
Scabrokol; Hall 5
ISs.
178.7
174,9
6.18
+ 1.8
-0.27
20-19
En. 5 ; Sea. 3-2 ; HI. 5 ; Tar. 7
178.4
1 r,
-.,,x
+ 2.2
-0.28
1
Smith
1 sss.66
1 V- N
182.1
; -01
+ 0.7
-0.23
11
Svahroko 2 ; Maw 5; Hull 4
L86.6
184.6
5.00
+ 1.0
-0.19
7
Seabrokc3; Hall 4
188J5
5.07
4.96
- 0.1
+0.12
5
Hall
1891.61 I '.'17
191 J
I •.'•-'
4- 0.5
-0.02
9-7
Sea 6-4; Maw 4-3
196.0
4.87
+ 1.3
-0.05
r.
Com. 3; Col. 2; Jo. I
l.xn::.'.Mi 1117.1
IMS:,
5.00
4.84
- 1.4
+0.16
2
ConiHtock 1 ; I.i ,v.-i i I
•I "7 ' 200.9
199.0
4.92
4.83
+ 1.9
+0.09
2
('ouiMtock 1 ; Maw 1
1895.29 203.4
202.9
I M
4.79
+ 0.6
+0.05
3
See
,
9,
ErilKMKKIft.
f>f (
A
*
O
g
e
§1
1896.60
207.6
4.73
1899.50
217.2
4.55
1S'.»7.50
210.1
4.68
1900.50
221.1
4.46
1898.50
81!
L63
)\i; nr=^ 38,
a = 1" S7-.8 ; & = +41° 51'.
6.5, bliiiuli ; 7, blui.li.
DUrortred by Otto Stnn-e in 1
OMBBTAXUN
(
$.
p.
n
ObMirrn
(
0.
P.
•
11 '.'.7
I
Dawes
IM
Ill .::
Mit<-l»-l
IM
ll'.'N
V 1
;ler
L847.U
117.-.I
:.
o. Struve
i •-•:. :.
<• Strove
184"
111.::
o.fi ±
4
Dawes
1K45.15
in.'.i
, ,
1
Midler
1 •« J9.69
1 1 !.'.»
n 17
J
-trove
78
y ANDROMEDAE BO = 01 38.
t
Bo
Po
n
Observers
t
60
Po
n
Observers
O
f
O
n
1851.19
116.6
0.40
4
Madler
1869.84
107.0
0.63
3
0 Struve
1852.21
114.5
0.48
2
Madler
1869.95
105.6
0.5 ±
13
Dembowski
1852.78
111.3
0.5 ±
2
Jacob
1871.01
110.6
0.68
15
Duner
1853.23
116.0
0.47
3
Madler
1872.83
101.5
0.63
4-2
1 ii'iinnow
1853.79
108.5
0.55 ±
4
Dawes
1872.92
91.8
0.5 ±
2-1
\Y. & S.
1853.94
106.8
0.4 ±
4
Jacob
1854.75
112.0
0.61
1
Dawes
1873.17
105.4
0.63
5
O. Struve
1855.02
119.4
1
Madler
1874.00
109.3
0.53
1
Newcomb
1855.09
109.8
0.40
1
Secchi
1874.53
96.3
0.51
2
Gledhill
1856.12
116.7
0.5 ±
1
Jacob
1876.79
105.7
—
1
\V. & S.
1856.20
116.5
0.45
1
Madler
1877.05
104.1
0.48
6
Schiaparelli
1856.21
121.7
0.41
2
Winnecke
1877.71
103.9
1
] )oberck
1856.84
113.0
0.67
3
0. Struve
1877.94
102.4
0.84
1
Seabroke
1856.90
109.7
0.47
3
Secchi
1878.21
101.0
0.36
8
Hall
1857.23
115.4
0.45
3-1
Madler
1878.65
102.1
0.43
2
Burnham
1858.06
114.0
—
2
Jacob
1880.06
107.9
0.36
1
Burnham
1858.22
115.4
—
2
Madler
1880.11
106.7
2
Seabroke
1858.99
108.9
0.45
3
Secchi
1880.12
94.1
—
8
Jedrzejewicz
1859.81
108.7
0.53
1
Dawes
1882.05
104.0
0.49
6-1
Bigourdan
1862.55
115.2
0.50
4-2
Mildler
1883.15
93.1
0.29
7
Englemann
1863.27
108.5
0.45 ±
8
Dembowski
1883.16
106.7
—
1
Seabroke
1863.86
107.7
0.59
1
Dawes
1883.87
103.1
0.40
2
Perrotin
1863.99
107.6
0.61
-
Romberg
1884.18
113.3
—
3
Seabroke
1865.67
107.1
0.59
4
Knott
1884.65
117.6
0.35
1
Perrotin
1865.68
106.9
0.60
1
Dawes
1886.83
101.0
0.29
1
Newcomb
1865.76
106.3
0.58
2-1
Leyton Obs.
1889.51
98.2
0.09
1
Burnham
1866.21
110.0
0.70
3
O. Struve
1866.74
132.3
—
1
Winlock
1891.72
312.6
0.05 ±
3
Burnham
1866.74
107.2
_ —
1
Searle
1893.79
121.8
0.14
3
Barnard
1866.74
1866.85
100.4
104.2
0.64
1
1
Winlock
Leyton Obs.
1894.56
121.6
0.15
3
Barnard
1867.79
104.3
0.5 ±
1
Newcomb
1895.63
1895.72
118.5
121.2
0.18
0.29
3
3
Barnard
Sec
1868.82
102.0
0.69
6-5
Brfinnow
1895.72
115.3
elongated
1
Moultou
Since OTTO STUUVE'S discovery of this extraordinary binary in 1842 the
companion has described nearly an entire revolution, but as the orbit is very
eccentric and highly inclined nearly all the observations lie in the narrow region
included between position-angle 120° and 100°. Only in recent years has it
been possible for observers to prove the reality of orbital motion; some ten
years ago the object was found to be getting more and more difficult, and
y \\Hi:«>MI I>\l ISi "1 .'18. 79
li. UK it became clear that tin- di-tance \\.i- liimiui-liiii-. In 188<J NKWCOMH
tiiiiml the distant-. ii •_".! and tin- anirlc 101°; in small telcsco]>es tin1 star
appeared -iiijrlc. When Hi I:\II.\M examined the ol>ject in 1880 he found il
exceedingly difficult even with the M-inch refractor of the Liek Observatory, and
during 1800 the companion was whollv invisible. When the star was examined
in 1S01 it \\.i- r»nnd thai thf companion had changed to the opposite quadrant .
the angle being .'il- .<> and the distance so excessively small that it was esti-
mated at 0*.05±. I{\I:N \i:n'- i \aiiiination of the object in 1803 gave the key
to the situation. Tin companion had swept rapidly round to 121°.8, thus pass-
ing o\cr about I520" of position angle since the measure in 1880. liritxiiAM
at once undertook an invocation of the orbit, and obtained a very satisfactory
M-t of clfiin-nt-. Hi- pajH-r, in the Monthly 3folicr# for December, 1803, contains
an illustration of the apparent orbit, and a complete list of measures down to
\\ added the measures made since that date, and derived a set
• if elements verv similar to that found by BritxiiAM. IIi« elements are:
/' = 54.8 yean Q - 11.T,1
T - 1892.1 • = "K'.y
e mm 0.875 X = L'lxr.s
a mm 0».37
\\'e tin.l the following elements of y Amlroinnlar:
I' mm 54.0 y«m Q mm II." . I
T = 1892.1 * - 77°.85
f = 0.857 X = 200M
a =» 0*.3705 n m. -G0.«MM57
Apparent orbit:
length of major axis - 0*.7O(>
Ix-iiRtli of miiKir axis » O'.OfU
Ani;lf of major axis = 109".9
An-l<- of ]M-ria.stron
Distance of star from centre -
The table of computed and oh-er\cd (daces shows a good agreement for
an object of this difliculty. The residuals are easily within the limits of the
errors of observation. The orbit is remarkable for its great eccentricity and
high inclination. Both of these elements are well d« lint <1, and the values given
above will never be materially altered. Tim- tin- error in the eccentricity can
hardU -in-pass ± 0.02, while a variation of on*- year in the period is to be
•.rded a- improbable. In regard to the shape of the real orbit, y Amlromrilae
takes its place b.t\\i-n y r/Y///n/.< and y 1 'catnm-i. The-e three remarkable
-y-tems are al-o -imilar a- regard- the relative bright in--- of their coin]>onciitt<,
80
y ANDEOMEDAE BC = 01' 38.
which in each case are nearly equal. Since the companion of y Andromcdae is
now within the reach of ordinary telescopes the accompanying ephemeris will
be useful to astronomers.
COMPARISON OF COMPUTED WITH OBSERVED PLACES.
t
60
Oc
Po
PC
/) /)
(70 Vc
Pa— PC
n
Observers
1843.25
121.6
116.6
0.43
0.34
+ 5.0
+ 0.09
7-6
Dawes2; Madler 2-1; 02'. 3
1845.15
116.9
115.1
0.39
0.41
+ 1.8
-0.02
4
Madler
1846.64
111.3
114.3
0.43
0.45
- 1.0
-0.02
7-3
Mitchell
1847.47
114.6
113.9
0.56
0.48
+ 0.7
+ 0.08
9
02. 5 ; Dawes 4
1849.G9
114.9
113.0
0.47
0.53
+ 1.9
-0.06
4
02.
1851.19
116.6
112.5
0.40
0.56
+ 4.1
-0.16
4
Madler
1852.49
112.9
112.1
0.49
0.58
+ 0.8
-0.09
4
Miitller2; Jacob 2
1853.65
110.4
111.8
0.47 ±
0.59
- 1.4
-0.12
11
Madler 3 ; Dawes 4 ; Jacob 4
4854.75
112.0
111.5
0.61
0.60
+ 0.5
+ 0.01
1
Dawes
1855.05
114.6
111.4
0.4 ±
0.61
+ 3.2
-0.21
2-1
Madler 1-0; Secchi 1
1856.18
118.3
111.1
0.45
0.62
+ 7.2
-0.17
4
Jacob 1 ; Miidler 1 ; Winn. 2
1856.99
112.7
110.9
0.53
0.63
+ 1.8
-0.10
9-7
02.3; Secchi 3; Miidler 3-1
1858.42
112.8
110.6
0.45
0.64
+ 1.2
-0.19
7-3
Jacob 2-0; Madler2-0; Secchi 3
1859.81
108.7
110.2
0.53
0.65
- 1.5
-0.12
1
Dawes
1862.55
115.2
109.6
0.50
0.66
+ 5.6
-0.16
4-2
Madler
1863.71
107.9
109.3
0.55
0.65
- 1.4
-0.10
9
Dem. 8 ; Dawes 1 ; llomberg
1865.70
106.8
108.9
0.59
0.64
- 2.1
-0.05
7-6
Knott 4 ; Dawes 1 ; Leyton 2-1
1866.21
110.0
108.7
0.70
0.64
+ 1.3
+ 0.06
3
OS.
1867.79
104.3
108.3
0.5 ±
0.63
- 4.0
-0.13
1
Newcomb
1868.82
102.0
108.1
0.69
0.62
- 6.1
+ 0.07
6-5
Brtinnow
1869.90
106.0
107.8
0.57
0.61
- 1.8
-0.04
16
02.3; DeinbowskilS
1871.01
110.6
107.5
0.63
0.60
+ 3.1
+ 0.03
15
Duner
1872.83
101.5
107.0
0.63
0.58
- 5.5
+0.05
4-2
Brtinnow
1873.17
105.4
106.9
0.63
0.57
- 1.5
+ 0.06
5
02.
1874.26
102.8
106.5
0.52
0.55
- 3.7
-0.03
3
Newcombl; Gledhill2
1876.79
105.7
105.6
—
0.51
+ 0.1
_
1-0
Wilson and Seabroke
1877.05
104.1
105.5
0.48 ±
0.50
- 1.4
-0.02
6
Schiaparelli
1878.43
101.6
104.9
0.40
0.47
- 3.3
-0.07
10
Hall 8; 02
1880.10
102.9
104.1
0.36
0.43
- 1.2
-0.07
11-1
01; Seabroke 2-0; Jed. 8-0
1882.05
104.0
102.9
0.49
0.38
+ 1.1
+0.11
6-1
Bigourdan
1883.39
100.9
101.9
0.35
0.34
- 1.0
+ 0.01
10-9
Englemann 7; Sea. 1-0 ; Per. 2
1884.41
115.4
100.9
0.35
0.30
+ 14.5
+ 0.05
4
Seabroke 3 ; Perrotin 1
1886.83
101.0
96.8
0.29
0.19
+ 4.2
+ 0.10
1
Newcomb
1889.51
98.2
79.7
0.09
0.07
+ 18.5
+ 0.02
1
Burnham
1891.72
312.6
300.5
0.05 ±
0.05
+ 12.1
±0.00
3
Burnham
1893.79
121.8
125.6
0.14
0.11
- 3.8
+0.03
3
Barnard 3
1894.56
121.6
121.4
0.15
0.16
+ 0.2
-0.01
3
Barnard
1895.63
118.5
118.8
0.18
0.23
- 0.3
-0.05
5
Barnard
1895.72
118.2
118.6
0.29
0.24
- 0.4
+0.05
4-3
See 3; Moultonl-0
EPHEMERIS.
1896.70
1897.70
1898.70
0c
O
117.2
116.2
115.5
PC
0*30
0.35
0.39
t
1899.70
1 '.100.70
ft
114/70
114.4
PC
0^42
0.44
\.«..i . I
CAMS MA.lolM> >IKirS = A.G.(\ I.
1
9.
• •. 0o 40-.4 ; 3 = -16s 34'.
1, wbllo ; 10, yellow.
lH»fo»»nd l<j .l/r-m G. Clark, January 31, 1862.
OBSKUVATIONB.
P. • Ob««nr«ii ( $. p.
it
OlMvrvrn
O
9
O
f
1862.08
85 ±
10 ±
1
AlvanClark
1868.02
73.2
10.25
'£
Searle
1X62.19
84.6
10.07
3
Bond
iMl.S.IPl
72.1
—
1
1'eirce
lM.'.',20
184
10.09
5
Hiitherfurd
18(W.23
70.3
11.25
7
Vogel
I-",--'.23
84.5
10.42
2
C'haooruac
1X<W.24
69.6
11.35
5
Itrulins
1862.28
(4.92)
1
Lassell
1868.26
71.7
10.95
5
Bnglenuuui
1863.15
88.4
7.6.3
1
Secchi
1869.10
74.7
10.26
7-4
HrQniiow
1863.21
82.5
10.15
2
O. Struve
1869 15
73.6
11.23
3
Vogel
LSI
81.3
9.54
6
Huthcrfurd
68.7
11.17
1
Dun^r
84.9
10.00
1
1 hiwea
1869.20
68.6
11.07
\\'iuliH-k
;.27
82.8
—
1
Bond
1X69.23
69.4
10.93
1
1'eirce
Ixr.i 1 1
79.4
10.60
3
Marth
!>.,;
x., 1
.,,,,
1-3
1--WS.-11
1870.13
68.1
11.16
12-4
1'eirce
1864
78.6
10.70
4-2
Bond
1870.17
65.9
11.06
7-5
Wiiilock
lx.,;
74.8
10.92
6-3
O. Struve
1870.24
65.1
1206
5
Vogel
1 X..;
84.9
1
Ihiwea
1X64.24
79.7
10.08
1
Winnecke
1871.16
1871.20
65.9
70.3
10.75
11.19
8
2-1
Seochi
1'eirce
1X65.10
76.8
—
3
LMs.&Mar.
1871.23
64.1
11.11
2
hiin.'-r
1X65.21
77.6
10.59
a
O. Struve
1871.25
60.1
12.10
4-3
1'echQle
1X65.22
75.5
9.59
8
Seechi
1865.23
77.8
10.77
5-4
Foe rater
1872.18
59.8
11.05
2
Ihim'r
1M.V25
76.9
3
Tietjen
1872.21
66.6
10.69
3
Hiirgen
• 26
76.0
^^
_
Bond
1X72.24
62.4
11.50
1
Nfwcomb
1X65.26
76.9
(9.0)
1
Engleiuann
1872.24
64.3
11.46
6
Hall
1 ">7-.-li
61.3
—
3
Skinner
1866.07
77.2
10.43
2-1
Knc.tt
1866.21
—
1H.7J
1
I'.rulins
1878JO
884
11.12
1
Hall
186631
7.'. I.1
in.:i:;
3
M. Stnivi-
187&B
K>:,7
1-4
l»nn.:r
10.97
•2 1
Tii-tjt-ii
1X7.V_':{
70.0
1
Itorgen
74.1
H
3-1
Foerster
1X7
i... .;
10.42
1
KruhiiM
-
74.0
10.1M
2-3
Hall
1S7
864
11.29
1
W. & 8.
10. .".7
Newcomb
1
Ttittl.-
187416
59.0
11. 1C.
7
Newcomb
1866.26
717
10.09
3
Hast mail 11
I>7I I'.i
58.7
11 !.'.»•»
2-1
Holden
1866.29
7U
10.11
3
Secchi
584
11.111
2
Hall
1867.02
71 '_•
11.15
7-6
Winlock
1^7J.83
:,: B
1
Iturtoii
1867.10
10.66
Searle
\^.r< in
67.1
10.78
4
Puntfr
1867.22
72.1
10.98
1
0 -truve
1876J1
H .;
ll.il
•_'
Ni-wcomb
1X67.24
72.3
__
•-'
i • •• .
1875.-.-1
56.9
1 1 V.
.-, I
llol.lcll
1^'.7.27
74.9
,,,,_.
2-1
Kastuiann
K5.28
51 i
11.08
4
Hall
SL>
a CAXIS MA.JORIS = SIRIUS = A. G. O. 1.
t
00
o
Po
If
n
Observers
t
60
Po
n
Observers
1876.03
57.8
11.12
1
Watson
1881.99
43.6
9.38
11
Burnham
1876.05
54.6
11.45
1
Peters
1882.13
43.1
9.30
9
Hough
1876.09
54.9
11.82
6
Hoklen
1882.13
42.4
9.76
4-3
Bigourdan
1876.14
55.0
11.55
4
Russell
1882.18
42 2
9.95
6
Frisby
1876.22
55.2
11.19
6
Hall
1882.23
42.5
9.67
7
Hall
1877.11
52.8
11.19
4-3
Cincinnati
1882.54
44.0
—
6
Englemann
1877.16
52.8
11.35
4
Holden
1877.26
53.4
10.95
5
Hall
1883.10
40.1
9.05
10
Burnham
1883.10
39.0
9.41
1
Young
1877.97
52.4
10.83
8
Burnham
1883.12
39.7
9.02
11
Hough
1878.07
50.5
11.07
4
Holden
1883.14
41.3
—
4
Wilson
1878.15
51.0
10.71
9
Cincinnati
1883.17
41.4
9.75
7
Frisby
1878.19
54.4
11.24
5
Pritchett
1883.19
39.9
9.10
2-1
Bigourdan
1878.22
53.2
11.4
-
Eastmann
1883.21
39.1
9.26
6
Hall
1878.24
51.7
10.76
5
Hall
1884.05
36.0
9.67
6
Perrotin
1878.70
1879.05
1879.12
50.0
50.7
47.8
10.61
10.44
11.35
20-14
10
5
Cincinnati
Burnham
Holden
1884.17
1884.18
1884.19
35.3
36.7
36.4
8.79
8.51
8.39
3-1
11
10
Bigourdan
Hough
Burnhani
1879.15
50.3
10.78
5
Pritchett
1884.23
37.7
8.81
8
Hall
1879.20
50.1
10.55
6
Hall
1884.2Z
36.3
8.70
5
Young
1879.75
46.5
10.29
1
Cincinnati
1880.00
48.8
10.55
1
Russell
1885.11
34.1
8.09
8
Young
1880.10
47.1
10.48
4
Holden
1885.20
32.7
7.96
10
Hough
1880.11
48.3
10.00
11
Uurnham
1885.27
34.7
8.06
8
Hall
1880.17
1880.18
1880.22
49.6
46.7
51.1
9.87
9.92
3
6-4
1
Hough
Bigourdan
Smith
1886.05
1886.14
1886.22
29.8
28.7
30.6
7.59
7.21
7.39
4
12
6
Young
Hough
Hall
1880.25
47.8
10.30
8
Hall
1880.28
48.6.
10.38
2
Frisby
1887.14
25.4
7.08
4
Young
1881.07
46.3
9.77
8
Burnham
1887.19
23.7
6.78
7
Hough
1881.12
43.3
10.83
2
Holden
1887.23
24.2
6.51
4
Hall
1881.14
44.3
10.62
5-3
Bigourdan
1888.24
23.3
5.78
5
Hall
1881.17
46.9
10.11
6
Frisby
1881.18
46.5
9.81
7
Young
1889.97
13.9
5.27
5
Burnham
1881.26
45.3
9.60
5
Hough
1881.26
45.3
10.00
6
Hall
1890.27
359.7
4.19
3
Burnhani
The discovery of the companion of Sirius is one of the justly celebrated
events of modern Astronomy. It extended to the regions of the fixed stars
the principle of theoretical prediction which has proved so admirable in the
solar system, and which in the hands of LEVERKEER and ADAMS had led to the
discovery of Neptune. BESSEL had occasion to make a careful examination of
the proper motions of a considerable number of stars, including Sirius and
Procyon. The two dog stars, instead of moving uniformly on the arcs of
a CAKI8 M.\.I«>I:I- -IKM'S = A.ii.r 1. H.'l
i-iivli-, srrmrtl to trace out irregular -iiinotis paths across the sky, and
a further study of tln-M- anomal'ii - convinced HKSSEI, that the two stare were
perturbed by invisible boilii •-. In 1SJJ In- wrote, in a letter to HUMIIOI.DT:
"I adhere to the conviction that /'/•»«•//»« and Si'rin* form real binary systems,
ec-M-isting of a \i-ihlc and an invisible star. There is no reason to snp|>ose
luminosity an essential Duality of co-mical botlies. The visibility of countless
star- is no trgfuumA igaiiMl tin InvinbUhj of ooontleM othera."
In ls.17 tin -ii^^-tion of BESSEL was taken up by PETERS, who made an
investigation of tin- oli-cm-d inc<|iialitu-s, and found the following clrmriits for
the orbit described by Sirius alnmt the common centre of gravity of the system :
Periastrou passage =« 17U1.4.'<1
Mean yearly motion »- "".ISC.1!
. Period — 50.01 years
Eccentricity — 0.7994
In 1S<)1 the question was again examined by SAFKORD, who transmitted to
I'.Ki \\<>\v an investigation which assigned to the companion a position-angle
of 83°.8 for the epoch 1862.1. A short time afterwards, on Jan. 31, 1802, Mit.
AL\.\\ G. CLARK was trying the new 18-inch object glass of the Dearborn
trlr-<-i»|>r. and on pointing the instrument on Siriits exclaimed: " Why, fat In-l-
it has a companion!" And sure enough the faint but massive disturbing Inxly
announced by BESSEL was seen within a few degrees of the place assigned by
the theoretical astronomers. It now became a matter of great interest to ascer-
tain from the motion of the new companion whether it was really the disturb-
ing body; a few years showed that it had sensibly the required motion, and
li-lt no doubt of the identity of the two objects. In 1864 AUWKRS undertook
a iii-w ill-termination of the elements based on all the observations, and found:
; iastron passage — 1793.890
Mean annual motion — 7°.2847.~>
Period - 49.418 yean
Eccentricity - 0.6010
A definitive determination afterwards published gave the following results:
P = 49.999 years Q = 61°.96
T - 1843.275 * - 47M4
e - 0.6148 X - 18°.91
When the microim-trica! measures began to accumulate, \arious computers
made new investigations of the orbit The following table of elements is very
84
a CANIS MAJORIS = SIR1US = A.G.C. 1.
complete. The last set credited to DR. AUWERS were based on all the obser-
vations up to 1892.
p
T
e
a
8
i
A
Authority
Source
yr§.
49.6
1891.8
0.58
8.41
o
42.4
o
57.1
o
Colbert, 1885
Dearborn Report
58.47
1896.47
0.4055
8.58
50.0
55.4
216.3
Gore, 1889
M.N., XLIX, no. 8
51.22
1890.55
0.945
—
188
—
—
Mann
49.46
1893.18
0.7512
8.31
10.2
53.
—
Mann
57.02
1894.17
0.538
8.50
40.75
51.43
48.58
Howard
A. J. 235
49.399
1844.216
0.6292
7.568
37.51
42.43
39.94
Auwers, 1892
A.N. 3084
51.97
1893.5
0.568
8.31
40.3
50.8
135.4
Burnham,lS93
Tub. Lick Obs.II,p.239
51.101
1893.759
0.6131
7.77
37.06
44.6
223.61
Zwiers, 1895
A.N. 3336
During 1890 the distance of the companion became so small that it was
lost in the rays of the large star, even when viewed with the 36-inch refractor
of the Lick Observatory. As it was evident that no further observations could
be made until the object emerged on the other side, BURNTIAM collected all the
measures with great care and embodied them in his important paper in the
Monthly Notices for April, 1891.
The orbit which we have given in this work is very similar to that found
by BURNIIAM, except that the eccentricity is higher and more nearly in accord
with the value of this element found by AUWEHS. The orbit is based wholly
on the micrometrical measures, and the data used in deriving the mean places
have been very carefully selected.
We find the following elements of the orbit of Siritis:
P = 52.20 years
T = 1893.50
e = 0.620
a = 8".(>316
Q = 34°.3
t = 46°.77
A = 131°.03
n = — (>°.89655
Apparent orbit:
Length of major axis = 14".(53
Length of minor axis = 9".50
Angle of major axis = 50°.7
Angle of periastron = 252". 4
Distance of star from centre = 4".16
EPHEMEKIS.
(
1896.20
6,
193?9
PC
4.12
t
1899.20
0,
158?9
PC
4.97
1897.20
180.8
I.It
1900.20
149.5
5.25
1898.20
169.0
4.72
i \\l- M \.l.iiMS = SIKH'S = A. <..r. I.
> AKIftOX OF COMPUTKII WITH OMKKVRD 1'LACKM.
ff_ ft
OhuH^MB
Pf—Pi
ww*~r*
I
•
9
t
1" P.'
+0.41
10
Bond V; Kuthrrfunl 5: fharornar 2
H '.<•:;
-0.13
10-9
OZ. 8; Kulherfun) 0; Umwv* 1 ; Ilonil 1 o
1864 20
10.25
+ 0.11
1'. IV
Mar. 3; LM. 1-3; Bond4-S; OZ.0-3; Dm. 10; \Vlnn 1
77 .1
10.35
HI. IS
-0.3
ii i::
•-••-• i:.
Lai.3-0; 02.J; 8M.8; Ffi.5-4; TJ.3; 11.1. -; En. 1-0
71 1
10.63
-0.6
o i:.
•.•i I'll
Kn. 8-1 ; Ilrk 1 ; OZ. 3 ; Tj. S 1 ; F.i. 3- 1 : III. 23: X. 3 ;
. •
10.61
" i:.
;» i;;
Wk.O-4J; 8r.«-6; OZ.l ; Hii.2^> [Tut.0-1 ; Kjwt.3; S«-.S
Iv, x 1,
71 1
n.o
;,..,..
m.'.i:
+0.4
20-19
S<«rle2; Pelrce 1-0; VI. 7; HnihniA; Knglrnmnn ft
;•• i
11.1"
11 .''.I
+ 1.2
4 d.OI
7
VI. S; IMIII.T 1: \\ii.n.-.k.--J: ivir... 1
Is7" l>
II I'J
11. VI '
±0.0
+ i 1.22
19-14
IVIrrria 4; Wlnnwke 7 6; VI. 0-5
is7i :•!
1 1 ..s
11 V7
±0.0
+ 0.01
11-9
Srrrhl:!; lVlrrr2 1; Dum'-r 2; 1'wh. 4-3
82.9
11.17
11.:; 1
-0.2
-0.14
i:. i::
I)uin'T3; lUirpi-na: N.I; Hall it; Dolx-n-k 3-0
Ins;,
1 1 S3
-0.47
1-7
Hall 0-1; Dimr-rl 4; Umhn* 0-1; W.4S.O-I
IS7I I'.'
ll.l.s
1 1 .-.••.•
ftj
-0.11
11 l«i
N.7: llohlenS 1; Hall 2
is;.-. .1
56.3
1 1 L's
11. VV
-1.0
+0.06
16-14
Bur. 1-0; I>.n,.r4; N.8; Hoklen 5-4; Hall 4
M ••
11 !.:
11.14
-0.8
+ O.V.I
17 is
WaUon 0-1: Peten 1; Hnlilen 0; Uiu. 4: Hall (I
1877.18
:, „
ii.n;
11. ov
-0.7
+0.14
L: IV
i'in.4 :i: II. .1.1. n 4; Hall &
.Ml
.M s
ILOO
III S|
-0.4
+0.115
ft. 8; llol.l.-n 4: (in. »: IV. 0.1: K»«t.O 1: Hall 5
1 ...
10.75
10.C8
-0.4
+ o.ti7
46-40
Cln. 20-14; ft. 10; Hol.lcn 5; l'rii.-l..-n :.: Hall (1
ISM, |;,
!. i
L0.32
+0.4
-0.17
.; i
i in. 1; Km. l;Hol.4;0. 11; Ho. 3; lilR.lt 4: HI. 8; Km. 2
ISM 17
uu
HMi
|ll.| IS
+ 0.2
+0.03
39-37
tl.»; HoldenS; Big. S3; Kri.il: V. 7; HOUR|I&; Hall «
1883 90
18.9
1.60
9.n
+0.2
ii IV
ft. 11; Hough 0 ; Big. 4-3; Km. 0; Hall 7; Knglrniann U
|u 1
+0.3
+0.09
11 ::r.
,i.l": Y.I; II. .null 11: Wi. 4-0; Kn.7; Big. 8-1; III. 0
ISM is
M ;
-0.8
-t-o.ol
43-41
PerrotinO; BlR.3-1; HOIIR|I 11; ft. 10; Hall 8; Young :>
1881 19
:•.'
8.04
- VI
-0.7
-0.16
26
Young 8; Hough 10; Hall 8
L8M : i
7 1"
-0.7
<>•_•:;
20
Young 4; Hough 13; Hall 0
1881 19
-•II
25.5
-1.1
15
Young 4; Hough 7; Hall 4
:^,.-,
17.'..
17.7
+0.2
-0.22
i :.
Hall 8; ft. 1-9
U.7
5.26
5.24
-0.9
+0.02
3
Bnmliam
1H90.27
.'.> :
0.2
4.19
4.09
-0.5
+0.10
3
Buniham
The comparison of the computed with the observed placet* shown an
« • \m-iiK-ly satisfactory agreement, and we are led to believe that the elements
_M\.M alwve will prove to be near the truth. The difference* between these
«•!< UK nl> ami those found by At \M.I:> an- not greater than might be expected
from tin- mall-rial u-t-d in tin- two cases. Adopting the foregoing elements
and <-ii i '- parallax of 0*..'>s. \M liml the mans of tin- .-v-irni to 1x5 3.473 times
that of tin- sun and «arili: thi- major semi-axis (unics out 21.136 astronomical
units. Tim- the system of N/Y///.< i- a magnificent one. having .'M7 times the
mass of the planetary -v-tem. ami slightly larger dimensions than the orbit of
the planet I'l-iniHu. Tin- ma>-r-. accor.ling to ArwKiis. are in the rat.io 1:2.11*.!:
or, in units of the sun's mass, 1.113 and ±.'HJ<> respectively. The future ol»er-
vatinii of this *\:\r \- a matter of the higlu-t interest. There is some rca-mi
i.. -ii|ipo-i- thai s - i~\.r\ much expanded, more nearly re-cinbling a nebula
than the -mi: if thi- inference !>«• true, the action of the companion \\ill rai-e
enormoii- bi.ilil\ i'nl»-- in the ma-- of >'»/•///>•. Since the height of the tiile-
varic- in\er-elv a- the cube of the di-tance. it will follow that the tidal rl
86
9 ARGUS = ft 101.
tion at periastron will be about 80 times higher than at apastron. There
would thus arise a periodic disturbance in the mass of Si?-ius depending on the
revolution of the companion. It seems probable that high tides would increase
the radiation of Sirius, and hence if it were possible to make photometric
measures of absolute accuracy, or of such a character that the brightness could
be compared at intervals of 25 years, it might some day be possible to detect
the alteration in brightness arising from the tidal action of the companion.
The excessive faintness of this massive body is an extraordinary anomaly
which is not easily explained. From the shape of the orbit, however, we may
believe that the system has been formed by the usual process, and for some
reason the companion has rapidly become obscure. As the companion is
apparently still self-luminous, its darkness is not so conspicuous as the exces-
sive brilliancy of Sirius. The change in the color of Sirius since ancient
times is even more remarkable.
1882.21
1883.11
a = 7" 41"U ; 8 = —13° 38'.
5.7, yellow ; 6.3, yellow.
Discovered by Burnham with his celebrated six-inch Clark Refractor, March 11, 1873.
OBSERVATIONS.
6,
Po
n
Observers
t
60
Po
n
Observers
O
i
O
IT
19 double
—
1
Burnham
1891.0G
91.5
u.:;i
4
/3. & Sell.
24 289.7
0.58
2
Dembowski
1892.0.")
98.7
0.22
3
Burnham
50 302.2
0.45
4
St. & 0.
1 S93.94
282.1
0.44
8
Barnard
08 30(5.2
0.38
2
Hall
1894.18
282.0
0.42
3
Barnard
21 319.7
0.35
4
Schiaparelli
1894.1T.
286.G
0.35
3
Comstock
11 33G.2
0.30
1
I'liirnliani
1894.86
287.3
0.63
5-4
Barnard
08 7G.4
0.34
4
Burnham
IS! 15.21
1895.25
285.2
285.4
0.42
0.59
2
5
Comstock
Barnard
22 83.8
0.84
G
Bornbam
1895.30
283.8
0.58
3
See
The first investigation of the orbit was made by GLASENAPP and pub-
lished in the Montlilij Notices for June, 1892. His elements are:
P = 40.54 years
T = 1844.02
e = 0.090
a = 0".45
a = H6-.7
i = 59°.2
X = 251°.3
« = +8°.880
0 \IM.I s = £ KM.
>7
l»i I:\H\M re \i-ed tlii- nrl»it. in Ma\. ISO.'l. and by relying on the distances
a- well a- tin- angle*. arri\ed ;it an apparent ellipse of very different character,
from which wo derived the following elements (Astronomy and A
.Inne. 1803):
P T years
T - 1892.706
« - 0.68
a - OM.1J
Q - 900.75
i - 76«.87
A - 73°.92
ii - + 16e.399H
It did not take long to decide which set of elements was to be preferred.*
I'. M:\ \i:n examined the star with the .'Mi-inch refractor of the Lick Observa-
tory in I>ecciulicr. 1S«»:>. and found that since 1802.05 the radius vector of the
companion had >wept over about ISO , so that the small star was in the fourth
i|uadranl. I took occasion recently, while measuring double stars with the
iM-iueh refractor of the l.eandcr McCormick Observatory of the University of
Virginia, to mca-iirc 0 Aryil* on three good nights. The observations confirm
those <>| ll\i.v\i:i>. and *how that KritxiiAM's apparent orbit is not far from
the truth. With the new iiiea-uiv-. it seemed worth while to re-investigate the
orbit: accordingly, from a c<ui-ideration of all the observations, I find the fol-
lowing elements of 0 J
P = 22.00 years
T mm 1892.30
o — 0.70
a - 0*.6549
8 - 96°.5
t - 77°.72
A - 75:2*
Apparent orbit:
Length of major axis = 0".941
Length of minor axis = 0".2C7
Alible of major axis = iW.2
Angle of jieriastron = t.'U'.S
Distance of star from centre = OM52
It i- confidently believed that thoc eleincnt> will prove to be nearly cor-
iu -pile of the small number of oh-ervations upon which they are based.
CoMPAKIftOJC OF THE (.'tiMffTRD WITH OBSRRVII> I'l \r-fC8.
i
6.
9,
P*
ft
•*-9,
P*~?€
II
Obcerten
1875.24
289^7
29 L 7
n'.'.s
-2.0
2
iH'inbowski
l>;->..*iO j .'M)2.2 .'M)L'..!>
0.45
"17
-0.3
_4)
4
Cinciiiiiati :nnl Itiinihain
•a SOfi.2 »V».4
0.38
» II
+0.8
_i.
Hall
.•I ::i'.i.7 .•:•-•!:.
0.35
0.31
-4 -
+ 0.o|
4
S-hia|Kirvlli
1 1 :;::•. •_•
0.30
0.2fi : -r (>.."» +0.04
1
Huniliam
0.34
o..T< +2.8 +«>i.l
t Itimiliam
- -
> j 0..14
n :;c, -flu
— 0
i'i I'.iiiiili.nii
1.06
91.5
90.1 0.34 0.34 +1.4
0.00
4
ItiinilKini :iml Sclii:i|>:irclli
lii;.ii ii •_••_• <i. n;
+0.06
3
|liini)i:ini
M ;:
0.42 +.1.3
+ 11
3
K:irnanl
1895.W
L's •',
+0.2
+ 0.01
3
See
8W7.
88
£ CANCRI AB = 1 1196.
It will be seen that the residuals are very small for such a close and difficult
star; and it is evident that future observations will not change the present
orbit materially, although it is desirable to secure additional exact measures
which will improve the elements as much as possible. If adequate attention is
given to this object, its orbit will soon be one of the best in the heavens. A
short ephemeris is:
t
ft
PC
t
ft
PC
0
n
O
II
1896.3
285.8
0.39
1899.3
295.2
0.55
1897.3
288.8
0.60
1900.3
299.0
0.51
1898.3
291.9
0.59
As the eccentricity of the orbit is well determined by the rapid motion of
the companion round the periastron, the established conspicuous magnitude of
this element must be regarded as the most remarkable phenomenon of the
system.
For the next few years the star will be relatively easy, and double-star
observers should give it particular attention.
CANCRI AB= v
a = 8h 6">.2 ; 8 = +17° 58'.
6.5, yellow ; 6.2, yellow.
Discovered ly Sir William Herschef, Noiiember 21, 1781.
OBSERVATIONS.
t
60
Po
H
Observers
t
A.
Po
n
Observers
0
t
o
ft
1781.90
363.5
—
1
Hersehel
1835.:;<>
28.8
—
1
Miidler
1825.27
57.8
1.09
-
South
1835.31
1835.60
20.2
15.7
1.14
8
3
Struve
Miidler
1826.22
57.6
1.14
3
Struve
1836.27
15.4
1.20
3
Struve
1828.80
38.4
1.04
2
Struve
1836.31
15.1
5
Miidler
1831.16
31.8
1.34
5-3
I [erschel
1836.68
16.1
—
4
1 >:twes
1831.28
29.8
1.05
6
Struve
1831.30
30.8
1.09
3
Dawes
1840.15
6.1
1.24
35-23 oi>8
Kaiser
1840.20
4.4
1.19
8
Dawes
1832.12
27.9
—
8
Hersehel
1840.29
7.5
1.00
7
O. Struve
l.s:;2.12
27.0
—
7
Dawes
is:!i.'.19
31.3
1.32
5
Bessel
1841.16
0.9
1.1S
5
Dawes
1832.28
27.5
1.15
4
Struve
1841.31
1.0
LOB
6-4
Miidler
1833.13
26.3
—
9
Herschel
1842.22
:;:,<;.;;
1.18
6
Dawes
1833.21
26.2
1.19
9
Dawes
1842.L'G
368.9
1.07
6
Miidler
1833.27
22.1
1.15
3
Struve
1842.29
369.3
1.29
4
( >. Struve
CAXCIU AH = .i'1196.
«
0.
P»
*
, , ..:..-.
1
*
P.
»
Ohcerven
1843.18
...:,,.
l!l2
8
Dawea
1856.07
3041'
9
l±
7
Deinhownki
1843.19
356.9
1.06
4
Midler
1866.21
306.3
1.21
4-3
Jacob
1843.30
354.3
1.17
3
o Strove
18545.23
309.4
1.16
2
Morton
1K56.25
307.2
0.77
2
Secchi
1844.28
.,. :
1.16
4
: UVC
18545.28
34)7.5
1.00
2
M feller
|S|| •
..1 1
1.02
10
Midler
307.3
1.01
14)-7
1845.25
350.4
1.05
13
Midler
1856.93
296.6
1.03
3
ItemhowBki
1845.31
347.9
0.97
3
O. Strove
1857.27
298.4
0.98
8
4). Struve
1845.83
349.4
1.2
1
Jacob
1857.29
0.96
3-2
M fuller
1846.27
347.5
1.02
16
Midler
1857.29
303.9
0.78
45
Secchi .
1846.29
344.8
M ,.,
3
O. Struve
1857.90
299.7
1.14
3-1
Jacob
1846.29
344.4
1
Jacob
1858.18
294.2
1±
7
IVmbuwiki
1M7.18
.11 t
1.09
4
Midler
1858.20
297.6
1.05
8
M feller
1" 17.33
342.2
0.96
5
O. Strove
1858.28
295.5
0.98
1
4). Strove
1848.13
B88J
1.05
1
Da we«
1859.27
294.9
0.98
8
Ma.ll.-r
L848J4
338.1
1.06
6
Da was
1859.30
286.5
0.91
g
4). Strove
L848
1.0
1
W. C. Bond
184J0.26
282.9
Diillen
1848.28
340.0
1.03
7-6
Midler
283.3
1848.30
337.7
0.91
5
O. Strove
18450.26
281.0
0.70
1
Da wen
1849.29
1.11
5
Da wa§
1860.26
284.8
—
-
Schiaparelli
1848
4
O. Struve
18410.27
281.3
0.81
2
43. Strove
1860.28
279.9
—
_
D..11.-H
332.9
0.94
3
O. Strove
1860.28
282.0
—
-
Wagner
1850.71
.. :..,,
1.03
1
Midler
1860.28
283.4
—
-
Schiaparelli
1851.18
IV. 1.21
333.6
329.0
1.1 ±
1.05
3
9
Fletcher
Midler
1860.28
1860.30
285.0
286.0
1.02
5-4
Winnecke
Midler
UK
i U
3
(». Strove
1861.14
282.8
—
5
Powell
1851.26
•
1 III
7
I hi we*
!>'•.!. 26
282.2
0.97
2
M feller
L6
l.o ±
8
Fl.-t.-lif-r
1861. -'7
275.3
0.87
8
O. Strove
IV,.
::•_•« 1
1 ...;
8
Dawec
lsr,2.31
88741
ii 71
]
O. Strove
. 25
LM
6
Midler
"7 1 1
OJ7
4
Mit.ll,-r
2
: UVf
186,-u:?
"71
15
iK-inbowski
1853.20
322.0
i i-j
3
Jacob
0.95
_
I^-vtoii <M,K
185.'! .1
L06
8-7
!er
L'r,-.'.:,
Ml
1
Dawea
1853.30
319.8
•J
< • Strove
184;.
»~n
1
Knott
1854.20
315.3
,,.,,
3
Dawes
188418
8B8J
10
Dembowaki
1854.27
318.6
1.08
10-9
Midler
; i-.i
o.71
2
Dawes
1854.29
.-•••-•
1.02
1
Morton
1864 ..1
0.64)
1
KiiK'li-inaiin
1854.37
321.9
—
12
Powell
253.3
0.72
2
O. Strove
1866.10
.:,,,,,
1±
7
Dembowaki
1866.21
245.7
0.50
12
Dembowftki
1855.19
312.4
1.07
3
Secchi
1865.30
243.4
g g ;
3-2
Dawea
1855.26
SUM
1.06
4
Midler
is.,
245.3
0.64
2
Secchi
1855.31
18 .
0.91
3
O. Strove
1865.36
241.4
0.61
3
Km At
1855.31
305.9
1.04
7-6
Winnecke
1865.30
-.- 1 1 -
4
Englemann
90
£ CASTCRI AB — 1' 1196.
t
Bo
Po
n
Observers
t
60
Po
n
Observers
Q
If
0
It
1866.19
238.4
0.52
9
Dembowski
1877.17
108.7
0.68
7
Dembowski
1866.27
237.8
0.70
1
O. Struve
1877.23
107.9
0.79
7
Schiaparelli
1866.28
234.6
0.40
2
Secchi
1877.23
110.3
0.81
3-6
Plummet'
1866.31
233.3
0.78
4
Knott
1877.24
108.1
0.87
3-2
Doberck
1866.37
231.5
0.72
1
Leyton Obs.
1877.27
108.0
0.72
3
O. Struve
1866.94
228.3
0.66
1
Knott
1877.32
107.3
0.74
1
Pritchett
1867.08
229.7
0.59 •
3-1
Harvard
1878.16
104.1
1.01
1-2
Doberck
1867.22
224.4
obi.
9
Dembowski
1878.18
100.3
0.66
6
Dembowski
1868.20
210.9
0.5
7,
Dembowski
1878.26
1878.29
100.8
99.1
0.7
0.76
7
3
Jedrzejewicz
0. Struve
1868.28
214.7
0.72
2
0. Strove
1878.32
102.3
0.81
3
Hall
1869.26
197.6
0.64
1
Peirce
1879.27
. 93.1
0.87
6
Schiaparelli
1869.32
198.4
0.62
2
0. Struve
1879.29
91.8
0.74
3
0. Struve
1869.37
203.6
0.48
4
Dune'r
1880.21
85.2
0.61
5
Hall
1870.08
188.1
0.64
5-2
Harvard
1880.22
89.8
0.89 ±
6
Jedrzejewicz
1870.15
187.3
0.5
9
Dembowski
1880.24
88.9
—
2
Doberck
1870.28
186.3
0.66
4
0. Struve
1880.29
85.2
0.73
6
Burnham
1870.30
1870.56
188.3
181.0
0.43
0.2
3-4
2
Dune'r
Gledhill
1881.24
1881.24
81.1
84.9
0.91 ±
0.84
4
5
Jedrzejewicz
Doberck
1871.15
175.5
Contatto
7
Dembowski
1881.28
86.8
0.88
3
0. Struve
1871.26
175.1
0.2
2
Gledhill
1881.30
79.0
0.71
3
Hall
1871.29
178.2
0.55
3
Dune'r
1881.30
80.2
0.92
6
Schiaparelli
1871.30
169.4
—
-
Scharnhorst
1881.31
73.7
0.77
2
Pritchett
1871.31
171.3
0.59
3
0. Struve
1882.09
75.7
0.74
1
Bigourdan
1872.11
166.7
0.6
2
Knott
1882.20
73.3
0.79
4
Hall
1872.21
167.5
0.70
3
Wilson
1882.22
76.2
1.05
6
Englemann
1872.23
162.8
Coutatto
7
Dembowski
1882.25
75.1
0.98
6
Schiaparelli
1872.31
163.0
0.58
3
O. Struve
1882.26
75.0
0.94 ±
4
Jedrzejewicz
1872.33
163.3
0.69
2
Dune'r
1883.24
72.4
1.05
6
Englemann
1873.19
150.2
0.5
10
Dembowski
1883.29
69.3
1.00
6
Schiaparelli
1873.22
150.9
0.5 ±
4
W. &. S.
1883.31
66.4
0.82
4
Hall
1873.28
152.0
0.61
3
O. Struve
1884.19
62.7
1.06
3
Perrotin
1873.63
149.3
0.55
2
Gledhill
1884.22
61.9
—
8
Bigourdan
1874.09
141.6
0.74
7
Dembowski
1884.25
63.9
0.98
7
Schiaparelli
1874.13
140.1
0.45 ±
2
Gledhill
1884.26
60.6
0.98
3
O. Struve
1874.18
141.3
0.58
3-2
W. &S.
1884.27
64.5
0.88
5
Hall
1874.28
144.5
0.64
3
O. Struve
1884.28
67.0
0.94
4
Englemann
1874.29
142.8
0.62
2
Dune'r
1884.38
64.4
—
3
Sea. & Smith
1875.14
130.1
0.74
8
Dembowski
1885.27
59.0
1.25
2
Seabroke
1875.26
128.9
0.70
8
Schiaparelli
1885.29
58.0
1.04
5
Schiaparelli
1875.28
132.4
0.62
3
0. Struve
1885.29
59.4
1.05
4
Englemann
1875.29
133.3
0.77
2
W. &S.
1886.08
57.2
1.09
4
Tarrant
1875.33
129.5
0.59
5
Dune'r
1886.24
51.4
1.06
2-1
Sea. & Smith
1876.14
119.4
0.72
6
Dembowski
1886.28
55.0
1.03
4
Hall
1870.26
120.7
—
0
Doberck
1886.29
51.2
0.98
3
Jedrzejewicz
1876.29
119.45
0.66
2
O. Struve
1886.30
56.3
1.08
5
Englemann
CANCItl AB = 1*1190.
'.M
t
«.
P.
•
. • -. : •
I
0.
P.
n
Obwrren
Q
9
O
f
1887.24
.-.•• !
4
Hall
1891.22
35.7
.04
5
Hall
•_»6
48.4
0.97
11
S-hiaparflli
1891.24
34.1
.14
3
ltig(mrilan
l^s; .;:,
46.0
1.21
4-1
So*, & Smith
1892.24
31.0
.09
3
Maw
II ,
1.03
4
Hall
1892.25
31.3
.20
2-3
Kiuirre
1888.26
49.2
—
3
Smith
1892.20
.'W.l
.11
11
Schiuparelli
1 ^vs.27
i
1 ' ' 1
I
Srliiaparelli
1892.28
30.4
.10
(i
lti-..ui.l:m
] x s*
45.8
! "•'
2
<\tve
1892.89
28.7
0.99
3
•lonM
! ^ v - '
41.4
1 1.:
1
M
1893.20
27.2
0.98
g
< 'lllllstlM-lx
18X9.17
42.0
1 '_•"
4
flM UTTndgin
1893.22
20.4
1.07
8
Maw
1889.19
1.05
3
Leaven worth
1893.24
27.0
1.12
13
Sc.hiaparclli
18H9.21
1889.21
1889.23
1889.28
•J9
43.4
43.6
43.7
!•>•'
I M
0.99
1.23
1.07
12
2
5
2
3
Schia|>arelli
(ilaHfiiapp
Hall
O. Strove
Maw
1894.15
1894.10
1894.23
1894.24
1894.24
20.0
23.8
22.9
23.5
25.0
1.47
1.24
0.93
1.08
1.05
1
3
3
13
4
Ebell
H.r. Wilson
('omxtock
Schiaparelli
Maw
ls'.M>.23
37.2
11.1
9-7
Schiaparelli
1894.39
23.2
1.39
5-4
liigoimlan
•-•6
30.4
36.9
0.95
,,.,-,
2
4
Comstock
Hall
1895.23
1895.23
21.9
20.9
1.22
1.01
2
8
Lewis
( 'miistix-k
l.v.H.ii.-,
32.3
1.04
5-4
Flint
1895.2?
17.1
1.09
l
1 >.i\ i'1-i'ii
ivi) .-_•!
34.3
1.14
9-10
Schiaparelli
1895.28
22.8
1.13
4
s...
The closer coni|>onent« of thi» ternary (or quarternury) syHtt-in have been
found to revolve rapidly in a period of about sixty years, while the remote
ronipoiu'iit moves much more slowly, and probably will complete its orbit in
six or seven centurii-s. Both stars move retrograde, and the system thus made
up is inn- of great interest to the physical astronomer. From the time of
\Vn.i.i\M >u:i\i; ilir iili-tTvations are both abundant and exact, and hence
llu- «irb5t of tin- cln-r pair can now be determined with a high degree of pre-
ei-imi. We >li:ill treat only of the clo.se binary, neglecting the remote com-
panion and tlie dark body which PuoPESSOK SKKI.K;KH supposes to attend it.
It i- evident that the third component will exercise a considerable disturbing
influence upon the close pair, but I'I:«»KK-.. .1: M i I.KJKK has shown that this
influence is probably obscured by the larp- errors incident to the measurement
of a s\st,.iu which i> never much wider than one second of arc. Assuming
that the linn will !»• scn-ililv undisturbed, we -\\-.\\\ deduce the orbit of the
closer pair bv the same process which is employed in the ease of other binaries.
The motion of thi- -\-i.m has U-cn investigated by numerous computers; the
following list of orbits i* fairly complete:
92
£ CANCRI AB = -T 1196.
p
T
e
a
ft
i
A
Authority
Source
58.91
1853.37
0.2346
1.292
O
1.47
63.3
266.0
Miidler, 1840
Dor pat obs. IX, p. 177
58.27
1816.687
0.444
0.892
33.67
24.01
133.01
Madler, 1848
Fixt.-Syst. I, p. 248
42.501
1805.67
0.4743
1.013
10.52
65.65
227.15
Villarceaul849
A.N. 967
58.94
1815.53
0.256
1.030
18.4
48.6
141.9
Winnecke 1855
58.23
1872.44
0.3023
0.908
150.3
36.24
171.78
Plummer, 1871
M.N. XXXI, ]>. 1!).->
60.45
1869.9
0.365
0.908
107.5
23.5
85.3
Flam., 1873
Catal. d. Pt. doub. p. 49
G2.4
1869.3
0.353
0.908
109.0
20.7
199.0
0. Struve,1874
C.R.LXXIX, p. 14(17
59.486
1870.82
0.3318
0.886
358.05
18.52
188.55
Doberck, 1880
A.N. L'.'iL'L' [1881
60.3
1866.0
0.391
0.853
81.55
15.53
109.73
Seeliger, 1881
Wicn.Akad.LXXXin,
59.11
1868.112
0.3819
0.853
80.18
11.13
109.73
Seeliger, 1888
Akad.d.Wiss.,Mune.'S8
An examination of all the measures led to the mean places given in the
accompanying table; from these we find the following elements:
Apparent orbit:
P = 60.0 years
T = 1870.40
i =
88°.7
7°.4
e = 0.340
\ =
264°.0
a = 0".8579
n =
— 6°.000
Length of major axis
Length of minor axis
Angle of major axis
Angle of periastron
Distance of star from
centre
= 1".704
= 1".632
= 8°.8
= 184°.9
= 0".290
The comparison of the computed with the observed places shows a good
agreement, and indicates that no radical change in the above elements is to be
expected. The period is perhaps uncertain by half a year, while the eccentricity
can hardly be varied by more than ±0.03. The motion extends over more
than one revolution, and is well represented by the above elements in all parts
of the orbit. The apparent ellipse is remarkable for its circularity, and the
small inclination renders the motion almost the same in the apparent as in the
real orbit. The general interest thus attaching to this system is greatly
enhanced by problems arising from the perturbations of the third star and its
theoretical companion.
COMPARISON OF COMPUTED WITH OBSERVED PLACES.
t
e.
Be
Po
P«
Oo-6,
Po—Pc
n
Observers
1781.90
363.5
359.6
i
1.14
+3.9
1
1
Hersclid
1SLV..27
57.8
.V.I.I i
1.09
(».'.»;
-1.2
+0.13
—
South
1826.22
57.6
55.0
1.1 1
0.9S
+ 2.6
+ 0.16
3
Strove
1828.80
38.4
44.1
1.01
L.03
-5.7
+0.01
2
Struve
1831.29
30.3
34.9
1.07
1.07
-4.6
±0.00
9
Stnive 0; Dawcs 3
1832.23
29.4
30.9
1.2."
1.09
-1.5
+ 0.14
9
Bcssel 5 ; Stnive 4
is:;: MM
24.2
28.0
1.17
l.ld
-3.8
+ 0.07
12
Da weal); Stnive 3
• 1875
I88S
182} ••«•"
• •
CAM 1:1 AH = .i' 119(5.
1
»
••
f.
ft
*-*
• •
'
ObMTWM
Is ,111
21.5
1.14
9
12
+0.1
7-3
Midler 1; Z.3; Midler 8
15.5
17.4
1.20
i::
1 •.'
Z. 8; Midler 50; Dawe* 4-0
is 10.24
6.0
1.09
1 ;
+ O.S
in.;.
15
Dawe* 8; OZ. 7
IN li ... 0.9
2.1 111
: i
1 •-•
11-9
Dawe.:,; Midler «-4
Is I. .-."• :t.'»8.2
1.18
II
-0.7
1
16
Uaweafl; Midler 0; OZ. 4
:.V».4
1.12
.1:;
-0.4
0.01
15
Da we* 8; Midler 4; OZ. 3
1 s 1 I.:i3 .".."•-. 1
1.09
.12
0.08
14
OZ. 4; Midler 10
ls|. -,.57 348.6
1.08
.13
+ O.5
-0.04
4
OZ. 8; Jacob 1
184(5.29344.6
• ; • .
O.95
.11
-1.1
-0.16
4-,'!
OZ. 8; Jacob 10
Is 17.31 312.6
.10
+ 0.3
• ill
7
Midler 2; OZ. 5
1848.24
1.01
.09
+ 0.2
-0.08
20-19
Dawe* 1; DawcxO; Bond 1; Midler 7 0; OZ. 5
.07
-0.2
-0.12
9
Dawe* 5; OZ. 4
.1 I
< • i
IM;
+0.5
,,,,S
4
OZ. 8; Midler 1
I s:, !
1.04
.04
+ 1.1
:
22
Fletcher:!: Midler »; OZ. 3; Dawe* 7
is;, •-•:•! .;•-•:,.-,
1.00
.02
+ 1.8
" U
14
FleU-ber3; Dawe*3; Midler 0 ; OZ. 2
•-'.•• 32 1.8
320.3
1.01
.00
+ 1.5
+o!oi
13-9
Jacob 3-10; Midler 8 7; OZ. 2
i s:, i
316.0
l.oo
+3.0
+0.02
26-1
;,,,,.. M •.•:*< M Ho i fern • ' . "
311.S
2.2
+ 0.02
.'4-17
Dem. 7; Secchl 3-0; Midler 40; OZ. 3; \Vlnnockc7-tf
1 N.'.'
O.96
0.93
-1.1
+0.03
TO-21
Dem. 7; Ja. 4-0; Mo. 2-0; Sec. 2; Ma. 2; Wlnn. 10-7:
is:.:. II ::.u.r.
0.91
0.90
+0.6
+ 0.01
15-17
OZ. 8; Midler 3-2; Secchl 6 ; Jacob 8-1 [Dem. 3
3 •---• 295.8
0.99
0.88
-0.9
+0.11
11-8
Dem. 7; Midler 3-O; OZ. 1
• -JN 290.7
0.85
-0.2
+ 0.10
10
Midler 8; OZ. 2
1860.28:
' i. , i»
-1.8
-0.06
8-3
Dawe* 1 ; OZ. 2; Midler :, <i
is.; 1.22
280 I
0.79
+ 1.5
+ 0.08
10-3
Powell 6-0; Midler 2; OZ. 3
2 ::i
:'7".'.'
270.9
0.86
0.75
±0.0
+0.11
(5-2
OZ. 2; M«.ll«-r 4
:•'•,: I
• 1.70
0.72 +1.2
-0.02
17
Dembowikl 15; Dawe* 1; Knott 1
lsr.i.2l
0.660.69 -1.2
-0.03
14
Dembowikl 10 ; Dawe* 2 ; Kngleinann 1 ; OZ. 2
24 4 .0
.' I.V2
i>.r,iio.C5 —1.2
-0.05
24-19
Dembowskl 12; Dawm3-2; Seech! 2; Knott 3; Kn. 4
o.c.:: o.62 +0.1
+0.01
18-13
Dem. 0; OZ. 1; Secchl 2; Knott 4^), !.••>. 1 O; Knott
1867.18
.--'II
225.3 O..V.MM-.I
—0.9
-0.02
9-1
Harvard 3-1; Itenilwwikl V-0
:-'-.;
212.8
212.I'"-! 0.58
+0.4
+ 0.03
9-7
Dembowikl 7; OZ. 2-0
1869.32
1 '.t'.i.'.i
li'.t. 1
0.58 0.57
+0.8
+0.01
7-6
Pelrce 1-0; OZ. 2; DuWr 4
1870.27
isi;.2
186.7
o.MJO.56
-0.5
:
23-21
Harvard 5-2; Dembownkl 0; OZ. 4; Dun. r :: 4; Gl. 2
1871.25
175.0
173.7
0.570.56
+ 1.3
+0.01
15-6
Dembow*kl7; Gledhlll2-0; Dun. r :! . OZ. 8
1872.24
164.6
161.3
o.r, 10.58
+3.3
+0.06
17-10
Knott 2; Wilwn. :!: Dcnibowikl 7-0; OZ. 3; Dm,, i -
1873.33
150.6
147.8
0.510..V.I
+ 2.8
-0.05
19
Demlmwikl 10; W. & S. 4; OZ. 8; Gledhill 2
1874.19
142.1
138J
n. t;i d.r.2
+3.0
-0.01
17-1(5
Dembowtki 7; (iledhlll 2 ; W. & S. 3-2 ; OZ. 3 ; Dum-r 2
|.-.o..s
1 26.5.0.68 o.r,:,
+ 4.3
+0.03
24
Dcnibowskl 8; Sch. 0; OZ. 3; W. & S. t; Duner &
1 1 '.1 S
117.4
0.690.68
+ 2.4
+0.01
13-7
DembowiklO; Doberck 00; OZ; 2
1877 -i
lus |
0.74)0.72
-0.2
+0.02
24 -2C
!>. m. 7: s<-h. 7; Plummer3-«; Dk. 3-2; OZ. 8; Pr. 1
I'll.
100.4
0.730.74
-fO.'.l
-0.01
20 I-.'
Dnlx-rrk 1 0; DemlmwiUO; Jed. 7; OZ. 3; Halls
'.'•_• 1
92.7
0.810.78
-0.3
+0.03
!•
Scblaparelll 0; OZ. 3
• - • _' !
86.4
H 7.-,,. S]
+0.9
-0.06
I'.t 17
Hall B; Jedrzrj,-» in rt; Doberck 2 0; ft. 6
188LS8
M ,
79.9
+ 1.0
±0.00
Jed. 4; Doberck :.: '»!. I] Hall :: ; s..|,. ii; PriU-hett 2
7.V I
74.4
0 90 o s~
+ 0.7
+ 0.03
21
HlKounlan 1 ; Hall 4: Knglcmann A; Sch. 6; Jed. 4
69.3
0.96)0.90 1 +0..'>
+0.06
16
Knglemann )1; Sehlapan-lll <>; Hall 4
,,•,.-.,-..
+0.04
Per.3; Big. s «; Sch. - 11.5; En.4; 8.&8.3-0
1.11
+ 1.7
+0.16
11
Seabroke 2; Kchlaparelll 5; Englemann 4
1.00
-0.6
+0.07
18-17
Tarrant 4; s. \ s. I'-l ; Hall 4; Jed. 3; Knglemann 5
1 02
1.IMI
-1.9
+0.02
1'.. D
Hall 4; Srhlaparelll 11 : S. & S. 4-1
I.:. 1
1 "7
1.02
-1.1
+0.05
P.I li
Hall 4 : Smith 30; Schlaparelll 0; OZ. 2; Maw 1
!ss '•_•_'
I'-' 1
I'.'.-.
L10
1 04
-0.4
+0.06
.'11 2'.i
Sea. 4; Ix-av.3; 111.5; OZ.2; Maw 3; Sch. 12: Gl. '.' "
! v" _•-
1.02
-1.7
-0.04
ir. n
Srhlaparelli »-7; ComMork 2; Hall 4
•V4 1
: ic.i
1 "7
-1.1
+0.02
Flint 5-4; Schlaparelll 0-10; Hall 6; Blgourdan 8
111
; < •
-0.6
+ 0.02
Maw 8; Knott 2-3; Schiaparelll 11 ; Blgourdan «; Jo. 8
'- _•:
:•: l
:•: i
: i>«;
l.lo
-0.04
18
Coan*tock2; Maw 8; Schlaparelll 13
L894J
14,0
: If,
1.11
-0.6
Kb. 1; H.C.W. 8; Com. S; Sch. 13; Maw 4; Big. 6-4
is ,-. _•:,
20.7
21.3
; :;
1.12
-0.6
in.i
10
I>ewl* Ss Cooirtock Si DftTidMNi 1 ; 804 4
94 23121.
A more critical investigation of these problems will commend itself to the
attention of astronomers; the best results will depend upon the reduction of
exact observations by the refined methods of analysis. In the present state of
micrometrical measurement, a very refined treatment is seriously embarrassed
by the errors of observation; but the methods of physical Astronomy ought
eventually to enable us to improve the theory of the motion of the system,
which is here taken as undisturbed.
The following is a short ephemeris for the use of observers:
t Oc PC
1896.25 IS^O l"l3
1897.25 14.8 1.13
1898.25 11.6 1.13
t 6c PC
1899.25 8^4 l"l3
1900.25 5.3 1.14
60
Po
£3121.
a = 9h 12m.l ; 8 = +29° 0'.
7.2, white ; 7.5, yellowish.
Discovered by William Struve in 1831
OBSERVATIONS.
n t e<>
Po
n
O
H
O
n
1832.31
20.0
0.85
3
Struve
1868.30
27.6
0.81
2
O. Struve
1840.31
246.5
0.40 ±
3-1
0. Struve
1869.31
26.1
0.88
1
0. Struve
1844.28
193.5
0.33
2-1
O. Struve
1870.33
206.9
0.65
2
Dune'r
1846.29
27.6
0.55
1
0. Struve
1870.44
210.4
0.5 ±
1
Gledhill
1847.34
214.2
0.54
1
O. Struve
1871.20
212.7
0.5 ±
1
Gledhill
1871.27
208.2
0.75
3
Dune'r
1848.25
33.0
0.53
1
O. Struve
1871.30
35.3
0.79
2
O. Struve
1849.32
43.3
0.48
1
0. Struve
1871.44
211.0
0.57
5
Dembowski
1850.30
228.6
0.42
1
0. Struve
1872.09
209.3
0.68
1
Dune'r
1872.31
36.4
0.68
1
0. Struve
1851.26
59.7
0.33
1
0. Struve
1873.69
214.2
obi.
8
Dembowski
1861.29
Double vers le Norde 1
O. Struve
1873.70
214.5
0.5 ±
1
Gledhill
1861.30
8.9
0.67
1
O. Struve
1874.24
220.
<0.3
2
Dune'r
1863.11
194.8
0.7
1
Dembowski
1874.28
46.7
0.53
2
0. Strove
1864.30
13.0
0.71
1
O. Struve
1875.20
225.
0.2 ±
1
Dune'r
1865.77
206.8
0.80
2
Englemann
1875.29
1875.29
250.1
65.2
obi.
0.30
1
4
O. Struve
Schiaparelli
1867.65
201.3
0.70
5
Dembowski
1875.31
251.9
ovale
2
Dembowski
£8121,
1
«.
P.
»
1
0.
/••
it
A
f
f
1877.25
|s ;,,
nlilong
1
.. Strmi-
1885.30
215.8
0.4 ±
3
Scliiapari-lli
1878.21
185.2
0.25 ±
1
Hurtili.iln
1886.33
221 2
0.27
4
KiiKleiiiunn
1879.21
193.0
0.40
•
Hiirnhain
1887.27
250.4
0.22 ±
9
S-liia|iar«-lli
1879.38
1 8(1.8
0.43
1
U. Struve
1888.27
2841.3
0.22 ±
7
St-hiapart'lli
1879.57
200.4
0.43
5
S. hiapan-lli
1889.30
132.3
0.23 ±
7
Sc-hiaparelli
1880.26
200.3
o ,-,
3
Hall
1890.29
152.9
0.27 ±
4
Srhia|wiivlh
1880.31
199.8
OJQ
1
Kurnham
1891.26
163.3
0.35
1
Hall
1881.20
198.0
0.61
1
O. Strove
1891.32
166.7
0.33 ±
•2
Scliiaparflli
1881.34
205.3
0.46
•t
Schiaparelli
1892.26
175.3
0.41 ±
7
Sfhiapaivlli
1882.25
194.8
0.31
4
Kh^l.-iiKUin
18<«.25
182.3
0.47
7-2
Scliia]iart'lli
1882.31
205.8
0.45
4
St-hiaparelli
1893.25
185.9
0.44
1
<'(llUSt<K'k
1882.34
l»0o.2
0.53
1
O. Struve
1894.18
185.9
0.49
1
Wilson
1883.22
221 2
0.39
6
Kll^lrlliallll
1894.21
186.6
0.58
3
r.i^niirilan
1 wt.28
213.8
0.52
3
Schia|>arelli
1894.24
183.3
0.45
3
< '^Mistook
LSI
215.7
0.45
3
Hall
1894.25
186.3
0.48 ±
5
Schiapiin-lli
1^1.27
218.9
0.42
1
O. Struve
1895.23
190.5
iu;.-,
3
Ix>wia
1-^1.39
222.7
0.38
4
Schiaparelli
1895.26
8.8
0.50
3
1 '-'lll-stlK-k
1884.61
225.0
M ,.
4
Englemaiin
1895.31
12.6
0.55
2
>,,.
WILLIAM SnirvK rated the inngnitudeH of the cnm|>onent8 of this pair at
7.5 and 7.8* respectively. Keeent observations with the 26-ineh refractor of the
Ix-ander McCormick Obsen'atory of the University of Virginia convince the
writer that the brightness of the components has IK-CM over-estimated by at
least a whole magnitude. The star is close and very faint, and the natural
difficulty of the object will doubtless account for the rather large discordances
in some of the ul>-cr\ •.•itimis.
A- l.".r_'l h:i- I.CCM ..l.-cr\.-(l !'..i- MI:IM\ \.ar-. :unl tin- p:iii- rcv.ilvc- \\itli
great rapidity, several orbit > liavi- KCCM dftcrinined by previous !M\ estimators.
The following is Ixlicvcd to be a complete list of the elements hitherto pub-
lished:
p
r
•
fl
a
I
n
Authority
fclULU
39.18
40.62
37.08
34.642
1850.0
1850.0
1ML'.78
1878.52
0.3471
0.26
,, ,,,*,;
,.,,„,
0.715
0.71
"•;;•_•:,
I'.t.'.M
23.5
16.0
•Jl v-,
:.-j i
64.11
74.25
::. i ;
143.3
141.6
149.5
!_••> i:.
Fritache, 1866
Fritache, Jsiw;
ih.u-r.-k. !«*::
Celoria, 1887
( Bulletin del'Acad.de
( 8t IVtentmurg, t. X
A.N.2i:.<;
A. N. 2808
M !»••<•< m I Journal, S40.
96
23121.
From an investigation of all the observations, I find the following elements:
P = 34.00 years
T = 1878.30
e = 0.330
a = 0".6692
ft = 28°.2o
I = 75°.0<)
A = 127°.52
n = + 10°.5883
Apparent orbit:
Length of major axis = 1".318
Length of minor axis = 0".349
Angle of major axis = 27°.4
Angle of periastron = 189°.(>
Distance of star from center = 0".142
COMPARISON OF COMPUTED WITH OBSERVED PLACES.
t
6°
fcr
Po
PC
Bo — Oc
Po—Pc
' n
Observers
1832.31
20?0
0
22.3
0.85
0.79
o
- 2.3
+ 0.08
3
W. Struve
1840.31
66.5
47.3
0.40 ±
0.35
+ 19.2
+ 0.05
3-1
O. Struve
1844.28
193.5
189.8
0.33
0.29
+ 3.7
+0.04
2-1
O. Struve
1840.29
207.6
205.2
0.55
0.48
+ 2.4
+0.07
1
O. Struve
1847.34
214.2
210.1
0.54
0.52
+ 4.1
+ 0.02
1
0. Struve
1848.25
213.0
214.1
0.53
0.52
- 1.1
+0.01
1
0. Struve
1849.32
223.3
218.8
0.48
0.50
+ 5.5
-0.02
1
0. Struve
1850.30
228.6
223.9
0.42
0.45
+ 4.7
-0.03
1
0. Struve
1851.26
239.7
230.1
0.33
0.39
+ 9.6
-0.06
1
0. Stfuve
1861.26
8.9
9.9
0.67
0.58
- 1.0
-1.0.09
1
0. Struve
1863.11
14.8
14.6
0.7
0.66
+ 0.2
+0.04
1
Dembowski
1864.30
13.0
18.1
0.71
0.73
- 5.1
-0.02
1
0. Struve
1865.77
26.8
21.3
0.80
0.78
+ 5.5
+ 0.02
2
Englemaim
1867.65
21.3
24.8
0.70
0.79
- 3.5
-0.09
5
Dembowski
1868.30
27.6
26.2
0.81
0.79
+ 1.4
+ 0.02
2
0. Struve
1869.31
26.1
28.2
0.88
0.76
- 2.1
+ 0.12
1
O. Struve
1870.38
28.6
30.6
0.57
0.71
- 2.0
-0.14
3
DuneV, 2 ; Gledliill 1
1871.30
31.8
32.8
0.65
0.65
- 1.0
0.00
11
Gl. 1; Du. 3; O2. 2; Dem. 5
1872.20
36.4
35.6
0.68
0.58
+ 0.8
+0.10
1-2
02. 1 ; Duner 0-1
1873.70
34.3
42.8
0.5 ±
0.42
- 8.5
+0.08
9-1
Dembowski 8-0 ; Gledhill 1
1874.28
46.7
46.7
0.53
0.36
0.0
+0.17
2
0. Struve
1875.27
63.0
63.0
0.25
0.22
0.0
+0.03
8-5
Du. 1 ; 02. 1 ; Sch. 4 ; Dem. 2
1878.21
185.2
188.4
0.25
0.28
- 3.2
-0.03
1
Bnrnham
1879.57
200.4
200.2
0.43
0.41
4- 0.2
+0.02
5
Sc.hiaparelli
1880.28
200.0
205.1
0.43
0.48
- 5.1
-0.05
4
Hall 3 ; Ituruliam 1
1881.34
205.3
210.1
0.46
0.52
- 4.8
-0.06
2
Schiaparelli
1882.28
205.8
214.1
0.45
0.52
- 8.3
-0.07
4
Schiaparelli
1883.27
221.2
218.3
0.45
0.50
+ 2.9
-0.05
6-12
Kn. (i; Sch. 0-3; Hall 0-3
1884.39
222.7
224.5
0.38
0.44
- 1.8
-0.06
4
Schiaparelli
1885.30
215.8
230.5
0.4 ±
0.39
-14.7
+0.01
3
Schiaparelli
1886.33
221.2
239.9
0.27
0.32
-17.7
-0.05
4
Englemann
1887.27
250.4
L'.-,L'..-,
0.22
0.27
- 2.1
-0.05
9
Schiaparelli
1888.27
286.3
272.6
0.22 ±
0.22
+13.7
0.00
7
Schiaparelli
1889.30
312.3
299.7
0.23 ±
0.21
+ 12.6
+0.02
7
Schiaparelli
1890.29
332.9
323.5
0.27 ±
0.24
+ 8.4
+0.03
4
Schiaparelli
1891.29
343.3
340.8
0.34
0.30
+ 4.2
+0.04
6
Hall 4; Schiaparelli 2
1892.26
355.3
354.0
0.41 ±
0.37
+ 1.3
+0.04
7
Schiaparelli
1893.25
2.3
359.7
0.47
0.43
+ 2.6
+0.04
7-2
Schiaparelli
1894.22
5.2
5.0
0.48
0.50
+ 0.2
-0.02
9
Wilson 1 ; Comstock 3 ; Sch. 5
1895.29
10.7
9.8
0.53
0.58
+ 0.9
(M>r.
5
Sec 1' : Cdinstock ."
1847.
23121
Scat*.
w I.KOX1H = ^ 1 «»l
Some of the observations are vitiated l>\ sensible systematic errors, so that
occasionally <>ui l>< -i <.l>-.r\rrs diller by so much as 12°; and in succeeding
n the angles are made to retrograde where they ought to be steadily
ad \ancing. Under the-e rimim-taticcs the residuals may IK? considered small,
and the eleinei. satisfactory for M close and dillicult a star. In following
ilii- star, observer- -Ixmld take every precaution against systematic error, since
the orbit is highly inclined, and a small error in angle greatly affects the dis-
tance. Good <>!,-, r\ at ions arc essential for any further improvement of the
elements :
ElMIKMKKIM.
( Or ?' t if fl
1899.30 20°7 0.77
1900.30 22.7 0.79
Since the companion is now approaching its maximum distance, the star
will l>e relatively easy for a numl>cr of years.
e
i
1806.30
13.5
0.64
1897.30
16.2
0.69
ISM.S ;,.
18.5
0.74
LEONIS = 21356.
= 9" 23-.1
«, yellow
S = +0» 30'.
7, yellow.
by Sir William llrnrhrl, February X, 17X2.
OBWKKVATIOXB.
(
e.
f»
•
i > .,-.,•.
(
0.
ft
n
OlMrrvrni
•
i
•
9
_S6
iin.'.i
—
1
Hersclx-l
1841.18
354.5
—
1
I>;iwe§
09
130.9
^m
•2
-> lifl
IM1JB
194.0
0.3
1
M feller
18SSJ1
153.9
0.97
5
Strove
1XILV.M
184SJ1
MM
MS
1
4
Mftdler
< ». Strove
188&M
146.5
w»lg» ihnml
1
MtTM-hi-l
IM-.'.:;:;
cillfurli
1
M&.11.T
in-: I
0.51
3
Strove
IM
i-infai li.
ruti'l
Her
1 Tl'.s
0.45
3
Strove
1843.30
811
0.37
2
O. Struvi-
LT8J
0.3 ±
3-1
Strove
1844.29
32'
0 I-
3
O. Strove
1836.28
.:, ±
3-2
Strove
1844.32
337."
...:;•.-
4
M fuller
^
3
(). Strove
1845.31
321.1
0.44
3
O. Strove
ITU
—
1
Midler
184'
326.9
11
Midler
1846.30
322.9
" i:.
2
O. Strove
IM
•ji: .-.
I
rnvc
1840
—
_
DOlka
1847.28
337.0
n:::
3
Midler
I*ni::i
—
_
\\ Slruve
18-17.33
328.8
• •
O. Strove
98
w LEONIS = 2 1356.
t
00
Po
n
Observers
t
0.
Po
n
Observers
O
H
0
If
1848.32
332.1
0.43
4
0. Struve
1870.24
44.4
0.25 ±
6-4
Peirce
1848.35
346.8
0.38
1
Madler
1870.28
53.6
0.58
2
0. Struve
1849.32
331.8
0.43
3
O. Struve
1870.30
37.9
0.27 ±
2
1 hme'r
1850.63
335.8
0.49
3
0. Struve
1871.16
52.6
cuneo
3
Dembowski
1871.30
56.7
0.57
3
0. Struve
1851.23
342.6
0.35
9
Madler
1871.31
42.7
0.3 ±
1
Duner
1852.30
350.0
0.47
4
Madler
1872.18
66.3
0.48
2
Wilson
1852.6G
339.1
0.46
3
O. Struve
1872.31
58.8
0.52
2
0. Struve
1853.18
343.3
0.45 ±
2
Jacob
1853.27
1853.96
346.3
350.0
0.35
0.4 ±
7-6
2
Madler
Jacob
1873.23
1873.29
1873.58
56.2
57.0
62.0
0.4 ±
contatto
2
1
5
W. & S.
Gledhill
Dembowski
1854.23
346.2
0.55
2
Dawes
1873.96
63.6
0.59
3
0. Struve
1854.28
348.3
0.53
10
Madler
1875.25
64.6
0.46
5
Dembowski
1855.27
obi?
—
2
Madler
1875.26
62.7
0.49
7
Schiaparelli
1855.32
348.7
0.47
2
O. Struve
1875.31
66.8
0.43
5
Duner
1855.34
6.2
—
1
Winnecke
1875.32
66.4
0.59
3
O. Struve
1856.20
obi?
—
1
Madler
1876.16
69.4
0.44
2
Dembowski
1856.42
1.0
0.36
10-7
Secchi
1876.24
52.7
8
Doberck
1857.28
358.1
0.52
1
0. Struve
1876.27
73.5
0.55 ±
2
W. & S.
1857.31
obi.?
—
1
Madler
1876.29
65.6
0.57
2
O. Struve
1857.54
4.3
0.43 ±
3
Jacob
1877.21
77.2
0.88
1
Copeland
1858.28
16.2 ?
—
1
Madler
1877.21
71.2
0.54
5-1
Plummer
1859.25
16.7
0.35
4-3
Miidler
1877.21
73.0
0.51
8-1
Doberck
1859.30
6.7
0.60
2
0. Struve
1877.27
70.7
0.47
7
Schiaparelli
1877.28
71.6
0.54
2
O. Struve
1860.28
9.2
—
—
Winnecke
1877.36
76.6
0.41
2
Dembowski
1860.28
10.2
0.62
2
0. Struve
1860.33
19.1
0.25
1
Madler
1878.11
70.3
0.63
2
Burnham
1878i26
80.3
0.50
1
Doberck
1861.28
11.9
0.56
2
0. Struve
1878.28
74.7
0.44
5
Dembowski
1862.32
18.6
elong.
2
Madler
1878.63
77.7
0.60
3
O. Struve
1878.95
74.4
0.41
6
Hall
1864.30
29.2
0.52
1
O. Struve
1864.89
24.
cuneo
4
Dembowski
1879.31
76.6
0.55
7
Schiaparelli
1865.67
23.0
0.50
8
Englemann
1879.78
79.8
0.51
4
Burnham
1866.30
32.9
0.3
1
Secchi
1880.23
79.7
1
Bigourdaa
1867.08
1867.08
109.4
125.7
elong.
elong.
1
1
Winlock
Searle
1880.2(i
1880.26
95.2
81.3
obi.
0.46
4
6
Jedrzejewicz
Hall
1867.32
29.3
elong.
1
Winlock
1867.87
Kreisrund
1
Vogel
1881.10
81.0
0.61
2
Bigourdan
1868.21
1868.63
15.6
44.3
elong.
0.55
1
8
Peirce
O. Strnvr
1881.24
1881.26
82.3
98.7
0.50
obi.
5-2
2
1 )oberck
Jedrzejewicz
1881.28
83.7
0.68
2
0. Struve
1869.13
317.2
elong.
1
Peirce
1881.31
84.3
0.48
4
Hall
1869.26
36.7
elong.
1
Peirce
1881.33
84.4
0.58
5
Schiaparelli
I.KONIS = .11
1
A.
ft
•
, , , .. .
(
fl.
ft
ii
Otwerrw
0
9
O
9
1882.12
77.3
1
lUwrck
1888.21
97.4
0.68
3
Tarnuit
1882.12
80.5
—
1
.u nl
1888.26
91.6
—
3
Smith
1882.23
0.56
7
Englemaiiii
1888.27
98.5
0.68
6
Schiaparelli
1882.27
83.3
0.66
:<
Dob
1888.29
98.3
0.66
5
Hall
1882.30
84.1
0.49
i
H:ill
1888.33
94.9
0.87
2
O. Strove
I^-J.34
86.7
0.61
••
ruve
1888.57
95.8
0.71
7
Lv.
1882.36
90.0
0.55
4
S hiaparelli
1889.19
94.1
0.70
1
HodKM
1883.24
85.8
6
KMtflriiiaiin
1889.29
99.8
0.67
5
Hall
1883.31
90.5
6
S. Inu | LI n-11 i
1889.32
100.2
0.65
'.I
Schiapan'lli
1883.34
90.9
0.62
3
Hall
1890.27
101.8
0.68
2
Contstock
1884.18
90.6
0.55
£
1'ermtin
1890.31
101.2
'"'•I
I
Hall
1884.23
91.4
0.66
4
Knglemann
1890.31
101.6
0.68
4
Srhiaparclli
1884.26
1884.30
87.6
91.3
0.71
0.58
5
O. Strove
Schiaparelli
1891.21
1891.28
102.1
101.2
0.76
0.75
2
5
I'.ivliiiml.in
Hall
93.3
0.55
4
Hall
: -U
90.6
10
Bitfounlan
1891.31
103.9
0.66
5
Schiaparelli
: .»
85.9
l.o±
3-2
Sea. & Sin.
1892.25
102.4
0.77
3
Maw
1HXT..17
•„.,.
93.3
0.72
3
1
Knulomann
Doberck
1892.26
1892.27
104.'.)
104.5
0.72
0.87
7
5
Lv. & Col.
93.7
0.58
4
Schia|>arelli
1893.25
101.5
0.61
1
Conifttork
93.9
0.69
2
Tarnuit
1893.28
105.7
0.70
9
Schiaparelli
1.00 ±
1
Smith
1894.22
104.5
1 ..'to
1
Hi munl-in
1885.72
0.70
2
I'errotin
1894.23
KM;. 5
0.67
3
Comstock
1886.24
90.1
1.19
2-1
Sea. & Sm.
1894.25
103.3
0.74
2
H.C. Wilson
1886.32
92.2
0.73
6
Kngleniann
1894.25
100.7
0.75
8
Schiapaiflli
1887.26
95.0
0.62
9
Schiaparelli
1894.88
287.4
0.94
3
llanianl
1887.30
95.6
0.53
4
Hall
1895.24
100.1
0.67
3
Comstock
1^7.37
94.0
—
1
Smith
1895.28
I'M. !
0.83
2
Bei
At tin- tiiiu- of ili-<-MV»-rv Sn: Wii.i.i AM I Ii i:-< in.i. cBttmatcd the jmsition-
*to IK- l»i \\i-cii '.!."» and KK) , hut later in the year found by measurement
that tin- angle was IIO'.O. The pair was noon found to IK- in slow orbital
motion, and in 1801 HIIXIIM. «-onrlnd«-d that -inn- ITS'J the ehanjje in angle
hn»l amounted to •\-WFB8ftmA that tin- di-taner had -cii-il>ly im-n-a-i-d. When
the star wax thus recognized as binary, it naturally claimed the attention of
the prineipal double-star observers, and accordingly nnee the time of Srut'VK,
a long list of measures has been secured. lint while the closeness of the com-
panion in most part* of the apparent ellipse has made the pair a classic test-
object for the dividing ]M>wcr of small telescopes, it has, on the other hand,
rendered micrometrical measurement extremely difficult, and some of the observa-
tions are therefore far from satisfactory. In spite of the fact that the measures
AUr
3311.
100
co LEONIS = .£1356.
are sometimes difficult to reconcile, the angles and distances of the best ob-
servers, when properly combined, in conjunction with the important principle
of the preservation of areas, enable us to fix the apparent ellipse with a rela-
tively high degree of precision, and the resulting elements are found to be
incapable of any large variation. The orbit is based chiefly upon the observa-
tions of HERSCHEL, STRUVE, O. STRUVE, DAWES, DEMBOWSKI, BURNHAM, HALL,
SCIIIAPARELLI, and the measures which the writer recently secured at the
McCormick Observatory in Virginia. The elements of co Leonis are :
Apparent orbit:
P = 116.20 years
Q = 146°.70
T = 1842.10
i = 63°.47
e = 0.537
X = 124°.22
a = 0".88241
n = +3°. 0981
Length of major axis
= 1".576
Length of minor axis
= 0".738
Angle of major axis
= 141°.l
Angle of periastron
= 293°.4
Distance of star from
centre = 0".317
Several astronomers have previously investigated the orbit of this star;
the following table gives the elements hitherto published:
p
T
e
a
Q
i
i
Authority
Source
82.533
1849.76
0.6434
0.857
135.2
46.57
185.45
MMler, 1841
Dorp. Obs.IX, I'.is
117.577
1843.408
0.6256
0.8505
159.83
50.64
120.45
Mildler, 1840
Fixt. Syst. I, p.250
133.35
1846.44
0.3605
0.703
111.85
57.23
217.37
Klinkerf.lS.-)6
A.N. 990
227.77
1841.40
0.7225
1.307
169.2
60.22
84.17
Klinkerf. 1856
A.N.990
142.41
1843.39
0.6286
1.092
162.22
54.42
107.15
Klinkerf. 1858
A.N. 1127
136.4
1844.2
0.62
1.05
160.5
52.4
113.4
Klinkerfues
Theor. Astron. p. 395
107.62
1842.77
0.5028
-
151.57
65.37
122.9
Doberck, 1876
A.N. 2078
110.82
1841.81
0.536
0.890
148.77
64.08
121.07
Doberck, 1876
A.N. 2095
114.55
1841.57
0.5510
0.85
149.25
64.08
122.3
Doberck
115.30
1841.99
0.5379
0.864
147.1
64.15
122.9
Hall, 1892
A. J. 269
115.87
1842.16
0.533
0.8753
145.9
63.05
125.32
See, 1894
A.N. 3311
COMPARISON OF COMPUTED WITH OBSKKVED PLACES.
t
e.
0.
Po
PC
ft.— &
P°—P'
n
Observers
1782.86
110.9
1 1 '_'. 1
f
0.89
O
- 1.2
i
1
Herschel
1803.09
130.9
130.3
—
1.08
+ 0.6
—
2
Herschel
1825.21
153.9
150.4
0.97
0.81
+ 3.5
+0.16
5
Struve
1832.25
163.4
164.9
0.51
0.52
- 1.5
-0.01
3
Struve
1833.29
172.8
168.8
0.45
0.47
+ 4.0
-0.02
3
Struve
1835.33
178.3
179.9
0.3 ±
0.35
- 1.6
-0.05
3-1
Struve
1836.28
176.8
187.8
0.35
0.30
-11.0
+0.05
7-2
2. 3-2; O2. 3-0 ; Miidler 1-0
1840.29
247.5
263.8
0.3
0.21
-16.3
+0.09
2
O. Strove
1841.26
274.2
281.6
0.3
0.24
- 7.4
+0.06
2-1
Dawes 1-0; Miidler 1
1842.31
302.3
295.8
0.3
0.28
+ 6.5
+0.02
4
O. Struve
• HI
1.03
270
1842
Scalo.
I.KOXIS = .i 1356.
101
1
f.
«.
*
A
,. ,
*-*
II
« ht..,_M.__
* MnM»nrw
1 » 1.1.30
316.8
0.37
,, : .
•M..
4-0.04
2
O. Struvii
iM».:il
320.9
0.48
4- 8.6
4-0.10
3
(». Struve
1M.1.31
321.1
.-.17 -.1
• • II
" I1.'
4- 3.2
-•-0.02
3
O. Struve
isu;.3o
322.9
0.45
4- 0.3
0.00
2
O. Struve
lsi;.31
32X.8
» I-N
4- 2.0
+0.05
•>
o. striivo
iMx.32
332.1
0.50
4- 1.6
—0.07
4
O. Struve
IM'J.32
331.8
0.83
— 2.2
-0.09
3
O. Stmvc
1 vio.63
335.8
M:,;
- 2l4
-0.04
3
(). Struve
IV. 1. 23
342.6
.:|" 1
.. .-,
4- 2.6
-0.18
9
M .idler
J.48
344.fi
:;il 1
0.54
4- 0.4
-0.08
7
M;i.ll,.| 1 ; U. Struve 3
1 W».47
;< .
847.0
0.45
0.54
- 0.5
-0.09
11-10
Jncol>2; Mtullcr 7 (i ; .luro|( 2
lv.lt. 26
347.2
::»:• 1
0.54
0.54
- 2.2
0.00
12
Daw,.*'.'; Mii.ll.-r 10
348.7
IB 1 !
0.47
0.53
- 4.4
-0.06
2
O. Struve
0 1.
1.0
0.36
0.53
4- 4.7
-0.17
10-7
Se<-chi
ivir.ii
2.4
359.5
0.47
0.52
4- 2.9
-0.05
4
O. Stnivc 1 ; Jiu-oh 3
11.7
0.51
4- 6.1
+0.09
M toiler 4 3; O. Ktruvr 2
14.6
9.2
0.62
0.50
+ 6.4
+0.12
3
O. Struve 2; Mn.ll.-r 1
1 1 .;•
12.8
&M
- 0.9
+0.06
2
O. Struve
•ji "
•-M.o
0.52
0.48
- 1.0
+0.04
4-1
U. Struve 1 ; I)eiiihow>iki 4-0
88.1
0.48
- 6.1
+0.02
8
Kni;li-iiiaiiii
31.7
0.30
0.48
+ 1.2
-0.18
1
8*»hi
1868.63
40.7
M 1-
4- 3.6
+0.07
3
O. Struve
47.1
0.68
0.49
+ 0.2
+0.18
9-5
lVirce5-l; O. Struve 2; Dun. i '_•
: 90
.11 (i
0.67
0.19
- 1.3
+0.08
7-4
DemtxiWMki 3-0; U2. 3; I>u. 1
L87SJ1
64.7
0.89
0.50
+ 4.1
+0.02
2
O. Struve
187
59.2
".vj
0.51
4- 1.1
+0.01
11-4
W. & S. 2-0; Gl. 1 ; Dem. 5-0 ;
Ifl
.'.I 7
(4J
0 i.;
I'.VJ
- 0.2
-0.06
17
Dem. 5; St-h. 7; I hi. 5 [ttl'.3
187(
71 1
'-.7 7
.>.:..;
4- 3.7
-0.04
4
Dem. 2 ; W. & S. 2 [Cop. 0-1
71.3
oue
0.55
4- 1.6
+0.01
17-12
1*1.5-1; Dk.3-1; Sch. 7; Dem. 2;
1878.40
71'.'
74.8
0.63
0.56
+ 0.1
+0.07
14
ft. 2; Dk. 1 ; Drm. 5; Hall 6
\-79M
78.2
77.7
0.53
0.58
4- 0.5
-0.05
11
S.-liiaj>sirelli 7 ; Burnliain 4
1880.24
80.2
79.7
0.46
0.59
4- 0.5
-0.13
7-6
Bigounlaii 1-0; Hall 6
1881.24
x :,,
82.1
0.54
0.60
+ 0.9
-0.06
16-13
Big. 2; Dk. 5-2; HI. 4 ; Sc-h. 5
1882.29
84.4
84.7
M.-.,;
0.62
- 0.3
-0.06
18
En. 7; Dk. 3 ; HI. 4; Sdi. 4
-
•4
n i
0.63
0.63
+ 2.1
0.00
15
En. 6 ; St-h. 6 ; III. 3 [1% 10-0
1881 .7
91A
89.2
0.88
...•.:.
4- 2.2
-0.07
25-15
Per. 2; En. 4 ; Sch. 5; Hall 4;
1885..-17
.,._..,
90.9
0.66
0.68
4- 2.0
0.00
9-8
Dk. 1-0 ; Sch. 4 ; Tar. 2 ; I'cr. 2
18*'
93.3
O.M
- 1.1
+ 0.0.1
6
Englemann
1887.:!
M ••
B6J
".-,7
0.70
- 0.3
-0.13
14-13
S-li. «.»; Hall 4; Smith 1-0
188835
M i
•,.-.•.,
0.67
0.72
-1- 1.2
-0.05
M
Tarrant 3 ; Srh. 6 ; Hall 5
1889.30
100.0
08J
DM
+ 1.4
-0.07
11
Hall 5; S.-hiaI,ar<-lli '.»
u
101.6
100.3
0.67
+ 1.2
-0.08
10
Hall 4; Comst.H-k '.' : SI.. 4
' •_•;
1"1M
101.8
0.77
4- 0.6
-0.06
U
Hall .1 ; Hi-..ur.lan 1' ; S-li. 5
L08J
0.79
0.79
+ 0.6
L8
M»W:J; s.'h. ;: i.v. & c..l. 6
1ft'
10 g
104.8
0.74
- 1.2
-0.06
K>
Comstoc-k 1-0; Kfhia|Ntiflli '.' .1
L08.6
in.',;;
o.Sl
- 0.7
-O.ol
17 i:;
Big. 1-0; Com. 3-0; H.C.W. 2;
:-
.,„•. ,
in; :.
II.SI
- 1.4
-0.01
2
See [Sch. 8; liar. 3
The elements given above confirm the substantial accuracy of the orbit
found by HALL, and represent the observations as a whole remarkably well.
The changes which future observations will introduce arc likely to be very
small.
102
UKSAE MAJOKIS = 0,2208.
The following is an ephemeris for the next five years:
EPHEMERIS.
t
ft
PC
O
ft
1896.28
108.7
0.85
1897.28
110.0
0.87
1898.28
111.2
0.88
1899.28
1900.28
112 A
113.5
PC
0.90
0.91
It is to be noted that the distance is steadily increasing, and that for
many years the pair will be relatively easy. A number of observers of late
years have sensibly underestimated the distance. Owing to the closeness of
ID Leonin and its slow orbital motion, one would naturally think that this bril-
liant system probably has a small mass, and is comparatively near us in
space; for if the mass be large, the slow motion of so close a system would indi-
cate that it is very remote, and the resulting brightness of the components
would be very great. The eccentricity of this orbit is so well determined that
the value given above can hardly be in error by so much as 0.01, and a cor-
rection of half this amount does not seem probable.
•jlJKSAE MAJORIS= 0v2
a = 9h 45™.3
5.5, yellowish
8 = +54° 33'.
5.5, yellowish.
Discovered by Otto Struve in 1842.
OBSERVATIONS.
t
0,,
Po
n
Observers
t
00
Po
n
Observers
O
t
O
n
•
1842.80
4.2
0.42
1
Madler
1852.39
16.1
0.32
'2
O. Struve
1842.35
8.5
0.52
>2
0. Struve
1852.40
209.8
0.25
4
Madler
1843.37
5.6
0.48
3
Madler
1853.40
16.7
0.34
3
O. Struve
1843.47
188.5
0.39
1
0. Struve
1854.28
25.9
0.4 ±
1
Dawes
1844.26
186.6
0.51
1
O. Struve
1854.37
23.3
0.42
1
0. Struve
1846.01
193.8
0.45
3-2
Mildler
1857.34
30.6
0.3
1
Secchi
1846.37
9.2
0.42
1
0. Struve
1858.41
36.1
0.40
3
0. Struve
1847.41
196.8
0.30
2
Madler
1859.37
43.9
0.33
1
Winnecke
1847.41
12.1
0.36
1
0. Struve
1859.39
8T.8
0.35
2
O. Struve
1848.40
10.4
0.35
2
0. Struve
1861.40
55.0
0.44
1
Winnecke
1850.39
15.0
0.33
2
O. Struve
1861.41
48.5
0.37
2
0. Struve
1851.39
207.2
0.31
4
Madler
1862.39
46.8
0.38
1
0. Struve
1851.40
13.7
0.33
2
O. Struve
1864.43
48.5
0.27
1
O. Struve
9UR8AK MAJoitls = <O _ -
net
(
1XW5.27
1866.42
9.
46.5
48.2
?•
<0^4
0.24
•
1
1
Ml 1 1 ••! 1 •!
'
Knglt'iuann
<truve
I
1882.19
1882.34
9.
139?0
342.0?
P.
<0*2
M
3
1
OlNM-nren
Kngli'iiiann
O. Struve
1869.40
45.0
oblong
•»
Ihliirr
1887.4.')
218.9
0.23
•
Scli i:i pan-Ill
1870.42
xl •
nltlong
«»
Dun.T
1888.43
220.3
cuneiforim-
1
O. Stnivo
1872.41
77.7
0.23
<2
(). Struve
1889.39
214.0
rcrti'loni,'.
1
O. Stnive
1873.44
1873.45
187:147
87.5
,. ,
>-. ;
oblong
1
3
1
Liiulemann
O. Struve
II. P.r.ihns
1892.13
1892.31
1892.58
250.8
6M
single
0.24
0.29
3
1
1
liiirnhaiii
Itigounliui
('•HIlM'N-k
1875.47
115.1
oblong
>2
0. Struve
IV.::-.
339..V. i '.:;<i
1
S-liia pan-Ill
1876.42
54.0
elongated?
1
O. Struve
1894.25
round
1
CouiBtork
1877.43
single
—
1
O. Struve
1894.40
82.7
—
3
Kiguunlan
1879.44
single
—
1
O. Stnive
1895.73
276.2
0.29
8
>••
Although this clotwi ami rapid binary was discovered by OTTO STHUVK,
tin- first observation was secured by MAIJLKK, whose measures supplement
M IM \ i 's work in a very happy manner, and enable us to fix the original posi-
tion of tlu- companion with much precision. For a long time these two astrono-
imi- alum- followed the motion of the system, but in later years it has received
.-innal attmtion from several other obsen-ers. The stars arc nearly equal
in magnitude, and hence a few of the recorded angles require a correction of
180°. The arc already descril>ed amounts to alxnit 270°, and as this covers the
most critical parts of the orbit, most of the elements are defined with the
desired precision. The chief difliculty encountered by observers lies in the
closeness of the coni|>onents, which places them beyond the reach of small, and
»-\. n uf niiMlri-au-M/A'il, ti-lcscopcs. The pair is, however, gradually widening
out, and in a few years will be much more accessible to measurement.
Tlit- following i-U-mriits of this Mar hav<- lx-»-ii published by previous com-
puters:
r
r
•
a
a
i
• 1
Authority
Source
•• . ;
r .
is:; : _•
iss:, ;
•• 1.1
•• •:
l«".i :
It;.-, :
;i r
72.1
I'.MI
Cuey, 1882
Glw., 1892
AJT. 9417
A.N.3119
Using all the available measures, we find the following elements:
P - 97.0 yearn
7 - 1884.0
e mm 0.440
« -0-.3443
Q » 1GO°.3
i = 30°.5
X - 15-.9
»mm -J-.V.7114
UKSAE MAJORIS = O.i'208.
Apparent orbit:
= 0".G9
= 0".53
= 167°.6
Length of major axis
Length of minor axis
Angle of major axis
Angle of periastron = 174°.l
Distance of star from centre = 0".149
It will be seen that this orbit is essentially similar to that found by
GLASEN-APP. The table of computed and observed places shows so satisfactory
an agreement for this close and difficult object that we may regard these ele-
ments as substantially correct, and confidently conclude that such alterations
as future observations may render necessary will be of minor importance.
COMPARISON OF COMPUTED WITH OBSERVED PLACES.
t
&,
Oc
Po
PC
VO PC
Po— PC
n
Observers
1842.32
6.3
o
4.0
0.47
0.48
+ 2.3
-0.01
3
Miidler 1 ; O. Struve 2
1843.42
7.0
5.7
0.43
0.47
+ 1.3
-0.04
4
Miidler 3 ; O. Struve 1
1844.20
6.6
7.0
0.51
0.47
- 0.4
+ 0.04
1
0. Struve
1846.19
11.5
10.1
0.44
0.46
+ 1.4
-0.02
4-3
Miidler 3-2 ; 0. Struve 1
1847.41
14.4
12.0
0.33
0.45
+.2.4
-0.12
3
Miidler 2 ; 0. Struve 1
1848.40
10.4
13.8
0.35
0.45
- 3.4
-0.10
2
0. Struve
1850.39
15.0
17.2
0.33
0.43
- 2.2
-0.10
2
0. Struve
1851.40
20.4
19.1
0.32
0.43
+ 1.3
-0.11
6
Miidler 4 ; 0. Struve 2
1852.40
22.9
20.9
0.29
0.42
+ 2.0
-0.13
6
0. Struve 2; Miidler 4
1853.40
16.7
22.9
0.34
0.41
- 6.2
-0.07
3
0. Struve
1854.32
24.6
24.7
0.41
0.41
- 0.1
±0.00
2
Dawes 1 ; 0. Struve 1
1857.34
30.6
31.3
0.30
0.38
- 0.7
-0.08
1
Secchi
1858.41
36.1
339
0.40
0.37
+ 2.2
+0.03
3
O. Struve
1 859.38
40.8
36.2
0.34
0.36
+ 4.6
-0.02
3
Winnecke 1 ; 0. Struve 2
1861.40
48.5
41.8
0.40
0.34
+ 6.7
+0.06
2^3
Winnecke 0-1 ; 0. Struve 2
1862.39
46.8
44.6
0.38
0.33
+ 2.2
+ 0.05
1
O. Struve
1864.43
48.5
51.2
0.27
0.31
- 2.7
-0.04
1
O; Struve
1866.34
47.4
61.8'
0.32
0.29
-14.4
+ 0.03
2
Englemann 1 ; O. Struve 1
1869.40
45.0
70.0
oblong
0.27
-25.0
—
2
Duner
1870.42
81.5
75.6
oblong
0.26
+ 5.9
—
2
Pune'r
1872.41
77.7
86.4
0.23
0.24
- 8.7
-0.01
.2
O. Struve
1873.46
96.0
92.4
oblong
0.24
+ -3.6
—
4
0. Struve 3 ; H. Bruhns 1
1875.47
115.1
105.1
oblong
0.22
+ 10.0
—
2
0. Struve
1877.43
single
118.9
single
0.21
—
—
1
O. Struve
1879.44
single
134.7
single
0.21
•—
—
1
0. Struve
1882.26
150.5
149.6
'0.20
0.20
+ 0.9
±0.00
4-3
Englemann 3 ; O. Struve 1-0
1887.43
218.9
206.6
0.23
0.19
+ 12.3
0.04
4
Schiaparelli
1888.43
220.3
216.1
cune.
0.19
+ 4.2
—
1
0. Struve
1889.39
214.0
225.2
elong.
0.19
-11.2
—
1
O. Struve
1892.13
250.8
248.3
0.21
0.21
+ 2.5
±0.00
3-2
Burnham
1893.36
249.6
257.1
0.30
0.22
- 7.5
+0.08
1
Schiaparelli
1894.40
262.7
264.0
—
0.23
- 1.3
—
3-0
Bigourdon
1895.73
276.2
271.6
0.25
0.25
+ 4.6
±0.00
3-1
See
Some changes will doubtless be required in all the elements, but the two
elements of chief interest, the period and the eccentricity, will hardly be varied
O.I
9 Ursao Major!* =02208.
o
s, .,:...
lUBSAE MAJORI8 = £ 1523.
106
by more than five years, and ±0.03 rc«|M?ctively. It i* desirable to have the
theory of tlii- -\-inu care fit II \ i-nntiniied, and observers with good tele-cii|M-
will find it worthy of regular ai trillion. Tlie motion is still tolerably rapid.
but is gradually slowing up, as will be seen in the following cphcineris:
( 0. * t 6<
18-> IT 1899.40 288^8
. in ^».l 0.27 I'.MMMO 292.7
189S.I-. 284.6 0.28
f,
t
0.3O
9.
f I'RSAK MAJORIS = j
a = 11" 12-.U ; S = +W°
4, yellow ; 3, yellow lib.
IMMMWrW % Sir H'i/tiiiiH Ilenrhel,
OBNKKVATIONH.
p. H rvi>n (
•
May 2,
6.
1780.
n
< IbMnrrn
0
§
e
*
1781 JT
143.8
4.±
J
ll.-i>,-l,,-l
Iv:.: i |
ISK.'.I
2.06
8-2
llrrsrlirl
180108
97.5
—
-
llerwhel
1833.2:<
18.'«.38
189.8
188.2
1.98
1.69
4
5
I >;i wcs
Struve
1>"l.09
92.6
—
-
Ilenchel
lv;| ||
184.1
1.87
2
Strove
1819.10
284.5
—
2
Struve
1834.50
182.5
2.17
4-1
MiUller
1820.13
276.3
3
Struve
1835.27
176.1
1.93
1
MiUllcr
18.-i5.41
180.2
1.76
5
Strove
1821.78
264.7
1.92
3
Struve
1835.56
175.8
—
4
Madler
I UH
I'll.-.
2.44
6-4
South
183(>.28
171.4
1.92
1
Daww
1 77
8
Struve
1836.28
IS;M;.M
172.7
171.1'
1.94
1.97
7-2
4
Mu.ll.-r
Strove
-7
•_•.•> :
1.71
i
Struve
1837.17
3
Strove
8.01
I
h.-l
160.4
9
Struve
l.f.7
1
7
ht-1
Struve
1888 17
I."'..
1.89
-
Oalle
1830.18
•Jll 1
10±
h«-l
1841
l.V.M'
2. OS
40-3 lob
• . Kaiser
1' 1 1
6-4
:, ,,.,>
2.2,'J
10±
Herschel
1840.40
2.28
6
(X Strove
1831.08
•_'i •!..-.
.86
5
Benel
1840.44
—
2.29
—
W. Strove
1831.23
ML]
J8
ii I
Herarhel
1841.21
148.0
2.40
4-3
I)awtt
1831.34
m i
H
17-4
Dawes
1841.29
150.2
2.44
7-6
Midler
1881.44
203.8
.71
5
Struve
1841.40
147.5
6
O. Strove
1832.16
198.2
—
5
Ilernchcl
1842.24
147.0
2.41
4
Midler
1832.27
196.7
.76
|fl ->
Dawes
1842.27
144.8
2.44
4
Dawes
1832.41
in i
.75
1
Strove
1842.40
147.5
I .1
4
O. Strove
106
UTCSAE MAJOKIS = .11523.
t
60
Po
n
Observers
t
60
Po
n
Observers
O
H
0
tl
1843.28
142.2
2.48
7
Dawes
1854.35
116.3
2.90
15
M 'idler
1843.38
143.7
2.37
4
Madler
1854.36
115.9
2.96
3
1 )awes
1843.48
141.9
2.71
9
Schluter
1854.37
115.6
3.46
1
Luther
1854.38
115.9
2.90
4
0. Stnivc,
1844.34
140.4
2.45
3
0. Struve
1854.51
116.6
3.06
5
Dembowski
1844.34
141.0
2.60
11-10
Madler
1844.36
141.0
2.47
_
Liapunow
1855.09
1166
—
12
Powell
1844.36
144.5
2.65
_
Dollen
1855.15
115.6
3.23
7
Dembowski
1855.29
114.3
2.96
1
Secchi
1845.46
138.1
2.51
2
O. Struve
1855.33
114.1
2.98
1
Winnccke
1845.82
135.8
3.11
2
Jacob
1855.44
115.7
2.87
2
Madler
1855.44
115.2
2.85
3
O. Struve
1846.37
137.2
2.56
4
O. Struve
1856.05
114.2
6
Powell
1847.30
131.6
2.58
1
Dawes
1856.18
111.9
3.12
3
Jacob
1847.38
132.0
2.71
10
Madler
1856.26
113.9
3.13
4
Secchi
1847.41
133.2
2.61
3
0. Struve
1856.33
114.1
2.99
3
Winneeke
1848.13
129.5
2.70
1
Dawes
1856.34
112.3
3.15
7
Dembowski
1848.19
129.3
2.94
3
Dawes
1856.42
112.7
2.98
13
Madler
1848.31
129.7
2.71
4
Madler
1856.82
110.9
2.99
2
Jacob
1848.41
130.0
2.66
5
0. Struve
1857.36
109.7
3.11
2
Secchi
1848.45
129.1
2.90
2
£-,?• Bond
1857.43
109.6
2.74
8
Miidler
1849.30
126.6
3.01
5
Dawes
1857.46
110.2
2.97
3
O. Struve
1849.37
127.6
2.78
4
O. Struve
1858.00
108.1
2.90
4
Jacob
1850.01
127.0
2.65
1
Johnson
1858.20
108.1
2.85
2
Morton
1850.30
124.2
3.37
2
Jacob
1858.20
108.1
3.10
6
Dembowski
1850.39
124.1
2.68
4
O. Struve
1858.39
108.9
2.97
3
0. Struve
1850.85
124.6
2.85
2
Madler
1858.43
108.8
2.96
5
Madler
1851.19
123.1
2.83
6-5
Fletcher
1859.39
106.1
2.94
6-3
Madler
1851.27
123.3
2.93
6
Madler
1859.57
104.9
2.84
5
0. Struve
1851.31
122.9
2.98
2
Dawes
1860.08
105.2
2.84
2
Morton
1851.41
123.0
2.80
5
O. Struve
1860.16
104.1
2.99
6-5
Powell
1851.79
122.1
2.91
9
Madler
1860.32
105.2
2.88
2-1
Dawes
1852.13
122.3
2.90
7
Miller
1860.36
102.8
—
-
Oblomievsky
1852.20
119.8
2.92
6
Fletcher
1860.36
103.6
—
-
Schiaparelli
1852.29
120.9
3.01
1
Jacob
1860.36
103.9
—
-
Wagner
1852.34
120.8
2.73
6
Madler
1860.39
104.1
3.15
2
Madler
1852.36
118.2
2.85
2
Morton
1861.14
100.6
3.09
6-2
Powell
1852.38
120.0
—
1
Dawes
1861.40
101.1
2.70
4
0. Struve
1852.40
120.6
2.76
4
O. Struve
1861.42
100.8
2.83
8
Madler
1853.19
118.8
3.01
4
Miller
1861.76
100.4
3.04
5
Auwers
1853.20
119.5
3.01
2
Jacob
1862.36
100.1
2.95
4
Madler
1853.20
119.2
—
6
Powell
1862.39
99.3
2.62
4
0. Struve
1853.23
118.9
2.98
6
Fletcher
1862.42
100.2
3.20
-
Oblomievsky
1853.40
119.0
2.88
4
O. Struve
1863.20
89.5
2.61
2
Main
1853.45
118.8
2.94
13
Madler
1863.23
96.6
2.55
19
Dembowski
1854.12
117.2
3.1
10-1
' Powell
1863.46
95.7
2.55
2
O. Struve
I UHSAK MAJOKI8 = .11523.
107
(
6.
P.
*
OtMrwr*
(
0.
P.
H
OtHKTVITB
0
9
o
t
1864.31
94.0
2.29
9
IVMubowski
1873.28
• 1 ..
0.9
2-1
W. A 8.
1S4V4.38
92.9
2.40
:
Secchi
1873.33
358.9
0.98
10
1 Vlnl«'\\ -ki
1K4V4.42
94.2
2.33
3
O. Strove
1873.42
.'C>8.4
O.KX
1
Ihiiutr
1S4>4.46
92.8
2.44
1
Engloiuanu
1873.43
358.4
" •"-
5
O. Strove
1864.80
93.9
2.42
1
:•
1873.78
347.1
0.83
3
(i!,-,||,i]|
1865.12
91.4
2.44
19
Knglemann
1874.13
338.4
1.00
3
Glmlhill
1S4V5.30
90.1
2.17
10
m-ini.. \\ski
1874.20
336.2
0.92
2-1
W. & S.
1S4V5.51
89.9
2.53
4
Secchi
1874.21
337.0
1.48
1
Ferrari
1SIV6.25
1S4V6.30
92.8
86.5
2.72
2.26
4-3
3
Ley ton Obs.
Secchi
1874.26
1874.35
335.5
838.6
1.02
o
6
Ley ton < MM.
1866.30
86.8
84J.7
2.05
2.O9
10
5
Ik'inbowski
Kaiser
1874.41
1874.45
35!
1.03
" •"•
3
4-5
4>. Strove
1 IUIM-I
10
H i
2.12
3
O. Strove
1875.27
317.6
1.09
8
Ill-Ill U,U~ki
45
87.8
2.08
5
Kiiiaar
1875.31
317.5
1.31
7
Sehiapwelli
19
81.1
—
2
(illlilrli
1875.34
317.2
1.28
4-3
W. & s.
49
83.6
—
^
Abbe
1875.45
315.S
1.10
1
0. Strove
1866.49
87.0
—
•
i
1875.45
316.4
1.12
11
1 in in'- r
1875.99
31 1.7
i
... .
1867.21
75.5
2.89
1
Winlock
1
'
i^«:7.23
82.2
—
1
1 .••% !• in 4 MM.
1876.27
304>.:i
1.75
13-2
m-U-n-k
1 M-.7.31
82.2
1.90
8
DtMiibowMki
1876.30
304. 8
1.24
1
iVmUiWHki
1867.47
81.0
1.91
2
O. Strove
1876.34
334.5
1.65
1
I.i-\ lull
- 14
841.8
1.76
1
Searle
1876.36
305..-,
1.45
3
w. & s.
-23
1H4V8.3O
79.1
77.1
2.49
1.72
8
Leyton4)hii.
DMatmraU
1876.42
1876.46
34)1.2
1.35
1.52
3
5-4
O. Strove
I'liiniiiM-r
1S4VH.39
77.1
1.77
1
Main
1877.20
297.0
1.57
7-6
I'liiiiinii-r
1S4V8.42
72.6
1.63
I
O. Strove
1877.26
294.9
l'.42
4i
Dembowaki
1S4V9.40
68.6
1.34
11
IIIIIU'T
1877.26
294.2
1.76
14)-9
|i..U-i.k
1X459.42
69.9
n _
_
Kruger
1877.34
293.0
1.52
8
Schiaparelli
1877.40
294.6
1.52
3
W. & S.
L870.18
59.2
1.32
4
O. Strove
1877.43
291.15
1.45
O. Strove
.1
IM
'•'
I K-inlxjwski
1877.
291.5
1.35
1
1'ritdiett
|N7«i.:w
:.7 .
I
Qbdbill
1*77.11
L-.ll.-.
2.10
2-1
Hall
1870
—
-
LeytonOb*.
187C
1 •-•<•
'.•
Ihin,:r
1878JO
—
•jii|
I
Dolwrrk
1871
17 7
1 i'n
S
iVmbowski
187!
1 ..i,
6
Dembuwski
1871
17 7
l •_•
1
Gledhill
1S78.36
LfQ
3
C). Struvr
1871.39
• • :
—
-
Leyton Obs.
L8T8JI
1.82
3
Hall
1871.40
45.7
.12
2
O. Strove
187
1.79
7
Schiaparelli
1871.47
40.0
.02
11-10
Ihm.'r
1879.41
278.5
1.74
2
O. Strove
1871.48
: •
.1
1
Wilson
1872.06
30.7
.05
2
Gledhill
1880.13
1880.27
276.2
2.07
1.80
6
6
Franz
Hall
1872.26
23.2
.09
7-6
W. AS.
1880.28
274.9
2.05
5
Doberck
1872.33
1872.35
19.3
.07
.28
6
1-2
Knott
Leyton Oba.
1880.39
1880.48
273.0
272.0
1.90
1.82
3
Kigourdan
Jedra»jpwic2
1872.41
17.8
o n
10
Dembowgki
1872.46
16.6
•• •;
14
I>mn:r
1881.23
270.3
1.84
4
Doberck
1872.48
15.4
,. „
8
Ferrari
1881.31
! H
2-1
Bigourdan
108
UE8AE MA.JORIS = .i'1523.
(
0.
P.
n
Observers
t
60
Pa
n
Observers
O
If
O
n
1881.34
269.2
1.84
7
Hall
1889.37
216.9
1.81
3
Maw
1881.35
269.7
1.66
4-3
Burnham
1889.39
218.5
1.64
2
0. Struve
1881.36
268.9
1.92
6
Schiaparelli
1889.40
217.4
1.68
5
Tarrant
1882.25
263.5
1.99
6
Hall
1890.27
210.0
1.64
0
Hall
1882.25
259.4
2.00
4-3
Doberck
1890.36
209.7
1.61
7
Schiaparelli
1882.25
262.1
1.99
4
Englemann
1890.40
209.1
1.96
3
Maw
1882.39
261.1
1.93
9
Schiaparelli
1890.42
313.3
1.54
1
Hayn
1882.42
260.4
1.72
3
0. Struve
1890.45
209.4
1.87
2
Knorre
1883.32
257.8
2.00
6
Englemami
1891.13
202.6
1.78
1
Bigourdan
1883.38
257.1
1.88
11
Schiaparelli
1891.15
202.1
1.63
1
Flint
1883.40
258.2
1.95
6
Hall
1891.30
200.6
1.59
6
Hall
1883.41
258.1
1.88
3
Jedrzejewicz
1891.31
204.1
1.92
1
Knorre
1884.28
249.2
1.69
3-4
Perrotin
1891.41
1891.47
199.8
199.9
1.60
1.74
10
3
Schiaparelli
Maw
1884.32
249.0
1.89
7
Hall
1884.35
247.6
—
14
Bigourdan
1892.32
196.9
1.75
4
Maw
1884.38
249.3
1.82
11
Schiaparelli
1892.35
195.1
1.57
11-10
Schiaparelli
1884.41
249.6
1.92
4
Euglemann
1892.36
194.1
1.78
1
Bigourdan
1884.44
249.2 '
1.56
1
O. Struve .
1892.39
197.4
1.70
6
Knorre
1892.45
196.6
1.60
2
Leavenworth
1885.35
1885.30
244.7
245.2
1.80
2.12
5
4
Hall
Englemann
1892.46
197.5
1.57
4
Comstoek
1885.39
245.4
1.72
10
Schiaparelli
1893.27
188.0
2.05
2
Knorre
1885.41
243.4
1.87
3
Tarrant
1893.33
187.3
1.72
4
Maw
1886.37
1886.37
237.3
237.4
1.63
2.06
5
8
Hall
Englemann
1893.36
1893.37
186.4
186.1
1.65
1.75
7
1
Schiaparelli
Dav. 1'hotog.
1886.45
237.0
1.80
. 3
Jedrzejewicz
1894.22
183.2
1.79
3
Comstoek
1894.30
181.1
2.00
1
Ebell
1887.04
226.9
—
1
Glasenapp
1894.32
182.8
1.79
1
H.C.Wilson
1887.35
230.3
1.61
5
Hall
1894.34
183.6
1.84
2
Knorre
1887.36
230.9
1.65
12
Schiaparelli
1894.35
183.0
1.87
3
Maw
1888.28
222.2
1.68
6
Hall
1894.47
181.7
1.78
8
Bigourdan
1888.29
222.7
1.63
4
Schiaparelli
1894.56
184.6
1.77
1
Glasenapp
1888.43
226.2
1.61
1
O. Struve
1888.51
222.7
2.20
4
Maw
1895.30
176.5
1.93
3
Comstoek
1895.31
176.0
1.78
1
Dav. Photog.
1889.28
218.1
2.09
2-1
Glasenapp
1895.32
176.0
1.98
1
Lewis
1889.29
216.5
1.68
5
Hall
1895.33
176.6
1.95
3
See
1889.36
215.9
1.61
9
Schiaparelli
1895.46
175.9
1.79
4
Schwarzscliild
This celebrated system was first measured by HKRSCIIEL in 1781. A repe-
tition of the measures in 1802 and 1804 showed* that the smaller star had a
rapid relative motion (Phil. Trans. 1804, p. 363), and indeed gave indieations
for the first time that the motion of certain double stars is of an orbital nature,
f Ursae Majoris thus enjoys the unique distinction of having first aroused
interest in observational proof of the universality of the Newtonian law. This
• Aatronomische Nachrichten, 3323.
( UR8AB MAJORI8 = ^ 1 .. :
star also led SAVAHY in IS'-'T i<> derive a method for finding the orbit of n
double star on gravitational principles, and tbc first orbit ever computed appeared
in the C«w««iW'///c. «/» '/'<////>•> I'm- ls:U). When SAVAHY'S method for finding
double-star orbits had been successfully applied to ( Uranc Majnri*, the subject
was taken up by ENCKK and HKKSCIIKI,, who published methods of superior
elegance and of greater practical utility, with the result that numerous orbits
were soon computed.
The rapid orbital motion of £ Ursae Majori* insured it ample attention,
and accordingly since the time of SIR JOHN HKKSCIIKL and STKUVE, measures
ha\e lieen secured annually by the best observers. The number of orbitw com-
puted for this star is very large; the following list is fairly complete:
p
T
•
a
a
<
A
Authority
Source
1817.25
0.4164
3.857
•.'.-, .;
.V.t..7
i:n .,;
Savary, 1828
Conn, des Teni|M, ls::n
! N 1 r..73
0.3777
3.278
97.78
56.1
I.'i4.37
Henw-hel, 1K32
Mem. R.A.S. V, |).L'<i;i
60.4W6
1816.98
0.40368
2.290
95.0
129.68
Ma.ll.-r. l.v:r.
A.N.319
f.l.l.VI
1816.44
0.4135
1417
:,!•.».;
1.-U).8
Mwller, 1843
A.N. 486
IM 7.H>2
0.4037
2.295
96.35
:.«i.'.n'
132.47
Mfcller, 1X47
Fixt-Syst I, p. L'.:.:
•Lira
1816.66
0.4116
2.82
96.1
29.47
Jacob, 1K4«
Mein.H.A.S.XVI.p.:{-.'^
i;i :.:•;
181).
" i:U5
I I ••'
95.83
52.82
28.57
Villarw-anisi'.i
A.N. 680
1816
2.454
97.3
52.27
32.88
Brwn, 1S(,L-
M.X. XXII, p. 158
59.88
I8i«;. i.'.-,
0.3786
2.591
103.6
5,'J.l
35.3
lial), 1872
Pror. K.I.A.,Jtme,l.x7:'
.79
1815.006
0.3830
2.587
W0.7
56.33
27.15
Kn..tt, 1873
M.N. XXXIII, p. 101
60.63
1875.50
0.371
2.535
101.0
55.0
216.0
Flam., is:..
Cat.(li'«fct.IK)\it.. p. 65
00.79
1875.29
0.39.r.2
LV.VI'.I
101.5
56.9
i':u.:<
I>nii.;r, 1876
Meas. Mirr., p.!9l>
60.80
1X7.1.26
0.4159
2.580
KMK22
5«.«7
KULO
Pritchard, 1878
Oxford Ob*., No. 1
,,,.-.,,
1814.8
n lid
JM-;
IL'I'.'.I
.;..;,>
Birk., 1879
K . A kmd. Wte. Wtat. BAJS
It will IK- seen that among the more recent orbits there is no wide range
of value-, ami \et the elements are by no means identical. The different
1 1 -ult- depend u|M»n the observations used and the method of computation
employed.
From an inv« -libation of all the observation-. I am led to the following
elements:
Q = 100°.8
» =-
x - r.v
M - -6°.0000
Apparent orbit:
P - 60.00 yean
T - 187..
f - 0.397
a - 2".508
length of major axi* •- 4'.76
Ix»ii£th of minor axis •> 2*.70
Angle of major axis — I04°.6
Angle of jMTiastron — 318e.O
UMcnre of star from centre — O".75
110
URSAE MAJORIS =
The following table of computed and observed places shows that these
elements are extreifiely satisfactory.
COMPARISON OF COMPUTED WITH OBSERVED PLACKS.
1
ft,
ft
Po
PC
60— $c
Po— PC
n
Observers
1781.97
143.8
148.4
t
4 ±
2.34
0
-4.6
+1.66±
1
Ilerschel
1802.09
97.5
99.0
—
2.70
-1.5
—
1
Herschel
1804.09
92.6
93.3
—
L',17
-0.7
—
1
Herschel
1819.10
284.5
282.1
—
1.69
+2.4
—
o
Struve
1820.13
276.3
274.0
—
1.79
+2.3
—
3
Struve
1821.78
264.7
264.5
1.92
1.84
+ 0.2
+0.08
3
Struve
1823.29
258.4
255.8
2.81
1.83
+ 2.6
+ 0.98
58-20
Ilersohel and South
1825.22
244.5
244.5
2.44
1.78
±0.0
+ 0.66
7^
South
1820.20
238.7
238.4
1.77
1.75
+0.3
+ 0.02
3
Struve
1827.27
228.3
231.6
1.71
1.72
-3.3
-0.01
4
Struve
1828.37
224.0
224.3
2.01
1.69
-0.3
+ 0.32
2
Herschel
1829.35
213.6
217.7
1.67
1.67
-4.1
±0.00
7
Struve
1830.58
206.1
209.3
2.23
1.67
-3.2
+0.56
10±
Herschel
1831.28
202.4
204.5
1.85
1.68
-2.1
+ 0.17
27-14
Bessel 5; Dawes 17-4; W. Struve 5
1832.34
196.3
197.3
1.76
1.69
-1.0
+ 0.07
15-13
Dawes 10-8; W. Struve 5
1833.30
189.0
191.0
1.83
1.72
-2.0
+ 0.11
9
Dawes 4 ; W. Struve 5
1834.47
183.3
183.7
1.87
1.78
-0.4
+ 0.09
6-2
W. Struve 2; Miiiller 4-0
1835.34
178.3
178.7
1.84
1.82
-0.4
+ 0.02
6
Miidler 1 ; W. Struve 5
1830.33
171.7
173.1
1.94
1.89
-1.4
+ 0.05
12-7
Dawes 1; Miidler 7-2; W. Struve 4
1837.47
165.3
167.2
1.93
1.97
-1.9
-0.04
3
Struve
1838.43
160.4
162.7
2.26
2.05
-2.3
+ 0.21
9
Struve
1839.47
157.9
157.4
1.89
2.14
+ 0.5
-0.25
_
Galle
1840.34
152.2
154.5
2.36
2.20
-2.3
+ 0.16
12-10
Dawes 6-4; O. Struve «
1841.30
148.6
150.2
2.36
2.29
-1.6
+0.07
17-15
Dawes 4-«8; Miidler 7-0; O. Stnive 6
1842.30
146.4
147.3
2.40
2.37
-0.9
+ 0.03
12
Miidler 4; Dawes 4; O. Struve 4
1843.33
143.0
143.9
2.42
2.45
-0.9
-0.03
11
Dawes 7; Miidler 4
1844.34
140.7
140.7
2.52
2.54
±0.0
-0.02
14-13
O. Struve 3; Miidler 11-10
1845.74
136.9
136.6
2.81
2.65
+ 0.3
+ 0.16
4
O. Struve 2; Jacob 2
1846.37
137.2
134.9
2.56
2.69
+ 2.3
-0.13
4
O. Struve
1847.36
132.3
i:;i'.:;
2.63
2.76
±0.0
-0.13
14
Dawes 1 ; Miidler 10; O. Struve 3
1848.30
129.5
130.0
2.78
2.82
-0.5
-0.04
15
Dawes 1; Dawes 3; Miidler 4; O. Struve 5; Bond 2
1849.33
127.1
127.3
2.89
2.87
-0.2
+0.02
9
Dawes 5 : O. Struve 4
1850.51
124.3
124.8
2.96
2.94
-0.5
+0.02
8
Jacob 2; O. Struve 4; Miidler 2
1851.39
122.9
122.9
2.89
2.97
±0.0
-0.08
28-27
Fit. 6-5; Miidler 6; Dawes 2; O. Strove 5; Miidler 9
1852.30
120.3
120.9
2.84
3.00
-0.6
-0.16
27-26
Miller 7; Fit. 6; Jacob 1; Mil. 6; Mo. 2; Da. 1-0; OS. 4
1853.24
119.0
118.9
2.96
3.02
+ 0.1
-0.06
35-29
Miller 4; Jacob 2; Powell 6-0; Fl. 6; OS. 4; Mii. K!
1854.34
116.4
116.5
2.98
3.03
-0.1
-0.05
37-28
Powell 10-1; Miidler 15; Dawes 3; O. Struve 4; Dem. !i
1855.33
115.2
114.5
2.98
3.03
+0.7
-0.05
13
Dembowski 7 ; Sec. 1 ; Miiiller 2 ; O. Struve 3
1856.45
112.4
112.1
3.07
3.02
+0.3
+0.05
29
Jacob 3; Sec. 4; Dembowski 7; Miidler 13; Jacob '2
1857.42
109.8
110.0
2.94
3.00
-0.2
-0.06
13
Sec. 2; Madler 8; O. Struve 3
1858.24
108.4
108.3
2.96
2.97
+ 0.1
-0.01
20
Jacob 4; Morton 2; Dembowski 6; O. Struve 3; Mii. 5
1859.48
105.5
105.4
2.87
2.91
+ 0.1
-0.04
11-8
Miidler 6-3; O. Struve 5
1860.24
104.6
103.6
2.96
2.86
+ 1.0
+ 0.10
12-10
Morton 2; Powell 6-6; Dawes 2-1; Miidler 2
1861.32
100.8
101.0
2.87
2.77
-0.2
+0.10
18-14
Powell 6-2; O. Struve 4; Miidler 8
1862.38
99.7
98.2
2.78
2.67
+ 1.5
+ 0.11
8
Miidler 4; O. Struve 4;
1863.34
'.1C,. 7
96.6
2.55
2.56
+ 1.1
-0.01
21
Dembowski 19; O. Struve 2
isr.uo
98.7
92 2
2.36
2.42
+ 1.5
-0.06
16
Dembowski 9; Sec. 3; O. Struve 3; Dawes 1
1866.31
no.;;
S'.I.U
.'.37
2.27
+ 1.5
+ 0.10
33
Englemann 19; Dembowski 10; Sec. 4
1866.33
86.2
85.5
J.14
2.13
+ 0.7
+0.01
16
Sec. 3; Dembowski 10; O. Struve 3
1867.39
81.6
79.5
1.91
1.89
+ 2.1
+ 0.02
11
Dembowski 8; O. Struve 2
1868.28
76.S
75.0
1.70
L.73
+ 1.8
-0.03
13
Searle 1; Dembowski 8; O. Struve 4
1869.40
68.6 65.31.34
1.45
+3.3
-0.11
11
Dune'r
- I KSAK MA-ioiM- ^
111
t
JU «.
f.
*-*
*-»
*
Obaerrpn
IX7o.Hi
56.H
-r~
1 -J7
+0.05
1M
O. Strure4; Itembowikl 9; (iledhlll 3; Itun.-rli
1.1 H 1".:
.13
l.n.-.
+ 4.7
+0.08
JI I1.:
Dem. 8; Ql. 1\ O. Struvri; Hiin.-i 11-10; Wllnon 1
i •. i :.
Hi
17 if.
..I. %: W. A s. 7-6; Kn. 6: Item. 10; Du. 14; Per. 8
+ .TX
+ 0.0.'!
is 17
W. A S. 8-1; Itembowikl 10; Dum:r 1; (t. SlruveS
|s;i 29
:t34.5
+ 1.11
P.I is
Ul. 3; W. A 8. >-l; Per. 1-0; Drm. 6; OZ. 3; Du. 45
.-.If. 1 ::i 1 1
..o
1.18
+ 1.7
H-32
Item. 8; Soli. 7; W. 4 S. 4-3; Dun. r 14; Dotx»rrk. 1-0
;;|
+0.8
28-10
lh.U-r.-W 13-3: Item. 7; W. A H. 3; riumnirr ft 0
Isr: • .Y.'
+ 0.7
+0.13
16-33
PL 7-«; Dem. 6; Dk. 1O tl; Sch. 8; W. A S. 3; III. 2 O
1878
286.8 286 M .661.62; +0.3
!
6
Itembowtkl
.'279.3 .801.7.'t •
.
10
Hall 3; Srhlaparelll 7
-
M.7
+0.03
22-11
Franz 6-0; Hall 0: Dohrn-k .'> O; ItlRounlan 2: J«L 8
1 ss] ;••
4-2.1
-0.01
23-21 ItolnTi-k 4; HlKoiinlan 2 1 : Hall 7: ft. 4 :): s.-h r,
<.l :. jr.l 7
•.'7
! si _o.2
+ 0.13
23-19 Hall 6; Doberck 4-0; Knglcmann 4: Srhla|ian>lll 0
.'.Ml
. Q |
20-20 EnicU'iiiaiin (Mi: Srlila|«rplll 1 1 ; HalHl: .l.slr/.-j. »|.-«::
Iss;
L80
+ 0.1
+ 0.0.-5
.'W-26
l'.-rr..iin :: 4: Hall 7: Illnoiinlai) 14 0: Srli. 11; Kn. 4
-'J:;:.
.Ml
1.77
+ 1.0
+0.03
18
Hall !,; S.-lii»|«r.-lli 10: Tarrant 3
::-i'j:;7 :'
.71
171
+ 0.1
-0.03
16-8
Hall .V. Knulrntann H-O: Jmlrxfji-wlrx 3
2S1.B
L72
-0.1)
-0.09
17
Ball 5; Srhlaparelli I*
.'L'l 1
.('..'. l.<i«» —1.11
-0.04
14-10
Hall 6; Srhlapan-lll 4; Maw 4-0
-•17.li
-1.1
+ 0.02
P.I 17
Glaaenapp t-0; Hall .">: Srhlanarrlll (1; Maw 3
210.7
1 77
l.r.7 -1.2
+0.10
18
Hall 6; Sclilaparelli 7 ; Maw 3; Knorre X
.'i -.'"I :. .
' .:
-2.8
+ 0.0:1
22
Big- 1: Flint 1; Hall 6; Knonv 1: Sell. 10; Maw 3
p.'7 :: l •'•!'•
l.r.'.i _1.0
—0.03
J8-17
Maw 4; Srb. 11-10: lilg. 1 ; Knorre 0: l.v. t; Cum. 4
W.O I'.H.n
1.71 1 7'J
-o.o i 11 l-
Knorre SO; Maw 4: ScblapaivMI 7 : Davlilwin 1
Is-,;
1.811.77
-1.4
+ 0.04
17
Com. 3; II.C.W. 1; Knorre 3; Maw :l: Big. 8; Ola.. 1
1.901.83
-2.3
••
Uavldimn 1; Lewi* 1; 8wS
Fut in. «•!•>, ivationn are likely to produce only very slight alterations in
tin above values. Thus the period is not likely to be in error by more than
one-tenth of a year, and the error in the eccentricity can hardly surpass
±0.005. Indeed the orbit f Ursae Majoris is practically all that can be desired
in tin- proem state of double-star measurement. In order to effect any further
improvement of the orbit, astronomers will need to take every precaution against
-\~i.niatir riT(ii->: and rough measures by inex|K*rience(l uli-rrvt-rs are unlikely
to prove to he of any considerable value.
\\ . remark. IK. \\.A.-I-. that eontiniie.1 ..h-.-r\atioii of this star is desirable,
because the mi.-r.imetrieal measures of skilled observer* will be valuable in
throwing light upon the .pie>tion of the e \iMciice of dark (todies or other di—
tiirbing influence-, and in proving with all po--ihle experimental accuracy that
the force which retains the coinpaniitn in its orbit is directed exactly towards
the central star.
£{"--"• V', . like [IlrrcHli*, has a large proper motion in space, and
thi- cin •iiiiistanee in connection with the brilliancy of the components, conduces
to the In-lief that the system is comparatively near the earth. Measurement
for parallax ha- n.-ver been at tempted, but if suitable comparison stars could
be found, effort in this direction would be likely to prove successful.
112
O.i'234.
0-1-234.
a = llh 25"'.4
7, yellowisli
8 == +41° 60'.
7.8, yellowish.
Discovered by Otto Struve in 1843.
OBSERVATIONS.
t
&
Po
H
Observers
C
60
Po
n
Observers
0
t
9
I
1843.29
182.5
0.42
1
O. Struve
1870
.46
281.8
cert. obi.
1
0. Struve
1843.33
179.6
0.25
-
Miidler
1877
.26
127.
3
0.25
2
Dembowski
1844.31
172.7
0.46
1
O. Struve
1877
.32
cuneiforme sous 349° 1
O. Struve
1845.42
194.6
0.30
2
Miidler
1878
.28
168.4
0.27
2-1
Buniham
1846.37
177.2
0.40
1
0. Struve
1880.37
178.
4
0.18
1
Burnham
1847.40
187.2
0.25
1
Miidler
1882
130!
<0.3
3
Englemann
1847.41
183.7
0.38
1
O. Struve
1848.25
187.9
0.40
1
O. Struve
1883
350.
<0.25
3
Englemann
1850.31
195.2
0.33
1
0. Struve
1884
.10
20.
0.28
1
Englemann
1851.36
200.4
0.3
1
Miidler
1887
.42
231
2
0.18
6
Schiaparelli
1851.42
199.3
0.30
2
O. Struve
1889
.39
cuneiforme sous 98° 1
0. Struve
1852.46
196.
0.27
1
0. Struve
1891
.23
104.
2
0.14
3
Buniham
1853.41
201.3
0.33
1
0. Struve
1892
.28
114.
2
0.18
3
Burnham
1858.36
cert, elong.
in 244°
1
O. Struve
1892
.39
107.
i)
0.24
2-1
Bigourdan
1859.40
233.
0.24
1
0. Struve
1892
.40
293.
6
0.22
1
Schiaparelli
1861.26
255.0
0.28
2-1
0. Struve
1894
29
123.
2
0.22 ±
2
Comstock
1862.39
260. oblong
1
O. Struve
1894
84
121.
7
0.21
3
Barnard
1866.20
single
—
1
Dembowski
1895
20
122.
2
0.30 ±
1
Comstock
1866.49
oblong in
283°
1
0. Struve
1895
75
125.
1
0.36
1
See
Since the discovery of this pair by OTTO STRUVE, the companion has de-
scribed an arc of 305°. The object is always close and difficult, and hence the
measures are by no means so good as could be desired; yet when account is
taken of both angles and distances, there is reason to believe that elements
based on the observations now available will never be greatly changed. MTJ.
GOKE is the only computer who has previously investigated the orbit of this
pair; using the measures prior to 188G, he found the following elements:
P = C3.45 years
T = 1881.15
e = 0.3629
a = 0".339
Q = 124°.2
f = 47°.35
X = 71°.97
18S3
.Ic I
0 2 234
Oi-:; I.
find the following orbit of 02
P _ 77.0 years
r- 18X0 in
• . 0.302
a - 0*.34«7
X -. 11H5M5
n - +4°.G7.r>4
Apparent orbit:
Ix»ngth of major axis
Length of minor axis
Angle of major axift
Angle of ]TM.iM ion
- 0*.437
- 1C8°.0
- 3T»G0.2
Distance of star from center — 0*.OW
Tin- accompanying table shows that these rli-m«-m- are very satisfactory;
tin- |M ii...l j> perhaps uncertain by five years, and the eccentricity by perhaps
'I. l.nu'i variatioiiH in them* clement* are. not to be anticipated. It in
probably worth noting that BruxiiAM's distance in 181H is sensibly smaller than
the coinpntril distance, although the angle a^itt-H perfec-tly. By this we are
nut in infer that he nndcr-incaHiircd the distance with the great Refractor of
th< I.i.k Observatory, but that all small distances with a great Telcsco|>e a\t-
l-ar diiuinishe<l in comparison with their magnitude in a small instrument — a
phenomenon due mainly to the diminution of the spurious discs under the
>nperior separating power of great Telesco|>es. The computer must therefore
take account of the inequality of the distances due to the different |x>wer of
the Telescopes employed; but as most of the observations of 0^'2.'M wen-
made with instruments of about l.Vmch aperture, I preferred in make the scale
of the major axis such, that on the whole the computed would agree with the
olmerved distances.
CoMPAKIftOM or COM 1-1 IK!> WITH OBHKKVKII I'l.ACK*.
c
9.
•j
?•
P<
«.
/>•-*
M
/U— *—— «-
wwi*™ni
1R43.31
ISl II
irs.i
0.42
II !i
+ 0.01
2-1
02'. 1; Midler 1-0
I M 1.31
172.7
180.1
" i.;
0.41
- 71
+ 0.0.-.
1
< >. Strure
184&4S
r.'i •;
1X2.3
O..TO
0.40
+ 12.3
-0.10
>2
MMhr
IM'
K7.U'
1K4.2
0.40
0.3»
- 7.0
+0.01
1
0. Struve
1 1"
180.4
1HC.6
o.:w
0.38
- 1.2
±O.OO
2-1
Miller 1-0; O2A
184*
187.8
i^> :.
0.40
0.38
- 0.0
+0.02
(>. Htnivc
l '.'.-.•_•
o.:«
(».;M5
-1- l.f.
—0.03
0. Stnive
0.30
o.:tr>
+ 3.2
—0.05
Madler 1 ; 'M J
".-.• :
0.34
- 3.3
-0.07
0. Stnive
0.3.'$
- 1.4
±0.00
(). Struve
18f.-
.11
-••-••.'. l
4Si
n •.•:
+ 21.9
__
(). Struve
•> • :
0.26
+ fi.O
-0.02
0. Stmve
• •-••;
OM
+ 18.0
+ O.Q3
2-1
0. Struve
1862
• •l.liill^
+ 10.2
_
( ). Stnive
>., , ,
oblong
".-.'1
+ 11.7
-
0. Stnive
114
02' 235.
t
60
Be
Po
PC
60 — Be
Po—Pc
n
Observers
1870.46
281.8
297.5
9
cert.
obluiiK
0.24
o
-15.7
It
1
0. Struve
1877.29
328.1
337.3
0.25
0.25
- 9.2
±0.00
3
Dembowski 2 ; O.T. 1
1878.28
348.4
343.0
0.27
0.25
+ 5.4
+ 0.02
2-1
Burnham
1880.37
358.4
375.5
0.18
0.23
+ 0.9
-0.05
1
Burnh&m
1883.
350.
18.7
<0.25
0.20
-28.7
+ 0.05
3
Englemann
1884.10
20.
30.2
0.28
0.19
-10.2
+ 0.09
1
Englemann
1887.42
51.2
68.5
0.18
0.18
-17.3
±0.00
6
Schiaparelli
1889.39
98.
89.8
cune.
0.20
+ 8.2
_
1
0. Struve
1891.23
104.2
104.4
0.14
0.23
- 0.2
-0.09
3
Burnham
1892.36
111.6
111.5
0.21
0.25
+ 0.1
-0.04
6-5
Big. 2-1; 0.3; Sch.l
1894.56
121.7
122.6
0.22
0.29
- 0.9
-0.07
3-5
Comstock 2 ; Barnard 3
1895.20
125.1
125.2
0.33
0.30
- 0.1
+ 0.03
1-2
Comstock 0-1 ; See 1
The observation of this star which I made at Madison, is discordant in angle
(-4.e7.359), and hence I am led to think that an error of 30° occurred in read-
ing the circle; the unreduced reading was 04° .3, whereas it doubtless should
read 04° .3. As the angle was estimated at 130°, this correction is amply justi-
fied.
If good observations can be secured for the next decade, this orbit can be
rendered very exact. The following ephemcris will be useful to observers:
t
1896.40
ft PC
127?0 0.31
t Be P,
1899.40 13(i!8 0.36
1897.40
130.4 0.33
1900.40 139.5 0.37
1898.40
133.7 0.34
01-235.
a = llh 2fi"-.7 ; 8 = +61° 38'.
(!, yellowish ; 7.8, yellowish.
Discovered Inj Otto Struve in 1843.
OBSERVATIONS.
t
1844.33
60 Po
28Q.3 O.G7
n Observers
1 O. Struve
' t Oo Po n
1852.46 329J5 0*57 1
Observers
O. Struve
1845.47
296.7 0.54
1 O. Struve
1853.41 333.5 0.54 1
O. Struve
1846.42
306.8 0.57
1 O. Struve
1855.47 345.6 0.51 1
O. Struve
1847.45
315.8 0.53
1 O. Struve
1856.55 350.3 0.52 1
0. Struve
1849.47
320.8 0.49
1 O. Struve
1857.61 350.4 0.55 1
0. Strove
1850.31
316.5 0.56
1 O. Struve
1858.44 358.7 0.75 1
0. Struve
1851.42
328.0 0.54
2 O. Struve
1859.41 358.7 0.62 1
0. Strave
v2
11.-,
I
'•
ft
m
' •
I
».
f»
N
Otaervrn
t
9
O
f
1861.42
13.3
M, ,
o
Struve
1879.44
55.5
1.07
3
Hall
1862.38
20.3
0.76
1
" StriiTt
1882.59
64.8
1.26
6
EnKlemaiin
1864.43
25.3
1
ii Striive
1887.43
73.0
0.93
5-3
Schiaparelli
1888.43
69.4
1.12
1
O. Strove
1866.49
33.3
0.83
1
( >. Strove
1867.45
40.1 i
1
iVmhowHki
1888.69
72.6
1.32
4
Turrant
1868.13
31.0
0.84
1
Ik>mlx>wski
1889.35
70.9
1.07
5
Hall
1889.39
67.3
0.90
1
O. Strove
i^;<i.i8
42.6
0.9
1
l>t-niUi\\-.ki
1891.29
81.7
1.04
1
Itiifininlan
l.srn i.;
37.4
1
O. Strove
1892.12
84.3
0.97
8
r.imiliam
^7J.40
42.0
0.8
1
Dembownki
1892.44
88.1
1.03
1
KiKinmlai.
Is7-J.«0
43.1
1.00
1
0. Strove
1892.45
85.4
0.80
2
Lv.
51.0
0.95
1
O. Strove
1892.54
84.2
0.94
3-2
< 'ninstork
1871
1.07
2
DeuiUiwHki
1893.37
90.2
0.92
1
(k)m»U«-k
:,;
1.04
I
O. Strove
1893.41
1894.24
90.1
0.85
0.75
6-9
3
Iti^ourtlan
• '.illl-tc. k
n i
1.18
1
I)embow8ki
1895.27
93.9
0.79
8
('lllIlNtlM k
1^7•l II
0.76
1
O. Strove
1895.74
97.3
0.81
£
V..
Fur a niimlH-r <if yt-ars aflrr the1 diwcovfry of thiH pair, (>rr«> STKITVK
:il.iii.- ii. -tt-il I lie | >., -iti,. M of the companion, Init ax lii- measures -<.«.n cstaMislicd
the rapid motion of the system, DKMIUIWSKI, II \i i . SCHLAPAUELLI, and other
stihse<|iient observers have eontrihuted to the material now available for the in-
v estimation of the orbit.
'I'll. <il)sci-\:itii>n- .-irr not very ninneroiis, but for an object of ihi- diffi-
cultv, thcv aii- eoiniiaralivcly p>od.
Tin- arc il. M-rilx-d 1>\ the fompaiiion siner 1SJI i- ..nl\ ]i\i't\ and yet the
inotiiiii arniind the apa-tron «if the apparent orbit defines the elements with
e.iii-i<leralile preei-imi. !><IIIII:IK i- the niily a-troiiomer who has previously
in\< -.titrated the motion of this pair; his elements are as follows: —
p
T
«
•
n
t
X
Authority
Hourre
94.4
94.406
1839.1
• -
0.500
0.5870
Ml
; «• I
,.,,,
.„ _.*
&
54.5
60.22
! :| •>
129.92
Di.U-n-k.lN7'.i
Doberck.1879
\ N --'M
A can-fill study of all the observations leads to the following element-:
P — 80.0 yeas
T - 1834.30
« - 0.324
a - 0*^690
» - 49°.32
X - 137-.78
n - +4*f
116
Apparent orbit:
Length of major axis = l''.G82
Length of minor axis = 1".02
Angle of major axis = 72°.8
Angle of periastron' = 231M
Distance of star from centre = 0".242
COMPARISON OF COMPUTED WITH OBSERVED PLACES.
1
60
Oc
po
PC
00 VC
Po— PC
n
Observers
1844.33
289?3
288.6
0.67
0.60
+ 0.7
+ 0.07
1
0. Struve
1845.47
296.7
293.5
0.54
0.59
+ 3.2
-0.05
1
O. Struve
1840.42
306.8
298.1
0.57
0.58
+ 8.7
-0.01
1
O. Struve
1847.45
315.8
303.7
0.53
0.57
+ 12.1
— 0.04
1
(). Struve
1849.47
320.8
314.9
0.49
0.56
4- 5.9
-0.07
1
O. Struve
1850.31
316.5
318.7
0.56
0.56
- 2.2
±0.00
1
O. Struve
1851.42
328.0
324.7
0.54
0.56
+ 3.3
— 0.02
2
O. Struve
1852.46
329.5
330.2
.0.57
0.56
- 0.7
+ 0.01
1
O. Struve
1853.41
333.5
335.5
0.54
0.57
- 2.0
-0.03
1
0. Struve
1855.47
346.6
346.3
0.51
0.59
+ 0.3
-0.08
1
O. Struve
185G.55
350.3
351.8
0.52
0.60
- 1.5
-0.08
1
O. Struve
1857.51
350.4
356.6
0.55
0.61
- 6.2
-0.06
1
0. Struve
1858.44
358.7
1.0
0.75
0.63
- 2.3
+0.12
1
0. Struve
1859.41
358.7
5.5
0.62
0.65
- 6.8
-0.03
1
O. Struve
18(51.42
13.3
13.7
0.65
0.69
- 0.4
-0.04
2
0. Struve
18C2.38
20.3
17.5
0.76
0.71
+ 2.8
-£0.05
1
O. Struve
18(54.43
25.3
24.8
0.80
0.76
+ 0.5
+ 0.04
1
O. Struve
1866.49
33.3
30.8
0.83
0.81
+ 2.5
+ 0.02
1
O. Struve
1867.45
40.1
34.2
separated
0.84
+ 5.9
_
1
Dembowski
1868.13
31.0
36.0
0.84
0.86
- 5.0
-0.02
1
Dembowski
1870.32
40.0
40.4
0.94
0.90
- 0.4
+ 0.04
2
Dembowski 1 ; 0. Struve 1
1872.50
42.6
47.1
0.90
0.96
- 4.5
-0.06
2
Dembowski 1 ; 0. Struve 1
1876.63
51.0
55.9
0.95
1.02
- 4.9
—0.07
1
O. Struve
1877.29
55.1
57.3
1.05
1.03
- 2.2
+0.02
3
Dembowski 2 ; O. Struve 1
1878.35
58.1
59.3
1.18
1.04
- 1.2
+ 0.14
4
Dembowski
1879.44
58.2
61.5
1.07
1.05
- 3.3
+ 0.02
1-3
O. Struve 1 ; Hall 0-3
1882.59
64.8
67.3
1.26
1.05
- 2.5
+ 0.21
6
Englemann
1887.43
72.5
76.1
0.93
1.02
- 3.6
-0.09
4
Schiaparelli
1888.56
72.6
78.4
1.22
1.00
- 5.8
+ 0.22
4-5
Oi'. 0-1 ; Tarrant 4
1889.37
76.9
79.8
1.07
0.98
- 2.9
+ 0.09
5
Hall
1891.29
81.7
83.6
1.04
0.94
- 1.9
+0.10
1
Bigonrdaa
1892.39
85.5
85.9
0.94
0.92
- 0.4
+ 0.02
9-8
/?. 3 ; 1%. 1 ; Lv. 2 ; (bin. 3-2
1893.39
88.4
88.2
0.89
0.89
+ 0.2
±0.00
7-10
Cmiistock 1 ; Higoimlun 6-9
1894.24
90.1
90.1
0.75
0.87
± 0.0
-0.12
3
Coiustock
1895.50
93.9
93.3
0.80
0.83
+ 0.6
-0.03
3
('(linstock
A comparison of the computed with the observed places shows a very sat-
isfactory agreement, and we cannot doubt that the elements given above will
be found to approximate the truth. The period remains uncertain by perhaps
five years, and the eccentricity may be varied by ±0.0o; but larger alterations
in these elements are not to be expected. The motion of this pair will be ac-
celerated in approaching periastron, and hence for a good many years will
yCKN i u 1:1 11
117
<|i -i-rvi- tln« rv«fiilar atU'tition of ol*H'rvern. If good mramirvH can IK-
.luring thr ni'xt twenty yrarn, tlu- I'U'inrnU* can In* (li'tritniiutl with jfivat ac-
curacy. The following i.» a >lu»rt
1
it
r.
1
6,
ft
•
9
|
9
1896.50
95.9
0.80
1899.50
lie.;:
O.lill
1897.50
98.9
0.76
1900.50
loy.o
o.rrfi
1898.50
102.0
0.73
y CENTAURI = H. 5370.
a = if M" ; 5 = — M* 86'.
4, yellowish ; 4, yellowliih.
Ditcovertd by Sir Joint llrrwhrl, Mnrr/t 1, I8.V».
OtMKKVATIOXB.
I. By Slit JOHN HKI:S< HKI.:
MKAMIKK* WITH TIIK
n. n Ob«Tveri
.•:.;
1.8 <1
1
McnM-hel
....3 -
1
Hendifl
1835.X»0
351.3 0.67
1
IIlTM-ln-1
1835..-J5.S
346.8
I
II. . . • .
1835.367
349.6
1
H.TSl-lll'l
1 I.',
355.3
1
lllTs.-lll-l
! .V.
MKO
1
Ilt-rafhel
! '.!•_•
. I
1
H.Txchvl
::i;.l
1
Il.T.si lli'l
! Hi
! '-• 1
1
lit :
rime ami MTV illlHcult, »l Inut M rime a*
\'irijinin; 273 Imn-ly elongBUo It.
Oruiuly iloulrt.-. hut far loo ilifflriiU fur tliU i.-l<-
WI>|H-. Diniinrtly rlongatetl, hut the meanun** of nu
K»r UHI dlAirull for naUifartory mnuiirm: yrl I miul
Ix'licvc tlm« to lie somewhere about thr truth.
A lietter net of meaaiires than hitherto Rot with the
equatorial, but It I* too illlHcull for thin ohj<-cl-glaM.
Certainly ieen double, t. e. elongateil with parallel
fringe*.
ExcenlTely clows and dlfflrult, but the |x>wer No. 4
will act to-night, though not ijulte to well a» I could
wl»h. Kleld «lniiiKl> illiuiiinatml.
Tolrrably elongateil with No. 4. Urandlnhni, danrm,
and spread*, yet occasionally an elongated centre caui;ht.
rt \n..\- \\ mi Tin Hi i i i
: - ' • • _ _
.:•» :MOJ 0.07 1 lliT.s4-li.-l
.. ± _
•71 " ± — 1 II.
' .{•tr:,*oml»eke Itaekrickttu, 3381).
> I'rntauri, a *tar 4m, which I am very murh ln-
rliiu-d to hi-lii-vi- rlow* double, hut could not verify It
owing to ba<l dettniUon. Tried :<*>. but It will not bear
that power.
180 with triangular aperture ihowi It rlonitatad; MO
fairly douhl<- and alnvwl divided. Ton. with SWadSH0.!,
with 4X0 (which »how» a black dlrUion) = 34.1°.$. IJoth
•tan of 4th magnitude.
Seen decidedly elongated with 880 and dlmlnUhml
ajierture, but to violently agitated and ill dednnl th.it
no neairare could be got. That wt down may err «r .
(r Centaur*). [Po*. e«tlm. from «liag]. Seen deci-
dedly elongated In a ponltlon an per diagram, with 3SO
and triangular aperture, but all attempt at a tneaaar*
confounded by corurtanl boiling and working of the »iar.
118
y CENTAUKI = H2 5370.
II. By other observers:
f
1856.20
60
2()?G
Po
0.7 ±
n
3
Observers
Jacob
t
1887.58
0.
3591
Po
L76
u
2-1
Observers
Tebbutt
1857.97
18GO.G8
13.7
12.8
1.11
5
lOobs.
Jacob
Powell
1887.53
1888.47
1889.32
358.5
359.5
359.1
.1.75
1.87
1.73
6
4-6
4
Pollock
Tebbutt
Pollock
1870.23
C.9
1.5*±
6
"Powell
1890.36
1.2
1.81
1
Sellers
1871.38
3.8
1.18
1
Russell
1890.36
359.0
1.84
2-1
Tebbutt
1873.36
4.2
2.29
1
Kussell
1891.40
357.0
1.33
1
Sellors
1874.20
1.6
1.61
1
liussell
1892.32
1892.48
357.3
358.7
1.21
1.66
5
7-8
Sellers
Tebbutt
1876.03
8.5
1.30
-
Ellery
1893.36
356.7
1.40
3
Sellors
1880.44
1.3
1.39
1
Russell
1894.40
356.6
1.24
3
Sellors
1882.22
2.1
—
1
Tebbutt
1895.33
356.4
1.75
11-7
Tebbutt
In the course of the three years following the discovery, HEUSCIIEL secured
several microinetrical measures with his seven-inch equatorial, but it appears
that the records he has left us in his sweeps with the 20-feet reflector are
much nearer the truth as regards the position-angle of the stars at that epoch.
It is singular that his measures with the equatorial give angles almost identical
with that of the pair at the present time (350° .4), while his estimates made
under the superior power of the reflector give the angle as 840° ±. A careful
study of all of his observations of y Centauri (Results of Observations at the
Cape of Good Hope, pp. 211, 256, 269), and of the other measures by subse-
quent astronomers leaves no doubt that his estimates with the reflector are
essentially correct, while for some reason the measures taken with the equato-
rial are vitiated by systematic errors which render them worthless. In the
above list of measures I have inserted HEUSCIIKI/S notes, with a view of
throwing light upon this interpretation of his observations.
Contrary to the opinion of HERSCHEL, it is now evident that the motion
of y Centauri is retrograde; and hence we perceive that the radius vector has
swept over nearly an entire revolution since 1835. The recent measures of
TKBHUTT, to whom we are so much indebted for observations of this star, prove
beyond doubt that the distance of the components in angle 350° must be at
least 1".48; and hence it could easily have been divided by HEHSCIIEL with
his seven-inch equatorial. He says, however, that the object was " extremely
close and very difficult, at least as close as y Virginia;" and since it is known
that y Virginia, to which HEKSCHEL gave regular attention, was less than 0".7,
180
7 Centauri.
yCKvr \i KI 11. :.;»70. 110
we may conclude that tin- distanee of y Centauri did not surpass I'.O. If thin
be the appr«i\iinnte distance at tin- epoch 1835.25 we see that the angle must
have been substantially what Hi i:-i nri. > Miniated with the reflector, and we
are thus enabled to reenneile hi* inea-iires with those of later observers. His
estimate of 340* ± I'm- tin- angle i- based on three nights' work and can hardly
be in error by more than two degrees. If we adopt the position thus indicated
340' ± l'±
and make n-<- "I" the measures -eeiired since 18o<i, we shall obtain an orbit
which is near the truth, ami the resulting elements will never be greatly changed.
Mi:. <• i- the only computer who has previously investigated the orbit of
ihi- binary; using 1 h.ix IIKI.'S equatorial measures, and relying mainly on the
anirle-. he found:
P - 61.88 yean Q = 177°.95
T - 1840.84 i = 84M
0 - O.ttUi; A = 4G°.81
a -. I "..Vi
Making u-e uf the mean places given in the following table, and basing
our work on Inith angles and distances, we are led to the following elements
of y Centauri:
f - 88.0 years ft = 4°.6
T = 184S.O i - (K»°.ltf
• = 0.800 A =* r.'l ::
a - 1".0232 i» - -4a.O«Jll
Appan-nt nrbit:
tli of major axis = U" 1"
tli <if minor axis •• 0"..".s
Angle of major axis =()".!
Angle of periastnui -. 177°.8
Distance of star from centre = O'.T'.'I
The period here found may Iw uncertain by perliaps three years, and the
:itrii ity by ±0.03, but larger variations in these important elements are not
to be expeeted. The orbit of y Crntauri is remarkable for its considerable
inclination and high eccentricity, which renders the pair very difficult in the
periastron part of the apparent ellipse. Binaries with equal components are
very frequent among double stars, and arc types of systems which possess ft
P<-i-!iliar interest when studied in respect to their evolution.
120
VIKGENIS = Jl'1670.
It is clear that y Centaur i will move rather slowly for a good many years,
but it deserves the regular attention of southern observers. The following is a
short ephemeris:
t
6,
PC
O
It
1896.40
356.0
1.75
1897.40
355.6
1.74
1898.40
355.2
1.72
t
1899.40
1 900.40
A,
354°.8
354.4
PC
0.71
1.70
COMPARISON OF THE COMPUTED WITH OBSERVED PLACES.
1
0,
Oc
Po
PC
6.-Oc
Po—Pc
n
Observers
1835.25
340. ±
338.2
1.00
0.88
O
+ 1.8
+ 0.12
3-1
Herschel
1856.20
20.6
19.7
0.7 ±
0.77
+ 0.9
-0.07
3
Jacob
1857.97
13.7
16.7
1.11
0.91
-3.0
+0.20
5
Jacob
1860.68
12.8
13.4
_
1.10
-0.6
-_
10
Powell
1870.23
6.9
6.5
1.5 ±
1.54
+ 0.4
—0.04
6
Powell
1872.37
4.0
5.6
1.73
1.59
-1.6
+ 0.14
2
Kussell
1874.26
1.6
4.7
1.61
1.64
-3.1
-0.03
1
Russell
1876.63
8.5
3.7
1.30
1.69
+4.8
-0.39
_
Ellery
1 880.44
1.3
2.2
1.39
1.75
-0.9
-0.36
1
Russell
1882.22
2.1
1.4
_
1.77
+ 0.7
_
1
Tebbutt
1887.55
358.8
359.5
1.76
1.80
-0.7
-0.04
8-7
Tebbutt 2-1 ; Pollock 6
1888.47
359.5
359.1
1.87
1.80
+ 0.4
+ 0.07
4-6
Tebbutt
1889.32
359.1
358.8
1.73
1.80
+ 0.3
-0.07
4
Pollock
1890.36
360.1
358.4
1.82
1.80
+ 1.7
+ 0.02
2
Sellors 1 ; Tebbutt 1
1891.40
357.0
358.0
1.33
1.79
-1.0
-0.46
1
Sellers
1892.48
358.7
357.6
1.66
1.79
+ 1.1
-0.13
7-8
Tebbutt
1895.33
356.4
356.4
1.75
1.77
0.0
-0.02
11-7
Tebbutt
y V1RGINIS = 2 H)7().
a = 12h 30"'.0 ; S = —0° 54'.
3, yellow ; :i.2, yellow.
Discovered by liradley and Pound, March 15,
1718.
OBSERVATIONS.
1
Bo
Po
n Observers
t
60
Po
n
Observers
O
It
O
it
1718.20
330.8
—
2 B. & P.
1819.40
—
3.56
-
Struve
1720.31
319.0
7.49*
1 Cassini
1820.28
284.9
2.76
5
Struve
1756.20
324.4
6.50
T. Mayer
1822.02
282.8
—
2
Struve
1777. ±
310. ±
9.8
C. Mayer
1822.25
283.4
3.79
2
H. & S.
1780.0
—
5.70±
Herschel
1823.19
1823.32
281.6
3.30
2.95
1-3
Ainici
Struve
1781.89
310.7
—
Herschel
1825.32
276.9
3.26
4
South
1803.37
300.2
—
Sobs. Herschel
1825.32
277.9
2.37
6
Struve
* Computed from Lunar Decollation — of no value.
y viiiiiiNis = ^
121
1
*.
f.
n
1 '
1
••
l>.
n
( M»M-r> rr»
O
9
0
i
1828.35
27001
1
II. Is. li.-l
IK.-t9.31
31.6
1.26
2 1
IhiWM
1828.38
271.5
2.07
1
Stnive
1839.35
35.5
1.30
.
(Jail.-
1829.22
267.7
1.79
2
IllTlM-llfl
1K40.26
27.9
.:to
37 24
Kuiwr
1829.39
268.3
1.78
5
Struve
!K40.:i8
25.5
.24
11-7
IhtWI'M
lS.-tO.31
1152.1
1..LU
6-4
llerwhel
1840.45
26.4
.31
5
O. Struve
lK.-tO.59
262.2
1.59
7
Kwwel
1841.19
20.9
.42
2
Mi. ill is
18:11 :tO
258.4
1.99
tt-2
I hiwrs
1841.34
20.0
.58
7 5
IhlW.'H
IN.; 1.32
257.2
1.74
10 6
ll«-n«-liel
IK! 1.35
20.1
.73
12 11
Mii.ll.-r
1831.36
260.9
1.49
5
Struve
1K41.I1
22.4
.63
1
O. Struve
lK.-t2.27
250.2
1.21
18-1
llvrm-livl
1842.21
16.6
.58
7-5
Mil.ll.-r
1K32.30
249.9
1.33
9-1
|)awwt
1842.34
7.4
.67
-
Main
1832.33
1.94
Cooper
1K42.35
7.6
.83
-
Airy
lK.-t2.52
253.5
1.26
I
Stnive
1842.35
2.2
.85
o
Mi.,llis
1842.38
4.9
.73
9-5
I >UW<*M
1833.20
241.8
1.41
12-3
HlTM-hol
1K42.41
7.1
.S6
1
O. Struvi!
IS.-L-t.24
64.9
1.14
1
ItpHxel
1842.82
4.5
.76
-
K.I!-. 1
lK.-Ki.35
236.4
—
1
M.i.ll.-r
1842.K8
4.7
.S4
6 1
Ma.ll.-r
1833.36
240.1
1.14
8-2
IhkWM
lK.-Ki.37
245.5
1.05
7
Stnive
1K43..'tO
0.7
2.05
1
<'l.:il]|s
1K43..-W5
• 12.0
1.77
7
M:i.ll.-r
lK.-i4.29
227.3
—
K
1 fclWI-.H
1843.39
13.6
2.0K
_
Mui n
1K.-14.34
214.8
—
1
Madler
IM.il"
12.2
1.83
10-5
1 >;i « i-s
lK.-i4.37
223.1
1.51
8-1
II. -i-lii-l
1843.48
11.4
2.45
_
Kn.-ki-
1834.38
231.6
O.'.M
5
Struve
1K.-i4.54
214.9
^_
6
II.-I-. li. 1
1844,33
9.0
2.153
1
M.allis
] V.I M
213.6
—
1
Stnive
1844..-M
2.9
2.20
-
Kichardxon
1 M l..:r.
8.9
2.06
8-7
M.i.ll.-r
1835.11
201.5
—
K
Hrrsfln'1
1844..'t8
8.6
2.27
_
Kncku
1K35.3K
195.5
0.51
9
Stnive
39
195.2
0.57
1
Sen IT
1845.28
8.9
2.41
-
r.n.-k.-
rj
ItTJ
—
1
O. Struve
1845.37
7.0
—
-
M.i.ll.-r
1845.46
4.5
1'. '_'.'!
n
O. Struve
li'.'i.'i
—
•-'
Dawea
n
l.Mr.
U8
;i
Stnive
1841
5.0
—
—
Hind
1836.11
1 ."•>• 7
—
•j
0. Struvi-
i -v K;.:;'.'
•> •>
2.91
2
Jacob
1836.11
—
1
S;il,ler
lK4c,.:t'j
L'.-J.'i
-
Main
1836.59
113.9
—
_
Klirk.-
IMl
2J
2
O. Stnivo
1836.59
117.5
— •
—
Madl.-r
184&4B
4.1
1.83
1
Mit.li.-ll
1837.41
78.3
0.58
1
Ma.ll.-r
1846.90
3.8
2.45
<2
Dkwea
1837.41
77.9
0.5K
6
O. Struve
1847.07
1.9
2.62
-
Hind
1837.41
78.5
0.67
1
Encke
1847.35
2.5
2.40
8
1K.-t7.41
77.9
—
1
Aigelander
1847.41
13.0
2.37
-
Main
1S.-tS.OK
1838.32
57.5
53.4
0.67
1
1
Henwhel
1
1847.42
1847.56
1847.94
2.5
2.5
359.9
2.40
3.09
2.88
3
1
2-1
O. Stnive
Mit.h.-ll
1K38.36
—
1.24
—
I^ainont
1K38.40
51.9
0.86
_
Struv.-
1848.34
360.8
2.71
7-fl
M.i.llrr
1S.-IS.43
51.1
0.80
_
O. Stnive
1848.37
.'{60.6
2.62
9
: •
1838.43
49.2
0.83
3±
. \!
1848.43
359.1
2.55
3
O. Stnivo
122
y viEorais =
t
Bo
/><•
71
Observers
t
A.
Po
71
Observers
0
n
•
II
1848.45
360.4
2.60
2
W.C.&G.P.B.
1855.18
351.6
3.30
4
O. Struve
1848.4o
360.6
2.80
1
Mitchell
1855.19
351.3
3.51
4
Dembowski
1848.48
360.5
2.60
2-3
Main
1855.30
353.4
—
4
Powell
1855.39
353.5
3.45
_
Main
1849.37
359.0
2.85
5-4
Dawes
1855.40
352.6
3.37
1
Seech i
1849.41
352.9
2.64
2
0. Struve
1855.45
354.1
3.42
2
Madler
1849.45
359.8
3.0
2
W.C.&G.P.B.
1855.46
351.2
3.31
4-3
Dawes
1849.50
357.0
2.92
3
Main
1855.53
353.3
3.51
3
Morton
1850.23
359.7
2.85
8
Johnson
1856.10
350.5
3.45
4
Jacob
1850.30
358.0
2.90
2
Jacob
1856.29
349.0
354
-
Main
1850.30"
357.5
2.90
3
Hartuup
1856.38
351.7
3.55
6
Seech i
1850.30
356.7
2.95
6-3
Fletcher
1856.39
350.5
3.56
5
Dembowski
1850.39
355.2
2.74
4
O. Struve
1856.39
351.7
3.59
6
Madler
1850.42
359.1
1
Madler
1856.43
172.1
3.34
4
Winnecke
1850.48
359.7
2.94
4
Main
1856.96
353.0
3.64
-
Carpenter
1856.97
351.6
3.66
3
Morton
1851.17
356.8
2 92
4
Philpot
1851.19
357.7
3.12
o
Jacob
1857.07
—
4.50
-
Schmidt
1851.28
357.9
2.99
4
Madler
1857.09
348.4
3.76
6
Dembowski
1851.36
356.3
3.04
3
Main
1857.35
350.1
3.59
7
Dawes
1851.40
356.0
3.05
6
Fletcher
1857.39
350.8
3.74
7
Seech i
1851.40
356.5
2.99
5
Dawes
1857.40
352.9
3.58
6±
Baxendell
1851.42
353.0
2.88
3
O. Struve
1857.41
351.6
3.54
-
Fletcher
1851.47
355.9
3.04
3-1
Miller
1857.42
350.2
3.59
9-8
Madler
1851.98
356.4
3.30
4-3
Madler
1857.42
349.9
3.56
6
Dawes
1857.44
350.2
3.63
2
O. Struve
1852.24
355.5
3.12
3
Jacob
1857.96
350.7
3.50
5
Jacob
1852.26
355.5
3.12
6-3
Miller
1858.34
348.5
3.80
6
Dembowski
1852.32
355.3
3.02
2
Dawes
1858.37
349.9
4.01
2
Madler
1852.42
355.4
3.15
5
Fletcher
1858.39
350.0
3.57
_
Fletcher
1852.43
354.6
3.17
2
Madler
1858.40
352.0
3.62
3
Seech i
1852.43
353.0
3.00
3
O. Struve
1858.44
349.3
3.67
2
0. Struve
1852.45
356.9
3.05
-
Fearnley
1858.45
348.8
3.68
8
Dawes
1852.47
359.7
3.20
3
Main
1858.47
348.0
3.85
-
Carpenter
1858.48
350.7
3.40
3
Morton
1853.24
353.2
3.12
2
Jacob
1853.24
354.4
rr
t
Powell
1859.15
350.7
3.95
4
Morton
1853.27
354.9
3.10
7-5
Miller
1859.37
349.2
3.88
9-8
Madler
1853.32
354.6
3.18
6
Fletcher
1859.38
347.9
3.76
3
0. Struve
1853.36
354.1
3.06
3-2
Dawes
1859.39
350.0
4.18
-
Wakelin
1853.38
357.4
3.30
2
Main
1859.44
349.5
3.91
3
Secchi
1853.39
354.2
3.25
6
Madler
1859.46
348.2
3.77
5
Dawes
1853.40
352.0
3.13
4
O. Struve
1860.24
347.9
3.95
1
Auwers
1853.91
353.0
3.06
2
Jacob
1860.30
358.0
2.90
-
Jacob
1860.35
345.9
3.90
1
Madler
1854.39
352.0
3.45
8
Madler
1860.36
350.2
—
1
Schiaparelli
1854.39
352.7
3.21
8
Dawes
1860.36
347.1
—
1
Wagner
1854.40
352.1
3.40
3
Morton
1860.36
347.3
—
1
Oblomievsky
1854.47
353.6
3.23
7
Dembowski
1860.44
349.3
4.05
2
Knott
1
ft.
ft
*
t
9.
•
n
< llMMTVrrm
O
9
O
t
1861.15
347.0
3.93
4
1869.22
344.9
4.77
-
Uruimow
1861.10
• » - — •*>
Sol .<
3.12
_
Jar<>li
1869.22
840.9
5.27
2
I.i-Xli.ll i)\M.
1861.28
347.8
3.99
4
M:iin
1X69.49
:;:;'.i.s
4.74
3
Main
1861.31
346.1
3.93
5
i •,.««•!!
1869.98
34 1 .8
4.43
17
l)un«:r
1861.. '16
348.5
4.12
7
An wen
1861.41
347.8
4.11
Ma.ll.-r
1870.33
::rj.r,
4.65
Q
(iir.il, ,11
1870.38
.'.I'M-.
4.76
6
Muin
1862.03
346.5
I>iwe»
1870.39
.•{.•w.i;
—
-
Ix-yU.n <Hw.
lv.-j.33
345.3
raO
1870.72
.•ML'.O
l.i-.::
11
iK-inbowHki
I-M.-J.38
345.5
3
Ma.ll.-r
1870.77
343.4
4.45
3
O. Struve
1862.38
349.3
I ;i
1
Auwers
1871.21
33«> 8
5.31
1
I'rirt-e
1 V/J..N
| INI
-
Main
1871. 35
340.9
4.54
5
Main
1862.40
1862.42
347.6
3.62
1
O. Struve
Obloraieviiky
1871.38
.'{43.1
.'139.8
4.76
4.49
S
Ix-yton < '!.-
Knott
1863.25
346.7
4.06
3
Main
1871.38
;t.T.).7
5.35
•i
W. & S.
1863.27
345.1
4.34
-
I'.ainU-r,'
1871.53
341.8
4.77
3
Uledhill
1863.46
347.3
3.90
2
O. Struve
1872.12
• ill 1
4.59
17
I>IIII.'T
345.6
4.08
2-6
iVmbowftki
1872.30
:t;{9.7
I.I
1
(illMlllill
18IV4.40
345.7
4.27
I
Main
1872.34
842.2
5.59
3
W. &. S.
ivj.41
345.5
4.28
2
Heccbi
1872.37
:fw.r,
I.XO
-
l.i-\ (mi < MM.
lx.,1.42
345.1
4.06
3
O. Stnive
1872.40
341.5
4.82
1
Knott
iv. 1.44
315.4
4.10
4
I hiw.-s
1872.41
310.0
4.64
3
0. Struve
.'145.4
4.27
Knott
1872.41
310.3
4.78
3
Main
1864.48
348.3
4.03
3
1872.X6
3IO.X
1.59
10
IH-nilHiwMki
1873.40
:uo,2
4.83
t-
Main
1X65.45
.". I.V 1
4. 02
n
l**iitrif*tii'iiiii
' "
1873.41
XM.7
1 -..'.
Q
1 't Irilllill
1 v.:, .;•.
1865.37
1865.42
345.2
344.0
4.28
4.18
4.37
4
4
7-6
Main
Kaiiier
1 hiwcs
1873.43
1873.46
:uo.8
340.5
4.55
4.96
3
3
«>. Struve
LiiuUU-dt
IB
844.3
1 -.1
3
Knott
1874.27
340.5
5.08
2
(iledhill
71
I.IS
M
Dembuwaki
1874.30
341.8
5.(H)
i
W. & H.
;|
::i i ::
_
8ee.-lii
1X7I.:;-J
339.3
5.39
i
1 ,f\ i • m ' >!M.
.Vixi
.: 1
1
'.ill < >l,s.
vTinlook
1874
1.S7I.I1
1 ..x7
6
3
Main
O. Struve
.:n ..
l.'Jl
6
Kaiaer
1ST. VI 1
889.1
1 •'..;
II
IMIII.'T
1866. rj
::i I ii
1
o. Struve
187&3S
4
i;;,., II, ill
1866.45
84U
••
Main
L87BJ8
.Vi»'.»
6
Main
1866.46
345.9
4.01
-
Kaiaer
187.-..:{«i
840.0
4.97
1
Scaliroke
1867.24
1867.29
1X67.38
342.9
344.3
341.4
5.28
4.50
4.40
1
5
6
Leyton Olw.
Harvard
Main
1875.32
1875.41
1875.44
339.2
339.6
339.9
4.80
4.86
4.87
11
13
2
Dciulwwiiki
S-lii:i|i:in-lli
O. Struve
1867.80
343.2
4.30
12
Dembowaki
1876.24
338.7
5.34
5
])..U-t. k
1876.27
338.7
4.78
13
Glcdhill
1868.17
344.3
4.58
2
Searle
1876.36
340.0
—
1
!..-> i. .n Otm.
1868.23
341.0
5.21
2
Leyton Ota.
1876.38
3398
5.30
4
Cincinnati
1868.42
341.0
4.63
7-6
Main
1876.40
339.7
4.64
1
Waldo
1868.44
343.2
4.30
2
O. Struve
1876.41
340.2
5.14
4
Hall
124
VIRGINIS = .I" 1070.
(
0,,
P.>
n
Observers
t
60
P.,
»
Observers
1876.42
339?7
4.95
3
O. Struve
1883.07
O
335.6
tt
5.22
7-5
Englemann
1870.45
339.0
4.84
4
Schiaparelli
1883.30
336.X
5.45
5
Hall
1870.48
338.2
5.18
5
Main
1883.41
335.0
5.23
8
Schiaparelli
1877.07
338.5
—
2
Gledhill
1884.33
335.2
5.65
5-3
II. ('.Wilson
1877.24
340.0
4.05
5-4
Phimmer
1884.37
330.1
5.42
5
Hall
1877.28
335.8
5.04
-
Knott
1S84.38
335.7
5.43
3
I'eiTotin
1877.30
338.1
5.19
8-7
Cincinnati
1884.10
337.0
5.53
'>
Seabroke
1877.40
339.5
4.91
0
Jedrzejewicz
1X84.89
330.1
5.32
4
Englemann
1877.41
337.9
4.91
14
Schiaparelli
1884.40
335.0
5.19
!)
Schiaparelli
1877.4:5
338.4
4.90
-
Flammarion
1884.44
330.5
5.32
1
1
O. Struve
1 877.4:3
338.9
4.97
»>
O. Struve
1877.83
338.1
4.97
8
Dembowski
188525
334.4
5.30
1
Cop.&Lolise
1878.20
340.1
5.01
2
\V. & S.
1S85.32
333.7
5.35
'>
11. C.Wilson
1878.37
337.1
5.00
3-5
Goldney
1885.38
330.8
5.35
3
Tarrant
1878.37
337.5
5.03
1
O. Struve
1885.44
335.2
5.30
16
Schiaparelli
1X79.0
330.3
5.07
1
Tritchett
1886.28
335.0
5.08
•>
Glasenapp
1879. 12
337.3
5.20
20
Cincinnati
1886.30
336.4
5.38
2
1 1. C.Wilson
1879.13
337.5
4.97
10
Schiaparelli
1880.36
334.9
5.57
•1
Hall
1879.35
338.6
5.00
1
Gledhill
1879.37
338.3
5.20
3
Hall
1887.20
335.7
5.63
2
Glasenapp
1879.38
338.3
5.04
2
Sea. & Smith
1887.35
334.8
5.58
4
Hall
1879.44
340.0
5.09
1
O. Struve
1887.38
335.5
5.65
2
Tebbutt
1887.41
334.2
5.42
7
Schiaparelli
1880.19
336.7
5.30
1
Burton
1 880.25
337.4
5.35
6
RadcliffeObs
1888.27
333.5
5.93
•>
Glasenapp
1880.20
336.5
5.67
3-2
Tiss. & Big.
1888.33
334.6
5.50
5
Hall
1880.;'.0
338.2
5.27
5
Hall
1888.35
334.2
5.33
*>
Schiaparelli
1880.30
337.5
5.36
2
Hurnham
1888.40
335.1
5.29
2
Maw
18X0.31
337.3
4.90
-
Gledhill
1888.43
333.3
5.53
1
O. Struve
1XX0.32
336.9
5.13
6
Cincinnati
1888.48
334.8
5.74
«>
Tebbutt
18X0.37
338.1
4.95
3
Doberck
1888.91
333.8
5.50
'.)
Leaven worth
18X0.40
337.5
4.89
•>
Seabroke
1880.40
337.1
5.74
«>
Tebbutt
1889.27
333.5
5.93
2
Glasenapp
18X0.45
337.9
5.24
3
Jedrzejewicz
1889.31
333.4
5.72
3
liurnham
1X80.06
337.9
5.22
0
Franz
1889.39
333.1
5.51
2
0. Struve
1880.70
338.4
5.32
2
Pritchett
1889.43
333.0
5.54
5
Hall
1881.24
336.3
5.40
_
Gledhill
1889.44
333.8
5.41
3
Schiaparelli
1881.24
337.1
5.02
4
Doberck
1890.30
333.3
5.10
4
Glasenapp
1881.30
336.1
5.57
3
E. J. Stone
1890.43
332.8
5.59
3
Hall
1881.35
1881.39
337.7
330.8
5.33
5.20
4
9
Hall
Schiaparelli
1890.43
1890.44
333.2
330.0
5.53
6.13
8
1
Schiaparelli
Hayes
1881.42
338.7
5.28
2
Hough
18X1.44
336.2
5.23
14-13
Bigootdaa
1891.15
330.4
5.75
1
Flint
1882.28
335.0
5.13
3
H. C. Wilson
1891.32
332.0
5.78
«>
Wellniann
1X82.28
337.4
5.36
5-4
Doberck
1891.32
332.9
5.09
II
Knorre
1882.34
335.X
5.50
2
Sea.&Hodges
1891.39
333.1
5.04
3
Hall
18X2.41
330.0
5.23
10
Schiaparelli
1891.42
332.6
5.51
7-0
Schiaparelli
VIKI.IMS = .i
12:.
1
«.
p.
•
OoMBTYcni
I
9.
P.
n
(HMWnrrni
O
9
O
9
1891.44
331 .0
5.ni
1
Hi|;ounliui
1893.42
331.9
5.47
8
S.!ii;i pan-Hi
1891.44
332.5
5.70
3
-
1893.43
333.1
5.r,c,
1
Comstork
1893.4(1
331.7
5.04
4
|lipmi<laii
1> 'J I"
1892.43
332.0
332.2
5.55
5.67
I
2
Hrhiaparelli
I/eavenworth
1894.40
332.1
5.50
>2
< 'lltll.s|lH-k
l^'.'.49
333.0
5.55
3
Conuturk
1894.42
332.2
6.«2
2
Si-lii:i|i;ir«-lli
1X92.51
332.3
5.50
2
T.-I.IMIM
1894.47
328.9
5.71
t\
Iti^niiiiLiii
1892.52
3.31.8
fi.61
.
Itigounlan
1895.30
331.1
5.84
5-4
>. ,
1892.91;
332.1
5.K3
2
•Iimet
1895.43
332.0
5.(M
3
('<iiiiM<K-k
The olw*ervations of this celebrated system date back almost to the begin-
ning <>f double-star Astronomy. The only double star previously reco«*ni/.rd
which hat* proved to be binary in a Ow/aurt.t It was resolved into its coin-
l>«.iifiii- in December, 1(589, by FATIIKH HifiiAi'D, at Pondicherry, India. On
putting one eye to the teleHco|>e, and looking at the heaveiiH with the other,
|{I:\IH.I v found the two comi>onentH of y V!ryini# to IK* approximately in line
with the naked-eye stars a and S I'm/iwix; this allineation gives a ]>ositioii-
angle of 3IK»°.8 at the ejMX'h 1718.20. Such an observation has of course sonic
historical interest, but is worthy of little consideration in the discussion of a
modern double-star orbit. Neither can any confidence !><• placed in the ]>ositi<m
for 1720, which was calculated from a lunar occultation observed by (,'AS>IM
while searching for evidence of an atmosphere surrounding the Moon.
The observation which results from the Catalogue of TOIIIAS MAYKU would
be entitled to more weight were it not for the uncertainty of double-star )>osi-
tions deduced from diflercnces of right ascension and declination.
Therefore in the present discussion of the orbit I have relied principally
up. .1, iili>erv:itii>n- -'nice the time of Wn. 1,1AM STltrvK, but have not entirely
• i-ed the mr:i-i. -MI: WII.I.IAM UKIISCIIKI., which ap|K*ar to be as good
:i- fiuild In- expeeted IVoiu the means at his di>pn>:il. Alter an examination of
all tin- observation-, it appeared ad\i>aHc to base the orbit mainly u]K>n the
work of the great standard oli-<-r\«-r-. This sifting of the obserx ational mate-
rial is rendered the more necessary by virtue of the great mimlier and miscel-
laneous chanicter of the observers who have occupied themselves with an easyj
ami celebrated star like y Virginia. It is probable that more orbits have been
computed for this star than for any other binary in the heavens, but as all of
these are defective, according to trustworthy recent observations, a new deter-
mination of the elements based upon the best measures now available, would
seem to be desirable. In dealing with an orbit which has long occupied the
t Ailronomlral Journal, 86S.
t SOBM of the obMrrmUon* here omlttnl are good, bat In working with Uie grmplilml rortliotl I li»vr not tliouglil
ll nrrrf*»Tf In IIM- all of the »ii|«r-«t>iin.l«nt
12G
VIRGINIS = 2" 1670.
attention of eminent men, including SIR JOHN HERSCIIEL and the illustrious
ADAMS, we could hardly hope for material improvement over the results already
obtained, were not the investigation rendered more complete by recent obser-
vations, and by the use of the observed distances, which have generally been
rejected, but which here acquire a high importance owing to the slow angular
motion. The nature of the motion of y Virginis is such that some of the ele-
ments, especially the periastron passage and the eccentricity, are determined
with great precision; but the period has been underestimated by nearly all
recent investigators, and will still remain slightly uncertain, perhaps to the
extent of one year.
ELEMENTS DERIVED PROM PREVIOUS INVESTIGATIONS.
p
T
e
a
ft
i
A
Authority
Source
yrs.
513.28
1834.01
0.8872
11.830
87.83
68.0
290.0
Herschel, 1831
Mem. E.A.S. vol. V.p. 193
628.90
1834.63
0.8335
12.09
97.4
67.03
282.35
Herschel, 1833
Mem. R. A.S.,vol. VI. p. 152
145.409
1836.313
0.8681
3.402
60.63
24.65
78.37
Madler, 1841
Dorpat Obs., 1841 p. 174
157.562
1836.103
0.8680
3.638
58.38
35.6
94.0
Madler, 1841
A.N. 363
143.44
1836.29
0.8590
—
70.6
23.1
319.38
Heud'n, 1843
' Spec. Hartw.,' p. 345
141.297
1836.228
0.8566
—
78.47
25.23
319.77
Hind, 1845
Mem. R.A.S., vol. XVI,
133.5
1836.30
0.8525
3.499
69.67
24.6
249.3
Jacob, 1846
[p. 401
109.445
1836.279
0.8806
• —
62.15
25.42
79.07
Madler, 1847
Die Fixs.-Syst. II. p. 240
182.12
1836.43
0.8795
—
5.55
23.6
313.75
Elerschel, 1847
' Results,' p. 297 [p. 67
183.137
1836.385
0.8860
4.336
28.7
30.65
290.5
Herschel, 1850
Mem. R.A.S., vol. XVIII,
171.54
1836.40
0.8804
—
20.57
27.38
300.2
Hind, 1851
M.N., vol. XI., p. 136
174.137
1836.34
0.8796
—
34.75
25.45
284.9
Adams, 1851
184.53
1836.40
0.8794
—
19.12
27.6
295.2
Fletcher, 1853
M.N., vol. XIII, p. 258
148.2
1836.2
0.8725
3.617
41.67
31.95
269.3
Smyth, 1860
'Cycle,' p. 356
177.7
1836.50
0.8878
4.226
35.62
37.33
281.7
Smyth, 1860
' Cycle' cont., p. 451
185.0
1836.68
0.896
3.97
35.6
35.1
283.7
rhiele 1866
A.N., vol. XVIII
ong. per.
175.0
1836.45
0.8715
3.385
—
0.0
= 320.0
Fl., 1874
'Catalogue,' p. 72
180.54
1836.47
0.8978
4.09
45.82
37.0
93.98
Doberck, 1881
Copernicus, vol. I, p. 143
179.65
1836.45
0.8904
3.94
46.0
33.95
93.92
Doberck, 1881
Copern., vol. I, p. 143 ['93
192.07
1836.51
0.895
4.144
54.9
34.12
274.23
See, 1893
Astron. & Astro.- I'hys. , Dec.
From an investigation of the long list of observations, including the very
careful measures recently secured with the 26-inch refractor of the Leander
McCormick Observatory of the University of Virginia, we find the following
elements of y Virginia:
P = 194.0 years
T = 1836.53
e = 0.8974
a = 3".989
Q = 50°.4
i = 31°.0
X = 270°.0
n = -1°.8557
Apparent orbit:
Length of major axis = 6".824
Length of minor axis = 3".530
Angle of major axis = 140°.4
Angle of periastron = 140". 4
Distance of star from centre = 3".062
180
Virglnis=Sl670.
127
The accompanying table of computed :ind observed placet* shows (bat the-e
are perhaps the inont exact elements \,-t determined for any star. For although
all the measures have not been u>< •«! in forming the mean observations on whi< h
the orbit is based, yet those mea-im- which have IM-CII employed have In-en HO
combined as fairly to n-pn-nii the lient material for each year. Accordingly,
the n-idiial- are uniformly small, except just In-fore pcriastron pannage, when
tin- object \\;i- .\iivniely dillieult; ami, as no variation of the elements will
materially improve the ivpre-eiitation of the observations in this part of the
orbit without a corresponding damage elsewhere, we infer that the dillcrcnccs
are due mainU i" ^\ -tmiatic errors in STKUVK'S measures.
MPAKISON or ('OMPUTr-D WITH OnHK.RVKI) I'I.A< KM.
1
«.
'•
*
p.
8.-1
P.— ?<•
M
Olwrnrrn.
s —
o —
7
1 —
1718.20
6.27
+ 4.6
—
2
Knullcy and 1'omnl
i ;•.•('. -.1
819.0
7.49
C,M
- 6.0
+ 1.15
1
Ca-sKiiii
I7.VJ.20
.•:•_• i.t
6.50
"'.I''.
+ 5.7
-•-0.04
-
Tnlii.-iM Mayer
17sl.89
810.7
806 l
5.70
5.(»7
+ 2.6
+0.03
1
Hcnwhel
_«.
4.60
+ 0.6
__
8olM.
Hcrachel
LSI
—
3.56
3.16
—
+0.40
1 +
Struve
i w
2.70
2.97
0.0
-0.21
5
Struve
1885
0.0
-0.06
2
1 l--i M-hi-l and Soutli
L82
•JM i;
281 .a
2.70
- 0.2
+0.25
1,3.
Stnive
•-•:;.'.i
•_•:«.•-•
2.43
- 0.3
-0.06
6
Stmve
•-•:i .:.
•_'71.t
LM'7
2.01
-1- 0.1
+0.06
1
Stnive
2<W.8
.78
i.s<;
- 0.8
-0.08
7
If. 2; 2: 5
• .V.I
264.1
.59
.6.'»
- 1.9
-0.04
7
BMM!
1831.36
L-iai.'.t
21)0.8
.49
.50
+ 0.1
—0.01
5
Struve
1832.52
2.^3.5
2M.8
.26
.26
- 0.3
0.00
4
Struve
:.36
240.1
247.2
.14
.09
- 7.1
+0.05
8'»
Ihiwes
:• i:..:.
LM7.1
.08
.08
- 1.6
-0.03
7
Struve
L38
0.91
» -1
- 3.4
+0.07
5
Stmve
18,'U M
213.6
—
0.73
-12.9
1
Stnire
213J
t'.r.l
-16.7
-0.07
9
Struve
LML'.o
0.57
0.57
-16.8
0.00
1
S«-nfT
r.c i
:-il :;
__
-14.2
—
1
<i. Struve
a n
I.M i;
160J
+ 1.4
-0.10
3
Si nive
11
in :
i i • i
—
...,,.
+ 8.5
•_'
<>. Struve
141
!.. -
150.2
_
+ 3.6
-
I
Sabler
; 11
- 0.3
+0.06
1
O. Struve
: ii
• ".;
0.52
+ 0.3
+0.1.-,
1
Kix-ke
1838.08
58.0
o.r,7
0.70
- 0.5
-0.03
1
Herschi'l
51.9
+ 1.1
+0.08
_
Struve
.-.1.1
50.0
0.80
+ 1.1
+ 001
_
< >. Struve
10.0
OtT9
- 0.8
+0.04
3±
<;:iM.'.ind Midler
1839
M
.<»!
- 1.8
+0
-..1
(Jilli-'.-O; Dawn 0-1
181'
-•
28.1
.23
- 1.8
+0.05
ir-.r-'r
Kaiser 1 ± ; Daweti 11 7; (t£. 5
1R41 11
.44
+ 0.4
+0.19
4
r live
1842.21
16.6
17.7
••-
.60
- 1.1
—0.02
7,5
Mftdler
1841.M1
17.1
16.1
;::
.67
+ 1.0
+0.06
4,5
02. 4-0; DaweaO-S
1843.37
12.1
U.1
.78
- 1.6
+0.02
17,12
Midler 7; Dawea 10-5
1844.36
8.9
10.1
'.'7
- 1.2
+0.09
8,7
Midler
184&46
: 1
7.2
•-' I.'.
- 2.7
+0.08
2
O. Stnive
1846.59
3.6
4.6
2.21
2.31
- 1.0
-0.10
5
O£S| Dawes 2; Mitchell 1
128
y VIRGINIS = ^1670.
(
9,
A,
Po
PC
00-0C
P<:—pc
n
Observers
1847.38
O
2.5
O
3.0
2.40
"
2 42
o
- 0.5
-0.02
11
Dawes 8; 02.3
1848.34
0.8
1.3
2.71
2.55
- 0.5
+ 0.16
7,6
Madler
1848.40
359.8
1.1
2.57
2.56
- 1.3
+ 0.01
12
Dawes 9 ; 02. 3
1849.37
359.0
359.5
2.84
2.67
- 0.5 •
+ 0.17
5,4
Dawes
1850.40
358.0
357.9
2.74
2.80
+ 0.1
-0.00
11,4
Jacob 2-0; 02. 4; Mildler 1-0;
1851.28
357.9
356.8
2.99
2.90
+ 1.1
+ 0.09
4
Madler [Madler 4-0
1851.40
356.5
356.4
2.99
2.95
+ 0.2
+ 0.04
5
Dawes
1852.38
354.6
355.4
3.06
3.01
- 0.8
+ 0.05
7
Dawes 2; Madler 2 ; 02.3
1853.30
353.6
354.3
3.21
3.13
- 0.7
+ 0.08
5,4
Jacob 2 ; Dawes 3-2
1853.56
353.1
354.0
3.15
3.16
- 0.9
-0.01
12
Madler 6 ; 02'. 4 ; Jacob 2
1854.43
353.2
353.0
3.22
3.26
+ 0.2
-0.04
15
Dawes 8 ; Dembowski 7
1855.18
351.4
352.3
3.40
3.33
- 0.9
+ 0.07
8
02. 3 ; Dembowski 4
1855.67
352.8
351.8
3.40
3.40
+ 1.0
0.00
10,9
Seuff 1 ; Mildler 3 ; Dawes 4-3 ;
1856.39
350.5
351.3
3.56
3.44
- 0.8
+ 0.12
5
Dembowski [Morton 3
1857.28
349.1
350.2
3.70
3.56
- 1.1
+ 0.14
20
Dembowski 6; Dawes 7; Senft'7
1857.50
350.2
350.1
3.57
3.57
+ 0.1
0.00
22,21
Ma. 9-8; Da. 0; O2\; Ja. 5
1858.36
349.2
349.3
3.80
3.05
- 0.1
+0.15
8,6
Dembowski 0 ; Mildler 2-0
1858.44
350.2
349.3
3.59
3.00
+ 0.9
-0.07
16
Seuff3; 02.2; Da. 8; Mo. 3
1859.3(5
349.1
348.0
3.83
3.72
+ 0.5
+ 0.11
24,23
Mo. 4 ; Ma. 9-8; O2. 3 ; Senff 3
1860.40
347.6
347.0
3.97
3.84
0.0
+ 0.13
3
Madler 1; Knott2 [Dawes 5
1861.23
340.6
347.1
3.93
3.90
- 0.5
+ 0.03
9
02. 4; PowellS
1861.38
348.1
347.0
4.11
3.91
+ 1.1
+0.20
3 +
Madler 3 ; Auwers —
1862.28
346.0
346.3
4.01
3.99
- 0.3
+ 0.02
13, 10
Da. 5-3 ; Po. 3-2 ; Mil. 3 ; 02. 2
1863.54
346.4
345.5
3.99
4.06
+ 0.9
-0.07
28
02. 2 ; Dembowski 26
1864.43
345.3
344.9
4.18
4.14
+ 0.4
+ 0.04
11
Senff 2; 02. 3 ; Da. 4; Kn. 2
1865.54
344.2
344.2
4.36
4.22
0.0
+0.14
36, 35
Da. 7-6; Kn. 3; Dem. 26
1866.36
344.1
343.7
4.34
4.28
+ 0.4
+ 0.00
5
Senff 3 ; 02. 2
1867.80
343.2
342.8
4.30
4.40
+ 0.4
-0.10
12
Dembowski
1868.43
342.2
342.4
4.47
4.45
- 0.2
+0.02
9
O. Struve2; Main 7
1 869.98
341.8
341.6
4.43
4.53
+ 0.2
-0.10
17
Duner
1870.74
342.7
341.2
4.54
4.60
4- 0.5
-0.06
14
Dembowski 11 ; O2. 3
1871.43
340.5
340.9
4.87
4.65
- 0.4
+0.22
8
Kn.3; Gled. 3 ; W. & S. 2
1872.12
341.1
340.5
4.59
4.68
+ 0.6
-0.09
17
1 hiuer
1872.63
340.4
340.0
4.01
4.74
+ 0.4
-0.13
13
02.3; Dembowski 10
1873.43
340.3
339.9
4.77
4.70
+ 0.4
+ 0.01
13
Gled. 2; 02. 3; Ma. 5; Lin. 3
1874.64
340.4
339.3
4.97
4.84
+ 1.1
+ 0.13
5
Gledhill2; 02.3
1875.18
338.8
339.0
4.76
4.88
- 0.2
-0.12
18
Duner 14 ; Gledhill 4
1875.36
339.4
338.9
4.83
4.89
+ 0.5
—0.06
25
Dembowski 1 1 ; Schiaparelli 13
1876.34
339.1
338.5
5.02
4.95
+ 0.6
+ 0.07
26
Gled. 13; HI. 4; Soli. 4; Dk. 5
1877.62
338.0
337.9
4.94
5.01
+ 0.1
—0.07
22
Schiaparelli 14 ; Dembowski 8
1878.37
337.1
337.6
5.00
5.06
- 0.5
0.00
3,5
Goldney
1879.25
337.9
337.2
5.08
5.12
+ 0.7
-0.04
13
Schiaparelli 10 ; Hall 3
1880.30
337.5
336.8
5.30
5.17
+ 0.7
+ 0.19
2
Burnham
1881.44
336.2
336.3
5.28
5.22
- 0.1
+ 0.06
14,17
Hall 0-4 ; Bigourdan 14-13
1882.41
33(5.6
335.9
5.23
5.28
+ 0.1
-0.05
10
Schiaparelli
1 883.28
335.6
335.6
5.30
5.31
0.0
-0.01
20,18
En. 7-5 ; Hall 0-5 ; Sch. 8
1884.38
335.8
335.1
5.34
5.38
+ 0.7
-0.04
17
Hall 5; Per. 3 ; Sell. 9
1885.35
334.1
334.8
5.32
5.40
- 0.7
-0.08
19
Cop. 1 ; H.C.W. 2 ; Sell. 16
1886.36
334.9
334.4
5.45
5.45
+ 0.5
0.00
4,6
11 all 4; H.C.W. 0-2
1887.38
334.5
334.0
5.50
5.50
+ 0.6
0.00
11
Schiaparelli 7 ; Hall 4
1888.32
334.1
333.6
5.58
5.55
+ 0.5
+ 0.03
9
(Jlas. 2; Hall 5; Sch. 2
1889.40
333.4
333.3
5.56
5.60
+ 0.1
—0.04
11
BurnhamS; Hall 5 ; Sch. 3
1890.43
332.8
332.9
5.59
5.64
- 0.1
-0.05
3
Hall
1891.44
332.5
332.6
5.70
5.67
- 0.1
+0.03
3
See [Jones 2
1892.56
332.3
332.2
5.64
5.71
+ 0.1
-0.07
16
Sch. 6; Lv.2; Com. 3; Big. 3;
1893.44
332.2
331.9
5.65
5.75
+ 0.3
-0.10
11,5
Sch. 6; Com. 1; Big. 4
1894.33
331.1
331.6
5.71
5.79
- 0.5
-0.08
10,6
Com. 2-0; Sch. 2-0; Big. 6
1895.30
331.1
::::].:!
5.84
5.83
- 0.2
( (1.01
5,4
See
It will be -een thnt in ilii- m-liii tin- line of nodes coincides with the minor
:i\i- of the real ellipse, which is also the minor a\i- of it- projection; and
owing to the small inclination the apparent ellipse is only slightly less eccentric
than the real cllip-c, -o that the loci of the two ellipses very nearly coincide.
This renders the motion of the radius vector in the apparent orbit very nearly
the same as in the real orbit, and makes y Virginia an object of peculiar inter-
est from the point of view of the study of the law of attraction in the stellar
systems. From direct oh-er\ation we are enabled to say that if there is any
deviation from the Keplcrian law of areas, it must be extremely slight. There-
fort' the force i- certainly central, and the probabilities are overwhelming that
the principal star, which is so near the focus of the apparent orbit, occupies the
foe 1 1- <>r the real orbit, or that the law of attraction is Newtonian gravitation.
Other researches in double-star Astronomy increase the probability of the law
of gravitation, and leave no adequate ground for doubt as to its absolute uni-
versality. Yet a prolonged study of the motion of y Virginia will eventually
give a very precise criterion for the rigor of this law, tut well as throw light
upon the question of the existence of disturbing bodies in binary systems.
The orliit of y Virginia is very remarkable for its high eccentricity, which
surpasses that of an\ other known stellar orbit. This characteristic of y I'm///;/.*,
which Sn: .Imix I It i:-< IIKI. recognized when he declared the eccentricity to l>e
"physically sjieaking, the most import. -mi of all the elements " (Jtrgutt* ut CII/H
of (food I/ojte, p. 204), seems to preclude the permanent existence of a third
body in the system; for if a companion to either of the component- existed,
it- motion would be affected by an equation of enormous magnitude, analogous
to the annual equation in the moon's motion, and at the time of |>cria8tron
passage would probably soon cause the body to come into collision with one
of the -tar-, or be driven oil' in an orbit analogous to a hypcrl>ola.
Tim-, although the above orbit is exact to a very high degree, the system
will still deserve the occasional attention of a-tronomera.
Since the angular motion for many years to come will be extremely slow.
oljservations of distance will IK- more valuable than angular measures in effect-
ing a further improvement of the element-.
130
42 COMAE BERENICES = .£1728.
42 COMAE BERENICES = t 1728.
a = 13h 5™.l ; 8 = 4-18° 4'.
0, orange ; 6, orange.
Discovered by William Stritve in 1827.
OBSERVATIONS.
1
60
Po
n
Observers
t
60
Po
n
Observers
O
§
O
If
1827.83
189.5
obi.
2-1
Strove
1853.09
194.2
0.62
4
Dawes
1829.40
191.6
0.64
3
Strove
1853.35
194.1
0.61
14-12
Madler
1853.40
190.8
0.57
3
0. Struve
1833.37
170.7?
obi.
1
Strove
1854.38
194.1
0.60
1
0. Struve
1834.43
228.3
obi.
1
Strave
1854.39
193.6
0.61
8-7
Mildler
1835.39
11.2
—
4
Struve
1854.39
192.8
0.55
5
Dawes
183G.41
10.2
0.30
3
Struve
1855.38
198.7
0.55
2-1
Madler
1837.40
11.0
0.39
6
Struve
1855.44
189.1
0.62
2
O. Struve
1838.41
11.5
0.36
3
Struve
1856.40
192.7
0.52
5^
Madler
1839.42
12 2
0.59
Galle
1856.42
192.0
0.78
3
Winnecke
1856.96
192.5
0.47
6
Secchi
1840.45
15.7
0.55
3
O. Struve
1840.74
18.5
0.4 ±
3
Dawes
1857.39
198.3
0.50
3-1
Madler
1857.49
187.7
0.44
2
0. Struve
1841.40
14.7
0.32
12-5
Mildler
1841.41
14.5
0.49
2
O. Struve
1858.40
196.3
0.4 ±
6
Madler
1842.40
13.9
0.32
3
0. Struve
1858.44
188.5
0.38
2
0. Struve
1842.45
15.6
—
4
Madler
1859.36
215.8
0.2 ±
3
Madler
1842.53
single
—
-
Dawes
1859.37
single
—
-
0. Struve
1843.28
single
—
1
Madler
1860.34
3.5?
0.2 ±
1
Dawes
1843.45
single
_
Dawes
1861.37
10.7
—
2
Madler
1844.32
189.5
—
2
Madler
1861.40
182.8
0.50
-
Winnecke
1845.47
single
—
-
0. Struve
1861.42
15.6
0.43
2
0. Struve
1846.40
66.8?
obi.?
3
0. Struve
1862.26
9.1
cuneo
7
Dembowski
1862.37
16.5
—
2
Madler
1847.42
195.5
0.20
1
0. Struve
1862.40
11.6
0.54
2
0. Struve
1848.42
192.7
0.27
3
0. Struve
1862.42
2.9
—
—
Oblomievsky
1849.42
188.6
0.42
3
0. Struve
1863.25
11.0
0.5 ±
1
Dawes
1863.44
9.3
0.55
1
0. Struve
1850.39
191.4
0.48
3
0. Struve
1850.99
193.3
0.40
1
Mildler
1864.42
10.9
0.3 ±
2
Secchi
1864.42
12.5
0.51
3
O. Struve
1851.27
191.3
0.35
1
Madler
1864.43
13.4
0.45
1
Dawes
1851.42
187.0
0.49
4
0. Struve
1851.96
194.5
0.45
3-2
Mildler
1865.53
13.9
0.25 ±
2
Secchi
1865.57
9.5
cuneo
5
Dembowski
1852.42
191.0
0.54
6-5
Madler
1865.59
13.7
0.54
6
Englemann
1852.43
190.9
0.56
3
O. Struve
1852.45
12.2
0.48
-
Fearnley
1866.64
8.5
0.40
3
0. Struve
<>MAK BKRRN1C7K8=
1
6. •
P.
•
ObMrren
(
9.
P.
ii
Observer*
O
9
O
•
1867.32
•JI.I
1
\Vinl.H-k
1881. •-•:,
192.2
0.70
2
Higounlan
1^.7.32
24.7
_
1
Hetrle
1881 I':,
190.9
4-3
Doberck
47
13.0
0.36
|
0. Struvo
l.vsl :::
193.0
0.64
4
lUirnhaiu
77
14.8
cuneo
•_•
IVmlxiwski
1K81.38
191.6
0.6 ±
5
Si-hiaiNin-lli
1868.44
15.8
"'.•I
2
: uvi-
1.39
1881.41
192.6
193.5
,,:,.;
0.5 ±
4
7-0
Hall
1'erry
1869.24
11.6
—
1
Leyton Obe.
1882.35
194.4
1.00
4-2
Seabrokc
18K9.4O
: •
,,1,1.
Doali
• 1882.38
191.9
0.54
4
Hall
1869.47
: •
ol.l.V
1
M1M-
1882.42
191.4
0.6 ±
6
Schiapawlli
1870.44
•ingle
—
_
< i Strove
1882.46
184.6
0.51
1
O. Strove
i>7o.4S
,,1,1.
4
Duti^r
1882.93
192.1
0.56
7
Kngleiiiann
L87L40
I'.u r,
(.1.1.
.-{
m-mliowski
1883.42
193.2
0.50
4
Hall
1871
single
,^_
_
« >. Strove
1883.42
191.1
0.5 ±
8
Si-lii;i|,;irrlli
1883.48
193.4
0.55
5-4
K ii - 1 1 H • r
iv-.1 IL-
<,!.!.
1
O. Strove
1883.51
191.5
0.53
>2
I'errotin
1873
ol.l.
>2
Dunlr
1884.39
195.8
0.3 ±
4
Si-liia|,an-lh
single
—
1
.1. M. Wilson
1884.40
189.7
0.36
3
Hall
M
i.O
0.20
2
O. Strove
71
200.5
obi.
3
Itemliowski
1885.41
single
—
1
1'errutin
1885.42
single
4
S, lu,i|,:il,-lli
1^71.41
189.2
0.30
2
O. Strove
1885.49
10.2
0.35
1
Hall
-
1H2.5
0.5 ±
1
Seahroke
1886.42
10.0
0.27
3
Hall
1875.43
L9U
0.4 ±
10
Sc-hia|>arelli
1886.51
15.8
0.26
6
Schiaparelli
LMM
M.-.l
5
Dembowski
M
18'.» 7
0.39
3
O. Strove
1887.42
13.1
0.38
9
Si-liia|,ari'lli
.53
191.5
0.32
7-6
Ihm.'-r
1887.44
13.6
0.42
4
Hall
1876.36
18C.4
0.5 ±
1
\V. Smith
1888.27
12.0
0.48
3
Schiaparclli
1876.38
191.2
0.58
4
Iti'inlM.wski
1888.40
13.8
0.45
8
Hall
1^ 7U.40
193.4
0.40
4
Hall
1888.43
8.7
0.42
1
O. Strove
U
188.0
0.50
3
o. strove
1889.08
10.5
0.56
1
I<eavenw»rth
193.1
0.5 ±
4
Srliiapan-lli
I889J8
11.8
0.61
1
0. Strove
1>77.41
<'.4
o.VJ
St-liiaparelli
l-vi.ll
IOJ
0.48
5
Srhiaparelli
1^77 I.'.
I'.'l »
.-.
1 K-iiibowski
1890.:«
o.7o
4
Itiirnliani
isn
186.0
" 17
O. Strove
lv,, M.;
10.5
0.51
\'2
Srhiaparelli
!•'•
,.,.:.
1
O. Sinn.-
1 v.i 1.44
11.4
O..M
:<
Hall
-:»
Ifl
ohl.
;{
.Ifil rzejewiez
1. vi 1.44
lo.T
,, )•.
9
Scliiapart'lli
tan
ii..-, l
4
Hall
188UI
11.7
o 17
_• 1
Leavonwi.rlli
190.8
1 >• inlxiwuki
• lo
lo.T
M. I.'
6
Sfliiaparelli
I'.'.' I
0.08
o
Ituniham
1 Vl'J. | |
11.7
1, |U
8-6
Hignunlan
• \j
l-.i
...M
4
Hall
10.L'
5
Schiaparvlli
1879.42
r.n.4
0.6 ±
5
Schiaparelli
L8M
0.1
OJB
3
CVjmstook
1879.44
190.9
...:.
1
O. Strove
l.vu.i:.
16.6
—
1-0
Bigounlan
1880.3G
191.7
4
Hall
1894 1',
lu.;s
0.22
1 /.
Schiaparelli
1880.41
194.3
obi.
4
Jedrzejewicz
18'.'
13.9
0.14
3
>...
Since the date of discovery this remarkable star ha« descril)cd almost three
revolutions. From the first it was given particular attenlion by WILLIAM and
132 42 COMAE BERENICES = 2"
OTTO STRTJVE, and the peculiar and unique character of the system has fully
justified the care with which it has been measured. The only previous inves-
tigation* of the orbit is that made by OTTO STRTJVE and DUB r AGO in 1874
(Monthly Notices 1874—5, p. 367) . O. STRUVE'S elements are as follows :
P = 25.71 years & == 11°.0
T = 1809.92 i = 90°
e = 0.480 X = 99°.18
a = 0".G57
Some three years ago BURNIIAM placed at my disposal a list of measures
which was nearly complete; I have since added to it such as were omitted,
and besides made new observations during 1895. "When scrutinized under the
fine definition of the 26-inch Clark Refractor of the University of Virginia the
pair proved to be excessively close, and with a power of 1300 could only be
elongated. The object has now become single in all existing telescopes and
can not again be separated until about 1899.
The method followed in the present investigation of the orbit is not very
different from that employed by OTTO STEUVE, except that the results are based
upon the measures of all reliable observers and are rendered more complete by
the observations made since 1874. The list of measures is complete to the
occultation of 1896.
It will be seen from an examination of the observations that the motion
is to all appearances exactly in the plane of vision, and hence with the excep-
tion of the node and inclination, the elements are based wholly on the distances.
O. STKUVE'S elements are very good, and it would therefore be sufficient to
apply differential corrections to his values, but as I had independently discovered
a graphical method similar to that employed by him, it seemed of interest to
make use of it in deriving approximate values directly from the phenomena.
With the elements approximately determined, the observations furnished 52
equations of condition, which were solved for the five unknowns, the weights
assigned being proportional to the number of nights. An application of the
corrections resulting from the Least Square adjustment gave the following
values' of the elements:
P = 25.556 years Q = 11°.9
T = 1885.69 i = 90°
e = 0.461 X = 280°.5
a = 0".6416 n = ±14°.0867
•Monthly Notices, June, 1890.
•
§
1
o
5
!
• . ..M \i 111 1:1 si«'K8 =
A|'|«:iiVnt MI I lit:
Length <>f in.ij.ii axis — I'.l 17
Length <>f tuin.ir axis — O'.OO
\ ..;leof major axis — 11°.'J
Anglf »f (H-riastron — ll'.'J
-Uir fruin centre — 0*.054
The apparent motion is shown in the accompanying diagram, to which is
:nl<l< .1 n lignre <>f t lie real <>rl>it. A graphical illustration of the motion, ol>-
taincd In taking the jr-axis to represent the time, while the ordinatcs represent
tin- di-tanre». ua- employed in finding the approximate values of the elements;
tin- mrvr here traced rcpn-ent- the motion according to the element* as
eorreeted. This orbit of 42 Comae llerenices in one of the most exact of double-
-tar orbit*. MM. I will never n-.|iiire any but very slight modifications. The
period (an hardly be in error by more than 0.1 year, while a variation of ±0.01
in the eccentric -it\ i- very improbable.
•I-ARISOX OF COMPUTED WITH OIMRRVRII
(
«.
H
ft
P€
«^-fl.
P*-t,
•
OUenren
1827.83
iv..-.
I'.M •
obi.
|J ;
A
- 2.4
4-0.01
2-1
Strove
r.'i «;
I'.tl.'.i
B • :
—
- 0.3
—
3
Strove
17"; •
191.9
obL
—
-21.2
—
1
Strove
1834.43
I'.H.'.t
obi.
__
+ 36.4
1
Strove
11.2
11. '.i
—
—
- 0.7
__
4
Strove
'..41
10.2
11.9
0.30
0.42
- 1.7
-0.12
3
Strove
1837.40
11.0
11.9
0.39
0.50
- 0.9
-0.11
6
Strove
1838.41
11.5
11.9
0.3(5
0.51
- 0.4
-0.15
3
Strove
i.41'
1 •_' •_•
11.9
OJ|
0.50
+ 0.3
+0.09
_ .
Galle
1840.60
17.1
11. '.»
0.44
+ 5.2
+0.04
6
O. Strove 3 ; Dawes 8
1M1.40
14.6
11.9
H |U
+ 2.7
+0.02
14-7
0. Strove 2; M idler 12-5
184.
14,7
1 1 .'•
0.30
+ 2.H
+0.02
7-3
i >. Strove 3 ; Miuller 4-0
i > »3.36
—
single
—
__
__
2
M :,.•:.: 1 : Ihiwes —
184!
•, , -.
i9i e
_
_
2
Midler
iH4.Yi;
—
single
—
—
_
—
_
i ). Strove
184'
191.9
obL?
—
•f54.9
—
3
«i. Strove
184
!••:..-.
0.18
4- 3.6
+0.02
1
n Strove
I'M ;.
+ 0.8
±0.00
8
u Strove
184
188 B
191.9
0.36
- 3.3
+0.06
8
1 1. Strove
> ... •
191.9
-' II
M i:,
+ 0.4
-0.01
4
ruvp.'i; Mfull.T 1
1851.55
r.M •.»
0.47
0.51
- 1.0
-0.04
MAdler 1-0; <C 1 M.odler 3-2
I'.M .0
191.9
- 0.9
-0.01
9-*
Madler6-5; O. Strove .!
18T.
• . o
191.9
0.00
+ 1.1
±0.00
•Jl n;
Dawes 4; Madl. r 1 1 12; OJ.'. 3
18.-. :
ItSJ
191.9
0.80
4- 1.6
-0.02
11 i::
"± 1 : Madler 8-7 ; Dawes 5
18.V. J 1
I'-1-''
191.9
4- 2.0
-0.02
4-3
-:nive2; Miller 2-1
>:,,
193.4
191.9
0.67
4 0.5
±0.00
II i.;
Madler 5-4 ; Winn. 3 ; Hecchi 6
1857.44
1919
0.47
M.M
4 1.1
-0.04
5-3
Madler 3-1 ; O. Strove 2
1858.42
192.4
191.9
,, ,
' ..-.
4 0.5
+0.04
8
Midler 6 ; O. Strove S
>-,•. ,;
I9L9
0.14
+ 23.9
+0.06
3
Madler
181 -..;
3.6?
11.9
0.2 ±
•> r_'
- 8.4
+0.06
1
Dawes
1861.40
13.1
11.9
0 i .
0^4
+ 1.2
+0.09
I •_•
Midler 2-0: O. Strove 2
1882.34
12.4
II ;i
• • :. i
0 M
4 0.5
+0.08
11-2
DHL 7-0; Midler 2-0; OX 2
01269.
t
00
Be
Po
PC
/J (\
VO — 0c
Pa—P<-
n
Observers
1863.35
10.2
0
11.9
0.53
0.52
o
- 1.7
+0.01
2
Dawes 1 ; 0. Struve 1
1864.42
12.3
11.9
0.48
0.51
+ 0.4
-0.03
6-4
Secchi 2-0 ; 02. 3 ; Dawes 1
1865.56
12.4
11.9
0.44
0.47
+ 0.5
-0.03
13-8
Secchi 2 ; Dem. 5-0 ; En. 6
1866.64
8.5
11.9
0.40
0.41
- 3.4
-0.01
3
O. Struve
1867.62
13.9
11.9
0.36
0.33
+ 2.0
+ 0.03
4-2
O. Struve 2 ; Dembowski 2-0
1868.44
15.8
11.9
0.21
0.25
+ 3.9
-0.04
2
O. Struve
1869.37
15.2
11.9
obi.?
—
—
5
Ley. 1 ; Duner 3 ; 0. Struve 1
1870.45
16.0
11.9
obi.
—
—
4
Dimer
1871.41
194.6
191.9
obi.
—
—
3-0
Dembowski
1872.47
200.0
191.9
obi.
—
—
3
O. Struve 1 ; Duner 2
1873.60
194.7
191.9
0.20
0.23
+ 2.8
-0.03
5-2
Dembowski 3-0 ; 0. Struve 2
1874.41
189.2
191.9
0.30
0.30
- 2.7
±0.00
2
0. Struve [Du. 7-6
1875.42
191.3
191.9
0.43
0.40
- 0.6
+0.03
26-25
Sea. 1 ; Sch. 10 ; Dem. 5 ; O2. 3 ;
1876.40
190.4
191.9
0.50
047
- 1.5
+ 0.03
16
Sm. 1 ; Dem. 4 ; Hall 4 ; 02. 3 ;
1877.43
190.9
191.9
0.52
0.53
- 1.0
-0.01
17-13
Sch. 9-5 ; Dem. 5 ; O2. 3 [Sch. 4
1878.40
191.4
191.9
0.58
0.58
- 0.5
±0.00
11-8
Jed. 3-0 ; HI. 4 ; Dem. 3 ; 02. 1
1879.40
191.9
191.9
0.61
0.61
± 0.0
±0.00
12
/3. 2 ; Hall 4 ; Sch. 5 ; 02. 1
1880.38
193.0
191.9
0.52
0.62
+ 1.1
-0.10
8
Hall 4 ; Jed. 4 [Perry 7-0
1881.34
192.3
191.9
0.59
0.61
- 0.4
-0.02
26-18
Big.2; Dk.4-3 ; 0.4; Sch.5; HI. 4:
1882.52
190.9
191.9
0.56
0.54
- 1.0
+ 0.02
22-18
Sea. 4-0; HI. 4; Sch. 0; O2. 1 ; En. 7
1883.46
192.3
191.9
0.52
0.43
+ 0.4
+0.09
19-18
HI. 4 ; Sch. 8 ; Kii. 5-4 ; Per. 2
1884.40
192.7
191.9
0.33
0.26
+ 0.8
+ 0.07
7
Schiaparelli 4 ; Hall 3
1886.4IJ
12.9
11.9
0.27
0.25
+ 1.0
+ 0.02
9
Hall 3 ; Schiaparelli 6
1887.43
13.3
11.9
0.40
0.41
+ 1.4
-0.01
13
Schiaparelli 9 ; Hall 4
1888.33
11.5
11.9
0.47
0.49
- 0.4
-0.02
7-6
Schiaparelli 3 ; Hall 3 ; 02. 1-0
1889.25
11.1
11.9
0.55
0.52
- 0.8
+ 0.03
7
Leavenworth 1 ; Sch. 5 ; 02. 1
1890.38
9.9
11.9
0.60
0.51
- 2.0
+0.09
16
ft. 4 ; Schiaparelli 12
1891.44
11.0
11.9
0.50
0.45
- 0.9
+ 0.05
12
Hall 3 ; Schiaparelli 9
1892 40
11.4
11.9
0.43
0.39
- 0.5
+ 0.04
16-13
Lv. 2-1 ; Sch. 6 ; Bigourdan 8-6
1893.45
10.2
11.9
0.32
0.31
- 1.7
+ 0.01
5
Schiaparelli
1894.41
9.0
11.9
0.23
0.22
- 2.9
+ 0.01
8
Com. 3 ; Big. 1-0 ; Sch. 4-5
1895.29
13.9
11.9
0.14
0.14
+ 2.0
±0.00
3
See
02-209.
a = 13h 28'".3 ; 8 = +35° 46'.
7.3, yellowish ; 7.7, yellowish.
Discovered by Otto Struve in 1844.
OBSERVATIONS.
t
Oo
Po
n
Observers
t
O
t
1844.31
218.0
0.33
1
0. Struve
1855.47
1846.38
231.1
0.39
3
O. Struve
1861.26
1847.30
222.7
0.25
1
Miidler
1865.50
1847.41
215.1
0.18
1
Miidler
1868.26
1849.47
218.0?
oblong
1
O. Struve
1872.47
1851.30
222.4
0.20
1
Miidler
1851.39
228.9
0.33
1
O. Struve
1877.26
223.6 0.27
242.8 0.33
45 oblonga
n
Observers
1
0. Struve
1
0. Struve
1
Dembowski
1
Dembowski
1
O. Struve
1
Dembowski
L36
1
1XK.T4 1
0.
CL4
h
0.22
4
1885.42
1HS9.52
195.
207.7
elong.
0.22
2
181)0.41
2«.3
0.22
1
1 v.i 1.26
213.4
0.22
3
1'i-rri'tin
Hnnihaiii
< f.
I .vi 1.49 28^9 o!l9
1892.4U 215.0 0.21
1894.40 210.5 O..'(0±
1895.41 219.0 0.225
74 235.4 0.44
I
o
a
!
Si-liiiiparelli
lillMllt.llll
ComsUx-k
Since the cpoeh of .li-covery in 1*11 tin- companion has descril>ed an entire
revolution, hut the discordance of the observations rentiers it difficult to define
tin- cxaet charaeter of the orhit. The measures are frequently very inconsistent,
:iinl the most can-fill -elections arc necessary in forming the mean places.
During tin- pa-t lew years the system has received merited attention from
Hi I:\II\M ami S« HI Ai'AitKLM ; their measures make known the nature of the
motion and enable us to fix the elements with considerable precision. Hi'RN-
ii \M was the first to give a proper interpretation of the earlier observation*
(Ok*' rrnt'iri/, July, 1801), and to find a satisfactory apparent ellipse. (JoitK
afterward- attempted an investigation of the orbit based on the angles only;
In found the following elements:
47.70 years
1KX.-M2
= 51°.93
i o 82-.81
\ - 43°.51
a — O*.58
Tin- e\i -lu-ive use of angle* in deriving the orbits of close and difficult
-tar- lia- frei|iieiitly led to erroneous results, because when the distance
i- \<TV -mall it is even more reliable than the angle. The use of distances
become- not only ini|>ortuiit but al-o necessary when the orhit is highly inclined,
and the companion therefore has an angular motion which is small compared
to the errors of obserxation. a> is the case with 6/,1'lV.i. Accordingly in deal-
ing with the orbit of this star we have given rather more attention to the
• li-taner- than to the discordant and frequently retrograding angles. Using
certain -< 1, ,-ir.l measures of the best observers we find the elements of 0.T269
to be as follows:
P - 48.8 years
7- 1882.80
e -0.361
a - 0».3248
Q - 46*.2
» - 71°.3
A - 32°.63
M - +7*.3771
136
0^269.
Apparent orbit:
= 0".G4
= 0".20
= 47°.7
= 57°.8
Length of major axis
Length of minor axis
Angle of major axis
Angle of periastron
Distance of star from centre = 0".102
The period here found is undoubtedly very nearly correct, but the other
elements are subject to greater uncertainty. However, the observation of
ENOLEMANN in 1883 and DEMBOWSKI'S estimate in 1877, establish the essential
nature of the periastron end of the apparent ellipse, and assure us that no
large correction of our apparent orbit will ever be required. The eccentricity
is not likely to be altered by more than ±0.05, nor can the node and inclina-
tion suffer changes which are proportionately larger. Thus it appears that the
orbit is very satisfactory for the scant material now available; and while large
corrections are not to be anticipated, it will be desirable to improve upon these
elements when more good measures are secured. The ephemeris shows that
the star will be comparatively easy for a good many years, and it will there-
fore commend itself to the regular attention of observers.
t
ft
PC
o
If
1896.40
222.4
0.37
1897.40
224.0
0.39
1898.40
225.5
0.40
t 6c PC
1809.40 226/J 0^41
1900.40 228.2 0.41
COMPARISON OK COMPUTED WITH OBSEKVKD PLACES.
t
0.
6.
P°
PC
Oo — Oc
P,—PC
n
Observers
1844.31
218.0
215.6
0.33
0.30
o
+ 2.4
+ 0.03
1
0. Struve
184(5.39
223.8
219.9
0.39
0.35
+ 3.9
+ 0.04
1
O. Struve
1851.34
228.9
227.9
0.33
0.41
+ 1.0
-0.08
1
0. Struve
1861.26
242.8
243.0
0.33
0.34
- 2.0
-0.01
1
O. Struve
1872.47
257.1
298.6
oblong
0.12
-41.5
—
1
0. Strove
1877.26
0.0?
28.0
oblonga
0.19
-28.0
—
1
Dembowski
1883.41
61.4
62.8
0.22
0.16
- 1.40
+0.06
4
Englemann
1889.52
207.7
199.5
0.22
0.17
+ 8.2
+ 0.05
3
Schiaparelli
1890.41
206.3
205.4
0.22
0.21
+ 0.9
+0.01
1
Schiaparelli
1891.26
213.4
209.5
0.22
0.24
+ 3.9
-0.02
3
Huniham
1891.49
208.9
210.4
0.20
0.24
- 1.5
-0.04
2-1
Schiaparelli
1892.40
215.0
213.6
0.21
0.28
+ 1.4
-0.07
2
Burnham
1895.07
222.9
220.0
0.37
0.35
+ 2.9
+ 0.02
2
Comstock 1 ; See 1
1895.41
219.0
220.7
0.23
0.35
- 1.7
-0.12
2
Schiaparelli
25 OAKUM VKNA I !< • »:< M = i'1768.
I'.-, i \\l M \I\\IK (MM M - SIT
i
fc
• _ \» 88- ; 8 = +w°
5. «liltr ; «.5, blue.
• ••ii-rrnl by H'iHiiiin A'
v 1 loMH.
p. j. oliwnren (
48'.
in 1827.
e.
( H .«.- M .• r -.
i
o
P
1829.89
.•»
.
St nive
1872..-W
run ud
—
\V. & S.
lH33.r.'
;•-• i
1 ,,.,
••
Strove
1872.47
58?
—
O. Struve
71 x
1 "7
8
Struve
1875.:<6
1875.48
single
167.1
0.63
Hall
O. Struve
Ixil 17
I «H
l
ruve
1875.49
round
—
I'llll'T
lx|l
IM
Madler
1876.42
doubtful
_
1
Hall
1841
:: 1
I >aww
1876.45
161.4
0.4 ±
4
Schiajian-lli
184!
IM
2
Ifciwea
1877.37
154.5
0.4 ±
10
Schiapart-lli
|x|
7".-,
o.71
3
Mftdler
1877.54
154.7
0.60
1
O. Strove
|X|,
II.7-.'
3
O. Strove
1878.41
151.8
0.75
4
I*mbow.ki
lx|7.71
0 .10
1
Madler
1879.43
155.7
0.5 ±
5
SchiajianMIi
1848
3
O. Strove
1879.49
157.6
0.51
5
Hall
1811
B8J
0.39
6-4
Mftdler
1880.37
1880.46
157.5
155.0
0.35
0.60
2
Hall
Hurnliam
1852.32
45.0
0.3 ±
4
Madler
1881.24
27.6
—
1
I MNTC k
1853.32
36.2
0.35 ±
1
M&dler
1881.32
151.6
0.49
1
Itipiunian
36.2
0.35 ±
3
I>awe§
1881.40
153.4
0.60 ±
5
S< -In a |>at rill
I H i
i».:i.-,±
• •
M.l.ll.T
1881.40
lxsl.43
157.4
155.9
0.53
0.41
3
3
Hall
I'.unili.iin
ol.longa
-
Secrl.i
L88U7
16.0
_
1
IKilierfk
1868.65
o.l»±
1
Midler
1889
119.3
0.78
5
Kn-l.-iiiaiiii
ls.Vj.41
single
—
1
ii >• .
188'.' I.'.
I.VJ.7
1.-.1.3
• • r,
0.7 ±
3
x
Hall
1860.36
!«• I.'.
ii l.~>±
1
Dawes
18.x
nr.o
11. Vi
1
Hall
]x,;i
single
—
1
IBM
|
lx,;i.58
14J
—
1
Midler
If.MI
0.7±
S<-liia|iarelli
IM
•
—
1
, i -•
148
O..VI
'2
l'.-ir..tin
IM
—
1
Ik-mU.wski
18.x
11
_
1
Kigourdan
18631.-.
: '.
—
1
Demhowski
1141
1 1:...-.
0.63
8
Hall
1865 1 1
—
round
1
Dawes
1 1-
0.8 ±
1
Srhia|.an'lli
^_
1
Dembowski
14<> 1
0.89
3
1'errotin
149.6
0.77
3
Tarrant
1880.40
: re
—
1
I»uner
1886.18
143.1
1
I'l-rmtin
1870.43
>'
1
Duiidr
1886.45
146.2
0.78
4
Hall
1871.45
47?
—
1
Duner
1886.51
146.7
0.78
4
Hchiaparelli
138
25 CANUM VENATICOKUM = .11768.
1
60
Po
n
Observers
t
tio
Po
n
Observers
O
IT
O
H
1887.41
145.8
0.67
4
Hall
1892.17
137.5
0.98
3
r>urnham
1887.46
142.7
0.72
9
Sehiaparelli
1892.64
140.0
0.95
3-2
Coinstcx'k
1888.44
145.8
0.73
3
Hall
1893.50
138.4
0.81
2
Sehiaparelli
1888.54
142.9
0.76
5
Sehiaparelli
1893.58
138.9
0.89
1
Comstoek
1889.48
140.5
0.84
5-4
Sehiaparelli
1894.47
138.1
0.86
1
Sehiaparelli
1890.42
137.9
0.81
4
Sehiaparelli
1895.11
1895.20
132.6
134.5
1.35
1.11
3
4-5
Barnard
Barnard
1891.48
141.4
0.80
4
Sehiaparelli
1895.28
136.4
1.06
3-4
See
1891.51
143.6
0.93
3
Maw
1895.52
137.4
0.90
2
Comstoek
The observations of this remarkable system prior to 18-10 gave evidence of
a slow retrograde motion, and accordingly it received the attention of OTTO
STRUVK, MADLEH, DAWES, and subsequent observers. Up to this time the
radius vector has swept over 308° of position-angle, while the distance has
diminished from 1".13 to 0".23 and again increased to about its former value.
The data furnished by observation do not suffice to fix the elements of the
oi-bit with great accuracy, but we believe that it is now possible to get a fail-
approximation to the motion, and that the resulting elements will not be sensibly
improved for a great many years.
When the measures of this star are examined it is found that they are far
from satisfactory, and therefore we must not expect an agreement such as
could be obtained for easier objects, where the components are wider or more
nearly equal in magnitude. Some of the recorded measures are so inconsistent
that the mean places must be formed with care, and even then the representa-
tion of the motion is not entirely satisfactory. The smaller distances have been
under-measured, as is clear from the fact that a star of this difficulty could not
be seen with small telescopes (such as those used between I860 and 1875),
unless separated by something like 0".3. Under these circumstances it seemed
proper to increase the measured distances near pcriastron, in order that when
plotted on the diagram of the apparent ellipse they might not convey to the
reader an erroneous impression. In the table of computed and observed places,
however, we have retained the original values, and it will be seen that the
differences are not at all considerable. DOHEKCK is the only astronomer who
has previously computed an orbit for this pair; using measures up to 1880 he
found:
P = 119.9 years
T = 1863.0
c = 0.72
a = 0".81
ft = 42°.4
i = 338.3
A. = 245°.0
I
25 r\\i M \ i \ \rn ->i:i M = .11768.
A cnnTul investigation of nil the ol»i-rvations leads to the following ele-
ments of U"» < ''ilium Vrnnlif»rntn:
/» - 1M " v-an
T -
t *
a - 1M307
0 . I2.r.o
X - 201 '.0
M - -r.9fl6T»
Ap|Nircnt orbit:
Length of major axis — I'.'.H
Length of minor axu — 1".08
Annie of major axis — 108*.9
Angle of iieriaatron «• 28.V.4
mce of star from centre = 0*.71 1
Thi- orliit is remarkably eccentric, and so far as known is surpassed in
i hi- iv-|><-( -t l>\ four stars only — y Km/mix (0.9), y Ainlnnnednr (0.85), y Cm-
t'lmi (<>.84>) and (Jl> llrrculi* (0.78). Whatever changes may hereafter be re-
quired in these results, it is certain that the eccentricity will remain conspicuous,
and will not be varied sensibly from the value here obtained. The period,
Imwever, remains uncertain by |>crha|>s 25 years, so that the motion of the
-N-tem is not so well determined as could be desired. An ephemeris is ap-
pended for the use of observers.
or CoMiTi-rn WITH OIMKKVKH I'LACMM.
(
«.
«r
P*
. *
e^e.
Pr- ft
•
ObMmn
1827.28
82.4
7'.i 7
1.13
1 15
+ 2.7
-0.01
1
Strove
'.M
77.1
1.10
1.09
4- 1.8
+0.01
4-3
Stnive
O3
TIM
71 »
1.06
L04
- L'.2
+0.02
5-4
.Struve
71.1
71..-,
1.05
,,•„.
- 0.4
+ 0.09
2
Stmve
1841
,.:..,
1.00
+ 5.2
+o.ir>
4-3
M:uller
1845
Q x :
+ :u
:: 1
1 >.iwes
IMfl M
n -
M 1
"71
+ 11.1
+ 0.01
3
(t. Stnnc
1841
+ 3.9
-0.13
1
Miullt-r 1 ; 0. Stnn.' .;
1851.28
0.39
,.,,.
+ 9.2
-o.-.-i
6-4
ICldkt
40.6
I'M
0 1 •
OLM
+ 0.5
-0.19
6-1
Ifldkc
•
DM
+ 1.0
-0.1.1
3
DMVM
1857.57
19.8
" ti
+ 6.4
_0.-'o
:: -J
Secchi 1 o; M:i<ll<>r2
I860 .,
I". ±
..-.,.,
0.15±
o.:«
+ 1S.1
-fclfl
1
Dawn
0?
0 !
n.-.'.s
+29.6
—
1
1 h-mlioWHki
1MB :.'.
.::.
! M i
.
OJW
-13.4
_
1
Dembowski
1868.76
•-•«•_•:.
_
• ••-•I
+ 6.0
^
•2
I>i-iiil)owski 1 ; lhim;r 1
elong.
QM
-24.8
-- -
2
Ihin#r
1 i;
- -
1 •.•«'.!
_
-.:.-,
+48?
__
1
: uve
ierj
ITU
0.47
- 4.2
+0.1'-,
1
uve
161.4
itrj
0.5 ±
",-,!
- 6.8
-0.01
4-1
- .aparelli
1877 I-
154.6
0.60
- 9.0
+0.06
11-1
Hchiaparelli 10-0 ; O. Struve 1
1878.41
1.11 s
L«OJ
0.76
- 8.8
+ 0.17
4
Dembowski
1879.46
;-....
1.-.7 7
0.62
- 6.9
-0.02
10-1
Sohiai«reUi 6-1 ; Hall 5-0
ISM- ;:
I.'... :
,,,,,
- 0.2
4-2
Burnham 2 ; Hall 2-0
140
a CEXTAURI.
t
o.
9e
Po
PC
9.-9.
Po—Pc
n
Observers
1881.40
153.4
153.3
0.60
0.69
0
+ 0.1
-0.09
5
Sehiaparelli
1882.39
150.3
151.0
0.72
0.73
- 0.7
-0.01
13
Engleniann 5 ; Sehiaparelli 8
1883.45
149.1
149.0
0.75
0.76
+ 01
-0.02
14-11
HI. 1-0 ; En. 6 ; Sch. 5 ; Per. 2-0
1884.42
145.5
147.4
0.66
0.80
- 1.9
-0.14
3-1
Hall
1885.41
149.0
145.8
0.82
0.82
+ 3.2
±0.00
15
Sch. 9 ; 1'errotin 3 ; Tarraut 3
1886.48
146.0
144.2
0.78
0.86
+ 1.8
-0.08
8
Hall 4 ; Sehiaparelli 4
1887.46
142.7
143.0
0.73
0.88
+ 1.3
-0.15
13-9
Sehiaparelli 9
1888.49
144.3
141.5
0.75
0.92
+ 2.8
-0.17
8
Hall 3 ; Sehiaparelli 5
1889.48
140.5
140.7
0.84
0.94
- 0.2
-0.10
5-4
Sehiaparelli
] 890.42
137.9
139.3
0.84
0.97
- 1.4
-0.13
4-3
Sehiaparelli
1891.50
142.5
138.1
0.87
1.00
+ 4.4
—0.13
7
Sehiaparelli 4 ; Maw 3
1892.17
137.5
137.5
0.97
1.02
± 0.0
-0.05
6-5
Hurnham 3
1893.54
138.6
136.1
0.92
1.05
+ 2.5
—0.13
3
Sehiaparelli 2 ; (Jomstock 1
1894.47
138.1
135.4
0.86
1.07
+ 2.7
-0.21
1
Sehiaparelli
1895.20
133.9
134.7
1.11
1.09
- 0.8
+0.02
7-5
Barnard
1895.28
136.4
134.6
1.06
1.09
+ 1.8
-0.03
3-4
See
EPHEMKKIS.
t
Oc
pc
t
Oc
PC
0
K
0
H
1896.50
134.0
1.11
1899.50
131.6
1.17
1897.50
133.2
1.13
1900.50
130.9
1.19
1898.50
132.4
1.15
a CENTAURI.
a = 14h 32'". 0 ; 8 = —00° 25'.
1, orange yellow ; 2, orange yellow.
Discovered by Father Richatid at Pondicherry, fndia, December, 1689.
OBSERVATIONS.
t
0,,
Po
n
Observers
t
Bo
Po
n
Observers
o
If
O
W
1690.0
—
—
1
Riehaud
1834
.33
217.33
17
.83
1
Herschelf
1834
.45
218.78
17
.50
2
Herschel
1709.5
—
—
1
Feuille'e
1752.20
218.73
20.51
-
Lacaille
1835
1835
.08
.89
218.80
219.59
17
17
.33
.02
1
11-1
Hersehel
Herschel
1761.5
—
15.6
1
Maskelyne
1836.61
220.26
16
76
1
Hersehel
1822.00
209.6
28.75
-
Fallows*
1837
.22
220.65
16
.39
4
Hersehel
1824.00
215.41
22.45
35 +
Brisbane
1840
.00
223.2
14
.74
_
Maclear
1826.01
213.18
22.45
Dun lop
1846.21
232.4
10.96
3
Jacob
1830.01
215.03
19.95
-
Johnson
1846.80
234.3
9.56
4
Jacob
1831.00
215.97
22.56
-
Taylor*
1847.09
235.7
9.33
2-3
Jacob
1832.16
216.35
19.85
-
Johnson and
Taylor*
1847.36
234.5
9.31
3
Jacob
1833.0
217.45
18.67
7±
Henderson
1848.00
237.93
8.05
13-12
Jacob
•Taken on the authority of SIK JOHN HKK.SCII KI..
i means have been formed anew.
a CEXTAi 1:1.
Ill
1
«.
*
•
, , .. • . ..
t
«.
P.
•
,, ..
«
9
•
1
1S49.63
244.5
6.23
- •
Jacob
185448
283.44
3
I'owell
IM1'1'!
245.25
, .,,
1
Mttlew
185446
282.81
4.43
5
MaHear
1849.97
245.42
7.04
3-2
M ,
1854.93
285.88
3.96
:. I
Maclear
1S50.10
246.63
7.01
1
M
U .1 M
288.02
—
^
I'owell
1850.17
245.76
6
M
HUM
289.32
__
10
I'owell
1850.20
245.85
.. M
3
Mat-lew
1855.23
290.19
4.38
3
Mucloar
1X50.31
247.07
4
Maclear
1855.29
292.60
_^
5
I'owell
1850.37
247.52
7
Jacob
1855.33
293.8
4.11
10
I'owell
is.-io.3X
245.74
7.12
1
Maclew
1855.36
291.96
4.38
4
Maclear
1X50.41
242.0
7.78
15
Gillte
L88B M
294.73
_
5
I'owell
1850.61
248.84
UM
3
M . , ,
1850.64
249.1
7
Jacob
1850.02
301.02
3.99
11-6
Powell
1820.92
250.27
6
Jttoob
1856.02
302.13
3.85
7-6
Miu-lcar
1X.TO.IM
251.84
6.02
3
Matli-ar
1856.10
303.00
3.88
IS
Jacob
1856..'i8
306.92
4.05
1
Maclcar
1851.02
251.05
5.88
8
Jacob
1856.51
3O9.84
3.93
10-9
Jacob
1M1.08
252.50
6.12
3
Ma.-lew
1856.91
311.26
4.21
4
Mann
1851.20
252.13
5.94
u ^
Jacob
1856.94
311.88
_
11
(J. Maclew
1K51.33
253.92
6.02
5
Maclew
1856.95
310.78
4.05
6
Mann
1X51.56
254.42
5.88
3
Mat-tear
1856.96
315.77
3.96
10-9
•I.H -nil
1851.70
256.38
5.27
8
Jat-ob
1851.94
256.58
5.80
3
Maclear
1857.15
318.19
4.02
15
Jacob
1851.94
258.2
5.11
9-8
Jacob
1857.39
320.60
4.47
2-1
Maclear
1851.99
258.85
M|
8-7
Jat-ob
1857.86
326.48
4.14
14
Jacob
1852.25
259.02
5.72
3
Mai'lrar
1858.17
330.51
4.39
5
Jacob
1852.27
261.07
5.03
7
.l.ii -i ili
1858.23
339.42
5.09
3
Maclear
1852.3R
261.88
4.94
r,
.lai-nli
1859.34
339.71
5.18
15-12
Powell
1852.43
261.67
5.27
5
Maclew
1859.43
343.44
5.10
5
Mann
1852.53
264.16
5.00
4
Jacob
1859.52
341.8
4.92
4
Powell
1 VM.-.56
262.8
5.03
-
.M:u-lt-ar
1859.97
346.08
5.00
3
Maim
I-:,.
-•;:
.Vl.s
7-9
Maclew
L8B9
IB
i M
.". -2
Maclear
1860.05
346.55
—
1
G. Maclew
I8H
:tl
4
>ar
ISOo.ic.t
345.4
5.65
17-13
Powell
ism us
::i'.i.;i
sjsa
4-1
Maclear
:67
i :,.-.
-
Jacob
.-V4S.S7
3
Maclew
.-.I
4.84
1 ..
M , . .:
1860.48
34S.7
1
Pow.-ll
It
- .1.1
1 .-.-.•
_
Jacob
185.:
• :•-•
i n
.-,
lH>
: n.-,
:i.-,].(»8
r,o:
10-9
Powell
lS.Vt.50
27 LOT
(i
ear
1861.<«i
.;.-,
3
Maclear
lS5:t.58
272.17
4.57
2-1
Man n
1 si; 1.31
3.VI.03
(•..-_• i
7
Powell
1853.58
270.10
I'owell
1861.58
354.26
5-3
Powell
1853.92
275.19
4.44
4-3
Maclew
1862.0
0.0
10.0
—
Ellery*
1854.00
•j;r,.63
4.21
_
Jacob
1862^0
357.84
7
Powell
1854.03
276.85
7
Powell
1862.47
,,,,
—
-
Elleryf
1854.24
278.98
4.62
4
Marlew
1862.56
1.38
7 ,V,
3
V
1854.25
279.06
4.16
2
Jacob
1863.03
1.4
7.2
6-4
Powell
1854.26
279.62
—
4
Powell
1863.75
5.2
•»•••
-
Kll-ry
• ApjuurnUjr a roofh '
t From truult ob*err»Hotu.
142
a CENTAUTM.
(
60
Po
n
Observers
t
60
Po
n
Observers
1864.11
O
5.7
7.85
7-5
Powell
1878.16
11 6^98
tf
1.77
1
Russell
18C4.72
8.1
_
Ellery
1878.22
119.82
1.95
3
Russell
1878.28
127.37
1.77
1
Russell
1865.56
17.3
9.95
1
Ellery*
1878.38
139.10
2.40
—
Maxwell Hall
1866.06
11.1
9.3
3
Powell
1879.25
174.40
3.41
_
Ellery
1868.17
—
9.2
-
Ellery
1879.47
173.55
3.41
2
Hargrave
1868.18
1868.38
1868.51
13.59
21.8
9.6
10.29
11.02
2
5
Ellery
Mann
Ellery*
1880.18
1880.39
1880.45
183.9
185.2
184.98
5.22
5.56
5.52
4
3
1
Tebbutt
Tebbutt
Russell
1869.13
17.97
10.4
2
Powell
1881.28
189.88
5.07
1
Hargrave
1870.1
20.45
10.24
13-12
Powell
1881.54
190.13
7.52
1
Hargrave
1870.61
21.8
10.09
5^4
Powell
1881.65
193.15
7.94
2
Tebbutt
1870.65
10.2
—
Ellery
1870.65
24.7
10.45
3
Ellery*
1882.00
194.44
8.23
18
Gill
1870.75
22.53
10.46
4
Russell
1882.22
194.6
8.70
1
Tebbutt
1882.50
195.82
9.12
52
Elkin
1871.05
23.01
9.89
11
Powell
1871.31
23.7
9.8
7
Powell
1884.19
199.0
11.96
-
Russell
1871.48
22.91
10.22
2
Russell
1884.43
199.5
12.32
-
Russellf
1871.51
24.2
9.41
1
Ellery
1884.53
199.80
12.93
6
Tebbutt
1872.47
25.31
9.73
2
Russell
1885.56
200.8
14.05
4-3
Tebbutt
1872.55
24.1
10.36
1
Ellery
1886.27
202.5
14.89
5
Pollock
1873.16
_
8.3
Ellery
1886.38
200.4
14.74
1
Russell
1873.33
28.1
9.50
1
Russell
1886.52
201.2
15.19
1
Russell
1886.55
201.02
14.87
4
Pollockt
1874.15
30.5
8.0
-
Ellery
1886.56
202.42
15.13
10
Pollock
1874.47
30.0
7.97
2
Russell
1886.58
201.7
15.18
3
Russell
1874.55
34.17
—
-
Lindsay
1886.60
201.41
15.16
4
Tebbutt
1875.02
34.21
6.82
—
Seeliger
1887.39
202.3
16.06
3-5
Tebbutt
1875.94
39.3
6.68
1
Ellery*
1887.43
202.08
15.83
6-5
Pollock
1887.60
202.35
16.28
3-2
Tebbutt
1876.41
46.97
4.35
2
Russell
1887.72
202.16
16.18
2
Tebbutt
1876.61
51.05
4.15
2
Ellery
1887.74
203.0
15.73
4
Pollock
1876.90
64.3
4.94
1
Ellery
1876.94
51.2
4.5
1
Ellery
1888.30
203.4
16.87
3
Tebbutt
1888.63
202.93
17.12
1
Tebbutt
1877.14
64.4
3.30
—
Maxwell Hall
1877.25
69.1
3.13
5
Ellery
1889.45
204.5
17.91
3
Pollock
1877.52
72.77
2.60
2-1
Russell
1890.41
205.2
18.58
2
Tebbutt
1877.56
77.25
2.11
3
Russell
1890.47
204.75
18.66
4-3
Sellers
1877.57
80.50
2.13
2^3
Gill
1890.60
205.05
19.06
3-2
Sellers
1877.59
81.74
1.90
3
Russell
1890.74
204.6
18.69
1-3
Tebbutt
1877.63
81.49
1.94
3-1
Gill
1877.82
97.12
1.85
2-3
Gill
1891.43
205.62
19.15
5-4
Sellers
1877.89
101.12
1.62
2
Gill
1891.56
207.17
19.25
4-2
Tebbutt
* From transit observations.
t From Ja anil JS.
u i I N 1 \l III.
ii.;
1
9.
ft
•
OWnrrrt
1
9.
p.
•
"
o
9
0
§
1891.57
205.3
19.24
2
S*Uor§
1893.21
206.75
20.22
2-1
M.II.IVkrrinK
1891.64
206.4
: - •
•
..lit
200.4
19.92
8
Sfllon
1892.30
206.45
19.52
2
i.ill * KluUy'
1893.49
206.73
206.5
20.32
20.24
6-4
8
Tobbutt
1892.40
1892.45
205.46
205.53
19.73
19.75
• i
7-4
S-llow
..ill
1893.50
206.75
20.53
4-2
Teltbutt
1X92.58
205.83
: • : •
T.-l.lmtt
1894.47
207.2
20.58
6
S.-1I..IS
|vrj.;o
206.9
: . ...
1
\\ ll.l'kkrrinn
1894.78
208.0
20.72
19-11
T.-l.l.iitt
1893.21
• •
_.,,,.
1
A. K.Dou(laM
!-...,-.
207.8
20.97
16-10
Tebbutt
In attempting to invc-lijratc tin- orbit of a Crntauri it seems desirable to
review hriclly (In- w«.rk alivad \ done on this celebrated system:
I'll. !•«•«•.. nl left n- I iy KiciiAfD d<H'H not throw inuc-h li^lit II|MIII tin- nature
of tin- orliit. i'nt i- »f coiiHiiK-mhle historical
:i I'licoawioii clt- la Conu'te pliiHiourH foiH Iwt piwlw du Ci-iitanrr
:i\.« HIM* hmette d'enyiron tlou/c pii-ilw, je raoHrqni qoe le pied !«• plu« oriental
• •I It- plus lirillant i-toit niif double etoik- aiiMwi bit-n (jiu- le pitnl «lt- la croiflade;
aveo celtt* differcnct' <|in- daiiH la oroinde, line etoilc paratt :IM-C la lunette
tiiitalileiiieiit eloi^m-e de 1'autre; ail lieu <pi' au pie«l du fV//A/»/rr, les deux
etoiles |i;ii-aiswnt niOmc avec la lunette pivwjue »o toucher; quoique eependaut
on les distingue aiseiuent."t
The next n»conl of a Cfnl-auri w«u« made by FATIIKH FRI'IM.KK, who ol>-
t*en-ed at Lima. Peru, July 4, 1700; in hi* Journal ilr* OfaervotioiM, &e., I'arix,
1714, toinc I, p. 425, we find the following account:
"Sur !«••. ili-iix In-mv- ilu matin, en atlnnlant ijue j<- pn^-.- «.l)-(-i-\ i-r IVmersioii
du premier satellite de Jn/iifti-, (|ii<- ilcs niiageH me ea«-herent, j'oliservai ave<- line
lun. -it.- ill- IS |.i.<U l'< t»ilf .If la |ir. mi. i- ^i aiuli-iir <|iii ent au pied boreal du
• I. \:int >lii ('>iitiiiin: j<- ti-ouxjii ci-ttr rtoili- <-<>ni|>osee ill- <leii\. dont Tune iwt (It-
la tn>i-irme ^nimleur i-t 1'autn- il<- la i|iiatrieme. (.'elle di- la ipiatririm- grandeur
e-t la pins oeeideiitalr. rt U-nr distance est egale an diam«-tre de retlr ••toile."
From thi» rather indefinite <>liM-rvatiou I'OWKM. infers that the distance of
the com|M>nent« in 17(H> wan about 10*, and attaches considerable im]x>rtanc<> to
the remark that the companion wax "the more westerly" (la plus occidentale).
I'nfortunately the language is rather ambiguous, and we can not tell whether
l-'i i n.i.i ». in.-ant that the companion was really to the west of the central star,
or whether it merely apj>eared to the west in the inverU-d field of view. As
• By photography.
t Publication* of tin- Royal Aradrmy of Sci«-nr«, ParU, 1002; or MoulMlg JToUcM, 18*4-6, p. 18.
144 a CENTAURI.
a Centauri was low in the southwest when the observation was made, it is also
possible that the remark may have arisen, as MR. ROBERTS has observed, from
the position of the heavens at that instant rather than the position-angle of the
companion. In any case it follows from the orbit here deduced that the
position-angle was 24°.3, and the distance 10" .07.
The third observation of a Centauri was made by LACAILLE at the Cape
of Good Hope in 1752. While determining the positions of southern stars he
observed the components of a Centauri, and from the resulting J« and Jo we
find the values of p and 6 given in the list of measures. The observations of
LACAILLE were first printed in the Ccelum Aastrale Stelliferum, which was pub-
lished at Paris- in 1763, and reprinted in 1847 by the British Association for
the Advancement of Science, under the auspices of a Committee composed of
HEUSCHKL, HENDERSON and BAILY. LAOAILLE'S observations appear to be as
good as could be expected from the instruments and methods employed.
In 1761 a Centauri was observed on one night by MASKELYNE while at
the island of St. Helena; by means of a rough divided-object-glass micrometer
he found a distance of 15" .0.
The observations made early in the present century by FALLOWS, BRISBANE,
DUNLOP, JOHNSON, TAYLOR and HENDERSON, rest on measures of J« and Jo.
The observation of FALLOWS was made with a small and defective Altitude and
Azimuth Instrument, and is entirely erroneous. For a long time this measure
was very misleading to computers, as it indicated an eccentricity of about O.fMi.
The results of BRISBANE, DUNLOP, JOHNSON, TAYLOR and HENDERSON are
likewise unworthy of any high degree of confidence. The first observations of
conspicuous worth are the micrometrical measures made by SIR JOHN HERSOHEL
at the Cape of Good Hope. The measures of HERSCHEL taken in conjunction
with others recently made expressly for the purpose have enabled us to de-
termine the orbit of a Centauri with a degree of precision which appears extra-
ordinary when we consider the character of the observations. It will be found
on inspecting the list of measures that many of them are vitiated by sensible
errors of observation, which are partly systematic and partly accidental. We
must remember, however, in judging of the value of results that a Centauri is
a very bright star, so that the images are unusually large; and hence if the
telescope is not practically perfect, and the atmospheric conditions favorable,
we could hardly expect that the measures will be very accordant. It is also
to be remembered that the southern observers are not specialists in double-star
work, and hence we can not expect results such as could be obtained by the
skill of a BURNHAM or a STRUVE. Nevertheless, the measures of a Centauri
u <I:NTM 1:1.
II.-.
taken M a whole, will enable UH to obtain one of the bent orbits yet deduced
for nny binary, ami we may gratefully acknowledge our deep obligation to
the southern ohM-rxcr-. who Jim'nl many dillicnltics have measured thin star
will) care ami assiduity.
In tlu* lint of measures given above will lie found all tlu» records which
are of any value. Tin- O|»M -nation* of T. M \CI.KAI:. (J. M \< I.KAK and W. MANN,
which were math alMiut the middle of the century, are taken from Die. KI.KIN'M
Inauyural l>i*9erinfi"ii, in which they were first printed; the numl>er of night*
was kindly -npplicd by Di:. KI.KIV in a private letter. Most of the other
meaxiireM are takt-u from tin- Mmioir.t and Monthly Xoticea of the Royal Antro-
nonii«-al Sx-irty. In thi-« <-i>mu-i-tion I take occasion to acknowledge my
obligati.in* In Ml>-.|>. rKmillT, I'lCKEHIXiJ, DorULAHH, l.'i --I I I .
«.n.i. and FIM.A^ for wt-uring seta of measures expressly for thin in vewtigation;
:iU.. in thank HUM: II \\- l.i i»KM»o«FH of the Royal Obnervatory, Berlin, for
eontirming fnuu original source** the im-annreH of L.vr.MU.K, HKIKIIANK, DUNI.OP
and J«.ii\-"\.
M"-i «>f the orl»its determined In-fore 1875 have now only historical interest,
and among those more recently determined only three are approximately
eorn-et: namely, ihose of ROBERTO (^(^.,3175), SEE (Af JV., Dec., 1893), and
i:< K i . I.. V. , :KKJ< I). The following table of the elements found by previous
computers is essentially complete:
/•
T
•
a
a
i
\
Authority
SOOTM
7fi>
1851.50
1 B B
N i-
a
17 77
:»>l .'.:
Jacob, 1848
Mem. K.A.S., XVII, p. 88
kgU
—
—
—
.TJ.7
Jacob
A.N., XI.IV. p. 48
0.77.-.J
n-..;
OJ
Hin.l. is.-.l
;-. .;
185K.M1-.'
80.
177.83
— .
Powell, 1 x:. 1
Mwn. i: \ ». \\1V,«
8L76
Powell, 1S.-.J
Mem. K.A.S.. XXIV. '.•:!
77 M
1871
osa
MJ0
H 1 :
Copeland.lM''.'
76
; •_•
0.63944
L'0.13
59.2
Powell. 1>7«.
\XX. 1VS
85'
1^71.85
•ji :•.«;
n ;
BBJB
llin.1, is"
M.X., XXXVII, VJ
12
18 i:.
U.U-nk. 1^77
\ \ MO
77.4-
O.ft.
H M
•
M n
Klkin. 1^^'
DUwrtaUon, p. 8
0.5158
17..-U
MUM
Downing, 1884
M N \uv. no
138
i:,
0.544
L&M
Powell, 1886
M N xi.vi, yyj
1875.T4
17.20
(Jill
Mem. K A.S. XI. VIII, i:,
81.185
n«
0.52865
IT.T1
.:. l
52.03
ItoberU,
v -^ . :»I75
81
17 7".-.
:.l :..;
See,
M N
79.rj:t
187(
0.51 1M
> r.
•::• ::
Doben-k, l.vi:.
A.V.. :ttw)
K.H.565
>;:. -.;
».-.-•.•.-..•
!> I..:.
-•••'
:•• -
49.42
Doberck, 1895
A.K..8UO
After careful study of all the observations we have formed mean places
and reduced them for precession to 1900.0. These places are given in the
146
a CENTAURI.
accompanying table, which also contains the comparison resulting from the
elements found below.
COMPARISON OF COMPUTED WITH OHSEHVED PLACES.
t
».
».
Po
PC
o0-ec
Po—Pc
it
Observers
1G90.00
o
258.94
H
6.67
o
t
1
Kichaud
1709.50
23.86
9.94
—
—
1
Feuillee
1752.2
217.84
217.21
20.51
18.36
+ 0.63
+ 2.15
_
Laeaille
1822.0
209.05
211.17
28.75
22.06
— 2.12
+6.69
Fallows
1824.0
214.88
212.2122.45
21.28
+ 2.67
+1.17
35 +
Brisbane
1826.01
212.66
213.07
22.45
21.26
-0.41
+ 1.19
_
Lhmlop
1830.01
214.54
215.01
19.95
19.95
-0.47
±0.00
_
Johnson
1831.0
215.49
215.77
22.56
19.28
-6.28
+ 3.28
—
Taylor
1832.16
215.87
216.47
19.85
18.68
-0.60
+ 1.17
—
Johnson and Taylor
1833.0
216.98
217.03
18.67
18.42
-0.05
+ 0.25
7±
Henderson
1834.33
216.87
217.92
17.83
17.68
-1.05
+ 0.15
1
Herschel
1834.45
218.32
217.99
17.50
17.67
+ 0.33
-0.17
2
Herschel
1835.08
218.35
218.4717.33
17.63
-0.12
-0.30
2-1
Herschel
1835.89
219.14
219.07
17.02
17.06
+0.07
-0.04
11-1
Herschel
1836.61
219.82
219.67
16.76
16.43
+ 0.15
+ 0.33
1
Herschel
1837.22
220.21
220.18
16.39
16.17
+ 0.03
+ 0.22
4
Herschel
1840.0
222.78
222.89
14.74
14.42
-0.11
+ 0.32
_
Maclear
1846.21
232.02
232.87
10.96
9.70
-0.85
+ 1.26
3
Jacob
1846.80
233.93
234.33
9.56
9.18
-0.40
+ 0.38
4
Jacob
1847.09
235.33
235.21
9.33
8.90
+ 0.12
+0.43
2-3
Jacob
1847.36
234.13
235.87
9.31
8.76
-1.74
+ 0.55
3
Jacob
1848.00
237.57
237.80
8.05
8.35
-0.23
-0.30
13-12
Jacob
1849.63
244.15
243.97
6.23
7.12
+0.18
-0.89
_
Jacob
1849.95
244.98
245.48
7.00
6.83
-0.50
+0.17
4-3
Maclear
1850.20
244.97
246.55
6.92
6.57
-1.58
+0.35
14
Maclear
1850.38
246.28
247.91
6.82
6.46
-1.53
+0.36
8
Jacob 1 ; Maclear 7
1850.41
241.65
247.96
7.78
6.44
-6.31
+ 0.34
15
Gilliss
1850.62
248.62
249.22
6.39
6.32
-0.60
+0.07
10
Maclear 3 ; Jacob 7
1850.93
250.7
250.48
5.95
6.10
+0.22
-0.15
10-9
Jacob 7-6 ; Maclear 3
1851.10
251.55
251.45
5.98
6.04
+0,10
-0.06
21-19
Jacob 8 ; Maclear 3 ; Jacob 10-8
1851.44
253.33
253.90
5.95
5.75
-0.57
+ 0.20
8
Maclear 5 ; Maclear 3
1851.87
256.14
256.55
5.53
5.53
-0.41
±0.00
11
Jacob 8 ; Maclear 3
1851.95
258.18
257.19
5.09
5.48
-0.99
—0.39
17-15
Jacob 9-8 ; Jacob 8-7
1852.33
260.58
259.95
5.24
5.28
+ 0.63
-0.04
21
Maclear 3 ; Jacob 7 ; Jacob 6 ; Maclear 5
1852.64
262.78
262.40
5.03
5.01
+ 0.38
+0.02
20-15
Ja. 4 ; Mac. - ; Mac. 7-9 ; Mac. 5-2 ; Mac. 4
1853.27
268.73
268.18
4.69
4.75
+ 0.55
-0.06
19-18
Ja. - ; Mac. 4-6 ; Ja. - ; Mac. 5 ; Mac. 6 ;
1853.75
272.32
272.61
4.44
4.50
-0.29
-0.06
4-3
Powell - ; Maelear 4-3 [Maim 2-1
1854.16
277.91
277.60
4.33
4.36
+ 0.31
-0.03
17-6
Jacob - ; Po. 7-0 ; Mac. 4 ; Ja. 2 ; Po. 4-0
1854.79
284.72
285.35
4.19
4.16
-0.63
+0.03
15-9
Powell 3-0 ; Mac. 5 ; Mac. 5-4 ; Po. 2-0
1855.25
291.26
290.90
4.29
4.20
+ 0.36
+0.09
32-17
Po. 10-0 ; Mac. 3 ; Po. 5-0 ; Po. 10 ; Mac. 4
1856.13
302.97
302.33
3.94
4.08
+0.64
-0.14
42-31
Po. 5 ; Po. 11-6 ; Mac. 7-6 ; Ja. 18 ; Mac. 1
1856.51
309.84
307.72
3.93
4.10
+2.12
-0.17
10-9
Jacob
1856.94
312.11
312.80
4.07
4.16
-0.69
-0.09
31-19
Mann 4 ; G. Mac. 11-0 ; Mann. 6 ; Ja. 10-9
1857.27
319.09
317.57
4.24
4.24
+ 1.52
±0.00
17-16
Jacob 15 ; Maclear 2-1
1857.86
326.18
326.15
4.14
4.42
+0.03
-0.28
14
Jacob
1858.17
330.22
328.09
4.39
4.50
+2.13
-0.11
5
Jacob
1859.33
340.6
339.49
5.12
5.06
+ 1.11
+ 0.06
23-20
Maclear 3 ; Powell 15-12 ; Mann 5
1859.52
341.52
341.38
4.92
5.15
+ 0.14
-0.23
4
Powell
IS.V.I.-.I7
345.8
344.89
5.00
5.40
+ 0.91
-0.40
3
Mann
1860.27
347.78
346.70
5.62
5.56
+ 1.08
+ 0.06
26-15
G. Mac. 1 ; Po. 17-13 ; Mac. 4-1 ; Mac. 3-0 ;
1861.07
352.09
351.96
6.08
6.05
+0.13
+ 0.03
13-12
Powell 10-9 ; Maclear 3 [Po. 1
1861.44
353.38
354.15
6.26
6.25
-0.77
+0.01
12-10
Powell 7; Powell 5-3
1S61M1
359.47
358.15
7.17
7.10
+ 1.22
+0.07
10
Powell 7 ; Ellery - ; Maclear 3
I7SJ. .
o i KVTU 1:1.
117
1
*
4
P.
p.
*.-*,
• i'
II
ii , . . • -
IV, :,,
\ 1 !
_ • ;
; i
: ....
0 1 1
i; i
Powell
1 i
4.43
8.5
_
Kll.
Isi.l 11
.. .;,
5.74
. -
o 11
7-6
I'., well
_
7.70
8.1
_ -
3±
17.06
10.14
•i . .
+ 1.20
1
Kll.
•-.,,.,,
Ml si
11.60
9.3
+0.08
S
IWell
\ • . • .
15.70
10.01
+ 0.21
|
Maim
M •_•!.. YS
l«.W
1 1 OL-
+0.8H
5
Kllery
13 17.76
1 «, ( ;.
I'M
In In
1
1W.-11
Is7" 1
1,. ..
-0.18
-0.06
].; r.1
PowtO
•J1 .V.i
.1 17
10.1 B
+ H.12
-0.19
5-4
P..well
1870.65
. i :.
3-5±
Kll,-rv
1 s 7 1 1 7 .".
21.78
l" n.
4
Russell
I.s71 is
• s|
In Is
+ IM1
18
PMW.-H 11 ; Powell 7
1871 r>
. "
+ 0.0.%
.:
BlMUll 2 ; Kllery 1
VI .'.I
111 III
•.,,.
•n|i
;{
Russell 2 ; Ellery 1
s ...
. „.
-0.43
:
Kllerv -; Russell 1
ls74.31
+ 0..'W
3-4±
Kll.-ry - ; Russell 2
is7:,
-0.41
_
S«>«-liger
L876J4
i,, N
1 s,
1
Kllerv
,, |Q
; . -.
! ...
8.98
+ o.s7
2
MO
1 I.'.
.;:.,;
+ O.SO
2
Kllery
67.09
.".:, M,
1 7.
8.0Q
+ 1.23
+ 1.72
2
Kllerv
1871 It
. ; BO
2.60
+ 2.90
+ 0.70
_
Maxwell Hall
. - <;
, ...:.
-.• i:.
In]
5
Ellery
77 11
240
-4.80
+0.50
2-1
Banell
•-' 11
•j"l
1 r.l
+0.10
3
BDMell
-• .1
2.13 '.'.(HI
+0.13
+0.13
2-3
Gill
.'.Ml 1.98
+0.21
-0.08
3
Russell
'.'• 1.92
-2.25
+ 0.02
3-1
Gill
>:> 1.75
+0.73
+0.10
2-3
Gill
1871
100.97:101 .1:.
.62 1.70
-0.18
'MIS
2
Gill
1878 I'. 11'. s.; rj-:{;i .77 l.r.7
-5.56
+0.10
1
Russell
1878
119.67 127.51
.95
! • -
-7.84
+0.27
3
Russell
187s
127.12 131.01
.77
1.71
-3.89
1
Russell
1X7^
2.40
1 7s
+0.73
+0.62
_
Maxwell Hall
lS7'.i .'."- 17 1 .!•:. I7'J I'l
:u l
8JJ
+ 1.96
+0.29
_
Ellery
17 17", 11
.". n
::.,.
-0.15
•_'
II .. • .•: ...
184.97
4.93
1 -Jl
+0.29
4
Tebbatt
06
186.70
5 M
1 ill
+0.20
;{
Tebbatt
ir. 1st si is;
1
-ell
]s»] •_•.» is-.i 7:. l-.il.7-
7.11
-2.04
1
Har^rave
1.64 90.00| 192.77
7.64
-'.'.7:
-0.12
1
Bhq wi
-'.; "L1 I:'.: is 7-.H
-0.16
+ 0.12
•_•
Tebbott
•-: •"
''l II iv. 8.45
+ 0.11
18
(fill
94.481 194.871 8.70 8.80
_o.:w
-0.10
1
Tebbatt
•'•.-_• i •".••.. M- ;i •_••.•
-0.21
-0.17
52
Klkin
• ' - - • : . . :'.'.-»• \ _• • • i
-0.48
0.08
_
Russell
1. ssi ;
••'.:•• 1 ''-.-..-, '„• ;•_• ]•_• v
-on;
_
Russell
L8B4 53
.... : "• 1 2.93 12.53
i
+0.40
6
Tebbatt
;,s -..
:-" : _•'•,•*_• 1 i ...-. • ,;
-0.12
+0.21
4-3
Tebbutt
;>-. .;
' s-.i 1 | 7.;
+0.16
|
Pollock
>,. ,
2 "• '• -'"] 7(1 14.74 14.78
-1.40
-0.04
1
Russell
's,, -.;
•j"l i i:. .11
-0.39
+0.05
15
Russell 1 ; Pollock 4 ; Pollock 10
.•"1 If. •_••••_• '.il i:. 171. '."7
-1.45
+0.10
7
Russell .-{; Tebtni-
:-: n
."I.1 1 •-••••-•••.« l.-.-.C.I. -,-•..
-0.64
-0.01
9-10
Tel,lmtt3-^; PollcK-k 6-f
•
-0.57
" 1 1
., ,
Tebbutt 3-2 ; Tebbatt 2 ; Pollock 4
|s» ,
H'..87|l6.87
-0.02
:
3
Tebbutt
148
a CEKTAUKI.
t
4,
ec
Po
0o 0c
n
Observers
o
O
g
i
O
i
1888.63
202.85
203.62
17.12
17.14
-0.77
— 0.02
1
Tebbutt
1889.45
204.43
204.22
17.91
17.81
+ 0.21
+0.10
3
Pollock
1890.49
204.93
204.89
18.77
18.64
+ 0.04
+0.13
9-7
Tebbutt 2 ; Sellers 4-3 ; Sellers 3-2
1890.74
204.53
205.05
18.69
18.85
-0.42
-0.16
1-3
Tebbutt
1891.55
206.01
205.52
19.25
19.28
+ 0.49
-0.03
14
Sel. 5-4 ; T. 4-2 ; Sel. 2 ; T. 3-6
1892.30
206.45
205.97
19.52
19.73
+0.48
-0.18
2
Gill and Finlay
1892.43
205.47
206.04
19.74
19.83
-0.57
-0.09
12-8
Sellers 5-4 ; Tebbutt 7-4
1892.67
205.87
206.18
19.84
19.93
-0.31
-0.09
9-6
Tebbutt 8-5 ; Pickering 1
1S9.-J.25
206.70
206.50
20.06
20.21
+ 0.20
-0.16
11-10
Douglass 1 ; Pickering 2-1 ; Sellors 8
1893.47
206.66
206.59
20.36
20.30
+ 0.07
+0.06
18-14
Tebbutt 6-4 ; Sellors 8 ; Tebbutt 4-2
1894.62
207.6
207.21
20.65
20.81
+ 0.39
-0.16
25-17
Sellors 6; Tebbutt 19-11
1895.55
207.8
207.67
20.97
21.09
+0.13
-0.12
16-10
Tebbutt
In dealing with this orbit it seems probable that the graphical method
will be superior to any process involving a least-square adjustment, because
of the undoubted existence of sensible systematic errors in the observations.
An adjustment based on both angles and distances will eventually be desirable,
but before this definitive determination can be made with advantage, it will
be necessary to have an additional revolution. In the present state of the
observations it is wholly useless to apply corrections of a very minute char-
acter. Basing the work upon all the best observations we find the following
elements of a Centaur i:
P = 81.1 years
T = 1875.70
e = 0.528
a = 17".70
Q = 25M5
i = 79°.30
X = 52°.00
n = +4°438954
Apparent orbit:
Length of major axis
Length of minor axis
Angle of major axis
Angle of periastron
Distance of star from
= 32".18
= 6".16
= 27°.25
= 38°.65
centre = 5".90
If we adopt the parallax of GILL and ELKIN (0".75), we find that the major
semi-axis of the orbit is 23.6 astronomical units. It follows that the combined
mass of the components is 2.00 times the mass of the sun and earth.
Thus we see that the companion of a Centauri moves in an orbit with a
major axis which is about a mean between those of Uranus and Neptune. But
owing to the eccentricity of the orbit the distance at periastron (11.2) only
slightly surpasses that of Saturn from the sun, while at apastron it extends
considerably beyond Neptune (36.0).
According to preliminary researches of STONE in 1875, it was found that
the masses of the two components are sensibly equal. Mu. A. W. ROBERTS has
ll'.i
recently made a very careful d« i« iiniii:iii«»n of this mass-ratio, ami iiinl- i .1. .V.
'.V,\\:\) that the masses of a* and a1 (tin- «iiii|>:iiiiuii) are ns 51 : 4!> ± A of the
amount. A very similar result wa- obtained l»y Dlt. EhKIN in his /mini/ unit
/>iWr/«/«M, and hence we may conclude that in thin case the relative ma--. -
aiv known with almost the desired precision.
Mil. KOIIKUTS has also made a careful di-cn—iim of the parallax of a ''•//-
tauri from the meridian observations of 1879-81 and obtained (A. A'., 3324) re-
-ults which confirm the work <>f < iii.l, and KLKIN with the helioineter. Usin^
lM>th right ascensions and declinations Mit. KOIIKKTS finds:
, . +0-.71 ±0-.05.
Our knowledge of this system is therefore far more accurate than that of
any other -\~i«-m in the heavens, and it does not seem )HJSM|>|C that the
results here obtained will ever be sensibly altered, lint as some refinement is
-till jNissibk* this glorious object will always merit the attention of observers.
0*285.
a = 14" 41-.7 ; 4 = -H2' 48'.
7.5, yellowish ; 7.0, wbllUli.
Discovered by Otto Strure in 1S4">.
Itt
1847.96
1855.84
:- -•. •
186&6S
1H76.40
1881.50
issaM
1885.40
., .,
58.4
36.0
„,,,
n I'.'
0.49
0.51
0.40
.:
5
I
1
1-0
1
doubtful 1
258.3 0^2 5
elong. 1
OMKKVATIOX*.
OfcMrren
t
o. Struve
1887.00
Midler
1888.61
:<>r
O. Strure
l.s'.u.:wi
Seeehi
1891.49
Dembowaki
1892.30
Huniham
1893.46
1893.51
Burn ham
1894.47
Englemann
1895.32
Perrotin
187.5
!•> 7
159.1!
162.2
156.0
l.vs s
147.3
143.2
OJB
0.24
0.20
0.24
0.24
136.8 —
0.30
0.35
N
4
3
1
.
1
.
1
Obnrrven
S-liiaporelli
liiinihatn
Schiaparelli
3-2 Kurnham
1 Buniham
1-0 Bigounlan
1-0 Bigourdan
-
gchiaparelli
150 01285.
This close double star was measured by OTTO STKUVE several times
during the few years following its discovery.* The other early measures were
by MADLER and SECCHI, while in later years the pair has been measured only
by ENGLEMAKTN, SCHIAPARELLI, BURNHAM and the writer. Thus, only a small
number of observations are available for the determination of an orbit, but it
happens that these are distributed so as to give a fairly good set of elements.
The star has always been a difficult object, and hence the measures are
necessarily less accurate than in case of easier pairs. BURNIIAM was the first
to attempt an investigation of the orbit (Sidereal Messenger, June, 1891). His
apparent ellipse and the resulting elements are not very different from those
found in this paper. MR. GORE has since attempted an orbit by a very differ-
ent process, and obtained results of a wholly different character (Monthly
Notices, April, 1893). These two sets of elements are :
GORE BURNHAM
P = 118.57 years 62.1
T = 1881.93 1885.3
e = 0.58 0.429
a = 0".46 0".387
8 = 107°.0 54°.3
i = 45°.7 44°.3
X = 161°.4 180°.0
Using all the measures, and basing the work on both angles and distances,
I find the following elements of 01' 285 :
P = 76.67 years Si = fi2°.2
T = 1882.53 i = 41°.95
e = 0.470 X = 162°.23
« = 0".3975 n = -4°.6953
Apparent orbit:
Length of major axis = 0".788
Length of minor axis = 0".522
Angle of major axis = 67°. 1
Angle of periastron = 255°..'5
Distance of star from center = 0".182
The following table of computed and observed places shows that the
measures are represented as well as could be expected in the case of an object
of this difficulty.
• Astronomical Journal, 350.
I
0.
l.-.l
('••MPABKOX OF < D WITH H|i«Hi\M> 1'LACm.
1
«.
«.
*
P
IU-«r
t*-*.
»
"
:
. .'
• • :
- 1 •'
+ •'
3
O. Strove
1847.96
72.2
4- .
— 0.1.'.
M feller
l8.-i2.7l
58.4
• •
,, ...
- 4.5
— O.(i7
5
Midler
1805.84
•
- 4.1
-0.03
3
ruve
'- .
•
+ 10.4
-0.12
1
Kwwhi
1868J8
38.4
__
- 2.4
—
1
iK-lll IN. \\-kl
187'
,,-jl
- 7.4
+0.06
1
Iturnluuii
1881.50
__
d»M(.l
_
_
1
liimiham
18V
. >
.11 ••
UJ1
-1-17.3
+0.01
I
KiiKleniann
18Jv
0.24
- 1.4
+0.02
4
S. ln;i|.;in'lli
1801
I7...1
0.34
OJM
- 1.4
±0.00
3
Hurnliant
1.VJ2.30 j 1».
ir.^.n ii-ji
+ 0.2
—0.01
3-2
Itiirnhaiii
H. 1.-.C.H l.V. '.'
(KM
-1- |
-0.02
1
Hurnhain
18U.
1 1;.;
i r.Mt
, ,,
0.28
+ 8.3
+0.02
3
>..
Tin- only large residual is that of ENOLEMAXN, whose small U'leKco|)c
would ii»-t-f««arily render h'm ohservntioiis subjec-t to considerable muvrtainty.
Indofil, li«- jjives the angle a» 78°^, but I have assumed that he really saw the
companion, and have therefore changed the angle by 180°. The estimate of
3<r for the position-angle in 1865.53 is very nearly correct, and leaves no
doubt that the elongation observed by DEMIIOWSKI was real.
When I measured the object recently with the 26-inch refractor of the
Lcandcr McConnick Observatory in Virginia, the stars were not separated,
except on one night, and hence the difficulty of the pair will doubtless account
for the error in angle. The star is slowly separating, and ought to be observed
annually. The following is an cphemeris for the next five years.
(
lvn',.40
*
1.^.6
P<
1801
188.7
1898.40
126.5
I'.NMI. HI
133 J
nvi
p*
0.35
0.36
The comparatively long p«-ri<nl of this close star may probably lie con-
strued to mean that the system is very remote from the AV/rM, otherwise the
mass would be excessively small. The eccentricity of the orbit is fairly well
defined, and is near the mean value of this element among double stars.
152
BOOTIS = ^1888.
a = 14'1 46'".8 ; S = +19D 31'.
4.5, yellow ; 6.5, purple.
Discovered by Sir William Herschel, April 19, 1780.
OBSERVATIONS.
t
60
Po
n
Observers
t
00
Po
n
Observers
0
f
0
H
1780.69
24.1
3.23
1
Herschel
1841.06
325.1
7.03
5
0. Struve
1791.39
nf
—
1
Herschel
1841.42
1841.43
323.4
324.7
7.27
7.10
3
4
Dawes
Madler
1792.30
355.7
—
1
Herschel
1841.65
322.1
6.72
-
Kaiser
1795.32
354.9
_
1
Herschel
1842.30
322.7
7.03
2
Dawes
1802.25
352.9
1
Herschel
1842.40
323.4
6.88
3-1
Madler
1804.25
353.9
6 ±
1
Herschel
1843.33
1843.35
322.7
322.4
6.70
6.81
1
7-5
Dawes
Madler
1821.20
342.4
9.25
1
H. and So.
1843.58
323.8
6.91
7
Schluter
1822.69
335.8
7.54
_
Struve
1843.68
322.2
6.64
- *
Kaiser
1823.30
6.67
Amici
1844.36
321.6
6.90
3
Madler
1823.34
340.2
8.42
1
H. and So.
1845.36
320.9
6.81
8-6
Madler
1825.37
337.0
7.78
4
South
1845.37
1845.40
322.3
318.6
6.12
6.76
28
Hind
Morton
1828.54
336.0
7.18
2
Herschel
1846.29
320.4
6.69
5
Madler
1829.46
334.2
7.22
4
Struve
1846.46
319.2
6.75
20
Morton
1830.29
333.7
7.62
5-4
Herschel
1847.37
319.4
6.68
6
Madler
1831.40
331.2
7.30
5
Bessel
1847.44
1847.63
318.8
317.7
6.80
6.48
2
Dawes
Mitchell
1832.40
331.1
7.14
2
Struve
1847.82
319.4
6.53
3
0. Struve
1833.23
330.7
7.54
2
Herschel
1848.28
318.0
6.63
5-4
Madler
1834.44
330.4
7.54
3
Dawes
184850
317.9
6.71
2
Dawes
1835.43
1835.45
329.0
330.4
7.07
7.63
5
3-2
Struve
Madler
1850.77
1851.11
1851.49
316.5
317.4
316.1
6.56
6.56
6.21
1
5
5
Madler
Fletcher
Madler
1836.37
1836.49
329.1
328.2
7.52
7.09
1
4
Madler
Struve
1852.30
1852.56
316.6
315.3
6.51
6.22
32
15-13
Miller
Madler
1837.31
327.0
6.79
-
Encke
1853.44
314.4
6.31
8-7
Madler
1838.22
326.7
6.97
—
Madler
1853.54
313.4
6.23
3
0. Struve
1838.47
327.1
6.85
2
Struve
1854.46
312.0
6.26
3
Dawes
1838.54
326.5
7.26
—
Galle
1854.48
312.4
6.07
5-4
Madler
1839.41
325.8
7.07
-
Galle
1854.75
311.7
5.99
8
Dembowski
1840.26
325.1
6.70
34-25ou.Kaiser
1855.38
311.7
6.07
2
Madler
1840.43
324.1
7.16
3
Dawes
1855.42
310.5
6.00
3
Secchi
• i: - 2 L8H
1
fl.
P.
•
Ob*»nr«-f«
I
9-
p.
H
ObM>m>n
o
9
o
9
1856.39
312.4
5.89
4-3
Midler
is;
2W.O
5.41
2
Main
18.Vi.45
310.8
5.95
-
Drinbowaki
IN;.. |C.
211.1.8
4.64!
-
Ley ton < MM.
18.Vt.45
311.9
6.76
2
l.iiiln-i
1 N70.66
21M.4
4.95
1
iMin.-r
1856.55
311.7
6.00
\\ iniiifkr
1856.88
310.0
6.02
u
1871.35
1871.49
21»2.8
21»3.5
4.93
4.73
o
4
Main
Duni'r
1857.40
311.2
5.76
.'.
Midler
1871.82
21MI.9
4.75
8
DwabowskJ
1857.42
310.0
I
I>aw«
1873.19
286 7
4.62
4
O. Struve
1857.56
:uix.u
*_'
iN-iiibowiiki
1873.39
286.0
4.113
1
Main
1858.36
8«
:. ;c.
5
1 Vtnlii.w-iki
1873.43
287.0
4.84
1
I. in. Ntnll
1858.38
12
M»rton
1873.48
286.6
4.71
1
Leyton (Mm.
1858.54
7
Her
1873.91
287.8
4.62
8
I)enibnw8ki
1859.39
,..., i
3
Madk-r
1874.22
289.2
5.0
-
Cl.-.lliill
1874.36
283.9
4.92
4
Main
: :•••
35
Powell
1874.43
287.3
4.71
2-1
Leyton Olw.
: .MI
.".;•.!
10-9
M.i.ll.-r
1874.44
288.4
4.72
5
W.&8.
1861. .17
,,.-,,,
5.78
5
O. Struve
1875.34
286.5
4.76
4
Main
I 1.1
303.4
5.93
6
Auwers
1875.48
283.9
4.43
1
O. Struve
|N,._
• 305.9
1
Main
1875.36
285.4
1 C.II
_
(Jl.-.lliill
1862 17
304.1
5.59
4
O. Strure
1875.38
286.3
—
_
Nobile
.'.51
302.9
—
£
A u were
1875.40
284.3
4.41
5
Srliiapardli
.M
302.2
—
—
Winnecke
1875.51
286.6
4.45
4
Dun^r
306.4
5.27
>>
Madler
1875.90
284.7
4.43
8
iHsiulKiWNki
1863.15
303.0
5.59
14
Derobuwiiki
1 876.:t4
284.8
4.31
5
I>. ilx-ri-k
1863.28
302.4
5.79
-
!..•> t..ii i i|.-.
1876.43
283.4
1 c.l
3
Hall
1863.56
302.0
5.67
5
O. Struve
1876.58
282.0
4.111
1
O. Struve
1864.46
303.4
5.32
1
Englemami
1877.24
282.9
4.70
3
Dobcrck
:MI 1.6
5.44
16
DcmlioWHki
1877.45
283.0
4.35
5
Jetlrzejewicz
1866.33
301.6
5.61
3
Enirlemann
1S77.45
280.7
4.23
5
Schiaparelli
186.177
no s
5.41
4
Seech i
IS77..VI
27H.4
4.21
1
O. Struve
1877.93
J86J
1 _c,
8
DembowKki
'-•- •
H6J
6JO
2-4
•<m Obs.
186f> 1 1
299.6
5.2J)
_
Kaiser
1^78.40
•JN].:;
4.r,2
4
Jtiilillli'V
1866.43
299.8
•_' 1
KiiK'lemanu
IN> |j
177 i
4.32
••
Hall
298.0
5.81
3-2
Searle
1871
L'N| •_•
II.:
3
I»..|--r. k
1866.50
299.2
6.27
3-2
\Y:ii!.«-k
IN; -
1 "1
5
Schiaparelli
1861 M
299.0
-. ,,
11
Dembowiiki
IS;N.M
.;•.•. i
I i::
1
U. Struve
1867.30
1867.42
298.4
196.7
5.43
1
2
Winlock
Searle
1878151
277.6
170 7
4.10
4.18
6
5
Schiaparelli
Hall
1880.16
278.8
4.28
5
Franz
1868.40
294.7
5.33
1
Main
1880.48
4.19
.:
Jedrzejewirz
1869.09
295.4
BJ8
4
O. Struve
1880.51
HI ;
3.97
3
8chia]iarelli
1869.47
6u01
5
Diinrr
1881.40
MfJ
4.04
3
Hall
L868JM
1869.61
292.4
298.8
:. :.
.I I-'
3
1
Main
Leyton Obs.
1881.50
1881.60
273.2
273^
3.87
i e i
3
3
Schiaparelli
Seabroke
152
BOOTIS = ^1888.
a = 14'' 46"'.8
4.5, yellow
S = +19D 31'.
6.5, purple.
Discovered by Sir William Herschel, April 19, 1780.
OBSERVATIONS.
{
6o
Po
n
Observers
t
00
Po
n
Observers
O
n
O
n
1780.69
24.1
3.23
1
Herschel
1841.06
325.1
7.03
5
0. Struve
1791.39
nf
—
1
Herschel
1841.42
1841.43
323.4
324.7
7.27
7.10
3
4
Dawes
Mildler
1792.30
355.7
—
1
Herschel
1841.65
322.1
6.72
-
Kaiser
1795.32
354.9
—
1
Herschel
1842.30
322.7
7.03
2
Dawes
1802.25
352.9
1
Herschel
1842.40
323.4
6.88
3-1
Mildler
1804.25
353.9
6 ±
1
Herschel
1843.33
1843.35
322.7
322.4
6.70
6.81
1
7-5
Dawes
Madler
1821.20
342.4
9.25
1
H. and So.
1843.58
323.8
6.91
7
Schliiter
1822.69
335.8
7.54
_
Struve
1843.68
322.2
6.64
-
Kaiser
1823.30
6.67
Amici
1844.36
321.6
6.90
3
Madler
1823.34
340.2
8.42
1
H. and So.
1845.36
320.9
6.81
8-6
Madler
1825.37
337.0
7.78
4
South
1845.37
1845.40
322.3
318.6
6.12
6.76
28
Hind
Morton
1828.54
336.0
7.18
2
Herschel
1846.29
320.4
6.69
5
Madler
1829.46
334.2
7.22
4
Struve
1846.46
319.2
6.75
20
Morton
1830.29
333.7
7.62
5-4
Herschel
1847.37
319.4
6.68
6
Madler
1831.40
331.2
7.30
5
Bessel
1847.44
1847.63
318.8
317.7
6.80
6.48
2
Dawes
Mitchell
1832.40
331.1
7.14
2
Struve
1847.82
319.4
6.53
3
O. Struve
1833.23
330.7
7.54
2
Herschel
1848.28
318.0
6.63
5-4
Madler
1834.44
330.4
7.54
3
Dawes
184850
317.9
6.71
2
Dawes
1835.43
1835.45
329.0
330.4
7.07
7.63
5
3-2
Struve
Madler
1850.77
1851.11
1851.49
316.5
317.4
316.1
6.56
6.56
6.21
1
5
5
Madler
Fletcher
Madler
1836.37
1836.49
329.1
328.2
7.52
7.09
1
4
Madler
Struve
1852.30
1852.56
316.6
315.3
6.51
6.22
32
15-13
Miller
Madler
1837.31
327.0
6.79
-
Encke
1853.44
314.4
6.31
8-7
Madler
1838.22
326.7
6.97
_
Madler
1853.54
313.4
6.23
3
0. Struve
1838.47
327.1
6.85
2
Struve
1854.46
312.0
6.26
3
Dawes
1838.54
326.5
7.26
-
Galle
1854.48
312.4
6.07
5-4
Madler
1839.41
325.8
7.07
-
Galle
1854.75
311.7
5.99
8
Dembowski
1840.26
325.1
6.70
34-25ot».Kaiser
1855.38
311.7
6.07
2
Madler
1840.43
X'l.l
7.16
3
Dawes
1855.42
310.5
6.00
3
Secchi
I r. i^ .1
1
$.
*
•
,....:.
(
i.
P.
n
< ilMM>rvrr»
o
9
O
9
1856.39
:;i. i
5.89
4-3
Ma.ll.-r
1X7'
2II3.0
5.41
••
Main
1856.45
310.8
5.95
8
h.-niU.w*ki
1x7" !•;
2515.8
4.66
-
Lejrton (Mm.
18.Vi.45
311.9
6.76
2
l.lltlliT
is;
2511.4
4.95
1
hiin.-r
lS5f! 55
311.7
6.00
\Vlliln-<-kr
1 856.88
310.0
6.02
|]
1871.35
292.8
4.93
o
Main
1871.49
2513.5
4.73
4
hi M n -i
1857.40
311.2
5.76
.
Madler
1871.82
25M.9
4.75
9
DembowKki
1857.42
310.0
. , ,
1
:•
1873.19
286.7
4.62
4
O. Struve
1857.56
308.9
-
iK-iiilxiwKki
1873.39
2K6.0
4.93
1
Main
1858.36
308.2
5
m-inUiwuki
1873.43
287.0
4.84
1
Liinl-.ii-.il
1858.38
-
II
Morton
1873.48
286.6
4.71
1
Leyton Olm.
1858.54
7
Midler
1873.91
287.8
4.02
8
Dmbowiki
1859.39
.-i 1
5.57
3
Midler
1874.22
289.2
5.0
_
Ulitlhill
1874.36
283.9
4.92
4
Main
: i-.i
5.52
35
Powell
1874.43
287.3
4.71
2-1
!.'• \ii.n C>|M.
1861 ."iii
•
5.79
10-9
Midler
1874.44
288.4
4.72
5
W. AS.
1861.57
5.78
5
O. Struve
1875.34
2X6.5
4.76
4
Main
1862.15
303.4
| | ;
6
Auwers
1875.48
283.9
4.43
1
O. Struve
1862.33
• 305.9
1
Main
1875.36
285.4
I '•"
_
Gledhill
1862.47
304.1
5.59
4
O. Struve
1875.38
2X6.3
_
_
N nl nit •
1862.51
302.9
—
-
A M were
1875.40
284.3
4.41
5
Scliia|iari-lli
:.i
302.2
—
—
Winnecke
1875.51
286.6
4.45
I
hiini-r
J.65
306.4
5.27
-'
Midler
1875.90
284.7
4.43
8
Danbomkl
1863.15
303.0
5.59
14
Dumlxiwski
1K7<>.34
2S4.8
4.31
5
DolN-rck
1863.28
302.4
5.79
-
I.'-vton ()bn.
1876.43
2S3.4
4.64
3
Hall
1863.56
302.0
5.67
5
O. Struve
1876.58
282.0
4.19
1
O. Struve
1864.46
303.4
5.32
1
KM-].- 111:111 n
1877.24
282.9
4.70
3
hi.U-r.-k
1864.87
301.6
:. II
16
Perobowski
1877.45
283.0
4.35
5
Jeilrzejewicz
1865.33
301.6
5.61
3
En -It-Hi um
1X77.45
280.7
4.23
5
Schia|ian-lli
18«.
300.8
:. 11
1
Sew-In
1X77.54
'-'"'•• -1
4.21
1
O. Struve
1877.98
4.26
8
Deiulxiwuki
5.59
2-4
ton Obs.
186«; it
299.6
B40
_
Kaiser
1S78.40
•jsl .:
i •;•_•
1
Ci'ltlncy
1866.43
:. •_• I
1' 1
Kl IK It -ti 1:111 n
1X7*. I-J
•-'77.4
-
Hall
1866.50
298.0
5.81
3-2
Searle
1X78.45
.s| '_•
4.13
8
h'.lx«rfk
1866.50
299.2
6.27
3-2
WinU-k
1871
27H.8
4.01
1
S-liiapan-lH
It , M
299.0
5.30
11
l»rinln.W..ki
1X78.64
1-7-.I »
i I.;
1
O. Struve
1867.30
1867.42
298.4
296.7
5.64
:. :.;
1
2
Winlock
Searle
1879.51
is;
277.6
4.10
4.18
t
5
Srliiaj«arelli
Hall
1868.40
294.7
B : .
1
Main
1880.16
1880.48
278.8
276.0
4.28
4.19
5
3
Franz
Jedrzejewicz
|M , ,
295.4
5.09
4
0. Struve
1880..M
276.3
3.97
3
Schiaiiarelli
1869.47
295.6
5.07
5
Dune>
1881.40
269.2
4.04
3
Hall
LM
1869.61
292.4
298.8
:. :,
5.42
3
1
Main
Leyton Obs.
1881.50
1881.60
273.2
273.3
3.87
4.03
3
3
Schiaparelli
Seabroke
154
BOOTIS = .T1888.
(
60
Po
n
Observers
(
ft
Po
n
Observers
0
f
O
*
1882.33
267.6
4.73
1
Glasenapp
1887.43
256.0
3.54
3
Hall
1882.42
270.4
3.99
3
Hall
1887.50
257.0
3.31
12
Schiaparelli
1882.50
271.4
3.86
7
Schiaparelli
1888.25
250.2
3.51
1
Glasenapp
1883.43
267.1
3.90
3
Hall
1888.42
251.9
3.40
3
Hall
1883.47
268.1
3.72
9
Schiapavelli
1888.54
255.0
3.15
2
0. Struve
1883.50
269.4
3.72
3
Jedrzejewicz
1888.62
253.9
3.51
2
Maw
1883.52
1883.57
267.6
268.1
4.14
3.79
3
4
Seabroke
Perrotin
1889.31
1889.48
250.5
249.1
3.83
3.40
2
3
Glasenapp
Hall
1884.42
262.8
4.30
2
Glasenapp
1889.61
249.9
3.31
3
Maw
1884.45
266.6
3.65
6
Engleraann
1890.41
246.2
3.15
3
Maw
1884.45
266.1
3.71
2
Perrotin
1890.43
246.3
3.21
3
Hall
1884.49
266.3
3.58
9
Schiaparelli
1890.53
244.4
3.47
2
Hayn
1884.50
266.2
3.56
1
0. Struve
1891.44
241.0
3.26
5-4
See
1885.37
264.3
3.44
3
Tan-ant
1891.45
242.4
3.18
3
.Hall
1885.37
261.4
3.68
3
Hall
1891.48
243.4
3.18
4
Maw
1885.44
262.9
3.51
4
Perrotin
1892.32
240.0
3.08
3
Leavenworth
1885.44
262.1
3.55
5
deBall
1892.41
239.4
3.11
3
Maw
1885.48
263.1
3.61
12
Schiaparelli
1892.49
238.3
2.91
3
Coin stock
1885.55
263.1
3.61
7
Englemann
1885.64
263.6
3.63
4
Jedrzejewicz
1893.47
235.8
2.96
3
Maw
1886.40
259.6
3.56
3
Perrotin
1894.53
231.2
2.90
3
Maw
1886.43
259.3
3.59
3
Hall
1895.49
226.4
2.88
3
Com stock
1886.51
260.2
3.49
7
Schiaparelli
1895.70
223.8
2.57
4
See
1886.60
259.4
3.32
6
Englemann
1895.73
224.4
2.65
2
Moulton
The stars of this system are somewhat unequal in magnitude, and are
moreover distinguished by very striking colors. The principal star is yellow,
while the companion is reddish purple; and hence the appearance of the sys-
tem, so far as it depends on contrast in color and inequality of the components,
is very similar to those of 70 Ophiuchi and 17 Cassiopeae* The early observa-
tions of HKKSCHEL established the physical connection of the stars, and since
the time of STRUVE the measures are both sufficiently numerous and sufficiently
exact to give the position of the companion with the desired precision. In
spite of the fact that since 1780 an arc of only about 170° has been described,
we are enabled by the favorable shape of this arc to make a very satisfactory
determination of the elements. The companion is now approaching periastron,
and in the course of a few years the motion will become very rapid. For the
next fifteen years this system will deserve special attention from observers, as
the part of the apparent ellipse swept over by the companion during this interval
• Astronomische Nachrlchten, 3334.
1847 •
1822
17*0
r . r
. T
. T
1888.
Sc.l..
( IIOOTIH = .11888.
will IK- the in..-! eritieal, and measures secured near jx-rinHtron will enable UM
to render the orbit exact to a very lii^li .1
The following table gives the element- of this interesting system published
by previous computers:
p
r
•
•
a
1
1
Authority
Sourre
NW.91
140.64
1 L'7.97
I-.-7.-C,
177"
177'.».7.*i
17C..
177" II
1770.69
• .... I
<• I.M
133
"i.it
>i
0.7081
I. ,.,
, ,,i
i 813
i -.
0.0
17:- 7
111
ii •;
13.03
80.1
71 i;
i> i
|O|. (I
815.3
516.4
r.M.1.-.
117 77
' hel, 1888
M...I1.T
Ilinil. 1S7L'
Wii.JMsrm.l.ky-7-.'
Dolwrck, 187(1
l>..lK5rok,1877
Mem i; \ - vol \ 1
H;...«I.I).S.|,.304[|,.14'I
M.X.,vol.XXXII(J>.l'.V»
Gore's Catalogue
A.N.2118
A. N. 2 129
11 an in\< -ti^ation of all the observations we are led to the following
element- <>!' £ /•'
P - 128.0 years
T - 100SJO
0 - 0.721
• - 5'JWi78
Q - 10".5
i — fll'M'M
X - 23«»M'.-|
Apparent <>rl»it :
Length of major axis
Length of minor axis
Angle of major axis
Angle of periastron
Distance of star from centre
'.»*.07
A*.7(i
1(»7*.7
144°."
L".94
COMPARISOX or CoMPl-TKU WITH ORHKKVKII I'l.ACRH.
(
f
«r
P.
P<
».-4«
P.— PC
•
ObMTTWI
1780.69
•Jl 1
.;:. ;
2.18
-11.2
41.05
1
Hemrhel
17«5
_
- 6.5
-
1
lid
1 7'.»5.S2
.M •>
__
.-. 71
- 3.6
1
• lu'l
183.9
+ l.o
1
bel
6±
+
-0.66
1
li.-l
+ 1 ..
+ 1.92
1
Il.Tvli.-l :ui<l S<iiitli
7.-. I
- 1.0
40.20
_
Struve
.'W6.4
+ .
40.-JO
1.2 ±
. h.-l :unl S«.. 1; Atniri0.2±
1 V.T..87
+ !.'.•
40.43
4
SMltll
ISM M
7.1H
7.:«
+ :: l
-0.15
1
h.-l
7 .'.I
+ 2.0
-0.09
4
St ruve
ls.-W.29
-.:«»
+ 2.1
40.32
5-4
Hsnekd
1S.-M in
7.30
+ 0.3
40.01
5
BSM)
18.T.' 1"
:ui.i
7 11
'.27
4- 0.9
-0.13
I
Strnve
18."
- :
7,M
.L'.-.
4- 1.0
40.29
1
. hel
I II
• i
7.M
7.33
+ 1.6
40.32
3
Dawes
1835.43
19
4- 1.0
-0.12
5
Struve
16
4 1.0
-0.07
4
Strure
.'' '•
' 1 -
+ 0.4
-0.34
_
Knrke
1838.41
7.03
7.09
4- 1.0
-0.06
24
Madler-; i'.2; Oalle -
1839.41
7.06
4 0.6
40.01
K
Galle
1840.34
..:i i
.:_'! 1
.; •• :
7 --•
- 0.3
-0.00
3-6 ±
Kaijer 34-25 ob«.; Dawe«3
156
BOOTI8 = 2 1888.
t
60
A,
Po
PC
Bo Be
Po—Pc
n
Observers
1841.39
323.1
323.6
7.03
6.97
o
- 0.5
+ 0.06
7-12 +
02. 0-5 ; Da. 3 ; Ma. 4 ; Ka. -
1842.35
323.0
322.8
6.95
6.93
+ 0.2
+ 0.02
5.3
Dawes 2 ; Madler 3-1
1843.48
322.8
322.0
6.77
6.88
+ 0.8
-0.11
15-13 ±
Ma. 7-5; Da. 1 ; Schl. 7; Ka. -
1844.36
321.6
321.3
6.90
6.83
+ 0.3
+ 0.07
3
Madler
1845.38
320.6
320.4
6.56
6.78
+ 0.2
— 0.22
-
Ma. — ; Hi. — ; Mo. 28 obs.
1846.37
319.8
319.6
6.72
6.73
+ 0.2
-0.01
8±
Madler 5 ; Morton 20 obs.
1847.56
318.8
318.6
6.62
6.67
+ 0.2
—0.05
11 +
Ma. 6 ; Da. 2 ; Mit. - ; 02. 3
1848.39
318.0
317.9
6.67
6.62
+ 0.1
+ 0.05
7-6
Madler 5-4 ; Dawes 2
1850.77
316.5
315.9
6.56
6.48
+ 0.6
+ 0.08
1
Madler
1851.30
316.7
315.4
6.44
6.44
+ 1.3
0.00
10
Fletcher 5 ; Madler 5
1852.43
316.0
314.4
6.37
6.37
+ 1.6
0.00
18-1 6 ±
Miller 32 obs. ; Ma. 15-13
1853.49
313.9
313.4
6.27
6.31
+ 0.5
-0.04
11-10
Madler 8-7 ; O2. 3
1854.56
312.0
312.3
6.11
6.23
- 0.3
-0.12
16-15
Dawes 3 ; Madler 5-4 ; Dem. 8
1855.40
311.1
311.6
6.03
6.18
- 0.5
-0.15
5
Madler 2 ; Seochi 3
1856.56
311.3
310.4
6.12
6.09
+ 0.9
+0.03
29-28
Ma.4^3 ; l)em.8 ; Winn.3; Lu.2 ;
1857.46
310.0
309.5
5.85
6.03
+ 0.5
-0.18
8
Ma. 5; Da. 1 ; Dem. 2 [Sec. 12
1858.43
308.6
308.5
5.78
5.96
+ 0.1
-0.18
24
Dem. 5; Morton 12; Madler 7
1859.39
309.4
307.5
5.57
5.90
+ 1.9
-0.33
3
Madler
1861.45
305.7
305.2
5.70
5.74
+ 0.5
-0.04
18-1 7 ±
Po. 35 obs.; Ma. 10-9 ; 02. 5
1862.40
304.9
304.1
5.62
5.66
+ 0.8
-0.04
13
Au. 6; Mainl; 0 2. 4 ; Ma. 2
1863.33
302.5
303.0
5.68
5.59
- 0.5
+ 0.09
19 +
Dem. 14 ; Leyton obs.— ; O2. 5
1864.67
302.5
301.4
5.38
5.47
+ 1.1
-0.09
17
Englemann 1 ; Dembowski 16
18(55.55
301.2
300.3
5.51
5.41
+ 0.9
+ 0.10
7
Englemann 3 ; Secchi 4
1866.52
299.0
299.1
5.57
5.33
- 0.1
+ 0.24
21-20 +
Ley. 2-4; Ka.- ; En.2-1; Sr.3-2;
1867.36
297.5
297.9
5.54
5.25
- 0.4
+ 0.29
3
Wlk. 1 ; Sr. 2 [Wlk.3-2; Dem.ll
1868.40
294.7
296.5
5.33
5.17
- 1.8
+ 0.16
1
Main
1869.43
295.5
295.0
5.23
5.08
+ 0.5
+ 0.15
13
02A; Dn. 5; Ma. 3 ; Ley. 1
1870.47
294.4
293.5
5.01
4.98
+ 0.9
+ 0.03
3 +
Madler ; Leyton — ; Duner 1
1871.55
292.4
291.9
4.80
4.89
+ 0.5
-0.09
15
Ma. 2 ; Du. 4 ; Dem. 9 [Dem. 8
1873.48
286.4
288.7
4.74
4.71
- 2.3
+ 0.03
15
02. 1; Ma.l; Ley.l ; Lin. 1 ;
1874.36
286.5
287.1
4.84
4.63
- 0.6
+ 0.21
11-10+
Gl. - ; Ma.4 ; Ley.2-1 ; W.& S. 5
1875.45
285.4
285.1
4.51
4.53
+ 0.3
-0.02
22 +
Ma.4; aiM;Gl.-;No.-;Soli.:>:
1876.45
283.4
283.3
4.38
4.45
+ 0.1
-0.07
9
Dk.5; H1.3; O2.1 [Du.4 : Dcm.S
1877.52
281.4
281.2
4.39
4.34
4- 0.2
+ 0.05
22
Dk.3; Jed.5; Sch.5; 02.1; Dem.8
1878.46
279.6
279.4
4.24
4.26
+ 0.2
-0.02
15
Go.4; H1.2; Dk.3; Sch.5; 02.1
1879.52
276.7
277.1
4.14
4.16
- 0.4
-0.02
11
Schiaparelli 6 ; Hall 5
1880.38
277.0
275.3
4.15
4.09
+ 1.7
+0.06
11
Franz 5; Jed. 3 ; Sch. 3
1881.50
271.9
272.8
3.98
4.00
- 0.9
-0.02
9
Hall 3 ; Sch. 3 ; Sea. 3
1882.46
270.9
270.4
3.93
3.90
+ 0.5
+0.03
10
Hall 3 ; Schiaparelli 7
1883.50
268.1
268.1
3.85
3.82
0.0
+.0.03
22
H1.3; Sch.9; Jed.3; Sea.3; Per.4
1884.47
266.3
265.2
3.65
3.72
+ 1.1
-0.09
18
En. 6 ; Per. 2 ; Sch. 9 ; O2. 1
1885.47
262.9
262.6
3.58
3.64
+ 0.3
-0.06
38
Tar.3; H1.3; Per.4; Sch.12; deBal!5;
1886.48
259.6
259.5
3.49
3.57
+ 0.1
-0.08
19
Per.3;II1.3;Sch.7;En.6[En.7;Jed.4
1887.47
256.5
256.6
3.43
3.46
- 0.1
-0.03
15
Hall 3 ; Schiaparelli 12
1888.46
253.0
253.6
3.39
3.37
- 0.6
+ 0.02
8
Glas. 1 ; HI. 3 ; 02. 2 ; Maw 2
1889.45
249.8
250.4
3.35
3.29
- 0.6
+0.06
8-6
Glas. 2-0; Hall 3; Maw 3 .
1890.46
245.6
247.0
3.28
3.21
- 1.4
+0.07
8
Maw 3; Hall 3; Hayn 2
1891.46
242.3
243.3
3.21
3.13
- 1.0
+0.08
12-11
See 5-4 ; Hall 3 ; Maw 4
1892.41
239.2
239.5
3.03
3.04
- 0.3
-0.01
9
Lv. 3; Maw 3; Com. 3
1893.47
235.8
235.6
2.96
2.96
+ 0.2
0.00
3
Maw
1894.54
231.2
230.8
2.90
2.86
+ 0.4
+0.04
3
Maw
1895.59
225.1
225.7
2.72
2.75
- 0.6
-0.03
7
Comstock 3 ; See 4
The table of computed and observed places shows that the set of elements
given above is extremely satisfactory, and we may confidently conclude that
the general nature of the orbit here obtained will never be materially changed.
CXIRONAK noKKAI.IH = 2
I."
It is jMwsihlc thut the IKTHK! may l>< varied l>y ><> much a- one year, and
thut the eccentricity i- uncc»rtain to the extent of al»out ±0.02; larger altera-
tions in th«M»c t|iiantitie8 an not to be expected, ami the values of the other
dement* are correspondingly well determined.
The system of £ IttHtii* is chiefly remarkable for the great eccentricity of
the orbit, and for the wide angular separation of the components The great
li-nirth of the major-axis and the comparatively short |>criodie time would su|>-
|K>rt the belief that the -y-tcin is not very far from the earth, and this view
of relative proximity is rendered the more probable by the brightness of the
component*. Hut while these considerations tend to render it probable that the
parallax i- ~«-IIM|>IC, such a view is not supported by the small proper motion
of the system in space, which is only 0*.1G1 per year. We might, therefore,
infer that the system is perhaps very remote from the earth, and hence of
enormous dimensions, or comparatively near us, with the proper motion mainly
in the line of sight. In any case the parallax of this system is particularly
worthy of investigation, and it might be determined either by the ordinary
process of direct measurement, or by the sjK'Ctroscopic method (A.J?., .'i'H4, or
§;>, Ch. I.), which here seems likely to be entirely practicable.
The following is an ephemeris for the companion for the next ten years :
t
1896.50
1897.54)
1898.54)
1899JW
1900.50
1901. .'MI
221.2 2.65
216.2 2.53
210.1 2.40
203.4 2.25
195.7 •-'"••
184-..1 1.83
' *'.
1902.50 173J 1
1903.50 154.7
1904.54) 125.5
1905.50 90.1
1906.60 63.2
P,
.55
.25
.03
.or.
.3.H
,ro|;n\ VI- l',n|:K.VMS=r. v|«i;;7.
a = 15» 19-.1 ; 8 - +30' W.
5.5, yrllowl.li ; «, yellowish.
Urrtchrl, September 9, 1781
-
« «. />.
1781.69 30J
1 • •
m ObMrren
1 Hcnchel
ATIOW*.
« 0. P.
1826.77 35?3 1*07
1802.69 179.7
1 Henehel
1829JB 43.2 0.96
1823.27 25.9 1.58
2-1 H. & 8a
1830.30 44.5
Strure
Strure
Henehel
158
CORONAE BOREALIS = .21937.
t
0«
Po
n
Observers
t
60
Po
n
Observers
O
It
O
a
1831.34
50.8
—
2
Dawes
1849.44
218.3
0.69
2-1
Dawes
1831.47
52.7
1.02
10-1
Herschel
1849.65
220.3
0.60
3
0. Struve
1831.63
50.6
0.88
3
Struve
1850.50
221.2
0.46
1
W. Struve
1832.50
57.1
0.69
9-2
Herschel
1850.52
230.8
0.49
3
0. Struve
1832.55
56.7
—
1
Dawes
1850.56
235.0
0.7 ±
2
Fletcher
1832.76
66.9
0.79
3
Struve
1850.69
228.8
0.42
3
Madler
1833.27
61.9
0.72
8-2
Herschel
1851.31
236.8
0.35
3-2
Madler
1833.39
63.5
—
3
Dawes
1851.42
238.1
0.55
2
Dawes
1834.84
69.1
0.70
1
Struve
1851.56
241.8
0.48
10
0. Struve
1851.83
234.8
0.31
7-5
Madler
1835.41
75.7
0.74
5
Struve
1852.52
250.1
0.5 ±
2
Dawes
1836.49
98.8
(Schatzung) 1
Madler
1852.62
261.2
0.43
6
0. Struve
183G.52
88.8
0.56
6
Struve
1852.67
241.1
0.30
13-11
Madler
1839.59
119.8
0.5 ±
2
Dawes
1839.82
132.1
0.76
2
0. Struve
1853.20
257.9
0.4 ±
2
Jacob
1839.82
126.9
0.59
3
W. Struve
1853.37
267.8
0.27
5
Madler
1853.56
280.9
0.32
5
O. Struve
1840.52
137.2
0.51
5
0. Struve
1853.64
273.3
0.44 ±
4
Dawes
1840.62
135.9
0.50 ±
2
Dawes
1853.79
270.4
0.3
1
Madler
1841.42
150.4
0.48
5
Madler
1854.04
285.3
0.5 ±
3
Jacob
1841.50
149.7
0.52
5
O. Struve
1854.42
301.5
0.47
3
Dawes
1841.65
149.4
0.49
6-1
Dawes
1854.66
313.2
0.33
4
0. Struve
1854.74
317.1
0.26
4-3
Madler
1842.26
157.6
0.55
5
Madler
1842.58
156.6
0.5 ±
2
Dawes
1855.39
325.6
0.32 ±
2
Secchi
1842.60
159.1
0.57
2
O. Struve
1855.50
324.9
0.45
10-6
Winnecke
1855.51
322.5
0.45 ±
1-3
Dawes
1843.37
166.9
0.57
6
Madler
1855.62
330.2
0.40
4
0. Struve
1843.63
171.6
0.60
7
Madler
1855.77
330.2
—
2
Madler
1844.38
174.0
0.57
3
Madler
1856.35
336.8
0.51
9-6
Winnecke
1845.46
179.3
0.58
6
O. Struve
1856.37
341.7
0.45
1-3
Dawes
1845.50
186.1
0.59
19
Madler
1856.39
327.7
0.5 ±
2
Jacob
1845.64
188.3
0.60
1
W. Struve
1856.51
341.6
0.55
8-4
Winnecke
1856.59
344.4
0.47
7
Secchi
1846.61
195.7
0.61
3
0. Struve
1856.62
342.6
0.47
3
0. Struve
1846.50
194.0
0.56
14-13
Madler
1857.38
347.2
0.47
2
Madler
1847.07
196.6
—
3
Hind
1857.45
350.8
0.60
2
Dawes
1847.24
199.0
0.69
11
Madler
1857.48
351.0
0.58
7
Secchi
1847.64
204.0
0.56
5
O. Struve
1857.62
351.8
0.65
4
0. Struve
1847.71
204.6
0.62
5
MiUller
1857.95
355.8
0.6 ±
3
Jacob
1848.29
205.7
0.62
3
Madler
1858.48
356.5
0.79
1
Winnecke
1848.34
204.4
0.65
2
Dawes
1858.51
359.2
0.53
3
Secchi
1848.47
207.4
0.69
1
Dawes
1858.52
1.1
cuneo.
10
Deinbowski
1848.62
208.7
0.8 ±
2
J-,f • Bond
1858.54
359.6
0.76
5
O. Struve
1848.72
209.8
0.57
2
O. Struve
1858.61
6.2
0.69
6
Madler
<x»i:<>\ \\ it"i:h M.IS = .1
I.V.I
1
0.
P.
ii
Oil BUSH
I
1
ft
•
(Hwrvrn
e
9
9
9
1859.39
5.0
0.70
4
Midler
1870.38
43.6
1.04
8
lt.-lnl.nw ski
1859.48
4.5
0.53
4
Seorhi
187-
47.2
0.98
4-1
1'eirre
1859.61
5.9
0.79
4
-truve.
1870.44
44.6
1.1
2
(il.-illiill
1859.62
5.5
0.72
:
:•
1870.46
44.1
1.29
-
l..-\ ton Obit.
1870.47
46.8
1.13
1
Knott
1860.35
8.4
0.87
2
Dawes
1870.51
43.7
QJQ
7
|iiun-r
1870.54
47.2
0.97
3
O. Struve
1861.58
3
O. Strove
1861.68
li •
••••!
6
Madler
1871.41
47.7
—
-
I-ieyton Obs.
1871.45
47.8
1.09
8
IVIII|M. \\ski
i t*i;i.'.54
16.4
1.27
3-2
Winnecke
1871.53
47.3
0.88
9
Dun^r
1862.56
16.9
0.71
11
Dembowski
1871.54
45.7
1.00
5
Kin ill
1862.58
22.8
3
Madler
187 1.56
47.6
1.42
o
S-abntko
1862.76
22.5
0.91
2
O. Strove
1871.57
46.4
0.95
1
< il.-dlii 11
1863.43
20.8
M Si
13
IVmbowski
1872.29
47.8
1.29
_
I.I- \toll OllH
:- :
23.6
1.10
4
O. Struve
1872.43
51.3
1.03
9
It. ml, on -ki
:>,..-.,
19.7
1.07
-
Leyton Ota.
1872.48
51.7
0.92
7
Ferrari
•s. ,,
23.3
.. v ;
2
Seech i
1872.49
51.0
1.01
1
W. & S.
1872.58
51.2
0.84
7 •
DUIH'T
1864.44
24.2
0.74
10
Dembowski
1872.59
55.4
0.91
5
O. Struve
1864.46
28.3
1.09
2
Knglemann
1873.40
57.1
1.11
a
W. & S.
1865.15
30.1
1.13
5
Kiigleiuann
1873.44
56.1
1.04
8
Dembowski
1865.35
29.7
1.14
3
O. Strove
1873.47
56.0
—
1
LeyUm Ot>s.
1865.41
27.4
1.03
1
Dembowski
1873.53
58.0
—
1
I. mil. -111:11111
1865.44
27.3
1.07
3
Dawes
1873.53
59.0
—
3-0
Moll,,
1865.50
26.3
0.79
2
Secchi
1873.53
53.9
—
1-0
Komberg
1865.52
30.1
1.59
1
Leyton Obs.
1873.53
57.4
—
1-0
Sch wane
1873.53
50.3
—
1-0
Wagner
1866.38
32.3
1.40
2
Leyton Obs.
1873.54
54.1
1.00
5-3
Gledhill
1866.44
30.1
1.04
9
Dembowski
1873.54
63.1
^^
1-0
ItllllllloW
54
33.1
1.12
3
Secclii
1873.54
57.4
0.81
4
0. Struve
1866.r,|
.11 1
1.47
4-3
Harvard
1873.72
55.0
1.08
2
l»iiii.'-r
1866.66
1.13
4
O. Strii
L874J8
58.6
,i .,'i
3
Gledhill
1867.34
LOT
3
Knutt
1 87-1.1 1'
8
Dembowski
1867.40
1.19
1 1 • vard
\^:i »:;
6U
0.69
2-1
Leyton Obs.
\:
L34
1 ' Struve
L874.40
OJ8
2-1
W. &8.
LM
7
Dembowski
1X74.61
64.7
o n
4
O. Strove
1867.52
31.5
—
1
Leyton Obs.
iv
•;«t.7
^^_
1
Leyton Obs.
1867.62
1
Winnecke
187.Y I 1
8
Dembowski
1867.89
29.2
1.12
1
Duner
1875.42
66. 1
,,.,,
4
Schiaparelli
1868.39
36.0
1.05
7
Dembowski
1875.48
1875.55
62.5
. - |
0.74
0.70
1
11
O. Strove
; N. ,
41.3
1.05
5
O. Strove
1868.61
36.0
—
2
Zdllner
1X76.38
70.3
0.79
8-2
Doberck
1868.65
37.0
1.15
4
Duner
1876.44
70.5
0.77
4
Hall
1868.80
>
1
Peiroe
1876.45
70.3
1
Leyton Obs.
1876.46
74.8
n s|
9
Dembowski
1869.53
40.1
1.03
'
Dune>
1876.51
72.3
0.79
5
Schiaparelli
1869.61
44.7
—
1
Leyton Obs.
1876.61
73.6
......
4
O. Strove
160
f) COROTSTAE BOREALIS = .£1937.
1
Bo
Po
n
Observers
t
60
Po
n
Observers
0
it
O
it
1877.25
77.7
0.78
1
Copelantl
1885.26
—
0.57
1
Copeland
1877.30
82.0
0.69
4-2
Doberck
1885.41
170.1
0.65
4
Hall
1877.36
70.3
—
6
W. &S.
1885.51
171.6
0.57 ±
10
Schiaparelli
1877.42
79.6
0.75
5
Schiaparelli
1885.53
170.7
0.70
5-1
Sea. & Smith
1877.48
81.1
0.78
9
Dembowski
1885.58
170.0
0.61
7
Englemann
1877.53
71.9
1.0 ±
1
Plummer
1877.5G
77.9
0.58
4
0. Struve
1886.46
177.0
0.70
5
Hall
1886.49
180.8
0.72
4
Perrotin
1878.41
90.8
0.62
1
Burnham
1886.51
178.6
0.63
3
Tarrant
1878.45
93.3
0.62
3
Doberck
1886.51
181.3
0.80 ±
3-1
Smith
1878.50
91.0
0.60
8
Dembowski
1886.52
178.8
0.66
11
Schiaparelli
1878.53
88.3
0.75
9
Schiaparelli
1886.64
179.1
0.57
8
Englemann
1878.59
87.6
0.57
4
O. Struve
1878.80
84.4
0.67
1
Pritchett
1887.43
186.6
0.82
1
Hough
1887.51
185.6
0.60
15
Schiaparelli
1879.52
102.4
0.62
7
Schiaparelli
1887.63
186.0
0.72
3
Tarrant
1879.54
98.7
0.48
4
Hall
1888.45
195.7
0.62
5
Hall
1880.45
lllfO
2
Bigourdan
1888.53
199.0
—
1
Copeland
1880.50
116.7
0.52
3-2
Doberck
1888.55
194.8
0.60
14
Schiaparelli
1880.53
115.6
0.50
6
Schiaparelli
1888.63
193.9
0.74
3
0. Struve
1880.59
1880.62
114.2
114.3
oblong
0.46
5
5
Jedrzejewicz
Burnham
1889.42
1889.50
182.0
202.3
0.63
1
4
Hodges
Hall
1880.70
114.9
0.76
2
Copeland
1889.52
200.8
0.64
6
Schiaparelli
1881.26
121.3
—
2
Doberck
1889.58
202.1
0.72
1
0. Struve
1881.40
1881.50
124.9
126.9
0.46
0.61 ±
4
4
Hall
Schiaparelli
1890.43
1890.50
oblong
210.1
0.64
1
6
Glasenapp
Hall
1881.64
125.8
0.48
1
0. Struve
1890.67
208.2
1
Bigourdan
1882.30
134.8
0.55
3-2
Doberck
1891.48
218.4
0.61
3
Hall
1882.45
138.4
0.51
4
Hall
1891.50
213.5
0.67 ±
1
See
1882.50
1882.55
135.4
141.7
0.59
0.50
8
2
Schiaparelli
0. Struve
1891.52
1891.54
216.8
222.0
0.57
0.75
8
3
Schiaparelli
Maw
1882.61
153.2
0.56
6-4
Englemann
1892.44
226.1
0.69
1
H.C.Wilson
1883.48
147.2
0.69
10
Schiaparelli
1892.45
230.1
0.72
2
Leavenworth
1883.51
1883.51
1883.56
152.5
153.2
156.0
0.57
0.51
0.61
6
7
7
Hall
Englemann
Perrotin
1892.50
1892.57
1892.65
230.2
229.5
229.8
0.57
0.57
0.48
11
G
3
Bigourdan
Schiaparelli
Comstock
1883.59
151.6
0.58
3
O. Struve
1883.64
150.5
0.5 ±
6-5
Jedrzejewicz
1893.48
244.7
0.63
1
Maw
1884.43
159.4
—
6
Bigourdan
1893.48
1893.50
243.2
242.8
0.51
0.50
7
3
Schiaparelli
Leaveuworth
1884.48
160.1
0.57
3
Hall
1893.52
245.6
0.49
7-6
Bigourdan
1884.52
163.1
0.64
6
Perrotin
1884.52
162.0
0.54 ±
6
Schiaparelli
1894.48
262.1
0.44
6
Schiaparelli
1884.54
161.7
0.67
1
Pritchett
1894.49
261.4
0.44
1
Bigourdan
1884.58
158.0
0.58
3
0. Struve
1884.64
165.6
0.58
5
Englemann
1895.30
285.0
0.45
8
See
1884.66
172.4
—
3
Seabroke
1895.51
285.9
0.30 ±
3
Comstock
ijOOi:..\\i BORKAU8 = ^
Tliis iM'uutiful pair prmed t«> !><• ..n< ..f tin- first objects which gave dis-
tinct evidence of orbital motion, and the binary character of the system was
fully recognized by HKRSCIIKI. in 1803. Since the time of STWVK the meas-
ure* iin :'-''i inimrron* ami -.it i-i'a.-t..r\ . Tin- |>:iii- i- al\\a\- rath, r elosr, l.iil
as tlu> com|H>nents an- nearly i-«|iial in magnitude, it is generally easy to scpa-
rate. Numerous orbits have been publi-ln-<l by previous compiiterH ; the fol-
lowing table of rlenieiit- i- fairly complete.
p
T
•
a
a
<
2
Authority
Ba ;•• .
i : -• I I
1806.20
0 MOM
:••_•<"•,
37.4
.;:.-,,:;
Herachel, 1889
M«m. R.A.8., VI, 156
-
1.0879
24.3
71.13
261.35
MJUller, 1H42
Dorp. Obs., IX, 195
1S|.
0.3537
1.11H2
22.fi
71.5
263.17
M fuller, 1842
lM'7 '-'I
OJ89
IH90M
20.1
59.47
215.2
Mn.ll.-r. 1847
Fixt. Syp., I, p. 243
]SII
•• 1743
1.0128
10.52
65.65
227.17
VillarceaulX42
1780.124
0 16D.-,
1.1108
4.42
5&M
194.62
VillarceanlK.r>2
i:7'.t.338
0.4043
1.2015
9.87
59.32
185.0
Villarreaul852
A.N.,868
i.; n:,
..••:,..;
'"' .'{
60.67
215.48
Winnecke
41.58
'26
0.2625
0.827
26.7
.-.s.i
211.4
Wijkander
UJF76
1K.V).2G
M.-j»;-.>5
0.827
26.7
:,s,,
215.6
Dun««r, 1871
A.N., 1868
««>.17
22.2
60.4
224.1
Flainina'nlK74 Cat. <<t. l>nub.,p.88
11 .-..;:•
.«»7
0.892
25.72
.-,'.,. s
218.6
lfc.U-r.-k. 1880 A.N.,2.'W8
i: i>
1892.3 1 0.33
MS,;
_••_••>.-.
Com8tock,1893 Proc. Am. AMOC., 1894
Making use of all the measurcH up to 189;"5, we find the following clcmcntH
of i Corona* Borealiit*:
P = 41.60 years
T - 1892.50
« - 0.2C7
a - 0*.9H,.-,
JJ - 27MO
t . 58°.50
X - 217 SI
n - +8«.653846
Apparent orbit:
Lrngth of major axiH • » 1".804
Length of minor axis » 0*.934
Aagle of major axis « 28*. 7
Angle of periastron « -
DinUuce of star from center = 0"
The accompanying table shows that the motion is well represented, and
that the present clement* will finally undergo but slight corrections.
• A*tro»omi*che Ifaekrirkln, ML
162
CORONAE BOREALIS = .21937.
COMPARISON OP COMPUTED WITH OBSEKVED PLACES.
t
00
e
f\ f\
Po—Pc
n
Observers
O
0
7
i
O
f
1781.69
30.7
27.4
—
1.08
+ 3.3
—
1
Herschel
1802.69
179.7
174.8
—
0.63
+4.9
—
1
Herschel
1823.27
25.9
27.3
1.58
1.08
-1.4
+ 0.50
2-1
Herschel and South
1826.77
35.3
37.9
1.07
1.09
-2.6
-0.02
4
Struve
1829.55
43.2
47.0
0.96
1.01
-3.8
-0.05
2
Struve
1831.48
51.4
54.5
0.95
0.92
-3.1
+ 0.03
15-4
Dawes 2-0; Herschel 10-1 ; 2.3
1832.60
56.9
59.5
0.74
0.86
-2.6
-0.12
13-5
Herschel 9-2 ; Dawes 1-0 ; 2. 3
1833.33
62.7
63.4
0.72
0.82
-0.7
-0.10
11-2
Herschel 8-2 ; Dawes 3-0
1834.84
69.1
72.5
0.70
0.73
-3.4
-0.03
1
Struve
1835.41
75.7
76.6
0.74
0.70
-0.9
+ 0.04
5
Struve
1836.52
88.8
85.9
0.56
0.63
+ 2.9
-0.07
6
Struve
1839.70
125.9
122.2
0.63
0.53
+ 3.7
+0.10
4
Dawes 2 ; 02.2
1840.57
136.0
133.4
0.51
0.53
+ 2.6
-0.02
7
O2. 5 ; Dawes 2
1841.52
149.8
146.0
0.50
0.54
+ 3.8
-0.04
16-11
Madler 5; 02.5; Dawes 6-1
1842.48
157.8
157.5
0.54
0.57
+ 0.3
-0.03
9
Madlei 5 ; Dawes 2 ; O2. 2
1843.50
169.2
168.2
0.58
0.60
+ 1.0
-0.02
13
Madler 6 ; Madler 7
1844.38
174.0
176.4
0.57
0.64
-2.4
-0.07
3
Madler
1845.46
179.3
184.8
0.58
0.68
-5.5
-0.10
6
0. Struve
1846.61
195.7
194.1
0.61
0.71
+ 1.6
-0.10
3
0. Struve
1847.42
201.0
200.0
0.63
0.71
+ 1.0
-0.08
24-21
Hind 3-0; Madler 11; 02.5; Madler 5
1848.49
207.2
207.8
0.66
0.70
-0.6
-0.04
10
Madler 3 ; Dawes 2 ; Dawes 1 ; Bond 2 ; O2.
1849.54
219.3
216.0
0.64
0.66
+ 3.3
-0.02
5-4
Dawes 2-1; 02. 3
1850.59
231.5
225.6
0.54
0.60
+ 5.9
-0.06
8
02. 3 ; Fletcher 2 ; Madler 3
1851.53
237.8
235.9
0.42
0.53
+ 1.9
-0.11
22-19
Madler 3-2 ; Dawes 2 ; O2. 10 ; Madler 7^5
1852.60
250.8
253.5
0.41
0.44
-2.7
-0.03
21-19
Dawes 2 ; O2. 6; Madler 13-11
1853.51
270.3
272.9
0.35
0.40
-2.6
-0.05
17
Jacob 2; Madler 5; 02.5; Dawes 4 ; Madler 1
1854.46
304.3
296.5
0.39
0.38
+ 7.8
+ 0.01
14-13
Jacob 3 ; Dawes 3 ; 02. 4 ; Madler 4-3
1855.56
326.6
321.6
0.43
0.43
+5.0
±0.00
19-13
Sec. 2-0 ; Winn. 10-6 ; Da. 1-3 ; '02. 4 ; Ma. 2-0
1856.47
339.ll337.7
0.49
0.50
+ 1.4
-0.01
30-25
Winn.9-6 ; Da.1-3 ; Ja. 2 ; Winn.84 ; Sec.7 ; 02. 3
1857.57
351.3
350.6
0.61
0.61
+ 0.7
±0.00
18-16
Madler 2-0; Dawes 2 ; Secchi 7 ; 02. 4; Jacob 3
1858.54
1.3
359.0
0.73
0.70
+ 2.3
+ 0.03
24-11
Secchi 3-0; Dembowski 1 0-0 ; 02.5; Madler 6
1859.52
5.2
5.6
0.74
0.79
-0.4
-0.05
15-11
Mtidler 4 ; Secchi 4-0 ; O2. 4 ; Dawes 3
1860.35
8.4
10.1
0.87
0.86
-1.7
+ 0.01
2
Dawes
1861.58
16.1
15.6
0.92
0.94
+ 0.5
-0.02
9
02. 3 ; Madler 6
1862.61
19.6
19.7
0.87
1.00
-0.1
-0.13
19-16
Winn. 3-0; Dembowski 11 ; Madler 3; O2. 2
1863.53
21.8
22.9
0.95
1.04
-1.1
-0.09
19 +
Dem. 13 ; 02. 4 ; Leyton Obs. - ; Secchi 2
1864.45
26.3
25.9
0.91
1.07
+0.4
-0.16
12
Dembowski 10 ; Englemann 2
1865.40
28.5
28.9
1.12
1.09
-0.4
+0.03
23
En. 5; 02. 3; Dem. 9; Da. 3 ; Sec. 2; Ley. 1
1866.52
32.5
32.4
1.23
1.10
+ 0.1
+0.13
22-21
Leyton Obs. 2; Dem. 9; Sec. 3 ; Hv. 4-3; 02.4
1867.50
33.0
35.3
1.10
1.10
-2.3
±0.00
18-16
Kn.3 ; Hv. 3-2 ; 02. 2 ; Dem.7 ; Ley.1-0 ; Du. 1 ;
1868.59
37.5
38.6
1.03
1.09
-1.1
-0.06
17
Dem. 7; 02.5; Dune"r4; Peirce 1 [Winn. 1
1869.57
40.7
41.6
1.03
1.06
-0.9
-0.03
10-9
Dune"r 9 ; Leyton Obs. 1-0
1870.45
45.1
44.6
1.07
1.04
+ 0.5
+0.03
25-22
Dem.8 ; Pei.4-1 ; G1.2 ; Ley. -; Kn.l ; Du.7; O2. 3
1871.51
47.1
48.3
1.06
1.00
-1.2
+0.06
25
Ley. — ; Dem.8; Du. 9 ; Kn.9; Sea.2; Gl. 1
1872.47
51.2
52.0
1.00
0.96
-0.8
+ 0.04
29 +
Ley. - ; Dem. 9 ; Fer. 7 ; W. & S. 1 ; Du. 7 ; 02. 5
1873.52
55.9
56.4
1.01
0.90
-0.5
+ 0.11
22-20
W.&S.3; Dem.8; Ley.-; Gl.5-3; O2.4; Du.2
1874.47
60.5
61.0
0.89
0.85
-0.5
+0.03
19 17
Ley. 2-1 ; Gl. 3 ; Dem. 8 ; W. & S. 2-1 ; 02. 4
1875.44
67.2
66.2
0.82
0.79
+ 1.0
+ 0.03
23
Dembowski 8 ; Schiaparelli 4 ; Dun^r 11
1876.45
71.9
72.6
0.80
0.73
-0.7
+ 0.07
31-25
Dk. 8-2; HI. 4; Ley. 1 ; Dem. 9; Sch. 5 ; 02.4
1877.41
77.2
79.4
0.80
0.68
-2.2
+ 0.12
30-22
Cop.l ; Dk. 4-2 ; W.& S. 6-0 ; Sch.5 ; Dem.9 ; Pl.l ;
1878.55
89.2
89.7
0.64
0.61
-0.5
+ 0.03
26
ft. 1 ; Dk. 3 ; Dem. 8 ; Sch. 9 ; 02. 4 ; Pr. 1 [ 02. 4
1879.53
100.5
100.2
0.55
i :>7
+ 0.3
-0.02
11
Schiaparelli 7 ; Hall 4
1880.56
114.5
112.5
(i.r.l
0.54
+ 2.0
±0.00
23-20
Big. 2-0; Dk.3-2; Sch. 6; Jed. 5 ; ft. 5; Cop. 2
1881.44
124.7
123.9
0..-.1
1.5:;
+ 0.8
-0.02
11-9
Doberck 2-0 ; Hall 4 ; Schiaparelli 4 ; 02. 1
1882.49
140.7
137.8
0.51
0.53
+ 2.9
+ 0.01
23-20
Doberck3-2; Hall 4 ; Sch. 8 ; 02.2; En. 6-4
1883.55
151.8
150.9
0.58
0.55
+ 0.9
+0.03
39-38
Sch.10; H1.6; En.7; Per.7; 02.3; Jed.6-5 [Sea.3-0
1884.54
163.5
1C2.5
0.60
I..VS
+ 1.0
+0.02
33-24
Big.6-0 ; H1.3j Per.6; Sch.6 ; Pr.l ; 02.3 ; En.5 ;
ISO
1MB
Seal*.
7 Coronae Borealis = £ 1 937.
ft.* IMM>TIS — 2-1988.
L63
•
,.
i ftl.
,. ,.
Pr-»
a
ObMrrrre.
|ss.-. |,
1 • ' .
' -•
-1.1
:
•-•• -
•• 1; H1.4;Sch. 10; Se«,&Sm.5-l; En.7
1886.52
' . • IH
• •.,.,.,,,.
-1.8
.; ._•
Hall :. : I'.-r. 4 ; Tar. 3 ; Sin. 3-1 ; Hrh. 1 1 ; Kn. 8
1887.51
184 MX
I.IMI 71 (1 ,,•'
-2.9
19
Ilimch 1 : Srhiajiaivlli 15; Tarnint .'!
1888.54
;,,,•,
;:.. i ,..-.,.; i
Hall.-.; r,r-hin,l l ii; S<-l.ia|.ar.-lli 14; O2. 3
1889.53
.-•I ; _-..
• • - . :
11
Hall; Srlnai.ar.-lli (1; <>2. 1
:- • . .••' • .-:
: IIM-.I ..,;•, •• :
7-6
Hall (i; llitfour.laii I "
l.v.O .'.I .1 7.i'i .1
.;....... i i . ;,
i
u
Hall :i ; SCH> 1 ; S-lnapai.-lli X ; Maw 3
1892.50
. - ••;:•.
>:•>.••..
III \V 1 ; l.v. 1' ; Itij;. 1 1 ; Srll. 6 ; tVjJIl. 3
•,,.;,
JIM :• i
+ <Mi3
\- 17
Maw 1 ; Scliiai>arelli 7 ; l.v. 3 ; Hig. 7-6
IVH Hi
...i - .-:.
> : ; " i ••_•.".
+ 0.01
7
Schiapan-lli C. ; Itip.unlan 1
IV'.-. .M
285.9]282.7|0.. •
-0.01
3-fl
- n :i; c<.niHt.« k :;
Tin- uncertainty in tin- |n-rio<l does in it -nr|>.i-> o.l year, ami an altcnition
of the eccentricity amountjnj? t« ±d.(H is not probable. It HCCIIIH, however, that
there arc occasional Hyutcinatic ernire in the angles, and hence careful measure-
ment Bhouhl be continuiHl. It will not lie many years Ix-fon* a (U-finitive deter-
mination of the elements of this interesting binary can lie advantageously
undertaken. The following is n short ephemeris for the use of olwervere.
L8MJO
1897.50
1898.50
B06JB
327.7
342.9
P.
0.39
0.45
1899.50
1900.50
9.
353?8
1.6
P.
0.64
0.73
BOOHS ==$1938.
15k SO-.7
8.5, whlt«
S *s -J-370 48'.
; 8, white.
Dutorered l»j Sir William Hrrtrhel, Sr/.trmber 10, 17N1.
OlWKKVAII. x-
1782.68
9.
357
P»
i
1
Obnrrvrr
HM
1802.86
346^.'
—
- -
Hi-rschol
1822.21
3307
—
2
Strove
1823.41
333.7-
1.65
3
H. & So.
1825.46
333.53
1.43
I
South
1826.77
327.0
1.38
2
Strore
1889.73
324.0
1.24
2
Strove
1830.24
324.1
2
Henrhel
1831.36
321.7
1.14
1
Hrnohd
(
9.
P*
a
Otwtnren
e
f
LOO
3-1
HlTHTln-1
1833.39
11.-.
1
I)awe«
319.7
l.l'.i
3
Strure
1835.55
318.6
1.10
3
Htruve
1835.65
309.1
—
1
Midler
1836.45
310.1
_
2
Madlcr
1836.69
315.1
1.06
3
Strure
1837.37
314.9
1.0±
1
Dawes
1837.70
315.0
Oj
—
Strove
1839.83 310.4 —
W. Strove
164
/A2 BOOTIS = 21938.
t
6,
Po
n
Observers
1
60
Po
n
Observers
0
•
0
f
1840.39
306.0
0.83
3
Dawes
1857.38
239.2
0.35
2
Madler
1840.46
313.8
0.98
3
0. Struve
1857.52
231.7
0.55
1
Secchi
1841.47
308.7
0.82
2
Madler
1857.65
237.9
0.58
3
O. Struve
1841.66
303.2
0.86
6.3
Dawes
1858.56
225.9
0.45
1
Secchi
1842.23
1842.40
303.8
305.2
0.85
0.72
3
3
0. Struve
Madler
1858.56
1858.57
228.3
236.0
0.57
0.32
3
4
0. Struve
Madler
1842.40
300.9
0.85 ±
3
Dawes
1859.39
226.4
0.42
3-2
Madler
1842.66
304.9
0.78
2
Madler
1860.95
211.3
0.58
3
0. Struve
1843.57
301.5
0.76
10
Madler
1861.58
215.1
0.42
2
Madler
1844.39
299.2
0.71
2
Madler
1862.56
202.9
0.3?
3
Dembowski
1845.54
295.8
0.64
10
Madler
1862.63
217.7
0.4 ±
1
Madler
1846.40
1846.68
291.8
287.1
0.64
0.57
12-11
4
Madler
0. Struve
1863.38
1863.63
195.8
195.8
0.55
0.75
12
Dembowski
Leyton Obs.
1847.08
281.3
2
Hind
1847.30
286.5
0.65 ±
4
Dawes
1864.41
193.0
0.51
4
Knott
1847.38
288.1
0.55
15-13
Madler
1864.48
189.5
cuneo.
5
Dembowski
1848.37
282.4
0.42
2
Madler
1865.45
184.8
0.53
10
Dembowski
1848.52
280.0
0.65
4
Dawes
1865.46
190.1
0.48 ±
3
Dawes
1848.52
282.9
0.56
3-4
w c- Bond
1865.72
197.9
—
1
Leyton Obs.
\j. L .
1865.78
187.5
0.57
5
Englemann
1849.44
276.2
0.68
2
Dawes
1866.40
179.2
0.60
8
0. Struve
1850.46
272.7
0.53
2
0. Struve
1866.41
196.4
0.85
3-2
Leyton Obs.
1850.69
276.7
0.40
3-2
Madler
1866.48
181.2
0.50
7
Dembowski
1866.54
180.3
in cont.
1
Secchi
1851.28
264.9
0.32
3
Madler
1851.42
266.6
0.52
2
Dawes
1867.48
175.8
0.60
6
Dembowski
1851.48 '
262.7
0.44
3
0. Struve
1851.77
263.4
0.31
4
Madler
1868.38
174.2
0.53
5
Dembowski
1852.52
262.2
0.55 ±
1
Dawes
1869.49
171.1
0.53
6
Dune'r
1852.60
261.3
0.41
10
Madler
1869.54
167.5
0.54
2
0. Struve
1852.65
268.2
0.49
3
0. Struve
1870.39
165.8
0.62
7
Dembowski
1853.23
265.1
0.45 ±
2
Jacob
1870.44
164.0
—
1
Gledhill
1853.34
256.2
0.33
4
Madler
1870.52
163.9
0.59
4
Dune'r
1853.71
254.6
0.5 ±
1
Dawes
1870.65
170.8
—
-
Leyton Obs.
1853.77
256.6
0.40
2
Madler
1871.43
161.2
0.61
7
Dembowski
1854.06-
253.7
0.5 ±
2
Jacob
1871.54
160.8
0.67
5
Dune'r
1854.41
249.3
0.47
3
Dawes
1871.57
167.0
0.76
1
Seabroke
1854.70
247.2
0.44
4
Madler
1871.65
158.4
0.5 ±
1
Gledhill
1855.11
247.2
0.53
4
O. Struve
1872 29
167.5
—
-
Leyton Obs.
1855.52
256.9
0.42
2
Madler
1872.35
163.4
0.35 ±
2
W. &S.
1872.44
164.1
0.65
8
Dembowski
1856.42
236.5
0.45
1
Secchi
1872.46
152.0
0.6 ±
4
Knott
1856.57
242.1
0.59
2
O. Struve
1872.52
158.0
0.55
2
Dune'r
liooTIS = .11938.
1
0m
f.
•
,,
I
it
f.
M
Ohm » in
1873.09
' - :
0.63
4
O. Strove
i.50
1 1 .Vn
0.70
O
Hall
1873.34
151.0
0.62 ±
W. 48.
117:.
0.76
6
KngliMiiaiiii
1873.41
151.0
7
ibowski
1883.59
11 •-••.•
0.75
1'errotin
1873.48
' • -
—
1
LeytonOba,
>. ,
110.2
0.64
1
O. Strove
1873.47
152.3
0.48 ±
•
Oleilhill
1884.48
113.8
,,, ,
3
Hall
1874.22
150.7
I
(iledhill
1884.51
112.3
0.74 ±
4
Kfhia|Mirelli
1874.44
149.1
1
\\ & 8.
1884.62
110.2
0.86
2
O. Struve
1874.44
Ml
1
ivinhowski
1884.67
119.9
—
4
Seabrokc
1874.54
' • !
—
1
Ley ton Ota.
1885.40
110.8
0.75
|
1'errulin
1875.41
I4L9
.., ,
8
Dembowtki
1885.49
]".. •>
1.00 ±
3-1
Smith
1875.47
: .
0.64 ±
4
Schiaparelli
1885.49
110.1
0.79
3
Tarrant
187:,
QJQ
1
Ihme'r
1885.4'J
111.3
0.71
4
Hall
' : •
2
Doberck
1886 JO
109.4
0.89
4
MehiaiHiKUi
1 16.9
li v°.
7-6
II
1876.46
145.4
: - :
0.73
0.70
4
8
Hall
Deinbowski
LSMI ra
110.6
0.7 ±
6
Jedrzejewicz
1871
: - •
0.75
1
Schiaparelli
1886.49
106.7
—
2
Smith
i.-.i «;
4-2
Doberck
1886.51
107.3
Ml
3
Hall
1^7.
• • •
0.71
7
Dmbowski
1886.51
106.0
0.72
2
1'errotin
11.-,.:
0.73
4
W. AS.
1886.54
107.7
0.74
1
Schia|circlli
1S7.
Ml
1
O. Strove
1886.78
106.2
0.7 ±
5
Jedrzejuwicz
^41
: • 1
Ml
1
liurnham
1887.44
105.4
0.70
4
Hall
v49
0.62
4
Doberrk
1887.55
•.,-, Q
—
1
Smith
v52
132.0
0.62
6
Deinbowski
1887.56
103.0
0.74
6
Schiaparclli
1878.53
1878.58
132.7
137.7
,,,.;:
N .
5
1
Schia]>areUi
O. Strove
1888.45
1888.59
100.0
101.5
0.60
0.75
4
B :
Hall
S-lii;i]iar<-lli
1879.51
128.6
0.79
4
Schiaparelli
1888.91
103.1
0.73
'2
Tarrant
0.73
4
Hall
101.6
0.87
1
U. Strove
188'
128.7
0.78
5
If urn ham
1889.35
97.8
0.73
3
M , .
ISM i"
0.64
Hall
IXX'.Ml'
'.'«: •_•
LOO
1
Doberck
98.7
0.84
3
Schiaparelli
1880.53
196 1
0.79
Schiaparelli
LSI •••:.
0.7 ±
Jedrzejewicz
ISMJO
1
uienapp
1881 -v.
LMJ
_
Doberck
'1.49
M i
Q H .
1
Schiaparelli
1881.38
126.0
0.63
Kurnham
1891.53
N.7
".71 t
1
-
1881.50
121.6
0.78
Schiapardli
1891'. 11'
1
Collins
1S81.50
123.7
0.62
6-4
Kigourdan
u a H
4
Comstock
1881.50
121.9
11 ' • _'
3
Hall
1881.63
0.72
1
O. Struve
1893.47
4
Itigourdan
1893.49
0.77
2
•,:
•-•- :
0.75
2-1
Doberck
1882.43
r.M .7
<•• i
3
Hall
1894.48
1.19
1
CalUndreau
>-- -
I'.'" 1
0 : '
4
Schiaparelli
1894.50
1.05
5
Kiguurdaii
>'- ' •
121.9
4
Engletnann
:-::.'
H !
0.75
1
H. C. Wilson
1882.55
116.9
• • i
1
O. Strove
1895.31
0.84
.
-
1883.47
III.:
Ml
4
Schiaparelli
1895.52
0.64
Comstock
166
BOOTIS == .T1938.
When the observations of 1782 were compared with those of 1802, the
physical character of the system was fairly indicated.* Since the time of
STKUVE it has been carefully followed by the best observers, and accordingly
the material now available for an orbit is highly satisfactory. The companion
is only slightly smaller than the principal star, and is therefore never very
difficult to measure. In all parts of the orbit the pair is sufficiently wide to
be seen with a six-inch telescope, but as the minimum distance of 0".49 in
angle 230° was passed in 1858, it is not surprising that the observers on either
side of this epoch, with few exceptions, have made their observed distances too
small. Thus, although the measures of different observers are not infrequently
affected by systematic errors of sensible magnitude, yet by combining the best
measures into mean positions for each year, we obtain a set of places which
give an orbit that seems likely to be very near the truth.
Some of the elements hitherto published are as follows :
p
T
e
a
a
i
i
Authority
Source
JTO.
146.649
1851.57
0.8529
1.320
94?7
49.4
87.1
Madler, 1847
Fixt. Syst., I, 252
182.6
1866.0
0.491
1.165
166.1
47.5
23.0
Winagr.,1872
314.34
1860.88
0.5641
1.761
163.2
41.9
54.4
Hind, 1872
M.N.,vol.XXXII,p.250
200.4
1865.2
0.51
—
172.0
45.0
20.1
Wilson, 1872
Handb. B.S., p. 313
198.93
1865.5
0.4957
—
169.0
46.4
23.6
Klinkerfues
Handb. D.S., p. 313
290.07
1863.51
0.6174
1.500
183.0
44.4
17.7
Doberck, 1 S75
A.N., 2026
280.29
1860.51
0.5974
1.47
173.7
39.9
20.0
Uoberck, 1878
A.N., 2194
266.0
1862.55
0.5668
1.057
166.7
35.2
40.9
Pritchard, "
Ox. Obs., No. 1 , j >.<;.!
From an investigation of all the observations which appear to be reliable,
we find the following elements of p? Bootis:
P = 219.42 years
T = 1865.30
e = 0.537
« = 1".2679
Q = 163°.8
* = 43°.9
A. = 329°.75
n = -l".64t)7
Apparent orbit:
Length of major axis = 2".6r)(>
Length of minor axis = 1".480
Angle of major axis = 173°.5
Angle of periastron = 186°.7
Distance of star from centre = 0".638
An examination of the computed and observed places, given in the follow-
ing table, seems to justify the conclusion that the elements found above will
*Astronomische Nachrichten, 3309.
• ISM
4* HOOTI8 = .11938.
167
not In- materially changed by future iii\e-iii:ati<iii. Tims, tin- period will hardly
Ix varied liy MI much a- tt-n \t-ar-. while the re-ullinjr alterations in the ,«•<•< n-
trieity, inclination and other elements will he relatively iiicon-id,
TABUC . \\i. iin-ntMi. l'i \> KH.
I
H
4
P.
P.
H-«r
f.—ft
N
Oteerren
178948
;.-..,.,
t
: - •
• • :
8
1
hcl
is. 12.86
:• -
.1 ..
_
+2.6
_
_
Heradii-1
_
i M
-0.1
__
I
Striive
1823.41
..•'.•
+ 4.7
+ 0
3
Il.Tsrhfl ami South
.
:.-..-.•
+ 0.17
5
South
IM
+ 1.1
+ 0.13
2
Stnive
:•. 1
•Jl
IM
-0.9
+ OMI
2
Stnive
1.17
+ 2.o
-0.32
'2
Herachel
.:•_•! :
11
in
+ O.S
0.00
1
Herwhol
11
i ii-.i
+ 15
+0.02
r :,
Herarhel3-l; Dawes 1 ; 2. 3
.II.-..1
1.10
Loa
+3.5
+0.07
3
Stnive
9U 1
1.06
1.INI
+ 1.7
+0.08
3
Strove
:;ll s
+ 3.2
-0.02
_
Dawea 1 ; i'. —
1840.42
ii id
089
+3.2
+0.02
6
DMNi8j 01 8
1M
304.1
-0.9
+0.01
6-3
Dawai
1842
801 i
fttJt
(>.«:{
-0.2
+0.02
6
02. 3 ; Dawea 3
|S|
SOU
0.76
+ 2.0
-0.04
10
Miuller
Isl
0.71
0.77
+ 1.9
-0.08
1
Ma<ller
1841
981 I
0.71
-3.2
-0.14
4
O. Stru\.'
L84
0.60
0.68
-1.1
-0.08
19-17
I)awe84; M&cller 15-1 3
isj> i:
-si 7
0.54
,,,..-,
-2.6
-0.11
9-10
Ma.ll.-r 2 ; ]>awe» 4 ; Itoiul 3-1
isf.. ||
noj
,,,.>
OJ :
-4.3
+0.05
2
Dawea
274.7
275.6
0.47
0.60
-0.9
-0.13
.-, !
02.'>; M.1<ller3-2
1851.49
263.9
271.2
0.40
0.58
-7.3
-0.18
12
Mftdlt-r 7 ; Dawcs 2 ; O2. 3
1852.55
268.2
265.8
0.49
0.55
+ 2.4
-0.06
3
<). Strove
1853.50
260.9
260.1
0.42
+0.8
-0.11
4
Jacob 2; Miiller 2
1854.39
•-•:." i
255.5
0.47
0.52
-5.4
-0.05
9
Jacob 2 ; Dawea 3 ; Mudlur 4
1855.11
247.2
250.8
0.53
0.51
-2.6
+0.02
4
O. Strove
L8M I'1
841.1
«'..VJ
0.49
-1.8
+0.03
3
Secohi 1 ; O2. 2
:.•-•
0.49
0.49
+ 1.3
0.00
8
Ma.lli-r 2: S.-n-hi 1; O2. 3
828.0
"I.-,
ii r.i
+ 2.1
-0.04
^
Secchi l; 0^.3; Madli-r 1
0 !•.•
+ 2.7
-0.07
3-2
MAdli-r
•Jl-j i
-1.1
+ 0.08
o. Strove
•-•!.-. i
: •_•
-0.08
•j
Mhller
M&9
+ 0.7
-0.20
:t
Dembowski
:.38
198 •>
".-..-,
+ 1..-,
+ 0.02
I-.'
Ixjwski
ISM II
l-.il •_•
l'.»1 2
o.-.i
-0.03
9
KiM.tt 1 : Dembowxki .'.
1865.56
i •»: :.
IM :
M.-.,;
+ 2.S
-0.03
Dem. 10; Dawes3; EtiKlemann 5
i860 i;
180.2
181.4
0.57
-1.2
-0.02
11
'• mbowski 7 ; Secx-hi 1
1867 is
175.8
178.9
,.,,,
,.:/.
-0.1
+0.01
6
Iwwski
174.2
171.8
DJB
+2.4
-0.07
5
Dembowski
UM ' ••:
169.3
166.7
0.54
0.61
-0.07
8
DunrrC,; ov.2
181
164.fi
162.7
0.62
+ 1.9
-0.02
IL' 11
Dem. 7; Gledhill 1 n: Dm
1871.54
160.1
58.4
0.59
n.r.:;
+ 1.7
-0.04
u
I VIM. 7: Duner :•; (il<-<lhill 1
1873 II
54.K
0.54
0.65
-1.8
-0.11
16
W.&S. ; D.-M..S; Kn 1; Du.2
l.v: l
51.5
0.57
0.65
+ 1.6
-0.08
16-15
-0 1. \\ I>.-rn.7;G1.2
1 in •_•
47.6
0.69
0.66
+ 1.6
+0.03
9
Oledhill 2 ; W. & S. 1 : Dem. 6
1^75.46
Hi"
i:::,
0.71
0.67
+0.5
+0.04
13
Dem. 8 ; Schiaporelli 4 ; Duntfr 1
.;•.> i
0.70
O.f>8
-1.2
+0.02
8
Dembnwuki
181
S6J5
0.67
0.68
+ 1.1
-0.01
•J" is
8ch. 5 ; Dk. 4-2 ; Dem.7 ; W.A 8. 4
» i.
134.6
32.7
0.64
0.69
+ 1.9
-0.05
16
/}. 1; Dk.4; Dem. 6; 8ch. 5
163
2 298.
1
6o
Oc
Po
PC
6^-Oc
PO—PC
n
Observers
1879.52
131.0
129.3
0.76
0.69
O
+1.7
+0.07
8
Schiaparelli 4 ; Hall 4
1880.44
127.7
126.3
0.72
0.70
+ 1.4
+ 0.02
17
y3. 5 ; HI. 1 ; Dk. 4 ; Seh. 4 ; Jed. 4
1881.43
123.8
122.8
0.66
0.70
+ 1.0
-0.04
21-15
Dk.4-0; (8.4; Sch.4; Big.6-4 ; H1.4
1882.45
121.3
119.6
0.74
0.71
+ 1.7
+0.03
13-12
Dk. 0-1 ; Hall 3 ; Sch. 4 ; En. 4
1883.53
114.9
116.2
0.77
0.72
-1.3
+ 0.05
14
Sch. 4 ; Hall 2 ; En. 6 ; Per. 2
1884.49
113.0
113.1
0.72
0.72
-0.1
0.00
7
Hall 3; Schiaparelli 4
1885.52
110.4
110.0
0.77
0.73
+ 0.4
+ 0.04
19
Per. 2 ; Tar. 3 ; H1.4 ; Sch.4 ; Jed.6
1886.58
106.5
107.3
0.70
0.74
-0.8
-0.04
12
Hall 3 ; Per. 2 ; Sch. 2 ; Jed. 5
1887.50
104.2
104.2
0.72
0.75
0.0
-0.03
10
Hall 4 ; Schiaparelli 6
1888.65
101.5
101.0
0.69
0.76
+0.5
-0.07
11-9
Hall 4 ; Schiaparelli 5-3 ; Tarrant 2
1889.43
97.6
98.7
0.86
0.77
-1.1
+ 0.09
7
Maw 3 ; Hodges 1 ; Schiaparelli 3
1891.51
95.0
93.2
0.77
0.79
+ 1.8
-0.02
4
Schiaparelli 2 ; See 2
1892.50
90.9
90.6
0.78
0.80
+ 0.3
-0.02
5-4
Collins 1 ; Comstock 4-3
1893.48
88.3
88.2
0.87
0.81
+0.1
+0.06
6
Bigourdan 4 ; Maw 2
1894.54
85.7
85.6
0.88
0.82
+0.1
+0.06
6
Bigourdan 5 ; H. C. Wilson 1
1895.31
83.5
83.8
0.84
0.84
-0.3
0.00
3
See
The following is a short ephemeris
t Oc pc t
.1896.50 8l!l o'85 1899.50
1897.50 78.9 0.86 1900.50
1898.50 76.9 0.87
Be PC
74°8 0.89
72.6 0.90
0*298.
a = 15h 32"'.4 ; 8 = +40° »'.
7, yellowish ; 7.4, yellowish.
Discovered by Otto Struve in 1845.
OBSKRVATIONS.
t
1845.50
1 o/\ •*
J. O".O
Po
1.25
n
2
Observers
O. Struve
t
1865.53
60
210^2
Po
1.0
n
1
Observers
Dembowski
1846.28
186.5
1.41
2
Madler
1866.29
207.0
0.8
1
Dembowski
1847.32
189.6
1.51
2-1
Madler
1867.61
209.5
0.99
1
Dembowski
1848.46
183.9
l.ll
1
O. Struve
1868.52
32.5
0.84
1
O. Struve
1848.68
185.8
1.23
1
Dawes
1869.46
214.1
0.61
3
Dundr
1851.75
1856.58
191.8
193.1
1.40
1.21
2
1
Madler
O. Struve
1870.26
1871.63
225.8
226.6
gepn ration
doubtful
contatto ?
1
1
Dembowski
Dembowski
1857.68
196.8
1.24
1
0. Struve
1872.58
235.8
0.58
1
0. Struve
1859.62
197.4
1.13
1
O. Struve
1875.52
84.2
0.53
1
O. Struve
1861.44
13.5
1.16
1
O. Struve
1875.65
265.5
0.37
2
Dembowski
Iliil
1
0.
P,
II
Otwertrn
(
e.
P»
ii
ObMTOn
o
9
o
§
1876.47
280.8 0.3 cuneo 3
Itembowski
i r.'u
0.39
3
Hall
1877.53
..,-.,
0.3
.
Dembowiiki
IM
II.: o
o.:u
6
Hc)iiu]Mirvlli
1878.33
130.8
0.27
1
Kurnhaiii
UM
188C
IM;:,
0.42
1
5
O. Struve
8clii;i|>uri-lli
1879.46
335.0
4
Hall
1879.49
327.8
1
Schia|>aivlli
1889.52
158.1
0.55
3
8dii;i|>;irrlli
1881.41
175.4
Hall
'1.48
167.3
0.68
3
Hall
1S82.47
1
apanlli
1891.49
347.5
0.63
1
Scl.iai.ar.-lli
1882.52
I •
F.ii^li-inuiiii
1882.55
.>,,
1
0. Struv,-
1892.42
169.9
0.82
1
Collins
1892.47
169.3
0.88
J*
I'.i^niifil.in
-
'•
Scliiiiparclli
1892.59
168.9
0.64
4
Cotnatuck
ii 17
:
Hn^leiuauii
II
; IjQ
o ,.
1
Perrotin
1893.43
1893.71
351.5
173.6
0.91
0.64
1
1
liigourdun
CoiiiBtock
L8MJI
••; •
5
S-liia|>arelli
60.9
7-4
Eugleniaiin
1895.54
1X95.56
173.1
174.2
' 0.85
0.82
3
1
Coin Block
Schiaparclli
1886.67
2
Schiaparclli 1vO7l
179.4
0.95
2
->...
•-., ,,,
104.9
7
Kn^ltMiiaiiu l^'.'.'i 71
177.2
1.05
1
Moultoii
tin- <li-(',\»i\ .,(' tlii^ binary in 1845, the companion hits
-iil>-t:intially an t-ntirr revolution. The period is therefore fixed with Htiflicient
prrcisioii; indeed, the numerouw and hatisfaetory measures of this pair weenred
during the last lilt \ years define the other elements in a manner almost equally
satisfactory. The shape of the apparent orbit is such that the pair is never
-sively difficult, and yet measurement near ]>eriastron, where the distance
reduces to 0*.22, requires a good telescope. The components are of nearly
equal brightness, and lienee a number of the measures as recorded requires a
correction of 180°.
The following orbits of this pair have been published by previoii-. e -
paten:
r
*
•
•
a
i
A
Authority
*-•>.• •
68*Sb2
70.
56.653
:,! 0
1812.96
1883.0
0.4872
0.51
»:,:;
0.8835
,, >,,
• i ...
i •_• -.-.I
:• li
4.1
.-.<• 17
61.2
342.52
M6.U
:•! :•
•j» :
Dobetfk, 1879
Dolgoniko
reloria,
See, 1895
\ N.,2280
\ N .-J.v;i
A.N
Unpubluhed
An investigation based on all the best observations leads to the following
elements of 0£ 296.
/' - 52.0 year* Q - 1*.9
T - 1883.0 • - 60*.9
• - 0.581 X - 26*.l
a - 0-.7989 « - +6T9231
170
0^298.
Apparent orbit:
Length of major axis = 1".546
Length of minor axis = 0".(J56
Angle of major axis = 186°.9
Angle of periastron = 15°.3
Distance of star from centre = 0".427
COMPARISON OF COMPUTKD WITH OBSERVED PLACES.
t
9.
Oc
Po
PC
00-0C
Po—Pc
71
Observers
1845.50
180.5
180.5
1.25
1.07
± 0.0
+0.18
2
0. Struve
1846.28
186.5
181.6
1.41
1.09
+ 4.9
40.32
2
Madler
1847.32
189.6
183.1
1.51
1.12
+ 6.5
40.39
2-1
Madler
1848.57
184.9
184.8
1.17
1.16
+ 0.1
40.01
2
O. Struve 1 ; Dawes 1
1851.75
191.8
188.8
1.40
1.19
+ 3.0
40.21
2
Madler
1850.58
193.1
190.2
1.21
1.20
+ 2.9
40.01
1
O. Struve
1857.68
196.8
196.2
1.24
1.15
4- 0.6
40.09
1
0. Struve
1859.62
197.4
198.9
1.13
1.11
- 1.5
40.02
1
O. Struve
1861.44
193.5
201.6
1.16
1.06
- 8.1
40.10
1
0. Struve
1865.53
210.2
209.1
1.0
0.90
+ 1.1
+ 0.10
1
Dembowski
1866.29
207.0
210.8
0.8
0.87
- 3.8
-0.07
1
Dembowski
1867.61
209.5
214.2
0.99
0.80
- 4.7
+0.19
1
Dembowski
1868.52
202.5
216.9
0.84
0.75
-14.4
+ 0.09
1
0. Struve
1869.46
214.1
220.0
0.61
0.71
- 6.9
-0.10
3
Dune'r
1870.26
225.8
222.7
—
0.67
+ 3.1
—
1
Dembowski
1871.63
226.6
229.6
—
0.58
- 3.0
—
1
Dembowski
1872.58
235.8
235.3
0.58
0.53
+ 0.5
+ 0.05
1
0. Struve
1875.57
264.7
263.2
0.45
0.37
+ 1.5
+ 0.08
3
0. Struve 1 ; Dembowski 2
1876.47
280.8
275.9
0.3
0.34
+ 4.9
—0.04
3
Dembowski
1877.53
295.9
292.8
0.3
0.33
+ 3.1
-0.03
5
Dembowski
1878.33
310.8
306.4
0.27
0.33
+ 4.4
-0.06
2
Burnham
1879.47
331.4
325.0
0.29
0.34
+ 6.4
-0.05
8
Hall 4 ; Schiaparelli 4
1881.41
355.4
352.1
0.35
0.36
4- 3.3
-0.01
3
Hall
1882.47
7.5
6.6
0.33
0.34
+ 0.9
-0.01
4
Schiaparelli
1883.57
22.4
26.7
0.31
0.28
- 4.3
+ 0.03
6
Schiaparelli
1884.47
53.1
53.7
0.31
0.22
- 0.6
40.09
7
Perrotin 2 ; Schiaparelli 5
1885.65
60.9
102.4
0.27
0.22
-41.5
+ 0.05
7-4
Englemann
1886.68
133.7
130.6
0.29
0.29
4 3.1
±0.00
2
Schiaparelli
1887.53
142.5
144.1
0.36
0.38
- 1.6
— 0.02
9
Hall 3 ; Schiaparelli 6
1888.56
153.4
153.6
0.53
0.48
— 0.2
+ 0.05
5-6
0. Struve 0-1 ; Schiaparelli 5
1889.52
158.1
159.1
0.55
0.56
- 1.0
-0.01
3
Schiaparelli
1891.49
167.4
167.8
0.65
0.74
- 0.4
-0.09
4
Hall 3 ; Schiaparelli 1
1892.49
169.4
170.8
0.78
0.81
- 0.6
-0.03
7
Collins 1 ; Bigourdan 2 ; Com. 4
1893.62
172.5
173.4
0.78
0.88
- 0.9
-0.10
2
Bigourdan 1 ; Comstock 1
1895.55
173.7
177.3
0.84
0.99
- 3.6
-0,15
4
Comstock 3 ; Schiaparelli 1
1895.74
178.3
177.6
1.00
1.00
4- 0.7
±0.00
3
See 2 ; Moulton 1
The table of computed and observed places shows that these elements are
extremely satisfactory. Future observations are not likely to vary the period
given above by more than one year, while an error of ±0.02 in the eccentric-
ity is highly improbable. In spite of the accuracy of the present elements some
improvement will ultimately be desirable, and hence astronomers should con-
tinue to give this interesting system regular attention. The star will be easy
WIT,
1808
OS 298.
b. .>:.-.
f Of H:. -x \ I HORKAI.IS = .1 1967.
171
a nninber of yean, and observers with small n !.-<,. pc* will find it an
important ol.j.-rt for im-aMiri-mi-nt.
l!i»- following i* a short r|>lu-nn-i i- :
1896.50 s.9 In:
18" i •>:
1898.50 J.O 1 1<>
' **. 1'
1899.50 I- M.;
l'J00.50 181 7 I i:,
t
y< n|;n\ \|. r,(UJ|- \US = SlJMi
4. jr*Uow ; 7, Woe.
IHtnrertd by William Sir,,,; !„ IKI'G.
OMKKVATIOXS.
i •
P.
H
Obterrrni
o
|
o
g
181''
110
1'
Struve
1MM.39
297.0
0.39
1
M Siller
1828.98
lid
OLM
Struve
1848.40
292.8
0.4 ±
8
5-£ Itond
1881' -1
1".
0.4 ±
3
Struve
1849.(i3
289.4
0.50
»
O. Htnive
1833..-M
105.8
0.4 ±
1
Struve
1850.G9
289.9
0.53
3
Midler
1835.46
•implex
—
3
Struve
1851.33
1851.50
292.5
287.6
0.3 ±
0.48
1
4
Midler
O. Stnive
1K36J52
338?
obi. :•
4
Struve
1W.'.07
2851
0.57 ±
4
Dawn
>51
ru
iieifiiriiiu
1
\V. Struve
[81
"i.4
0.46
7-6
Midler
'.78
255. cuneiforme
1
ruve
is:,:: n|
O.H;
5
O. Struve
1841.50
3.T.
0.18
10-1
Midler
IM
i;<
'_*
Jacob
184.
114.3
0.20
4-1
Midler
1.5
.' in
MU.H.T
IK.%1 !«
, .:
• •
IHiwes
1K42.80
" 17
Midler
IN.'.! 7i.
MU
0.4 ±
1
Midler
1H43.30
0.41
:t
nive
18B6JQ
. - . .
_
_
Secrhi
1843.45
0.6 ±
1
I)awe>
tU i
—
1
Ml.ll.-r
1843.48
276.6
Midler
IS.-4 n
wu
Ml
3
Winnwk,-
1844.37
.- -
1
Midler
1801 ••••
288.9
0.45
8-7
Serein
1K45.37
292.1
'
Midl.r
1856.62
-- -
0.47
6
O. Struve
1*45.61
296.0
" II
5
O. Struve
M8J
1
Midler
1H45.57
292.7
0.43
•• -
Midler
18T,:
0.5 ±
1
Dawea
M ,.
5
Seochi
184646
294.2
0.45
11
Midler
Ul
L'M il
cuneo
3
IVmbowski
1847.29
292.6
0.44
••
O. Struve
18.'-^
•-'^1 1
0.33
4-3
Midler
1847.43
295.1
0.36 11-9
Midler
: - - • :
0 H
•
O. Struve
172
COROXAE BOREALIS = .T1967.
t Bo po n Observers
Go Po n Observers
0 ff
O If
1859.36 282.6 0.45 ± 1 Dawes
1883.53 142.6 0.16 ± ' 3 Perrotin
1859.38 290.4 obi. 3 Madler
1883.57 129.1 0.41 5 Schiaparelli
1861.59 287.7 0.42 3 0. Strove
1883.60 149.3 0.58 1 O. Struve
1883.64 146.9 0.20 8 .Englemann
1862.56 292.9 cuneo 3 Dembowski
1862.91 227? doubtful 1 Madler
1884.52 125 cuneiforme 2 Perrotin
1884.53 305.6 0.34 1 Perrotin
1863.25 semplice 1 Dembowski
1884.53 132.4 0.34 6 Schiaparelli
1863.64 290.5 0.41 3 0. Struve
1884.61 " 166.8 0.28 6 Englemann
1865.6 semplice 4 Secchi
1885.48 round 1 Smith
1865.26 semplice 1 Dembowski
1885.54 134.3 0.35 3 Schiaparelli
1865.50 280. <0.5 1 Englemaim
1885.63 164.6 0.38 10-6 Englemann
1865.53 einfach 1 Englemann
1886.51 129.1 0.38 6 Schiaparelli
1866.30 201.2 4 Harvard
1886.69 159.9? 0.93? 8 Englemann
1866.61 205.3 1 Wiulock
1866.62 286.0 0.43 2 O. Struve
1887.51 126.6 0.38 13 Schiaparelli
1887.55 round 1 Smith
1867.75 simple 10 Dune'r
1888.55 124.3 0.40 16-15 Schiaparelli
1868.02 260.2 0.36 2 0. Struve
1888.61 132.0 0.85 2 O. Struve
1868.72 252 cuneiforme O. Struve
1889.42 109.2 1 Hodges
1869.36 280.4 1 LeytonObs.
1889.52 122.4 0.41 4 Schiaparelli
1872.45 190 ? — 1 W. & S.
1890.68 124.1 0.51 1 Bigourdan
1873.38 195 ? — 1 W. & S.
1891.50 120.0 0.5 ± 1 See
1891.51 122.5 0.42 4 Schiaparelli
1874 simple O. Struve
1891.51 125.6 0.36 4 Hall
1874.56 166.9 1 LeytonObs.
1891.58 118.8 0.51 1 Bigourdan
1875.40 single 1 Hall
1892.44 122.3 0.83 ± 1 H.C. Wilson
1875.41 165.4 1 LeytonObs.
1892.44 121.1 0.69 1 Bigourdan
1892.60 122.8 0.47 7 Schiaparelli
1876.32 simple 1 Flanunarion
1892.72 121.9 0.40 3 Comstock
1876. single 1 Doberck
1876.45 single 1 Hall
1893.49 120.0 0.52 2 Schiaparelli
1876.81 simple Schiaparelli
1893.50 118.4 0.65 2 Bigourdan
1877.54 163.3 0.44 2 0. Struve
1894.48 119.7 0.53 2 Schiaparelli
1894.60 121.3 0.60 5-4 Barnard
1878.60 150.7 0.56 2 0. Struve
1895.30 114.8 0.67 3 See
1879.56 single 2 Hall
1895.55 117.1 0.43 3 Comstock
1879.81 single 5 Burnham
1895.61 123.7 0.64 4 Barnard
The components of this remarkable system are of the 4th and 7th magni-
tudes, and of yellow and bluish colors respectively, so that the object is
generally very difficult. STUUVE happened to discover* the companion near the
time of its maximum elongation, when the polar coordinates were 6 = 111°.0,
* Astronomical Journal, 310.
< «>I:..N \i it..i:i:\i is — vi9fl7. 173
p == 0".72. Measures in 1H28, IS'51 ami is:w, showed that both angles and
di-tanccs were steadily dei-rca-ing, and in is:{.~> the star appeared -in^le under
the best seeing. Tin- < -ompanion was not again recognized with certainty until
1SJ-J. ;ilth..uu'h SUM VK. O. SUM VK and M.MM.KI: searched for it repeatedly
during the intervening period, and occasionally suspected an elongation. Hut (lie
discordance in the angles of the supposed elongations justify the l>elief that
the phenomena observed were probably nothing more than points of diHVaetion
fringes, or some other kind of spurious images. MAULER'S observation of 332°.3
and OM8 at the e|>och 1841.50 may be genuine, although at this time the star
must havr heeii exec— ivdy clu-e. The binary character of the pair was early
recognized by STKUVK, who |>ointcd out the particular interest attaching to the
-ystcin on account of its high inclination, y Corona* Boreal!* has since been
mca-nrcd by many of the best observers, and yet the stars are so unequal and
BO close that the errors of observation assume formidable proportions, and
render a satisfactory determination of the elements very difficult. The great
inclination of the orbit throws nearly all the position-angles into small regions
of alxnit 10° on either side, and while the retrograde motion ought to make
all angles steadily decrease, we are sometimes confounded by an appearance of
direet motion (aa from 1859 to 1863) which proves the existence of sensible
systematic errors, probably due to the placing of the micrometer wires parallel
to the edges of unequal images.
It is equally confusing to find that instead of a steady increase and de-
crease in the distance, nearly all of the distances are in the immediate neigh-
borhood of 0*.4 ; such measures are of course misleading, as the companion
cannot he -landing still at a constant angle and distance. While, therefore, it
is clear that the elements can not lay claim to such accuracy as could be de-
-ired, it will yet appear that they are good and even excellent for oh-ervations
which are so badly vitiated by accidental and systematic errors.
It is obvious that in case of a system whose orbit plane lies nearly in t In-
line of vision, the angles will IK- practically useless unless measured with the
greatest accuracy ; yet, in this instance, even when the pair is fairly wide, we
frequently find the angles of individual observers differing by so much as 10",
and when the stars are close the uncertainty in angle will amount to at least
twice this quantity. On account of such conspicuous errors in angle we have
based the present orhit largely upon the distances.
DOBKRCK and CELORIA are the only astronomers who have previously
attempted an orbit for this pair.
174
COROJfAE BOREALTS = 2:1967.
p
T
e
a
8
t
;.
Authority
Source
yre.
95.50
1843.7
0.387
0.75
111.0
83.0
239.0
Doberck, 1877
A.N., Bd., 88
95.5
1843.70
0.350
0.70
110.4
85.2
233.5
Doberck, 1877
A.N., 2123
85.276
1840.508
0.3483
O.C..-M
113.47
81.67
250.7
Celoria, 1889
A.N., 2904
From an investigation of the beet observations we find the following ele-
ments :
P = 73.0 years
T = 1841.0
e = 0.482
a = 0".7357
SI = 110°. 7
i = 82°.63
A = 97°.95
n = -4°.9315
Apparent orbit:
Length of major axis = 1".30
Length of minor axis = 0".175
Angle of major axis = 111°.3
Angle of periastron = 329°.6
Distance of star from centre = 0",068
The accompanying table shows the agreement of the above elements with
the mean places.
COMPARISON OF COMPUTED WITH OHSEKVED PLACES.
t
9.
8c
Po
ft
00—0.
PO—PC
n
Observers
1826.75
111.0
114.5
0.72
0.70
o
- 3.5
+0.02
2
Struve
1828.98
110.7
113.5
0.54
0.69
- 2.8
-0.15
3
Struve
1831.68
109.3
111.2
0.4 ±
0.63
- 1.9
-0.23 ±
1
Struve
1833.34
105.8
110.0
0.4 ±
0.57
- 4.2
-0.17±
2
Struve
1835.46
simplex
107.4
—
0.44
—
—
3
Struve
1836.52
oblong?
105.5
—
0.37
—
—
4
Strave
1840.78
75
95.1
cune.
0.16
-20.1
—
4
O. Struve
1841.50
332.3
314.8
0.18
0.10
+ 17.5
+0.08
10-4
Madler
1842.64
300.4
301.9
0.33
0.21
- 1.5
+ 0.12
6-3
Miidler
1843.30
292.5
298.6
0.41
0.28
- 6.1
+ 0.13
3
0. Struve
1844.37
286.2?
295.5
—
0.37
- 9.3
—
1
Madler
1845.61
296.0
293.1
0.44
0.45
+ 2.9
-0.01
5
O. Strave
1847.36
293.8
290.8
0.40
0.54
+ 3.0
-0.14
16-14
0. Struve 5 ; Madler 11-9
1848.44
294.9
289.7
0.4
0.57
+ 5.2
-0.17
7
Ma. 4 ; W. C. & G. P. Bond 3
1849.63
289.9
288.6
0.50
0.58
+ 1.3
-0.08
3
0. Struve
1850.69
289.9
287.7
0.53
0.59
+ 2.2
-0.06
3
Madler
1851.50
287.6
287.0
0.48
0.60
+ 0.6
— 0.12
4
0. Struve
1852.07
285.1
286.5
0.57 ±
0.60
- 1.4
-0.03 ±
4
1 >;iwes
1853.17
286.2
285.6
0.45
0.59
+ 0.6
-0.14
9-10
02. 5 ; Ja. 0-2 ; Ma. 4-3
1854.40
284.3
L'SI.I
0.69
0.58
- 0.1
+ 0.11
• 2
Dawes
1855.73
292.4
283.3
—
0.56
+ 9.1
-
1
Madler
1856.62
283.8
282.4
0.57
0.54
+ 1.4
+0.03
6-9
0. Struve
1857.52
281.0
281.4
0.50
0.52
- 0.4
-0.02
1
Dawes
1858.97
284.7
279.8
0.46
0.48
+ 3.9
-0.02
5
0. Struve
1859.36
282.6
279.4
0.45
0.47
+ 3.2
-0.02
1
Dawes
1861.59
287.7
276.2
0.42
0.41
+11.5
+0.01
8
0. Struve
1862.73
260.0
274.0
cuneo
0.38
-14.0
—
4
Dembowski ; Madler 1
1863.64
290.5
272.3
0.41
0.35
+ 18.0
+ 0.06
3
0. Struve
I
yOOi:«>N\i ii"i:i \M8 = 2
IT.'.
<
«.
«.
*
*
«.-*.
*— P.
•
f 1I.AA»WABM
WOTTTrrB
1st , ,..
4
280.
-•--.:;
. ,, .
,, ,,
+ 12.3
+0.2-
1
hflHMan
1866.62
286.0
260.0
+ -•
+ 0.1-.I
2
O. Struve
1868.02
260.2
257.9
M ...
+ 1
+0.14
2
(). Struva
1872.91
192.5
_K
_
2
Wilson ft Kcabruko
1874.56
1M s
_,j.
0.14
_l
_
1
I<eyton Olmorven
1875.41
'• :
!... .
„-,-!-
• • II
- 9.9
1
Ley ton oliscrvera
1877.54
u It
+ 7.0
+ 0.26
2
<). Stnive
1X78.60
150.7
L47.0
+ :t:
+0.34
2
O. Struve
1883.57
r.-.i.i
• i 11
- i •_•
+0.05
5
Schia|wrt>lli
1884.53
mjt
0.33
M 11
_ 0 1
-0.08
9-13
Per. 3-1; S<-h. 6; En. 0-6
18-v
! 1
o ::,
+ :..-•
—0.08
3
S*-hia|>arelli
1886.51
I'."' 1
0 M
+ :J.H
-0.08
6
Schiaparvlli
. :.i
134,2
0.38
0 i>
+ •-• i
-0.10
13
Schiaparelli
0 LQ
0.52
+ 1.3
-0.12
16-15
S|.lii:i|>:ui-lli
l^sOJJO
HM
133.0
•• II
- 2.2
-0.13
5-4
]{(Mlgeal-0; S<'lii;i|iari'lli 4
1.1 l
121.1
+ 3.0
-0.06
1
Ki^'ounlaii
r.M :
120J
0.45
OJO
+ 1.5
-0.14
10
Seel; S<-h. 4 ; Hill 4; 1%. 1
L33.0
ll'.U
0.62
+ 2.6
-0.02
12
H. C. Wilson 1 ; Soh.7 ; Com. 3
;,, ;,,
11s |
118.7
0.58
0.64
- 0.3
-0.06
2-4
Kigounlon 2; NUttpUvQiO-3
'i :.i
ii7.il
0.57
..,.,.
+ 2.5
-0.09
6
Si-liiaparelli 2; Harnard 4
]v,:, IJ
I1.-...I
117.3
,,,,,
0.67
- 1.3
+0.02
6-3
See 3 ; Comstock .'10
The following is a short ephemeris :
1
Ar
ft
e
9
L896JO
116.6
0.69
1897 JO
116.0
0.69
•- •-
115.3
0.70
1K99.50
1900.50
1153
114.1
0^70
0.70
According to this orbit previous investigators have materially overestimated
the period. While the time of revolution munt at present remain wlightly un-
(utain. it does not seem at all probable that this element can surpass 75 years.
It follows, therefore, that y Coronae Boreali* belongs to the class of unequal
Kiuarit - with moderately short periods. The inclination and line of nodes here
iibtaiiu-d will probably be nearly correct, while the eccentricity is not likely to
be varied by so much as ±0
K- • cut diftanri-s have IK-I-II a|i]>ri-cialily uiulermeasured by several observers;
the separation of the coinpoiu-nts is now about 0*.68, and will not change
M-n-ihly for several years. yCoronaf Boreali* net-els further observation, and
astronomers should continue to give it regular attt-ntion; but owing to the
peculiar shape of the apparent orbit great care must be exercised to avoid
systematic errors, if the measures are to be of much value in effecting a fur-
ther improvement of the elements.
176
£SCOKPI1 = ,11998.
fSCORPII = 21998.
a = 15h 5S'".0
5, yellow
8 = —11° 5'.
5.2, yellow.
Discovered by Sir William Herschel, September 9, 1781.
OBSERVATIONS.
t
60
Po
n
Observers
t
60
Po
n
Observers
O
V
O
n
1782.36
188.0
—
1
Herschel
1846.17
23.2
1.00
3-1
Jacob
1825.47
355.3
1.15
3
Struve
1846.47
24.1
0.97
9-8
Mitchell
1828.48
1.0
1
Herschel
1847.58
26.0
1.71
1
Mitchell
1830.25
1.4
1.46
4-3
Herschel
1848.54
30.6
1.19
3
Dawes
1848.54
27.2
0.84
1
Mitchell
1831.38
9.4
1.32
2-1
Herschel
1831.48
3.5
1.21
1
Struve
1853.53
46.3
—
1
Dawes
1832.52
4.8
1.24
1
Struve
1855.36
48.2
—
4
Dembowski
1855.53
53.1
0.46
3
Secchi
1833.37
5.0
1.19
1
Struve
1833.39
6.2
1.15
1
Dawes
1856.20
65.5
0.63
3
Jacob
1856.41
58.1
—
4
Dembowski
1834.45
8.3
1.24
2-1
Herschel
1856.49
70.3
0.36
10-8
Secchi
1834.45
6.7
1.24
1
Struve
1856.58
69.8
0.47
1
0. Struve
1834.50
7.1
1.17
4
Dawes
1856.55
59.6
—
2
Winnecke
1834.51
14.6
3
Madler
1857.68
81.4
0.50
1
Jacob
1835.39
10.6
1.58
5-1
Herschel
1858.13
79.4
0.40
1
Jacob
1835.48
11.0
—
4
Madler
1858.22
116.8
0.30
1
Jacob
1836.49
1830.50
9.5
11.0
1.02
1
3
Dawes
Madler
1862.56
137.9
—
3
Dembowski
1837.33
11.4
_
1
Herschel
1863.44
142.1
—
9
Dembowski
1839.61
16.7
1.28
2
Dawes
1864.45
1864.51
147.8
150.9
0.21
4
10
Secchi
Dembowski
1840.56
1840.57
18.6
17.2
1.19
0.96
3
1
Dawes
O. Struve
1865.44
1865.51
151.4
155.5
0.35
10
7
Dembowski
Secchi
1841.48
16.7
1.28
4-3
Madler
1865.55
166.9
0.49
7
Englemann
1841.57
20.8
0.84
1
O. Struve
1866.46
156.6
0.53
8-3
Dembowski
1841.58
19.0
1.20
3-2
Dawes
1866.52
161.0
0.40
2-1
Secchi
1841.61
17.7
1.30
2-1
Kaiser
1867.45
160.7
0.83
7-4
. Dembowski
1842.42
1842.46
1842.53
20.4
21.6
21.0
1.05
4-2
2
1
Madler
Dawes
Kaiser
1868.40
1868.48
165.0
166.5
0.90
0.99
7-4
1
Dembowski
Knott
1869.51
172.5
0.83
6
Dune'r
1843.40
23.5
1.09
2
Dawes
1869.52
168.2
0.88
5
Dembowski
1843.40
23.8
1.16
6-4
Madler
1843.62
20.8
1.20
11-1
Kaiser
1870.21
168.2
—
1
Gledhill
1870.39
169.8
0.89
7-5
Dembowski
1844.40
23.7
1.82
3
Madler
1870.54
173.3
0.88
2
Dune'r
laoonrii = 21998.
17'
(
9.
?•
•
OllCf 1 VMI
(
•j
P.
ii
i MMM*rvrn
A
»
e
t
1871.41
173.1
1.06
7-6
Demtxtwxki
M
1.19
1
IM...IV
1X71.49
174.0
1.00
1
lull
181
1.44
1
KlI^lrllMIlll
1871.GO
174.8
5
1 •UII.'T
i---j in
192.7
1.12
3
Hull
1872.45
177.3
Ml
1
\\ A a
1-S2.54
191.8
1.31
5
Srlii;i|.:it.-lll
1872.46
176.9
.12
1
Knot i
1K82..VJ
192.1
1.35
3
Priaby
1872.46
173.8
.12
ivmbowski
1883.45
191.0
1.33
4
Fmby
1872.50
175.8
10
•2
I'Vrrari
1883.51
193.9
1.38
••
Hall
I-7-J.S3
177.4
"•
:\
lhin<<r
1— .: r.i
195.3
—
1
KflHtwr
1873.36
180.4
MI
1
\\ .\ s
]--:!•'
195.5
1.20
.'{
Bogtenmui
1873.36
in -
If
5-3
Dembownki
1883.52
191.5
1.16
3
IVrrntiii
1873.G8
:.• •
10
1
ofadun
1883.55
19TJ.5
1.24
12
Sfhiiiparclli
1874 II
I'.t
1
\V AS.
1884.38
19T..8
1.34
4-3
H.C. Wilson
1874
17- 7
M
6
Dembowski
1--I II
195.6
1.46
3
KlI^ll'IIMIIII
is;:, it
180.5
M
s
Deinbowski
1--I :."
194.6
1.28
5
Hall
.-.i
I-J"
i-
5
S4-ln:i|i:irrlli
1884.53
195.1
1.27
3
IVrriitin
is;:. :,i
180.0
1
W. &8.
18H4.54
195.G
1.41
1
II. 8. Pr.
;,. , .,.
180.9
Qjl
4
l>m,.T
1884.54
195.0
1.26
'.»
S. lii:i|.:nrlll
1871 ii
1-:,.;
1.04
1
Howe
1885.53
196.2
1.34
8
Ki-liiaparclli
1-7.U6
l-i -
1.21
0
Dembowski
1885.57
19S.1
1.38
5
Kiigleinaiin
52
183.9
l.H
3
Hall
183.6
1.1S
4
Schiaparelli
1886.35
197.4
1.19
1
H.C. Wilson
1.S7C..M
182.5
1.00 ±
1
riuiiiniiT
1886.46
197.5
1.24
2
IVrrotin
1876.61
I8M
,
3
Doberck
1886.49
198.6
1.54
2-1
Smith
1877.43
179.5
Mi
2-1
Doberck
1886.51
198.1
1.29
3
Tarrant
1877.43
183.3
1.20
5
Dembowski
i--r. :.«;
198.0
1.07
3
Hall
1877.43
1877.46
184.1
184.9
1.61
1.27
1
1
Upton
W. & 8.
1886.63
1886.55
198.9
197.2
1.07
1.19
7
8
KiiKltMiiann
Srliiaparclli
1-77.47
1.12
4-1
Howe
1887.54
;•.,,.
1.16
9
Sc-hiaparclli
1-77.56
184.0
1.25
9
Schiaparelli
1H88.50
200.4
1.24
2
Lv.
1-77.55
i s-j :,
1.27
.'{
Jedrzejewicz
1SX8.56
200.6
0.96
2
Hall
1878.46
IMJ
i n
5-4
Dembowski
I88f
•_•< •!.'.•
1.14
7
Schiaparelli
is.; i
i.3i
a
Schiaparelli
187J
1.20
2
Hwlgcs
1879.41
18BJ
i .•_••_•
:,
Howe
181 7
in
Stone
181
MM
—
•J
Glasenapp
17
187.6
1.45
1
Egbert
1891. «i;
200.6
l.L'7
2
Collins
-54
u u
1.07
3
Hall
1891.48
MM 7
2.87
1
B*
1S79.56
181 -
1.29
7
Schiaparelli
188SJI
l.'.'.'t
3
M •
1-7-.U58
18BJ
1.47
2
C. W. Pr.
•-'.58
0.82
4
Comstock
1879.60
1.16
3
Kiirnhaiii
1879.67
194.5
0.70
3-1
Sea. & Smith
18'.i
211.1
1.01
2
Huniham
1X80.36
1.12
2
Egbert
IS'.i
MMJ
210.9
1.10
0.89
1
2
8chia|>arelli
Lr.
1880.40
1880.52
L8B.1
is.-, :
1.17
1.13
4-2
1
Doberck
Frisby
1803.60
209.7
1.07
5
Higounlan
L880..M
u ,,,
LSI
6
Sahiajiarelli
1894.59
1.0±
2-1
Glasenapp
1880.87
IBM
1.10
3
H. 8. Pr.
is'j&M
210.3
1.04
3
-•
1881.24
191.3
1.03
1
Doberck
1895.41
213.9
0.91
2
Schia]>arpl]i
1881.40
190.8
1.21
2-1
Iligourdan
1895.53
213.4
0.81
3
OOlMtork
178
SCORPII = .£1998.
This bright star has been observed with considerable regularity since the
time of STRUVE, and much material is now available for the investigation of
its orbit. But while the measures are numerous, the considerable southern
declination of the object renders them rather difficult, especially for European
observers, and hence there is reason to suppose that the results are not free from
systematic errors. In the investigation of the orbit we have adopted the usual
method, depending on both angles and distances, and, as in case of £ Cancri,
have neglected the influence of the third star. This procedure has been
adopted by DR. SCHORR in his Dissertation on the motion of this system, and
is fully justified by the rough and somewhat unsatisfactory state of the meas-
ures, which will not yet permit any very fine determination of the elements.
Several computers have previously worked on the motion of this system; the
following list of orbits is believed to be fairly complete:
p
T
e
a
a
i
A
Authority
Source
10o™522
49.048
95.90
105.195
1832.611
1860.59
1859.62
1862.32
0.0768
0.122
1.287
1.749
1.26
1.3093
4.75
112.7
12.25
10.45
70.22
70.02
68.7
67.64
o
78.57
89.27
102.63
Madler, 1846
Thiele, 1859
Doberck, 1877
Schorr 1889
A.N., 1199
A.N., 2121
Dissertation, Munich
We find the following elements:
P = 104.0 years
T = 1864.60
e = 0.131
a = 1".3612
Apparent orbit:
Q, = 9°.5
i = 70°.3
X = 111°.6
n = + 3°.4616
= 2".696
= 0".884
= 9°.6
= 150°.2
Length of major axis
Length of minor axis
Angle of major axis
Angle of periastron
Distance of star from centre = 0".085
The table of computed and observed places shows a very satisfactory
agreement, and we may conclude that no very considerable alteration is likely
to be made in these elements. But the orbit is so nearly circular and so highly
inclined that the definition of X is not very exact, and in case of this element
a larger alteration may be found necessary, when the material shall be suffi-
cient for a definitive determination.
The small eccentricity of this orbit is rather remarkable. Among known
binaries there are very few which have such circular orbits, 8 Equulei, 2 2173
and fillerculif! being the principal objects of this kind, and as most of these
orbits are highly inclined, there is still some uncertainty attaching to the eccen-
tricity. It will be necessary to have more exact observations of these stars in
•ie»4
.HO
BOORIMI = .1 1998.
critical parts of thrir urliit- l.«-|i.n-
precision.
COMPAKUOV Or < i> WITH OlMKRVKD
» I, in. in < an lw de-fined with tin- «l.-ir««l
t
•.
*.
f.
*
„ ,.
„ .
•
Ml,,.,,.,,
i7s-j:;«;
*
9
9
J
1
II. :
IV.-:, ;
-1.9
-0.13
8
St ruve
ls.-to.-j:. 11 -J 7
1.46
i g
4-0.07
Hcndwl
1831. i^ .;:.
4.0
1 .1'l
I"
-0.5
-0.19
l
Strove
1832.52
4.8
1 Jl
11
-0.4
n 17
1
Struve
1833.38
•
.. 1
1 17
U
2
Struve 1 ; Da wen 1
1834.47
7.4
7.3
I JJ
.42
+ 0.1
HiTHrhcl 2-1 ; 2. 1 ; Dawea 4
in.,
1.58
.43
+ 2.3
+0.16
.1 1
. hel
in.;
9.7
1 i'J
.10
4-1
DMri l.M. -T :t o
16.7
+3.7
0.07
2
Dawec
17 ;i
ll.n
1.08
..T!
4
Duwr«3; O2.1
1MI
i:, 7
1 M
.!".»
nil
10-7
Madler4-3; O2\ 1 ; Daw«i3 2; KaiMcr 2-1
1MJ IJ -jo.|
!'• 1
1 ,H.-,
+ 4..'<
4-2
Midler 4-2
IM:: 17 JJ.7
18.0
11.-.
.1'!'
+ 4.7
-0.07
in :
Dmrti J. M.I.I:. -t fl l. K , • • u i
IM
M.7
1 in
.11
+ 3.0
• H.J.;
1.1 U
Mfcller 3; Jacob 3-1 ; Mitchell 9-8
1847
•Jl 7
1 71
.OJ
+ 1.3
l
M it. hell
1848
1 nl
I.'.M,
+ 2.3
+ 0.05
4
Dawes3; Mitchell 1
.,.,
53.5
on;
0..14
,, M>
7-3
Dembowski 4-0; Secchi 3
•-•., ;
..1 7
• '.I .
I..10
+ 3.5
-0.01
JO I'J
Jacob 3 ; Dem. 4-0 ; Sec. 10-8 ; O2. 1 ; Winn. 2-0
•W
§1.4
0.43
+*.»;
t -n.07
1
Jacob
iv.s !.: 7 n I
0.41'
+ 0.'.»
IMI-J
1
Jacob
1864 I-
111 s
>..u
+ 4.5
111
Seochi 4; Dembowski 10-0
• 50
158.4
l.M 1
.. !•_•
o 1
0.18
17-14
Deinbowski 10-0; Secchi 7; Kn^li'manii 7
ii I..
u*;
-0.5
— 0.2O
10-4
Demliowski X 3; Secchi 2-1
160.7
163.4
O.X3
-2.7
+0.11
7-4
Dembowski
:>..* ;;
165.7
LOl •
0.94
0.7X
-1.2
+0.16
Dembowski 71 ; Knott 1
>, , ,,
17"..
17.I.-J
0.85
O.S.-5
+0.1
+ 0.02
11
Duner6; Dembowski 5
K" !'•
i7ir.
I7J.;
0.89
0.90
-1.0
-0.01
9-7
Dembowski 7-5 ; Dun^r 2
1x7! .-,n
171.0
174.9
O.M
O.-.M;
-0.9
13-11
Dembowski 7-5 ; Oledhill 1 ; Diiner 5
17t',.J
177 1
1.05
1.05
-0.9
1.1 U
W. & 8. 1 ; Kn. 1 ; Dem. 8-5 ; Fer. 2 ; Du. 3
I77.;t
179.0
1.11
-1.1
7-5
W. & 8. 1; Dembowski 5-3; Ciledhill 1
1x71 ir.
iao.9
1.12
1.11
+0.1
+0.01
6
W & S. 1 ; Dembowski 5
1X1.1
1 x-j I
1 U
1.1:.
-1.3
(MM
1.1
lVinUiwski.1 ; S<-hiaparelli5; W. &. 8.1; DuneV 4
51
184.0
1.11
i.i'.'
-0.08
I> M
H..W.-1 : iMn.r, ; HI :t;Sh. I; I'l.l ; Dk. 3[Jed. 3
1x77 17 1
1 Jl
-1.1
+ 0.0-J
J.'f JI
Dk.2 1; IViu.1; Cptoli I; W A > 1; |l,,w<- J l;S.-h.JI;
1.1'r,
i.-ji
-0.7
+0.02
11-10
Dem. 5-4 ; Sch. 6 [ft. 3; Sea. & 8. 3-1
l>7'.i
1 -j::
1.26
+0.4
-0.03
Howe 5 ; Stone 3 ; Egbert 3 ; HI. :t ; SI,. 7 : IV. 2;
1.X.SH.M «
11.-,
1.27
-0.3
-0.12
15-14
Egbert 2: l»k 1 J. Kri.sl.y 1 ; S-h. C, ; Pr.3
1SX1..TJ '.M .Ol'.Ml..-.
1.12
+0.7
-0.16
3-2
Dolierck 1 ; ltiK',mr.i:in 2-1
•j.i r.c'.i
1.24
1 Jx
+0.4
-0.04
U
U.U-r.-kl: Hall.'t; S-l,i:»|,:ir.-lli .1 : Frinby 3
1XX3..10 •.»:; i i-.i.: | i -jr.
-0.03
j:. ji
Friabv 4 ; 111. 2 : Kn 1 o ; Kn. :t ; IVr. :t ; S-h. 12
IXX4.4'.» '.' 1.35
: I'M
+0.6
:
j.i i'i
HI \V I-.1; Kn. 3: HI..1; IVr. 3; Pr. 1 ; Sch.9
• •- •:•::•:'• »tj g
1.27
+ 1.1
U
S-hiaparelli X; KliKleinuiiti .1 [Sch. 3
1886..11 I'.iso 1-.I7.J i.-j;<
1.25
+0.6
-0.02
Jl I1"
H.r.W. 1 : IVr. -J ; S,,,. J 1 ; Tar. 3; Hall 3; Kn. 7;
1887.54 199.6J198.8 1.16
l.l'.'t
+0.8
-0.07
I
S-hiaparelli
ixxs.54
1.1 1
1.J1
+0.7
-0.10
11
Leavenworth 2; Hall 2; Schia|«relli 7
Ix.x-.i.l
197.5001.61 J"
1.18
-4.1
+0.02
2
Bodgw
1X90.39
205.2ffl03.1 —
1.1.1
+2.1
—
2
Glaaenapp
1891.47
• l.-JT
1. 11
+3.8
+0.16
1-2
(\>llinsO-2; See 1-0
1892.55
M7JQ08.8 1 "j
1 .07
+0.5
g
7
Maw 3; Ck>mstock4
1893..M
I.o2
-0.01
10
/3.2; Schiaparelli 1; I^eavenworth 2 ; Higourdan 5
I.X'.IJ .VI J. '7 .VJlO.'l
, , ,
-3.4
2-1
Glasenapp 2-1
1X95. 12 213.3 21 2.810.93
•
.,..-.
-0.02
4-6
See 1-3; Comstock 3
180
cr CORONAE BOREALIS = ^2032.
The following ephemeris will be useful to observers:
1896.50
1897.50
1898.50
216.3
219.3
222.4
PC
o"88
0.84
0.79
1899.50
1900.50
ft
225?G
229.6
Pr
0*74
0.70
The motion will be rather slow for a good many years, but as the object
becomes closer, about 1910, it will deserve the most careful attention.
CORONAE BOREALIS = 22032.
a = 10h llm
6, yellow
8 = +34°
7, bluish.
Discovered by Sir William Herschel, August 7, 1780.
OBSERVATIONS.
t
ft,
Po
n
Observers
t
ft,
Po
n
Observers
0
t
o
It
1781.79
347.5
—
1
Herschel
1836.47
138.5
5-0
Madler
1802.59
348.6?
1
Herschel
1836.59
134.7
1.43
6
Struve
1804.74
11.4
1
Herschel
1837.47
136.8
—
1
Dawes
1837.55
139.9
1.42
5
Struve
1819.62
48.0
_
Struve
*
1838.45
143.4
1.48
7
Struve
1821.30
65.2
—
-
Herschel
1839.52
147.8
1.55
Galle
1822.83
71.5
1.44
2-1
H. & So.
1839.53
144.3
1.60
1
Dawes
1823.47
72.9
—
-
Herschel
1840.57
147.8
1.66
3
Dawes
1825.44
77.5
1.48
6-3
South
1840.63
149.3
1.54
4
0. Struve
1840.68
145.2
1.53
1
Struve
1827.02
89.3
1.31
4
Struve
1841.48
150.3
1.66
3
Dawes
1828.50
92.1
—
6
Herschel
1841.56
148.8
1.57
_
Kaiser
1830.11
104.9
1.22
3
Struve
1841.56
152.3
1.60
7
Madler
1830.28
105.1
1.22
9-5
Herschel
1841.60
153.7
1.56
1
0. Struve
1831.36
108.8
1.38
3-2
Herschel
1842.31
156.4
1.81
4
Madler
1842.37
153.3
—
1
Dawes
1832.52
113.6
1.07
6-1
Herschel
1842.73
157.5
1.86
4
Madler
1832.55
115.4
3
Dawes
1843.45
156.8
1.85
6
Madler
1833.26
120.0
1.29
3-2
Herschel
1843.47
156.5
1.77
1
Dawes
1833.36
120.6
1.30
4
Dawes
1843.68
156.3
1.66
-
Kaiser
1834.55
125.6
—
3
Dawes
1844.40
160.6
2.05
4
Madler
1835.40
134.9
1.3 ±
4-1
Madler
1844.44
157.2
1.53
1
Greenwich
1835.50
130.5
1.31
5
Struve
1845.51
163.1
2.03
20-19
Madler
9 OOKOX AK BOBKALI8 = 2
181
1
9.
ft
•
, ,
1
9.
ft
*
• • .
O
*
O
9
1846.32
li-.-.' s
-
Id. i,l
•- , ,
2.52
1
Winnecke
1X46.36
162.4
2.25
—
Jacob
I I'.'
181.9
2.68
6
iViubowitki
1X46.46
165.1
2.07
11
Madl.r
i-^-j i
2.45
2
Seech i
1846.68
'• - :
1.76
J
."•,.67
2.46
4
O. Struve
1856.73
181.2
2.52
3
Jacob
1847.44
2.16
11
Midler
1847.44
166.0
1.88
2
Dawes
1X57.39
!- : :
2.46
2
M ii.11,- r
1847.69
!. • «;
1
(». Strtivi-
1857.r,l
2.43
2
Seech i
1847.70
MM
1.33
I
iit-ll
1857.66
1X3.1
2.53
3
Jacob
1857.66
ISM,,
2.52
J£
Deinbownki
1X48.41
LI - ;
-' 1
Mldl,-r
1848. U
171 11
1
Bond
1858.01
181.9
2.51
5
O. Struve
3
1858.20
184.0
2.57
3
.1.1 r,,|,
170.8
1 .'.U
1
O. Strove
1X58.50
184.7
2.69
6
DI-HI|H>\\ ski
1X58.54
183.6
2.64
7
Madler
L70J
2.09
1
I • .
184971
17.':;
3
O. Struve
1859.34
184.9
2.70
20obs
. Morton
1859.49
! U >
2.69
8-6
Matll.-r
LI 1 i
1 ' Ml
3
O. Struve
1859.94
1X6.1
2.62
4
U. Struve
2
Madler
1860.36
! s.-, ;,
2.71
2
Ihiwes
171 1
2.32
43oba. Fl.-toh.-r
IV. 1.25
171..-,
•_• :;i
6
Madler
1861.55
I.VS 1
2.95
5-3
Madler
I!'
•_• iv,
1
Dawes
18(51.58
187.4
2.69
5
O. Struve
l.v.1.63
17.-. 1
2.06
6
O. Strove
iv, 1.76
17.1L-
2.43
9
Madler
1862.71
190.5
3.01
6
Madler
1862.76
189.1
2.77
2
O. Strove
18.-.2.31
176.4
2.38
24-38ot.Mill.-r
1862.79
189.3
2.87
1
Scli.-uiiiaiiii
1852.60
177.5
2.39
12-11
Madler
1852.63
173.3
2.06
4
O. Struve
1863.09
11MI.1
2.76
14
Dwobowskj
1863.60
is.s j
2.77
4
O. Strove
1853.14
17711
2.18
2
Jacob
1864.45
190.5
3.09
2
En lemann
1853.38
177 .7
. If,
6
Midler
1864.95
191.2
2.79
12
Deinbownki
1.68
177 li
4-3
'•
1853.64
—
1
Argelander
.-,.36
in l.li
LM
<». Strove
1853.64
—
1
\V. Struve
1 si
r.n..-,
Dawes
Is/, ,,,
17.-..;
•-M7
1
<>. Strove
ini .-.
Kii-l'-inaiiii
1853.77
178.7
1
Madler
1.71
is-i ]
—
i Oli.s.
1865.74
IMJ
v. FUM
1854.05
177H
3
Jacob
1 '.'•-•::
4
Secchi
IBM M
1 7 S .I
;{
'• '
1854.66
I79u0
2.24
-j
o. Strove
IM
190.5
1
Kn-l.-iiiann
178.6
20 ol*. Morton
2
Leyton »>lw.
1854.67
179.8
2.36
1
Dembowski
L8M i-'
I8M
—
2
Wagner
1864.70
179.4
-.M
5
Mfedh-r
•-. , ; ,
—
2
Mi
1866.49
1 •..•.•;:
—
2
Sniy»loff
1865.19
179J
3
Dembowski
I860 ; •
1 •.'.:•_•
_
2
Kortazzi
1856.48
180.1
1
Dawes
•-,. ..
3
Winlock
1855.54
181.6
2.49
,. -,
Winnecke
LM6J9
If . |
3-2
-•
1855.61
4
Seech i
1866.63
193.0
M,
I
O. Strove
1855.61
179.1
4
,, ...
193.9
_
Kaiser
1855.78
181.8
2.64
J !
Midler
1866.92
:•• LI
2.88
11
l>, ....
<T CORONAE BOREALIS = ,£2032.
1
60
Po
n
Observers
t
ft
Po
n
Observers
O
V
O
ff
1867.30
190.2
3.15
1
Searle
1877.46
202.2
3.68
_
W. & S.
1867.31
195.0
2.95
1
Winlock
1877.49
200.1
3.49
7
Schiaparelli
1867.34
194.7
3.0
-
Knott
1877.53
201.6
3.61
5
Jedrzejewicz
1867.37
192.1
3.0
1
Main
1877.58
200.1
3.50
3
O. Stvuve
1867.72
195.5
2.79
1
Duner
1878.39
202.3
3.51
2-1
Knrnham
1868.29
193.8
3.62
1
Leyton Obs.
1878.50
202.0
3.51
5
Dembowski
1868.58
194.7
2.98
2
0. Struve
1878.51
201.1
3.39
3-2
Doberck
1868.60
194.7
3.14
4
Duner
1878.53
201.2
3.53
6 .
Sehiaparelli
1868.61
195.5
—
2
Zollner
1878.57
199.1
3.52
3
0. Struve
1868.88
195.3
2.99
9
Dembowski
1879.45
202.5
3.66
4
Hall
1869.57
195.2
3.60
1
Leyton Obs.
1879.54
202.1
3.68
6
Sehiaparelli
1869.63
195.1
3.05
5
Dune'r
1880.39
203.0
3.61
1
Burnham
1870.56
196.6
3.18
1
Dune'r
1880.55
203.4
3.71
9
Sehiaparelli
1870.97
196.8
3.10
12
Dembowski
1881.05
200.6
3.94
5
Hough
1871.41
197.9
3.23
2-3
C. S. Peirce
1881.46
203.0
3.64
3
Hall
1871.42
196.7
3.30
-
Leyton Obs.
1881.70
204.3
356
6
Seabroke
1871.54
195.4
3.23
-
Knott
1882.43
202.6
3.75
4
Hall
1871.61
196.5
3.14
3
Dune'r
1882.51
203.8
3.79
6
Sehiaparelli
1872.29
198.0
3.34
_
Leyton Obs.
1882.52
204.1
3.90
3
0. Struve
1872.57
195.3
3.26
3
0. Struve
1882.65
204.9
—
1
Seabroke
1872.96
198.1
3.20
12
Dembowski
1882.71
205.7
3.92
4
Jedrzejewicz
1873.42
198.4
3.14
W. &S.
1883.26
205.4
3.77
6
Englemann
1873.55
200.6
3.64
1
Leyton Obs.
1883.47
204.5
3.77
3
Hall
1873.56
197.6
3.14
2
0. Struve
1883.49
203.2
3.79
4
Perrotin
1873.68
198.9
3.4
_
Gledliill
1883.56
204.6
3.74
12
Sehiaparelli
1873.54
197.3
1
Muller
1883.63
206.0
3.99
2
Jedrzejewicz
1873.54
201.6
—
1
H. Bruns
1884.48
206.0
3.80
3
Hall
1873.57
199.6
—
1
H. Struve
1884.53
205.8
3.86
3
Perrotin
1874.44
200.5
3.55
1
Main
1884.53
202.4
3.63
2
0. Struve
1874.46
199.2
2.67
2
Leyton Obs.
1884.54
205.4
3.76
11
Sehiaparelli
1874.61
199.8
3.41
4
0. Struve
1885.43
205.4
3.88
4
deBall
1874.90
199.1
3.28
11
Dembowski
1885.43
205.7
3.89
3
Hall
1875.42
199.8
2.56
1
Leyton Obs.
1885.54
204.9
3.94
2
Perrotin
1875.46
1875.50
198.6
200.6
3.34
3.47
4
J
Sehiaparelli
W. &S.
1885.55
1885.66
205.8
206.8
3.86
3.93
9
3
Sehiaparelli
Jedrzejewicz
1875.54
199.6
3.28
5
Duue"r
1885.74
207.3
4.09
6
Englemann
1875.65
200.6
3.74
-
Nobile
1886.47
205.6
3.99
5
Perrotin
1876.29
199.3
Doberck
1886.48
206.9
3.96
6
Hall
1876.45
200.0
3.50
3
Hall
1886.49
208.0
4.01
4
Tarrant
1876.48
200.6
3.28
—
Gledhill
1887.44
205.5
3.99
4
Hall
1876.61
196.3
3.34
3
0. Struve
1887.53
207.1
3.78
7
Sehiaparelli
1876.61
200.7
3.45
1
Leyton Obs.
1888.44
206.6
3.92
4
Hall
1877.03
201.0
3.40
11
Dembowski
1888.57
207.4
3.92
8-7
Sehiaparelli
1877.33
199.6
3.58
-
Doberck
1888.62
207.8
3.82
3
Maw
<T Coronao Boroalis=^ 2032.
<r COKOXAK IK n:i M.IS = 2
1
0.
P.
•
,, ....
I
6.
ft
ti
Obtenrm
o
t
%
f
1889.14
207.7
i M
1
0. Rtruve
1 v.i.-JOMJ
209.3
4.28
4
Ki^uurtlan
1889.52
•_••>
4.05
-
M-n;i|.|,
I s-.i3.64
209.8
4.24
2
Maw
!- < :
M
1
Scliia|Ntn-lli
MM
4.09
2
Glaacnapp
1890.33
•_• . -
4.08
3
Iturnhain
1890.69
1891.49
207.3
4.00
1
1
iii r. l.i n
S-hiaparelli
1895.54
1895.59
210.8
210.7
210.3
4.28
II..
4.23
3
10
2
Comstock
St-liiajiarulli
( 'iillins
1892.61
4.06
Corostock
1895.59
209.9
4.25
4
ScbwaruK-hlld
1892.64
i • •:.
i'
Sohiaparelli
1895.72
4.1V,
3
>••-
-•' • •
I .1
1
Hi^uurdan
*»iii. •. Ill ix in i.'* discovery of tliis star tin- companion has described an
art-* of ±_'.'» . The -li:i|n- of this arc is such that it fixus the apparent ellipse
\\itli c. .n-iil. ralil, • |.i..i-iMii. and i-nahleH u- to obtain a set of elonu'iits which
iirvrr IK- railicallv chan^cil. It is singular, however, that the periods herc-
dlitaiiuil for thi> -tar an- \irv tlix-urdant, and in several instances more
than dmiliK- that f.uind Iwlnw. Such r\tra<>rdinary divergence of resultM may
bo explained hy tin- lack «>f siillicii-nt curvature in the arc swept over by the
companion at the time the earlier clement* were derived, and by the use of in-
judicion- method* in the determination of the orbit.
In this a* in most other cases the graphical method based on lx>th angles
and di-tances i* *nperior to analytical methods, and at once enables n- to trace
the apparent ellipse with the necessary precision. The following bible given a
complete summary of the element* found by previous computers who have
\\orkcd on the motion of this interesting binary.
p
T
•
a
a
i
a
Authority
Source
28&60
I> ;;.,•,,
n.r.iii'
::',;>
I .V"
1! _•:.
7.3
Herac-hel, 1888
M,-i I: V.S..V. ji 2().*i
• - ;.'.
60
..•'.
I'.Vll'
MAdler
Dorp. Olw., IX, p. 182
I7S.04
44
0.6406
3.90
OJ
884NI
•...:.
Madlcr, 1847
Fixt-Sj-Ht., I, p. 240
88
1826.48
0.7S
:, I-..J
•.•i ii.-,
•;;i. 1
Hind, IM;.
A.X., 551
11'
17
"88
8.78
1.95
mi. -.».-,
Jacob, 1 s...-.
MS., XV, p. 180
240.0
t.7
0.3887
j-i
:{.i:{
».V1
Powell, 1 BM
M.N., XV, p. 91
HO
0.5899
4M.S7
Kllnkerfuca^M
A.N., 990
1828.91
5.001
Doben-k, !>::.
A.N., 1'n:::
sj:, M;
1826.93
0.7515
! - .:.
31.37
71.6
I>oberck, 187(i
A.N., 2103
Making all the observations up to ISJtf we find the following ele-
ments
P - 370.0 years Q
T - 1821.80 i
0 - 0.540 X
a - 3*.8187 »
= 30°.5
- 4r.48
- 47*.7
- -J-90.:
s
184
cr CORONAE BOKEALIS = ,T2032.
Apparent orbit:
Length of major axis
Length of minor axis
Angle of major axis
Angle of periastron
Distance of star from centre
7".OS
4".71
42°.4
66°.9
1".735
There is of course some uncertainty attaching to a period of such great
length, but careful consideration of all possible variations of the apparent ellipse
convinces me that the value given above is not likely to be varied by more
than 25 years, and a change of twice this amount is apparently impossible.
The eccentricity is very well determined, and a change of ±0.04 in the above
value is not to be expected.
The distance of the components of <r Coronae Borealis is now so great
that the companion will move very slowly for the next two centuries. There-
fore, so far as the orbit is concerned observations of . the pair will be of small
value, as very little improvement can be effected for a great many years; but
it may still be worth while to secure careful measures of the system, with a
view of establishing the regularity of the elliptical motion, and the absence of
sensible disturbing influences. There are no irregularities in the measures here-
tofore secured which arc not attributable to errors of observation. The table
of computed and observed places shows an agreement which is extremely satis-
factory.
COMPARISON OF COMPUTED WITH OBSERVED PLACES.
t
60
».
Pa
Pf
<>„-(><
Po—Pc
n
Observers
1781.79
347.5
348.5
1
2.44
O
- 1.0
g
1
Herschel
1804.74
11.4
23.9
2.08
-12.5
—
1
Herschel
1819.62
48.0
59.1
1.57
-11.1
—
_
Struve
1821.30
65.2
65.2
1.50
0.0
—
_
Herschel
1822.83
71.5
71.0
1.44
1.45
+ 0.5
-0.01
2-1
Herschel and South
1823.47
72.9
73.3
1.43
- 0.4
—
_
Herschel
1825.44
77.5
81.6
1.48
1.36
- 4.1
+ 0.12
6-3
South
1827.02
89.3
88.6
1.31
1.33
+ 0.7
-0.02
4
Struve
1828.50
92.1
95.3
—
1.31
- 3.2
—
6
Herschel
1830.20
105.0
103.8
1.22
1.30
+ 1.2
-0.08
12-8
Struve 3 ; Herschel 9-5
1831.36
108.8
109.1
1.38
1.30
- 0.3
+ 0.08
3-2
Herschel
|s:;i'.:,|
114.5
111.7
1.07
1.30
+ 2.8
-0.23
9-1
Herschel 6-1 ; Dawes 3-0
1833.31
120.3
118.7
1.30
1.31
+ 1.6
-0.01
7-6
Herschel 3-2 ; Dawes 4
1S.-U.55
125.6
124.3
—
1.34
+ 1.3
—
3
Dawes
1835.50
130.5
128.5
1.31
1.36
+ 2.0
-0.05
5
Struve
1836.59
134.7
133.5
1.43
1.40
+ 1.2
+ 0.03
6
Struve
1837.51
138.3
137.0
1.42
1.43
+ 1.3
-0.01
6-5
Dawes 1-0 ; Struve 5
1838.45
143.4
140.7
1.48
1.47
+ 2.7
+0.01
7
Struve
1839.52
146.0
144.5
1.57
1.51
-1- 1.5
+0.06
2 +
Galle — ; Dawes 1
1840.63
147.4
148.3
1.58
1.56
- 0.9
+ 0.02
8
Dawes 3 ; O£. 4 ; Struve 1
1841.55
151.3
151.5
1.60
1.61
- 0.2
-0.01
12 +
Dawes 3 ; Kaiser — ; Madler 7 ; O2'. 1
1842.47
155.7
154.1
1.83
1.66
+ 1.6
+0.17
9-8
Madler 4 ; Dawes 1-0 ; Midler 4
,7 . ..i:..\ u: it..i;i; vi. is = .1.
188
1
«.
«r
P*
p.
•.-•.
• •
•
ObNrm.
isl . ,
: ., -,
! . _'
- 0.7
I
84
Dawe« 1 ; Midler 6 ; Kaiser —
1844.46
I.-.";:
: .. • '.'
1.87
I 7s
4 0.4
40.09
64
Midl.-r 4 ; (irevnwich 1 ; Madler -
sir. i:.
64.6
64.7 -"-
1.90J- 0.1
40.12
164
Hind—; Jacob—; Midler 11; OX. 2
1847.57
i ', ^ *_•
167.3
1.96- 0.1
40.06
18-16
Madler 14 ; Dawes 2; OX. 1 ; Mitchell 1
|si-
, i i
69." •-'!-
."I 4 0.9
4(1.11
. ',
Midler 2-1 ; Homl 1 ; Dawea 3 ; OX. 1
1849.60
71.2
J ' ' -
•t- o.<
—0.02
Dawea 1 ; OX. 3
1X50.61
71.0
2.11
'-Ml - 2.0
-0.03
i
i; Mn.ll.-r 2
1X51.46
1852.51
74.5
7.-, 7
177 >>
1 74.5 I.' I'*
177 7
.!•• 0.0
2.261- 0.5
2.31 - 0.1
40.09
40.02
244
1X4
Is 17
• ...
Fit. 43 oba. ; Ma. 6 ; Da. 1 ; OX. 6 ; Ma. 9
Mill.-r 24-38 olm. ; Madler 11 ; OX. 4
bl'; Ma.6; Dawea4-3; OX. 4; Mi. 2
~ t > *
1 . '. i .'
— O..1
JOT
Ja.3; Da.3; OX.'2; Mo. 20 olm. ; Mil. 5; Dem. 5
2.42
. I::
- 0.2
-0.01
." Is
Dem.3; Da.1; Winn.6^5; 8«!.4; O2.4; Ma.2-1
•J l-.i
- 0.4
40.03
16
Un. u.l; Dem. 6; Sec. 2; OX. 4 ; Ja.3
2.49
- 0.8
9
M.'tdlerl'; Secohil'; Jacob 3; DeuiUiwBki 2
l s i •_'
- 0.7
0.00
21
OX. 5 ; Jiu-ol>3; m-nilxiwMki •', ; Madler 7
iv. ' :•..:
- 0.3
-0.01
14-124
Mo. 1'Oolw. ; Madler 8-6; OX. 4
186.6 L-.71
L'.71
- 1.1
0.00
2
Dawgg
'-'.77
0.0
40.05
10-8
.Madler 5-3; OX. 5
•-' s 1
4 0.8
40.05
8
Midler 6; OX. 2
_' . .
2.89
- 0.6
-0.12
18
Deinhowski 14 : OX. 4
190.X
- 0.1
-0.01
14
Kn^li'iiianu 2 ; DemliowMki 12
: -• • . _
I'." Is
8.01
- 0.1
-0.03
13
OX.3; Da. 1; En.4; Ley.l ; Sw-.4; Dem. 4
1 •.••_•..;
in i
3.10
3.05
- 0.1
40.05
26-25
Ku.l ; l*y. 2 ; Wk.3 ; Sr.3-2 ; OX. 6 ; Ka. -
• S. , , i .
' • '. . :
1 93. 1
IM
3.09
4- 0.1
-0.11
64
Sr. 1 ; Wk. 1 ; Kn. — ; Ma. 1 ; l)un«tr 1
SI , S ~,\\
:>\ >:
548
3. 1 1
4 0.3
16
Ley. 1 ; OX. 2 ; Ihuier 4 ; I VniU.w ski 9
195.1
. : , IB
+ 0.1
-0.14
6-5
Ley. 1-0 ; Dun«?r 5
196 ;
."11
3.26
4 0.6
-0.12
13
Dimrr 1 ; Demliowaki 12
1871.49
'.H',.r,
I'.Ml.S
• v.um
3.30
- 0.2
-0.08
74
1'ierce 2-3 ; Ley. — ; Knott — ; Duner 3
'.•7.1
197.4
3.27
3.34
- 0.3
-0.07
164
Ley. — ; OX. 3 : I Vml>ownki 12
1873.55
9X.3
19X.O
3.38
4 0.3
-0.05
54
Ley. 1 ; OX. 2 ; Gledhill -
1X74.60
99.4
19X.H .:_•:.
3.44
4 0.5
—0.21
17-18
Main 0-1 ; Ley. 2 ; OX. 4 ; Dembuwidci 1 1
1X75.51
200.0
: ••. ;
3.36
3.47
4 0.6
-0.11
rj in •
Ley. 1-0 j 8eh. 4 ; W. & 8. - ; Du. 5 ; Mobile -
1876.47
200.2
200.1
3.39
3.52
4 0.1
-0.13
94
Dk. — ; Hall 3 ; Gl. - ; OX. 3 ; Ley. 1
1877.40
' *i II 1 X
20O.6
3.54
3.55
4 0.2
-0.01
284
Dem.ll; Dob.-; W.&8.-; St-h.7; J«1.5; OX.3
201.1
L'"I.."
3.47
- 0.2
-0.13
19-17
ft. 2-1 ; Dem 5 ; Dk. 3-2 ; Sch. 6 ; OX. 3
1'.'
901.9
8.64
4 0.4
40.03
10
Hall 4 , Schiaparelli 6
+ 0.6
un.;
10
ft. 1 ; Schiaparelli 9
: >s i )..
a 71
- 0.5
0.01
14
Hough "• ; Hall 3 ; Seahroke 6
.'"'.'• ,
:!.77
+ 0.5
4o.o7
is 17
Hall 4; S.-1..6; OX.3; S.-a. 1 0 .I.-.I. 4
Isv: is
4 0.4
40.03
L'7
Kn. 6 ; Hall 3 ; Ter. 4 ; Sch. 12 ; J.-.I. 2
__•, . ; •,
-i'l s
4 0.1
19
Hall:!; IVrrotin.". ; ( >X .2 ; Schiaparelli I 1
: ss.-, ,r,
_' ' i , M
806.4
4 0.6
4o.o4
n
,1,- I5all4: H1.3; Per. 2 ; Sch II ; .l.-.l. ." ; Kn. 6
1 "•_•
4 0.9
40.10
u
iVm-tin :. ; Hall 6; Tarrant 4
I s>7 |s
- 0.2
-0.08
11
Hall 4 ; S-hiapan-lli 7
4."0
4 0.4
" I'..
i.-. M
4 ; SH.iaparclli 8 7 ; Maw 3
|ss.,...,
-'"7 1 4.O2
1.".".
4 0.9
-0.01
5
OX. '-'; CkiM-iiapp 2; Schiaparelli 1
L8M n
208.CM 4.04
4.07
- 0.5
-0.03
4
ft. 3; Mfondaa 1
1891.49
208.5 —
4.11
0.0
—
1
Scliiapar.-lli
1892.63
208.9 4.11
4.14
4 0.6
-0.03
1
Cuinstock 3; Schiaparelli 2 ; liigourdan 1
! s-i:: ,..,
4.26
4.17
4 0.2
40.09
6
ISigourdan 4 ; Maw 2
1894.56
209.8 4.09
4.19
0.0
-0.10
2
Ulaseuapp
210.2J210.3I 4.23
i .' .
- 0.1
18
' . Iii8tock3; S, hiapar.' li !". Oo llM2| Bwl
18(5
HERCULIS = .T2084.
a = 16h 37ro.6
3, yellow
8 = +31° 47'.
0, bluish.
Discovered bij Sir William Herschel, July 18, 1782.
OBSERVATIONS.
t
Oo
Po
n
Observers
t
Oo
Po
n
Observers
0
1
o
If
1783
.55
69.3
—
-
Herschel
1847
45
104.4
1.23
18-17
Madler
1826
.63
23.4
0.91
5
Struve
1847
53
108.0
1.63
1
Dawes
1847
68
111.3
1.42
2
0. Struve
1828
.77
simplex
1
Struve
1848
.40
98.8
1.08
3
Madler
1829
.67
simplex
—
2
Struve
1848
.61
102.4
1.51
3
Dawes
1831
.65
simplex
—
1
Struve
1848
.76
104.2
1.53
<>
0. Struve
1832
.75
220.5
0.81
1
Struve
1849
.48
99.2
1.71
1
Dawes
1834
.45
203.5
0.91
2
Struve
1850
00
96.9
1.50
3
O. Struve
1850.54
91.7
1.4 ±
2
Fletcher
1835
45
196.9
1.09
5
Struve
1850
^
tJtJ
91.3
1.27
3-1
Madler
1836
.57
188.0
—
3
MiUller
1851.23
84.9
1.29
3
Mitdler
1836
.60
186.2
1.09
5
Struve
1851.51
89.3
1.3 ±
6
Fletcher
1838
.70
168.5
1.35
3±
Galle
1851.62
88.4
1.47
5
0. Struve
1851.65
89.1
—
2
Miller
1839.67
159.7
1.15
1
W. Struve
1839
76
161.9
1.22
4
Dawes
1852.63
84.2
1.52
5
0. Struve
1852.63
82.8
1.21
8-7
Madler
1840.58
161.7
1.49
1
W. Struve
1852.64
84.0
1.24
5-2
Fletcher
1840.66
157.1
1.25
5
0. Struve
1852.77
84.1
—
2
Miller
1840
66
161.9
1.22
4
Dawes
1853.15
81.2
1.58
2
Jacob
1841.44
149.3
1.12
9-8
Madler
1853
33
78.6
1.40
6-3
Miller
1841.60
147.0
1.23
3
O. Struve
1853.
39
77.3
1.23
8
Madler
1841.65
143.0
1.24
4-3
Dawes
1853
59
80.0
1.48
4
0. Struve
1842.40
141.6
0.92
3
Madler
1853
83
74.7
1.19
3
Madler
1842.58
138.5
1.07
3-1
Dawes
1854.
06
78.0
1.52
3
Jacob
1842.64
146.0
1.21
3
O. Struve
1854.
66
76.8
1.56
3
0. Struve
1843.60
130.5
0.90
8-7
Madler
1854
67
72.3
1.33
5
Miidler
1843.64
129.9
1.30
3-2
Dawes
1855.05
69.6
1±
13
Dembowski
1843.71
130.0
0.94
9-8
Maaier
1855.41
68.0
1.56
4-2
Winnecke
1844
29
124.0
1.05
5-4
Madler
1855.
53
69.7
1.41
3
Secchi
1844.71
125.4
1.12
2
O. Struve
1855.
62
70.8
1.55
4
0. Struve
1855.
66
73.3
1.45
4
Morton
1845
43
119.4
1.01
11
Madler
1845.64
121.3
1.24
3
0. Struve
1856.
25
66.2
1.60
3
Jacob
1856.
43
62.6
1.43
6-3
Winnecke
1846
54
111.5
1.18
16
Madler
1856.
62
64.1
1.2
15
Dembowski
1846.69
110.5
1.31
2
O. Struve
1856.
62
64.1
1.41
6
Secchi
1846
89
112.2
—
5
Dawes
1856.62
64.7
1.49
3
0. Struve
t IIEBCULIM — .i.osi.
lot
1
..
fc
M
....
t
6.
f.
w
Ob«*T«,
o
*
^
9
1857.38
60.0
1.07
4
Midler
IN 70.49
19Q ;
1.10
11
Dembowski
1857.46
• • !
1
v
188.6
1.21
t
1 >uiter
IN.'.. .
1.29
I
Seochi
IN? I |'_'
181.1
.27
14
IVmbowski
IN'.. , .
58.4
1.49
4
O. Strove
: :.-.'
178.6
.34
1
O. Strove
1857.75
1 '-•
.-•
Dombowski
1*71.64
IN ; ;
.02
B
Knott
1857.87
: Hi
:
Jacob
1871.60
183.7
.19
12
Ihiiu'r
1858.48
M 1
i 06
2
BteoU
1872.48
173.9
.34
12
Derabowski
:-'.-'•'•.
; • .
1 "
N
Deiubowski
is 7 2.58
177.2
.19
12
iMm.-r
> •.,.•_•
.M M
1 IN
4
O. Strove
IN;.
168.8
.14
3
O. Strove
>.*,.-.
INI;
LM
8-7
Midler
1873.50
I65J
^^
1
Midler
186846
1 i::
6
Mldl.-r
1873.50
164.7
1
•, ., ,
43.8
3
Secrhi
1873.52
169.5
2
H. HruliM
:>.....!
l 8 1
,. -,
Dawea
1873.46
KM;. 7
0.1)8
rf 3-2
W. & S.
4
O. Strove
1873.52
162.4
1.39
11
: |
31.5
3
Seochi
1873.52
1611.9
1.23
2
O. Strove.
1860.74
1
O. Strove
1873.54
rotunda
—
I
Ferrari
1873.70
lltt.3
1.40
4
Duller
IN,'.! II
0.8 ±
Midler
17.1
1.05
4
O. Strove
1874.53
157.0
1.36
10
Deinhuwitki
1874.57
155.5
0.78
•
(•liMlhill
IN. .'.'-I
361.8
fiineo
N
Dembuwski
1874.57
156.4
1.08
r,
W. & 8.
unsifhtbar
1
Winnecke
1874.62
162.9
1.40
4
O. Strove
84L
1.00
1
O. Strove
1874.65
154.9
1.35
1
Dune'r
:.,.-.
0.82
2
Midler
1874.66
156.5
1.22
9
1863.49
.:| L6
cuneo
4
Dembowgki
1875.52
149.1
1.41
8
iKMiilmwMki
1864.43
„
semplice
3
Dembowski
1875.55
147.2
1.21
7
Schiajiarclli
1875.57
150.3
__
2
W. & S.
186841
—
semplice
2
Dembowgki
1875.61
147.4
1.28
12
Ihindr
IN, './.I
rotunda —
3
Seochi
:>,,-,..:,
<0.5
3
1876.52
143.1
1.32
2
Hall
1876.54
138.1
1.17
7
Scliia|Kirelli
1881 II
M4.1
0.6
5
Ifc-mbowski
I> 76.66
1.37
7
IteiulMiwski
>,., ,,,
14 2.3
— -
1
Searle
1S76.61
140.1
l.'.'t
1
I'll mi HUT
1886 ra
235.1
3
Dawea
187649
1 IN N
LM
4
U. Strove
1866 :i
1881 U
228.6
229.2
0.83
1
1
O. Strove
Dfcv«
1871
l.'Ct.S
1 .:;•;
8
L.-MlM-wski
1 S77.68
l.'KI..'i
1 .'-'7
ft
1866J8
0.98
2
: •
IN77.58
1 II •-'
1 •."
1
rritchctt
181 : H
BB4
0.80
7
Dembowski
1877.58
1.::, 1
l.ir,
3
U. Strove
181 1 M
—
1
Wiulock
IN 77.59
l::i u
1 L'l
2
Hall
18) : n
•.-.I i
1.03
2
Duner
187841
TJ7n
i :.i
1
Humhara
1888 :i
210.1
0.94
6
Dembowski
1878
1.1 ii
4
S-ln;l|,;iri.|ll
LSM a
MM i
Ml
4
Knott
127.0
i -.-.I
2-1
Doberck
>. , .-.„
1.23
2
O. Strove
1871
1.38
7
Dembownki
>, >,.:
199.9
—
1
Zollner
1X78.59
128.7
i H
1
O. Strove
!>. > -.7
1.05
5
Dunei
187945
122.0
1.52
3
Ilurnham
200.6
, ,,,
8
Dembowski
187948
120.7
1.50
4
Hall
]s,
203.1
: M
11
Duner
1879.68
117.2
1.38
8
Schiaparelli
>• '7!
:••• :
— -
1
I'eirce
187*89
124.9
: H
1
Pritohett
188
C HHSKCULIS = ,12084.
t do
Po n
Observers
t
00
Po
n
Observers
0
r
O
It
1880.41 118.4
1.29 2-1
Doberck
1886.63
85.8
1.45
9
Schiaparelli
1880.48 115.0
3
Bigourdan
1886.73
88.0
1.42
9-7
Jedrzejewiry.
1880.49 114.1
1.34 5
Burnham
1886.75
89.9
1.78
7
Englemanu
1880.58 112.5
1.38 9
Schiaparelli
1887.55
83.6
1.59
6
Hall
1881.23 112.9
1.43 2
Doberck
1887.65
79.4
1.55
18
Schiaparelli
1881.45 110.6
1.53 5
Burnham
1881.51 109.2
1.41 4
Hough
1888.51
78.7
1.52
6
Hall
1881.51 110.6
1.43 5
Hall
1888.57
74.3
1.88
3
Comstoi-k
1881.64 101.8
1.41 2
0. Struve
1888.61
76.5
1.56
9-8
Schiaparelli
1881.74 108.9
1.47 1
Bigourdan
1888.65
74.9
1.71
3
Maw
1888.69
70.9
1.74
1
0. Struve
1882.47 105.0
1.48 2-1
H. Struve
1882.47 104.3
1.67 2-1
Doberck
1889.45
77.0
1.00
1
Hodges
1882.52 106.3
1.44 5
Hall
1889.52
72.6
1.67
3
Schiaparelli
1882.52 98.7
f.49 4
O. Struve
1889.52
76.2
1.2 ±
2-1
Glasenapp
1882.60 101.5
1.47 11
Schiaparelli
1889.53
72.4
1.49
6
Hall
1882.66 104.9
1.48 4-3
Jedrzejewicz
1889.56
72.0
1.67
4
Comstock
1882.76 107.0
1.75 6
Englemann
1889.66
70.2
1.73
3
Maw
1883.52 99.5
1.50 4
Ferrotin
1890.42
68.6
1.5
2
Glasenapp
1883.55 102.4
1.51 5
Hall
1890.51
68.5
1.49
6
Hall
1883.60 96.6
1.52 15
Schiaparelli
1890.70
65.8
1.68
3
Maw
1883.65 96.4
1.38 2
O. Struve
1890.77
64.2
1.46
5-4
Schiaparelli
1883.72 102.5
1.65 5
Englemann
1891.52
64.3 '
1.35
6
Hall
1884.45 94.9
2
Bigourdan
1891.54
60.4
1.45
7-4
See
1884.52 94.7
1.63 4
Hall
1891.55
63.3
1.50
2
Schiaparelli
1884.55 94.1
1.47 3
Perrotin
1891.62
62.7
1.45
5
Bigourdan
1884.55 90.9
1.32 1
Pritchett
1891.63
60.1
1.40
3
Maw
1884.58 90.8
1.64 9
Schiaparelli
1891.64
63.7
1.38
4
Tarrant
1884.68 88.4
1.57 2
0. Struve
1884.70 94.8
1.95 6-2
Seabroke
1892.57
55.5
1.51
5
Comstock
1884.71 98.8
1.89 3
Englemann
1892.63
56.0
1.37
8
Schiaparelli
1885.47 88.6
1.50 6
Perrotin
1893.68
47.6
1.42 '
3-2
Schiaparelli
1885.52 89.4
1.70 4
Tarrant
1893.80
47.6
1.27
5
Bigourdan
1885.52 92.0
1.61 7
Hall
1885.62 86.3
1.57 5
Schiaparelli
1894.51
43.8
1.24
3
Barnard
1885.64 92.1
1.59 4
Jedrzejewicz
1894.52
42.1
0.85
2
Glasenapp
1885.71 98.0
1.82 6-5
Englemann
1894.54
40.4
1.23
2
Lewis
1885.69 90.5
3
Seabroke
1894.73
39.6
1.28
9-8
Collandreau
1894.74
37.4
1.12
16-14 Bigourdaii
1886.54 88.8
1.50 6
Hall
1886.55 84.5
1.56 1
Perrotin
1895.32
36.7
1.17
3
See
1886.58 85.0
3
Seabroke
1895.57
30.2
1.00
4
Comstock
Sin WILLIAM HEKSCHEL made his first measure of
this star, July 21, 1782,
and found the position-angle to be G9°.S3.*
In 1795
he again examined the object, and
noted
that
the
distance had
* Astronomical Journal, 357.
IIKIirTI.I* = JT2084.
IS'..
decreased, hut that it was in the same i|ii:ulraiit as l>efore; this ap|>cars, how-
ever. t<> In- :i mi-take, as tin- companion at Umt Unit' must have liecn in the
op|»osite i|na. Irani. It is remarkable tliat HKKSCHKL could not separate the
companion in 1802, OM the angle was then 174°.5, and the distance I'.'JI.
Beginning with STIH \ K'S observation in 1H21> the record is practically con-
tinuous, and we have mcn-im- for each year, except when the companion wan
go close M to be lost in tin- ray* of the larger star.
Tin- pcriastron is so near the centnil star, on account of the considerable
eccentricity and tin- |M>sition of the node, that the companion has never IH-CII
MVH in this part of the orbit. According to the clement* found Mow, the
minimum distance is about 0".4o. Therefore, in spite of the comparative faint-
iii '>s of tin- companion, whose magnitude is (if), while that of the central star
d :;.n. this ol»j»-i-t ought to be constantly within the reach of our great refrac-
i..i-. In previous revolutions, however, the star has been lost, and it will
t Inn-fore be a matter of great interest to follow it during the next periantron
passage in 1899. Good ohsvrvations in this part of the orbit are needed, and
the rare phenomenon which will be presented by £ Ifcmili* alnmt the end of
thi- century will be worthy of the attention of observers with large telescope*.
Notwithstanding the three revolutions which have been completed since
HKKSOIKI.'S discovery in 1782, our knowledge of the orbit of this pair ha*
remained somewhat unsatisfactory; the element* heretofore obtained are by no
means accordant. Tlii- diwgCBq "f remttl m;i\ be ail ril-m. .1 partis )<> enOH
of observation incident to the inequality of the comiM)ncnt*, and partly to a
mistake in the old position-angle of HKKHCHEL, which ought to have
aln.ut 80*. Indccil, IlKits< IIKI.'S <iliscrvation d«H-H not seem to lay claim
to much accuracy, for on Augn>i •'!". ITS'J. he says: "Saw it better than I
erer did." — implying that on the previous occa>ion> the companion was not
well til-lined. The following table gives the clement* published by previous
investigators :
p
T
t
a
a
1
1
Authority
Qnnr,n*
' '
3l!4«78
>:•.-."
0.4545
1.189
. •.. i
:....,
MB i
Mfldler, 1842
Dorp. Ob*., IX, p. 1«J2
30.216
1830.42
0.432
1 _•<-
19.4
Ill
MAdler, 1M7
Fixt. Sy>t.. I. ).. 269
36.357
1830 IM
0.4482
_
!• I •::.-.
43.7
Villarceaa
\ \ . : \\VI,|,.305
37.21
;-...-..
0.4381
—
HeU-her, 1853
\l N . XIII, p. 258
36.715
0.4831
i n
41.9
49.1
MM
Vill»ix»»a, 18&4
C.R.,XXXVIII,p.871
34.221
1830."!
0.4239
|&M
Dun««r, is 71
, , ,
0.5T. 11
27.0
• t :
Plummer,lS71
M N . XXXI, 1M
: H
1WVI.90
0.405
26.13
.-,1.11
MO.VI
FUmnuulon. '74 CaUl. fit. IX.uh., |..1<»1
34.4
1864.8
0.463
i nt
41.73
Dolierck, 18W» \
! Ill
1864.78
0.4666
i -;.-,
44.1
44.53
--.: -
Dobaok
190
£ HERCULJS = ^2084.
After an examination of all the observations we formed mean positions for
each year, and from these mean places deduced the following elements :
P = 35.00 years
T = 1864.80
e = 0.497
a = 1".4321
ft = 37°.5
i = 51°.77
A. = 101°.7
n = -10°.2843
Apparent orbit:
Length of major axis = 2".492
Length of minor axis = 1".752
Angle of major axis = 43°.l
Angle of periastron = 289°. 0
Distance of star from center = 0".455
The following table of computed and observed places shows that the ele-
ments give a good representation of the observations, and render it probable
that the present orbit is very near the truth. There are some errors in the
position-angles which appear to be systematic, and we have not been able to
improve the representation; for whatever would improve the agreement in one
place would injure it in another, or in the same place during the next revo-
lution.
It will be seen that this orbit is slightly more eccentric than most of those
heretofore deduced, but it is not probable that the eccentricity will prove to be
too large. If any change should be required in this element, it is likely to
increase rather than diminish the value given above. The eccentricity of the
orbit of £ Ilercidis is near the mean value of this element among double stars.
COMPARISON OF COMPUTKD WITH OBSERVED PLACES.
(
o.
9.
Po
PC
l>.. (>
!>.: l>,
n
Observers
1 781'..-,.-,
69.3
80.5
i
1.51
0
-11.2
*
1
Herschel
1795.80
—
248.9
—
0.65
1
Herschel
1802.74
—
174.5
—
1.24
1
Herschel
1826.63
23.4
27.1
0.91
1.00
- 3.7
-0.09
5
Struve
1828.71
349.5
:;n.o
0.65
0.54
+ 5.5
+ 0.11
1
Struve
1832.72
220.5
216.0
0.81
0.97
+ 4.5
-0.16
1
Struve
1834.45
203.5
201.5
0.91
1.14
+ 2.0
-0.23
2
Struve
1835.45
196.9
191.6
1.09
1.20
+ 5.3
-0.11
5
Struve
1836.GO
186.2
182.8
1.09
1.23
+ 3.4
—0.14
5
Struve
1838.70
168.5
167.5
1.35
1.24
+ 1.0
+0.11
3±
Galle
1839.76
161.9
159.9
1.22
1.25
+ 2.0
-0.03
4
Dawes
1840.66
157.1
153.7
1.25
1.25
+ 3.4
±0.00
5
0. Struve
is i !..-,<;
146.4
147.2
1.24
1.25
- 0.8
-0.01
16-6
AI iidler 9-0 ; O2. 3 ; Dawes 4-3
1842.54
142.0
140.3
1.14
1.26
+ 1.7
-0.12
9-4
-Min Her 3-0; Dawes 3-1 ; OS. 3
1843.65
130.1
132.1
1.30
1.28
- 2.0
+0.02
20-2
Madler 8-0 ; Dawes 3-2 ; Madler 9-0
1844.50
124.7
127.1
1.12
1.30
- 2.4
-0.18
7-2
Madler 5-0; O2. 2
1845.64
121.3
119.3
1.24
1.32
+ 2.0
-0.08
3
O. Struve
1846.79
111.3
112.1
1.31
1.35
- 0.8
-0.04
7-2
O2. 2; Dawea5-0
180
00
1TM
I 111 i:« i i i- =
(
•.
«.
P*
P.
" "
*-*
•
OfeWTM
LSI; -, .
' . '
I". I
1.43
\ .IS
.'! -«
• r IS 17; Dtwea 1 ; O±'.'2
1848.59
101.8
LOU
1 11
+ 0.4
+ 0.11
6-S
Midler 3-0 5 Daww 3 ; OX. '2
INT. IN
99.2
•„ ,
1 71
! II
+3.1
1
DawM
1850.36
•
91.7
! •
1.46
-H.fi
0.07
0^.3; FleU-her2; Mfcller 3-1
1 s.-, 1
N. '
I .::.
1 in
+ 2.2
-0.14
if. 1 1
M,,.ll.-r::; Fletcher 6; (^..1; Miller 2-0
1H5V
79.8
l 52
+ 4.0
ji> 1 1
\li.ll«r8-7; FleU-her5-2; Miller 2 O
1H.V1.46
+ 2.2
-0.15
_•:: -ii
i.l': Miller 6-3; ML 8 ; 0.1.4; M&.3
iv. i n;
71 '-•
1 17
! B I
+ 3.K
11
Jacob 3; 02. X; M«<ller5
• 46
. . !
1 17
+ 4.4
-0.06
Jl 11
m-iu. i:» 0; 8etfhi3; O2. 4 ; Morton 4
1 1.:
:,l
31
.l;u-c.l. :>; Deinttowski 15; Sect-hifi; O2.3
•N .. • i
•.-,,,
-,-, ,
1.35
!'•
+;{..-,
-0.11
L'l
ML 4 ; Mo. 2 ; Sec. 6 ; O2. 4 ; D.MII. 5 ; .la. 3
|V-.N .s
51.0
:,..-.
L19
Ill
+n..-,
t> 1M
»• > •>]
Sewhi 2 ; IVmbowski 8 ; O2.4; Mii<ller8-7
II 1
l i::.
-1.0
0.06
lit I.'.
Mikller 6 ; Secchi 3-0 ; Diiwes 6-5 ; OZ. 4
late rc
.:..:,
1.05
16
n ii
4
8ecchi3; O£. 1
18.6
n
• ,.,
-0.09
6
Mii.ller2; O2. 4
:--•,
11 '_•
1.00
-1.7
+ 0.22
'.l 1
I^erabowski 8; O2. 1 ; MAdler 2
IN.. I'-
.1 :.•
:••_•
—
4
Dembowski
Is, ,:..-,
M&fl
<0.5
...-,.
-6.6
-0.09
3
Kli^lfiiiaiiu •
+:<..-,
±0.00
14
Dem. 5 ; Dawes 3; O2. 2 ; Dawes 2 ; Dawes 2
tan a
-M7.-J
0.91
,,.,.,
+»;.;{
-0.08
9
Dembowaki 7; Ihiner2
!N,.S.M
•.'117.7
1.05
1.09
+ IM;
-0.04
17
l)eniU)W8ki 6 ; Knott4; O2. 2; Punelr 5
>
J.'l N
198.2
1.08
i.if.
+ ;{.(-,
-0.08
19
iVmbowski 8; Ihim(r 11
L87OM
I'.rjii
190.9
1.1.-.
LK
+ 1.1
-0.05
17
Itembowski 11 ; l»un.:r 6
isn :,:•
181.9
IV.:.
l.-.M
1 .-.•::
-1.6
-0.02
32
Dembow8kil4; O±. I ; Knott5; Ihnu'-r 12
176.0
LU
l.-'l
-3.1
-0.02
27
Demliowski 12; Dunerl2; O2.3
\M.\
L6fl .
\ 'JL'
l.-Jl
— 2.2
—0.02
17
DembowHki 11; (U.'J; Ihmtr 4
!N;| I'...
!,,,,,,
ir.l.l
Ufl
l.JI
-l!l
+0.13
14-15
DembowHki 10; O2.4; DuiuVO-1
L8T5.M
L48J
i :, i :,
L8Q
I.'J.-.
i; ii
+0.05
29-27
Dem. 8; Sch. 7; W. & S. 2-0; Dunrfr 12
L8T&M
lil.it
ll.s.t;
l.3o
1.25
-7.6
+ 0.05
10
Hall 2 ; I Vmbowski 7 ; I'lummer 1
IN;;:.;
llti.l
1.40
1.26
-3.8
+ 0.14
11
Dembowski 8; PriU-hett 1 ; Hall 2
126.9
133.6
1.40
1.28
-6.7
+0.12
Hi 1:1
/i. 1 ; Sch. 4; Dobervk 2-1 ; IX>rnliowHki 7
122.5
126.6
f.47
1.30
-4.1
+0.17
8-16
0.3; Hall 4; Schiaparelli 0-« ; 1'ritchett 1
LS.N.I HI
115.8
120.4
1.34
1.32
-4.8
+0.02
in I.'.
Doberck 2-1 ; Big. 3-4) ; /}. 5 ; 8di. 0-9
L88J i •
110.6
11. -i.'.i
11.-.
1 .::.-,
-3.3
+0.10
17
Doberck2; /3.5; Hough 4; Hall 5; 1%. 1
L05.6
107J
l n;
1.38
-1.6
17 I'.i
Dk. 2-0 ; HI. 5 ; Sch. 0-1 1 ; Jed. 4-3 ; En. 6-0
101.5
im :;
1,M
1 11
+ (».!'
+ 0.1.-5
l i 39
IVr. 4 ; Hall 5 ; Sch. 0-15 ; En. 5 [En. 3 0
1884 n
•..1 1
9M
l.-.l
111
-I'..',
+0.07
-•N 17
Big.2 0; Ml.l; lVr.3; 1'rit.l ; Srh.9; 8e«.6-0;
INS.-.:,-,
•.,.:.
i .:.;
1 .17
-0.7
+0.10
29-22
Per.6; Tar.4-0; 111.7; S-h.:,; .I.-.1.4; fimti 0
MM
i .-.t
1.50
+ 2.0
+0.04
::. U
II -.. I'.T.l ; .S-a-.H n; S.-h.i); Jed.9-7; En. 7
188? BO
81.5
i .:.:
i .-.:•
+ 1.3
+0.05
M
Hall 6; S,-l,i.i|,.u,-lli IS
7f. i
i :.»
-0.5
+ 0.01
Jl 11
Hall il; < '...MM. «k:t n: S.-h.9-«; Maw 3-0
;-j7
70.6
: -.:,
l :.i
+ 2.1
+O.OJ
18-17
S,'h. 3; Gla«. L' 1; HalU',; C,,in 1 ; Maw 3
Ifl
,,:.,.
+ 0/.'
±0.00
16-15
Gla«. 2; Hall 6; Maw 3; S.-hi:i|,ur,-lli 5-4
is-.n :.;
l i.;
1.50
+ 1.3
-0.07
Hall 6; See 7-4 ; S, 1, . ; Maw 3
.-..-, :
Ill
1.46
-0.2
i:<
Comstock 5 ; Srhiii]>an-lli H
i; 6
48.2
i.3i
-0.6
8-7
S-liia|i:in-lli .'! - ; Hi^ounlan 5
r.M
II 1
1.1'n
1 ::i
-2.0
-0.11
7 I'.t
Itaniard3; Glas. 2-4) ; Lewis 2; Kig.0-14
1895.32
36.7
1.17
1.21
-2.1
" -I
3
See
The companion is worthy of regular attention in the ]>:irt of the orhit now
tleserilieil. luit <ili~< rv;ili<m will IxH-onie more urgent :i* the -t;ir :i|>],r<i:ielie-.
I>eriaHtron in iv.i'.i. If goo<l olwervatkmH can l)e secured they will enable iw to
give the hi^heM precision to the theory of the motion of thi- -t:ir: luit if the
measure* in go delicate a case ore affected by sensible systematic errors they
192
/3 416 = LAC. 7215.
will prove to be of little value. The phenomena of the approaching appulso
of £ Herculis will therefore be difficult to observe, and results of importance
can only be obtained by skillful treatment. It is hardly necessary to add that
this phenomenon will not again be witnessed for more than a third of a
century.
It seems worthy of remark that STRUVE, who devoted so much attention
to the colors of double stars, noted the color of the companion as reddish,
while it is now distinctly bluish, and although a change of color does not seem
probable, this has been suspected as well as variability.
In order that astronomers may be able to compare the present theory with
observations during the rapid motion of the companion in passing pcriastron,
we give an ephemeris for the next ten years:
t
1896.50
1897.50
1898.50
1899.50
1900.50
28.5
15.5
351.9
289.7
258.4
PC
t
It
1.02
1901.50
0.82
1902.50
0.56
1903.50
0.47
1904.50
0.58
1905.50
2330
218.4
207.8
198.9
191.0
PC
0*80
0.97
1.09
1.16
1.20
a = 17h 12m. 1
0.4, yellowish
7215.
8 = —34° 62'.
7.8, yellowish.
Discovered by Burnham in 1876.
OBSERVATIONS.
1
ft,
Po
n
Observers
t
6,,
Po
n
Observers
0
9
O
it
1876
.52
240 ±
1.8±
1
Burnham
1891
.53
81.2
0.53
3-2
Burnham
1877
.53
222.6
1.80
1
Cincinnati
1892
.38
24.4
0.61
4-3
Burnham
1877
.64
224.4
1.77
1
Eussell
1894
.57
330.8
0.94
7-2
Sellers
1888
.72
147.5
1.88
1
Burnham
1894
.63
334.7
1.27
3
Barnard
1889
.43
135.2
1.17
2-1
Burnham
1895
.60
321.7
0.91
2-1
Com stock
1889
.63
131.9
0.97
1
Pollock
1895
.74
320.0
1.30±
1
See
Since the discovery of this rapid binary the companion has described an
arc of 280°. The magnitudes of the components are 6.4 and 7.8 respectively,
and as the pair is never closer than 0".58 the object is difficult only on account
of its southern declination.* The period is surprisingly short for a system of
'Astronomical Journal, 372.
ISO
1178
270
1416 = Lac. 72 10.
b. Bl*.
ft 416 = LAC. 7215.
193
such considerable separation, ami this riiviiin-tanee lends decided probability to
the view that the parallax i- M-n.-iblr. l'i"\ isioiial elements for thin -\-t.m
have been eomputrd \>\ < •!. \-»-:\ \rr. <.<>I:K and BUHNUAM. Their result* are
a- follows :
P
r
•
•
a
<
a
lull : I)
•OHM
:*
..I i^
.1 .
1891.85
l> <: _••;
-..-.,.
1.62
1 i..
1-1 :
I--'"
I.", 1
M r
44.4
•..::.
GHawtuipp,1893
Gore, Ivr;
I: mill .; . ISlC!
Astron.aml Astr<>|>h.,May,lH<t.'i
Montlilv N"ti<-i's. March, IK'l.'i
Publ. Lick Obs., vol. 11, p -JI7
Tin- oli-< -r\ at ions \\liich I secured recently at the Washburn Observatory
have enabled me to redetcnniiie the orbit. Using all available measures, we
find the following elements of
Apparent orbit :
P — 33.0 yean Q —
T - 1891.85 i -
144°.G
37e.35
« - 0.512 X -
86M
a - T.2212 » -
-9°.0908
Length of major axis
Length of minor axis
Angle of major axis
Angle of periastron
Distance of star from centre
- 2».76
- 2*.38
« 142°.5
- 69°.5
- O'.Gl
COMPARISON or COMPUTKH WITH OBSKRVKD PLACIM.
(
e.
f,
p.
P<
«.-«,
P*— P,
•
Otwrnrrn
1876.52
240. ±
.'.;.; i
\ - •
1.79
+0.01
1
Ilurnham
is:.
1.80
,7'.i
-5.4
+0.01
1
Cinrinnati
1877.64
-•-•I I
1.77
7s
-8J
-0.01
1
Russell
n; :.
147.7
1 ss
19
-(l.L'
+ 0.69
1
Hurnham
1889.41
: 1 :
1.17
"4
-1..-.
+ 0.1.-5
•_• 1
Hiirnhaiu
1889.63
l::i '.•
1.-J3.1
0.97
oo
-u
-0.03
1
Pollock
1891.53
81.2
M.-,:
o.ao
-r-rt. 1
-0.07
3-2
Hurnham
1892.38
.11
34.0
0.61
0.61
-9.6
0.00
4-3
Kiirnhain
1894.57
HKU
333.6
,,.,!
1.10
-2.8
-0.16
7-2
BoUon
L896.6Q
19.S
0.91
+ 1.8
-0.39
2-1
(^mstock
>•:. :i
,..,,,,
SU i
I ;:.' :
1.32
+ 1.6
-0.02
1
8w
The angular motion during the last tlin-c vi-ars has not IH-CII very rapid,
and the constancy of areas shows that the di-tanrr- lia\«- ln-cu somewhat under-
measured. It is now apparent that the period will be sensibly longer than
Ht HMIAM -up|K>sed. The value found above is not likely to be in error by
more than one year, while the correction of the eccentricity will hardly exceed
±0.03. Considering the small number «>f uli-i-rxations on which this orbit is
baied, the elements may be regarded as highly satisfactory. As this system is
194
2-2173.
visible in the United States, it is worthy of particular attention from American
observers.
The following ephemeris gives the place of the companion for five years :
< ft- PC t Be PC
1896.50 31CK6 1*43 1899.50 287/7 L69
1897.50 302.1 1.54 1900.50 281.5 1.72
1898.50 294.6 1.62
22173.
a = 17h 25'".3 ; 8 = —0°
6, yellow ; 6, yellow.
Discovered by William Struue in
59'.
July, 1829.
OBSKRVATIONS.
t
6,
PC
n
Observers
t
ft
P»
n
Observers
O
H
0
|
1829.56
147.2
0.62
2
Struve
1851.32
334.1
1.27
4
Madler
1831.69
141.5
0.62
3
Strove
1851.74
335.6
1.18
2
Madler
1836.69
single
4
Struve
1852.72
334.1
1.23
2
Madler
1837.70
353.
obi.?
1
Struve
1853.12
331.2
1.04
4
0. Struve
1840.47
347.1
0.5 ±
1
Dawes
18,54.66
330.5
1.37
3
Madler
1840.64
358.8
0.61
3
0. Struve
1856.53
153.2
0.9 ±
1
Winhecke
1841.36
1841.61
1841.64
352.3
352.2
347.4
0.67
0.67
0.71
6-2
3
2-1
MMler
0. Struve
Dawes
1856.53
1856.53
1856.90
329.1
329.8
326.0
1. ±
0.97
0.94
4
1
4
Dembowski
Secchi
0. Struve
1842.45
354.9
5
Kaiser
1857.43
326.9
0.88
1
Secchi
1842.51
349.9
0.75
3
Madler
1858.56
325.9
0.84
2
Secchi
1842.67
343.3 "
0.7 ±
3
Dawes
1868.61
328.3
0.88
4-2
Madler
1843.30
343.1
0.74
3
0. Struve
1858.61
325.0
0.25 ±
1
Morton
1843.50
346.2
0.78
8-5
Madler
1859.33
324.2
0.71
3
0. Struve
1843.54
341.2
0.9 ±
6
Dawes
1843.65
345.1
0.68
10-2
Kaiser
1861.57
324.0
—
3
Madler
1861.63
315.2
0.48
1
0. Struve
1844.36
345.0
0.8 ±
3
Madler
1845.55
342.1
0.97
1
Madler
1864.45
1864.53
160? 0.6?
single
2
1
Englemann
Dembowski
1846.46
339.4
1.07
6-5
Madler
1846.47
336.1
0.85
5
0. Struve
1865.51
182.2
—
1
Leyton Obs.
1847.47
339.2
1.16
2
Madler
1866.32
1866.43
360.7
181.3
0.47
3
1
0. Struve
Leyton Obs.
1848.44
339.2
1.15
1
Madler
1866.59
107.7
—
1
Winlock
1848.45
339.4
1.10
1
Dawes
1866.62
139.4
1.60
5-1
Searle
1848.58
340.4
1.23
1
Mitchell
1866.69
167.7
—
1
Winlock
12178,
10",
1
0.
P.
•
1 ' • •
I
*
P.
ii
Otasrrrrt
e
9
0
f
1867.79
174.5
1
l>uiie>
1X81.74
elong.?
1
Higounlan
1868.18
161.3
•
ruve
L88UV
109.9
0.3
1
Hrhia]>are)li
|S, s ,
160.6
0.5 ±
I
, bom-ski
MM
oblong
1
O. Struve
iM'.s
169.3
, ,.s
:
Dun.-r
1X83.50
elong.
20*-45°
4
1'errotin
1860.68
157.1
6-1
Dembowski
1883.60
190.0
oblong
1
O. Struve
1869.93
161.1
• .
I»uin;r
1883.60
single
7
Srliiapan-lli
1870.35
: • t
0.8 ±
•-•
Oledhill
1883.88
24.8
0.22
1
Kiigletnann
1870.45
: .. s
0.81
1 !
Dembowski
1884.56
17.4
0.38
3-2
1'errotin
1870.67
4
Dunrfr
1X84.59
.,.,
—
1
Bigounlan
]SS| f.d
single
7
Srlnaii'tic'lli
1871.44
1*71.64
155.0
156.5
9M
9M
4-2
6
Dembowski
Duni'-r
1884.61
1884.62
42.7? 0.25 ±?
9.9 0.32
3
3
Scliiapurelli
Hall
1*7'.M5
1 .-..-. 7
5
O. Struve
188548
21.9
0.30
8-6
Fi 'lei aim
1 * 7 '.'.55
- •• ,
i a
Dembowski
1873.50
154.1
1.00
2
W. AS.
Iss,, , ,
356.6
0.56
3
1'errotin
160.8
o.77
4-1
Dembowski
ISS6JM
:::.:. !
0.41
7
Schi;i],.in-lll
un
1.1(1
1
Dune'r
I.XS6J8
353.0
0.42
3
Hall
I88JLM
365.6
0.30
8
Englcmann
, If.
150.0
0.91
4-3
Dmbowski
1874
l.M .1
0.99
2-1
Gledhill
1887.40
350.5
0.46
4
Tarrant
1874.59
i :.!.•-•
0.90
2-1
W. AS.
1887.56
348.5
..;,;
7
Srliiapan-lli
1*71
0.77
2
O. Struve
1X88.49
347.8
M..S
3
leaven worth
1*71.66
: U >
1.09
2
Newcomb
1X88.55
344.4
0.53
3
Hall
1*7. -,.53
147.5
0.74
4
Dembowski
1888.60
346.9
0.58
8
S- hi a part-Ill
1875.57
146.5
• - :
7
Schiaparelli
Isss,,.,
342.3
0.81
1
O. Struve
1876.57
147.8
l.±
1
W. AS.
1889.46
345.0
0.66
5
Tarrant
1875.67
148.7
5
iMmrr
1889.63
345.5
0.70
7
Schiaparelli
1876.52
149.3
0.77
3
Hall
1890.26
341.5
in cont.
10
Giacomelli
1876.55
1 II *
0.69
5
Dembowski
1890.49
340.9
0.8 ±
2
Ulasenapp
59
1 1.5.8
MS.;
4
B iai»arelli
1880J6
343.1
0.84
3
Maw
l*7f,.65
III"
n.r.l
1
O. Struve
1880.71
0.76
2
Kigourdan
119.9
—
4
Doberck
1890.74
::il.7
0.70
7-5
Schiaparelli
1*77.49
111 f.
—
1
Cincinnati
1891.51
340.1
0.97
3
Hall
1*77.53
1 1-2.6
0.62
.-. I
Dembowski
1891.53
340.0
0.81
4
Schiaparelli
759
141.4
- ' '•
2
0. Strure
1891.58
0.93
3
Jtuniham
1*77.59
1 12.0
8
Schia|>arelli
1891.69
340.3
0.91
3
Bigourdan
1*77.68
1.-.3.5
Ml
2
Doberck
18'X
341.X
0.90
4
Comstock
1878.40
M2J
0.52
1
Doberck
339.1
l.IO
1
Bigourdan
1878.48
139.4
0.60
4
Dmnbowski
188!
339.3
0.88
7
Schiaparelli
i;r
7-3
Cincinnati
814) ;
0.91
3
M .
1879.58
136.0
8
Schiaparelli
>,.,,,
338.0
1.08
3
Schiaparelli
1879.72
15-
0.7 ±
3
Seabroke
U 1 H
340.6
1.11
.;
H.C. Wilson
1880.47
131.3
0.36
1
Burnbani
> . : v,
336.8
1.15
2
Lewis
1880.65
133.9
0.4 ±
9
Schiaparelli
1894.74
IHJ
1.27
1
Callandreau
18801
114.9
0.24
3
Burnham
1895.30
337.3
1.19
3
See
1881.52
121.5?
0.27?
1
11 ...
1895.57
337.7
1.13
3
1 • •
196 12173.
When this interesting double star in the constellation Ophiuchus was
discovered by WILLIAM STRUVE, the companion was measured on two nights,*
and again observed in 1831; but in 1836 it had disappeared, so that under
the best seeing the star appeared absolutely round. STRUVE therefore sur-
mised (Mensurae Micrometricae, p. 294) that this is a case of occupation similar
to those of yCoronae Borealis and uLeonis, " summa attentione digna." The
companion came out on the opposite side in 1840, and was subsequently
followed systematically by the best observers, so that at the present time a
large amount of good material is available for the investigation of its orbit.
The components are so nearly equal in brightness that the angles frequently
require a correction of 180°, and for a time it remained uncertain whether the
period would be 46 or 23 years. Prof. DUJSTER was the first astronomer who
attempted to investigate the orbit of this pair; using measures up to 1876, the
illustrious Director of the Observatory of Upsala arrived at the following results:
P = 45.43 years Q = 152°.65
T = 1872.91 i = 80°.53
e = 0.1349 X = 7°.26
a = 1".009
From an investigation of all the observations, including the measures
recently secured at the Leander McCormick Observatory in Virginia, we find
the following elements of 2'2173:
P = 46.0 years Q, = 153°.7
T = 1869.50 i = 80°.7f>
e = 0.20 A. = 322°.2
a = 1".1428 n = -7°.8261
Apparent orbit:
Length of major axis = 2".22
Length of minor axis = 0".35
Angle of major axis = 154°.5
Angle of periastron = 1603.8
Distance of star from centre = 0". IS
The accompanying table of computed and observed places shows that
these elements are very satisfactory.
• Antronomlsche Nachrlchten, &
1674
COMPAKMOX .» < ..MM m. \\IIH OMKBVED PLACO.
t
«.
9.
•
ft
•.-*,
*-*
•
ObMTVM*
>. ' .
: ; :
!!>.-.
• ><.;
M -1
-1.3
-0.17
2-1
Struve
1831.69
141.5
11.: 1
-1J
-i.
3
Struve
1" 10.64
.NM
DJfl
0.47
+08
+ 0.08
3-4
ft] !; DawraO-1
1841.48
.:
D.61
D.W
-0.2
+ 0.08'
Ma«)ler6-2; O^'.S
1842.54
... ,
4-0.5
+ ('
11-6
Kaioer5-0; Midler 3; DtwwS
IM
1 , •
• '77
-0.2
_ 0.0.1
18-16
Mi.8-5; Ka.10-2; CC.0-3; Da.6
1844J6
•+-0.7
-O.io
3
Ma-ller
1845.55
"'.•7
-1.1
+0.02
1
Midler
1841
.07
06
-1.4
+0.01
Mn-ller
IM
.n;
it
-0.4
+ 0.02
2
Midler
n;
.'.'I
+1.2
+0.05
3
M.Lil.-r 1 ; DaweHl; Mitx-hcll 1
IvM 71
•'
na
.•-•••
+0.6
-0.07
2-6
M feller
-
89
M
-0.2
—4.05
2
Miller
185:! l _•
'
HI
.•-•:
-2.7
—0.23
4
O. Stnive
1 .:::
•ji
— 2.2
+0.13
3
Miller
l> •
.10
-1.9
-0.13
9
iVm. 4 ; Se. 1 ; O2. 4
.04
-2.4
-0.16
1
Bwchi
is.'. »;,.,
0.93
-1.1
-0.07
7 1
Se. 2; Mi. 4-2; Mo. 1-0
•- .' .
0.71
-1.9
-0.14
3
O. Struve
186140
819.7
ii i-
<i..-.7
-0.1
-0.09
4-1
Midler 3-0 ; Of. 1
1H0.7
IM s
" »7
-4.1
+0.19
3
O. Stnive
!7»:.
L68 •
n.M
+6.2
+0.17
1
Da4f
S I-
164J
0.61
QM
-0.7
+0.02
8
"2 3 ; DeinlMjwski 2 ; Dundr 3
1869.76
159.1
Hi""'
o.<;:i
0.75
-0.9
-0.12
11-7
I»«-III|HIW >ki 5-1 ; 1 >mn;r 6
168.1
0 B ;
+0.2
-0.03
10-8
DetnlM>wski '• 1 ; 1 >uin;r 4
1.54
i u a
1 .1.1.11
0.89
-0.1
+0.04
10-8
DenilKjwski 4-2; lium-i r,
154.0
Ml 1
0.92
-0.4
0.00
in -
1 >- 5 ; I >--iii 1 » •« -k i 5-3
!>:3J6
18&0
i :.-.•.:•
0.92
+0.3
-0.03
7-3
W. & 8. 2 ; Dem. 4-1 j Du. 1-0
1874.56
• .- ;
l".u J
Q x',
0.0
0.00
10-7
Dem. 4-8; Ol. 2-1; W.A S. 2-1; UZ. 2
1875.58
147.6
148.4
ii -1
-0.8
-0.02
17-16
Dem. 4; Sch.7: W.&S. 1-0; Du. 6
1X76.58
11-. ii
146.2
0.76
0.78
+0.7
-0.02
16-12
Ml. 3; DPMI. 5; Sch. 4; Dk. 4-0
1877.57
144.4
143.7
0.67
0.70
+0.7
-0.03
17-14
Cin.2-0; Dem.6-4;Sch.8; Dk. 2
s.48
; 19 i
140.6
0.56
0.61
-1.2
—0.05
5
Doberck 1 ; DembuwHki 4
1879.40
:....:.
13K.4
0.59
n.VJ
+0.1
+0.07
15-11
Cincinnati 7-3 ; Schiaparelli 8
138,0
ii |n
+ 4.6
-0.02
10
ft. 1 ; Schiaparelli 9
: .M
114.9
IU.;t
ojg
0.0
-0.05
:{
Itiirnhain
1881M-.1
91.6
ioj
0.2
ii.-.M
+ 1.1
-0.01
1
S<'liiaparelli
UL'U
-3.9
+0.02
4-9
IVrrotin 4-0; Englemann 0-9
23.3
o;tl
OJ7
+ 1.5
+ 0.04
9-8
I'.-rr.itiii 3-2; Sch. 3 ; Hall 3
rl •.'
» !•;:
-0.07
Knglemaiiii
1886.58
0.47
-01
-0.05
IM
Per. 3; Sch. 7; Hall 3; En. 8
1887 is
,,;,,
_.-.
-0.09
11
Tarrant 4 ; Srhiaparelli 7
:•
-1.8
-0.12
14
I.v. :?; Hall 3; Si-hiaparplli 8
>x ,,.;
0.70
_,,
-O.I-.'
7
8chia|»arelli fHi^. u j S<-li 7 :-
1890.58
343.8
0.78
QM
-L'.o
-0.11
•_'l 1L'
Gia. lo -0 ; Glaaenaiip 2; Maw 3 ;
18'.'
140X1
342.1
0.91
UM
-2.1
-O.lu
u
Hall.'t; S-h. 1; /*.:{; HiK. 3
18'.'.
•1" -'
I40J
..•.:.
1.09
-0.4
-0.11
15
Com. 4 ; Hi^. 1 . S,-h. 7 ; Maw 3
18H
1.09
1.19
+ 0.4
-0.10
6
.|«rt-lli3; H. C. W. 3
UMM
' -
.s.:
1.15
1.22
-1.5
-0.07
2
Lewis
1 895 JO
337.3
.; :.
1.22
1.24
-0.6
-0.02
3-1
See
Owing to the high inclination of the orbit, it is clear that a small error
in angle would very sensibly alter the apparent radius vector of the companion,
and for this reason good measures of distance- arc more trustworthy than
198
ft1 HEKCULIS BC = A.C. 7.
angles. Therefore, while the present orbit is based on both coordinates, unusual
weight has been given to the observed distances.
The residuals in angle are very small, except in the case of ENGLEMANN'S
measure of 1885, when the components were so close as to render all observa-
tions with a small telescope very uncertain. It should be remarked that the
position for 1882 is based on a measure which was rejected by SCHIAPAKELLI
on account of its discordance; but as the other six measures by that dis-
tinguished astronomer give
»„ = 109°.9
= 0".30 ,
which cannot well be reconciled with the theory of the star's motion, it appears
probable that the single outstanding observation is nearer the truth, and it is
therefore adopted in the above table.
The most remarkable characteristic of 2' 2173 is the relatively small eccen-
tricity of its orbit. Although this element is not so well defined as might be
desired, yet the value given above seems to be fairly indicated by the best
observations, and is not likely to need any large correction. Good measures
of distance about the time of maximum elongation, in 1898 and 1899, would fix
the eccentricity more accurately, and accordingly for the next five years this
system will deserve the particular attention of astronomers.
IIERCULIS BC = A.C. 7.
a = 17h 42m.6 ;
9.4, bluish white
= +27° 47'.
10, bluish.
Discovered by Alvan Clark in July, 1856.
OBSERVATIONS.
t
1857.47
Oo
63°±
Po
f
n
1
Observers
Dawes
t
1865.43
ft
8o!r>
Po
l!84
n
2-1
Observers
Knott
1857.50
59.3
1.82
2
Dawes
1865.44
82.0
1.27
5
Dembowski
1857.85
71.7
1.74
1
Secchi
1866.59
86.3
1
Winlock
1859.70
60.4
2.05
3
Dawes
1866.56
86.3
—
1
Searle
1860.30
67.7
1.64
1
0. Struve
1866.68
89.5
1.10
2
0. Struve
1862.83
1864.43
78.5
77.6
1.50
1.81
1
1
O. Struve
Dawes
1867.58
1867.59
97.9
93.0
—
3
1
Searle
Winlock
1864.49
1864.76
67.5
78.8
1.70
1.76
1
1
Engleinann
Winnecke
1868.50
1868.61
97.7
106.4
0.88
1
1
0. Struve
Winlock
,»' IIK!« I I.I- ItT = A.(
MKI
1
6.
P.
•
ObMrvcrt
<
fc
P.
m
Otaamn
o
*
o
p
1869.73
130.9
—
1
Itak
1883.53
0.74
3
Bumham
1889.73
111.7
—
-'
rt»
1-..1 I
0.84
3
Hough
LMfl H
,,,,.
3
Hall
1871.51
100±
2
\\ & 8.
1-
261.4
MS,.
2
Fn-l.v
1871.52
156.8
'"•-'
1
274.8
5
Schiaparelli
1873.50
180.5
_
1
: .
188
Mj
0.62
s ,.
Knglemaiin
1873.50
174.5
—
1
II l:iun>
1884.04
273.4
0.65
3
Hall
1X73.50
175.4
--
1
MQller
1884.68
272.7
0.77
1
O. Strove
1873.50
185.5
I
O. Strove
>.
90±
0.6 ±
1
\v
1885 .M
2fi8.1
1.15
2-1
Holetacliek
: > , . . 7
•em pi ice
—
1
DembowHki
ISS5J8
288.0
0.61
3
Hall
LM&a
245.2
—
2
Smith
i-n.48
m i
4-2
Newcomb
1874.65
100.5
0.4 ±
1
Oledhill
lvS6J0
302.1
5
Hall
1875.58
UBJ
_
6
S'hupurclli
1887.54
318.3
0.49
6-5
Schia]>arclli
225.9
—
1
Kewcomb
1887.58
321.5
0.42
3
Hall
:-, . .
220.6
1.1X
:. .;
Hall
1875.7"'
m
1
Holden
1888.47
330.7
0.45
3-2
Tar rant
188848
343.1
0.43
11-9
Schia|iarclli
|S7. •
223.4
0.72
4
Hall
ISH8J :
341.4
0.39
4
Hall
1876.60
228.7
1.01
4
O. Strove
I.S76.6I
-'16.0
M v;
4
Dembowaki
' -- . M
:;;,: •"
4
Itiiriihain
issg H
:;:.! i
" H
3
Holiiaparvlli
^77.47
'..0
—
1
Seabroke
IX.S9JB
0.6
0 :i
4
Hall
1 -77 56
234.3
1.10
2
O. Strove
1X77.59
1877.59
227.9
232.8
5
2
S-liiapan-lh
Hall
1890.38
1890.55
9.4
13.2
0.51
1
4
Kuriihani
Hall
1877.62
229.9
4
Dembowski
1890.78
15.0
0.57
3
S-liia]iari-lli
1878.45
234.9
1.05
6
Bum ham
1891.55
21.4
0.6
2
Schiaparelli
2
Hall
1891.57
24.8
0.54
4
Hall
1878.64
1 17
1
0. Strove
1891.60
M4
0.90
3
Bigourdau
1879.45
0.90
5
Burnham
1892.58
!•:• 1
0.83
4
Comstock
1879.55
239.5
0.97
3
Hall
189L' .r,-_»
30.3
0.87
:. 1
S-liiaparclli
1879.75
84 -
^_
11
Seabroke
.'.63
0.90
1
BiKourdan
1892.65
31.6
" -I
4
Hall
1880.46
0.7?
5
Schiaparelli
1880.47
u i.v.i
7
Burnham
18H
36.0
,,..„,
1
Bigourdan
1880.65
IM :
1.00
4
Hall
1891 1.:
41.1
1 . 1 ;i
7
Baniard
IM 1
1.18
3
Frisby
189 1 »•-.
38.0
0.95
4
Hough
1881.11
252.1
0.92
5
Bumham
1894.54
38.7
1.17
3
Stone
1881.52
M4J
0.87
3
Hough
1804.77
41.6
1.16
3
Comstock
ISM
249.1
1.01
1
Hall
1888J4
41.2
1
M8J
0.70
4
Hall
; | .:. 1 1
44.0
1.3?
2-1
Schiaparelli
•".."••
M i
—
1
II. Strove
44.4
1.16
:
Comstock
I>M
L'f.i :
•"'•'
3
igb
U i ;..
43.7
1.13
2
-••
1.03
1
O. Strove
1X95.73
43.4
1.34
1
...
1882.60
... |
—
7
Schiaparelli
1896.73
44.8
1.10
2-1
Moulton
HERCULIS BC = A.C. 7.
In July, 1856, ALVAN CLARK discovered that the bluish companion of
pHerculis = 2' 2220 is a close double star; he estimated the magnitudes of
the component to be 10 and 11. The object was first measured by DAWES
who predicted the binary character of the system; by repeating his observa-
tions in 1859 and 1864, he was able to announce a decided orbital motion. The
object has since received considerable attention from the best observers, and
the material now available for an orbit is sufficient to define the elements in a
very satisfactory manner. Owing to the faintness and difficulty of the pair,
the measures must be carefully combined in order to get a satisfactory set of
mean places; the distances of some observers are notably too small, and hence
they are omitted in forming the yearly means. Most of the early observations
of DAWES seem to be affected by sensible errors, and hence we give his work
in full.
t
&
P.
O
ff
1857.472
58.97
1.853
1857.562
60.08
1.75 ±
1859.650
58.91
2.304
1859.691
59.51
1.422
1859.757
62.02
2.040
distance indifferent
observation very poor
difficult in distance
1864.431 77.59 1.806 undoubtedly binary
While measuring the wide pair in 1857, he observed that " the stars B and
C certainly point rather to the north of /*." He gives the angle of /n Ilerculis
relative to B C as 242°.2; and hence we gather that the angle of the pair BC
must have been at least 63°.0. Since the allineation of the two faint stars with
p, Ilerculis would probably be more exact than even micrometer settings, it
seems certain that most of DAWES' measured angles are too small; we have
therefore chosen certain nights only in making up the means, and have selected
the distances with some regard to the subsequent motion of the star. This
selection of DAWKS' material is necessary in order to represent satisfactorily
the whole series of observations by an orbit based on both angles and distances.
The following list gives the elements published by previous computers:
p
T
e
a
Q
{
A
Authority
Source
yr».
+ 54.U5
+45.39
+48.65
ll'.O'.l
1877.13
1880.142
1839.585
1880.43
0.3023
0.2139
0.14853
0.16922
1.46
1.369
1.2807
1.356
57.95
62.11
63.38
r,i'.<;.-5
60.72
67.01
65.18
63.82
156°35
181.97
182.05
183.87
Doberek, 1879
Leuschner, 1889
Celoria, 1890
Hall, 1894
A.N., 2287
Pub. A.S.P.,p. 46
A.M., 2949
A.J., No. 324
I
HBRCULI8 BC = A.O. 7.
20]
We find the following elements of ft1 Iferculitt
P — 45.0 years
T - 1879.80
Apparent orliit :
a - T.390
ft - 61°.4
i - 64". 2.S
X - 180°.0
* - + 8".0
th of major axis — 2".78
ili of minor axis *» 1*.148
Angle of major axis «- 61°. 4
,•!<• of |H-ria.stron — 241°. 4
Distance of star from centre — 0".3O4
The |M ri.'il here ^ivi-n can hardly be in error by more than one year,
while the uncertainty of the eccentricity probably does not surpass ±0.02.
The elements are therefore well defined, and may indeed be regarded as
extraordinarily good for an object of such difficulty.
COMPARISON or COMPUTED WITH OMEKVKH PLACES.
(
».
«r
p.
P.
,. „
fr-ft
M
ObMrven
*
•
|
1857.47
61.8
1.69
+ 1.2
—
1
DMTH
60.1
1.75 ±
1.69
-1.9
+0.06
1
Iteww
62.0
SftJ
!.;:<
1.65
-4.9
+0.08
1-2
Dawes
. - !
t.64
1.63
-0.7
+0.01
1
(). Htmve
! H I B 1
1.50
1.46
+3.2
+0.04
1
(). Struve
[964 M
78.2
81.1
1.76
i .;••
-2.9
+ 0.46
2-3
I».i\vi-s 1 ; KiiirN-inaiin " 1 ; Winii. 1
1865.44
81.3
84.9
1.55
1.20
-3.6
+0.35
: i:
Knott 2-1 ; IX>mbuwKki 5
1H66.68
NJ
91.2
1.10
1.05
-1.7
+0.05
2
( ). Struve
95.4
97.2
0.94
-1.8
—
4
S.-.irl« 3 ; WinWk t
102.0
105.1
0.82
-3.1
+0.06
2-1
<). Struve 1 ; Winl<x-k 1-0
121.3
118.0
—
0.69
+ 3.3
—
3
Winlock 1 ; 1'cin-e 2
W71
;:.,. .
148.5
0.62
<>.:.;
+ *.:?
+0.05
1
O. Stmve
l U B
0.68
0.60
+ :{.:.'
+0.03
1
O. Struve
i»;i ix
._.„._. ,
0.70
+ l.;i
+0.06
1 'I
amb
1 lx
+ 4.L'
+0.:ir,
VI :•
S-h. I", ii; H:ill :. .'{; II. .Men 1
l x;»>.62
•_•!•.•. 7
0.93
L9
-0.07
x !•_•
Hall 4: 'C " 1 : l»-'iiil»'«r.ki 4
1.00
+•.'.«;
-O.o 1
OJ '.': S.I,..-, it; Hull 2; iK-m. 4
1 x7X.60
1.11
+ 1.6
+d
8-7
ft. li; Hall I' 0; 'C.H 1
I x:9.SO
_..;.,,,
0.94
1 MS
-0.7
-0.14
19-8
/?..-.: Hall :<; S.-al.mk.- 11-0
140 -'
M0.9
1.05
i «•:
+<»..-<
-0.02
11
fi. 7: H:ill 4; I
1881.49
..-„,,
25i ii
-0.4
-0.06
10
ft. 5; Hall -.
1 xs-j.56
:••;] •_•
258.0
,,.,;
Ojt
+ .T'.'
+0.01
18-6
111.4 i'; H.1.1 ". II---:. "^ •:. S.h.7 n
1883.64
.' ! J
-2.0
-0.05
I-. ~
/3.3; H».:{;lll i.vL': S-l,..', O
L8M M
ir&fl
+0.03
4-1
Hall 3-0; O2 1
1885.56
.-"
--..
0.65
..:,
+ 0.23
5-4
Hol.-t.s, l,.-k 2-1 : Hall 3
sow
0.39
OM
-3.4
-0.19
.-.
Hall
1887.56
,,,.,
tu i
0.4'J
M.-/,
-4.5
-0.06
- ^.an-lli «-.-,; Hal!
1888JJ7
.!J.:
.it . -
0.44
DM
-1.5
-0.14
1.-. 11
Tarranto •_•; s, •!,. 11 ;•; Hall 4-0
;sx • ",s
.:.:•:;
0.57
......
-1.4
-0.09
8-7
ft. 4 ; Strhinpan-lH 0-3 ; Hall 4 <•
1890.57
iu
11'"
.•::
+0.5
-0.13
11-7
ft. 4 ; Hall 4 -0 ; Sc-hiaj-an-lli 3
•1.57
22.5
D.90
0.87
+ O.S
+0.03
''
Srhiaion-llia-O; Hall 4-0; Big. 3
30.4
.••:>
,,,•,
1.00
• .. :.
-0.11
14-5
(•.,!,, 1 ii:8ch.5-4; Big. 1 ; Hall4-O
36.0
. , i
••••"
1.11'
-0.22
1
Hi^ourdan
18W BB
•• :
LIT
+ 0.2
-0.06
17 i:t
Bar.7; Ho.4-0; Stone 3; Com.3 [See 1
I-..-.:.:.
i . :
i .:,
1.34
1.33
-0.2
+0.01
9-1
See 1-0; Hch.2-0; Com.3-O; 8nS-0{
T OPHIUCHI = ^2262.
We remark the star is now wider than most observers have indicated by
their recent measures. The distance for 1895 is based upon two nights' work,
one of the observations being taken by SCHIAPARELLI, the other by the writer
at Madison and accidentally omitted in Astronomical Journal, No. 359. This
observation is:
1895.732 43°.2 1".34 In See
The images are noted as "good but faint." There is no doubt that the
distance is now at least 1".3, and it will increase for some years. Observers
should follow this system carefully. The following is an ephemeris:
1896.60
1897.60
1898.60
6*
47^0
49.9
52.6
PC
1A3
1.51
1.58
1899.60
1900.60
55. 1
57.5
PC
1.63
1.67
OPHIUCHI = 2 2262.
a = 17h 57"'.6
5, yellowish
8 = —8° 11'.
6, yellowish.
Discovered by Sir William Herschel, April 28, 1783.
OBSERVATIONS.
t
0,
Po
n
Observers
t
do
Po
n
Observers
O
u
O
If
1783.34
331.6
elong.
1
Herschel
1843.11
224.6
0.80
-
Kaiser
1802.74
360 ±
elong.
1
Herschel
1843.54
1843.61
228.8
229.0
0.80
0.95 ±
11
2
Mtidler
Dawes
1804.44
360 ±
eloug.
1
Herschel
1844.34
229.8
0.79
2
Madler
1825.71
176.0
cuneata
1
Struve
1844.74
218.7
0.79
1
Challis
1827.28
146.0
oblonga
1
Struve
1845.65
232.4
0.87
1
0. Struve
1835.68
192.9
0.35
6-2
Struve
1846.22
239.5
1.00
—
Jacob
1836.62
199.9
0.44
5
Struve
1846.51
229.4
0.78
8
Mitchell
1837.70
200.8
0.35
1
Struve
1846.69
230.7
0.97
2
0. Struve
1840.51
223.1
0.94
1
O. Struve
1847.82
233.9
0.97
1
0. Struve
1840.68
221.5
0.88
4-1
Dawes
1848.10
229.7
1.18
2
Mitchell
1841.53
217.3
0.75
8
Madler
1848.66
232.7
1.01
1
Dawes
1841.60
228.1
0.87
3-2
0. Struve
1841.66
225.7
0.79
5-1
Dawes
1850.77
234.0
1.0
21
Jacob
1842.57
225.6
0.77
5
Madler
1851.66
239.4
1.0
Fletcher
1842.64
226.9
—
1
Dawes
1851.67
238.2
1.19
1
0. Struve
- ..run . in .1 •_••>.•_•
1
f*
p*
m
y -• ' . : •
i
0.
ft
M
Observer*
> ,.-...-.
-• -• •
MO
2
Jacob
l» 70.04
247*3
1.43
8
IV»nibowaki
:- .:< •
239.7
1.23
2
I8TO.T1
1.26
1
Dun^r
: •».-,-.' •
. - •.
1.27
4-3
Midler
1871.66
251.0
1.31
o
Dunrfr
1853.79
- > .:
1.17
4
Midler
187-' "1
247.8
I :,:,
I
Detnbuwiiki
1854.67
'_
1 •_"_•
1
Dawea
1H72.58
248.1
1.69
1
O. Struve
1854.70
1854.74
- • 1
1.20
i M
1
1
O. Struve
Midler
1873.54
MM
2.12
1
Leyton Obs.
1855.49
: - !
1.30
..
Dembowski
1874.08
248.5
1.60
8
Deiiibownki
L8B&M
1 -J7
1
Secchi
1874.57
250.7
1.48
1
Ley tun Obit.
MO i
• >
O. Struve'
1874.67
251.1
1.63
1
O. Struve
L866J4
240.7
LM
I
Secchi
1875.61
LMS'.i
1.61
8
Si-lii.i|i:m-lli
], ,. '.s
MOJ
i j"
6
Dembowski
1876.02
249.3
1.67
10
IV'inbowiiki
1856.62
LM
1
Winnecke
1876.60
247.6
1.73
3
Srl,l.l|,:irrlli
1857.55
1.26
3
Secchi
1876.62
250.4
2.05
1
Stone
1857.63
241.4
LM
4
Dembowski
1876.64
251.1
1.72
3
Hall
67
MM
1 it
o
0. Struve
187647
LMS.1!
1.78
1
Waldo
1858.20
243.6
i n
_
Jacob
1876.70
246.5
1.58
1
O. Struve
•• 1 1 s
1.20
1
Dmbowski
1877.55
249.0
1.53
4
Hall
^64
l.-'U
.:
Midler
1877.61
250.5
1.90
-v
Cincinnati
185X.71
240.9
1 17
1
O. Struve
1877.66
248.6
1.64
7
S-liiapiirrlli
1859.63
Mi.7
LM
1
O. Struve
1878.02
250.4
1.72
8
Detubuwski
1K00.77
Ml (
1.30
1
Secchi
1878.52
254.1
1.69
2
Dolwrck
1861.60
244.4
1.29
3
Madlcr
1879.35
247.9
1.63
O
m
Hurnhaiii
1861.63
242.9
1.43
1
O. Struve
1879.41
250.1
1.78
26-25
Cincinnati
1868.05
244.6
L40
13
Dembowski
1879.72
250.3
1.74
5
Schia|>arelli
1863.57
1.20
4
Knott
1880.07
249.7
1.78
3
Cincinnati
1864.17
247.8
1.92
2
Englemann
1880.65
1880.66
251.6
251.1
1.80
1.64
6
2
Schiaparelli
Hall
1865.52
M8 i
1.1"
-
Kaiser
1880.67
252.2
1.89
3
Jedrzejewicz
186MQ
i M
1-2
Leyton Obs.
1881.55
•j:.i :;
1.71
3
Hall
186.-
'.Ml 1
i :.i
1
0. Struve
1881.79
262.7
1.67
Smith
I86BLM
MM
1.4-'
18
Dembowski
1882.49
252.0
LQ6
3
11 C.Wilson
1866.43
246.3
1.66
3-2
Leyton Obs.
1882.54
1.73
3
Hull
1866.58
1866.59
247.5
247.7
2.48
1.65
3-2
2-3
Winlock
Searle
1882.60
1889
250.8
1.86
2.13
7
1
Schiaparelli
0. Struve
L866J -
243.3
1.75
1
O. Struve
247.6
1.60
2
Secchi
1883.38
•_•.-. t :.
1 fU
1 .(rt
9
Englemann
188;: :.l
•J.VJ 1
1 1 .1,
3
Perrotiu
1861 M
251.5
2.49
2-1
Winlock
1883.53
2-1
H. C.Wilson
1867.96
Ml 0
1.43
1
Dembowski
l.Vt&M
253.8
1.60
1
Seabroke
1868.57
247.6
i N
3
C.-S. Peirce
1883.58
1.7*
5
Hall
1868.58
Ml i
—
1
Leyton Obi.
1883.61
252.0
1.83
6
Schiafiarelli
1868.61
MM
1.44
1
Winlock
[86841
n i •>
1.79
3
Jedrzejewicz
:-. UN
Ml i
—
1
Leyton Obs,
1884.41
M |
1.94
1
H.C.Wilson
: 1
I ! - |
1 .11
1
Duner
1884.60
• I
1.82
3
Hall
1869.73
MM
1.41
1
C. 8. Peirce
1884.78
251.6
1.74
I
Schiaparelli
204
T OPHIUCHI = 2 2262.
1
«,
Po
n
Observers
t
00
Po
n
Observers
O
W
O
a
1885.48
258.1
1.79
3
Tarrant
1890.57
254.6
1.78
1
Hayn
1885.56
253.5
1.66
4
Hall
1891.48
257.6
2.0 ±
1
See
1885.57
251.2
1.76
4
de Ball
1885.58
256.0
2.01
5
Jedrzejewicz
1892.65
255.2
1.75
4
Scliiaparelli
1892.58
254.6
1.78
4
Conistock
1886.22
1886.54
1886.62
254.8
254.0
256.2
1.98
1.67
1.85
7
4
6
Englemann
Hall
Jedrzejewicz
1893.50
1893.70
254.1
254.7
1.81
1.83
3
1
Maw
Bigourdtta
1887.09
1887.57
252.0
252.5
1.72
1.81
4
4
Schiaparelli
Hall
1894.59
1894.77
1894.78
254.4
254.7
253.2
1.88
1.64
1.91
2
3
1
Glasenapp
Comstoi-k
Bigourdan
1888.56
1888.61
253.1
254.4
1.70
1.71
5
4
Hall
Schiaparelli
1895.56
1895.58
256.1
255.4
1.78
1.98
3
2
Schiaparelli
Collins
1888.71
255.2
1.80
3
Maw
1895.59
253.4
1.94
5
Schwarzschild
1889.57
255.6
2.23
2
Glasenapp
1895.72
254.7
1.86
4
See
1889.68
253.5
1.69
1
Schiaparelli
1895.72
257.8
1.90 ±
2
Moulton
Since the discovery of this double star in 1783, the radius vector of the
companion has swept over an arc of 285°. But while the length of the arc
would ordinarily be sufficient to fix the character of the orbit, it happens un-
fortunately in this case that the observations are neither very consistent nor
very well distributed over the arc; and since by far the greater number of
observed positions lie in the sixty degrees described since 1836, a satisfactory
determination of the elements is embarrassed by difficulties of a somewhat
formidable character. But when we examine HEKSCHEL'S angle of 1783 in the
light of his remarks, there seems to be every reason to regard it as fairly
correct. In his notes on the observation ofrOphiuchi, he says: "The closest
of all my double stars can only be suspected with 460, but 932 confirms it to
be a double star. It is wedge-formed with 460; with 932 one-half of the small
star, if not three-quarters, seems to be behind the large star. The morning is
so fine that I can hardly doubt the reality; but according to custom, I shall
put it down as a phenomenon that may be a deception." If we depend on the
approximate accuracy of HERSCHEL'S earliest measure, and deduce the areal
velocity from the most recent observations, where both angles and distances
can be relied upon, we are led to an orbit which will not differ greatly from
the truth. The following orbits have been published by previous investigators:
p
T
e
a
Si
t
I
Authority
Source
87™036
120.0
185.2
217.87
1840.07
1824.8
1820.63
1818.50
0.03746
0.575
0.5818
0.6055
0.8178
1.111
1.193
O /
65 5
130 0
69 31
67 1
o 1
51 47
48 30
53 6
46 8
14540
146 6
2835
3626
Madler, 1847
Hind, is in
Doberck, 1877
Doberck, 1877
Fixt. Syst., 1, 255
M.N., IX, p. 145
A.N., 2037
A.N., 2041
- . mm . in = £2262.
We find the following elements of T
P
T
: « , .
- 1815.0
- 0.592
- T.2495
8
i
X
76T4
18°.05
+ 1'.5652
Apparent orbit:
Length of major ui* — 2*.46
Length of minor axis -» 1'.09
Angle of major axis — 80*.0
Angle of periastron *» 868.8
Distance of star from centre — 0*.712
The accompanying table shows that this orbit gives a very satisfactory
representation of both angles and distances.
or COMPUTED WITH OBSKRVKO I'LACKS.
t
0.
A
P*
P*
, ,
Pr-f,
•
OBMfWI
,.j.34
. . . i |
313 7
t
0 7 •'•
4-17 Q
I
1
Herschcl
1JUV' " 1
•!,:i| -i-
• i v
M I'l
' II-.'
•ii a
1
I I •• fxl • ) 1 1 *1
i ^* _ i *
I -"1 1 1
• r
• ' 1
1 1 ]
' -
0.51
1 '. ".
A
1
I 1 • I T « 1111
1 1 fT^i'llt'l
l.'.l II
l-'.l 8
oM«w»
- 3.6
__
2
Strove
U I6LM
192.&
•jn :•
".;:,
0.61
-18.3
-0.26
St ruve
18."..
,.,.,.,
DM
-13.9
-0.20
5
Strove
r.ro
216.6
o ..-.
0.88
-15.8
-0.33
1
Strove
1840.60
•-".'I'.;*
0.91
0.78
± 0.0
+0.13
5-2
O. Strove; Dawea 4-1
1841.60
i.'" i "
0.82
- 0.5
-0.02
16-11
MadlerS; OS. 3-2; l)awes 5-1
1842.60
226.2
:••_•:. ;
0.77
0.84
-I- 0.5
-0.07
Madiera; Dawes 1-0
1843.41
227.5
•-'L'T.il
+ 0.5
-0.03
12 +
Kaiser — ; M&dler 1 1 ; Dawes 2
LM4LM
0.79
0.91
+ 1.5
-0.12
2-3
Madler2; Challis 0-1
184
+ 2.5
-0.08
1
O. Strove
1841
28Q -
+ I.' I
-0.06
10 +
Jacob—; MilchellS; 'C.I'
is;
.03
+ 1.5
-0.05
1
ruve
1 > 18.66
.01
n|
- 0.5
-0.03
1
Dawes
.10
- 1 •-'
-0.1»>
Jl : -
Jacob
.....
.18
4- .
-0.04
1 +
Kl«-t<'her — ; <C 1
239.3 -
.L'o
.1C,
+ S
+ 0.1 • I
8-7
Jacob 2; O£.2; Madler 4-3
1H53.71»
.17
.r.i
+ H.7
-O.iiL-
4
Midler
1854.70 237.4 -
.17
32
- I.I
-0.05
5
Dawes 1; 'M 1 : Midler 3
1855.57 |2.-:-
'-':w.l
.28
•Ji
- 0.6
+ 0.«>l
7
Dembowski3; Sw-.-hi:-. "± .'
1856.48
240.6
239.7
.23
.26
+ 0.9
_».
11-10
Seech i 4 ; Dembowski 6 ; Winn. 1
1857.62
240.4
240.5
.30
.30
- 0.1
±0.00
9
Seoohi 3 ; Dembowski 4 . ' O .'
1858.52
241.7
241.1
.35
1.32
4- 0.6
+o.o:<
10 +
Jacob—; Dem. 6 ; Madler .:. -C 1
IvV. ,, .
242.7
241.8
.64
.34
4- 0.9
+0.30
1
O. Strove
1860.77
Mfl S
242.6
.30
.37
4- 3.2
-0.07
1
Seech i
ISfil.'.'J
243.7
243.3
.36
.39
4- 0.4
-0.03
4
Midler :<: "V ,
_• i -• :.
243.9
.30
.42
4- 1.6
-0.12
17
Dembowski 13 ; Knott 4
ISM i;
,\: *
•-'•l.r.
.92
.45
4- 3.2
+0.47
2
Knglem&nn
1865.68
-1.. '.
.47
4- 1.3
-0.08
! i \r>
Kaiser - ; Ley. 1-2 ; 0£. 1 ; Dem. 13
»•.'
4- 0.9
+0.17
8
Ley. 3-2 ; Wk. 3-0 ; 8r. 2-3 ; O£. 1 ;
18677:
18
JU
+ 2.5
-0.08
11-9
\Vinlock2-0; Dembowski 9 [Sec. 2
s.59
141 <
.:i;
4- 1.2
-0.16
4-3
Peirce3; Ley ton 1-0; Winlock 1
247.0
U
:.:,
4- 1 .:
-0.14
7
Leyton 1-0; Dun«fr 6; Peirce 1
1870.37
M9.0
247.3
.35
: .-.-;
4- 1.7
-0.21
9
Dembowski 8; Do4r 1
206
T OPHIUCin = ,£2262.
t
e.
Oc
P«
PC
6.-Oc
P.— PC
n
Observers
1871.66
251.0
248.0
1.31
1.59
+3.0
-0.28
2
Dune"r
1872.30
248.0
248.3
1.62
1.60
-0.3
+ 0.02
9
Dembowski 8 ; O2. 1
1873.54
248.9
248.8
2.12
1.62
+ 0.1
+ 0.50
1
Leyton Observers.
1874.44
250.1
249.1
1.57
1.63
+ 1.0
-0.06
10
Dembowski 8 ; Leyton 1 ; 02. 1
1875.61
248.9
249.6
1.61
1.65
-0.7
-0.04
8
Schiaparelli [02. 1
1876.54
249.6
250.0
1.75
1.67
-0.4
+ 0.08
17-19
Dem.10 ; Sch. 3; St.l ; HI. 3; Wdo. 1 ;
1877.61
249.4
250.4
1.69
1.68
-1.0
+0.01
19
Hall 4 ; Cincinnati 8 ; Schiaparelli 7
1878.27
250.4
250.6
1.71
1.69
-0.2
+0.02
8-10
Dembowski 8 ; Doberck 2
1879.49
249.4
251.1
1.72
1.71
-1.7
+ 0.01
33-32
ft. 2 ; Cincinnati 26-25 ; Sch. 5
1880.51
251.1
251.5
1.78
1.72
-0.4
+ 0.06
14
Cin. 3 ; Sch. 6 ; Hall 2 ; Jed. 3
1881.67
252.0
251.9
1.69
1.74
+ 0.1
-0.05
5
Hall 3 ; Smith 2
1882.56
252.1
252.2
1.88
1.75
-0.1
+ 0.13
14-13
H.C.W.3; H1.3; Sch.7; 02. 1-0
1883.53
252.8
252.6
1.84
1.76
+0.2
+ 0.08
17-28
En.9; Per.3; H.C. W.2-1; Sea.l; H1.5;
1884.60
252.7
252.9
1.83
1.77
-0.2
+0.06
10
H.C.W.l; H1.3; Sch.6 [Sch.6; Jed. 3
1885.55
253.5
253.2
1.81
1.78
+ 0.3
+0.03
13-16
Tar. 3 ; Hall 4 ; deBall 4 ; Jed. 5 '
1886.46
254.4
253.6
1.83
1.80
+0.8
+0.03
11-17
Englemann 7 ; Hall 4 ; Jed. 6
1887.33
252.3
253.9
1.77
1.81
-1.6
-0.04
8
Schiaparelli 4 ; Hall 4
1888.64
254.2
254.3
1.75
1.82
-0.1
-0.07
8
Hall 5 ; Maw 3
1889.57
255.6
254.6
2.13
1.83
+ 1.0
+0.30
2-1
Glasenapp
1890.57
254.6
254.9
1.78
1.84
-0.3
-0.06
1
Hayn
1891.48
257.6
255.2
2.±
1.85
2.4
+0.15±
1
See
1892.58
254.6
255.5
1.78
1.85
-0.9
-0.07
4
Comstock
1893.50
254.1
255.8
1.81
1.86
-1.7
-0.05
3
Maw
1894.68
254.5
256.2
1.76
1.87
-1.7
-0.11
5
Glasenapp 2 ; Comstock 3
1895.72
256.2
256.5
1.86
1.88
-0.3
-0.02
6^
See 4 ; Moulton 2-0
The following is an ephemeris for the next five years:
t
1896.50
6c
256.7
PC
1.88
1897.50
257.0
1.89
1898.50
257.3
1.90
t
1899.50
1900.50
2576
257.9
PC
1.90
1.91
It will be evident from what has been said that this orbit is still open to
some uncertainty, but a material improvement in the elements will not be
possible for many years. Since the companion is at present nearing the apas-
tron of the apparent ellipse, the motion will continue to be very slow; yet the
pair will still be worthy of occasional attention from observers. While the
period found above is perhaps uncertain to the extent of 15 years, it does not
seem probable that the eccentricity can be in error by more than ±0.05. Ac-
cordingly there is no probability that even the lapse of ages will radically
change these elements of r Ophiuchi.
70 OPIIIUCIII = .1 •-••-•:•-•
1MT
Tonl'llll < III S2272.
a - 18» 0».4 ; « = +»• S3'.
4.5. yellow ; 0, purplUb.
*y Sir William Hertfkel, Auyiut 7, 1779.
OBUBVATIONH.
t
9.
^
n
OtMrven
t
9.
P.
n
OtMrrrera
O
•
o
i
177'.' 77
.„,
—
1
hi'l
1836.42
128.9
i. n
8
M feller
17>! 71
i i:.
1 V
Henrhfl
1836.51
127.7
6.48
4
Encke
1836.52
129.5
6.34
5
liessel
1802.34
.: :
—
1
Herschel
L88&M
129.5
6.15
8
Struve
1804 IV
til I
—
2
Herachel
1837.13
127.7
6.47
3
Dawes
1819.64
l§l g
_
5
Struve
1837.46
ivs.'i
6.74
4
Kncke
1837.60
127.5
6.46
16
: •
!N-'"::
160.2
^m
2
Struve
1837.72
128.0
6.15
4
Struve
1 s"1 71
1 ^ — i . 1 ^
157.6
—
5
Struve
1838.57
126.6
6.64
7
Galle
IV
154.8
LSI
2
H. and So.
1889.52
125.2
6.78
2
Oalle
1-VV.64
L58J
—
3
Struve
1839.65
125.9
2
Dawes
!-. • -
1825.57
148.1
1 t- V
4.76
Ufl
14
14
South
Struve
1K40.35"
1840.48
128.0
126.6
6.00
10
Kaiser
O. Struve
1827.02
145.1
4.37
2
Struve
1840.59
124.9
6.63
4
Dawes
1828.58
140.6
6.37
1
Herachel
1841.50
125.4
6.40
8
Midler
1828.71
140.2
4.78
4
Struve
1841.65
123.4
6.54
5
Kaiser
1829.59
1829.60
138.1
140.6
5,08
g
i
Struve
Herschel
1841.68
1841.74
123.4
123.8
4
7
Dawes
Be. and ScL
184V .'H
125.1
6.63
8
0. Strove
> - -.
138.2
6.01
g
Herachel
1843
124.6
6.25
3
Midler
1830.50
18BJ
5.47
10
Bessel
1849
.. n
2
Dawes
1830.57
g n
6
Dawes
184 V.v.i
ivv r.
6.48
vv
Kaiser
1830.84
135.7
5.31
2
Struve
1842.60
IS8J
.. 7'.'
18
Schlater
1831
; ...:.
.-.-'I
8-6
Hersrhel
1843.47
IVV"'
^_
1
Dawes
1831.53
134.0
gjg
7
Bessel
184
1V1 1
8.70
.;
Kncke
1831.68
134 7
5.41
5
Strove
1 x 13.58
123.1
6.44
16
Madler
1832.55
133.8
6.71
3
Dawes
1844.36
IV" 7
6.84
g
Encke
183V
135.4
:. . 1
4-3
Herachel
1844.52
122.0
g i-
g
Madler
1832.69
133.0
6.79
g
Bessel
1845.43
UM •>
.. 77
I
Hind
1833.1V
6.14
i
Dawes
1845.48
1V1.0
g
O. Strove
1845.54
OM
g n
16
Madler
1834 17
1 •' ' 1 1
4
Strove
1884.7-7
: •".
6.13
7
Dawes
1846.25
120.2
6.83
1
Jacob
1834.61
g • ;
7
Bewel
1846.46
120.1
6.14
7
Hind
1846.56
117.1
7.43
In
Durham obs.
1835.60
180 7
6.11
g
Strove
i.s46jg
119.8
10
Madler
208
70 OPHIUCHI = .T2272.
t
60
Po
n
Observers
t
&
Po
71
Observers
O
a
O
/f
1847.25
120.5
6.56
4
0. Struve
1857.13
110.6
6.45
3
Jacob
1847.45
117.2
7.19
—
Durham obs.
1857.41
112.5
6.19
1
Wiunecke
1847.59
120.3
1
Mitchell
1857.51
110.4
6.20
4
Secchi
1847.60
118.5
6.79
8
Madler
1857.68
110.3
6.52
2
Dawes
1857.64
109.5
6.25
4
Dembowski
1848.12
118.8
6.80
3
Dawes
1857.67
110.2
6.15
2
Morton
1848.49
118.4
6.84
4
Madler
1857.69
110.1
6.40
4
0. Struve
1848.52
118.0
6.8
2
Bond
1858.12
109.7
6.10
3
Jacob
1849.39
118.1
6.64
5
O. Struve
1858.39
108.6
6.08
2
Morton
1858.44
109.3
6.04
4
Dembowski
1850.42
116.8
6.88
8
Radcliffe
1858.63
108.9
5.83
9
Madler
1850.49
115.2
6.86
2
Worster & Ja.
1850.64
116.7
6.94
4
Madler
1859.30
109.0
6.20
5
0. Struve
1850.66
117.0
6.46
4
Fletcher
1859.72
109.3
6.24
4
Dawes
1859.75
109.0
6.44
5
Auwers
1851.20
115.2
6.65
4
Madler
1859.76
107.8
6.10
5
Powell
1851.58
115.8
6.38
8
Fletcher
1859.80
107.0
6.25
1
Madler
1851.67
115.4
6.34
5
0. Struve
1851.73
115.5
6.67
7
Madler
1860.61
106.3
6.07
3
Secchi
1860.74
109.0
6.41
-
Luther
1852.63
116.0
6.36
6
Fletcher
1860.76
106.7
6.52
5
Auwers
1852.67
115.0
6.55
5
0. Struve
1852.71
114.7
6.56
11
Madler
1861.46
107.0
5.89
1
Kadcliffe
1852.74
114.0
6.73
15
Jacob
1861.69
106.6
5.92
7
Madler
1861.74
106.0
6.21
6
Auwers
1853.55
113.6
9
Powell
1861.81
105.4
5.8
3
Powell
1853.55
116.5
6.36
6
Dembowski
1862.40
105.6
5.86
3
O. Struve
1853.62
114.6
6.49
6
Dawes
1862.55
106.0
6.05
1
Winnecke
1862.62
105.5
5.72
9
Dembowski
1854.08
113.6
6.36
21
Jacob
1862.72
105.2
5.69
6
Madler
1854.24
113.0
6.51
2
Jacob
1854.24
113.3
6.51
6
0. Struve
1863.47
104.0
6.07
11
Adolph
1854.64
113.4
6.23
12
Dembowski
1863.51
104.1
5.28
2
Secchi
1854.67
113.0
6.27
10
Madler
1863.51
104.2
5.60
9
Dembowski
1854.73
113.7
6.34
3
Dawes
1863.55
104.5
5.76
1
Talmage
1854.78
112.9
3
Powell
1863.58
106.2
5.19
1
Ferguson
1863.64
105.8
5.82
• 5
Hall
1855.03
1855.45
1855.56
115.3
111.6
114.2
6.86
6.25
6.34
2
3
1
Luther
Searle
Winnecke
1864.48
1864.60
104.8
103.5
5.42
5.45
2
11
Englemann
Dembowski
1855.63
112.7
6.33
5
Madler
1865.30
102.6
5.27
8
Englemann
1855.69
113.3
6.47
2
Dawes
1865.51
102.7
5.43
4
Secchi
1855.75
112.4
—
7
Powell
1865.51
102.3
5.35
9
Dembowski
1855.82
—
7.23
1
Schmidt
1865.56
103.9
5.24
2
Talmage
1865.62
100.6
5.31
20
Kaiser
1856.09
111.8
6.44
5
O. Struve
1856.33
111.5
6.40
7
Jacob
1866.13
101.6
5.26
8
Dembowski
1856.50
111.5
6.32
3
Madler
1866.29
101.0
5.29
5
O. Struve
1856.50
112.6
6.40
8
Winnecke
1866.49
101.8
6.26
5
Talmage
1856.55
111.2
6.12
3
Secchi
1866.54
100.8
5.50
4
Harvard
1856.63
111.8
6.38
6
Dembowski
1866.69
101.1
5.27
3
Secchi
;..
-
1
9.
ft
*
' '
(
ft
P.
•
OlMwrvrr*
1867.41
98^1
6.33
1
Radcliffe
1875.82
83J
Ml
9
Dembowdd
1867.44
99.8
5.22
2
KlIHtt
1875.62
84.1
3.44
-
Hchiaparelli
1867.52
• ,, ,
—
1
Talmage
1875.68
M S
. M
4
Hadcliffe
1867.57
1867.57
100.4
99.2
5.10
7
.
Dembowski
1876.48
1876.52
82.1
n i
:: H
3.46
5
Schur
Doberck
1868.47
98.4
: H
7
ibowski
1876.52
1876.54
v,,.,
80.2
3.32
3.55
7
3
IfembowHki
I'liiiiinifr
1MW.57
1H68.72
1868.72
98.5
99.9
101.1
97.6
99.1
; i
:. 11
5.41
4.84
4.69
2
2
1
4
2
KM.. It
Kadcliffe
Talmage
Pui.fr
O. Struve
1876.59
1876.64
1876.64
187640
81.3
81.5
79.7
3.39
3.56
3.27
3.72
6
3
4
1
Schiapurvin
Hall
Jedrzejewicz
Waldo
1868.90
4.92
5
lirUnnow
1877.51
77.6
3.08
8
Deabomki
1877.52
77.6
3.47
2
Doberck
1869.68
100.2
5.31
1
Talmage
1877.55
75.8
3.36
4
Hall
„ ,
4.59
3
Dune>
187748
79.4
3.18
10
Jedrzejewicz
1869.73
98.1
5.12
1
I'ciroe
1877.65
78.5
3.39
8
riummer
1869.91
., -,
4.70
-
Dembowski
1877.66
77.3
3.12
10
Schi.i|Mirelli
1877.68
78.5
3.12
4
Cincinnati
1870.51
94.0
4.4
2
Gledhill
187748
71I..1
3.15
4
Schur
1870.51
94.1
4.55
8
Derabowski
1870.52
94.4
4.62
2
Titlmage
1878.51
1878.54
74.5
75.3
2.96
3.04
7
3
Dembowski
Seabroke
1>71.48
I 0
2
W. &8.
1878.54
75.5
3.03
4
Doberck
1x71.49
HI •
4.42
2
Radcliffe
1878.72
71.9
3.13
4
Goldney
1871.51
4.61
2
Peircc
1879.41
69.2
2.84
18
Cincinnati
1871.53
92.6
4.27
8
Dembowski
1879.50
69.8
2.84
10
Schiaparclli
1871.55
96.7
4.36
1
Talmage
1879.59
71.3
2.93
5
Hall
1871.59
94.9
; 0
3
KM.. It
1879.64
67.9
2.94
5
Cincinnati
1x7164
92.7
4.L>y
3
Gledhill
1879.65
70.3
3.04
4
Seabroke
1871. 7 J
4.20
1
PuMff
1879.66
6A.6
3.01
5
Jedrzejewicz
ix7. i7
91 I
4.19
1
HrQnnow
1880.47
65.8
2.44
3
Doberck
1873
91.5
;j
Ft -r ran
1880.49
62.1
2.69
6
Franz
2
Radcliffe
1880.57
.;:.:,
L'7.-,
6
Hall
lx7J.49
•••• :
4.04
9
Dembowski
188046
..i g
10
Schiaparelli
1872..M
91.5
3
W & 8.
1880.66
•J.7.-,
6
Jedrzejewicz
1872.60
I 8
; M
4
O. Struve
188071
62.7
2
Seabroke
187.1..M
HJ
3.90
1
Gledhill
r.1.7
•j r.i
2
6
Doberck
Hall
1873.51
1873.51
1873.55
88.8
3.89
4.10
3.95
8
1
1
Dembowski
W. & 8.
Talmage
I1.TJ
1881.77
I-.L-.7
•j i.-.
2.45
2
2
Kigourdan
Seabroke
1873.71
4.22
..
Radcliffe
1882.49
2.92
1
Wilson
1882.52
. '. ' .
2.29
2
Dorberck
1874.48
88.8
4.01
4
Radcliffe
1882.57
56.1
2.31
7
Hall
1-71 :.7
3.66
-
Dembowski
1882.61
51.8
2.33
I
Schiaparelli
1874.58
1
T-ilnngci
1882.62
48.8
2.25
4
Jedrzejewicx
1874.69
87.5
1 : •
3
O. Strove
1882.69
51.2
3
Seabroke
1874.73
3.92
1
Gledhill
1882.72
51.6
2.31
4
Euglemaun
210
70 OPHIUCin = £2272.
t
60
Po
n
Observers
t
00
Po
n
Observers
o
If
O
n
1883.49
45.6
2.28
4
Perrotin
1890.42
338.5
2.40
2
Glasenapp
1883.58
40.0
2.36
8
Seagrave
1890.49
338.3
2.42
8
Giacomelli
1883.62
43.7
2.21
15
Schiaparelli
1890.56
335.8
2.13
7
Hall
1883.64
42.2
2.22
6
Jedrzejewicz
1890.61
336.5
2.01
3
Maw
1883.68
45.2
2.51
3
Kiistner
1890.61
336.6
2.16 •
1
Wellmann
1883.68
44.0
2.30
3
Seabroke
1890.70
334.8
2.02
6
Schur
1883.72
43.6
2.25
6
Englemann
1890.70
334.9
2.22
16
Bigouvdan
1890.73
336.1
2.15
9
Schiaparelli
1884.41
37.6
2.30
1
Wilson
1884.53
35.9
2.18
1
Pritchett
1891.54
328.3
2.11
4
Maw
1884.56
34.5
2.09
6
Perrotin
1891.56
327.5
2.23
6
Hall
1884.59
37.6
2.16
7
Hall
1891.58
329.1
2.16
6
Schur
1884.62
35.3
2.07
8
Schiaparelli
1891.59
326.0
2.33
6
Knorre
1884.69
35.2
2.20
5
Englemann
1891.60
328.5
2.15
6
Schiaparelli
1884.70
34.8
2.45
3-1
Seabroke
1891.63
327.2
2.37
2
See
1885.50
26.0
2.08
4
Perrotin
1891.65
326.7
2.21
9
Bigourdan
1885.55
25.1
1.97
4-2
Sea. & Sin.
1892.37
321.9
2.28
4
Buraham
1885.57
29.5
1.88
7
Hall
1892.41
320.5
2.36
1
Collins
1885.64
24.3
2.07
8
Englemann
1892.49
321.7
2.26
3
Maw
1885.65
26.5
2.07
2
Schiaparelli
1892.57
321.3
2.19
4
Comstock
1885.71
23.4
2.19
5
Jedrzejewicz
1892.62
319.3
2.25
5
Bigourdan
1886.53
13.8
1.98
7
Hall
1892.64
321.0
2.24
6
Schur
1886.56
15.3
1.97
7
Perrotin
1892.65
320.3
2.22
17
Schiaparelli
1886.66
1886.66
1886.67
1886.67
13.7
14.1
14.8
15.6
2.01
1.81
1.88
2.01
7
14
7
4-2
Jedrzejewicz
Schiaparelli
Englemann
Smith
1893.47
1893.58
1893.62
1893.62
313.8
313.4
313.6
312.5
2.22
2.41
2.27
2.34
3
3
4
5
Maw
Tucker
Schur
Comstock
1887.55
359.6
1
Smith
1893.69
309.2
2.22
1
H. C. Wilson
1887.61
3.6
1.92
6 •
Hall
1893.70
312.3
2.21
11
Schiaparelli
1887.63
4.3
1.87
18
Schiaparelli
1887.81
3.5'
1.91
4
Tar rant
1894.50
309.8
2.47
8
Ebell
1894.54
307.4
2.29
3
Maw
1888.41
352.7
2.07
3
Comstock
1894.59
304.6
2.38
12-11
Knorre
1888.55
354.5
2.17
4
Maw
1894.60
306.3
2.26
4
Schur
1888.57
353.4
2.02
6
Hall
1894.76
302.5
2.30
4
Comstock
1888.62
355.4
2.00
3
Giacomelli
1894.77
301.3
2.45
5-6
Callandreau
1888.64
355.1
1.88
10-9
Schiaparelli
1894.77
303.2
2.21
6
Schiaparelli
1888.65
352.4
2.14
1
Leavenworth
1894.79
302.5
2.33
5
Bigourdan
1888.66
354.7
2.66
3
Copeland
1888.85
353.1
1.92
6
Tarrant
1895.32
298.6
2.22
3
See
1895.50
298.2
2.53
2
Glasenapp
1889.30
348.7
2.16
2
Burnham
1895.51
301.6
2.31
5
Schur
1889.48
344.9
1.60
2
Hodges
18'jr,.:,.-,
298.7
2.14
9
Schiaparelli
1889.50
345.7
2.18
5
Comstock
1895.58
296.9
2.26
4
Maw
1889.57
344.5
2.10
6
Hall
1895.60
297.0
2.35
4
Schwarzscliild
1889.64
346.4
1.96
5
Maw
1895.62
295.0
2.24
5
Hough
1889.70
344.9
1.99
17-16
Schiaparelli
1895.70
296.0
2.01
5
See
1889.77
343.6
1.84
4
Schur
1895.72
296.3
2.01
3-1
Moulton
70 onm nil = 2:2272. 211
Rfurarche* on thf <><!>,'/ •./ 7" Oj,liin>-/,i, mid on a Periodic Prrlnrlxition in tin-
i/ ' ..... / •"'•• Sys/rm Anting fnm n<- Aatio» <•/ ">, f „-..,, /;..-/.,/•
While engaged recently in tin- nh-crvation i»f double stars at the Lcander
McCorniick Observatory of the University of Virginia, I took occasion to
measure 70 O/»// /!/«•/// on three good nights (A. J. 349). On comparing the
results with Scum's ephemeris, four months later, I noticed with surprise that
the observed angle was over four degrees in advance of the theoretical place.
AH the Virginia measures had been made under favorable conditions and with
extreme care, it became evident that even the orbit to which PHOKKSSOK SciiUR
had devoted so much attention would need revision. Accordingly, alter all
tin- nli-, i -Nations had been collected from original sources and tabulated in
chronological order, I proceeded to investigate the orbit in the usual manner,
ami olitained a set of elements very similar to those which BUKXHAM has
Driven in Anfrtmomy and A*lrupby#tc# for June, 1893. On comparing the com-
puted with the observed places there appeared to be a sensible irregularity in
the angular motion; and as the observed places were admittedly exact to a
very high degree, it was impossible to attribute such large and continued
deviations to errors of observation. It was also observed that the sign of
6. — 0, showed a peculiar periodicity; the residuals l>eing for many years
steadily of one sign, and then as uniformly of the other. After making some
unsuccessful efforts to correct the apparent orbit, from which the elements had
been derived by the method of KLINKKRFUES, I decided to project the orbit
found by SCHUR, so as to compare his apparent ellipse directly with the places
•riven by the mean observations for each year. Though I was aware that
S( 111 i:'- orl>it had been based wholly on angles of position, I was not a little
surprised to find that the distances had IK-CM vitiated in the remarkable periodic
manner indicated by the pointed ellipse in the accompanying diagram. Ami
since I had uniformly adhered to the use of both angles and distances in
deriving the orbits of double stars, it was not allowable to violate the dis-
tances as PROFESSOR SCHUR had done, nor could we pass over such remarkable
periodic errors in the residuals of the angles. We were thus confronted with
a case in which it was apparently impossible to satisfy both angles and dis-
tances. A closer examination of the diagram suggested the idea of a periodic
perturliation, alternately in angle and then in <1 and the drawing, in
conjunction with the computations, enabled me to see that the case is one worthy
of special attention. After some delay (A. J. 358) the additional observations
• Agronomical Journal, M.
212
70 OPHIUCHI = .£2272.
placed at my disposal by PROFESSORS HOUGH and COMSTOCK, in conjunction
with the independent measures made at Madison by MR. MOULTOX and myself
(A.J. 359) confirmed the correctness of the Virginia measures, and left no
doubt of the rapid deviation of the companion from SCHUR'S orbit. Before
considering the physical cause of this unexpected phenomenon, I desire to
remark that, in the preparation of this paper, my friend MR. ERIC DOOLITTLE,
C. E., has rendered valuable assistance. He has carried out the calcula-
tions entrusted to him not only with care and accuracy, but also with zeal and
enthusiasm, and has, therefore, contributed in no small degree to the early
completion of this investigation.
Since SIR WILLIAM HERSOHEL'S discovery of this beautiful system the
companion has described considerably more than one revolution. More orbits
have been computed for this binary than for any other in the northern sky,
but, in spite of the immense labor which astronomers have bestowed upon this
star, the motion has proved to be so refractory and so anomalous that the
companion has departed from every orbit heretofore obtained. It follows from
the phenomena disclosed in this paper that the system contains a dark body,
and that no satisfactory orbit can be obtained until this disturbing cause is
taken into account. The following list of the orbits found by previous inves-
tigators will be of interest to astronomers; in most cases the data have been
taken from original sources, but in a few instances we have relied upon the
table of elements given by GORE in his useful " Catalogue of Binary Stars
for which Orbits have been Computed."
p
T
e
a
Q
i
i
Authority
Source
7^862
1806.88
0.430
4.3284
147.2
46.42
283.1
Encke, 1829
B.J., 1832
79.091
1814.155
0.34737
5.554
128.15
64.2
259.4
Encke, 1830
B.J.,1832,p.295
80.34
1807.06
0.4667
4.392
137.03
48.1
145.77
Herschel, 1833
Mem. E.A.S., vol. V, p. 217
80.61
1806.746
0.47715
4.3159
133.8
42.87
287.23
Madler, 1835
A.N., 289
92.869
1812.73
0.4438
5.316
126.9
64.86
279.8
Madler, 1842
A.N.,444; Dorp.Obs., IX,185
87.52
1807.60
0.482
4.675
128.55
51.5
293.3
Jacob
88.48
1807.48
0.4973
—
122.23
47.33
294.1
Hind, 1849
M.N.,IX,p.l45
92.338
1810.671
0.4445
4.966
127.35
61.05
212.97
Villarceau, 1851
C.R., XXXII, p. 51
98.146
1806.92
0.546
4.48
111.7
49.93
187.5
Powell, 1855
M.N..XV, p. 42
93.10
1808.12
0.4894
—
124.53
55.27
159.53
Jacob, 1857
A.N., 1082
95.966
1808.27
0.4935
4.731
123.13
57.35
160.53
Klinkerf., 1858
A.N.,1135
94.37
1808.79
0.49149
4.704
125.4
57.9
155.7
Schur, 1868
A.N.,1682
92.77
1807.9
0.3859
4.88
122.0
62.0
163.0
Flammarion 1874
C.R.,LXXXIX,p.l248
94.93
1809.64
0.47286
4.770
127.37
60.0
149.72
Tisserand, 1876
Flam. Cat. Et. Doub., p. 166
94.44
1808.90
0.4672
4.790
127.38
58.08
151.92
Pritchard, 1878
Oxf. Obs., I, p. 63
87.84
1807.65
0.4912
4.50
120.08
58.47
171.75
Gore, 1888
M.N.,XI/VIII, No. 5
88.04
1895.28
0.4994
4.45
120.8
57.0
174.92
Mann, 1890
Sid. Mes.. Nov., 1890
88.3954
1808.0707
0.4751
4.60
121.31
60.08
168.3
Schur, 1893
A.N., 3220-21 [1893
87.75
1895.6
0.50
4.56
123.5
58.3
190.8
Hurnham 1893
Astron. and Astroph., June,
87.70
1895.68
0.500
4.548
125.7
.->s. !•_•
198.25
See 1895
A.J.,363
• rim < MI : 213
•
An ins|>eetion of thi- table di-rlo-e- tin- I'm -I that the cnrly investigations,
so Tar as they are reliable, !«•«! t.. period- -eii-iblv !«•-.•. than JH) year.-, while
the determinations math- b.i\\..n l-l~> and 1880, or, when the companion was
describing the apa-tnm <>f tin- mil ellipse, favored a jieriod of at least 94
\, i!-,. I'lill- Tl>sKi:.VM> Mini l'i:l l« II \i:l», so lal.-ls as I^Tt'i ;ilh! 1-7". liinl
periods of 94.93 ami '.M.ll re>pcetivel\. In 1SUS St m i: obtained a
j>eriod ol '.' I.: 57 \i-ar-. and >iinilar jwriods before and since have been deduced
by other trn-tworthy computer-.
There i- tlin- nnmi-talvable e\ idencc of a retardation in the motion of the
companion near apa-Inm; in«n- recently this inequality has l>ecome an acceler-
ation. It wa- ob-er\ed b\ <;<>i:i in 1888 that the old orbits did not represent
:it mea-mv> >aii-l'a< toi ily, and, accordingly, he derived a new set of
element* «iili a period of 87.84 years, which was substantially confirmed by
Mili-eipient work ol M\N\ and HUKXIIAM. Finally PHOKESSOU SCHUR made an
e\li:ui>iive in\t->li^ation of all the observations up to 1893, and adjusted his
by the inetho<l of least squares to about 400 mean observations of
n^le. He says that in this work he could not advantageously employ
the measures of distance, owing to the differences of the individual observers.
The angles, however, were admitted to be admirably adapted to a fine deter-
mination of the elements, and, accordingly, PKOFKSSOK Scum's able discussion
of 400 observations inspired the belief that his orbit would give good places
of the companion for a great many years, if not for an almost indefinite
period. But this just expectation has not been realized, owing to the action
of an unseen body which disturbs the elliptical motion of the companion. To
e-talili*h the exi-teiiee and general character of the perturbations thus disclosed
we -nhmit the following considerations:
(1) A reference to lY'.iivsOR SCIIUR'S able and exhaustive paper in the
.\ttrnin, initH-li, .\iic/irirliti a. No. 3±JO, 21, will enable the reader to judge of the
improbability of an orbit based on such a multitude of good measures proving
to be defeeti\e within two years of its completion, unless disturbing causes
were at work to produce the sudden aeeel« -ration in angular motion. It i-
ineoneeivalile that this rapid deviation could take place without a true physical
cause. The error in the angle now amounts to about five degrees.
(2) In regard to the older ob-ervations we may remark, a- l'i:»i i --<>i:
SCIIUR and others before him have done, that SIR WILLIAM Hi ix in i.'s angles
are open to some uncertainty, owing to a possible error in the reading or in
the records; so that his observations do not give an exact or trustworthy
criterion for the period. HERSCHEL says, however, explicitly, that on " Oct. 7,
214 70 OPHIUCHI = 22212.
1779, the stars were exactly in the parallel, the following star being the
largest;" and, as it does not seem that any sensible error could affect the
angle which he has thus recorded, we see from the measures in 1872-3 that
the resulting period would be approximately 92 years. This is an additional
indication that the period of this star is not constant. A careful examination
of the other early measures shows that the first really good position is that of
STKUVE in 1825. These measures are so uniform and consistent, and appear
in every way so worthy of entire confidence, that I quote the record from the
Mensurae Micrometricae in full:
t a, p. t e, p.
1825.42 150.1 3.89
1825.43 147.0 4.05 4,G
1825.44 149.1 3.94
1825.48 148.8 4.05
1825.50 146.4 4.21
1825.60 148.1 3.90
1825.60 149.5 3.85
1825.61 149.3 4.05
1825.62 146.8 3.92
1825.63 147.3 3.85
1825.63 148.4 3.99
1825.64 147.0 4.01
1825.66 148.5 4.01 4,6
1825.71 148.8 4.02
Mean 1S25.56 148.2 3^98 14/t Struve
An examination of these separate measures clearly indicates that the error
in the mean result does not surpass 0°.5 in angle, and 0".l in distance. By
SCHUK'S orbit the angle is corrected two degrees, and when the radius vector
is thus thrown forward to 14G°.2 the computed and observed distances are
nearly identical. As STRUVE took special pains to secure good measures on a
large number of nights, and obtained the foregoing beautiful and consistent
results, we may regard his mean position as one of the highest precision. The
probable error of such measures would evidently be very small.
(3) "We see from the diagram illustrating the apparent ellipse that
SCHUR'S orbit falls within the positions given by the measures prior to 1845;
so that nearly all the observations of STRUVE, BESSEL, DAWES, MADLER, etc.,
require a sensible negative correction in distance. In figure B the differences
pu — pc of the individual measures used by SCHUR are plotted to scale, and a
glance at the figure will show the improbability of such classic observers as
STRUVE, BESSEL and DAWES making the constant errors here indicated. It
would be still more remarkable if the observers between 1845 and 1870 have
as uniformly erred in the opposite direction. How has it happened that from
1825 to 1845 the distances were steadily over-measured by the best observers,
while during the next period the distances were constantly under-measured?
Individual observers have what may be called a personal equation (though this
is far from constant and is diificult to determine with any certainty) but it
Tin. run « HI 215
could not |I:I|»|K-M that all tin- In-st observers would err alike, although in
oppo-it,- directions, during tin- two pcrio.U. I'KOKKHHOH SCIIUK'S corrections are
r\ idcntly inadmissible.
(4) The peculiar periodic manner in which SCHUR'S apparent ellipse
crosses and re-crosses the general path which best represents the mean {x>si-
tions, first Buggc-ted t«. m\ mind the- hypothesis of a disturbing body. Figure
C is l»ascd u|M)ii these UK an portions, and a comparison with the curve in /•'
shows that tlu- uu-an iK>Bition» are typical of all the observations for any given
year. Since I was desirous of avoiding any possible prejudice of the material
used. I have retained. \\ithout alteration, the mean positions whieh had been
formed in August before suspecting the existence of a disturbing influence.
NVe suggest that the companion of 70 Ojiliiuchi is attended by a
dark satellite, and that the visible companion, therefore, moves in a sinuous
curve about the common centre of gravity of the new system, with a period
-oinewhat less than 40 years, and in a retrograde direction. As SCIIUK'S orbit
i~ 1. .i-,<! ,.n ;i l«-a-t--'|ii:iM- a. I jn-t IIK nl "f all lli<- ol>-.-r\ at i-»ii- r \t. ndi IILT <<\<\'
two entire revolutions of the invisible body, it may reasonably be inferred that
his apparent ellipse will represent very nearly the true motion of the centre of
gravity, while the apparent ellipse whieh best represents the observed distances
will give a general outline of the path of the visible star in its sinuous motion.
Let us recur to the diagram of the apparent ellipse and imagine that the
visible companion and the centre of gravity are in the tangent to the ellipse
at the epoch of intersection in 1818. Then, the motion of the visible star
In-ing retrograde, we perceive that it will gain steadily on the centre of
gravity, and, in 1836, the two will be in line with the original position, after
half a sidereal revolution; from IS.".*! to lsi.1 the satellite will make another
quarter revolution, and again the bright companion will be- in the tangent to
the apparent ellipse and in advance of the common centre of gravity. As the
visible star will now steadily fall behind in its retrograde motion about the
centre of gravity, it is clear that from 1845 to 1872, which is three-fourths of
a revolution, the motion of the bright body //•/// n/i/Mnr to be abnonnally slow.
This is the apparent retardation previously mentioned a- giving rise to the
long period* found by computers who used observations extending over the
a pas iron portion of the real orbit. Assuming that the motion is undisturbed,
and hence that the areas are constant, PKOKESSOH SCHUR was compelled to run
his ellipse further out in this part of the orbit in order to represent the
observed angles. From the diagram we see that the retrograde motion of the
visible star continues after 1872, and, as this apparently accelerates the visible
216 70 OPHIUCHI = 22212.
motion of the companion relative to the central star, SCRUB'S ellipse is drawn
inside of most of the observations of this period. The falling of the measured
distances beyond SCRUB'S orbit shows plainly the periodic motion of the visible
star in accordance with the above theory. From this sketch of the effects of
the disturbing body it is evident that, at the time SCHUB completed his orbit,
the visible star and the unseen body were nearly in line with the central star.
And since the visible companion in 1825, according to STBUVE, had an angle
of 148°.2, whereas SCHUK makes it 146°.2, or, substantially the same as the
centre of gravity at that epoch, it follows that our hypothesis, making SCRUB'S
orbit represent the motion of the centre of gravity, is indeed very nearly cor-
rect. Any slight correction that may be required for the periastron of SCRUB'S
ellipse in order to make it represent the true path of the centre of gravity,
had better be deferred until additional observations disclose more clearly the
nature and extent of the perturbations.
(G) We may fix the approximate elements of the visible companion about
the centre of gravity as follows: From 1818 to 1890, or 72 years, is the time
required for two revolutions, as explained in the preceding paragraph, and
hence we see that the period is approximately thirty-six years. The motion is
retrograde, and from the diagram of the apparent orbit, we may conclude that
the distance of the visible star from the common centre of gravity is about
0".3. It is natural to suppose that the plane of the orbit is not greatly inclined
to that found by SCRUB, but existing data will not fix all the elements with
the desired precision. Perhaps until the path of the centre of gravity is known
with great accuracy, the simple hypothesis of a circular orbit, with node and
inclination identical with the similar elements of the visible pair, will be suffi-
cient to explain phenomena, and it follows that both angles and distances are
comparatively ivell represented by this hypothesis,
It is found, however, on more detailed examination that the representation
can be somewhat improved by the adoption of the following elements:
pi = 36 years
T> = 1822.0
e' = 0.475
a' = 0".30
ft' = 151°.0
i< = 60°.l
X' = 191 °.7
n1 = 10°.0
While this orbit gives a good representation of the motion of the bright
body about the common centre of gravity, the data arc so rough that the
determination of such delicate elements must be regarded as provisional only.
In the following table we have compared SCRUB'S elements with the mean
7001'IIM ( 111
•JIT
position-. fur each year; the n -idiial- arc given in the columns headed 00 — 0,
and p0 — />,. It is at once evident that tin- angles arc beautifully represented
down to 1 ->!•.'!. after \\liich tin- error in angle rapidly accumulates until it now
amount*, to uearlv fir> tlt-yrrrs! Tin- errors in distance arc illustrated in
diagram (\ which shows the same general features as diagram #, where the
]>oints represent tin- individual mea.»urc* employed by Sciirit.
The element- of tin- orbit whieh best represents the observed distances are
as follows:
4'.548
X - 11WMT.
n - -4a.U728
Apparent orbit:
-» 9*.00
«= 4M7
= 122°.9
= 295°.8
Distance of star from centre -« 2M98
CoMfAKlHOV or CiiMITTKH WITH OmKKVKD 1'LACRfl AI coKIMX.i TO TIIK Two Km or Kl.KMKXTH.
of major axis
uf minor axis
Angle "f major axis
Angle of
I
•.
'.
*-«,
'.-'•
*.-«,
V*t
&'
•
Otaervrrt.
1779.77
*
-8?8
z
O
-8.11
_f
-0.708
1
Hrnrhrl
1781.74
99.2
4.49
+ 1.6
-0.27
+ 4.40
-0.11
+0.359
1-2
Ilrnchrl
1S02.34
:«6.1
_
+ 1.4
—
+ 0.71
MM
+ 0.027
1 II.T..-I..-I
1804.42
IU -
—
-0.3
—
-3.15
_
-0.128
2
Ilrrm-tifl
L«8J
_
,,.,
+ 5.08
..^
-0.244
5
Struve
160.2
—
-2.7
—
+0.78
__
+ 0.042
2
Slrure
ivji ;j
i:.:.;
—
-0.8
_
+ 2.65
+0.154
5
Strure
154J
1 L'7
-O.X
+ 1.12
+ 2.04
+ 0.72
•n i-j,;
2
llrrm-hrl and South .
! :. I | •
—
1 o
+ 1.7.-,
_
+ 0.109
Strove
Mx'J
1M
+0.03+3.17 -0.37
I | >N,iiih 14 0; Strove 14
140.1
^-I'l + 0.07 +•_• ^J i"js • m-j7| 2
tStniTe
M"-
i :.s
+0.:« -t-o.Ki +(!.:•_• o.-.-.' +(1.062
4
Strure
>_.., -,,
(UN
-o.;{ -t-o.L-.-t -t-o.;{;i .u.-, +0.035
6
Strure
> :i..-.7
: Ifl
-o..->4 _(n.-_. . o-.-i - I-;
H,. 0; Itewel 10; Ifcwc. «: \V. MrureS
i> : :,s
185.1
1«
•O..H«;
+o.«.
H. 8-4J; Hrurl 7: W. Sinire 6
i> _•'..
f 0.36 -
-0.083
8
tMwe.8; Bend &
6.14
hO.r.l -0.34 +0.34
1
Dnm
IBM H
iaoj
• • :
•ti.:u -1. '.'.-, +0.12
-0.118
18
\V Mrore 4; I Hi we. 7; IleMel 7
u
1M.7
•ill
r-0.2 • 0.2i -ti.u;
-O.OL'.'f
0
Strure
> • :..•
1S8J
.. .:
*-o.:w -i.os +o.i»o
-o.n.-, !•:.
M.n.ll.T.1. Kn.kcJ; Ilnurl
UTJ
.. u
.. j +0.3.-, -d.-.u; +O.IM
-0.104 27
DmwwS; Encke4; BMM! Hi; W.Mr
! x
1* 1
, .,.,
-0.7
r-0.32
-0.1. V.' 7
(Ulle
•x
: :•:, :.
1 .M +0.25
-0.160
4 Calk 3; Dane* 3
18411.17
::• '.. -
+ 1.01 O.(H) +0.33 -0.09
+0.037
14+ KaUer — ; O. Stmre 10; Dawea 4
I i -.I rji 06.60
-0..", * -•• 1 •
-1.13+0.10
-0.129
26
M».llerH; K.lwrft; !Mwn4; llr. ami Srlil. 7
184L>..'.7 :
- o I
i
-0.50! -0.01
,,,,-,.-
.'.
o MnireS; Midler S; Dmwe*S; KalMTtt
1 -
-0.1
H0.20
-0.090
20
Schluter
1 .:.V. I •.'•.'.! «JJ7
-I.26-0.Ofi
-0.14620-19
I»we. 1-0; EiM-keS; Midler 10
: : ; i • _• : • • •
-0.7 +0.03
-1.361+0.01
-0.1581 10
KnrkeS; Midlera
70 OPHIUCHI == .2*2272.
t
60
PO
e-et
PO-PI
G0-e,
PO-PZ
d6"
n
Observers
1845.48
120.9
6.64
o"~
-0.3
-0.03
-0.86
-0.03
-0.101
30
Hind 9; O. Struve 5; Miidler 16
1846.46
119.3
6.76
-0.7
+0.06
-1.63
+ 0.07
-0.190
18 +
Jacob 1; Hind 7; Dur. Obs. — ; Miidler 10
1847.47
119.1
6.85
-0.3
+ 0.14
-0.96
+ 0.16
-0.112
13+
O. Struve 4; Dur. Obs. — ; Mitchell 1; Mii. 8
1848.38
118.4
6.81
-0.3
+ 0.09
-0.96
+0.13
-0.112
9
Dawes 3; Miidler 4; Bond 2
1849.39
118.1
6.64
+ 0.3
—0.09
-0.31
-0.03
-0.036
5
O. Struve
1850.55
116.4
6.78
-0.5
+0.07
-1.01
+0.13
-0.118
18
Rad. 8; W. & J. 2; Miidler 4; Fletcher 4
1851.54
115.5
6.57
-0.5
-0.13
-1.04
-0.04
-0.121
24
Miidler 4; -Fletcher 8; O. Struve 5; Miidler 7
1852.69
114.9
6.56
-0.2
-0.11
-0.63
0.00
-0.073
37
Fletcher 6; O. Struve 5; Miidler 11; Jacob 15
1853.57
114.9
6.42
+ 0.6
-0.22
+ 0.12
-0.11
+ 0.014
21-12
Powell 9-0; Dem. 6; Dawes 6 [To. 3-0
1854.48
113.2
6.37
-0.3
-0.22
-0.71
-0.11
-0.081
57-54
Ja. 21; Ja. 2; OS. 6; Dem. 12; Mii. 10; Da. 3;
1855.52
113.3
6.45
+0.6
-0.09
+ 0.35
+ 0.04
+0.039
20-13
Lu. 2; Sr. 3; Winn. 1; Mii. 5; Da. 2; Po. 7-0
1856.43
111.7
6.34
+ 0.1
-0.14
-0.41
0.00
-0.046
32
OS. 5; Ja. 7; Mii. 3; Winn. 8; Sec. 3; Dem. 6
1857.52
111.0
6.31
+0.2
-0.10
-0.04
+ 0.05
-0.005
20
Ja. 3; Winn. 1; Sec. 4; Da. 2; Dem. 4; Mii. 2;
1858.39
109.1
6.01
-0.9
-0.32
-1.07
-0.16
-0.116
18
Ja. 3; Mo. 2; Dem. 4; Mii. 9 [OS. 4
1859.66
108.4
6.24
-0.4
+0.02
—0.45
+ 0.18
-0.048
20
O2. 5; Dawes 4; Auwers5; Powell 5; Mii. 1
1860.70
107.3
6.33
-0.4
+0.21
-0.29
+ 0.40
-0.030
8 +
SecchiS; Luther — ; Auwers 5
1861.67
106.2
5.70
-0.5
-0.31
-0.50
-0.14
-0.052
17
Rad. 1; Miidler 7; Auwers 6; Powell 3
1862.59
105.6
.is:;
-0.2
-0.07
-0.02
+ 0.09
-0.002
19
O. Struve 3; Winnecke 1 ; Dem. 9; Miidler 6
1863.54
104.8
5.62
0.0
-0.17
+0.19
+0.01
+0.019
29
Adh. 11; Sec. 2; Dem. 9; Ta. 1; Fer. 1; 111. 5
1864.54
104.1
5.43
+ 0.5
-0.23
+0.84
-0.06
+ 0.082
13
Englemann 2; Dembowski 11
1865.50
102.4
5.32
0.0
-0.20
+ 0.22
-0.03
+ 0.021
43
En. 8; Secchi 4; Dem. 9; Ta. 2; Kaiser 20
1866.43
101.2
5.31
0.0
-0.07
+ 0.48
+ 0.11
+ 0.044
25
Dem. 8; O2. 5; Ta. 5; Hv. 4; Secehi 3
1867.50
99.6
5.18
—0.2
—0.03
+0.43
+ 0.14
+ 0.038
14-13
Rad. 1; Kn. 2; Ta. 1-0; Dem. 7; Hv. 3
1868.65
98.6
1.9(1
+05
-0.13
+ 1.26
+ 0.05
+0.101
22
Dem. 7; Kn. 2; Rad. 2; Du. 4; OS. 2 ; Brw. 5
1869.80
96.7
4.64
+ 0.4
-0.19
+ 1.32
-0.03
+ 0.109
11
Dum-r 3; Dembowski 8
1870.51
94.2
4.52
-1.0
-0.18
-0.40
-0.08
-0.032
12
Gledhill 2; Dem. 8; Ta. 2; [Gl. 3; Du. 1
1871.56
93.4
4.34
+ 0.1
-0.16
+ 1.27
-0.03
+ 0.099
22
W.& S.2; Rad. 2; Pei. 2; Dem.8; Ta. 1; Kn. 3;
1872.51
91.6
4.20
+ 0.2
-0.13
+ 1.41
-0.01
+ 0.105
23
Brw. 2; Fer. 3; Rad. 2 ; Dem. 9 ; W.& S. 3; O2. 4
1873.56
88.1
401
-0.1
-0.09
+ 0.43
0.00
+0.031
14
Gl. 1 ; Dem. 8; W. & S. 1 ; Ta. 1; Rad. 3
1874.61
87.7
3.81
+ 1.1
-0.09
+ 2.71
+0.01
+0.183
17
Rad. 4; Dem. 8; Ta. 1; OS. 3; Gledhill 1
1875.61
84.2
3.59
+0.1
-0.10
+ 1.74
-0.04
+0.113
21
Dem. 9; Sch. 8; Rad. 4 [Jed. 4; Wdo. 1
1876.57
80.7
3.48
-0.6
0.00
+ 1.53
+ 0.07
+0.093
31
Sh. 5; Dk. 2; Dem. 7; PI. 3; Sch. 6; Hall 3;
1877.60
77.4
3.23
-0.5
-0.05
+ 1.83
+0.02
+ 0.104
50
Dem. 8; Dk. 2; HI. 4; Jed. 10; PI. 8; Sch. 10;
1878.58
74.3
3.05
+0.1
-0.01
+ 2.49
+ 0.03
+ 0.134
18
Dem. 7; Sea. 3; Dk. 4; Gold. 4 [Cin. 4 ; Sh. 4
1879.57
69.5
2.95
-0.4
+ 0.09
+ 2.28
+0.12
+ 0.115
47
Cin. 18; Sch. 10; HI. 5; Cin. 5; Sea. 4 ; Jed. 5
1880.59
64.0
2.64
-0.9
-0.01
+ 1.98
-0.01
+0.093
33
Dk. 3; Fr. 6; HI. 6; Sch. 10; Jed. 6; Sea. 2
1881.56
60.3
2.55
+ 1.0
+ 0.08
+ 3.91
+ 0.06
+ 0.172
11
Doberck 2; Hall 5; Big. 2; Sea. 2 [En. 4
1882.60
52.5
2.48
+0.2
+ 0.20
+ 3.35
+ 0.16
+0.137
30
H.C.W. 1; Dk. 2; HI. 7; Sch. 9; Jed. 4; Sea. 3;
1883.62
44.0
£.31
-0.3
+ 0.18
+2.42
+ 0.11
+0.094
45
Per.4; Seag. 8; Sch.15; Jed.6; Kii.3; Sea.3; En.li
1884.56
36.0
2.17
+ 0.3
+ 0.16
+2.01
+0.07
+0.077
31-29
H.C.W.l; Pr.l; Per.6; H1.7;Sch.8; En.5; Sea.3-1
1885.61
25.9
2.06
+ 0.1
+0.13
+ 0.72
+ 0.02
+0.026
30-28
Per. 4; Sea. 4-2; HI. 7; En. 8; Sch. 2; Jed. 5
1886.61
14.3
1.93
-0.9
+ 0.04
-0.89
-0.07
-0.031
46-44
HI. 7; Per. 7; Jed. 7; Sch. 14; En. 7 ; Sm. 4-2
1887.68
3.8
1.91
-0.1
+0.01
-1.03
-0.09
-0.036
29-28
Sm. 1-0 ; HI. 6 ; Sch. 18; Tar. 4 [Cop. 3; Tar.O
1888.62
353.9
2.11
-0.4
+ 0.15
-2.10
+0.07
-0.075
36-35
Com. 3; Maw4; HI. 6 ; Giac.3; Sch. 10-9; Lv.l;
1889.53
345.9
2.08
+ 0.6
+0.06
-2.26
-0.01
-0.082
37-34
/3.2; Hod.2-0; Com.5; Hl.O; Maw5; Sch.17-10
1890.57
336.7
2.21
+0.6
+0.08
-2.38
+ 0.04
-0.090
46
Glas.2;Giac. 8; HI. 7; Maw 3; Well. 1; Big. 16;
1891.59
327.4
2.23
-0.6
0.00
-3.58
-0.02
-0.141
33
Maw4; H1.6; Knr.O; Sch.6; See2;Big.9 [Sch. 9
1892.52
320.8
2.26
-0.4
-0.04
-3.52
-0.05
-0.142
34
ft. 4; Col. 1; Maw 3; Com. 4; Big. 5; Sch. 17
1893.62
312.9
2.25
-0.8
-0.15
-2.30
-0.10
-0.094
19-20
Maw 3; Com. 5; H.C.W. 0-1 ; Sch. 11
1894.69
:;ol.L'
2.30
-2.7
-0.14
-4.80
-0.03
-0.195
30-29
Maw 3; Knr. 12-11; Com. 4; Sch. 6; Big. 5
1895.32 298.6
•1 •>•!
-4.3
-0.21
-6.98
-0.09
-0.280
3
See
1S95.64 296.1
2.14
-4.8
-0.28
-5.62
-0.12
-0.221
20-18
Maw 4; Com. 3; Ho. 5; See 5; Moulton 3-1
The values of P and T are taken from SCIIUR'S orbit, because the values
of these elements derived from so many observations may be regarded as very
nearly the meau of all the periods and epochs which result from the observa-
I ' •
I
:
. .IMIII tin n
lions prior t<» IS'.KJ. Tin- residuals wh'u-h follow from the use- of tin-si- elements
art- given in the column- marked 0, — 0, and p, — p,. In the eaMe of the second
elements the periodic error- in angle an \cry noticeable, but, as the simple
• lillV rences 0, — 0, would not IK- strictly comparable at different di-tanci-. we
have reduced all tin M- angular displacement* to sex'onds of the are of a great
circle by the formula
57*.3
where r" denotes the apparent length of the radius vector in seconds of are,
ami (#„ — Ht) the iv-iduals of po-ition-anglu expressed in degrees. The dis-
placement 'Iff is tabiilaietl ami also illustrated graphically in dingrain .1 It
will !><• seen that the maximum or minimum displacement in angle is practically
identical in time with the zero of the curves of distance in It and C; and that
I lie zero of the curve of angles corresponds to the maximum or minimum of
the curve of distances. This displacement of phase would be a necessary
t •oii-ei|uenec of the orbital motion of the visible companion about the common
centre of gravity, and may be said to establish completely the reality of that
phenomenon. The present theory does not require the several phases of the
curves to be of equal length, since the tangent to the ellipse itself revolves
unequally in different parts of the orbit, and the zero of the curve of
distance, for example, depends on the coincidence of this tangent with the line
connecting the bright with the dark l>ody.
(8) The problem here presented of finding the elements of the orbit of
the visible companion from irregularities in the elliptical motion is very much
more dillicult than those arising from the irregular proper motions of jicrturhcd
-tar-, such a- NI/-///X and I'rocymt. In the case of the phenomena first investi-
gated li\ Hi. --i.i.. the centre of gravity of the >\-tem moves uniformly on tin-
arc of a great circle: but in this case the centre of gravity moves on the arc
of a very small ellipse and with a velocity which follows a very complex law.
Indeed the velocity at any point of the orbit i> inversely as the perpendicular
from the central star to the tangent to the ellipse at the point in question;
ami. as the central etar may in general occupy any jMiint whatever of the
apparent ellipse, we see that the velocity varies in an extremely complicated
manner. In view of these facts it seems best, especially from the |K>int of
view of practical double-star work, to determine first of all the path of the
centre of gravity and the elements of its orbit. Suppose we designate the
rectangular coordinates of this centre, relative to the principal star, by ar', y';
and the coordinates of the visible companion referred to the same origin by
220 70 OPIIIUCHI = ,12272.
x, y; then if a and £ denote the differences of these coordinates, the observa-
tions will furnish a series of equations of the form:
(ti = a-/ — a-j
ft
= y.' - yi
«2 = xj — x2
ft
= y2' - y2
it • - f ' -r
"I — «•! " ' •'s
ft
= y8' — 1/3
«4 = a-4' — a:4
ft
= Vt — Vt
t/4 t/t
rt5 == -^e ^5
ft
= ys' - y»
«. = *.' - «„ ft = y.' - y.
Five points, each determined by two such equations, are theoretically
sufficient to fix the elements of the orbit of the visible star about the common
centre of gravity; a larger number of equations, when combined in an advan-
tageous manner, so as to render the errors of observation a minimum, will
make the determination more exact, and define the elements with the desired
precision. In the case of 70 Ophiuchi, SCHUR'S orbit is to all appearances a good
first approximation to the path of the centre of gravity, but it does not seem
worth while to enter upon the more refined analysis here indicated until
additional measures of the visible companion have confirmed the accuracy of
this hypothesis. Apart from these theoretical difficulties, the sensible perturba-
tions of the central star upon the motion of its attendant system will give
rise to obstacles which are scarcely less formidable.
(9) While we have spoken of the dark body as attending the com-
panion, it is clear that similar phenomena would result from the action of a
body revolving round the central star. In this case, however, the considerable
distance which would result from a period of 36 years might render the
stability of the system somewhat precarious, especially if the orbit be eccentric
like that of the visible companion. And as there is every reason to suppose
that the system is the outgrowth of nebular condensation, and is, therefore,
adjusted to conditions of stability and permanence, it is more natural to regard
the companion as the binary. In this case the small mass might give rise to
a period of 36 years even if the pair be very close. The separation of the
new system is not likely to be less than 0".4, and it may be more than twice
that distance. If we adopt the parallax of 0".162 found by KRUKGER it will
follow that the major semi-axis of the orbit of the visible companion is 28.07
astronomical units, and the combined mass is 2.83 that of the sun; and hence
we conclude that the orbit of the visible companion about the common centre
of gravity has a major semi-axis of 1.84 astronomical units. Therefore, while
the bright companion describes an eccentric orbit with a major axis which is
slightly less than that of Neptune, the action of the dark body causes it to
99 HERCUI.Ifl = A.0. 15.
221
describe anotlu-r ellip-e, which in -i/e considerably surpasses tliat of the planet
Mtirs.
(10) With regard to tin- po-iti«>n <>f the dark body we remark that an
exaet prcdietion is dillicnlt. hut tin- general indications are that at the ejxK-h
1800.50 it lies approximately in the direction of 2(JO°*. As the companion in
now near perin.-tron, the present i> a favorahle o|)|M>rtunity for searching for
the dark body, since in tlii- position the orbit will be expanded owing to the
perturbations of the central star. In case it should be imagined that the
unseen body attends tin- central star, it would be natural to locate it in the
direction of 1(50°.
(11) Many years ago a disturbing l>ody in the system of 70 O/////W///
was suspected liv MM-I i i:. .1 \<i.u and Mi: JOHX 1 1 1 i:-i in i.. and on two
occasion-, man recently, BIKMIAM im- searched r«.i- it \\itii. >m meoem AII.T
examining lx>th stars with the Dearborn 18-inch refractor in 1878 he adds:
I1, .tli -tars round;" while a still more critical search with the Lick W>-inch
refractor led him to remark: "I could not sec any third com]>onent and both
-tar- appeared to be round, with all powers." In spite of this negative evi-
dence, oloervers with great telescopes will find this system worthy of special
examination. Whatever be the result of optical search for the unseen Ixxly, it
will now become a matter of great interest to measure the visible companion
with the most scrupulous care until the nature and extent of its perturbations
are fully established.
= A.r. i:».
« = 18k S-.2 ; 8 a +30° 83'.
8.0, yellow ; 11.7, purple.
DUeovtnd by Alvan Clark, July 10, 1859.
Omr.KVATioNN.
i
18.V.I
347?4
P.
1.61
1
,,....
: •
1872.56
6.
G.Q
P.
I
MIVO
> .. ,
347.0
1.80
1
I)awe«
1860.30
2.28
1
O. Strove
1877
1 I'.t
1
O. Strove
1866.68
I.T8
1
0. Strove
L8TI M
l-l t
1.09
3-1
Buniham
1868.50
1
0. Strove
1879.47
1.13
1
Humham
•The ertlmatad podllon irftm In A.J. 8m far 1805 wu 890°; tba Mtngnit Botion would <linnnl.li llw
wifte coorfdermWy, but the principal change In the theorrtlcal pocltion raolu from UM eleoieaU above referred to.
222
99 HERCULIS = A.C. 15.
f
6»
Po
n
Observers
1
60
Po
n
Observers
O
W
O
a
1880.53
31.6
0.90
2-1
Burnham
1891.56
292.0
0.72
2-3
Burnliam
1881.43
29.4
0.51
1
Burnham
1892.40
299.2
0.70
3
Burnham
1883.60
72.9
1.30
1
0. Struve
1894.74
305.7
0.88
1
Comstock
1883.70
82.4
1.04
1
O. Struve
1888.54
77.4
1.05
1
0. Struve
1895.47
309.5
1.04
6
Barnard
1895.50
308.0
0.95
2
See
1889.50
281.2
0.65
1
Burnham
1895.73
315.2
1.12
3
See
1890.45
285.1
0.59
3-2
Burnham
1895.73
313.4
1.00
2-1
Moulton
This difficult double star was discovered by CLARK while testing the
telescope he had just made for DAWES, at the latter's private observatory.*
The physical connection of the pair was suspected, and during the same year
two sets of good measures were obtained by DAWES. OTTO STRUVE began to
give his attention to the pair the following year, and continued his measures
from time to time until 1888. His first observations are very satisfactory, and
of the highest value in fixing the elements of the orbit; but the later measures
are less trustworthy, owing to the great inequality and closeness of the compo-
nents. The series of measures begun by BURNHAM in 1878, and continued
until the close of his work in California, is of great importance, and in
conjunction with STRUVE'S observations and those recently made by the writer
at Madison, enables us to fix the elements with a relatively high degree of
precision.
In order to obtain a good orbit from such measures, the means must be
formed in a judicious manner, regard being had to the known motion of the
companion. After careful study of all the observations, we have formed a
suitable set of mean places, and deduced the corresponding elements. The
orbits previously found for this system are:
GORE, 1890
M.N., Nov. 1893
SEE, 1805
unpublisln'il
P = 53.55 years
T = 1885.58
57.5 years
1887.30
e = 0.7928
0.806
a = I'M 2
I'M 63
8 = 50°.l
77°.0
t = 38°.6
35°.5
X = 110°.73
90".0
' Axiniitiiiitii-iil Journal, 300.
180
99 Horculis = A.C. 15
99 HKRCULIS = \.< I •
Tin- adopted element- »f !•'.> //. /<•////>• an a- fi>llows:
/' - 54.5 year*
Tmm
e - 0.7M
« - r.014
Q mm indctcrininiiU'
• -
Angle <if jN-riantrun •• 169°.5
N - + '
The apparent i- the same a- tin- rral orhit.
2
I'.'.'TS
169*.5
Length of major axis
,'th of minor axis
Angle of major axis and periastron
TABLE or COMPVTKD AMI OBMKKVKD PLACE*.
<
«.
ft
*
P.
A.-&
P.-ft
*
Obwnrm
! W .,.:,
.1. ..
:;i.s i
1 x,,
1.81
- 1.4
-0.01
1
1' •
Mfl ••
1 •..»
1 M
- 4.1
+o.n
2
••s 1 ; O. Strive 1
1866.68
L73
.74
+ ::.o
-O.ol
1
O. Struve
,x,;
...,..-.
l.f.-.t
.70
- 1.9
—O.ol
1
O. Struve
1 N72.56
7..'
L48
..-H;
- 1.'
-0.10
1
O. Struve
1^77.66
17.J
l.l-.t
.'.".I
+ I '.
-O.lo
1
( ). Struve
1"7S.46
L'l.l
20.1
LM
.U'l
+ 4.3
-0.17
3-1
Hiirnhain
is;
l.i:»
.11
+ .
-0.01
1
Hurnham
l&v
..: g
DJO
LM
+ 4..'{
-0.14
2-1
Itimihain
ISM.I:;
31.0
8.77
- l.r,
-0.19
1-2
I'.urnliaiii 1 ; O. Struve 0-1
1889.50
•J.-.7 1
,.,,.
• I i-
+0.-23
1-1
Biirnhain 0-1 ; O. Struve 1-0
l> K) Uf
ll.. V.I
,.:.,.
-I- 4.6
+0.03
3-2
1'iui iiliam
1891.56
0.7J
o.7I
- 0.9
•fO.Ol
2-3
Kurnhaiii
IV. I"
1119.2
0.711
0.80
0.0
-0.10
3
Huniliatn
189 1 7J
;«..-, :
WLS
1.04
- 5.6
-0.16
1
Cniiistiick
.,,>,,
:;u •.•
..•,:,
1.11
- 6.2
-0.16
2
BH
iv.:. 7.:
.;].'..•
Kir. i
1.12
1.13
+ 0.1
-0.01
3
BM
ErilF.MRKIS.
I
fb
f.
a
*
L8MLM
317.5
1.18
32o i
LM
imejo
- :.0
1900.50
P,
1.45
While this (irliit may iHt-tl slight inoditicatioii in tin- coursr of time, it
not MTIII pnilKilih- that a >-fii-ililr improvi-im-nt can IM- »-ff<-ctc<l for a ^«MM! many
\rars.as I'M. motion is n-.\\ \.;\ ~!..\\.;nnl <-iii.-i!\ in lii. direotioa »t' ili< ndhM
\i-cti.r. 'I'lic crl.it is ivmarkalilr for its hiirh rrrrntricity, ami fi>r ha\in^ no
M-n-ili|«- inclination. Thin ciriMiinstanci- cnalili- n- to contcinplatr dint-tly tin-
real orliit. ami n-n<l»-rs W //./•••////>• an ohj(-<-t of tin- iii^licst inti-n-t. Tin-
pair i- nl\va\- ratln-r ilitlicnlt, o\\in^ \» th<- inequality of the component*, ami
exact measurement is sdilom possiliK-. But at pn-srnt the star w relatively
eat»y, ami onirht to IK- ^ivm -<nin attention l.y ol.-.i\, i-.
224
£ SAfJITTAim.
CSAGITTARII.
a = 18h 56m.3
3.9, yellow
8 = —30° 1 .
4.4, yellow.
Discovered by Winlock in July, 18G7.
OBSERVATIONS.
t
60
Po
n
Observers
t
6.
Po
n
Observers
0
it
0
If
1807.59
257.7
0.86
1
Winlock
1888.66
259.3
0.67
7
/3. & Lv.
18G7.80
260.8
0.48
1
Newcomb
1889.41
255.1
0.81
5
Burnham
1878.70
84.2
0.42
1
Burnham
1879.71
54.8
0.3 ±
1
Burnham
1890.49
251.1
0.76
3
Burnham
1880.62
62.1
0.55
2
Burnham
1891.53
246.5
0.61
3
Buvnham
1881.61
36.1
0.31
2
Burnham
1892.39
245.1
0.60
3
Burnham
1886.62
1886.74
271.3
271.1
0.65
4
1-0
Hall
Pollock
1895.32
1895.62
194.7
193.6
0.35
0.13
3
2
See
Barnard
1887.64
265.3
—
5-0
Pollock
1895.74
193.1
0.20 ±
1
See
Owing to the great southern declination of £ Sagittarii, which renders it
inaccessible to European observers, and makes observations difficult even in
the United States, the object was comparatively neglected for a number of years.
The first observations were made by WINLOCK and NEWCOMB in the year of
its discovery. The pair was not again observed until 1878, when BURNHAM
began to give it regular attention.* His series of measures now show that
£ Sagittarii belongs to the class of bright, close binaries with short periods.
This object has therefore become one of particular interest to American
observers.
The first investigation of the orbit was made by MR. J. E. GORE, who
published the following elements (Monthly Notices, R.A.S., 1886, p. 444) :
P = 18.69 years
T = 1882.86
e = 0.1698
a = 0".53
t = 58°.8
Q = 83°.37
X = 263°.35
MR. J. W. FROLEY has more recently examined this orbit (Astronomy and
Antropfi.y(tics, June, 1893), and obtained a set of elements which do not require
any large corrections:
P = 17.715 years Q = 75°..'55
T = 1878.62
e = 0.30
a = 0".68
i = 73°.95
X = 327°.35
* Aitronomical Journal, 305.
{ SAC; ITT M:II.
L-J.1
While in Virginia recently, I took o.-.-a-ion to measure this star, and,
although the object was seen with ditlicnltx. owini; to its low altitude, I could
dine-over a distinct elongation in the direction 1!>I .7: tin- di-tanee could not be
fixed with much confidence. Imt m\ - itingn of the micrometer gave if.IV>. The
estimates of distance wnv -nliMantiallv the same, but 1 am now convinced, from
my distinct recollection of the appearance of the object, that I with the measure
ami the i-timatc were too large. The star could not IK- -.) united, although it
was sharply elongated with a power of 1300; the di-tancc was probably less
than (T.i
From an examination of all the measures of this pair, we have derived the
following elements:
/• - 18.85 jean
T - 1878.80
« - 0.279
a - 0».686
8 - 69".3
• - 67°.32
A - 328M
n - -19«.098
Apparent orbit :
Length of major axis •• I'.SOO
Length of minor axis ~ 0".423
Angle of major axis — 74".8
Angle of periastron = 82*.8
Distance of star from centre — 0*.168
COMPABIIIOX or COMPUTED WITH Oiutr.RVK.n PLACES.
1
9.
«.
p.
?•
*v-«.
P^-?<
n
ObMnren
IM.: s,i
.:. i -
- i-
0 M
-f- 6.0
-o.ai
1
Newcomb
1878.70
-i I
UJ
ii u
• • 11
- l.l
+ 0.01
1
liiiniliuiii
18T9.T1
N i
0.3 ±
0.48
-14.6
-0.18
1
Hurnham
i 1
67.7
n »•_•
+ -4 1
+0.13
2
Burn ham
1881.61
36.1
- f> 1
-0.02
2
Kuniham
",.-,
- 2.4
+0.06
4
Hall
MO.t
0.67
0.79
- 1.6
-0.11'
7
Bumham 6 ; Leavenworth 1
Ut :
0.81
- 1.6
±0.00
5
Hum ham
LMO.it
851.1
L'.-.i :
0.76
o n
- 0.6
-O.i'-.'
3
Kurnham
1891.53
Ml -•
:;..-.
0.61
o ro
± 0.0
-0.09
3
Kurnham
M5.1
•Jil ->
0.00
+ 3.3
±0.00
3
Hurnhain
:-.-....•
l«M :
1M 9
i. :,
".'I'
+ 0.4
+0.13
3
See
EPH EMEUS.
1896.50
U •; :...
76.5
. ::,
P,
Q.24
0.47
n u;
I
u
i B '
P,
0*37
0.28
When we coiisiiler the small nnmlH-r of ob>i-rvations. and the discord-
ant character of some of them, we must regard these elements as highly
226
y CORONAE AUSTRALIS = H2 5084.
satisfactory. It is not likely that they will be materially changed by future
observations, but for some time this rapid binary will deserve careful attention.
The eccentricity of the orbit appears to be fairly well defined, and is rather
smaller than usual; good observations during the next five years will enable us
to fix this element with the desired precision. The star is now very difficult,
and will remain so for several years, but it is constantly within reach of our
large refractors.
y CORONAE AUSTRALIS = IL 5084.
a = 18" 59">.6 ; & = —37° 12'.
5.5, yellowish ; 5.5, yellowish.
Discovered by Sir John Herschel, June 20, 1834.
OBSERVATIONS.
t
Bo
Co
n
Observers
t
60
Po
n
Observers
O
H
O
t
1834.47
37.1
3 ±
1
Herschel
1859.
72
338.1
1
.5±
4-2
Powell
1835.43
37.0
—
1
Herschel
1861.
69
328.8
1
.5±
4-1
Powell
1835.56
36.7
—
1
Herschel
1862
27
325.3
1
.5±
5-1
Powell
1836.43
34.5
3.67
1
Herschel
1863
84
318.1
4
Powell
1837.35
1837.44
32.0
33.9
2.63
2.76
1
1
Herschel
Herschel
1870
19
286.9
2
Powell
1837.45
32.2
2.04
1
Herschel
1871.
22
281.9
1
Powell
1837.46
32.7
2.40
1
Herschel
1875
65
257.4
1
.45
4
Schiaparelli
1847.32
14.1
2.30
1
Jacob
1876.64
253.1
1
.67
_
Stone
1850.51
5.9
2.29
4
Jacob
1877.
43
248.4
1
49
5
Schiaparelli
1851.48
4.4
2.26
6
Jacob
1877
63
246.6
1
.44
4-3
Stone
1852.27
3.4
1.89
3
Jacob
1878
49
242.6
1
.36
2
Stone
1853.52
359.1
1.83
_
Jacob
1880
46
233.1
1
.15
1
Russell
1853.71
358.6
2 ±
4-1
Powell
1880.67
232.4
1
.32
1
Hargrave
1854.26
356.2
1.71
3
Jacob
1881
72
225.5
1
.42
3-2
H.C.Wilson
1854.78
355.6
—
3
Powell
1883
62
217.7
1
.66
4-1
H.C.Wilson
1855.77
352.9
—
5
Powell
1886
58
200.3
1
.37
6
Pollock
1856.22
350.8
1.68
8-7
Jacob
1886
70
203.5
1
.52
1
Eussell
1856.67
348.1
1.66
3
Jacob
1887
69
196.6
1
.16
4
Pollock
1857.21
348.4
1.67
5
Jacob
1887
73
196.2
1
.68
4-1
Tebbutt
1857.66
346.3
1.55
3
Jacob
1888
61
189.3
1
.71
6-3
Tebbutt
1858.20
343.4
1.53
3
Jacob
1888.71
188.0
1
.2
1
Leavenworth
AU8TRALI8 = H, 5084.
1
9.
P.
m
11 " ' ' "
1
0.
M
*
Obrr*nrrn
•
i
•
t
1.41
is:, |
1.70
4-3
Burn ham
•i.;:,
t;.. r
1 .M
9-4
Tebbutt
l>v».84
is:. |
2.30
4-1
i.utt
LTSJ
1.65
5-2
Tebbutt
1.00
182.9
l.r.l
4
T.-l.luitt
'65
180.3
,, ,,
i; i
Sellora
i>.,. n
165.5
1.62
Tebbutt
1891.53
176.9
: ' 9
:
Itiirnham
i8M.ra
ir.l.'.t
1.59
1-2
1891.70
177.6
.:
Sellora
If.l.l
i H
2-1
Moulton
During his sojourn at Fcldhauscii IIiixini. made careful measure- of
this object \\itli the seven-feet equatorial, and on two occasions swept over it
with tin- t \\cnt \-fect rclli-ctor.* In -weep 1»>1 In- saw the pair under specially
t'avoraMe conditions, and estimated the distance of the components at .T. This
value i- therefore adopted in the table of observations instead of the distance
(I'^'ty) indicated by tin inieroineter, which was vitiated by troublesome hitching
of the threads, and had to be rejected as worthless. HKIISCIIKI, showed fmm
hi- observations that the system had a considerable retrograde motion, and
hence it vva- subsequently followed by JACOB, PoWBLI., HrssKI.L, TEBHfTT and
other southem observer-. At \\\c present time the arc descrilnxl amounts to
238°, and even if the observations are not very numerous, they are sufficient,
l»oth in point of quantity and quality, to give an orbit which will undoubtedly
prove to be substantially correct
The component- are nearly equal in magnitude, and, as they are never
closer than 1".42, the pair is always comparatively easy; and even if difficulties
ari-c in the measurement of distance, there will l>e practically no difficulty, as
HKIXIIII. remarks, in determining the angle with the necessary accuracy. In
dealing with the orbit of a bright pair with equal component-, it Jg clear that
unusual weight should IK- given to the position angles, and especially when the
stars arc fairly wide, but the measured distances are affected by relatively large
errors. The orbit of this star is therefore based mainly on the angles, but the
distances have been of no small service in the final definition of the clement-.
Some of the orbits which have been publi-hcd by previous investigators are as
follows:
p
T
•
a
a
f
2
Authority
Source
100*5
:-...;..>
-• •_•
.• : •
_•'•'. !
Jacob, 1858
M.N., XV, p. 208
:,-.:,>
::
0.6989
2.400
L-.-.M.-.
in. r.
—
SrhU|»rvl!
\ N . 1
M i
1883.20
0.6974
•J II
L-J; i
iKiwning.
M N . M.III, p. 368
1886.53
i . i
i; I.:
141.0
• ; . 1888
M N . \I-VI, ,,. 103
n n
1.85
41.0
—
Wilson, 1886
• • ;
1885.19
,..;...;
i . .
1- -
1'owell, 1890
••'a Catalogue. •• II
121.24
187'.'
•_• I'.'l
:.; M
IMJ
Sellora, 1892
M.N., Mil. J..45
154.41
1876.84
0.4244
77.23
:;.-, -;
:.-•, .
Gore, 1892
M.X., LII, p. 503
JTaekrirktr*,
228
y CORONAE AUSTRALIS = H2 5084.
An investigation of all the observations has led to the
ments of y Coronae Australis:
P = 152.7 years £ = 72°.3
T = 1876.80 i = 34°.0
e = 0.420 X = 180°.2
a = 2".453 n = -2°. 3575
Apparent orbit:
Length of major axis = 4".906
Length of minor axis = 3".661
Angle of major axis = 72°.2
Angle of periastron = 252°.l
Distance of star from centre = 1".033
COMPARISON OP COMPUTED JVITH OBSEKVED PLACES.
following
ele-
t
&
6,
Po
PC
Bo— Qc
po—pc
n
Observers
1834.47
37.1
0
37.1
3 ±
2.80
±0.0
+0.20
1
Hevschel
1837.42
32.7
32.7
2.66
2.66
±0.0
±0.00
4
Herschel
1847.32
14.1
14.6
2.30
2.20
-0.5
+ 0.10
1
Jacob
1850.51
5.9
5.9
2.29
2.03
±0.0
+0.26
4
Jacob
1851.48
4.4
4.4
2.26
2.00
±0.0
+ 0.26
6
Jacob
1852.27
3.4
2.3
1.89
1.96
+1.1
-0.07
3
Jacob
1853.61
358.8
358.2
1.91
1.90
+ 0.6
+0.01
6±
Jacob ; Powell 4-1
1854.52
355.9
355.5
1.71
1.86
+0.4
-0.15
6-3
Jacob 3 ; Powell 3-0
1856.44
349.5
349.3
1.67
1.78
+ 0.2
-0.11
11-10
Jacob 8-7 ; Jacob 3
1857.43
347.3
345.5
1.61
1.73
+ 1.8
-0.12
8
Jacob 5 ; Jacob 3
1858.20
343.4
342.6
1.53
1.70
+ 0.8
-0.17
3
Jacob
1859.72
338.1
336.8
1.5 ±
1.64
+ 1.3
-0.14
4-2
Powell
1861.69
328.8
328.5
1.5±
1.58
+ 0.3
-0.08
4-1
Powell
1862.27
325.3
325.8
1.5 ±
1.56
-0.5
-0.06
5-1
Powell
1863.84
318.1
319.0
—
1.52
-0.9
—
4
Powell
1870.19
286.1
287.0
—
1.44
-0.9
—
2
Powell
1871.22
281.9
281.3
—
1.43
+ 0.6
—
1
Powell
1875.65
257.4
258.1
1.45
1.43
-0.7
+ 0.02
4
Schiaparelli
1876.64
253.1
253.0
1.67
1.43
+ 0.1
+0.24
—
Stone
1877.53
247.5
247.9
1.47
1.42
-0.4
+ 0.05
9-7
Schiaparelli 5 ; Stone 4-3
1878.49
242.6
243.0
1.36
1.43
-0.4
-0.07
2
Stone
1880.57
232.7
232.0
1.24
1.43
+ 0.7
-0.19
2
Kussell 1 ; Hargrave 1
1881.72
225.5
226.1
1.42
1.43
-0.6
-0.01
3-2
H. C. Wilson
1883.62
217.7
216.3
1.66
1.43
+ 1.4
+ 0.23
4-1
H. C. Wilson
1886.64
201.9
200.6
1.44
1.44
+ 1.3
±0.00
7
Pollock 6 ; Russell 1
1887.71
196.4
195.2
1.42
1.46
+1.2
-0.04
8-5
Pollock 4 ; Tebbutt 4-1
1888.66
188.6
190.6
1.46
1.47
-2.0
-0.01
7-3
Tebbutt 6-3 ; Leavenworth 1
1889.62
185.4
186.1
1.70
1.49
-0.7
+0.21
8-3
Burnham 4-3 ; Tebbutt 4-0
1890.62
181.6
181.6
1.61
1.51
±0.0
+ 0.10
10-4
Tebbutt 4 ; Sellers 6-0
1891.53
176.9
177.0
1.68
1.54
-0.1
+ 0.14
3
Burnliam
1892.64
172.9
172.3
1.65
1.57
+0.6
+ 0.08
5-2
Tebbutt
1894.80
165.5
163.5
1.62
1.65
+2.0
-0.03
5-6
Tebbutt
1895.73
159.2
159.9
1.59
1.69
-0.7
-0.10
2
See
EPHEMEBIS.
t Be pe t
1896.50 157?4 1.71 1899.50
1897.60 154.0 1.76 1900.50
1898.50 150.6 1.80
1472
143.8
1.85
1.90
ft HKi.riiiM = 0151.
It will be seen that my orbit is <|iiitr -imilar t<> that found by (ionic.
Though tlu- period in not defined \\itli tin- «;ivatc-.t ;ir<-m-.i<-\ . it <l<»" not seem
probable that the value given al><>\r can IK- uncertain by more than five years.
Tin- eccentricity will certainly be in the immediate neighborhood of the value
lien- a— -i^iu-il. and an error exceeding ±0.(rJ i- \< i\ improbable. The orbit of
•yt'orunat Australia is therefore comparatively well iletenninetl. and yet no great
:n-i-nr:ir\ in the orbits of double stare is nltiinately desirable, southern observers
\sill find tlii- -\-ti-m worthy of constant attentii>n.
/SDKLI'IIIM =/8l."»l.
a = *0» 8S-.9
4, jr«»ow
S = -I-I40 15'.
fl. yellowUh.
Ditforertd by Bumkam leitk his c*lebratrd tir-inrh Clark Hrfrartur !n Auyvtt, 1873.
OMKKVATIOX*.
1
e.
ft
*
ObMrrrn
1
9.
p.
II
OfeMrven
o
g
|j
»
1873.60
355. ±
0.7
1
Burnham
1885.61
<" •
1
H. Strove
1x71.66
15.5
0.65
5
Dembowski
INS.V.I.-,
216.6
KM
8
Englemann
1^1.70
13.6
0.49
3-1
Newoomb
1886.78
257.8
obi.
1
H. Strove
1874]
O.G9
1
(X Strove
1886.88
238.1
0.22 ±
7
Schiaparelli
USI5M
14.7
0.42
4
Schiaparelli
1886.91
219.5
0.39
4
Englemann
]s7.-, ,,;,
20.1
0.54
4
Dembowski
1887.65
278.5
0.36
5
Tar rant
1876.66
25.8
II IS
4
Dembowski
1887.66
1887.75
272.0
:;<..> i
0.39
0.3 ±
5
1
H. Strove
Hough
1871
17.7
• :.
2
Schiaparelli
1887.85
OJ±
1
Schiaparelli
1x7.71
29.7
0.51
5
Dembowski
MM "
.'.
Burnham
1877.79
; 1
Q I
2
Burnham
IBM
M ,-,
3
II Struve
1878.65
53.7
0.24
4
Burnham
1888.84
311.5
". I'.-.
17
SchiaparrlH
1878.76
—
1
Dembowski
1889.60
U4J
5
Burnham
1879.56
90±
«±Shi
2
Burnham
1889.78
a
H Struve
1880.68
133.6
0.26
1
Burnham
1889.86
0.37 ±
11
Schiaparelli
1880.75
214.5
0.2 ±
I
Hall
1 VMU9
»
Burnham
1881.54
149.2
• H
1
Burnham
1890.89
-• '.
u
S-hiaparelli
1881.88
l.'.l 7
—
1
Bigourdan
1891.45
OJ|
4
Burnham
1882.60
167.5
• M
3
Burnham
1891.64
1891 .:•;
M ,
0.48
1
Hall
H. Strove
1883.25
183.9
0.19
7
Englemann
1891.85
—
1
Bigourdan
1883.65
IS!'..-,
0.23
3
Burnham
1891 x
333.7
0 i 1
1
Schiaparelli
1884.69
: o •
0.32
3
Hall
>••: -
4
Burnham
1884.71
197.7
0.32
4
Englemann
1 VC',88
0 i .
2
Barnard
1884.77
199.2
0.29
1
Burnham
1892.93
; • 1
B
Schiaparelli
230
ft DELPHINI = 0 151.
1
0.,
Po
n
Observers
t
0.
Po
n
Observers
O
f
O
n
1893.52
339.2
0.58
2
Leavenworth
1894.79
348.6
—
1
H.C. Wilson
1893.53
338.8
0.73
2
H.C. Wilson
1894.83
347.2
0.48
13
Schiaparelli
1893.62
335.3
0.57
3
Hough
1893.70
342.2
0.56
5
Barnard
1895.31
351.8
0.50
1
See
1893.79
346.8
0.51
3
Comstock
1895.42
349.8
0.73
6
Barnard
1893.87
344.2
0.49
13
Schiaparelli
1895.61
352.1
0.80
1
See
1893.95
345.8
—
1
Bigourdan
1895.61
352.1
0.64
1
See
-tOf\A - 1
OAC O
A £/?
Q
i >.. .. ._,i
1895.66
350.8
0.58
3
Comstock
"When discovered in 1873 the companion was near its maximum elonga-
tion, and was easily measured by DEMBOWSKI in 1874. The measures
of the next few years showed that the pair had a rapid direct motion.* In
1879-80 the distance of the components became so small (about 0".20) that the
object could be elongated only by the most powerful telescopes. The measures
at this time are therefore few in number, and necessarily of doubtful accuracy.
Since the epoch of DEMBOWSKI'S measures in 1874, the radius-vector of
the companion has swept over 335 degrees of position-angle, and the intervening
observations enable us to determine the orbit with a comparatively high degree
of precision. The following table gives the orbits hitherto published for this
star:
p
T
e
a
SI
t
A
Authority
Source
in.
26.07
1882.19
0.357
0.55
163.6
54.9
:;r>»'.<;
Dubiago, 1884
A.N., 2602
30.91
1882.25
0.337
0.517
2.67
59.33
327.8
Gore, 1885iProc. E.I. A., IV; no.o
16.95
1885.80
0.096
0.460
10.9
61.6
220.9
Celoria, 1888
A.N., 2824
22.97
1882.37
0.260
0.501
174.2
64.1
343.9
Glasenapp, 1893
A.N.,3177
24.16
1882.38
0.284
0.51
174.4
64.6-1
344.2
Glasenapp, 1893
A.N., 3177
From an investigation of all the observations we find the following
elements for ftDelphini:
P = 27.66 years
T = 1883.05
e = 0.373
a = 0".6724
Q = 3°.9
i =61°.35
X = 164°.93
n = +13°.015
Apparent orbit:
Length of major axis
Length of minor axis
Angle of major axis
Angle of periastron
Distance of star from centre
1". 060
0".477
2°.5
176'.6
0".194
• Astronomical Journal, 357.
• tees
/jDelphinl=/?|5|.
b ....
ft DEI. I'll IM = /JIM.
231
The aeeonipanxin;: table of computed and observed places shows that
these elements are • \in MH 1\ sati*factory. The only large residual in that of
•. which i- |imli:il»ly tint- to an error of observation incident to the excessive
r the < itnipom nt-.
COMPANION or CoMrtmco WITH OMKBVKD
1
«.
9,
/>.
P.
fc-4
P>-?<
•
ObMrren
1.-, .
', :- _•
+ 0.3
+0.03
.'.
Iterabowtkl
is 7. -,.65
M.-...
-(- ol
-0.01
4
l)rmbow«kl
|»7<
0 is
0 Is
_ n »
±0.00
4
IVmbowtkl
" 11
- «•'.•
+o.a-)
7
IVmbomkl 5; liurnham .'
187*
R i
" _•!
+ «.3
-O.Ofi
:. i
llurnluun 4; Dcmbowtkl 1-0
is7«.s6
:i a
—
—
2
liurnhmii
in :
I.-.-,,
-1-1^
+0.06
3
Huniham
: :.J
1 I'.l.L'
1 i.vr.
..•.•.;
«'-!
+ 3.« +o.ii-j
5
liurnham
i..::.
If.'.i 1
o;;i
- 1.6 . -O.IW
3
Ilurnhaiii
181.7
o.iM
0.33
•H 1.5 -0.12
10
Englemann 7 ; Bumluiiii 3
! :•_•
201.2
O.:M
0.33
— 3.6 -0.02
12
Hall 3; Englemann 4; Burnham 5
- 0.9 i +0.11
9
Englemann 8; II. Struvr 1
1:17 i
O.VI
+ O.fi +O.IH, s 11
Sch. 7; Kngle niann O-l ; H. SlniTc 1-0
•-T1 s
o.:;i
1 '.•-•»
+ 3.4 j +0.07 l.s !'.»
Tar. 5; Ho. 1; Srhlanmrelll 8: II. Sinnre 5
OJ7
+ «.l +00.:
H-T>
liurnbam .'•: H. Stnive S-0
::i;.:;
0.34
n. -;|
+ :;:,
±0.00
16
ft. 5: Schlaparelll 11: II. Strure 9-0
nil
"11
+ 0.1
+0.03
16
Burnham 4 ; Srhlapart- III 13
it <•_•
- 1.1
—0.06
21
ft. 4; HI. 3; Schlaparrlll 0; II. Strove 5
O..M
".M
- 0.2
—0.03
9
Sclilaparrlll 5; Bumham 4 [Hlg. 1-0
;:i
841.7
::il s
o.r.i
- 3.1
-0.03
24-23
l.v. •-•: H.C.W. 1; Ho. 3; Com. 3; Sch. 13:
: si
•• Is
0.60
- 1.4
-0.17
14-13
Hi. Wlbon 1-0; Krhlaparelll 13
Is',.', M
.:.-,_•"
.-I 11
,..-.>
+ 0.1
-0.03
3
SM
The present orbit is somewhat more eccentric than those heretofore pub-
lished, ami in this respect it conforms better to the general rule among binaries.
That the orbit has an eccentricity of about this magnitude is evident from the
rapid motion of the radius-vector in the perinstral region, and its slow motion
at the present time. The slow, angular motion of the radius-vector during
reeent v«-ar- indicates, of course, that the di-tanec of the companion is much
inerea>ed: and this leads us to remind observers that the present distance is
sensibly larger than some have indicated by their measures. At pn-.-nt the
di-tance i> probably over 0".G5, and for some years will slightly augment.
It does not seem at all probable that the true elements of this remarkable
binary can differ materially from those here obtained. NYverthele-s, additional
exact measure* will be valuable in fixing the orbit with great accuracy, and as
tlu *tar \\ill be relatively ea*\ lor several years, observers should give it
jiilar attention. The following is a short ephemeris:
4 AQUAKII = -12729.
i
1896.51
1897.51
1898.51
6c PC t 6c PC .
355.3 o!Vl 1899.51 4?9 0*72
358.6 0.72 1900.51 8.2 0.69
1.7 0.72
Discovered
4AQUARII==22729.
a = 20'1 46m.l ; 8 = —6° 1'.
6, yellow ; 7, yellow.
by Sir William. Herschel, September
3, 1782
OBSERVATIONS.
t
9.
Po
n
Observers
t
C.
Po
n
Observers
o
g
O
g
1783.55
351.5
—
1
Herschel
1875.62
157.0
0.4 ±
4
Schiaparelli
1802.65
28.9
—
2
Herschel
1877.15
148.7
0.56
3
Dembowski
1825.60
27.5
0.80
2
Struve
1877.70
158.5
0.5 ±
1
Cincinnati
1830.92
13.4
0.69
1
Struve
1879.44
156.4
0.57
5-1
Cincinnati
1832.73
46.0
0.67
2-1
Herschel
J879.76
155.9
0.40
4
Hall
1832.90
23.0
oblonga
1
Struve
1880.78
165.5
0.51
2
Pritchett
1833.77
31.2
0.67
1
Struve
1881.54
159.6
0.52
3
Burnham
1836.05
46.3
0.41
4
Struve
1883.84
182.1
—
1
Seabroke
1839.68
62.2
—
2
Dawes
1884.77
166.8
—
7
Seabroke
1840.72
65.5
0.6 ±
2
Dawes
1885.64
156.1
1
Seabroke
1841.51
24.6
0.6 ±
1
Madler
1885.74
167.9
0.46
3
Hall
1841.80
72.7
—
1
Dawes
1886.69
162.5
—
1
Seabroke
1842.82
27.2
0.45
2-1
Madler
1886.74
168.3
0.54
3-2
Leavenworth
1886.84
174.8
0.47
2
Hall
1843.70
31.9
0.5 ±
3
Madler
1843.76
81.7
1
Dawes
1887.28
173.4
0.41
7
Schiaparelli
1887.79
175.9
0.53
3
Hall
1844.90
23.1
0.5 ±
1
Madler
1887.82
170.5
0.52
2
Tarrant
1853.70
95.9
0.5 ±
1
Dawes
1888.81
172.4
0.48 ±
5
Schiaparelli
1854.75
101.7
0.3 ±
1
Dawes
1889.51
155.5
1
Seabroke
1855.
—
—
1
Secchi
1889.88
176.7
0.49 ±
2
Schiaparelli
1856.81
107.8
0.3 ±
1
Secchi
1890.78
178.2
0.49
2
Tarrant
1862.68
137.5
oblonga
3
Dembowski
1891.77
178.1
0.50 ±
1
Schiaparelli
1865.71
125 ±
cuneo
1
Secchi
1892JO
184.5
0.55
3
Tarrant
1865.74
143.6
—
1
Tahnage
1892.80
181.7
0.33
2-1
Comstock
1866.08
139.6
oblonga
3
Dembowski
1892.91
187.0
0.4 ±
1
Schiaparelli
1866.65
125.5
—
3
Searle
1893.81
182.4
0.35 ±
2-1
Comstock
1866.66
110.0
—
5
Winlock
1894.86
186.5
0.38 ±
3
Schiaparelli
1867.86
141.1
0.30
1
Newcomb
1895.61
193.9
0.30 ±
1
Comstock
1872.88
147.5
oblonga
5
Dembowski
1895.73
184.2
0.33
3
See
4 AQfAKH = 2 .
2TW
This double star is always an exceedingly close and difficult object. SlH
WILLIAM IlKi:s4 IIKI. measured tin- po>ition-an.irlc in 17s:i. and on repeating Ui
observation in 180U. concluded that in nineteen \cars tin- motion had amounted
to 37*.4 (Phil. Trim*, isi'l. ,,. .171 ,. |,, | XL'.', the star was measured by STKUVK
on two nights; hi- tti..n- -rave 0 = 25".0, p = 0".81, 0 = «W.O, p = 0".80.
These results do not accord well with those of 1S<>;_'. l>ut we may infer with
DAWKS (Mmi. /.' I v. \..l. \xxv. p. 427 ) tliat IhixnKi.'s MOODd observation is
erroneous. For it is clear that the an^le could not have Keen the same in 1802
as in 1S'J."», and the -ulc.i-i|Uciit motion of the star shows that STKUVK'S first
position i-. (••.•.ciitially correct. All the early and some of the more recent meas-
ures of i ; are extreme! v discordant, and great difficulty is experienced
in determining what nu -a-nres on<^ht to be relied iip-.n. Carefid sifting of the
observations and judicious combinations of individual results will alone insure
suitable mean places for the derivation of a satisfactory set of elements We
liu\c relied principally u|»on the work of Silt WILLIAM HEKSCIIKI., STHUVE, SIK
.I"ii\ Hi i>< ii '\\VKS. MAOLKK, SKCCIII, DKMKOWSKI, HALL, I'.i I:\II\M.
Si ii \I-VI:KI.I.I and CoMSTOCK.
The following elements of 4 Aquarii have been published by previous
comput.
p
7
•
•
o
i
•
AoUiority
Source
!-•' -
1782.0
: s
ii n;
. • :. i .
" ::•
i r<m
:«(».-.'
::; i
;,,;,;
fix.r.i
:•.;:,"
; i :.'.
Doberck, 1877
8a^ 1896
A.X., 8287.
A. J., 841.
A revision of my former orbit of this star gives the following elements:
p
T
- 129.0 yean
- 1899.40
- o.r.i t
- 0».:
a -
Apparent orbit:
Length of major axis
I.«-tiurtli uf iiiiiii>r axis
Angle of major axis
Angle of periactroo
Dutaaoeof
68°.63
+2°.71K)7
- IM'SS
- 0-.4.-J
Hire
21:. .1-
0*.173
The accompanying table of computed and observed places shows a very
satisfactory agreement. The present orbit i* narrower than the one recently
published in the Agtronomi»if Journal, 341, but the great discordance of results
of individual observers shows that the object has always been extremely close;
234
4 AQUABII = ,i"2729.
and hence we think the chances favor the present orbit, which differs from the
previous one chiefly in the higher inclination. It is noticeable that the repre-
sentation of the more recent observations is sensibly improved.
COMPARISON OF COMPUTED WITH OBSERVED PLACES.
1
60
Oc
Po
PC
8o-0 c
Po—Pc
n
Observers
1783.55
351.5
352.2
ff
0.53
o
- 0.7
t
1
Herschel
1825.60
25.0
24.0
0.80
0.64
+ 1.0
+ 0.16
1-2
Struve
1832.18
27.5
31.4
0.69
0.55
- 3.9
+0.14
4-1
Struve 1 ; Herschel 2-1 ; Struve 1
1833.77
31.2
33.5
0.67
0.53
- 2.3
+0.14
1
Struve
1836.05
40.9
37.0
0.41
0.50
+ 3.9
-0.09
4
Struve
1841.12
45.0
46.4
0.6 ±
0.43
- 1.4
+ 0.17
3
Dawes 2 ; Madler 1
1842.31
49.9
50.3
0.45
0.40
- 0.4
+ 0.05
3-1
Dawes 1 ; Madler 2-1
1843.73
56.8
53.0
0.5 ±
0.39
+ 3.8
+ 0.11
4-3
Madler 3 ; Dawes 1
1849.30
59.5
68.8
0.5 ±
0.34
- 9.3
+ 0.16
2
Madler 1 ; Dawes 1
1854.75
101.7
85.9
0.3 ±
0.31
+ 15.8
-0.01
1
Dawes
1856.81
107.8
97.8
0.3 ±
0.31
+ 10.0
-0.01
1
Secchi
1864.20
131.2
125.4
euneo
0.34
+ 5.8
—
4
Dembowski 3 ; Secchi 1
1866.08
139.6
131.2
oblonga
0.36
+ 8.4
— .
3
Dembowski 3
1867.86
141.1
136.2
0.30
0.38
+ 4.9
-0.08
1
Newcomb
1872.88
147.5
142.6
oblonga
0.41
+ 4.9
5
Dembowski
1876.82
154.7
155.2
0.49
0.47
- 0.5
+ 0.02
8
Schiaparelli 4 ; Dembowski 3 ; Cum. 1
1879.60
156.2
159.7
0.49
0.49
- 3.5
±0.00
9-5
Cincinnati 5-1 ; Hall 4
1881.16
162.5
162.1
0.52
0.50
+ 0.4
+0.02
5
Pritchett 2 ; Burnham 3
1885.74
167.9
168.9
0.46
0.51
- 1.0
-0.05
3
Hall
1886.79
171.5
170.5
0.50
0.51
+ 1.0
-0.01
5-4
Leavenworth 3-2 ; Hall 2
1887.63
173.3
172.2
0.49
0.50
+ 1.1
-0.01
12
Schiaparelli 7 ; Hall 3 ; Tarrant 2
1888.81
172.4
173.5
0.48
0.49
- 1.1
-0.01
5
Schiaparelli
1889.88
176.7
175.3
0.49 ±
0.48
+ 1.4
-1-0.01
2
Schiaparelli
1890.78
178.2
176.9
0.49
0.47
+ 1.3
+ 0.02
2
Tarrant
1891.77
178.1
178.5
0.50 ±
0.45
- 0.4
+ 0.05
1
Schiaparelli
1892.85
181.7
181.0
0.37
0.42
+ 0.7
-0.05
2
Comstock 2-1 ; Schiaparelli 0-1
1893.25
183.4
181.8
0.45
0.41
+ 1.6
+0.04
5-4
Tarrant 3 ; Comstock 2-1
1894.86
186.5
185.3
0.38 ±
0.37
+ 1.2
+0.01
3
Schiaparelli
1895.67
189.0
188.8
o.::2
0.33
+ 0.2
-0.01
4
Comstock 1 ; See 3 ,
The period here indicated is not likely to be in error by more than five
years, while a variation of ±0.03 in the eccentricity does not seem probable.
It is therefore unlikely that future observations will greatly alter the present
elements, but as some improvement is still desirable, astronomers should con-
tinue to give this star careful attention. During the next few years the motion
will be very rapid, and the object excessively difficult; but for this very reason
observations will be the more valuable.
The following is an ephemeris for five years:
t
ft-
PC
O
a
1896.80
193.5
0.28
1897.80
199.4
0.24
1898.80
208.1
0.19
1899.80
1900.80
224X)
244.1
PC
0*14
0.12
1879
I BQUULKI = 0.1 535.
; S • +9° ST.
4.5, yellow ; 8.0, yellow.
IHtrotend Ay Otto Sfrwr?, .4«.;««f I'.i. 1 WJ
OMKftVATIONS.
(
0.
P.
»
f\l,mmmn i • n
II .. • , • ,
1
6.
P.
n
Observer*
O
9
O
9
1852.64
n i:.
1
ruve
1881.46
...» J
0.38
4
Biirnhatu
:w.-,.;
18.8
0 i •
1
O. Strove
1882.63
9.8
0.29
3
Kurnham
> . . ,1
11. ;i
on
1
O. Strove
ISN ;:,-,
307.6
0.21
3
Kurnhain
•,'.;. ,
simple
1
0. Strove
I.N.sr.M
203.5
0.47
2
Hall
iv., -.;
simple
1
O. Strove
204.6
0.35
6-2
S<-liia|iar<-lli
1857.67
ii.i
1
O. Strove
1886.91
203.2
0.47
4
EiiKlenunn
iMl.s
1
(X Strove
1887.78
195.2
0.49
2-1
HoiiKh
l( -
i>|,i
1
0. Strove
1887.79
195.8
0.44
5
Tarrant
1887.80
198.7
0.41
4
Hull
IV.-M :.
! U
0.39
1
O. Strove
1887.86
195.0
0.33
11-8
S-hi:t]i:in-lli
iMi n
236?
oblong
1
O. Strove
1888.69
189.9
0.25
4
Kurnliam
i-.:. •:
<0.5
1
0. Strove
1888.90
187.0
0.15
14-10
Schia|ian*lli
1869.74
15.6
—
6-0
Harvard
1889.51
1889.82
163.2
193.1
0.10±
0.2 ±
1
1
Kurnliam
Hou^h
8.0
—
1-0
Dune>
l.vyt.M
175.0
0.15
3
Srhiajiarclli
L'ln
oblong
1-0
( >. Strove
L89OM
single
—
I
Si ln;i|uiirlh
1^71 7 .">
uneifnrnu'
1-0
O. Strove
1 VI t *"'
1 -V'l.Wii
:;i r.
0.20
5
Kurnliam
1VI 7.-.
0.33
1
O. Strove
«>.:•!
5
S lil.i|i;il,-lh
IV7 7,'.
156.4
0.2 ±
1
Kuril li:iiu
26.6
BJB
4
Kurnliam
1878.65
elong. doubtful
Bumham
IVfJ.'.ll
OJQ
Sliiaparelli
150.0
doubtful
I
Hall
18'.»
•!.97
I.. -
200.2
6
1
S< Inajiarelli
Biguurdan
1880.60
5
Burn ham
1894.85
simple
—
4
Srhiai>arelli
The pair was first measured in 1852, and when the <.!,-, ivations were i<-
].« ated the following year it was found that there was a slight diminution in
the angle of position as well as in tin- di-tam •< •. In !>.">! and in 1856 the star
was noted as single, but in 1857 the eoinpatiion appi-arcd in the op|K>Mite <|Ma<l-
rant . and hence it became evident that the star is a binary in rapid retrograde
motion. Continued observation disclosed the fact that the orbit is highly
230
8 EQUULEI — 0^535.
inclined upon the visual ray, and STRUVE'S measures seemed to indicate a period
of 6.5 or 13 years. Since 1877 the star has been carefully followed by BURN-
HAM, and by means of his fine series of observations we are enabled to derive
a very satisfactory orbit.
The two orbits heretofore published for this star are as follows:
p
T
e
a
Si
i
I
Authority
Source
jn.
11.48
11.45
1892.0
1892.80
U.L'U
0.14
0.41
0.452
L'4.0
22.2
81.8
79.05
26.6
0.00
Wrublewsky, 1887
See, 189f>
A.N., 2771
A.N., 3290
An investigation of all the observations leads to the following elements of
8 Equulei :
P = 11.45 years
T = 1892.80
e = 0.165
a = 0".452
o = 22° 2
i = 79°.0
A = 0°.0
74 = -31°.441
Apparent orbit:
Length of major axis = 0".904
Length of minor axis = 0".171
Angle of major axis = 22°.2
Angle of periastron = 22°.2
Distance of star from centre = 0".075
The following table gives a comparison of the computed with the observed
places, and shows that the present elements will never require any considerable
correction. Only a few large deviations occur, and these are probably to be
explained by the extreme difficulty of the object.*
BURXHAM'S measure of 1877 is marked "doubtful," and is practically
only an estimate, as the object was very difficult to separate.
It will be seen that the eccentricity of this orbit is considerably smaller
than that generally found among double stars. It is also remarkable that the
real major axis coincides with the line of nodes, so that X is zero.
8 Equulei and uPegasi are the most rapid binaries in the heavens, and on
this account are worthy of special attention from observers who have large
telescopes. The elements given here need to be tested by further observation.
It is especially important to determine the maximum distances of the companion
when the angles are about 22° and 202° respectively, as this would furnish a
more exact determination of the eccentricity and the major axis.
• Astronomische Nachrichten, 3200.
IT PBC1A8I = 0989.
287
•i AKUOV or Court in, ui 111 OMKMVKO 1'i.Acn.
1
'.
*.
f.
^.
, ,.
*-*
•
...
is:,: • •
• i:
ft
- 1.9
,,MS
2
uve
iv. .:
191.9
: ... •
o u
- 4.7
1
0. Strove
iv,;,.;
9M
+ 0.1
nil
1
O. Strove
iv-.x.-.,
.1 i'
- 4.:»
1
mve
: •
13.5
• • •
+ 4.8
•HI 11
1
nive
•- •!
: • _• I
0.4 ±
+ lo..-,
+ 0'
1
: IIVI-
>. • ;i
15.6
_
- 7.9
_
6
;ird
8.0
M-J
_
- 6.2
1
Doafc
1874 :«
' ..:
0.48
+ 0.4
-0.15
•2 1
o. Strove
;-... :
0.2 ±
OUQ
-31.5
-O.K>±
1
Itiirnhain
• ,,,,,.
. • :
0.85
- 0.2
5
Hiirnhain
i8« M
.1 '_•
• 18
+ 0.9
+0.01
4
Ituniliaw
>-.-,.
9.8
7.1
+ 2.7
3
Hiirnliain
1XS -.:.
07 JJ
U3
+ 5.4
-HU1.'
3
Kiirnhnin
• — v
_•" -
' 17
".-._•
+ 0.7
n.o.-,
12-6
Hall'.'; S-liiaj.ar.-lli (', 2; Englemann 4
; ... 3
;.., ,
0.42
- 2.7
-0.08
--J 1.x
II.. I' 1 ; Tar..',; Hall 4 ; S.-hiaparelli 11-8
IXVVS.I
L88JI
,.,_.,,
" l-.'
- 4.4
18-14
]iimili:iin 4; S-hiai>an-lli 14-10
:-•• ;-.•
177.1
:x,,,,
• I.'.
- '.'.'.I
-0.07
5
Itimiham 1 ; lli.u-jh 1 ; Schiaparelli 3
iv... „
•Mete
, . i
—
n 1.
—
—
.:
BobianutDl
U.O
mo
QM
- 7.5
-0.06
10
Hiirnhain ', ; S-hiaparclli .',
:•« :
1 : |
'.:j
+ 1.2
6
Itiirnhain 4 ; Si-hiapaivlli 2
> . ;•..:
16.8
10.0
0.25
OJI
+ 6.8
-0.01
g
Schiaparelli
!-•! V.
•U.I4.
.-.:•« x
—
M 10
—
—
-
Schiaparelli
Thf following is a short ephenu-ri-:
1896.85
1X97.85
0.39
205.2
1899.85
1900.80
108J
18fi.4
ft
0.44
0.28
L89&U 200.8 0.52
I'M. \-l =
Sl» 40-.1
yeUowiah
< = +28° 11'.
5.0, yrllowiih.
Ditfovrred by Bumham, Auyutt 12, 1880.
i>x.,,.x
1883.02
1888.78
1889.51
1890.57
137.9
116.0
•j;i 7
262.3
187.1
0.16
0.23
0.14
0.10
i
4
1
I
4
!
OMRETATIOXM.
•
Humham
Englemann
Burn ham
Burnham
Ktirnham
1892.39
1892.96
l.-.I M
135.1
P.
O.'lO
1891.61 150.0
1891.81 144.6 0.13
1891.92 159.0 0.18
0.18
0.20
DUO
t
4
• •
4
1
I
Burn ham
Humliam
S<-liiaparelli
Itiirnliam
Itarnard
Schiaparelli
238
K PEGASI = /J989.
*
1893.51
Bo
12LO
P»
0*29
n
3
Observers
Leavenworth
1893.77
127.5
0.20
2
Barnard
1893.82
130.5
0.25
2-1
Comstook
1893.92
123.6
0.27
8
Schiaparelli
t Bo pa n Observers
1894.51 117?6 O.'l9 7-6 Barnard
1894.83 114.8 0.14 4 Lewis
1894.87 114.7 0.24 6 Schiaparelli
1895.62 107.9 0.17 6 Barnard
This remarkable double star was discovered with the 18-inch refractor of
the Dearborn Observatory. Its extreme closeness led to the belief that it
would prove to be binary,* and accordingly it has been found to be in rapid
revolution. DR. ENGLEMANN of Leipzig succeeded in making one measure of
the pair in 1883, which indicated a retrograde motion. BURXHAM'S measures
were continued at the Lick Observatory from 1888 to 1892, and the new data
thus obtained enabled him for the first time to get the approximate period of
revolution (Monthly Notices, March, 1891).
At the request of BURXHAM and the writer, BARNARD has since fol-
lowed the star, and obtained additional measures which appear to be sufficient
to give us a reasonably good approximation to the elements of the orbit.
In his first examination of the motion of this pair, BURXHAM made the orbit
nearly circular, but the recent observations show that the orbit has about
the usual eccentricity prevailing among binaries, and that the inclination of
the orbit is very high. In the Monthly Notices for November, 1894, MR. LEWIS
has given a set of measures recently obtained with the Greenwich 28-inch
refractor, and sketched an apparent orbit which would better satisfy the latest
observations.
Having collected all the observations of this difficult star, including some
unpublished measures kindly furnished by BARNARD last Autumn, we have
investigated the orbit by the method of KLINKERFUES, and find the following
elements:
P = 11.42 years
i = 81°.2
T = 1896.03
ft = 116°.25
e = 0.49
A. = 89°.2
a = 0".4216
n = -31°.5236
Apparent orbit:
Length of major axis
= 0".555
Length of minor axis
= 0".130
Angle of major axis
= 115°.7
Angle of periastron
= 30°.2
Distance of star from
centre = 0".032
* Astronomische Nachrichten, 3285.
1
K I'EOASI = 0989.
B89
COMTARIKOX OF COMPVTKD WITH OWKBVKK I'l »• I-
1
«.
A
f»
A
•r-fc
P*-*
•
......
IVMM'.S
: • ;
"'-•-'
+ IJ2
+0.05
4
Kurnliaiii
116.li 1
- 3.5
-0.11
1
KtiK'N'iiianii
i-^.X.78
. l'7l 1
„_•!
+ 0.6
4-0.02
Huriiliiini
1 ^v.»..-|l
" 11
o u
-1- 4.4
—0.01
1
Itiitnliain
"•.57
I-.M :.
0.10
_ 1 I
±OIH.
4
lUirnham
ISlM.r.l
lflO.0
n:. o
040
+ 5.0
_,.
Bvr&haa
1K1M "I
144.6
1 l<> L-
+ « 1
-O.dT
4
Ituriiliaiu
L891
4-19.8
_(l«.J
.'{
S4-lii;i|i;irt-lli
>•_' •
_d
4
Kuril h:iin
ISLO
!_••> 1
+ 1.9
MM;
1
;irtl
OJQ
+ !•
.,,.;
1
Schiu|iurelli
iat.0
i •_•.-,.:.
-
+ (».(»•_•
:t
Leaven worth
U7J
+ » B
_<.
9
liarnanl
123.0
I'L'.-,
+ :.-.
-0.0.-J
2-1
Cotnxtock
123.6
122.3
<>..'7
+ 1.4
-O.ul
8
S<'liia|Hir«*lli
i :, 1
UT.8
L1&8
0.19
- I.'.'
-0.07
.ittl
Ills
IK;;
0.14
- 1 •.'
-0.11
1
Lewis
189J v
HIT
lir.r.
• >-jl
0.25
- l.-.t
-o.oi
6
S.-|ii.ip:iri-lli
!>•'.-.'.-•
KI; n
H>.; :
0.17
0.1 fi
+ 1.2
+0.01
6
Kamard
I.I HI MKRI8.
t
1896.80
7.80
,
taaut
»7JO
OJ1
1900.80
L'7'.».o
_••.•• I
0.24
0.16
The agreement must be considered very Katisfaetory when account i« taken
of the extreme closeness of the components, and the high inclination of the
orbit, which permits a small error in angle to have a marked effect on the
distant-*-. From an t -xainination of all the measures it seems probable that most
observers have underestimated the di.-tam-fs and this certainly must have bi-rii
the case with l>i:. K\«.IIM\\\. who usi-d only a 7.")-inch rcfrai-tor, and tlx-n-
fore could nut hav»- divided tin- cuin|iuncnt.s at a distance of OM6. The cuin-
putt-d di-tancf is therefore much more prubablc, and especially since tin- cK-nn in-
are based principally upon the excellent measures of lii I:\IIAM and BARNARD,
made with the 30-inch refractor of the Lick Observatory.
I'.' IN ii AM ha- repeatedly called the attention of astronomers to the high
importance of systematically following such extremely rapid binaries with large
t < It-scopes, so that we could in a few years derive orbits, which, in the case
of most stars, would n-ijuin- the oh-crvations of centuriea.
\\ would In-g to add that it is not only important to observe * Pega#i
annually, but c-pccially at certain critical parts of its orbit, where measure-
would enable as to fix the eccentricity and the inclination more accurately.
Thus, according to the above elements, the minimum distance will occur just
240
85 PEGASI = /J733.
after periastron passage in 1896.03, and measures made on either side of the
periastron will be very valuable. At the minimum distance (0".034) the star
will be single in the largest telescope in the world, but it would be important
to ascertain just when this disappearance takes place, and how long it lasts.
According to the above orbit, the companion ought to be visible in a 30-inch
refractor until August, 1895, and hence we suggest that observers should
watch for it during the Summer of 1895 and the Autumn of 1896. Good
observations at these epochs will be of the greatest value in improving the
elements of the orbit.
85 PEGASI = /s 733.
o = 23h 56m.9
6, yellowish
8 = +26° 34'.
10, bluish.
Discovered by Burnham in 1878.
OBSERVATIONS.
(
0,
Po
n
Observers
t
60
Po
n
Observers
O
§
O
g
1 878.73
274.0
0.67
3
Burnham
1889.59
134.7
0.94
5
Burnham
1879.46
284.6
0.75
5
Burnham
1889.90
137.0
0.70
5
Schiaparelli
1880.59
298.3
0.65
5
Burnham
1890.55
139.0
0.78
4
Burnham
1890.96
146.4
0.71
6
Schiaparelli
1880.79
297.2
0.66
3-2
Hall
1891.56
151.8
0.79
3
Burnham
1881.54
311.5
0.58
1
Burnham
1891.94
152.7
0.78
3
Schiaparelli
1882.62
89.4
0.64
1
0. Strove
1892.75
169.7
0.57
1
Burnham
1883.75
333 ±
_
1
Burnham
1892.94
167.3
0.74
4
Schiaparelli
1893.96
176.1
0.75
6-3
Schiaparelli
1886.91
109.1
0.79
3
Hall
1886.98
111.0
0.58
1
Schiaparelli
1894.54
178.6
0.84
5
Barnard
1894.88
251.8
0.85
1
Lewis
1887.91
119.3
0.66
1
Schiaparelli
1894.93
188.6
0.65
2-1
Schiaparelli
i888.<;;»
126.7
0.95
5
Burnham
1895.65
190.2
0.80
10-9
Barnard
1888.96
124.1
0.83
3
Hall
1895.73
198.4
0.73
3
See
1888.96
128.3
0.70
7
Schiaparelli
1895.74
204.8
0.75
2
Moulton
Since BURNHAM'S discovery of this rapid binary, the companion has de-
scribed an arc of 285°.* The components are of the 6th and llth magnitudes,
and so great an inequality in brightness combined with the closeness of the
pair, renders exact measurement very difficult. Therefore it is not strange that
• Attronomische Nachricttten, 3339.
85 PEOAHI = 0733. '_' I 1
tin po-ition-aiiijU •- !1 a- tin- distance* obtained b\ the -aim- or h\ different
olf.er\ers -lion Id oeca-ionally exhibit -eii-ihle di-erepaneie-. Yet when the
measures are properh combined into -tillable yearly nu-aiis we olitain a MTU--.
<>)' places which will give an <>rl>it tliat is subf-tantialh correct.
The lir-t orbit of thi- pair \\a> computed hy I'ltoKEgaOR SriiAKHKKl.K ill
1889; hi- clrllH-lll- :r
/' - •-'•-'.:! yearn Q - 306*. 1
T - 1884.00 • - 68e.6
• - ' A - 70°.3
a - 0>.96 N - +16'.144
Thi- orhit represent^ tin- mca.-urcs prior to 1891 with the desired accuracy,
hut the error in an-rle rapidly accumulated and in 1892 surpassed 20°. Accord-
in^l\. l'i:»i i --"i; (ii A-KN AIM- attempted an improvement of the orhit (A.X.
."•II""). and olitaiued a set of elements which rendered the residuals in angle
i-d'mgly Miiall:
r - 17.487 yam Q - 307
r— 188421 <-66°.74
« - 0.1», I A - 69-.7S
a - O'.KO n - -H.'(i°.586
i-rt In-less the ephemeris computed by PKOFKSSOH GLASKXAPP has sig-
nally failed of its pur]M>se, as the error now amounts to about 80°. As the
iiiNc-tigation was based wholly on angles of position we may infer that these
coordinate- were affected by sensible systematic errors, which might the more
,\ re-nit from the inequality of the stars.
Tin- eareful inca-nre- which I recently secured at the Washburii Observa-
tory ( .I../. :'•"•'.! i li.i\e enabled me to make a new determination of the orbit
based on all the material of a tru-t worthy character. We find the following
elements of 8.~> /'"/"•".'
P - 24.0 yean Q - 116*.3
7 - 1883.80 i - 55*.6
e m. 0.388 A ^ MB I
a - 0-.8904 n - +15°.0
Apparent orbit:
length of major axu — 1
th of minor axis «- I'.INI
> of major axis — 118°.0
Angle of |ieria«tron ~ 1 !
Distance of star from centre — OM'.<7
24-2
85 PEGASI = ft 7 33.
The accompanying table gives a comparison of the computed with the
observed places.
COMPARISON OF COMPUTED WITH OBSERVED PLACES.
t
60
Oc
Po
' PC
0o vc
Po— PC
n
Observers
1878.73
274.0
275.5
0.67
0.77
o
-1.5
-O.'lO
3
Burnliam
1879.46
284.6
282.2
0.75
0.76
+ 2.4
-0.01
5
Burnham
1880.69
297.7
294^4
0.66
0.69
+ 3.3
-0.03
8-7
Burnham 5 ; Hall 3-2
1881.54
311.5
309.0
0.58
0.58
+2.5
±0.00
1
Burnham
1886.94
110.1
113.4
0.69
0.69
-3.3
±0.00
4
Hall 3 ; Schiaparelli
1887.91
119.3
122.8
0.66
0.77
-3.5
-0.11
1
Schiaparelli
1888.87
126.4
130.8
0.8,3
0.81
-4.4
+ 0.02
15
ft 5 ; Hall 3 ; Schiaparelli 7
1889.74
135.8
137.8
0.82
0.83
-2.0
-0.01
10
Burnham 5 ; Schiaparelli 5
1890.76
142.7
146.0
0.75
0.83
-3.3
-0.08
10
Burnham 4 ; Schiaparelli 6
1891.75
152.2
154.7
0.79
0.81
-2.5
-0.02
6
Burnham 3 ; Schiaparelli 3
1892.85
168.5
165.0
0.74
0.78
+3.5
-0.04
5-4
Burnham 1-0 ; Schiaparelli 4
1893.96
176.1
176.4
0.75
0.75
-0.3
±0.00
6-3
Schiaparelli
1894.93
188.6
187.5
0.65
0.72
+ 1.1
-0.07
2-1
Schiaparelli
1895.73
198.4
11)7.4
0.73
0.70
+1.0
+ 0.03
3
See
We are' justified in predicting that the true period of 85 Pegasi will not
differ from the value given above by more than one year, and that the error
of the eccentricity will not surpass ±0.02. The good representation of the
angles and distances shows that the other elements are equally satisfactory.
The foregoing elements will therefore never be greatly changed; but some im-
provement is desirable, and observers with great telescopes should continue to
give this important system regular attention. The following is an ephemeris
for the next five years:
t
1896.70
9.
209?6
PC
OJO
1897.70
222.4
0.69
1898.70
234.5
0.71
1899.70
1900.70
2458
256.1
PC
0.74
0.76
rilAI'TKK III.
RESULTS OF RESEARCHES »\ mi OHHITS OF FORTY BINARY STAKS, WITH
' iKNKKAL CONHIDEJtV ROOT Kl -I'l ' I IN« THE STKLLAK SVKTKMS.
§ 1. /-/A 1/1, ,!/* ttf II,, Orbit* of Forty Binary Star*.
IN i ii i pi-reeding chapter we have presented detailed researches on the
orbits of forty stars. To enable the reader to grasp readily the existing state
of our knowledge, we have also included diagrams of the apparent ellipses,
and of tin- mean observations from which the elements were derived. In many
• i-i-« we haVf -''in that lln- ••!>-. i \ atioii- an- r. laliv . h |-«.ii-jli. and llial uliil. the
errors an- small absolutely, they are yet very large in comparison with the
minute quantities measured. Under these circumstances it seemed useless to
attempt a Least-Square adjustment of the residuals, and hence we have through-
out employed graphical methods, and arrived at the adopted elements by suc-
cessive approximations of an empirical character. Accordingly, the orbits are
not definitive, but for reasons indicated in the several cases the changes which
future observations may necessitate will be confined within narrow limits.
In tin- following Table we give a summary of the elements, with the prob-
able uncertainty still attaching to the period and the eccentricity. From the
variations of these element* it is easy to see about the extent of the alterations
which may be required in the adopted values of the other element*. The final
changes which future ol>-er\atioii- ma\ produce in any given orbit can not yet
be determined with < . rtainty, and hence our variations may occasionally turn
out somewhat too small : but as care ha- l..-,-n exercised to avoid over-
estimation of the accuracy of results, the values here indicated ought not to
prove very deceptive.
In glancing over the apparent orbits of the preceding chapter the reader
should remember that the adopted elements depend not only on the agreement
of the observed distances with the apparent ellipses, but also on the accuracy
with which the law of areas is satisfied. These two criteria seem to justify
the comparatively small variations indicated in the Table of elements ; but as
I'll
ELEMENTS OF THE ORBITS
the orbits here presented depend essentially on the observations employed, and
as our choice is to some extent a matter of judgement, it is not certain that
we have always arrived at the best results.
RESULTS OF RESEARCHES ox THE
Star
a
8
P
T
e
a*
a
i
i.
23062
h 111
0 1
+57 53
104.6ir™'± 2.0
1836.26
0.450 ±0.02
1.3712
47.15
43.85
90.9
jjCassiopeae = 2" 60
0 42.9
+57 18
195.76 ±10.0
1907.84
0.514 ±0.03
8.2128
46.1
45.95
217.87
yAndrom.BC= 02'38
1 57.8
+41 51
54.0 ± 1.0
1892.1
0.857 ±0.02
0.3705
113.4
77.85
I'OO.l
«Can. Maj. = Sirius
6 40.4
-16 34
52.20 ± 2.0
1893.50
0.620 ±0.02
8.0316
34.3
46.77
131.03
F. 9 Argus = £101
7 47.1
-13 38
22.0 ± 1.0
1892.30
0.700 ±0.02
0.6549
95.5
77.72
75.28
£CancriAB = 21196
8 6.2
+ 17 58
60.0 ± 0.5
1870.40
0.340 ±0.03
0.8579
88.7
7.4
264.0
2'3121
9 12.1
+ 29 0
34.0 ± 1.0
1878.30
0.330 ±0.03
0.6692
28.25
75.0
127.52
wLeonis = 21356
9 23.1
+ 9 30
116.20 ± 1.0
1842.10
0.537 ±0.01
0.8824
146.70
63.47
124.22
g>Urs. Maj. = 02'208
9 45.3
+54 33
97.0 ± 5.0
1884.0
0.440 ±0.03
0.3440
160.3
30.5
15.9
t Urs. Maj. = 21523
11 12.9
+32 6
60.0 ± 0.1
1875.22
0.397 ±0.005
2.5080
100.8
55.92
126.33
02:234
11 25.4
+ 41 50
77.0 ± 5.0
1880.10
0.302 ±0.04
0.3467
157.5
50.8
206.8
02'235
11 26.7
+61 38
80.0 ± 5.0
1834.30
0.324 ±0.05
0.8690
81.7
49.32
137.78
yCentauri = H25370
12 36
-48 25
88.0 ± 3.0
1848.0
0.800 ±0.03
1.0232
4.6
62.15
194.3
y Virginis = 21670
12 36.6
- 0 54
194.0 ± 4.0
1836.53
0.897 ±0.005
3.9890
50.4
31.0
270.0
F.42Com.Bei-.=21728
13 5.1
+18 4
25.56 ± 0.1
1885.69
0.461 ±0.01
0.6416
11.9
90 ±
280.5
02'269
13 28.3
+ 35 46
48.8 ± 1.0
1882.80
0.361 ±0.05
0.3248
46.2
71.3
32.63
25Can.Ven.=21768
13 33
+36 48
184.0 ±25.0
1866.0
0.752 ±0.05
1.1307
123.0
33.5
201.0
« Centauri
14 32.6
-60 25
81.10 ± 0.3
1875.70
0.528 ±0.005
17.700
25.15
79.30
52.0
02^285
14 41.7
+42 48
76.67 ± 5.0
1882.53
0.470 ±0.05
0.3975
62.2
41.95
162.23
£Bootis = 2-1888
14 46.8
+ 19 31
128.0 ± 1.0
1903.90
0.721 ±0.02
5.5578
10.5
52.28
239.25
rt Cor. Bor.' = 2"1937
15 19.1
+30 39
41.60 ± 0.1
1892.50
0.267 ±0.01
0.9165
27.1
58.5
I'l 7.r>7
/i'Bootis = 2:1938
15 20.7
+37 43
219.42 ±10.0
1865.30
0.537 ±0.03
1.2679
163.8
43.9
329.75
02'298
15 32.4
+40 9
52.0 ± 1.0
1883.0
0.581 ±0.02
0.7989
1.9
60.9
26.1
y Cor. Bor. =21967
15 38.5
+26 36
73.0 ± 2.0
1841.0
0.482 ±0.05
0.7357
110.7
82.63
97.95
£ScorpiiAB=21998
15 58.9
-11 5
104.0 ± 4.0
1864.60
0.131 ±0.05
1.36 11'
9.5
70.3
111.6
<rCor. Bor. = 2"2032
16 11
+34 7
370.0 ±25.0
1821.80
0.540 ±0.04
3.8187
30.5
47.48
47.7
£ Herculis = 2-2084
16 37.6
+ 31 47
35.0 ± 0.3
1864.80
0.497 ±0.03
1.4321
37.5
51.77
101.7
3416 = Lac. 7215
17 12.1
-34 52
33.0 ± 1.0
1891.85
0.51 2 ±0.03
1.2212
144.6
37.35
86.1
2'2173
17 25.3
- 0 59
46.0 ± 0.4
1869.50
0.200 ±0.03
1.1428
153.7
80.75
322.2
/lt1HereulisBC = A.C.7
17 42.6
+27 47
45.0 ± 1.0
1879.80
0.219 ±0.02
1.3900
61.4
64.28
180.0
T Ophiuchi = 2"2262
17 57.6
- 8 11
230.0 ±15.0
1815.0
0.592 ±0.05
1.2495
76.4
57.6
18.05
V. 70 Ophiuchi = 2"2272
18 0.4
+ 2 33
88.3954 ± 1.0
1896.4661
0.500 ±0.02
4.548
125.7
58.42
I'.IS.LC,
F.99Herculis=A.C.15
18 3.2
+30 33
54.5 ± 3.0
1887.70
0.781 ±0.02
1.014
indeter.
0.0
(*)
£ Sagittarii
18 56.3
-30 1
18.85 ± 1.0
1878.80
0.279 ±0.02
0.6860
69.3
67.82
328.1
y Coronae Australia
18 59.6
-37 12
152.7 ± 5.0
1876.80
0.420 ±0.02
2.453
72.3
34.0
180.2
/SDelphini = 0151
20 32.9
+ 14 15
27.66 ± 1.0
1883.05
0.373 ±0.03
0.6724
3.9
M .35
164.98
F.4Aquarii = 2'2729
20 46.1
- 6 1
129.0 ± 5.0
1899.40
0.514 ±0.03
0.7320
177.7
72.53
68.63
8 EquuleiAB =02-535
21 9.6
+ 9 37
11.45 ± 0.2
1892.80
0.165 ±0.02
0.452
22.2
79.0
0.00
icPegasi = £989
21 40.1
+25 11
11.42 ± 0.4
1896.03
0.490 ±0.1
0.4216
116.25
81.2
89.2
F.85Pegasi = 0733
23 56.9
+26 34
24.0 ± 1.0
1883.80
0.388 ±0.02
0.8904
116.3
.vu;
256.4
(«) Angle Per. = 169°.5.
In the course of the next twenty years a sensible improvement can be
effected in the orbits of rapidly moving stars, such as K Pegasi ; but mean-
i "i: M IIIN VIM -i VMS.
while tin- rlcincntt* here adopted will give ephemendc- -nllieieiitly e\:i<-l f»r
tin- ii-r iif olMwrvcn*.
\ -roroUH prosecution of tin- nica-nrcmcnt of doiiMc -tars will lunii-li the
- • >i
^i vi>.
1111
4 1.8390
— 6.6667
i • >
4- 3.1
:iu
- 6.0000
: •
- 4.0'.U1
- 1
+ 7
- 1.9666
+ 4.4390
- 4.6953
— 2.ML'.".
4- .s •
•J. AxU Mil \
AH. OrUi Apt- .
•
•
4- 6. :'-•.: i
- 4.'.i::l.-.
•f- ii
1"
- 9.0908
4 8.000
-f- 1
- 4
4- 6.6066
-19.098
- .
413.nl.-,
4 L'.7'."'7
-31.111
-31.5236
+15.0
0.941
I 7"|
-
l 576
L' UNI
. vjl
1 .147
0.64
l.'.Ho
'."'7
I Ml|
2.656
1.546
r.o«
i M
i
I .'.I-
:
Ma Uk
L'.7iNi
I "•_••>
0.00
OJO
: os
6.16
I Is"
in ;.-..;
0.175
,, )84
4.71
L752
i us
i in
I 17
.... :
" 177
o.KI
1.00
1-7 I
111 1
L04.6
o I
1 1" I
17 7
IS6.1I
111.3
•.,,
4L'.4
I.: I
l :. l :,
'.! I
L69J
71 s
11. V7
-
I s | M
174.1
:•::! 1
177s
Ho |
144.7
is.; 7
15.3
16O2
I'll I
262 1
I7i;r.
is-
-..
•
0 in;
1 i«;
" i :.•_•
o Il-.i
0.054
07U
5.90
0.182
oi'o'.i
0.080
1.735
.. |.V,
0.61
0.712
Q 168
0.194
o.l 7:5
0.07.-.
f
M
0.611
1.161
0.670
o
i MIL' I
0.913
" 17'J
0 77'.'
1 >..V_'.-,
n i;7o
o.s.-.l
l.KNI
1.152
0.912
0.582
0.725
0.980
0.750
1.1. so
1 o|-
0 17.'.
1 17.-.
L040
O.H7
1 is..
0.610
0.716
o.o.Vt
0.716
0..-W7
0.577
0.1X7
I I - I X _•
" \ ll.
0.790
0.661
0.419
0.973
0.639
0.631
O..V.-.I
o II'.'
0.781
ii I
Magnitude Ughi rmilo
• ;7
1 . lo
7.7 ; r.:i
7.2 ; 7.5
« J7
I ;.-,
7 ;7J
6 ;7.8
4 j4
3 ; 3.2
6 ;6
7.3 ; 7.7
6 ;8.5
1 ;2
7.5 ; 7.6
i :, . .,:.
5.5 ; 6
6.5 ; 8
7 ;7.4
4 ;7
6 ; 5.2
6 ;7
3 ;6
.: l
10
11.7
4.4
5.5; 5.5
6 ;7
4/>
6.0; M
I 7.-.
ISM
171
1.91
I .;_•
l
1
1.20
1
1.45
25.12
2.51
1.10
6.31
1 .V.i
3.98
1.45
15.85
1.20
2.51
16.88
1
I 71
•J.M
!•„..,:.
i n
i
c.:u
! 59
1.91
.••-l
Colon
asr*
•
I .-.'«.
OJ15
onlii
nirjs
oil.'.
0.129
OJ578
0.488
0 J 14
.,.>:.
0.161
0.217
0.194
0.115
(MM
0.342
0.613
o.
o.xil
i I-.M
.. i.,.
OJM
r.7 I
7«».2
13.1
K3.0
54.0
62.4
81.1
13.4
26.4
IJ I
89.4
83.3
54.2
84.9
69.3
19.8
47.8
48.0
80.4
11.5
25.5
29.5
18.5
86.4
71.-.I
7(1.7
Id.
7.-, 7
59.3
/•I."'
X'.L'
70.7
68.3
67.6
56.2
65. 7
64. L'
57.5
64.6
19.3
74.0
50.8
84.9
60.5
47.3
88.1
47.7
24.7
89.5
77.5
83.1
89.6
71.0
88.7
21.2
<uu;
X3.1
7l'o
67.-.I
X7.:t
• • -
material for one hundred m-lnt* at the end of another half century, ami accord-
ingly sueh effort id urgently demanded l>\ the highest interest* of >cieii
246 RELATIVE VELOCITY IN THE LINE OF SIGHT FOK THE EPOCH 1896.50
§ 2. Relative Velocity of the Companion in the Line of Sight
for the Epoch 1896.50.
When the elements of the orbit are known, the theory developed in §5,
Chapter I, first published in the Astronomische Nachrichten, No. 3314, enables
us to predict the relative motion of the companion of a binary in the line of
sight for any given time. The columns marked - and ± * in the foregoing
Table contain the desired results for the epoch 1896.50. The numbers in the
column - express the orbital velocities in units of the radius of the hodograph.
As the scale of this radius is unknown, except in a very few cases, we are
not able to express this velocity in kilometres or in other absolute units ; but
when the parallaxes are determined this may be readily accomplished. The
column as it stands, however, shows the rate of orbital motion, compared to
what is approximately the average velocity, and we are thus enabled to select
those stars which have a rapid orbital motion. If the motion of any given
pair be rapid, and also mainly in the line of sight, as in the case of
70 Ophiuchi, the system so circumstanced will be favorable for spectroscopic
measurement. The column ± - shows what part of the orbital motion is in the
p
line of sight, and this enables us to select for measurement with the Spectro-
graph those pairs which have a large orbital velocity with the major portion
of it towards or from the earth.
The stars at present the most favorably situated for measurement of the
relative motion in the line of vision are : -q Cassiopeae, a Canis Majoris, 9 Argus,
% Bodtis, y Coronae Borealis, £ 2173, 70 Ophiuchi, ft Delphini, and a Centauri.
Adopting parallaxes of 0".75, 0".162, and 0".154 for a Centauri, 70 Ophiuchi,
and 77 Cassiopeae respectively, we find the line-of-sight components for the
several systems to be 6.66, 13.95, 8.89, where the unit is the kilometre. These
quantities are well within the limit of spectroscopic measurement, and therefore
an experimental determination offers an attractive problem to observers occupied
with this branch of Astronomy.
It will be seen that several of the above stars are wide, while others are
very close. If the two spectra can be photographed on the same plate, the
lines being only slightly displaced by the relative motion of the stars, as in
the case of spectroscopic binaries, the close pairs ought to be as easily measured
as the wide ones, whose spectra could perhaps be photographed separately.
In any case the prosecution of these researches with the powerful spectro-
scopic appliances of the great telescopes of our time is an urgent desideratum
KKLATION 01 nil ( >|;ii| T-|'t.ANKS l<> III! I'l.XM "I III) M\\ h\ \\ \ ^ JIT
»f A -iron., my. Ami until tin- relative motions of visible s\-icui- an- ihu-
dctermincd then- \\ill remain -<>ine doubt a- to tin- reality of (he so-called
•.pectiiiM-opie l>inaric>; not that an\ <m,- doubt- tin- theoretical validity of the
l>oi-pi n;-IIro<;i\- principle. hut rather that other explanations nf the phe-
ii"iiifiia interpreted as -peetro-eopic liinaric- an- con-idcred possible. Moreover,
the great intcre-t attaching \o hive-libation- which will give tin- absolute
dimcn-ioii-. parallaxi-- and iiiasst-H of binary h\-!<m-. a- u. II a- the |>i>--il>ilil y
of toting tin- validity of tin- lau ••!' -i a\ itatimi. mi^ht to iudiu-r a-tion.niHT8
to |.ro*ccut»- thr-r >tu«lir* \\itli a x.ral romim-ii-tnatc with their rc-al im-
<)\\inir to the small wixv of tin- earth's orhit. it seems that our principal
hop(- I'.ir kixiwlfdirc of the dinu-iinon* of the universe must he hased upon thi«
method. The change in wave-length due to motion in the line of sight wa»
originall\ pointed out li\ I )OIMM.KK, but IIii.i.ivs wa» the lirst to apply the
n-0-.cope to the heavenly Ixxlies, and to reduce IX'UM'LKu's principle to
actual practice, and to assign it a place in modern Astronomy. The applica-
tion of the principle to the determination of the dimensions of binary system*
\\a- tir-t propo-cd by Fox TALBOT. But as his theory was restricted to
the case of circular motion, it eould not he applied to the eccentric orbits
dc-crihed by the stars, and accordingly it has since been somewhat varied and
extended by others. The theory which we have developed is entirely general
for ellipses of every possible eccentricity, and from the point of view of rigor
and generality leaves nothing to be desired.
%.'?. fnrestigation •>> « /'.«•«.•//•/, /,'//<///o// o /'//// Orbit-I'lan'* nf' Jiinary SytttHU
I,, //// /'/./„. ,,f th. .»////// II ;/,/.
Owing to the well known arrangement of the stars and sharply-dclim-d
nebulae with re«i)ect to the Milkv \\ ;iy, it has U-en suggested that MHIK- rela-
tion might exist between the planes of the -tellar orbits and this fundamental
plane of the universe. An examination of this <|iicstioii is worthy of the atten-
tion of astronomers, and accord inirU we shall compute the inclinations of the
foregoing orbits by the formulae developed in the Hn-limr A*tr»nomi»chea «/<////•-
buck for 1832. The method of transformation which KNCKK has empl.
enables us to refer the plane of a double-star orbit to any absolute plane in
space.
Let us pass a plane through the central star parallel to the equator. The
pole of this plane will meet the celestial sphere at the same point as the pole
248 RELATION OF THE ORBIT-PLANES TO THE PLANE OP THE MILKY WAY.
of the heavens. Consider the triangle connecting the pole of the equator with
the poles of the real and of the apparent orbit. The pole of the apparent
orbit is determined by the right ascension and declination of the star (a, 8).
Let the coordinates of the pole of the real orbit referred to the same axes be
A and D, and let SI' be the angle which the great circle passing through the
poles of the real and apparent orbits makes with the meridian. The arc join-
ing the poles of the orbits is the inclination, i, and this is one of the elements
given in the foregoing Table. From the resulting spherical triangle we have
sinZ) = cos/ sin 8 + sin / cos 8 cos SI' = w cos ( J/— 8),
cosZ> sin (a — A) = sin t sin Q',
cos D cos (« — A) = cos* cos 8 — sin i sin 8 cos Q' = /« sin (J/— 8),
where sin i cos Q, ' = m cos M,
and cos i = m sin M.
1
Then tan M =
tan i cos SI '
sin(Jf-8)
tan(« — A) = - ,.
cos M tan SI '
cos («— A)
tanz> == tairp/-sr
When the right ascension and declination of the pole of the real orbit
have been determined, we may pass a plane through the central star parallel
to the Milky Way. In the spherical triangle which joins the pole of this
plane with the pole of the real orbit and the pole of the heavens, the incli-
nation of the real orbit to the plane of the Milky AVray is given by the arc
connecting their poles. Thus we have
cos F = sinZ> sin8' + cosi> cosS' cos(^4 — «'),
where a' and 8' denote the coordinates of the north pole of the Milky Way.
In our computations the coordinates of the north pole of the Milky W;iy
are taken on the authority of SIR JOHN HERSCHEL, who found
«' = 12h 47"' ; 8' = +27° .
There are two solutions for r, owing to the two values of A and 1) inci-
dent to the indetermination of the ascending node; and the resulting inclinations
to the Galaxy are tabulated as T and r'. Now, we do not know which of these
two possible inclinations to the Milky Way is correct, but since it is impossible
to select from either column any one prevailing angle, much less an evanescent
inclination, we conclude that the orbits are not directly related to the Milky
Way, or to any other fundamental plane of the heavens. Thus it is clear
that the orbit-planes lie at all possible angles to the Milky Way, with no
1 1 K.I I K<VKXTHICrriE8 A rUHDAMBXTM. I \« "I N \ M UK. J I' '
marked relation to tin- -«mral -cheme which di-tin-rui-hcs tin- arrangement of
tin- -tar- and well-dclincd nelmlae. 'I'll. consideration that tin- si/.c of a -tcllar
orbit i« -mall compared i.. tin- dim. n-i .11- of tin- Milkv \Va\. and that the
number of such -\-tcm- is \er\ v '•'••''• might ha\, enabled us to anticipate this
n-ii!t as probable •/ /•/•/../•/. -in.-c tin- condensation of nehuloti.* matter to M»
inaiiv centre- \\mild almo-t ••!' n. •••<• — it \ ha\e prodm-fd nUaliun- in all |M»Hi«ihK>
|>lam>*. ami i-vi-n if <-ontin«-d ori^inallv t<> «'in- plant- tin- paralK-li-ni \\<>\i\A hnvi-
Iwen di-turlu-d liv tin- a.-iii.n of fi.n-i^n l>«.dir> during the ages n-<iuiiv<l for thi-
d< -v.-l'-piin-nt of tin- \i-ilili- uiiiv.
!J I. Iliijh KIT, ,,lrit -if it-it a Fuiulnmnital Lota of Xuttirr.
It thu- ap|>tai- that the inclinatiotiH of the orbit-planes bear no definite
n-lution to any <;ivni plane of the heavens, ami an examination of the |>eriodK
of revolution shows that this element likewise has no charaeteristic pro|x?rty.
The jK-riods are found to range from 11 to 370 years.
It is evident that sueh elements as '/'. '/. Q, /. X, can have no relation to
phs-iial raiises, and an inujwetion of the Table shows no trace of sueh a eon-
II.M -lion. NVhen, however, we came to deal with the eccentricity the ease is
different. The results given in the preceding Table establish a most remarkable
law, which is of fundamental iiii|M>rtance in our theory of the origin and devel-
opment of the stellar systems, and is li.-i.li- of practical value to working
a-tronomiTs.
On glancing over tin rccrntricities it is found that while nearly all values
« \i-t. l'.-\\. if any. an- very Miiall like tlm-*- of the planets and satellites, nor
are any very large like those of the long-period comets. Tin- >malk--t eccen-
tricity is that of f >•"//'//, « = 0.i:il. the largest that of y I '//•«//// /s, « = (>.>: '7.
the mean value for the forty orbits, t = 0.482.
Let us take tin- ./--axis a- tin- a\i- of reeeiitririty. and the y-axis as tin-
axis of number of orbits, and divide the interval from e = 0.0 to e = 1.0 into
a convenient number of parts. Then, if \\\- « r. < t ordinatcs denoting the num-
ber of orbits falling in the given intervals, and connect the point- thus deter-
mined, we shall be able to illustrate the distribution of orbits as regards the
region of eccentricity.
\\ . find no orbits between 0.0 and 0.1: two ln-tween <>.! and 0.2; four
Ketween 0.2 and 0.3; eight between 0.3 and 0.4; nine between O.I and 0.5;
nine between 0.5 and 0.6; two between 0.6 and 0.7; four between <».T and 0.8;
250
HIGH ECCENTRICITIES A FUNDAMENTAL LAW OF NATURE.
two between 0.8 and 0.9; none between 0.9 and 1.0. The distribution is illus-
trated by the broken line in the accompanying figure. Since the number of
orbits is finite, the figure is an irregular line; if the number were indefinitely
increased, the figure ought to become approximately a smooth curve.
It is evident, therefore, that the true curve of distribution of orbits resembles
a probability curve with maximum near 0.482; the slope in either direction is
gradual, but the curve vanishes before it reaches zero and unity. "We have
drawn a pointed curve to illustrate what is conceived to be the probability
curve for the distribution of orbits, but it is based on forty orbits only, and
therefore is necessarily provisional. We may observe, however, that forty is a
number sufficiently large to realize the essential conditions underlying the
theory of probability, and accordingly we are justified in the inference that the
nature of the curve here indicated will never be greatly change3. There is
an irregularity in the broken line between 0.6 and 0.7, which may be attributed
to the effect of chance ; if the number of orbits were greatly increased this
gap would be filled up. In general, there will be irregularities in the distri-
bution so long as the number of orbits is finite, but they ought to become less
marked as the number is increased.
Thus, it is clear that in whatever intervals the axis of eccentricity be
divided, and however the number of orbits be increased, there will remain in
the curve of distribution a conspicuous maximum near 0.482, with a gradual
slope in both directions. The following table shows the eccentricities of the
orbits of the planets and satellites (Inaugural Dissertation, Berlin, 1893, p. 58) :
Planet
Eccentricity
Mean
Eccentricity
Planet
Eccentricity
Venus
Neptune
Earth
0.00684
0.00896
0.01677
L 0.06026 J
Jupiter
Saturn
Mars
0.04825
0.05607
0.09326
r I-HII a. <
0.04634
J I
'Merrur i/
0.20560
Satellite
Eccentricity
Mean
Eccentricity
Satellite
Eccentricity
Mean
Eccentricity
Satellite of Neptune
....
V (BARNARD) "I
....
)
These orbits
Ariel "|
VmbrM [Uran,ls
Titanui
• •
Jg
2
> Jupiter
Jkiiropa
Ganymede )
0.0013
- appear to be
circular
Oberon
. .
zL u
Sj
" *3
Deimos \ Marg
P hobos )
0.0057
0.0066
Mimas ~\
Enceladus |
Tethys ^ Saturn
Dinne
a|
r
1
Calypso } Jupiter
lapetus | Sa(urn
1 itan )
0.0072
O.OL".Mi
0.0299
^ O.O.'5-T.
Rhea J
£
Moon
0.05491
Hyperion } Stiturn
0.1189
•^
UK. ii ii < i MI:I. iin - \ i i M. VMI M vi i v\\ <» NATIHK.
•
Tin- orl.it- of several -atellite- appear t» be circular. or r:illn-r ill.- eeceii-
iricitv irt found I" IM- in-. -n-ib|e in con-c<piencc of tin- errors of nl.-, r\ :ili<ni.
U -hall not under. -Miniate these unknown eccentricities if w . a--i-_rn to them
tin- mean value of tin- known eccentricities of tin- satellite orbits (•MKlJ.'i).
Making tin- maximum as-uinption we find thai the average eccentricity for the
Holar system — tin- eight great plain-Is and tlu-ir twciitv-onc satellites — cannot
In these con-iih-ration- we have mnitti-d I In- comet- and tin- HMtfniitlH, IH--
can-c the foniiiT ha\c Ix-m drawn to our svMfin from outer H|>ace, while the
l.itl. i ha\i- originated l.\ an anonialoii- jiroc,— . and depart so radically from
the other Ixxlies of the -\-tein that thev eannot be eonsideriHl ax a ty|>o of
plain t.n-v i volution, luit rather as an ahnonnal development. It i- al-o to U>
remarked that tin- i-eenitrieitir- of the orbits of the planets and satellites are
still invoheil in -omc small dejrree of uncertainty, and mon-over they will vary
fnun eentiirs ioerntnr\ o \vin<£ to the cumulative effectM of the secular variations
and of the lonir-period ine<|iialitic8. Notwithstanding these changtw it is clear
that the values of the eecentricitieH given above represent the true nature of
the solar -\-tem.
It foil on-*. ///»/»/-.//. Hint the averaye eccentricity among the ilouMr slant in
more than tn-,1,-, tiun* I/mi t'onml in the jdanttary ttyntun. nml thin extra-
ordinary result is muni/mlfi/ the expression of a J'unilanu ntal Imr <,f nutnrr.
The eccentricities of the orbits of the stars discussed in this work an* still
subject to -li^ht changes, but there is reason to believe that the average value
i'1 !->•_' i \\ill never lx? altered except by a very small quantity. The apparent
orbits Lri\«'n in the preceding chapter enable the reader to make a direct in-
spection of the linear i-eei-ntricit \ . ami he mav thus judge of the magnitinli- -if
thi- element, as well as of tin- changes it i- likely to undergo. In order to
minimize the uncertainty in our final data, we have pnrpo-ely restricted our
researches to the- forty orbits which wen- capable of the mo-t exact determi-
nation. Since the orbits of the fortv stars will undergo no -en-iblc impn.v. -
nient, at least for a good many years, it seemed of intere-t to (.resent also fig-
ures of the real orbits.
In the accompanying illustrations the orlut- are arranged in the order of
eccentricity, and the reader is thus enabled to examine the different degrees of
elongation. Accordingly, it ap|>ears that while the orbits are much mot
trie than those of the planets and satellite-, thev an- vet much less eooentrie
than those of the long-period comets.
In the preceding diagram we have drawn one broken line to illn-trate th •
252 HIGH ECCENTRICITIES A FUNDAMENTAL LAW OF NATURE.
•
distribution of the orbits of comets, and another for the distribution of the
orbits of the planets and satellites. The number of cometary orbits is so large
that in this case the scale of ordinates had to be very much reduced. An in-
spection of these curves shows that the planetary orbits are heaped up about a
very small eccentricity, while the cometary orbits cluster around the parabo-
lic eccentricity. This characteristic of the orbits of comets indicates, as
LAPLACE first pointed out, that these bodies have been drawn to our system
from the regions of the fixed stars ; and therefore their eccentricities surpass,
equal or approximate unity. Some of the comets have passed near the larger
planets, and thus suffered perturbations which have reduced their eccentricities;
and hence the curve slopes down gradually on the side towards the origin.
The right branch of the curve is but little known, since the great perihelion
distance of hyperbolic comets enables them to pass through our system unnoticed,
unless they happen to be very bright.
Thus it is evident that the tendency of double-star orbits is to group about
a mean eccentricity which is almost equally removed from the two extremes
presented in the solar system. Orbits which are so much elongated have no
close analogy with those of the planets and satellites ; on the other hand their
lack of very great eccentricities excludes them from the category of comets,
and does not permit us to assign to these systems a fortuitous origin. We shall
see hereafter that the orbits were originally nearly circular; in the course of im-
measurable ages they have been gradually expanded and elongated by the work-
ing of tidal friction in the bodies of the stars. The visible elongation of the
orbits thus enables us to trace the changes of the stellar systems through mil-
lions of years, and to throw light upon the problems connected with their
evolution.
In discussing the motion of yVirginis, SIR JOHN HERSCHEL long ago remarked
that "the eccentricity is, physically speaking, by far the most important of all
the elements," and now we see that this element, which depends wholly on
mierometrical measures, and is independent of the parallaxes and relative masses
of the stars, gives the sole clue to the evolution of the stellar systems,
and will some day enable us to lay a secure foundation for scientific Cos-
mogony.
We may observe that besides throwing light upon the past condition of
the universe the general law of the eccentricity here established will also be
useful to practical astronomers. The eccentricity of any given orbit may depart
considerably from the mean here indicated as the most probable value, yet the
tendency towards this region will on the whole prove useful to computers.
>:> i \rivm MA88K8 <>i mi « > M I •( >mCNT8 IN STELLAR SYSTEMS.
The observer who is aware of tin- high eceeiitrieitie- and different inclinations
i-f tin- orbits will know thai in many cases tin- length of tin- apparent radin—
vector i- Mihject to -iv;tt \ ;iriat i. .11-, ami a- a -ho, telling of the radius-vector
eorresjxuids to accelerated angular motion of tin- companion, he will never find
it safe to assume that tin- motion i> uniform. Tin- forty stars treated in thin
work piv-eiit several instances where the angular motion at certain epochs ha-
l>een extreiiiclv rapid, and it is much to be regretted that more observations
were not secured at -m h critical point* of the orbit*. These general results
may proM- of \alne to the observer of the future, and stimulute an increased
int. rot in tin- -\ -tematie mea.-uremeiit of revolving liinarieH.
§5. I{,lnlir, Masses of the. CoHijtonent* in Stellar Syntein#.
A problem of fundamental importance in the study of the stars is the
determination of the relative masses of the components of a system. Such
determinations have been made heretofore in very few cases, and even when
undertaken lia\c been seriously embarrassed by the errors of observation. It
has been customary to base the investigations ii|>on absolute |M>sitions deter-
mined with the Meridian Circle. The errors of our absolute ]>ositions deduced
in this way are so large in comparison with the delicate quantities depending
on the irregularity of the proper motions of the individual component- of a
system whose centre of gravity move* uniformly on the arc of a great circle.
that the results obtained are afleeted by large probable errors.
The -\-tems in which Mich re-cardie- have been attempted arc:
(1) a Cants Majoris, when- Ai VSI.KS finds the miMfiB to be in the ratio
of 1:2.119.
(2) a On/aunf, in which STONE found the masses approximately equal;
Hi KIN* made them as l:l.l'_'l; and K<>UKI:TS finally concludes from a more
elaborate investigation that they are in the ratio of 1:1.041.
(3) ij Cassiopeae, investigated in 1881 by LUDWHJ STKUVK, who found
the masses to be in the ratio of 1:3.731.
So far as we are aware these three wide systems are the only ones whose
relative masses have been investigated, and we may remark that the condition
of each star is favorable to a determination from the circumstance that the
pairs are wide and tolerably rapid in their orbital motion, and therefore the
254 RELATIVE MASSES OF THE COMPOIfENTS IX STELLAR SYSTEMS.
irregularity of the proper motions of the components is conspicuous in com-
parison with the errors of observation.
There are other systems such as 70 Ophiuchi, £ Bootis, and y Virginis, which
are favorable for similar investigations, but none have yet been attempted. It
would be all the more interesting to investigate the relative masses of
70 Ophiuchi from the circumstance that the system contains a dark body which
sensibly perturbs the visible components.
In the case of y Virginis we might infer that the masses are nearly equal,
as in the system of a Centauri.
But even if the bright and widely-separated pairs were all investigated, it
would still be difficult to reach any of the small, close stars whose distances
are less than two seconds of arc. The investigation of the relative masses of
the components of such systems by means of absolute positions determined
with the Meridian Circle seems forever impossible, since the stars under such
power would seldom be separated, and when separated the errors of observa-
tion would be larger than the quantities involved in the determination of the
relative masses. The old method is therefore very limited in its application,
and a new method must be invented if we are ever to have precise knowledge
of the relative masses of the components of binary systems.
We suggest the following method as much more general and also much
more exact than the one depending on absolute positions. The distance and
position-angle of each component with respect to a neighboring star should be
determined at different epochs, the measures being taken with the Heliometer
if the distance is large, with the Micrometer if the neighboring star is close or
very faint. A series of such relative positions would disclose the location of
the centre of gravity by its uniform motion and the resulting conservation
of areas with respect to the neighboring star. And since the measures are
differential only, it ought to be possible to attain the desired degree of accu-
racy; the only difficulty likely to arise in practice would be one depending
on the personal equations and the constant errors affecting the work of
individual observers. Experience alone could determine how serious this
difficulty would be, but it seems probable from the results obtained in the
measurement of double stars that it would become considerable only in the case
of pairs which have no near companion.
Indeed, this method for finding the relative masses of stars is exactly the
same as that employed in parallax measurement, except that the observations
must extend over the period of a revolution (or a large part of such a period)
instead of over the period of one year.
ItKI.ATIVI M \>-l - "I I III ...Ml'.. MM- IS - II I I \ I: -\ - 1 I M-.
Tin- proposed method therefore is aa follows: Let tin- dill'i n nc-es in right
ascen-ion and declination with resjM-ct to t-itlu-r of the < ointments at the
• •(MH-h-. t,i'f be
/ - ^ «inf. ««cf, ; .«, -
.*< - ff.'tinf/MeV 8 -'V - *'«
/ _ *••»'." MO V » ^ -
Let the ditli-n-nees in right ascension and declinatimi of the com|M>nentH «if
the system in lik. inaiuu-r be
l,t — p »\t\0
./«' - f' tin f see 8' ; ./*' - p'
l.t' — p" sin** aecf ; Jf — p'
Then tin- rtHM-dinates of the centre of gravity of the system referred to the
ng star will be given by the expressions,
•
if
M+M
where the formula? are arranged for the case of the smaller star, which in
generally to be preferred, as the magnitude of the absolute orbital motion
about the centre of gravity is in the inverse ratio of the masses of the
components.
M
In these expressions the only unknown quantity is the ratio jjf+rjf • The
most natural condition for the determination of this unknown is furnished by
the principle of the con-i-r\ation of tin- motion of the centre of gravity of a
system of bodi< I, \\ lu-n the arc d»--<-ril><-cl by tin- centre of gravity in small,
tin- motion in right ascension and ilcdination is uniform like that in the arc of
a great circle. Thus we have
t'-t
(JT-Jt)
When n sets of indi-pendent oliM-rvations have been seen red, the number
of equations for the determination of the most probable value of the ratio
is 2 (n-2).
256 RELATIVE MASSES OF THE COMPONENTS IN STELLAR SYSTEMS.
If the precession is sensible, the observations of 00, 00', 6", and 0, 6' , 6",
etc., must be referred to a common epoch. An independent formula for the
determination of the ratio M _^^ may be deduced from the criterion that the
motion of the centre of gravity is confined to the arc of a great circle.
While the method may not prove to be entirely general, owing to the
occasional absence of suitable comparison stars, there is reason to think that
the Heliometer and Micrometer together ought to prove very effective. Such
measurements, if extended to groups of perspective involving two or more
objects, will furnish the means also of detecting the existence of any possible
irregularities in the proper motions of single stars. In the early days of star
cataloguing it was difficult to believe that the proper motions were uniform
and rectilinear, but as this has been found to be the general rule, it is now
difficult for some to credit the existence of irregularities in the proper motions,
or the presence of dark bodies perturbing the motions of the stars. The errors
of observation are relatively so large that sound method of procedure requires
caution in attributing anomalies to foreign causes, lest by undue credulity we
be led to introduce all manner of vain fictions; yet it is certainly unphilosophi-
cal to doubt the existence of numerous dark companions which disturb the
motions of the fixed stars. It will ultimately be a matter of great interest to
determine the extent and the character of such perturbations. These consid-
erations suggest fields of inquiry of the widest scope, and assure us that while
exact Astronomy shall be cultivated, the Heliometer and the Micrometer are
not likely to lose their present importance, through the introduction of any sort
of mechanical methods.
It will be some years before the above method can be applied, and hence
it is interesting to reach some general result as to the relative masses of binary
stars. The determinations above spoken of, except in the case of Sirius, show
that the masses are roughly in proportion to the brightness of the stars. This
rule would doubtless lead to erroneous conclusions in a good many individual
cases, yet in taking double stars as a class, it will give results which are not
far from the truth; and hence the light-ratios of the forty stars given in the
Table show that on the average the components of binaries are comparable,
and frequently almost equal, in mass. This we may infer to be a general law
for all binaries, and the corresponding relative masses accord perfectly with
those of the double nebulae drawn by SIR JOHN HKKSCIIEL, and with the mass-
ratios resulting from the rupture of the figures of equilibrium of rotating mass
of fluid investigated by POINCARE and DARWIN.
< i i-i I..N \i. . n \i: \. .1 IIIK 1-1 \\i i \in swn-.M.
;•''>. /•'.!•>•> />tional Character <>/ t/n
Tin- fundamental result indicated in the foregoing section is in striking
contrast with the phenomena prcsi -ntcd in the solar -\-tiiii. Tin- masses of
the planets are very small compared to that of the SUM. and tin- musses of tin-
satellites are very small compared to those of the plain-is an mini which they
revolve. The mass-ratio in the case of the Earth and Moon amount- to
I'B, and is by far the largest in the solar system. The mass of Jtijtitcr, ii4V.n,
i- much larger than that of any otln-r planet, and yet such a body is wholly
iiisi-rniiirant < ompared to the Sun. If such inconsiderable companions attend
the fixed stars, they would neither be visible, nor could they IH? discovered by
any pi-rtnrbations which they might produce. It is therefore impossible to
determine whether the stellar systems include such bodies as the planets, and
we are thus unaware of the existence of any other systems like our own. On
tlu- i >t her hand the heavens present to our consideration an indefinite numl>cr
of double xy.iteins, each of which is divided into comparable masses. These
double systems stand in direct contrast to the planetary system, where the
r. i ural body has 746 times the mass of all the other bodies combined. In
binary stars tin- mass distribution is evidently double, while in the solar system
it is essentially single. By a process extending throughout the universe it
seems that the nebulae frequently divide into approximately equal or compar-
able masses, and develop into double stars, while in the case of our own nebula
-nli-tantially all tin- matter has gone into the Sun.
Therefore while observation gives us no ground for denying tin- < -\i-tt nee
of other systems like our own, it docs not i-nalile us on the other hand to
affirm or even to render it probable that such systems do exist. And in
this state of insufficient evidence we are confronted by the undoubted < \i-icn< e
of a great number of systems of an entirely different type. Whatever theories
"f < 'osmogony are proposed, it is evident that in order to have any claim to
acceptance, they must be based upon what is really known, not upon what
may or may not exist. Those who have |>i i to deduce ( O-mogonic
processes from our own isolated and abnormal -\-tem. have therefore pursued
an illogical course, and it is not remarkable that they have failed to throw
much light upon the laws of Cosmogony.
The solar s\~t. m is rendered abnormal by the great number and small
masses of its attendant bodies and by the circularity of their orbits about the
large central bodies which govern their motion. The -\-tim is throughout so
258 EXCEPTIONAL CHARACTER OF THE PLANETARY SYSTEM.
regular, and adjusted to such admirable conditions ' of stability, that among
known systems it stands absolutely unique. Whether observation will ever
disclose any other system of such complexity, regularity and harmony, is an
interesting question for the future of Astronomy. It is certain that the number
of double stars will be augmented in proportion to the diligence of observers
and the improvement of our telescopes; and we may reasonably expect a
sensible increase in the number of triple and quadruple stars and of stars
attended by dark bodies.
Such systems as Sirius, Procyon, £ Cancri and 70 Ophiuchi are not likely
to be isolated cases; but caution is required where the observations are not
decisive, lest the number be unduly increased by imaginary bodies resulting
from errors of observation. It seems probable that a number of double stars
are likely to disclose perturbations which can be investigated, and we have
already some indications . that the motions of £ Herculis, g Ursae Majoris,
p.1 Herculis and 77 Coronae Borealis are not perfectly regular. But in the
present state of the measures it seemed best to attribute the apparent irregu-
larities to errors of observation. £ Hercnlis especially merits the most careful
attention of observers; after its periastron passage a refined investigation will
show whether the motion is really perturbed.
The question naturally arises whether the stars of these double systems are
attended by small dark bodies of a planetary character. We have seen that
most of the binaries have highly eccentric orbits, and hence if planetary bodies
revolved around either component, they would experience great perturbations,
besides the most violent changes of light and heat. It seems probable that
planets could not be formed without developing very eccentric orbits, and if
once in existence, it is questionable whether such bodies co'uld endure under
the violent perturbations to which they would be subjected at periastron
passage. Even if a planet were very close to its central star, its motion would
be affected by an inequality of enormous magnitude analogous to the annual
equation in the moon's motion; and if not destroyed by collision with one of
the stars or by disintegration under the tidal forces within ROCHE'S limit, in
all probability it would sooner or later be driven from the system on a curve
analogous to a parabola or an hyperbola. Thus, while the motion of a planet
around one of the components could hardly be so stable as the corresponding
phenomena of the solar system, it might yet continue for long ages if the orbit
of the binary be not too eccentric; the final state of the system would depend
upon the densities, relative masses and distances of the components, the mutual
inclinations, and above all, the eccentricities, of their orbits.
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BERKELEY
Return to desk from which borrowed.
This book is DUE on the last date stamped below.
ASTRONOMY LIBRARY
1VED
SEP 1 2 1996
(blRCULATION DEPT.
FEB 24 1996
R«c'd UCB A/M/J
i 4
LD 21-100m-U,'49(B7146il6)476
M (.48 1
v. I
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