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REESE LIBRARY
OF THE
UNIVERSITY OF CALIFORNIA.
x
Received.. 3& ^.: t i8\
Accessions No.~K&S. ^0 Shelf No.
e
Jb
HENRY FROWDE
OXFORD UNIVERSITY PRESS WAREHOUSE
AMEN CORNER, E.G.
OF THt
UNIVERSITY
OP
EESEAECHES IN STELLAR PAEALLAX
BY THE AID OF
PHOTOGRAPHY
FROM OBSERVATIONS MADE AT
THE OXFORD UNIVERSITY OBSERVATORY
UNDER THE DIRECTION OF
CHAELES PKITCHARD, D.D., F.E.S., F.G.S., F.R.A.S.
SAVILIAN PROFESSOR OF ASTRONOMY IN OXFORD ; FELLOW OF NEW COLLEGE, OXFORD
HONORARY FELLOW OF ST. JOHN'S COLLEGE, CAMBRIDGE
Published by the Delegates of the Clarendon Press, at the request of
the Board of Visitors
AT THE CLARENDON PRESS
M DCCC LXXXIX
[ All rights reserved ]
PREFACE.
THE introductory remarks and the ample Table of Contents which
precede them, render an elaborate preface unnecessary. The Observatory,
in which the observations contained in this volume have been made and
reduced, was erected by the University of Oxford at the instance of the
present Professor in the year 1874. The general plan is the Professor's,
but the external design is that of Mr. Charles Barry. In 1877, a large
and very convenient Lecture-room and Library were added, after the
design of the afore-mentioned eminent architect. The general aspect of the
building is very fairly represented in the collotype reproduction in the
Frontispiece.
The principal astronomical instruments are three. I. An equatorially
mounted telescope of twelve-and-a-quarter inches aperture and nearly
180 inches focal length, furnished with solar and stellar spectroscopes and
other necessary appliances, by Mr. (now Sir Howard) Grubb. In 1888, the
tube of a photographic telescope was mounted on that of the afore-
mentioned equatorial, and the driving apparatus was very greatly im-
proved, so as to permit the protracted exposures now rendered necessary
for the photography of the more faintly illuminated of celestial objects,
but the tube unfortunately has long waited for and still awaits its object-
glass of 13 inches aperture. This photographic telescope is the gift of the
recently deceased Dr. Warren De La Rue, whose long continued generosity
to the Observatory entitles him to be regarded as a co-founder of the
Observatory, in conjunction with the University of Oxford. II. A
Transit Circle by Troughton and Simms. Its aperture is four inches, and
its two divided circles are three feet in diameter. The microscopes and
field of the telescope are illuminated by electricity, and the instrument is
capable of reversion. The whole arrangement is the gift of J. Gurney
Barclay, Esq. III. An equatorially mounted Reflecting Telescope of 13
inches aperture and 10 feet focal length. This instrument, with its singu-
larly excellent metallic mirrors, was constructed personally by the late
Dr. Warren De La Rue, and after long and effective use by him was presented
to the University of Oxford. Its clock and motive machinery were entirely
renovated and improved by Messrs. Troughton and Simms at Dr. De La Rue's
vi Preface.
expense. It is now capable of permitting many hours of exposure for
photographic plates without distress to the observer. With it all the
photographs necessary for the researches contained in this volume have
been taken. The munificent donor had expressed his desire to replace the
13 inch mirror by a larger one of 24 inches aperture ; but, unfortunately,
his decease occurred before the realization /of his intention.
Besides the important and costly gifts to the Observatory referred to
above, Mr. James Nasmyth has deposited therein his remarkable pictorial
map of the Moon, and his other cartoons of the Lunar surface (seven in
number), and these beautiful works of art now adorn the walls of the
Lecture-room.
The staff of the University Observatory consists of two assistants-
Mr. William E. Plummer, F.R.A.S., and Mr. Charles A. Jenkins, F.R.A.S. :
these gentlemen have been attached thereto since its first institution, and
their able co-operation has been repeatedly acknowledged by the present
Director. There is also provided for the Observatory, a skilled mechanic,
whose services are important to the general routine.
Independently of the original researches carried on in this Observatory,
the instruction of the students in practical astronomy, and the delivery of
various courses of lectures, are among the principal duties attached to the
Institution.
The Observatory is, by University Statute, under the inspection of a
Board of Visitors, consisting of
The Vice-Chancellor of the University.
The Astronomer Royal (W. H. M. Christie, Esq., M.A., F.R.S.).
The Lowndean Professor of Astronomy, Cambridge (J. C, Adams,
Esq., M.A., F.R.S.).
The Radcliffe Observer.
The Senior and Junior Proctors.
Rev. Bartholomew Price, M.A., F.R.S., Sedleian Professor of Natural
Philosophy, Oxford.
W. Huggins, Esq., D.C.L., F.R.S.
WTEsson, Esq., M.A., F.R.S.
E. B. Elliott, Esq., M.A.
Through this Board an annual report is presented to the University in
Convocation.
OXFORD UNIVERSITY OBSERVATORY,
1889, August.
TABLE OF CONTENTS,
General Introduction on the photographic method applied to the determination of
Stellar Parallax . , . . . . . . . . i
Reasons for selecting 61 Cygni ^ ....... i
Advantages of photographic method . . . . . . . 2
Examination of the field of the telescope ....... 2
Establishment of the uniformity and constancy of the film .... 2
The selection of the comparison stars ....... 3
Difficulties attending prolonged exposure ....... 3
Method of taking the plates and making the measures . . . . . 4
Examination of the measuring screws . . .. . ... ... . .... , 4
Probable error of bisection of star image . . . . . . . . . ... . 4
Difficulties of focussing ' . <,.....,.*, .. . . . 5
Parallax of 61 Cygni .... . . . . . . 5
Measures of ' diagonal ' distances : Table I . . . . . . 6
Explanation of the columns of Table I ....... 8
Effects of error of focus and removal of such errors ..... 9
Measures of 6i x Cygni from star of comparison (a) : Table II . . .10
Explanation of the columns of Table II . . . . . . .12
Application of correction to remove causes of irregularity, however produced, by means
of * diagonal measures ' . . ... . . . . 12
Equations of Condition for 6 i t Cygni and Star (a): Table III . . . . 13
Explanation of Table III t . . . . . . . . .16
Discussion of the possible variation of the Constant of Aberration . . . 16
Concluded Parallax of 6i l Cygni and Star (a) . . . . 17
Comparison of Probable Error with that of Bessel . . . . . 17
Parallax of 6 1 2 Cygni and Star (a) . . . . . . . . 18
Parallax of 6 i x Cygni and Star (&) . . . . . . . . 25
Parallax of 6i 2 Cygni and Star (6) . . . . . . - . . 31
Parallax of 6i x Cygni and Star (c) . . .' . . i . . 38
Parallax of 6 1 2 Cygni and Star (c) . . , . . . . . 47
Parallax of 6 ij Cygni and Star (d) . .v . ". . , . 54
Parallax of 6i 2 Cygni and Star (d) . . . . . . . 59
General summary of results . . . . ... . . 65
On the use of the term ' mean of the parallaxes ' . .. .. . . . 65
On the mass of the system 61 Cygni . . . . . .66
Comparison of the measured distances between the components with those derived by
Professor Peters . , . . . . * ' . . . 66
Parallax of /* Cassiopeiae . .66
yiii Table of Contents.
PAGE
Concluded Parallax of p Cassiopeiae and Star (a) . . . . . -73
Concluded Parallax of /* Cassiopeiae and Star (&) . . . . . 75
Comparison of Kesulting Parallax with other authorities . . . . . 75
Parallax of Polaris . . . . . . . . . -75
Stars of Comparison . . . . . . . . .76
General Summary of results ......... 96
Parallax of Stars from selected epochs . . . . , . . 97
Reasons for curtailment . . . . ...... . . . 97
Absolute Parallax from meridional observations (Dr. Belopolsky) ... 98
Errors from change of focus and unknown causes, compared with those of the Heliometer 99
Parallax of a Cassiopeise . . . . . . . . .99
Collected Results . . . . . . . . . .108
Parallax of Cassiopeiaa . . . . . . . . 109
Collected Results . . . . . . . . ..117
Parallax of 7 Cassiopeiae . . . . . .. . .118
Collected Results . . . . . . . . . 126
Remarks on the negative sign accompanying this Parallactic determination . . 126
Parallax of a Cephei . . . . . . . ... 127
Collected Results . . . . . . . . . 135
The effect of altering the number of nights of observation . . . 135
Tabular Summary of Parallactic determinations in this volume . . . .137
On the relation of Parallax to the magnitude and Proper Motion of Stars ;
(Dr. Oudemans's suggestion) . . . . ' . . .138
[NTRODTJCTION.
I. IN the year 1878, 1 had been engaged in the investigation of the moon's
physical libration by the aid of lunar photographs on collodion plates. In the
course of this research a series of measures had to be taken for the determination
of the lunar diameter. I found that the results possessed such delicacy and
accordance, that the thought occurred to me of applying photography to the
determination of stellar parallax. But for the prosecution of this design it
became necessary to obtain the photographic images of faint stars with a few
minutes exposure, a result which could not be accomplished on the ordinary
wet plates. This difficulty was however removed by the adoption about that
time of the processes of the more sensitive dry plate photography. This
method easily renders evident the images of faint stars, and it is with reference
to measures connected with such faint stars, that the very idea of parallactic
determination necessarily depends.
II. In May, 1886, I communicated to the Royal Society a method of
determining the magnitude of stars from the measures of their discs impressed
on dry photographic plates, and of the suitability of photographic methods to
the purposes of accurate measurement in general. These results were again so
accordant that I at once commenced with confidence the necessary observations
for the determination of stellar parallax. The star chosen for the first attempt
was naturally 61 Cygni, on which Bessel had bestowed such extraordinary
care, and whose measures have been generally confirmed by later astronomers.
A comparison on an extended scale of the probable errors of measured
distances on the photographic plates, with those obtained by Bessel with the
Heliometer, would at once confirm or condemn the photographic process.
Another cogent reason for the selection of this star arose from the fact of the
existence of an undoubted orbital connection between its two components ; for if
the identity of the parallaxes of two stars thus relatively so close to each other
with reference to a third, were independently established by photography, then
there would be both furnished and satisfied a most crucial test of the applic-
ability and accuracy of this method of investigation. But this photographic
method of astronomical enquiry was so entirely novel, that I determined still
further to exhibit its value, and accordingly as many as four faint stars
of comparison were selected, and I proposed to determine the parallaxes of
the two components with reference to each of the four stars. Thus there
would be no less than eight independent determinations of the quantities which,
at that time, I thought, would be practically identical.
III. A more enlarged experience has taught me that there is no necessary
and a priori ground, for expecting the so-called parallax of a star to be
B
2 Introductory Account of the Precautions
identical in amount with respect to any two other stars in the apparent
vicinity, however faint. For recent researches have shown that the lustre
of a star depends greatly on many other elements besides that of the distance
at which it is viewed ; and it must never be forgotten that the parallax obtained
by BesseFs method, or by any variation of it, is not absolute, but is relative to
the parallaxes of the stars of comparison employed. Attention will be drawn
to this point in the sequel of these investigations, and it is here insisted
on chiefly in order to modify the reasons for anticipating an identity in all the
eight results referred to above.
IV. Notwithstanding this remark, it has been an almost unvaried practice
in these researches to select four stars of comparison, suitably situated, instead
of the usual one or two. For it is a peculiarity of the photographic method
that it lends itself to the multiplication of data for measurement in the
photographic field to an almost unlimited extent. Moreover, all these
measures possess the great advantage of referring to the same instant of time,
and they can also be made leisurely in the day time, without distraction or
constraint, and, when necessary, can be repeated and examined at any distant
intervals. But all these great advantages are on the assumption that the
picture on the plate is and remains a perfect representation of the actuality in
the heavens.
V. In order to satisfy myself on this important and fundamental point,
an investigation of the amount of distortion of the field, at remoter distances
from the axis of the telescope than are generally relied upon in observations,
had been made, and the result is published in vol. xlvii. of the Mem. Hoy.
Ast. Soc. Extended experience has still further satisfied me of the reliability
of the focal field up to the limits of the picture required. It remained therefore
only to enquire, whether this reliable field is practically transferable to the
photographic plate. Proof of this can only be had by the establishment of the
identity of measurement of the visual picture with those made on the film.
For this purpose I may refer to the communication in the Proc. Hoy. Soc.
May, 1886. Later enquiries made by other astronomers* have put this question
altogether beyond reasonable doubt, and it is not necessary here to produce
numerical data to support the fact.
VI. It was however still further necessary to establish the uniformity
of the film with regard to its capacity for accurate measurement of wide extent
and in every direction. A part of the same question is the enquiry whether
measurements between the same stars on different plates, even if taken on
different nights, were identical with each other. Repeated trials have satisfied
me that there is no cause for the apprehension of inaccuracy in these directions,
provided that suitable methods of reduction (to be explained hereafter) are
employed in the discussion of the measures.
VII. Another necessary enquiry also presented itself, viz. as to whether the
photographic film remained constant after a lapse of time. In order to test
this question, the same plates were measured at dates separated by sufficiently
wide intervals of time, and the difference between the two results was found
not to exceed the errors of observation.
* Bulletin du Comite" International permanent, nasaim.
Necessary for Accurate Photographic Measurement. 3
VIII. Having- thus discussed the general methods of the process, I proceed
to explain the particular application of them to the determination of parallax,
and this I feel compelled to do with a very considerable amount of detail,
because the introduction of a new element of danger, viz. the effects of the
possible inconstancy of the film, require to be very scrupulously examined,
and the details to be very carefully described.
IX. The first step in the process is the selection of four stars of comparison
suitable for the purpose. The suitability in question implies that two of the
stars should be as nearly as possible in the same line with the star whose
parallax is sought, and if possible at approximately equal distances therefrom.
The other pair ought to satisfy similar conditions, but to be as nearly as
convenient at right angles to the former direction. This condition of the
picture may occasionally be satisfied by the inspection of Argelander's Charts,
but in general it is found necessary to appeal to the heavens, by taking a
picture of the district required. For this purpose it is necessary to select such
stars of comparison as could generally be measurably impressed on the plate
with an exposure not exceeding five minutes. This essential limitation of the
time of exposure prevents in some cases the selection of stars of comparison rigidly
fulfilling the conditions of configuration stated above. For from the very first
it was felt that if an exposure considerably greater than five minutes was
necessary to produce the required images, it would be impossible to mark the
precise epoch of the formation of the image, and hence impossible accurately to
eliminate the effects of refraction from the measures. Another reason for this
limitation arose from the fact, that when a bright star such as that of the
second magnitude was in question, a longer exposure than that mentioned
would give so extended an image, that it would not be possible to bisect
it with the accuracy required. For although it would be possible to employ
means for temporarily covering the bright star during a part of the exposure
required for the impression of the fainter stars, a question would always arise
as to the accuracy of the process. Bearing this in view, I venture to digress
so far as to record my gratification, that Dr. Elkin, by his admirable discussion
of the parallaxes of stars of the first magnitude, has rendered it unnecessary
for me to encounter the difficulties of photographic processes applied to such
bright objects.
X. It is almost unnecessary to explain to astronomers that it is further
desirable to select one pair of stars approximately in the direction of the axis
major of the parallactic ellipse, or in other words, parallel to the ecliptic. This
consideration will also modify the otherwise advisable condition of the rec-
tangularity of the second pair referred to above.
XI. The selection of comparison stars being thus completed, the next step
is to proceed to the more direct operations necessary to the production of the
plates. The first step consists in determining the proper position of the
photographic plate with reference to the mirror. Experience with the De La
Rue instrument has shown, that the focal plane remains by no means at
a constant distance from the mirror itself, as measured along the tube, and
consequently it becomes necessary before commencing observations for the
night, to find the best position of the plate by actual trial and development.
4 Introductory Account of the Precautions
This preliminary trial also enables the observer to judge of the necessary
duration of the exposure, for it is a well ascertained fact, that this necessary
duration varies extremely from night to night.
XII. Having ascertained the proper position of the plate, the exposure was
continued in general for about five minutes, or whatever other time had been
indicated by the trial plate. Four plates were in general exposed as probably
sufficing for a night's work on a particular star. After the development, which
was carried no further than was necessary for the complete exhibition of all
the star-images required, the four plates were submitted to measurement in the
De La Rue Macromicrometer elsewhere described *. The plate was so inserted
in this machine that the principal star coincided with the centre of the position
circle attached thereto, this disposition of things being made in order to
secure the use of the same portion of the screws in all the operations, thus
eliminating the effects of any possible small irregularities in the screw itself.
Notwithstanding this precaution the screw had been carefully examined by the
method described by Bessel in the Untersuckungen. The result was to give
as a correction (which however is quite insensible in its application)
Horizontal screw = o"-oo22 sin# o"-oo66 cosu
o"-oo44 sin 2 u + o"-ooo3 cos 2 u
Vertical screw = + o"-oc>36 sin# + o"-oi 27 cos u
o"-ooc>3 sin 2 u + o"-ooo7 cos2.
It may be well to mention that in the course of the measurements a second
examination of the screws was made, in order to detect any possible defects
arising from usage. The new correction, like the old, is quite insensible.
Each of the eight distances was measured five times, and the mean of the
measures on each plate was taken. Further, the diagonal distance between
each pair of comparison stars was also independently measured on each plate.
The absolute necessity of these diagonal measures, in order to connect the
measures of the several plates into a consistent whole, will be explained here-
after.
Before proceeding to exhibit the detailed measures of 61 Cygni, it will be
desirable to state the amount of accuracy with which the bisection of these
star discs can be effected. The probable error of measurement naturally varies
as the size of the disc increases.
For a disc 5" in diameter the Prob. Error is 0.08
10" o.i i
j> J 5" ' I2 >
20" 0.16
25" 0.17
3" - 20 -
Consequently the probable error of a measure of distance will be the square
root of the sum of the squares of certain pairs of these quantities.
Preliminarily to all other computations, it is necessary to enquire if any
correction must be made to the measures, on account of possible variation of
* Memoirs Royal Ast. Soc., vol. xlvii.
Necessary for Accurate Photographic Measurement. 5
the film, and of the focal length of the mirror from night to night, or from
plate to plate. It is on this account that the diagonal distances (a) to (#),
(c) to (d), are to be regularly measured and tabulated. It is assumed that
these actual diagonal distances are absolutely constant in the sky, and such
would probably appear to be the case with the measures also, were it not for
change in the film and focus. These changes in a presumably constant distance
are to be transferred proportionately to the varying distances of the comparison
stars from the principal star, and in this way it is presumed that imperfections
in the film, or in the focus, or arising from any unknown cause, will be sensibly
eliminated.
PARALLAX OF 61 CYGNL
The accompanying figure is a diagram of the principal stars 6i x and 6i 2
Cygni with the comparison stars , b ; c, d : round the former is exhibited the
North
A
West
East
form and direction of the parallactic ellipse. The stars of comparison are
designated by
( a D.M. 37 No. 4189 Magnitude 7.9
\b ,,38 No. 4336 8.8
( c D.M. 37 No. 4175 9.0
\d ,,38 No. 4348 9-5
In Table I are exhibited the conditions under which the diagonal distance
0, b was measured and the result of the necessary reductions freeing it from
aberration and refraction, and consequently leading to the correction of the
distances of the comparison stars from 61 Cygni, which result from unknown
changes in the film, focus, &c.
6
Measures of the diagonal Distances (a) to (b)
TABLE I.
Measures of the (diagonal) distance of Star (a) from Star (b) for
the determination, at the times of exposure, of the correction
to their measured distances from 61j and 61 2 Cygni.
No. for
Refer-
ence.
Date of
Exposure of
Plate.
1886.
Measured
Distance
of a to b
in arc.
Average
Deviation
from the
Mean.
Refraction.
Aberration.
Corrected
Distance
of a to 6.
Difference
from
Assumed
Mean.
d. h.
May 26 12.3
//
2379.026
//
//
4- 3OO7
//
+ O.I4.6
H
//
2
28 11.9
80-335
0.414
1 O ww /
M45
W. 1 i|.W
.145
2381.925
+ 0.275
3
30 11.7
79.921
353
1.812
145
81.878
+ 0.322
4
June I 11.7
81.009
.029
1.463
.145
82.617
0.417
S
4 n. 8
81.036
.174
1-316
.144
82.496
0.2<)f>
6
8 11.9
2379.892
0-305
+ 1.199
+ 0.142
238L233
+ 0-967
7
15 ii. 2
81.193
193
l - 2 95
137
82.625
0. 4 25
8
16 11.7
81.204
.179
1.103
136
82.443
0.243
9
23 11.6
80.189
.326
0.997
.129
8I.3I5
+ 0.885
10
24 1 1. 6
81.813
285
I.OOI
.128
82.942
0.742
ii
28 12.0
2381.471
0.329
+ 0.858
+ 0.124
2382.453
0.253
12
30 11.4
80.435
93
94 1
.121
8 1 .498
+ 0.702
13
July i 11.3
80.798
.242
937
.II 9
8.. 854
+ 0.346
H
Aug. 20 1 1. 1
81.637
137
.671
.OI9
82.327
0.127
15
24 9.8
81.029
.089
.708
.009
81.746
+ 0.454
16
26 9.3
2380.745
0.329
+ 0.758
+ 0.004
2381.507
+ 0.693
i?
28 9.5
81.273
327
703
.001
81.975
+ 0.225
18
2 9 9-5
81.895
243
.707
.004
82.598
0.398
iQ
30 8.9
81.366
.292
.742
.006
82.102
+ 0.098
20
31 8.8
81.037
.136
735
.008
81.764
+ 0.436
21
Sept. 7 8.6
2381.609
0-335
4-0.724
0.025
2382.308
0.108
22
10 8.4
81.026
.183
725
.027
81.724
+ 0.476
23
ii 8.5
81.885
.209
.716
035
82.566
0.366
2 4
13 8.4
82.112
364
.713
.040
82.785
-0.585
25
15 8.1
82.168
057
725
.045
82.848
0.648
26
16 9.8
2380.803
o-^S
+ 0.667
0.046
2381.424
+ 0.776
27
17 8.1
82.052
.132
.720
.049
82.723
0.523
28
18 8.0
81.938
243
723
.052
82.609
0.409
29
20 9.0
81.012
.269
.672
.056
81.628
+ 0.572
30
22 9.4
81.884
193
.668
.061
82.491
O.29I
31
27 10.2
2382.015
0.322
+ 0.693
0.072
2382.636
0.436
32
29 8.6
81.044
.386
.669
.076
81.637
+ 0.563
33
30 8.4
81.365
.244
.671
.079
8i.957
+ 0.243
34
Oct. 2 8.2
81.616
.129
.674
083
82.207
0.007
35
6 9.1
81.548
.302
-673
.091
82.130
+ 0.070
for the Correction of the Scale.
No. for
Refer-
ence.
Date of
Exposure of
Plate.
1886-7.
Measured
Distance
of a to b
in arc.
Average
Deviation
from the
Mean.
Refraction.
Aberration.
Corrected
Distance
of a to b.
Difference
from
Assumed
Mean.
d. h.
//
n
//
//
n
//
36
Oct. 13 i o.i
2381.630
0.193
+ 0.714
0.104
2382.240
0.040
37
21 7.5
81.759
3'7
.667
.117
82.309
0.109
38
22 7.5
81 428
.242
.667
.II 9
81.976
+ 0.224
39
Nov. 3 6.6
81.642
.229
.669
134
82.177
+ 0.023
40
5 8.8
81.740
.262
.740
135
82.345
0.145
4i
16 75
2382.057
0.098
+ 0.708
0.143
2382.622
0.422
42
i7 8.3
81.517
3H
754
.144
82.127
+ 0.073
43
18 8.6
81.866
.252
.78.
.144
82.503
0.303
44
23 8.6
82.075
173
.805
145
82-735
0-535
45
29 69
81.589
.269
.717
-145
82.161
+ 0.039
46
Dec. i 7.3
2381.458
0-325
+ 0-747
0.145
2382.060
+ 0.140
47
2 68
81-736
155
.721
145
82.312
O.I I 2
48
4 6.4
82.040
.172
.708
.144
82.604
0.404
49
7 6.3
82.093
.249
.7,6
143
82.666
0.466
50
9 7-2
82.034
275
.781
.142
82.673
o-473
Si
14 6.2
2382.749
0.302
+ 0.734
0.138
2383-345
1.145
52
16 6.2
82.946
.07 4
747
.136
83-557
J-357
53
24 6.2
82.759
.183
.780
,I2 9
83.410
I. 210
54
87 Jan. 5 6.9
83.018
.265
.918
.III
83.825
-1.625
55
8 6.4
82.437
.129
.877
.104
83.210
I.OIO
56
10 6.7
2381.126
O.2IO
+ 0-934
O.I02
2381.959
+ 0.241
57
12 6.3
83.019
133
.899
.099
83.819
1.619
58
20 6.4
82.630
.104
.969
.083
83.516
1.316
59
25 6.3
81.007
309
993
.072
81.928
+ 0.272
60
3' 6.5
82.363
.240
i. 066
.058
83371
1.171
61
Feb. .s 6.0
2380.697
O.262
+ 1.047
0.048
2381.696
+ 0.504
62
8 5-9
82.052
.405
1.069
.038
83.083
0.883
63
17 17.1
80.629
193
2.464
.014
83.079
0.879
64
25 17-4
80.093
.271
1.816
+ -005
81.914
+ 0.286
65
26 16.9
80.558
.322
2.134
.008
82.700
0.500
66
27 16.9
2378.930
O.262
-f- 2.221
+ O.OIO
2381.161
-f 1-039
67
Mar. 12 16.1
80.054
313
2.053
043
82 150
+ 0.050
68
16 15.7
80.655
.280
2.133
.052
82.840
0.640
69
23 16.4
80.964
.092
1 .390
.068
82.422
0.222
70
27 14.8
79-37
.'47
2-3>4
077
81.761
+ 0.439
7 1
Apr. 2 15.3
2380.059
0.209
+ I-563
-f 0.089
2381.711
+ 0.489
72
16 14.4
79.198
.322
1-559
.114
80.871
+ I-329
73
19 14.6
81.328
.153
1.407
.118
82.853
0.653
74
20 15.0
80.301
.205
1.249
.119
81.669
+ 0.531
75
2 5 '3-4
80.515
.164
1.901
.127
82.543
0-343
Measures of the diagonal Distances (a) to (b)
No. for
Refer-
ence.
Date of
Exposure of
Plate.
1887.
Measured
Distance
of a to 6
in arc.
Average
Deviation
from the
Mean.
Refraction.
Aberration.
Corrected
Distance
of a to 6.
Difference
from
Assumed
Mean.
d. h.
//
//
//
//
it
7 6
Apr. 26 14.2
2380.797
0.243
-H 1-390
+ 0.128
2382.315
O.II5
77
29 13.8
80-575
.312
1.520
131
82.226
O.O26
78
30 ! 3-8
80.584
.279
I. 47 4
132
82.190
+ O.OIO
79
May 5 13.7
81.230
.080
1.362
137
82.729
0.529
80
7 U-o
80.784
153
'597
139
82.520
0.320
Bi
9 J 2-4
2380.167
0.302
+ 1.984
+ 0.140
2382.291
0.091
82
10 12.8
80.893
155
1.647
.I 4
82.680
0.480
83
13 13.0
81.584
.2 4 2
1.429
.142
83.155
-0.955
84
14 12.8
81.415
.270
I-5I7
143
83.085
0.885
85
16 12.8
81.470
.I2 9
1.442
.144
83.056
0.856
86
18 12.8
2381.172
0.362
+ 1-371
+ 0.144
2382.687
-0.487
87
20 13.1
81.328
193
1.199
H5
82.672
0.472
88
26 13.2
80.954
.204
'.075
.I 4 6
82.175
+ 0.025
89
31 u.8
80.369
.247
1.444
.144
81-957
+ 0.243
Column i contains the number for reference to the Notes which are here,
for convenience, deferred to the end of Table VII.
Column 2 is the date of the exposure of the plates. Here it is necessary
to refer back to IX. in the Introduction : the remarks there being taken into
the account, it is here only necessary to state that the epoch of exposure is
taken at one minute before the removal of the plate from the instrument : the
exposures necessary for the production of a measurable disc were not in all cases
uniformly the same, but were on the average about five minutes. See XI. of
the Introduction. Any considerable departures from the five minutes exposure
are mentioned in the Notes. It was considered that the real visible formation
of the photographic discs of the faint stars occurred about one minute before
their completion. It is unnecessary further to enlarge on the effects of the
epoch of exposure on the refraction ; these considerations indicate the desirability
of using the most sensitive plates procurable.
Column 3. The distance of (a) from (b) was measured on each of the four
plates by means of five bisections of each of the star discs. The same part of
the screw was always used for the reasons given in XII.
Column 4. I have here preferred an average deviation of the twenty
measures from their mean to the more usual quantity, termed ' probable error/
as bearing a more precise and significant meaning. The mean of all these
average deviations through the whole series of distance in this Table is
o".23i.
Column 5 is the effect of refraction on the measured distance of a from b.
The usual form, here adopted, is that originally given by Bessel
ds = k . s { i + cos' J (/; r;) tan 2 z} .
for the Correction of the Scale. 9
Column 6 gives the correction to the measured distance in order to remove
the effects of Aberration. The quantities inserted in this Table have been
computed from the expression originally due to Bessel's investigation :
ds= {aA + bB}
where A and B are taken from the Nautical Almanac, and
= [tan e sin + cos sin a]
a =
b = , , cosScosa.
206265
Column 7 is derived from column 3 by the algebraical addition of the
last two terms. The discrepancies in these final and adopted measures are very
noticeable. Differences in the unknown proper motions of (a) and (b) and also
some possible difference of their parallaxes might account for some very trifling
differences here, were it not that there are no signs of periodicity discernible.
It is therefore necessary to attribute these apparent variations of distance to
changes in the film, and in the inconstant position of the plates in regard to
the focal plane. Another consideration is that the practical difficulty of
accurately adjusting the photographic plate to the focus of the mirror for the
moment is formidable, and accompanied with a greater amount of uncertainty
than is the case with an ordinary refracting telescope. Further, these effects
are cumulative over long distances. An alteration of o.i inch in the focal
length will affect the distance here measured by i".9.
Column 8. For the computations of this column, which refer to the
correction to be made to the measured distances on the photographic plates,
owing to the various causes of distortion already described, the process adopted
is as follows. After a considerable number of plates have been measured and
corrected for refraction and aberration, the mean of the whole is taken and
assumed to represent the true distance and to remain constant throughout the
year. It might have been more logical to have completed the whole measures
for the year, and to have then taken the average for the year, but no sensible
increase of accuracy would have resulted from the delay. The constant
quantity assumed for the distance of a from b was 2382^.20. It is moreover
to be observed that after the solution of the Normal Equations, this distance
can be computed with greater accuracy. In the present instance this diagonal
distance so derived is 2382".295. This is the mean of the two determinations
from 6ij and 6i 2 Cygni. With the above explanation it will be seen that
these quantities are obtained by subtracting column 7 from 2382 // .2O.
10 Relative Parallax of 61^ Cygni and Star (a).
TABLE II.
Adopted measures of 61^ Cygni from the comparison Star (a).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance of
Star (a) to
61, Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (a) from
61 1 Cygni
Average
Devi-
ation.
I
d. h.
May 26 12.3
//
I 370.084
//
-f- 1.686
//
+ 0.084
it
1. 7*3
H
//
1380.021
//
0.162
2
28 11.9
' / 7 " ^
80.731
0.843
.084
/ oo
1.717
+ 0.159
80.100
293
3
30 11.7
80.462
1.039
.084
1.704
+ .186
80.067
317
4
June i 11.7
81.030
0.852
.084
1.685
.241
80.040
274
5
4 ii. S
81.013
0-759
.083
1.662
.171
8O.O22
183
6
8 11.9
I380.37
+ 0.687
+ 0.082
1.630
+ 0.560
1380.070
0.275
7
15 ii. 2
81.006
.741
.080
1-575
- .246
80006
139
8
16 11.7
81.263
.631
079
1.567
- .141
80.265
.I6 7
9
23 1 1.6
80.597
572
075
1.512
+ -52
80.244
.129
10
24 1 1.6
81.574
.581
074
1.504
"430
80.295
.246
ii
28 12.0
1381.298
+ 0.494
+ 0.072
1-473
0.146
1380.245
0.304
12
30 1 1-4
80.836
540
.070
1-457
+ .406
80.395
243
13
July I 11.3
80.893
552
.069
1.449
+ .200
80.265
225
14
Aug. 20 1 1. 1
81.421
389
.Oil
1-052
- -074
80.695
.274
J5
24 9.8
80.884
.409
.005
1.024
+ -263
80-537
257
16
26 9.3
I380.7I3
+ 0.422
+ O.OO2
1.008
+ 0.401
1380.530
0.136
17
28 9.5
81.024
.410
.OOI
0.992
+ 0.130
80.571
293
18
29 9-5
8I.3SI
.407
.OO2
0.984
.230
80.543
.264
T 9
30 8.9
81.178
.428
.004
0.977
+ -057
80.682
.170
20
31 8.8
80.960
425
.005
0.969
+ -252
80.663
.125
21
Sept. 7 8.6
1381.112
+ 0.418
0.015
0.914
0.063
1380.538
0.183
22
10 8.4
80.873
.417
.Ol6
.890
+ -276
80.660
.196
23
ii 8.5
81-375
4'5
.O2O
.882
.212
80.676
304
2 4
13 8.4
81.501
.411
.023
.867
-339
80.683
.242
25
15 8.1
81.558
.418
.026
.851
- -377
80.722
137
26
16 9.8
1380.869
+ 0.385
O.O27
0.842
+ 0.449
1380.834
0-205
27
17 8.1
81.366
.418
.028
-835
-303
80.618
-3"
28
18 8.0
81.352
.414
.030
.827
-237
80.672
.083
29
20 9.0
81.074
39 1
033
.811
+ -321
80.942
.096
30
22 9.4
81.291
385
035
795
.168
80.678
.147
31
27 10.2
1381.209
+ 0.396
0.042
-0-755
0.252
1380.556
0.207
32
29 8.6
80.667
.388
.044
.740
4 .326
80.597
093
33
30 8.4
80.933
389
.046
732
+ -Hi
80.685
.127
34
Oct. 2 8.2
8 1 .009
390
.048
.716
- .004
80.631
309
35
6 9.1
80.986
389
053
.685
+ -041
80.678
.146
Concluded Distances of Q1 1 Cygni from Star (a). 11
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance of
Star (a) to
61i Cygni.
Refraction
Correction
Aberratior
Correction
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (a) from
61i Cygni.
Average
Devi-
ation.
d. h.
//
//
//
//
//
//
//
36
Oct. 13 10.1
1381.101
+ 0. 4 28
O.o6o
0.629
0.023
1380.817
0.242
37
21 7-5
81.14!
.385
.068
.567
- -063
80.828
183
38
22 7.5
80.901
.385
.069
559
+ .130
80.788
.192
39
Nov. 3 6.6
80.990
-385
077
.465
+ -013
80.846
.107
40
5 8-8
81.006
.428
079
.448
- .084
80.823
.130
4i
16 7.5
1380.897
-H 0. 4 I 2
0.083
0.362
0.244
1380.620
0.264
42
17 8.3
80.583
.442
-08 3
354
+ .042
80.630
302
43
18 8.6
8o.8l8
.458
.084
.346
- -i75
80.671
-093
44
23 8.6
80.848
.476
.084
.306
-310
80.624
.129
45
29 6.9
80.629
.417
.084
.260
+ .023
80.725
.064
46
Dec. i 7.3
1380.523
+ 0-436
0.084
0.244
-f 0.081
1380.712
0.093
47
2 6.8
80.741
.420
.084
236
- -065
80.776
.129
48
4 6.4
80.885
.412
.084
.221
-234
80.758
175
49
7 6.3
80.885
.418
.083
213
.270
80.737
.242
50
9 7- 2
80.907
.458
.082
.I8l
.274
80.828
.206
5i
14 6.2
1381.222
+ 0.428
0.080
0.142
0.662
1380.766
O.I22
52
16 6.2
81.093
434
.079
.126
- -785
80-537
.I 49
53
24 6.2
80.843
.456
.074
~ -063
.701
80.461
274
54
87 Jan. 5 6.9
80.985
.546
.064
+ -034
-94 1
80.563
.076
55
8 6.4
80.572
519
.061
057
- ,S85
80.502
.230
56
10 6.7
1379.711
+ 0-555
0.059
+ 0.073
+ 0.141
1380.421
0.163
57
1 2 6.3
80-559
-537
059
.08 9
-937
80.191
.204
58
20 6.4
80.451
-585
.048
.152-
- .762
80.378
.079
59
2 5 6.3
79-357
.600
.042
.I 9 I
+ -158
80.264
-083
60
31 6.5
80.047
663
033
239
- .678
80.238
.302
61
Feb. 5 6.0
1 379-59
+ 0.642
O.O28
+ 0.170
+ 0.292
1380.231
0.205
62
8 5.9
79-963
0.658
.022
.302
-5"
80.390
173
63
17 17.1
78.907
1.405
.008
376
.509
80.171
.I6 4
64
25 17-4
78.541
1.034
+ .003
439
+ .166
80.183
.207
65
26 16.9
78.758
1.222
.004
447
- .290
80.141
.198
66
27 16.9
I377.7I5
+ 1.264
-f O.OO6
+ 0-455
+ 0.602
1380.042
0.204
67
Mar. 12 16.1
78-234
I.I82
.025
557
+ .029
80.027
075
68
16 15.7
78.582
1.223
.030
.589
- -37
80.053
'33
69
23 16.4
78.671
o-795
.040
644
.129
8O.O2I
.196
70
27 14.8
77-803
1-326
45
675
+ -254
80.103
-244
7
Apr. 2 15.3
1378-017
+ 0.931
+ 0.052
+ 0.723
+ 0.283
1380.006
O.I24
72
16 14.4
77-502
0.927
.066
833
+ -764
80.092
173
73
19 14.6
78.695
0.805
.068
.856
- -378
80.046
.262
74
20 15.0
78.239
0.697
.069
.864
+ -307
80.176
-08 5
75
2 S 13-4
78.243
1.091
073
.904
.199
80.112
ijn
12
Relative Parallax of 61 j Cygni and Star (a).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887.
Measured
Distance of
Star (a) to
61 1 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (a) from
61i Cygni.
Average
Devi-
ation.
d. h.
//
//
ft
//
//
//
7 6
Apr. 26 14.2
1378.372
+ 0-795
f 0.074
+ 0.911
0.067
1380.085
0.243
77
29 13.8
78.222
.864
.076
935
-015
80.082
.271
78
30 13-8
78.181
.845
.077
.942
+ .006
80.051
265
79
May 5 13.7
78.616
.782
.079
.982
- .306
80.153
.209
80
7 13-0
78.206
.927
.080
0.998
- .185
80.026
.162
81
9 12.4
1378.013
+ I.I40
+ 0.o8l
+ 1-013
-0.053
1380.194
0.097
82
10 12.8
78.244
938
.081
1. 02 1
- .278
80.006
035
83
'3 i3-o
78.646
.815
.082
1.045
-553
80.035
.136
84
14 12.8
78.429
.866
.083
1.053
.512
79.919
.204
85
16 12.8
78.492
825
083
1. 068
- .496
79.972
'35
86
18 12.8
1378.205
+ 0.785
-j- 0.084
-f 1.084
0.282
1379.876
0.207
87
20 13.1
78.412
.687
.084
1. 100
.273
So.OIO
132
88
26 13.2
78.215
.616
.084
1.147
+ .014
80.076
.205
89
31 n.8
77.857
.82.S
083
1.187
+ -Hi
80.093
077
The preceding 1 Table (Table II) applies to the measures of the distance of
the comparison star (a) from the principal star ; and, after what has been said
already by way of explanation of Table I, it is unnecessary to make any
further remarks regarding the first five columns of Table II. Column 6
gives the proper motion of the principal star reckoned in the direction of the
star of comparison, in order to reduce the measures to the common epoch 1887,
Jan. i. The annual proper motion of 61 Cygni has been assumed to be,
after examination from various sources, that given in the Standard Stars of
Prof. S. Newcomb, viz.
in K.A. + o".
in 8 -f 3".23i2
equivalent to a motion of 5". 2 264 in a great circle inclined at 51 48' to the
parallel of declination, and this quantity has been reduced in the direction of
the star of comparison.
Column 7 contains the necessary corrections to the foregoing measures, on
account of the various causes of irregularity already referred to when treating
of the diagonal measures. The amount of correction applied is proportional to
the measured distance, on the scale that the total amount of correction inserted
in column 8 of fche last Table is applicable to the distance of 2382".2O.
For instance on 1886, May 28, the correction made
23 8" - D ' 159
which is the number inserted in the column now being described. It is here
confidently assumed that all irregularities depending on the distance measured
Equations of Condition: 61 X Cygni and Star (a). 13
are virtually corrected hereby, whether the causes are known or unknown, and
hence no separate corrections are applied for temperature, either at the time of
measurement, or at the time of exposure. Having regard to the variety and
amount of some of these corrections, it might have been feared that they would
have been fatal to the ultimate value obtained for the parallax. On the other
hand the frequent changes of sign have a tendency to remove the apprehension.
In order to ascertain the real effect of the correction in question, the parallax
was computed both with and without it. The result of the computation was
that though there was no material difference in the total amount of TT, on the
other hand, the residuals in the equations of condition were very seriously
affected, even to ten times the present amount, introducing of course a
proportional theoretical uncertainty in this value. The final conclusion is
that the corrections in question are both real and absolutely necessary. Never-
theless it does occasionally happen that the measures of one or other of the
stars do show glaring and enormous discrepancies from the remainder of the
series. Sometimes such evident deviations from the general accuracy can be
traced to some mechanical injury of the film, but at others can only be supposed
to arise from some local distortion, the cause of which cannot be traced. It
has been the practice to reject all measures on a plate thus abnormally
disfigured, and the cases of such rejection (which do not amount to 3 per
cent, of the whole) will be found mentioned in the notes.
Column 8 speaks for itself, as being the concluded value of the distance
of star (a) from 6i 1 Cygni, obtained by the application of the small corrections,
contained in the last four columns, and, when slightly modified, forms the
independent term in the equations of condition.
Column 9 is the correlative of column 4 in Table I, to which the same
remarks apply. The mean of the whole series is o".i82.
TABLE III.
Equations of Condition formed from the measures of 6^ Cygni
and Star (a).
No.
Date,
1886.
Equations of Condition.
Residual.
d. h.
//
//
I
May 26 12.3
0.329 = x 0.7029 TT 0.6018 dfjt.
+ 0-037
2
28 11.9
.250 = x .6827 .5961
-043
3
30 11.7
.283 = x .6628 .5918
.OOO
4
June i 11.7
.310 = x .6420 .5853
+ .046
5
4 11.8
.328 = a? .6088 .5771
+ .078
6
8 11.9
0.280 = x 0.5625 0.5660
+ 0.051
7
15 ii. 2
.344 = x .4759 -5469
+ .153
8
16 11.7
.085 = x .4627 .5442
.101
9
23 n.6
.106 = x .3685 .5250
.038
10
24 1 1.6
.055 = x .3545 .5223
.083
Equations of Condition for the
No.
Date,
1886.
Equations of Condition.
Residual.
d. h.
//
//
II
June 28 12.0
0.105 = x 0.297977 0.5114 dp
0.008
12
30 11.4
+ .045 = x .2692 .5059
~ -H5
13
July i 11.3
.085 = x .2546 .5031
.009
H
Aug. 20 1 1. 1
+ -345 = x + -4753 -3653
.019
IS
24 9.8
+ .187 = x + .5250 .3556
+ .061
16
26 9.3
+ 0.180 = x +0.5491 0.3501
+ 0.079
17
28 9.5
+ .221 = X + .5729 .3445
+ .048
18
29 9-5
+ .193 = x + .5851 .3418
+ .081
19
30 8.9
+ -332 = # + -5955 -3392
- -052
20
31 8.8
+ -313 = * 4- -6067 .3364
.029
21
Sept. 7 8.6
+ 0.188 = x +0.6807 0.3174
+ 0.129
22
10 8.4
+ .310 = x + .7096 .3091
+ -019
23
ii 8.5
+ .326 = x + .7186 .3064
+ -007
2 4
13 8.4
+ -333 = * 4- -7363 -3009
+ .009
2 5
15 8.1
+ .372 = x 4- -7531 -2955
-023
26
16 9.8
+ 0.484 -= x +0.7617 0.2925
0.131
27
17 8.1
+ .268 # + .7697 .2900
+ .088
28
18 8.0
+ .322 = * + .7767 .2872
+ 037
29
20 9.0
+ .592 = x + .7924 .2815
- -225
30
22 9.4
+ .328 = x + .8057 - .2761
+ -045
31
27 10.2
+ 0.206 = x +0.8359 0.2623
+ O.lSl
32
29 8.6
+ .247 = x + .8458 .2570
+ .144
33
30 8.4
-1- -335 = * 4- -8506 .2543
+ .058
34
Oct. 2 8.2
+ .281 # + .8592 .2488
+ .118
35
6 9.1
+ .328 - .* + .8739 .2380
+ .076
36
13 10.1
+ 0.467 = x +0.8896 0.2185
0-055
37
21 7-5
+ .478 = x + .8914 .1969
- -065
38
. 22 7.5
+ .438 - x + .8905 .1942
.02 5
39
Nov. 3 6.6
+ .496 = x + .8583 .1615
- -095
40
5 8.8
+ .473 = x + .8487 .1557
.076
4 1
16 7-5
+ 0.270 = x +0.7808 0.1257
+ O.IOO
42
17 8.3
+ .280 = x + .7730 .1229
+ .087
43
18 8.6
+ .321 = X + .7651 .1201
+ .042
44
23 8.6
+ .274 = x + .7220 .1064
+ .072
45
29 6.9
+ -375 = x + - 66 36 .0904
-054
46
Dec. i 7.3
+ 0.362 = x +0.6420 0.0847
0.050
47
2 6.8
+ .426 = x + .6316 .0820
.118
48
4 6.4
+ .408 = x + .6093 .0766
.110
49
7 6.3
+ -387 - a? + -5743 -739
.104
50
9 7.2
+ .478 = x + .5494 .0628
- .204
Relative Parallax of 61j Cygni and Star (a).
15
No.
Date,
1886-7.
Equations of Condition.
Residual.
d. h.
//
//
51
Dec. 14 6.2
-4-0.416 = X + 0.4862 TT 0.0492 d [A
o. 1 70
52
16 6.2
+ .187 = x + .4599 .0438
+ .049
53
24 6.2
+ .in = x + .3484 .0219
+ .078
54
87 Jan. 5 6.9
+ .213 = x + .1683 + .0118
.099
55
8 6.4
+ .152 = X + .1222 + .0198
+ .058
56
10 6.7
+ 0.071 = x +0.0909 -|- 0.0253
+ O.OIO
57
12 6.3
.159 = x + .0600 -f .0308
+ .228
58
2O 6.4
+ .028 = x .0654 + .0527
.012
59
25 6.3
.086 = x .1440 + .0664
.068
60
31 6.5
.112 = X .2360 + .0829
+ .056
61
Feb. 5 6.0
0.119 a= X 0.3098 +0.0938
+ 0.032
62
8 5-9
+ .040 = x .3538 + .1048
- .146
63
17 17.1
-179 = x .4838 + .1306
+ .019
64
25 17-4
.167 = x .5845 + .1526
-035
65
26 16.9
.209 = x .5961 + .1553
+ .002
66
27 16.9
0.308 = x 0.6076 +0.1581
+0.097
67
Mar. 12 16.1
.323 = x .7400 + .1935
+ -57
68
16 15.7
.297 = x .7736 + .2044
.017
69
23 16.4
.329 =B X .8236 + .2236
+ .029
70
27 14.8
.247 = x .8464 + .2344
- .063
7i
Apr. 2 15.3
0.344 = x 0.8736 +0.2509
+ 0.023
72
16 14.4
.258 = x .9006 + .2891
.072
73
19 14.6
.304 = x .8997 + .2973
+ .025
74
20 15.0
.174 = x .8989 + .3000
- .155
75
25 13-4
.238 = x .8910 + .3137
- .087
76
26 14.2
0.265 = X 0.8884 +0.3165
0.059
77
29 13-8
.268 = x .8798 + .3246
- .052
78
30 13-8
.299 = x .8765 + .3272
.019
79
May 5 13.7
.197 = x .8556 + .3410
.in
80
7 !3-o
.324 = x .8458 + .3465
.020
81
9 12.4
0.156 = x 0.8349 +0.3519
0.143
82
IO 12.8
.344 = x .8290 + .3546
+ .150
83
13 13-0
.315 = x -8099 + .3628
.028
84
14 12.8
.431 = x .8032 + .3655
+ -H7
85
16 12.8
-378 = x .7890 + .3710
+ .100
86
18 12.8
0.474 = x -0.7736 +0.3765
+ 0.203
87
20 13.1
.340 = x .7576 + .3820
.076
88
26 13.2
.274 = x .7042 + .3984
+ -34
89
31 1 1.8
.257 = x .6547 + .4120
+ .038
16 Concluded Result of the Relative Parallax
Table III contains the 89 equations of condition from which the Parallax is
to be deduced. The Parallax in distance, as computed from Bessel's expression
(demonstrated in the Appendix) is
Rm cos ( M O ) TT
where m cos M = sin a sin P + cos a sin 8 cos P.
m sin M = ( cos a sin P + sin a sin 8 cos P) cos a> cos cos P sin a>,
and if P be assumed 108 26' this expression becomes
R [9.95260] cos (206 8' O) TT
where R = the Earth's Radius Vector :
and O = the Sun's Longitude, both at the time of exposure.
Again if 8/x be the unknown small correction required to the assumed
annual proper motion (/u) in the direction of distance, this term multiplied by
the fraction of year will enter into the equations of condition. Lastly, since
Concluded Distance = True Distance (x^ + Ait + Bdn
if from each side of the equation a constant be removed, in this instance
I 3^o // -35o, there will result the equations of condition in a convenient form
for computation. In this way Table III has been formed.
Before solving this Table by the usual method, it should be stated that
a term (K) depending on a presumed difference of aberration of the two stars
has not been inserted. Presumably, there can be little question but that there
may be a difference in the coefficient of aberration on account of the varied
conditions of the stars themselves. If this difference be taken into the account
the equations of condition become altered by the insertion of a term,
but on mature reflection, it is seen that the alteration in the coefficient of
aberration would be so slight, that a priori no appreciable effect would result in
the value of TT. To set this question at rest, I had recourse to Sir R. Ball's com-
putation for the parallax of 61 Cygni, where this term is taken into the account.
The result, according to Sir R. Ball, is an alteration of o".O3, amounting
to -5^-3 of the whole constant of aberration. Now the actual correction to
the measured distances rarely exceeds o".i, so that the distances would not be
altered by more than ^Vir of a second of arc.
As a matter of fact the value of it deduced from Dr. Ball's equations of
condition, neglecting the term, is changed from 0^.4659 to 0^.446 1, whereas,
on the other hand, the weight of TT is increased from 4.887 to 7.057. Similar
results are derived from a similar enquiry based on the parallactic computa-
tions of Prof. Asaph Hall. On these grounds I regard it as desirable to
omit all consideration of any presumed change in the aberration constant.
Further, it will be observed that no inequalities of weight have been assigned
to the various equations of condition, for it was felt that any such inequality of
weight must be connected with physical variations of the film and the images
impressed thereon. At first sight the varying values in columns 5 and 9 of
Tables I and II might appear to indicate the varying security in the equations
of condition themselves, and would furnish the means of deriving the necessary
multipliers to bring them into greater uniformity. On the other hand, it will
be found that measures taken on the same parts of the plate are affected by
of Glj Cygni and Star (a). 17
very different errors, and that therefore any multipliers introduced for the
purpose of establishing- uniformity in the measurements on the plate would be
utterly inconsistent. The supplementary Table IV (page 18) has been drawn
up in order to show at a glance that the variations in measuring in the same
direction and on the same plate are purely accidental and do not depend upon
the condition of the film.
In this Table (III) the last column contains the residuals arising from the
introduction of the values obtained of the unknown quantities, and I am induced
to regard them as exceptionally small, and with a felicitous succession of changes
of sign, justifying- a high degree of confidence in a novel method which has
now been for the first time put upon its trial on a very considerable scale.
The normal equations have been formed after the usual method and are as
follows :
+ 3.1520= + 9.0000# 7.3917 /X O.I7I07T
- 3- I 737 = - 7-39I7 +8.8384 - 9.0374
+ 17.2577=- 0.1710 -9.0374 41.2547
whence are derived the following results
n
x = + 0.0406
dp = +0.0514
TT = + O.4294.
The quantity expressed by the symbol x is of no practical importance, for
it depends mainly on the somewhat arbitrary assumption that the distance
between the two diagonal stars is 2382". 20. A similar remark may be made
as to any physical significance in the quantity b p, inasmuch as it here depends
upon months, whereas to be of value it should be measured by years. I have
therefore not concerned myself with any determination of a theoretical probable
error of either of these quantities which, under the circumstances, may be
properly regarded as illusory.
Very different is the case with the value of TT, being in reality the sole and
final object of this investigation. For the present it will be sufficient to add
that its probable error is o".oi62, so that with reference to star (a)
TT = 0".4294 + 0".0162.
Further, the probable error of the resulting measures derived from four
plates, by this method of treatment, on the same night is + 0^.09 1.
It is here interesting to remark in passing, and especially as appertaining
to a method so novel as the present, that Bessel's probable error is practically
identical with that here stated. So far then as the present results are concerned,
they may be regarded as expressing an equality of accuracy between the
photographic and Bessel's Heliometer measures ; the great advantage in point
of convenience and rapidity in the multiplication of observations is on the side
of photography.
18
Relative Parallax of 61 2 Cygni and Star (a).
TABLE IV (Supplementary).
The 'Average deviation' derived from all the measures on the
same plates for one night.
Date,
1886.
a-6.<
61i-a.
61,-a.
61i-&.
61 2 -fc.
c-d.
61i-c.
61a-c.
6h-d.
61 2 -d.
//
//
//
tr
II
n
n
//
//
n
May 30
0-353
0.317
0.096
0.133
0.132
0.305
0.203
0.283
0.262
0.092
June i
.029
.274
342
.301
137
.211
135
.2 9 6
133
.188
4
.174
.183
.183
.252
.293
243
139
.049
157
.240
8
.305
275
.202
.096
.087
.092
.296
.I 7 6
159
.183
15
193
139
134
.074
.165
.136
.087
.091
.097
.136
16
0.179
0.167
0.127
0.165
0.193
0.274
0.243
0.207
0.247
0.274
23
.326
.129
.296
.283
.242
.381
"3
.170
.225
.225
24
.285
.246
.079
.224
.302
.115
295
.183
.303
.243
28
.520
.304.
.IO4
,I*O
.08 s
30
o*y
193
o wi r
*43
*^f
.120
*o
.245
w J &
.225
.144
.187
.2 4 2
.08 5
.211
July i
0.242
0.225
0.243
0.137
0.138
O.2O2
0.220
0.270
0.162
0.096
Aug. 20
'37
.274
.225
.217
.243
.150
.164
135
139
243
24
.089
257
.262
.144
.262
309
.244
.206
.192
.164
26
3 2 9
.136
239
.209
HJ
371
311
.209
!57
.175
28
327
293
.136
.093
.270
244
.2 4 6
139
.244
.190
29
0.243
0.264
0.074
0.062
0.126
0.262
0.087
0.224
0.209
O.I5I
30
.292
.170
.092
.147
k l6 3
.203
.162
.242
.250
.206
3i
.136
.125
.177
*43
.192
135
.207
.26 5
i33
.26 4
Sept. 7
335
.183
.250
.128
.247
.129
.138
.129
.182
.083
10
183
.196
139
253
.103
.322
.192
M3
.209
.320
Parallax of 61 2 Cygni and Star (a).
I now proceed to a similar discussion of the parallax of the second com-
ponent of 6 1 Cygni, with regard to the same star of comparison (a). Very
sufficient reasons for adopting- the somewhat unusual course of investigating
the parallax not only of a star, but also of its close companion, will be found on
reference to II. of the Introduction.
The Tables are in all respects, mutatis mutandis, analogous to those already
described, the measurements of the same diagonal distance referring to both
components. This being the case, no further description is required, and the
Tables are given consecutively without additional comment ; the respective
headings of each column are sufficient indication of their meaning.
Relative Parallax of 61 2 Cygni and Star (a).
19
TABLE V.
Concluded measures of 61 2 Cygni from the comparison Star (a).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance of
Star (a) to
61 2 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (a) from
61 2 Cygni.
Average
Devi-
ation.
d. h.
H
//
//
H
ft
H
ii
I
May 26 12.3
I 359-790
+ 1.657
+ 0.083
1.727
I359-803
0.172
2
28 11.9
60.439
0.827
.083
I.7II
+ 0.157
59-795
.225
3
30 11.7
60.196
1.019
083
1.699
+ -184
59-783
.096
4
June i 11.7
60.901
0.836
.083
1.680
- .238
59.902
342
5
4 ii. 8
60.710
o-745
.082
1.656
.169
59-7 12
.183
6
8 11.9
1360.086
+ 0.675
+ O.oSl
1.624
+ 0.552
I359-770
O.2O2
7
15 ii. 2
60.783
.728
.078
1.570
.243
59-776
134
8
16 11.7
60.837
.621
.078
1.562
-139
59.835
.127
9
23 n.6
60.160
563
.074
I-507
+ -55
59-795
.296
10
24 ii. 6
61.178
572
073
1.499
- .424
59.900
.079
ii
28 12.0
1361.063
+ 0.485
+ 0.071
1.468
0.144
1360.007
0.104
12
30 11.4
60.463
532
.069
1.452
+ -4 01
60.013
.I2O
13
July I 11.3
60.786
534
.068
1-444
+ .198
60.142
243
H
Aug. 20 1 1. 1
61.112
383
.Oil
1.048
.073
60.385
.225
J 5
34 9.8
60.534
.402
.005
I.O2O
+ -259
60.180
.262
16
26 9.3
1360.306
+ 0.416
+ 0.002
L005
+ 0.396
1360.115
0.239
17
28 9.5
60.749
43
.OOI
0.989
+ .128
60.290
.136
18
29 9-5
60.917
.400
.OO2
0.981
.227
60.107
.074
19
30 8.9
60.846
.422
.004
0-973
+ -056
60.347
.092
20
3i 8.8
60.638
.419
.005
0.965
+ -249
60.336
.177
21
Sept. 7 8.6
1360.971
+ 0.412
0.015
0.9II
0.062
1360.395
0.250
22
10 8.4
60.628
.411
.015
.887
+ -272
60.409
.139
23
ii 8.5
61.117
.409
.020
.879
.209
60.418
.192
24
13 8.4
61.142
403
.023
.863
-334
60.325
.097
2 5
15 8.1
61.267
.412
.026
.848
- -370
60.435
.146
26
16 9.8
1360.480
+ 0.381
0.026
0.839
+ 0-443
1360.439
0.312
27
17 8.1
61.009
.409
.028
.832
.299
60.259
.242
28
18* 8.0
61.109
.404
.030
.82 4
-234
60.425
193
2 9
20 9.0
60.710
383
.032
.808
+ -327
60.580
.209
30
22 9.4
61.015
381
035
.7 9 2
- .166
60.403
254
3
27 IO.2
1360.869
+ 0-39 1
0.041
0-753
0.249
1360.217
0.177
32
29 8.6
60.309
.382
.044
738
+ -321
60.230
.202
33
30 8.4
60.698
383
45
730
+ -139
60.445
317
34
Oct. 2 8.2
60.713
383
.047
.714
.004
60.331
075
35
6 9.1
60.812
.382
.052
-683
+ .040
60.499
.. 4 6
20 Concluded Distances of 61 2 Cygni from Star (a).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance of
Star (a) to
61 2 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of.
Star (a) from
61j Cygni.
Average
Devi-
ation.
d. h.
//
it
//
//
//
//
it
36
Oct. 13 10.1
1360.720
+ 0.425
0.059
0.627
0.023
1360.436
0.207
37
21 7-5
60.831
.381
.067
.565
- .062
60.518
-093
38
22 7.5
60.631
-381
.068
557
+ .128
60.515
.152
39
Nov. 3 6.6
60.551
.381
.076
463
+ -013
60.406
133
40
5 8.8
60.647
-425
-077
447
- -083
60.465
.246
4 1
16 7-5
1360.669
+ 0.407
0.082
0.360
0.241
1 360.393
0.262
42
17 8.3
60.324
439
.082
353
+ -042
60.370
.305
43
18 8.6
60.428
455
.082
345
-!73
60.283
.129
44
23 8.6
60.666
.472
083
305
-305
60.445
-173
45
29 6.9
60.290
413
-08 3
259
+ .022
60.383
.156
46
Dec. i 7.3
1360.285
+ 0.434
0.083
0.243
+ 0.080
1360.473
0.135
47
2 6.8
60.411
.416
.083
-235
- .064
60.445
.182
48
4 6.4
60.557
.407
-083
.220
.231
60.430
.12 9
49
7 6.3
60.530
4'3
.082
.212
.266
60.383
244
50
9 7-2
60.640
454
.081
.180
.270
60.563
-283
5i
14 6.2
1361.026
+ 0.425
0.079
O.I4I
0.653
1360.578
0.272
52
16 6.2
60.792
431
.078
.126
- -775
60.244
.225
S3
24 6.2
60.633
454
73
0.063
.691
60.260
.279
54
87 Jan. 5 6.9
60.791
546
.064
+ 0.034
.928
60.379
093
55
8 6.4
60.376
5'9
.061
+ 0.057
~ -577
60.314
.128
56
10 6.7
1359.461
+ 0.555
0.058
+ 0.073
+ 0.138
1360.169
0.200
57
12 6.3
60.640
535
.056
.088
-925
60.282
.144
58
20 6.4
60.187
.585
.047
151
~ -751
60.125
.207
59
25 6.3
59-097
.601
.041
.191
+ -155
60.003
093
60
31 6.5
59-9I5
.664
033
.238
.669
60.115
.160
61
Feb. 5 6.0
1358.902
+ 0.640
0.027
+ 0.269
+ 0.288
1360.072
0.205
62
8 5-9
59.605
0.657
.022
.301
-54
60.037
.302
63
17 17.1
58.780
1-393
- .008
374
.502
60.037
.142
64
25 17-4
58.371
I.OIQ
+ -003
-438
+ -163-
59-994
.190
65
26 16.9
58.635
1.203
.004
-446
.286
60.002
-08 5
66
27 16.9
I357-632
+ 1.248
+ 0.006
+ 0.454
+ 0.593
1359-933
0.073
67
Mar. 12 1 6.1
58.190
1.164
.024
555
+ -029
59.962
.240
68
16 15.7
58.413
1. 2O6
.030
-586
- -365
59.870
.262
69
23 16.4
58.380
0.780
-039
.641
.127
59-713
!35
70
27 14.8
57-543
1.309
.044
673
+ -251
59.820
-156
7i
Apr. 2 15.3
1357-739
+ 0.915
+ 0.05 I
+ 0.720
+ 0.279
I359-704
0.093
72
16 14.4
57.116
.911
.065
.830
+ -759
59.681
.240
73
19 14.6
58.379
790
.067
.853
- -373
59.716
.222
74
20 15.0
57-793
0.683
.068
.861
+ -303
59-708
.174
75
25 13-4
57.876
I.O7I
.072
.900
.196
59-723
-139
Equations of Condition: 61 2 Cygni and Star (a). 21
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887.
Measured
Distance of
Star (a) to
612 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (a) from
612 Cygni.
Average
Devi-
ation.
d. h.
//
//
it
ii
//
//
if
7 6
Apr. 26 14.2
I357-97 2
+ 0.780
+ 0.073
+ 0.908
O.o66
1359.667
0.153
77
29 13.8
57-879
.850
075
930
- -CIS
59.7I9
.180
78
30 13-8
57-793
.829
075
939
+ .006
59.642
.127
79
May 5 13.7
58-105
.768
.078
979
-303
59.627
.242
80
7 !3-o
S7.9 2 3
.910
.079
994
- -183
59-7 2 3
.270
81
9 I2 -4
1358.532
+ I.TI8
-f 0.080
-f- I.OIO
0.052
1359.688
0.304
82
10 12.8
58-033
.920
.080
1.017
-275
59-775
.262
83
13 *3-o
58-513
.800
.081
1.041
-546
59-889
153
84
14 12.8
58.199
.851
.081
1.049
- .506
59.674
.190
85
16 12.8
58.213
.808
.082
1.065
.490
59.688
.185
86
18 12.8
1358.113
+ 0.769
+ 0.082
-|- 1.080
0.279
I359-765
0.204
87
20 13.1
58.213
.675
.083
1.096
- .270
59-797
135
88
26 13.2
57.88 4
.600
.083
1.144
+ -014
59-725
157
89
31 u.8
57-506
.808
.082
1.182
+ -139
59-7I7
.172
TABLE VI.
Equations of Condition formed from the measures of6I z Cygni
and Star (a).
No.
Date,
1886.
Equations of Condition.
Residual.
d. h.
//
//
I
May 26 12.3
0.197 = x 0.7022 TT 0.6018 d fj.
0.035
2
28 11.9
.205 = x .6820 .5961
.018
3
30 11.7
.217 = x .6621 .5918
+ -003
4
June i 11.7
.098 = x .6413 .5853
- .107
5
4 u.8
.288 = x .6080 .5771
+ .098
6
8 11.9
0.230 = x 0.5617 0.5660
+ 0.060
7
15 n. 2
.224 = x .4751 .5469
+ -092
8
16 11.7
.165 = x .4619 .5442
+ -039
9
23 1 1. 6
.205 = x .3676 .5250
+ .120
10
24 n. 6
.100 = x .3536 -5223
+ .022
ii
28 12.0
+ 0.007 = x 0.2971 0.5114
0.061
12
30 11.4
+ .013 = x .2684 .5059
- -054
13
July I 11.3
+ .142 = x .2538 .5031
-177
14
Aug. 20 1 1. 1
-f .385 = x + .4758 .3653
.101
15
24 9.8
+ .180 = x + .5255 .3556
+ .!2 7
22
Equations of Condition for the
No.
Date,
1886-7.
Equations of Condition.
Residual.
d. h.
//
16
Aug. 26 9.3
-f O.I 15 = X +0.5496 7T 0.3SOI dp.
+ 0.201
17
28 9.5
+ .290 = x + .5733 .3445
+ -037
18
29 9-5
+ .107 = x + .5855 .3418
-f- .225
'9
30 8.9
-f .347 = x + .5959 .3392
.010
20
31 8-8
-f .336 = X + .6071 .3364
+ .006
21
Sept. 7 8.6
-f -395 = x +0.6810 0.3174
O.O2I
22
10 8.4
+ .409 = x + .7099 .3091
.021
23
n 8.5
+ .418 = x + .7189 .3064
.026
24
13 8.4
+ .325 - x + .7365 .3009
+ .074
25
15 8.1
-f -435 = x + -7533 -2955
.029
26
16 9.8
+ 0.439 = x +0.7617 0.2925
0.028
27
17 8.1
+ .259 = x + .7700 .2900
+ -155
28
18 8.0
+ .425 = # + .7769 .2872
.008
2 9
20 9.0
+ .580 = x + .7926 .2815
- .156
30
22 9.4
+ .403 = x + .8059 .2761
+ .028
31
27 IO.2
+ 0.217 = x +0.8360 0.2623
+ 0.227
33
29 8.6
+ .230 - x + .8458 .2570
+ .219
33
30 8.4
+ .445 = x + .8506 .2543
+ .005
34
Oct. 2 8.2
+ -33 1 = a? + .8592 .2488
+ .124
35
6 9.1
+ .499 = x + .8739 .2380
- -038
36
13 xo.i
+ 0.436 = x 4-0.8894 0.2185
+ 0.034
37
21 7-5
+ .518 = x + .8911 .1969
.046
38
22 7.5
+ .515 = x + .8902 .1942
.044
39
Nov. 3 6.6
+ .406 = x + .8579 .1615
+ .06 4
40
5 8.8
+ .465 = x + .8482 .1557
.009
4i
16 7-5
+ 0.393 = x +0.7803 0.1257
+ 0.037
42
17 8.3
+ .370 = x + .7724 .1229
+ .056
43
18 8.6
+ .283 = X + .7645 .1201
+ .140
44
23 8.6
+ .445 = x + .7214 .1064
.040
45
29 6.9
+ -383 = x + .6629 .0904
.OOI
46
Dec. i 7.3
+ 0.473 = x +0.6413 0.0847
O.IOI
47
2 6.8
-f- .445 = x + .6309 .0820
-056
48
4 6.4
+ .430 = x + .6087 .0766
.070
49
7 6.3
+ -383 = x + .5738 .0739
.038
50
9 7.2
+ .563 = x + .5486 .0628
.228
5i
14 6.2
+ 0.578 = x +0.4855 0.0492
0.268
52
16 6.2
+ .244 = x + .4592 .0438
+ -054
53
24 6.2
-f- .260 = x + .3476 .0219
- .009
54
87 Jan. 5 6.9
+ .379 = x + .1675 + .0118
.201
55
8 6.4
+ .314 = x + .1214 + .0198
- .156
Relative Parallax of 61 2 Cygni and Star (a).
23
No.
Date,
1887.
Equations of Condition.
Residual.
d. h.
//
//
56
Jan. 10 6.7
+ 0.169 +O.O9OI 7T +O.O253 dfJl
+ 0.024
57
12 6.3
+ .282 = x + .0592 + .0308
-M9
58
20 6.4
+ .125 = x .0662 + .0527
.036
59
25 6.3
+ .003 = x .1447 + .0664
+ -054
60
3i 6.5
+ .115 = x .2366 + .0829
- .106
61
Feb. 5 6.0
+ 0.072 = x 0.3104 +0.0938
0.093
62
8 5.9
+ .037 = x .3544 + -1048
+ .076
63
17 17.1
+ .037 = x .4845 + .1306
+ ^30
64
25 17-4
.006 = x .5850 + .1526
- .129
65
26 16.9
+ .002 = X .5965 + .1553
.142
66
27 16.9
0.067 = x O.6o8o +0.1581
+ 0.077
67
Mar. 12 16.1
.038 = x .7403 + .1935
.161
68
16 15.7
.130 = x .7738 + .2044
.082
69
23 16.4
.287 = x .8237 + .2236
+ -055
70
27 14.8
.180 = x .8466 + .2344
.062
7i
'Apr. 2 15.3
0.296 = x 0.8736 +0.2509
+ 0.044
72
16 14.4
.319 = x .9003 + .2891
+ -057
73
19 14.6
.284 = x .8996 + .2973
+ .066
74
20 15.0
.292 = x .8986 + .3000
+ -075
75
25 13-4
.277 = x .8906 + .3137
+ .063
76
26 14.2
0.333 = x 0.8881 +0.3165
+ 0.120
77
29 13.8
.281 = x .8796 + .3246
.030
78
30 13-8
.358 = 5 -8761 + .3272
+ .109
79
May 5 13.7
- -373 = * -8552 + -34IO
+ -134
80
7 J 3-o
.277 = x .8453 + -3465
.042
81
9 i 2 -4
0.312 = x 0.8344 +0.3519
+ 0.082
82
IO 12.8
.225 = x .8285 + .3546
.OO2
83
13 13-0
.in = x .8093 + .3628
- .108
84
14 12.8
.326 = x .8026 + .3655
+ .110
85
16 12.8
.312 = x .7884 + .3710
+ .102
86
18 12.8
0.235 = x 0.7731 +0.3765
+ 0.032
87
20 I3.I
.203 = x .7570 + .3820
- .007
OO
00
26 13.2
.275 = x .7035 4- .3484
+ -103
89
31 ii.8
.283 = x .6540 + .4120
+ -133
The normal equations derived from these equations of condition by the
ordinary method are as follows :
+ 8.8480= +89.0000^7.3917^/01 0.15567:
4.0289= 7.3917 +8.8384 9.0391
+ 16.9205=- 0.1556 -9.0391 +41.2537
24 Concluded Parallax of 61 2 Cygni from Star (a).
//
whence a = +0.1056
dp = +0.0659
TT = +0.4250
while the probable error of it o".oi76, and the probable error in the deter-
mination of a distance of the principal star from the star of comparison
is o".ioo.
Before entering upon the tabular statement connected with the second star
of comparison, it may be well to give as a matter of interest, but which may
be passed over if regarded as superfluous, a table exhibiting the difference of
the measures of the two components from the same star, it being borne in
mind that the measures and their reductions are independent. It will be seen
that the average difference of the measures is 20". 28 7. An interesting use of
this result will be found on page 66.
TABLE VII.
Difference of the measured distances of Star (a) from
61 X and 61 2 Cygni.
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
//
//
//
n
//
//
I
2O.2I8
0.069
21
20.143
0.144
41
2O.227
O.o6o
2
305
.018
22
.251
.036
42
.260
.027
3
.284
.003
23
258
.029
43
.388
.IOI
A
.138
.149
2 4
.358
.071
44
.179
.108
5
310
023
25
.287
.000
45
342
55
6
20.300
0.013
26
20.395
0.108
46
20.239
0.048
7
.230
57
27
359
.072
47
331
.044
8
430
143
28
.247
.040
48
.328
.041
9
449
.162
2 9
.362
075
49
354
.067
10
395
.108
3
2 75
.012
50
.265
.022
ii
20.238
0.049
31
20.339
0.052
5i
20.188
0.099
12
.382
095
32
.367
.080
52
.293
.006
13
.123
.164
33
.240
.047
53
.201
.086
4
.310
.023
34
.300
.013
54
.184
.103
15
357
.070
35
.179
.108
55
.188
.099
16
20.415
0.128
36
20.381
0.094
56
20.252
-035
17
.281
.006
37
.310
.023
57
.009
.278
18
.436
.149
38
273
.014
58
.253
034
19
335
048
39
.440
153
59
.261
.026
20
.327
.040
40
.358
,071
60
.123
.164
Relative Parallax of 61 j Cygni and Star (b).
25
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
6l
20.159
0.128
7
if
20,302
it
0.015
8l
n
20.506
0.221
62
353
.066
72
.411
.124
82
231
.056
63
134
153
73
330
043
83
,146
-143
64
.189
.098
74
.468
.181
84
245
.042
65
139
.148
75
389
.102
85
.284
.003
66
20.109
0.178
76
20.418
O.I3I
86
2O.III
0.176
67
065
.222
77
373
.086
87
213
074
68
.183
.104
78
.409
.122
88
351
.064
69
308
.O2I
79
.526
239
89
-376
.089
70
-283
.004
80
303
.Ol6
The intention of the foregoing- Table (VII) is to exhibit, from another
point of view, the accuracy of the measures.
NOTES.
No. i. The exposure was only two minutes, and the fainter stars are not visible.
No. 2. On this night the stars c and d, were too faintly impressed to be measurable.
No. 6. Images elongated, but measurable.
No. ii. Cloudy, and images faint: those of c and d are visible on only one plate, and the
measures of these stars have not been retained.
No. 1 8. One of the plates rejected from injury to the film.
No. 23. Exposure was continued for eight minutes.
No. 30. Cloudy : images feeble.
No. 35. One of the plates rejected on account of obviously discordant measures.
No. 41. Images elongated, but measurable.
No. 49. Exposure was continued for ten minutes, on account of fog.
No. 53. Plates ' fogged ' : one plate rejected, accidentally damaged.
No. 54. Instrument imperfectly driven.
No. 55. Bright moonlight : plates somewhat fogged : exposure ten minutes.
No. 61. Altitude low : images feeble.
No. 66. One of the plates rejected : measures very discordant.
No. 70. Images elongated. Driving-clock went badly. (Oil congealed.)
No. 72. Clouds passing. Exposures of variable length.
No. 76. One of the plates rejected through accident to the film.
No. 81. Images faint.
No. 83. Images elongated : one of the plates rejected owing to discordant measures.
No. 85. Exposure continued through ten minutes.
No. 88. Images faint and elongated.
The total number of plates rejected is eight : the total number taken is 332.
RELATIVE PARALLAX OF 61j CYGNI AND STAR (B).
Here again a similar arrangement of the Tables for the discussion of the
parallax with this star is pursued, and the same diagonal of reference is still
employed. It is only necessary to mention that the parallactic factors in the
equations of condition have been computed from the expression
sf G) 2T ii'\ TT.
26
Relative Parallax of 61 j Cygni and Star (b).
TABLE VIII.
Concluded measures of61 1 Cygni from the comparison Star (b).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance of
Star (6) to
61i Cygni.
lefraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (6) from
61, Cygni.
Average
Devi-
ation.
d. h.
//
//
it
//
//
//
//
I
May 28 11.9
1001.578
+ 0.633
+ 0.06 1
+ 1-502
-f-o.n6
1003.890
0.124
2
30 11.7
1-354
.763
.061
1.489
+ -136
3-803
J 33
3
June i 11.7
1.940
.635
.061
1-475
- .176
3-935
.301
4
4 n.8
2.IS3
.568
.060
1-454
- -125
4.110
.252
S
8 11.9
1.716
52
.060
1.426
+ -47
4.121
.096
6
15 ii. 2
1002.275
+ 0.554
+ 0.058
+ 1-378
0.179
1004.086
0.074
7
16 11.7
2.297
.469
057
i-37i
.102
4.092
.165
8
23 1 1. 6
i-5i7
.424
055
1-323
-373
3.692
.283
9
24 1 1.6
2.196
.426
054
1.316
.312
3.680
.224
10
28 12.0
2.166
.364
.052
1.288
.107
3-763
.130
ii
30 II-4
1001.611
+ 0.400
+ 0.051
+ 1-275
+ 0.296
1003.633
0.245
12
July i 11.3
1.938
43
050
1.268
+ -146
3-805
.'37
'3
Aug. 20 1 1, i
2.182
-283
.008
0.920
- -053
3-340
.2T 7
14
24 9.8
i-93i
.298
.004
.896
+ -I9 1
3-320
.144
'5
26 9.3
1.900
309
.OO2
.882
+ -292
3-385
.20 9
16
28 9.5
1002.432
+ 0.299
0.001
+ 0.868
+ 0.095
1003.693
0.093
17
29 9-5 '
2.446
.301
.002
.861
.168
3-438
.062
18
30 8.9
2.254
3M
.003
-855
+ -041
3.461
.147
J 9
31 8.8
2,150
-315
.003
.848
+ -184
3-494
243
20
Sept. 7 8.6
2.270
.306
.on
.800
- -045
3-320
.128
21
10 8.4
1002.044
+ 0.306
O.OI I
+ 0-779
+ 0.200
1003.318
0.253
22
ii 8.5
2.323
-303
.015
.772
- -^54
3.229
139
23
13 8.4 !
2.424
.299
.017
-758
- .2 4 6
3.218
.290
2 4
15 8.1
2.521
-306
.019
744
-273
3-279
.182
25
1 6 9.8
1.891
.281
.019
-737
+ .327
3.217
.247
26
17 8.1
1002.616
+ 0.303
O.O2O
+ 0.731
0.220
1003.410
O.229
27
18 8.0
2.486
.302
.022
.724
.172
3-318
.270
28
20 9.0
2.104
.284
.024
.709
+ -2 4 I
3-3 H
-193
2 9
22 9.4
2.506
.281
.026
.696
.123
3-334
.147
3
27 10.2
2 -536
.286
.030
.661
.184
3.269
.225
3^
29 8.6
IOO2.122
+ 0.283
0.032
+ 0.648
+ 0.237
1003.258
O.2O7
3 2
30 8.4
2.505
.283
033
.641
+ .102
3-498
I 4 2
33
Oct. 2 8.2
2.523
.284
035
.627
-003
3.39 6
.263
34
6 9.1
2-357
.282
.038
.600
+ -03
3-231
!35
35
13 10.1
2.602
304
.044
550
.017
3-395
-193
Concluded Distances of ftl^ Cygni from Star (b). 27
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance of
Star (b) to
61i Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (6) from
61i Cygni.
Average
Devi-
ation.
d. h.
ff
rf
it
//
//
tf
36
Oct. 21 7.5
1002.754
+ 0.281
0.049
+ 0.496
0.046
1003.436
0.252
37
22 7.5
2.572
.281
.050
.489
+ -094
3-386
.129
38
Nov. 3 6.6
2.784
.282
.056
.407
+ .010
3.427
-093
39
5 8.8
2.758
304
057
*39*
.061
3.336
-134
40
16 7.5
2.898
.295
.060
3*7
- .178
3.272
.276
4i
17 8.3
1002.840
+ 0.312
O.o6o
+ 0.310
+ 0.031
1003.433
0.229
42
1 8 8.6
2.838
.320
.061
.302
.128
3.271
.274
43
23 8.6
3-125
331
.061
.268
.225
3.438
139
44
29 6.9
3.830
.297
.061
.228
+ .016
3.310
.183
45
Dec. i 7.3
2.741
309
.061
.214
+ .058
3.261
.205
46
2 6.8
1003.056
+ 0.299
O.o6 1
+ 0.207
0.047
1003.454
0.039,
47
4 6.4
3-097
295
.061
-193
.170
3-354
.172
48
7 6.3
3-258
2 97
.060
.186
- .196
3-485
.144
49
9 7.2
3.241
.320
.060
.158
.199
3.460
193
50
14 6.2
3-733
304
.058
.124
- .482
3.621
.260
5i
16 6.2
1003.925
+ 0.308
0.057
+ O.IIO
0.571
1003.715
O.2II
52
24 6.2
3-7 11
.320
.054
+ -055
-59
3-523
.183
53
87 Jan. 5 6.9
4-133
.367
.047
.030
.684
3-739
.151
54
8 6.4
3-859
355
045
.050
- -425
3-694
.204
55
10 6.7
3-187
-372
-043
.064
+ .101
3-553
.096
56
12 6.3
1004.288
+ 0.362
0.041
0.078
0.682
1003.849
O.l62
57
20 6.4
4-034
-385
035
.133
~ -554
3.697
.305
58
25 6.3
3-502
39 2
.030
.167
+ -1x5
3.812
.183
59
3' 6.5
4.198
.416
.024
.209
-493
3.888
'75
60
Feb. 5 6.0
3-44'
.409
.O2O
.236
+ .212
3.806
.244
61
8 5-9
1003.999
+ 0.415
0.016
0.264
0.372
1003.762
0.105
62
17 17.1
3-347
1.081
.006
.329
- -370
3.723
.149
63
25 17-4
3.276
0.784
+ .002
.385
+ .120
3-797
73
64
26 16.9
3-486
930
.003
.391
.211
3-817
.126
65
27 16.9
3.014
963
.004
.398
+ -437
4.020
.293
66
Mar. 12 16.1
1003.616
+ 0.894
+ 0.018
-0.487
+ 0.021
1004.062
0.272
67
16 15.7
3.837
0.924
.022
S5
.269
3-999
.185
68
23 16.4
4.159
0-596
.029
-563
- -093
4.128
304
69
27 14.8
3-5o6
1.015
.032
591
+ .1*5
4.147
.242
70
Apr. 2 15.3
3-698
0.703
.038
-632
+ .206
4.013
.167
7i
16 14.4
1003.437
+ 0.701
+ 0.048
0.729
+ 0.568
1004.025
0.218
72
19 14.6
4-346
.604
.050
749
- -275
3-976
153
73
20 15.0
4.060
-533
.050
-756
+ -224
4.111
.227
74
25 13-4
3-9 J 4
.819
-053
.790
-144
3-852
.244
75
26 14.2
4.168
596
054
797
.048
3-973
131
28
Equations of Condition for the
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887.
Measured
Distance of
Star (6) to
61i Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (b) from
61, Cygni.
Average
Devi-
ation.
d. h.
n
//
H
//
//
//
7 6
Apr. 29 13.8
1004.133
+ 0.652
+ 0.055
0.818
0.01 1
IOO4.OII
0.205
77
3 13-8
4.263
.624
.056
.825
+ .004
4.122
.190
78
May 5 13.7
4402
.584
.058
859
.223
3.962
133
79
7 13.0
4-303
.701
.058
-873
- -135
4-054
307
80
9 12-4
4-153
-859
059
.887
.038
4.146
.I8 S
81
10 12.8
1004.422
+ 0.708
+ 0.059
-0.893
0.202
1004.094
0.262
82
13 i3-o
4.800
.612
.O6O
.914
.402
4.156
.105
83
14 12.8
4.741
652
.060
.921
-373
4-59
.240
84
16 12.8
4.693
.619
.060
935
- .360
4.077
183
85
18 12.8
4.701
.588
.061
949
-205
4.196
235
86
20 13.1
1004.696
+ 0.512
+ 0.061
0.963
0.199
1004.107
O.2O8
87
26 13.2
4-447
-457
.061
1.004
+ .on
3972
-265
88
31 1 1.8
4-213
.618
.061
1.038
+ .102
3-956
133
TABLE IX.
Equations of Condition formed from the measures of Q\ l Cygni
and Star (b).
No.
Date,
1886.
Equations of Condition.
Residual.
d. h.
//
n
I
May 28 11.9
+ 0.190 = x +0.621377 0.5961 dfj.
+ -79
2
30 11.7
*+ .103 = x + .5999 .5908
+ -157
3
June i 11.7
+ -235 - * + .5788 .5853
+ -015
4
4 1 1.8
+ .410 = x + .5489 .5771
- -173
5
8 11.9
+ .421 = x + .4946 .5660
.208
6
15 ii. 2
+ 0.386 = x +0.4051 0.5469
O.2I2
7
16 11.7
+ .392 = x + .3935 .5442
- -223
8
23 ii. 6
.008 = x + .2958 - .5250
+ -134
9
24 ii. 6
.020 = X + .28l8 .5223
+ -139
10
28 12.0
+ .063 = x + .2245 .5114
+ -031
ii
30 11.4
0.067 = x +0.1956 0.5059
+ 0.148
12
July i 11.3
+ .105 - x + .1811 .5031
-030
13
Aug. 20 I I.I
.360 = x .5247 .3653
+ -124
'4
24 9.8
.380 = x .5707 .3556
+ .124
15
26 9.3
.315 = x .5929 .3501
+ -049
Relative Parallax of 61 X Cygni and Star (b).
29
No.
Date,
1886-7.
Equations of Condition.
Residual
d. h.
//
//
16
Aug. 28 9.5
O.OO7 = X 0.6150 7T 0.3445 dp
0.268
17
29 9-5
.262 = x .6257 .3418
.018
18
30 8.9
.239 = x .6352 .3392
-045
19
31 8.8
.206 = x .6454 .3364
.078
20
Sept. 7 8.6
.380 = x .7118 .3174
+ .064
21
10 8.4
0.382 = x -0.7373 0.3091
+ 0.053
22
ii 8.5
.471 = x .7450 .3064
+ .138
23
13 8.4
.482 = x .7605 .3009
+ .142
2 4
15 8.1
.421 = x .7747 .2955
+ .065
25
16 9.8
.483 = x .7822 .2925
+ -134
26
17 8.1
0.290 = x 0.7890 0.2900
0.062
2 7
18 8.0
.382 = x .7950 .2872
+ .027
28
20 9.0
.386 = x .8078 .2815
+ -031
2 9
22 9.4
.366 = x .8187 .2761
.001
30
27 10.2
.431 = x .8429 .2623
+ -056
31
29 8.6
0.442 = x 0.8505 0.2570
-|- 0.064
3 2
30 8.4
.202 = X .8541 .2543
- .I 7 8
33
Oct. 2 8.2
.304 = x .8604 .2488
.078
34
6 9.1
.469 = x .8700 .2380
+ .082
35
13 10.1
.305 = x .8769 .2185
- .085
36
21 7-5
0.264 = x 0.8692 0.1969
O.I22
37
22 7.5
.314 = x .8671 .1942
- .071
38
Nov. 3 6.6
.273 = x .8206 .1615
.092
39
5 8-8
.364 = x .8097 .1557
-f .004
40
16 7.5
.428 = a .7311 .1257
+ -103
4 1
17 8.3
0.267 = x 0.7224 0.1229
0.054
4 2
18 8.6
.429 = X .7138 .1201
+ .III
43
23 8.6
.262 = x .6665 .1064
-035
44
29 6.9
.390 = x .6037 .0904
+ .122
45
Dec. i 7.3
.439 = x .5808 .0847
H- .181
46
2 6.8
0.246 = ar 0.5698 0.0820
0.006
47
4 6.4
.346 = x .5463 .0766
+ -104
48
7 6.3
.215 = x .5097 .0739
.Oil
49
9 7-2
.240 = x .4838 .0628
+ .026
50
14 6.2
.079 = x .4184 .0492
.106
Si
16 6.2
+ 0.015 = x 0.3914 0.0438
0.188
5 2
24 6.2
.177 = x .2779 .0219
+ -053
53
87 Jan. 5 6.9
-f .039 = x .0974 + .0118
- .083
54
8 6.4
.006 = x .0518 -j- .0198
.018
55
10 6.7
- .147 - x .0209 + .0253
+ -137
30 Equations of Condition for Glj Cygni and Star (b).
No.
Date,
1887.
Equations of Condition.
Residual.
d. h.
//
//
56
Jan. 1 2 6.3
+ O.I49 X ~\~ 0.0096 TT + O.O3O8 dfJi
0.145
57
20 6.4
.003 = x + .1322 + .0527
+ .061
58
25 6.3
+ -112 = X + .2084 -}- .0664
.O2O
59
31 6.5
+ .188 = x + .2968 + .0829
-057
60
Feb. 5 6.0
-|- .106 = x + .3675 -f .0938
-f .056
61
8 5-9
-{-0.062 = x +0.4090 -f 0.1048
+ O.II8
62
17 17.1
+ .023 = x + .5310 -1- .1306
+ .211
63
25 J 7-4
+ .097 = x + .6235 -f .1526
+ .178
64
26 16.9
f .117 = x + .6341 + .1553
+ -163
65
27 16.9
+ .320 = x + .6446 -f .1581
.036
66
Mar. 12 16.1
+ 0.362 = x +0.7624 +0.1935
0.026
67
16 15.7
+ .299 = x + .7912 + .2044
+ .050
68
23 16.4
+ .428 = x + .8326 + .2236
- .061
69
27 14.8
+ .447 = x + .8508 + .2344
- .072
70
Apr. 2 15.3
+ -313 - a? + -8702 + .2509
+ .071
7*
16 14.4
+ 0.325 = x +0.8801 +0.2891
+ 0.068
72
19 14.6
+ .276 = x + .8756 + .2973
+ .117
73
20 15.0
+ . 4 n = x + .8736 + .3000
-025
74
25 13-4
+ .152 = x + .8600 + .3137
+ .229
75
26 14.2
+ .273 = x + .8564 + .3165
+ .106
76
29 13-8
+ 0.311 = x +0.8445 +0.3246
+ 0.063
77
30 13-8
+ .422 = x + .8401 + .3272
-050
78
May S 13.7
+ .262 = x + .8140 + .3410
+ .098
79
7 i3-o
+ .354 = x + .8021 + .3465
+ .001
80
9 12.4
+ .446 = x + .7893 + .3519
.097
81
10 12.8
+ 0.394 = x +0.7824 +0.3546
0.048
82
13 i3-o
+ .456 = x + .7604 + .3628
.120
83
14 12.8
+ .459 = x + .7529 + .3655
.126
84
16 12.8
+ .377 - * + .7369 + .37!
.051
85
18 12.8
+ .496 = x + .7199 + .3765
+ -177
86
20 13.1
+ 0.407 = x +0.7021 +0.3820
0.096
87
26 13.2
+ .272 = x + .6442 + .3984
+ -013
88
31 n.8
+ .256 = x + .5913 + .4120
+ .OO6
The normal equations, after the ordinary treatment, become
//
1.3140= +88.oooo# 6.7889 d\L 2.544271
+ 4.3827= - 6.7889 +8.4762 + 9-7965
+ 17.1716=- 2.5442 4-9'79 6 5 +3 8 -7724
Concluded Parallax of 61 1 Cygni and Star (b). 31
whence is derived by solution
//
x = 0.0016
d[L +0.0055
77 = +0.4414
The probable error of TT proves to be +o",O32S, so that the value of the
relative parallax from this star is
v = + 0"-4414 + 0".0222.
The probable error in one complete measure of distance is o".n5.
PAR ALL AH OF 61 2 CYGNI AND STAR (B).
The following- set of tables are analogous to and in the same order of
sequence as those already described in the three preceding cases, and hence
call for no further remark.
TABLE X.
Concluded measures of 61 2 Cygni from the comparison star (b).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance of
Star (6) to
612 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (b) from
61 2 Cygni.
Average
Devi-
ation.
d. h.
11
11
//
it
//
//
it
I
May 28 11.9
1022.078
+ 0.646
+ 0.063
+ 1.510
+ 0.1I8
1024.415
0.203
2
30 11.7
22.065
.798
.062
1.497
+ -138
24.560
.132
3
June i 11.7
22.417
.646
.062
1.482
-79
24.428
J 37
4
4 n.8
22-733
.580
.062
1.462
.127
24.710
293
5
8 11.9
22.201
.522
.061
'434
+ -416
24.634
.087
6
15 ii. 2
1022.519
+ 0.565
+ 0.059
+ 1-386
0.183
1024.346
0.165
7
16 11.7
22.809
479
.058
1-378
.104
24.620
193
8
23 1 1. 6
22.053
433
.056
1-330
+ .381
24-253
.242
9
24 ii. 6
22-733
435
055
1-323
.319
24.227
.302
10
28 12.0
22.696
372
053
1.295
.109
24.307
085
ii
30 11.4
IO22.268
+ 0.408
+ 0.052
+ 1.282
+ 0.302
1024.312
0.225
12
July i 11.3
22.476
.409
,051
1-275
+ -149
24.360
.138
*3
Aug. 20 1 1. 1
22.766
.289
.008
0.925
-055
23-933
243
H
24 9.8
22.428
.306
.004
0.900
+ -195
23.833
.262
IS
26 9.3
22-574
.316
.OO2
0.887
+ -298
24.777
113
32
Relative Parallax of 61 2 Cygni and Star (b).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance of
Star (f>) to
612 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (b) from
61 2 Cygni.
Average
Devi-
ation.
d. h.
//
//
//
//
//
//
//
16
Aug. 28 9.5
1022.839
+ 0.307
O.OOI
+ 0.873
+ 0.097
1024.115
0.270
17
29 9-5
23-I79
-308
.002
.866
.171
24.180
.126
18
30 8.9
22.960
.321
.003
.859
+ -042
24.179
.163
iQ
31 8.8
22.760
.321
.003
-852
+ -187
24.117
.192
20
Sept. 7 8.6
22.931
SIS
.on
.804
.046
23.991
.247
21
10 8.4
1022.525
+ 0.313
0.01 1
+ 0.783
+ 0.205
1023.815
0.103
22
ii 8.5
23.089
3"
.015
-776
~ -'57
24.004
.244
23
13 8.4
23-235
.308
.017
.762
.252
24.036
.225
24
15 8.1
23.262
.313
.019
-748
- -279
24.025
.293
2 5
1 6 9.8
22.598
.287
.019
.741
+ -334
23.941
137
26
17 8.1
1023.267
+ 0.311
O.O2I
+ 0.735
0.225
1024.067
0.150
27
18 8.0
23.240
.310
.023
.728
- .176
24.079
.203
28
20 9.0
22.587
.290
.025
.712
+ -246
23.810
.072
2 9
22 9.4
23-I45
.287
.027
-699
.125
23-979
.146
30
27 10.2
23-053
.292
.031
.664
- .187
23.791
285
31
29 8.6
1022.638
+ 0.288
0.033
+ 0.651
+ 0.242
1023.786
0.307
32
30 8.4
23.112
.289
.034
643
+ -104
24.114
.322
33
Oct. 2 8.2
22.957
.290
.036
.630
-003
23-838
H3
34
6 9.1
23.012
.288
039
.603
+ -030
23.894
.205
35
13 10.1
23.007
3"
.045
553
- .017
23.809
.069
36
21 7-5
1023.166
+ 0.287
0.050
+ 0.499
0.047
1023.855
0.143
37
22 7-5
23.057
.287
.051
.492
+ .096
23.881
.182
38
Nov. 3 6.6
23.372
.287
.057
-409
-+ .010
24.021
-243
39
5 8.8
23.419
311
.058
394
.062
24.004
.20 5
40
16 7-5
23.637
.301
.062
.318
.181
24.013
.190
4i
'7 8.3
1023.291
+ 0.320
0.062
+ 0.311
+ 0.031
1023.891
0.311
42
18 8.6
22.427
.329
.063
304
.130
23.867
.227
43
23 8.6
23-619
-339
.063
.269
-230
23-934
.086
44
29 6.9
23-353
.305
.063
.229
+ .017
23.841
154
45
Dec. i 7.3
23401
316
.063
.214
+ .060
23.928
.212
46
2 6.8
1023.585
+ 0.307
0.063
+ 0.208
0.048
1023.989
0.165
47
4 6.4
23.690
301
.062
.194
- -174
23-949
.190
48
7 6.3
23.830
305
.061
.187
.200
24.061
-253
49
9 7.2
23.870
.329
.061
'59
- -203
24.094
.227
50
14 6.2
24.106
311
059
.124
-49 2
23-990
.184
5 1
16 6.2
1024.268
+ 0.315
0.058
+ 0. 1 1 1
-0.583
1024.053
0.294
5 2
24 6.2
24.275
.328
055
+ -056
.52
24.084
.102
53
87 Jan. 5 6.9
24-375
375
.048
-030
-699
23-973
.280
54
8 6.4
24.476
364
.046
.050
- 434
24.310
.198
55
10 6.7
23-890
.381
.044
.064
+ -104
24.267
.219
Concluded Distance of 61 2 Cygni from Star (b). 33
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887.
Measured
Distance of
Star (b) to
61 2 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (6) from
61 2 Cygni.
Average
Devi-
ation.
d. h.
//
//
//
n
H
//
n
56
Jan. 12 6.3
1024.845
+ 0-37I
0.042
0.078
0.696
1024.400
O.226
57
20 6.4
24-633
.394
.036
133
- .566
24.292
243
58
25 6.3
24.065
.402
.031
.168
+ ."7
24-385
175
59
31 6.5
24-73I
.426
.025
.210
-504
24.418
.292
60
Feb. 5 6.0
24.053
.419
.O2O
.238
+ -217
24.431
.205
61
8 5.9
1024.787
+ 0.425
0.016
O.266
0.380
1024.550
0.183
62
17 17.1
24.065
1.116
.006
-331
- -378
24.466
.169
63
25 17-4
24.164
0.798
+ O.O02
-386
+ -123
24.701
.272
64
26 16.9
24-3I5
945
.003
393
.215
24.655
.240
65
27 16.9
23-57I
.981
.004
.401
+ -447
24.602
139
66
Mar. 12 16.1
1024.165
+ 0.910
+ 0.018
0.490
+ O.O22
1024.625
0.087
67
16 15.7
24.607
0-945
.023
517
- -275
24.783
154
68
23 16.4
24.679
0.608
.030
.566
- -095
24.656
.227
69
27 14.8
24.158
1-035
033
594
+ -l8 9
24.821
275
70
Apr. 2 15.3
24.371
0-713
.038
.635
+ .210
24.697
.165
7i
16 14.4
1024.038
+ 0.712
+ 0.049
0.732
+ 0.572
1024.639
0.273
72
19 14.6
25.126
.617
.051
753
- .281
24.760
.207
73
20 15.0
24.598
-544
.051
.760
+ .228
24.661
H5
74
25 13-4
24.782
.835
054
794
.147
24-730
.209
75
26 14.2
24.862
.608
055
.801
-049
24.675
.163
76
29 13.8
1024.744
+ 0.664
+ 0.057
0.822
O.OII
1024.632
0.190
77
30 13-8
24.893
-637
057
.829
+ .004
24.762
139
78
May 5 13.7
25.063
.596
.060
.864
- .227
24.628
.244
79
7 i3-o
24.852
.713
.060
.877
- .138
24.610
.292
80
9 12.4
24.652
875
.060
.891
-039
24.657
.087
81
10 12.8
1024.936
+ 0.721
+ 0.061
0.899
0.206
1024.613
0.305
82
13 i3-o
25-2I5
.623
.061
.919
.411
24.569
.242
83
14 12.8
25.292
.664
.061
.926
- .381
24.710
.129
84
16 12.8
25-304
.631
.062
.940
- .368
24.689
.290
8 5
18 12.8
25.122
599
.062
953
.209
24.621
163
86
20 13.1
1025.310
+ 0.522
+ 0.062
0.968
0.203
1024.723
0.207
87
26 13.2
25-023
-465
.063
1.009
+ .on
24-553
153
88
31 n.8
24.711
.706
.062
1.044
+ .104
24-539
.I 9 8
34
Relative Parallax of 61 2 Cygni and Star (b).
TABLE XL
Equations of Condition formed from the measures of 61 2 Cygni
and Star (b).
No.
Date,
1886.
Equations of Condition.
Residual.
d. h.
//
n
I
May 28 11.9
+ O.II5 - * +0.6226 7T 0.5961 dfJL
+ 0.140
2
30 11.7
+ .260 = x + .6024 .5908
-1- -013
3
June i 11.7
+ .128 - x + .5812 .5853
+ .109
4
4 n.8
+ .410 - x + .5514 .5771
- -185
5
8 11.9
-1- -334 - x + -4972 -5660
.114
6
15 11.2
+ 0.046 = x +0.4079 0.5469
+ O.II5
7
16 11.7
+ .320 = x + .3963 .5442
- .164
8
23 1 1. 6
.047 = x + .2987 .5250
+ .160
9
24 1 1. 6
-073 = x + .2847 .5223
+ .170
10
28 12.0
+ .007 = x + .2274 5 II 4
+ -73
ii
30 1 1. 4
+ O.OI2 = X +0.1985 0.5059
+ 0.056
12
July i 11.3
+ .060 = x + .1840 .5031
.002
'3
Aug. 20 1 1. 1
.367 =* x .5227 .3653
+ .S
14
24 9.8
.467 = x .5686 .3556
+ - ! 95
15
26 9.3
.223 - x .5910 .3501
-59
16
28 9.5
0.185 = x 0.6128 0.3445
0.106
17
29 9-5
.120 = X .6239 .3418
- .176
18
30 8.9
.121 = X .6335 .3392
.179
19
31 8.8
.183 = x .6438 .3364
.122
20
Sept. 7 8.6
.309 - x .7105 .3174
- .025
21
10 8.4
0.485 = x 0.7361 0.3091
+ 0.138
22
ii 8.5
.296 = x .7439 .3064
-053
23
13 8.4
.264 = x .7595 .3009
.092
24
15 8.1
.275 = x .7737 .2955
- .08 7
25
16 9.8
-359 = * -7813 ~ -2925
.106
26
17 8.1
0.233 = * 0.7881 0.2900
0.135
27
18 8.0
.221 = x -7941 .2872
.150
28
20 9.0
.490 = x .8070 .2815
+ .114
2 9
22 9.4
.321 = x .8180 .2761
.060
30
27 IO.2
.509 = x .8425 .2623
+ .117
31
29 8.6
0.514 = x 0.8503 0.2570
+ 0.120
32
30 8.4
.186 = x .8539 .2543
.2IO
33
Oct. 2 8.2
.462 = x .8602 .2488
+ .063
34
6 9.1
.406 = x .8701 -2380
~\- -003
35
13 10.1
.491 = x .8773 .2185
+ -085
Equations of Condition : 61 2 Cygni and Star (b). 35
No.
Date,
1886-7.
Equations of Condition.
Residual.
d. h.
tt
n
36
Oct. 21 7.5
0.445 -= X 0.8700 7T 0.1969 dp.
+ 0.044
37
22 7.5
.419 = x .8680 -1942
+ .019
38
Nov. 3 6.6
.279 = x .8220 .1615
.099
39
5 8.8
.296 = x .Sin .1557
~ -077
40
16 7.5
.287 = x .7331 .1257
.049
4i
17 8.3
0.409 = x 0.7244 0.1229
+ 0.076
42
18 8.6
.433 = X .7156 .1201
+ .104
43
23 8.6
.366 = x .6686 .1064
-f -059
44
29 6.9
.459 = x .6060 .0904
+ .l8l
45
Dec. i 7.3
.372 = x .5832 .0847
+ -105
46
2 6.8
0.311 = x 0.5722 0.0820
+ 0.049
47
4 6.4
.351 = x .5487 -0766
+ .099
48
7 6.3
.239 = x .5122 .0739
+ .004
49
9 7-2
.206 = x .4863 .0628
.Ol6
50
14 6.2
.310 = x .4211 .0492
+ .126
5i
16 6.2
0.247 = x 0-394 1 0.0438
+ 0.066
52
24 6.2
.216 = x .2807 .0219
4- .087
S3
87 Jan. 5 6.9
-327 = x .1002 + .0118
+ .281
54
8 6.4
+ .010 = x .0546 + .0198
-035
55
10 6.7
.033 = x .0237 + .0253
+ .022
56
12 6.3
-f o.ioo = x -|- 0.0068 -1-0.0308
0.097
57
20 6.4
.008 = x + .1296 + .0527
+ -067
58
25 6.3
+ .085 = x + .2058 + .0664
+ .010
59
31 6.5
+ .118 = x 4- -2944 + -0829
+ .017
60
Feb. 5 6.0
+ .131 = x + .3649 + -0938
-1- -037
61
8 5-9
+ 0.250 = x +0.4067 +0.1048
0.063
62
17 17.1
+ .166 = x + .5291 + .1306
+ .077
63
25 17-4
+ .401 = x + .6219 + .1526
- -"5
64
26 16.9
+ -355 = * + .6325 -f .1553
- .065
65
27 16.9
-f- .302 = x + .6430 + .1581
.007
66
Mar. 12 16.1
+ 0.325 = x +0.7614 +0.1935
+ 0.025
67
16 15.7
+ .483 = x + .7904 + .2044
.080
68
23 1 6-4
+ .356 = x + .8322 + .2236
+ .027
69
27 14.8
+ .521 = x + .8504 + .2344
.129
70
Apr. 2 15.3
+ -397 = * + -8702 + .2509
+ .004
7i
16 14.4
+ 0.339 = * +0.8808 +0.2891
+ 0.068
72
19 14.6
+ .460 = x + .8765 + .2973
- -053
73
20 15.0
+ .361 = x + .8745 + .3000
+ -044
74
25 13-4
+ .430 = x + .8612 + .3137
.031
75
26 14.2
+ -375 -= x + -8576 + -3165
+ .023
36
Concluded Parallax of 61 2 Cygni and Star (b).
No.
Date,
1887.
Equations of Condition.
Reeidual.
d. h.
//
//
7 6
Apr. 29 13.8
+ 0.332 = a? -f 0.8458 TT + 0.3246 dfj.
+ O.o6o
77
30 13-8
+ .462 = x + .8414 -f .3272
.071
78
May 5 13.7
+ .328 = x + .8155 -f .3410
+ .052
79
7 13-0
+ .310 = x + .8038 + .3465
+ .065
80
9 12 -4
+ -357 = * + -7910 + -3519
+ -013
81
10 12.8
+ 0.313 = x +0.7842 +0.3546
+ 0.054
82
13 i3-o
+ .269 = x + .7623 + .3628
+ .088
83
14 12.8
+ .410 = x + .7548 + .3655
-055
84
16 12.8
+ .389 = x + .7389 + .3710
.042
85
18 12.8
+ .321 = x + .7220 + .3765
+ .019
86
20 I3.I
+ 0.423 = x +0.7042 +0.3820
0.091
87
26 13.2
+ .253 = x + .6465 + .3984
-f -S4
88
31 n.8
+ .239 = x + .5938 + .4120
+ .044
The normal equations in this case are
//
1.534 = + 88.oooo# 6.7889^ 2.546377
+ 4.7542=- 6.7889 +8.4762 + 9.7649
+ 17.9295=- 2.5463 +9.7649 +38.8860
whence is derived by solution
//
X O.OOI2
dp = +0.0406
TT = +0.4508.
The probable error of TT proves to be o".oi9i, so that the value of the
relative parallax from this star is
TT= +0".4508 + 0".0191.
The probable error of a complete measure of distance is +o".ioo.
In the adjoining Table are exhibited the differences in the measured
distances of the star (b) from each of the components of 61 Cygni. The mean
difference is 2o".594.
Test of the Accuracy of the Measures.
37
TABLE XII.
Differences of the measured distances of Star (b)/rom
61 t and 61 2 Cygni.
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
fro.m
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
//
//
/;
H
M
//
I
20.525
0.069
31
20.528
0.066
61
20.788
0.194
2
-757
I6 3
32
.6l6
.022
62
743
.149
3
493
.101
33
.442
.152
63
.904
.310
4
.600
.006
34
.663
.069
64
.838
244
5
5*3
.081
35
.414
.180
65
582
.012
6
20.260
0-334
36
20.419
0^75
66
20.563
0.031
7
.528
.066
37
495
099
67
784
.190
8
.561
033
38
594
.000
68
528
.066
9
547
.047
39
.668
074
69
.674
.080
10
544
.050
40
.741
.147
70
.684
.090
ii
20.679
0.085
4 1
20.458
0.136
/i
20.614
0.020
12
555
039
42
.596
.002
72
790
.196
13
593
.OOl
43
.496
.0 9 8
73
550
.044
14
.513
.081
44
531
06 3
74
.878
.284
15
.692
.098
45
.667
073
75
.702
.108
16
20.422
0.172
46
20.535
0.059
76
20.521
0.073
17
.742
.148
47
595
.001
77
.640
.046
18
.718
.124
48
576
.018
78
.666
.072
J 9
623
.019
49
634
.040
79
556
.038
20
.671
.077
50
369
.225
80
5"
083
21
20.497
0.097
5i
20.338
0.256
81
20.519
0.075
22
775
.181
52
.561
033
82
4'3
.I8l
23
.818
.224
53
234
.360
83
551
043
24
746
.152
54
.616
.022
84
.612
.018
25
.724
.130
55
.714
.I2O
85
425
.169
26
20.657
0.063
56
20.551
0.043
86
20.616
O.O22
27
.761
.167
57
595
.001
87
.581
.013
28
.496
.098
58
573
.O2I
88
583
.on
2 9
6 45
051
59
530
.064
30
.522
.072
60
.625
.031
PARALLAX OF 61, CYGNI AND STAR (C).
Having regard to the importance of establishing, on what I hope are
incontrovertible grounds, the accuracy of the photographic method, I have
thought it prudent to proceed a step further in the enquiry, and as is not
unusual in parallax researches, I determined to continue the enquiry with
reference to another pair of comparison stars situated at a very considerable
angle to the direction of the former diagonal. In adopting this course I had
also at the time another thought in my mind, viz. that by selecting many
stars of comparison I might derive an approximate value of the absolute
parallax itself. It is already hinted in the Introduction, III, that similarity
of magnitude is very far from being attended by similarity of parallax, at all
events it certainly is not so in individual cases.
The additional pair of stars selected is D.M. + 37, No. 41 75 and D.M. + 38,
No. 4348, of the magnitudes 9-0 and 9-5 respectively. Of course the diagonal
of reference is now different from that employed in the other determinations ;
and, before proceeding to the Tables involving the parallactic processes, it will
be interesting to compare the variations of these measurements conducted along
two directions on the film nearly at right angles to each other. Inasmuch as
these diagonals of reference are of somewhat different length, viz. (a) to (#)
2380" and (c) to (d) 2066", the variations are, for the purpose of this comparison,
taken proportionally for 1000" in each direction.
TABLE XIII.
Comparison of the measures of the two diagonals
approximately at Right Angles.
Variation in 1000" from an Adopted Mean.
Date,
1886.
Variation
in measxire
of a to b.
Variation
in measure
of c to d.
Date,
1886.
Variation
in measure
of a to 6.
Variation
in measure
of c to d.
Date,
1886.
Variation
in measure
of a to b.
Variation
in measure
of c to d.
H
H
H
H
it
n
May a8
-j- 0.116
Aug. 20
-OS3
0.019
Sept. 1 6
+ 0.326
-f 0.160
3
+ -135
O.I7I
24
+ -I9 1
+ .142
17
.220
- .179
June i
~ -175
- -273
26
+ -291
+ .415
18
.172
.262
4
- .126
+ .180
28
+ -095
-1/9
20
+ .240
+ .184
8
+ .406
+ .223
29
- .167
.207
22
.122
- .292
*S
- -179
"I- -ISS
30
+ -041
- -038
27
- -183
- .281
16
.102
- -3IS
31
+ -183
+ -l6 9
29
+ .236
+ -157
23
+ -372
.220
Sept. 7
- -045
+ -238
30
-f .IO2
- .176
24
.312
- -SSI
10
-f .200
+ -042
Oct. 2
-003
4- -070
28
- .106
.046
ii
-154
.080
6
+ .029
+ -109
3
+ . 2 9S
.296
3
- .246
-013
13
.017
-013
July i
+ -MS
+ .316
J 5
- .272
.161
21
.046
+ -004
Comparison of the Diagonal Measures.
39
Date,
1886.
Variation
in measure
of a to 6.
Variation
in measure
of c to d.
Date,
1887.
Variation
in measure
of a to b.
Variation
in measure
of c to d.
Date,
1887.
Variation
in measure
of a to b.
Variation
in measure
of c to d.
Oct. 22
4- 0.094
it
4- 0.058
Jan. 5
0.682
it
0.592
Apr. 1 6
n
4- 0.558
4-0.156
Nov. 3
4 .010
-f- -044
8
- -424
- -312
19
- -274
+ .016
5
.061
- .148
10
4- .101
4- .092
20
+ -323
4- -449
16
- -177
.004
12
- .680
.542
25
.M4
-047
17
+ -031
.035
20
-553
-509
26
.048
+ -035
18
.127
-i55
25
4- .IH
4 .136
29
.Oil
4- -061
23
-225
-025
31
-492
-398
30
4- .004
4 .011
29
4 .016
.002
Feb. 5
4- -212
4- -312
May 5
.222
.227
Dec. i
+ -59
4- -063
8
-37'
.442
7
-134
.181
2
- -047
+ .003
17
-369
.302
9
-038
.040
4
.170
4- -063
2 5
4- .120
4 .066
10
.202
-273
7
.196
- .148
26
.210
- -'50
13
.401
- .336
9
.199
.052
2 7
+ -436
+ -303
H
.372
- .196
'4
- .476
-398
Mar. 12
4- .021
4 .118
16
- .360
.031
16
.570
.198
16
.269
- .256
18
.205
.186
24
- .508
.136
23
- -093
4 -123
20
- .I 9 8
4- .079
27
4- .184
+ -'55
26
4- -on
4- .109
Apr. 2
+ -205
4- -17
31
4 .102
4- -15
The inspection of the Table suggests, I think, that the principal cause of
the variations in question lies not so much in accidental or local variations of
the film as in actual variations in the focal length of the mirror. This
suggestion seems to me to be borne out by the general prevalence of the same
sign being attached to the variations on the same night.
Having premised thus much, I proceed to give the following sets of Tables
for the determination of the parallax of the two components with regard to
the two comparison stars, and these Tables will not require any further
comment.
The expressions for the computation of the parallactic factors with regard
to these two stars are for
D.M. + 37, No. 41 75-
61 1 Cvgm .#[9.92281] COS (O 121 29') 77.
61 2 Cygni. R [9.92247] cos (O - 1 3O 23') TT.
D.M. 4-38, No. 4348.
61 1 Cygni. It [9-9376] cos (0 292 46') TT.
61 2 Cygni. R [9.93539] C <> S (O -^93 5 6/ ) 7r -
Measures of the Diagonal Distance (c) to (d)
TABLE XIV.
Measures of the distance of Star (c) from Star (d), for the determina-
tion, at the times of exposure, of the correction to their
measured distances from, 61j and 61 2 Cygni.
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance
of c to d
in Arc.
Average
Deviation
from the
Mean.
Refraction.
Aberration.
Corrected
Distance
of c to d.
Difference
from
Assumed
Mean.
d. h.
tt
H
//
//
//
//
I
May 30 11.7
2065.420
-305
+ 0.967
+ O.I26
2066.513
0-353
2
June I 11.7
6 S-779
.211
.819
.126
66.724
- .564
3
4 11.8
64.898
243
.766
.124
65-788
+ -372
4
8 11.9
64-855
.092
.722
123
65.700
+ .460
S
15 n. 2
64.967
.136
753
.119
65-839
+ -321
6
16 11.7
2065.990
0.274
+ 0.701
+ 0.119
2066.810
0.650
7
23 11.6
65-837
.381
665
113
66.6!5
0-455
8
24 xi.6
66.579
"5
.669
.III
67-359
+ 1.199
9
28 12.0
65-514
...
.635
.107
66.256
+ 0.096
10
30 11.4
66.014
.144
-653
.105
66.772
+ 0.612
ii
July I 11.3
2064.753
0.202
+ 0.650
+ 0.104
2065.507
+ 0.653
12
Aug. 20 1 1. 1
65-573
.150
.611
.Ol6
66.200
.040
13
24 9.8
65.247
.309
.612
.008
65-867
+ .293
'4
26 9.3
64.685
37'
.615
+ -003
65-303
+ .857
15
28 9.5
65.918
.244
.613
.OOI
66.530
.370
16
29 9-5
2065.978
0.262
+ 0.612
0.003
2066.587
0.427
'7
30 8.9
65.627
.203
.616
.005
66.238
- .078
18
31 8-8
65.202
.135
.615
.007
65.810
+ .350
J 9
Sept. 7 8.6
65.077
.129
.614
.022
65.669
+ .491
20
10 8.4
65.482
322
.614
.023
66.073
+ .087
21
ii 8.5
2065.743
0.274
+ 0.613
0.031
2066.325
0.165
22
13 8.4
65.609
.289
.612
035
66.186
.026
23
15 8.1
65.918
.096
.614
039
66.493
-333
24
16 9.8
65-253
H5
.616
.040
65.829
+ -331
2 5
17 8.1
65.958
.273
.613
.042
66.529
-369
26
18 8.0
2066.134
0.304
+ 0.613
0.045
2066.702
0.542
27
20 9.0
65.218
135
.611
.049
65.780
+ -380
28
22 9.4
66.201
.211
.616
053
66.764
.604
29
27 10.2
66.166
'93
.638
.063
66.741
- .581
30
29 8.6
65.290
.244
.612
.066
65.836
+ -324
3
30 8.4
2065.980
0.309
+ 0.611
0.068
2066.523
0.363
32
Oct. 2 8.2
65.477
.242
.611
.072
66.016
+ -144
33
6 Q.I
65.389
.097
.624
.079
65-934
+ .226
34
13 10.1
65-583
.149
.693
.090
66.186
.026
35
21 7-5
65.638
.216
.616
.IO2
66.152
+ .008
for the Correction of the Scale.
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance
of f to d
in Arc.
Average
Deviation
from the
Mean.
Refraction.
Aberration.
Corrected
Distance
of c to d.
Difference
from
Assumed
Mean.
d. h.
//
//
n
//
n
H
36
Oct. 22 7.5
2065.526
0.242
+ 0.617
0.103
2066.040
+ o. 120
37
Nov. 3 6.6
65-57
.315
.616
.116
66.070
+ .090
38
5 8-8
65.891
.250
.692
.118
66.465
- -305
39
16 7.5
65.630
.072
.664
.125
66.169
.009
40
17 8.3
65-635
I 3 l
.722
,I2 5
66.232
- .072
4i
18 8.6
2065.846
o.i93
+ 0-759
0.125
2066.480
0.320
42
23 8.6
65-535
-250
-803
.126
66.212
-052
43
29 6.9
65.616
.183
.674
.126
66.164
.004
44
Dec. i 7.3
65.447
.191
.709
.126
66.030
+ -130
45
2 6.8
65.604
.079
.676
.126
66.154
+ .006
46
4 6.4
2065.49!
0-363
-f 0.665
0.126
2066.030
+ 0.130
47
7 6.3
65-9*7
-324
-673
.125
66.465
-SOS
48
9 7-2
65.631
.167
.760
.123
66.268
.108
49
14 6.2
66.412
.'53
.691
.I2O
66.983
- -82.3
5
16 6.2
65.979
.209
.710
.119
66.570
- .410
Si
24 6.2
2065.797
0.183
+ 0-757
O.I 12
2066.442
0.282
52
87 Jan. 5 6.9
66.396
.274
1.085
.097
67.384
1.224
53
8 6.4
65.944
.246
o-953
.092
66.805
0.645
54
10 6.7
64.908
309
1.150
.089
65.969
+ 0.191
55
12 6.3
66.330
362
1-033
.086
67-277
1.117
56
2O 6.4
2065.960
0.244
+ 1-324
0.072
2067.212
1.052
57
25 6.3
64523
J 73
1.417
.062
65.878
+ 0.282
58
31 6.5
65.046
.209
1.987
.050
66.983
0.823
59
Feb. 5 6.0
63.810
132
i-747
.042
65-5 I 5
+ 0.645
60
8 5-9
65- J 93
347
i-9!3
033
67.073
0.913
61
17 17.1
2065.461
0.262
+ 1-335
O.OI2
2066.784
0.624
62
25 '7-4
65.051
385
0.969
+ 0.004
66.024
+ -136
63
26 16.9
65-329
.153
I-I33
.007
66.469
-309
64
27 16.9
64.349
.174
i- T 75
.009
65-533
+ -627
65
Mar. 12 16.1
64.791
.209
1.089
037
65-9 T 7
+ -243
66
16 15.7
2065.517
0.342
+ 1-127
+ 0.045
2066.689
0.529
67
23 16.4
65.061
173
0.786
59
65.906
+ -254
68
27 14.8
64-532
.207
1.240
.067
65-839
+ -321
69
Apr. 2 15.3
64.849
.292
0.881
.078
65.808
+ -35*
70
16 14.4
64.855
.036
0.884
099
65.838
+ -322
7i
19 14.6
2065.238
0.069
+ 0.786
+ 0.103
2066.127
+ 0.033
7 2
20 15.0
64-397
H3
0.732
.104
65-233
+ -9-Z7
73
25 13-4
65.142
.272
1.005
.no
66.257
-097
74
26 14.2
65.191
-135
0.786
.11 1
66.088
+ -0/2
75
2 9 13.8
65-105
350
0.814
.114
66.033
+ .127
42
Relative Parallax of 6l l Cygni and Star (c).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887.
Measured
Distance
of c tod
in Arc.
Average
Deviation
from the
Mean.
Refraction.
Aberration.
Corrected
Distance
of c to d.
Difference
from
Assumed
Mean.
d. h.
n
H
//
//
//
n
7 6
Apr. 30 13.8
2065.209
O.207
+ 0.814
+ 0.115
2066.138
+ O.O22
77
May 5 13.7
6 5-747
.160
0.763
.II 9
66.629
- -469
78
7 !3-o
65-53I
-093
0.881
.121
66-533
-373
79
9 I2 -4
65.078
.282
1.042
.122
66.242
- .082
80
10 12.8
65-715
-H5
0.887
.122
66.724
- -564
81
J3 13-0
2065.937
0.322
+ 0.793
+ 0.124
2066.854
0.694
82
14 12.8
65.605
.144
.836
.124
66.565
.405
83
16 128
65.291
.274
.809
125
66.225
.065
84
18 12.8
65-635
.365
.784
125
66.544
- .384
85
20 I3.I
65.148
-253
.722
.126
65.996
+ -164
86
26 13.2
2065.125
0.382
+ 0.683
+ 0.127
2065.935
+ 0.225
87
31 1 1. 8
64.919
.179
.807
125
65.851
+ -309
TABLE XV.
Concluded measures of Q\ l Cygni from the comparison Star (c).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance of
Star (c) to
61 1 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (<) from
61i Cygni.
Average
Devi-
ation.
d. h.
n
//
//
//
H
/,
I
May 30 11.7
1115.467
+ 0-593
-1-0.072
+ i-9 10
0.191
1117.851
0.203
2
June I 11.7
I5'839
.491
.0/2
1.895
-305
17.992
'35
3
4 11. 8
15-427
451
.071
1.866
+ .201
18.016
139
4
8 11.9
15-431
.420
.070
1.830
+ -249
18.000
.296
5
15 n. 2
!5-564
-444
.068
1.768
+ -74
18.018
.087
6
16 11.7
1116.310
+ 0-399
+ 0.068
+ 1.760
0.352
1118.185
0.243
7
23 11.6
16.345
379
.064
1.698
- .246
18.240
H3
8
24 1 1. 6
16.584
.380
.064
1.689
-649
18.068
295
9
30 11.4
16.349
.368
.061
1.636
-331
18.083
.187
10
July i 1 1. 3
15.848
370
059
1.627
+ -353
18.257
.220
ii
Aug. 20 1 1.1
1116.588
+ 0.332
+ 0.009
+ 1.181
O.O22
IIl8.o88
0.164
12
24 9.8
16.383
334
+ .004
1.150
+ -'59
18.030
.244
'3
26 9.3
16.158
337
-|- .002
1.132
+ -464
18.093
3 1 '
14
28 9.5
16.820
334
.000
1.114
.200
18.068
.246
Iji
2 9 9-5
16.824
335 - 002
1.105
.231
18.031
.087
Concluded Distances of 61 x Cygni from Star (c). 43
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance of
Star (c) to
6l! Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (c) from
61i Cygni.
Average
Devi-
ation .
d. h.
//
//
/,
//
H
n
//
16
Aug. 30 8.9
1116.645
+ 0.338
0.003
+ 1-097
O.O42
1118.035
0.162
l l
31 8.8
16.612
338
.004
1.088
+ -ISP
18.223
.207
18
Sept. 7 8.6
*6.373
.336
.013
1.026
+ .266
17.988
.138
19
10 8.4
16.541
.336
.013
I.OOO
+ -47
17.911
.I 9 2
20
n 8.5
16.971
335
.017
0.991
.089
18.191
255
21
13 8.4
1117.023
+ 0.335
O.02O
+ 0.973
0.014
1118.297
0.203
22
15 8.1
16.918
-336
.022
956
.180
18.004
.172
23
16 9.8
16.803
332
.023
.946
+ -179
18.237
154
24
17 8.1
17.164
-335
.024
938
.200
18.213
.086
25
18 8.0
17.064
334
.026
.929
-293
18.008
305
26
20 9.0
1116.470
+ Q-332
0.028
+ 0.909
-f 0.206
1117.889
0.260
27
22 9.4
17.081
332
030
893
- -327
17.949
.144
28
27 10.2
17.167
339
.036'
.848
-3H
18.004
.205
2 9
29 8.6
16.789
332
038
.831
+ -175
18.089
133
3
30 8.4
17.106
332
039
.822
- .196
18.025
.279
31
Oct. 2 8.2
1116.619
+ 0.332
O.O4I
+ 0.804
+ 0.078
1117.792
0.227
32
6 9.1
16.787
335
045
.770
+ .122
17.969
145
33
13 10.1
16.835
-361
.051
.707
.014
17.838
.208
34
21 7-5
16.831
-332
.058
.636
+ .004
'7-745
.162
35
22 7.5
16.768
-332
-059
.627
+ -065
17-733
.156
36
Nov. 3 6.6
1116.847
+ 0.332
0.066
+ 0.522
+ 0.049
1117.684
0.097
37
5 8-8
17.013
.361
.067
503
- -165
17.645
.222
38
16 7.5
16.962
349
.071
.406
.005
17.641
.265
39
17 8.3
16.970
372
.071
-398
-39
17.630
-J43
40
18 8.6
17.047
.388
.071
.388
I 73
17-579
.182
4i
23 8.6
1116.982
+ 0.409
O.O72
+ 0.344
0.028
iti7-635
0.229
42
29 6.9
16.926
354
.072
.292
.002
17.498
-073
43
Dec. i 7.3
16.809
.368
.072
.274
+ -070
17.449
'35
44
2 6.8
16.955
354
.072
.265
+ -003
I7-505
.208
45
4 6 -4
16.941
349
.071
.248
+ -070
17-537
.148
46
7 6.3
1117.215
+ 0.353
0.071
+ 0.239
0.165
1117.571
0.206
47
9 7-2
16.794
.386
.O7O
.203
- .058
I7-255
.083
48
14 6.2
17-377
.361
.069
159
-445
I7-383
.132
49
16 6.2
I7-H5
-367
.068
.142
.221
17-365
.197
50
24 6.2
17.215
.386
.064
.074
- -153
17.458
.250
5 1
87 Jan. 5 6.9
1117.706
+ 0.522
^0.055
0.038
o.66a
IH7-473
0.206
52
8 6.4
I7-350
474
053
.064
-349
17.358
-313
53
10 6.7
16.911
545
.051
.082
+ -103
17.426
.087
54
12 6.3
17.707
.492
.049
.100
- .604
17.446
.142
55
20 6.4
I7-386
.621
.C 4 I
.170
-569
17.227
205
44
Concluded Distances of 61 x Cygni from Star (c).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887.
Measured
Distance of
Star (c) to
61i Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Htar (c) from
61i Cygni.
Av rage
Devi-
ation.
d. h.
//
it
//
it
//
//
n
56
Jan. 25 6.3
1116.805
+ 0.676
0.036
0.215
+ 0.153
III7-383
0.262
57
31 6.5
17.301
938
.029
.268
-445
17-497
139
58
Feb. 5 6.0
16.531
.821
.024
303
+ -349
'7-374
.240
59
8 5-9
I7-436
9 J 3
.019
339
.494
17-497
135
60
17 17.1
17.426
.847
.007
423
- -338
1 7-505
.207
61
25 17-4
1117.266
+ o-593
+ O.OO2
0-493
+ 0.074
1117.442
O.lSo
62
26 16.9
17-453
705
.004
.502
- .167
1 7-493
.211
63
27 16.9
I7.00 5
734
.005
5"
+ -339
I7-572
133
64
Mar. 12 16.1
17.494
-677
.021
.625
+ .131
17.698
.292
6 5
16 15.7
17.760
705
.026
.660
.286
17-545
.2 4 1
66
23 6. 4
1117.706
+ 0.467
+ 0.034
0.723
+ 0.137
1117.621
0.262
67
27 14.8
17.300
.780
.038
758
+ -174
17-534
.125
68
Apr. 2 15.3
17.670
533
.044
.811
+ -190
17.626
.270
69
1 6 14.4
I7.86 7
535
057
935
+ -174
17.698
139
70
19 14.6
18.308
.472
058
.961
+ .018
I7-895
244
7"
20 15.0
III7.6l8
+ 0.432
+ 0.059
0.970
+ 0.502
1117.641
O.260
72
25 13-4
18.046
.621
.063
1.014
- -052
17.666
139
73
26 14.2
18.172
.467
-063
1.023
+ -039
17.718
.204
74
29 13-8
18.109
.502
.065
1.049
+ .069
17.696
-08 3
75
30 13-8
18.427
.486
06 5
1.058
+ .012
'7-932
.III
7 6
May 5 13.7
1118.637
+ 0.460
+ 0.068
1.103
0.254
1117.808
0.293
77
7 J 3-o
18.640
533
.069
1. 120
.202
17.920
H5
78
9 12.4
18.180
.648
.069
I.I38
- .044
I7-7I5
.207
79
10 12.8
18.666
-538
.070
I.I 4 7
^05
17.822
.132
80
J 3 i3-o
18.691
477
.O7O
I-I73
-375
17.690
.I 9
81
14 12.8
1118.594
+ 0.502
+ 0.071
I.I82
0.219
1117.766
0.222
82
16 12.8
18.472
.481
.071
1.200
- -035
17.789
-147
83
18 12.8
18.603
457
.071
I.2I8
.208
I7-705
.I6 9
84
20 13.1
18.548
.420
.072
1.236
+ .089
1 7-893
257
85
26 13.2
18.606
396
.072
1.289
+ .122
17.907
08 3
86
31 u.8
"18.535
+ 0.481
+ 0.071
1-332
+ 0.167
1117.922
0.2T5
Relative Parallax of Q1 1 Cygni and Star (e).
TABLE XVI.
Equations of Condition formed from the measures
of 61 ! Cygni and Star (c).
No.
Date,
1886.
Equations of Condition.
Residual.
d. h.
//
H
I
May 30 11.7
+ O.I5I = X +0.5177 7T 0.5908 dfJL
+ 0.227
2
June i 11.7
+ .292 - x + .5401 .5853
+ -095
3
4 u.8
+ .316 = x + .5726 .5771
+ .085
4
8 11.9
+ .300 = x + -6134 .5660
+ .H7
5
15 ii. 2
+ .318 = x + .6776 ^469
4- -125
6
16 11.7
+ 0.485 = x +0.6864 0.5442
0.038
7
23 11.6
+ .540 = x + .7404 .5250
~ -073
8
24 ii. 6
+ .368 = x + .7474 .5223
.102
9
30 11.4
+ .383 = x + .7841 .5059
.101
10
July I 11.3
+ -557 = + .7894 -5031
.072
ii
Aug. 20 1 1. 1
+ 0.388 = x +0.7601 0.3653
+ 0.063
12
24 9.8
+ .330 = x + .7332 .3556
+ .108
*J
26 9.3
+ -393 = * + -7!84 -3501
+ .038
J 4
28 9.5
+ .368 = x + .7026 .3445
f -55
'5
2 9 9-5
+ .331 = x + .6945 .3418
+ .088
16
30 8.9
+ 0.335 = * +0.6866 0.3392
+ 0.081
17
31 8.8
+ .523 = x + .6780 .3364
.112
18
Sept. 7 8.6
+ .288 = x + .6128 .3174
+ .091
19
10 8.4
+ .211 = X + .5819 .3091
+ -'53
20
ii 8.5
+ .491 = x + .5716 .3064
-132
21
13 8.4
+ 0.597 = x +0.5500 0.3009
0.248
22
15 8-1
+ .304 = x + .5279 .2955
+ -034
23
16 9.8
+ -537 = * + -5!59 -2925
- -205
2 4
17 8.1
+ .513 = a? + .5041 .2900
- .187
25
18 8.0
+ .308 = x + .4933 .2872
+ .014
26
20 9.0
+ 0.189 = x +0.4686 0.2815
+ O.I2I
27
22 9.4
+ .249 = x + .4450 .2761
+ .049
28
27 10.2
+ .304 = x + .3817 .2623
.036
29
29 8.6
+ .389 = x + .3562 .2570
-133
3
30 8.4
+ .325 = x + .3430 .2543
-075
3i
Oct. 2 8.2
+ 0.092 = x +0.3165 0.2488
+ 0.145
32
6 9.1
+ .269 = x + .2623 .2380
- -OSS
33
13 10. i
+ .138 = x + .1631 .2185
+ .026
34
21 7-5
+ .045 - x + .0501 .1969
+ .065
35
' ? 2 7-5
+ .033 = x + .0355 .1942
+ .070
46 Equations of Condition : Gl l Cygni and Star (c).
No.
Date,
1886-7.
Equations of Condition.
Residual.
d. h.
i>
/;
36
Nov. 3 6.6
0.016 = x 0.1368* 0.1615 dp.
+ 0.038
37
5 8.8
-055 = x .1668 .1557
+ .062
38
16 7.5
.059 = x .3180 .1257
.006
39
17 8.3
.070 = x .3317 .1229
.001
40
18 8.6
.121 = X .345O .I2OI
+ -043
4i
23 8.6
0.065 = x 0.4094 0.1064
0.043
42
29 6.9
.202 = x .4819 .0904
+ .060
43
Dec. i 7.3
.251 = x .5054 .0847
+ .097
44
2 6.8
.195 = x .5162 .0820
+ -035
45
4 6.4
.163 = x .5384 .0766
.006
46
7 6.3
0.129 = * 0-5704 0.0739
0.056
47
9 7-2
.445 = x .5945 .0628
+ -250
48
14 6.2
-317 = x -6393 -0492
+ .097
49
16 6.2
-335 = * -6570 .0438
+ .108
5
24 6.2
.242 = x .7203 .0219
- .017
5i
87 Jan. 5 6.9
0.227 = * 0.7881 +0.0118
0.069
5*
8 6.4
.342 = x .7995 + .0198
+ -043
53
10 6.7
.274 = x .8059 -1- .0253
.031
54
12 6.3
.254 = x .8113 + .0308
- -054
55
20 6.4
.473 = x .8229 -f- .0527
+ -157
56
25 6.3
0.317 = x 0.8218 +0.0664
O.OOI
57
31 6.5
.203 = x .8120 + .0829
-"3
58
Feb. 5 6.0
.326 = x .7971 + .0938
-f -015
59
8 5-9
.203 = x .7851 + .1048
.104
60
17 17.1
.195 = x .7335 + .1306
- -093
61
25 '7-4
0.258 = x 0.6740 +0.1526
+ 0.007
62
26 16.9
.207 = x .6658 + .1553
-055
63
27 16.9
.128 = x .6572 + .1581
-130
64
Mar. 12 16.1
.002 = X .5292 + .1935
.204
65
16 15.7
.155 = x .4838 + .2044
-033
66
23 16.4
0.079 = x 0.3989 +0.2236
0.075
67
27 14.8
.166 = x .3483 + .2344
+ .033
68
Apr. 2 15.3
.074 = x .2685 + .2509
.026
69
16 14.4
.002 = X .0737 + .2891
- .017
70
19 14.6
+ .195 = x .0308 + .2973
.196
7 1
20 15.0
0.959 = x 0.0161 +0.3000
+ 0.064
72
25 13-4
.034 = x + .0543 + .3137
+ .068
73
26 14.2
+ .018 = x + .0693 + .3165
+ -023
74
29 13-8
.004 = x + .1115 + .3246
+ -055
75
30 13-8
+ .232 = x + .1256 + .3272
.168
Concluded Parallax : 61 X Cygni and Star (c).
47
No.
Date,
1887.
Equations of Condition.
Residual.
d. h.
//
M
7 6
May 5 13.7
+ 0.108 = x + O.I9587T + 0.3410 dfJL
0.015
77
7 i3-o
+ .220 = X + .2231 + .3465
.116
78
9 12.4
+ .015 = x + .2503 + .3519
+ .100
79
10 12.8
+ .122 = a? + .2639 + .3546
.001
80
13 i3-o
.010 = x + .3046 + .3628
+ -149
81
14 12.8
+ 0.066 = a? +0.3177 +0.3655
+ 0.078
82
16 12.8
+ .089 = x + .3439 + .3710
+ .066
83
18 12.8
+ .005 = x + .3699 + .3765
+ .165
84
20 I3.I
+ .193 = x + .3956 + .3820
- .017
85
26 13.2
+ .207 = x + .4693 + .3984
+ .005
86
31 n.8
+ 0.222 = X +0.5267 +0.4120
+ 0.017
The formation of the normal equation gives the following result :
+ 7.3000= + 86.ocoo# 5.6824^ + 3.121571
- 4.8285= - 5.6824 +7-^594 ~ 5-6322
+ 13.7118= + 3.1215 5.6322 +24.0247.
The values of the unknowns are
H
x = +0.0581
dfji = 0.1518
TT = +0.4448.
The probable error of TTIS +o".O2i2, while the probable error of a complete
determination of the distance between this star and 61 x Cygni is +o".iO2.
RELATIVE PARALLAX OF 61 2 CYGNI AND STAR (C).
TABLE XVII.
Concluded measures of 61 2 Cygni from the comparison Star (c).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance of
Star (r) to
61 2 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (c) from
61 2 Cygni.
Average
Devi-
ation.
d. h.
n
//
//
//
n
//
ii
I
May 30 11.7
1105.150
+ 0-574
+ 0.068
+ 1.962
0.189
1107.565
0.283
2
June i 11.7
.5-613
477
.067
1-945
.302
7.800
.296
3
4 1 1. 8
5.118
44
.067
1.916
+ .199
7-740
049
4
8 11.9
S-I?^
.411
.066
i. 880
+ -247
7.782
.176
,S
15 11.2
5-217
433
.064
1.817
+ ^72
7-703
.091
48
Relative Parallax of 61 2 Cygni and Star (c).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance of
Star (c) to
61 2 Cygni
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (c) from
61a Cygni.
Average
Devi-
ation.
d. h.
ii
ii
//
n
H
//
H
6
June 1 6 11.7
1106.045
+ 0.391
+ 0.064
+ 1. 808
-0.348
1107.960
0.207
7
23 1 1. 6
6.028
372
.060
1-744
-244
7.960
.170
8
24 n.6
6.204
-373
.060
J-735
~ .637
7.735
.183
9
30 11.4
5-979
362
.056
1.681
- .328
7-750
.242
10
July I 11.3
5.612
-363
.056
1.671
+ "350
8.052
.270
ii
Aug. 20 1 1. 1
1106.324
+ 0.329
+ 0.009
+ 1.214
0.021
1107.855
0.1.35
12
24 9.8
6.161
331
.004
1.181
+ I 57
7.834
.206
1 3
26 9.3
5-945
333
+ .002
1.164
+ -459
7.903
.209
H
28 9.5
6.517
331
.OOO
I-I45
- .198
7-795
-139
15
29 9-5
6.476
33
.002
I-I35
.229
7.711
.224
16
30 8.9
1 106.370
+ -334
0.003
+ 1.125
0.042
1107.784
O.242
'7
31 88
6.221
334
.00 4
1.117
+ .188
7.856
265
18
Sept. 7 8.6
6.229
332
.OI2
1-055
+ .263
7-867
.129
19
10 8.4
6-443
332
.012
1.027
+ .047
7-837
-M3
20
ii 8.5
6.694
332
.Ol6
i.oiS
.088
7.940
.207
21
13 8.4
1106.461
-ho.33i
0.019
+ I. OOO
0.014
1107.759
O.l62
22
15 8.1
6.672
332
.O2I
0.982
- .178
7.787
*93
23
16 9.8
6-344
330
.022
972
+ -177
7.801
237
2 4
17 8.1
6.669
332
.023
.963
.198
7-743
.182
25
18 8.0
6.887
33J
.024
954
- .291
7.857
'43
26
20 9.0
1106.182
+ 0.329
O.026
+ 0.935
+ 0.204
1 107.624
0.098
27
22 9.4
6.724
330
.028
.917
-324
7.619
-244
28
27 10.2
6.947
337
034
.87.
-3"
7.810
39
29
29 8.6
6-4'3
329
035
-854
+ -174
7-735
.182
30
30 8.4
6.835
-329
037
-845
- -195
7-777
.267
31
Oct. 2 8.2
1106.311
+ 0.329
0.038
+ 0.827
+ 0.077
1107.506
0.154
32
6 9.1
6.532
333
.042
.791
+ .121
7-735
.183
33
13 10.1
6.450
360
.048
.726
.014
7-474
.129
34
21 7-5
6-495
330
055
-655
+ .004
7-4 2 9
244
35
22 7-5
6-5*5
330
055
-645
+ .06 4
7-499
.192
36
Nov. 3 6.6
1 106.608
+ 0.330
O.O62
+ 0-537
+ 0.048
1107.461
0.264
37
5 8.8
6-749
.361
063
.518
- -I6 3
7.402
-'53
38
16 7-5
6.722
348
.067
.418
.005
7.416
.202
39
17 8.3
6.751
372
.06 7
.409
.039
7.426
.183
40
18 8.6
6.825
.388
.067
-399
- .172
7-373
.074
4i
23 8.6
1106.707
+ 0.412
0.068
+ 0-353
O.O28
1107.376
O.I26
42
29 6.9
6.675
351
.068
.301
.002
7-257
.305
43
Dec. i 7.3
6.607
367
.068
.282
+ .070
7.258
093
44
2 6.8
6.622
354
.068
273
+ .003
7.184
.222
45
4 6.4
6-599
-348
.06 7
-255
+ .070
7.205
.247
Concluded Distances of 61 2 Cygni from Star (c). 49
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance of
Star (c) to
612 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (c) from
612 Cygni.
Average
Devi-
ation.
d. h.
//
//
n
n
n
H
H
46
Dec. 7 6.3
1106.83!
+ 0.352
0.067
+ 0.246
0.163
II07.I99
0.173
47
9 7.2
6.644
.388
.066
.209
- .058
7.II7
139
48
14 6.2
7.269
.360
.064
.164
- -441
7.288
.026
49
16 6.2
6.936
366
.064
.146
.220
7.l64
.244
5
24 6.2
6.974
388
.060
073
-I5 1
7.224
.180
Si
87 Jan. 5 6.9
1107.398
+ 0-534
0.052
0.039
-0.656
II07.185
0.045
52
8 6.4
7-37
478
049
.066
-34<5
7-054
.262
53
10 6.7
6.680
550
.048
.084
+ .102
7.1 9 9
.312
54
12 6.3
7-374
.498
.046
.102
-599
7- I2 5
.242
55
20 6.4
7.089
.633
039
J 75
- .564
6-944
.183
56
25 6 -3
1106.608
+ 0.688
0.033
0.221
+ 0.151
1107.193
0.127
57
31 6.5
7.010
.941
.027
.276
- -441
7.207
.205
58
Feb. 5 6.0
6.251
.836
.022
.312
+ .346
7-099
.290
59
8 5.9
7.161
.921
.018
349
- .489
7.226
.226
60
17 17.1
7.192
.824
.006
435
-334
7.241
143
61
25 17-4
1107.160
-1-0.574
+ 0.003
0.507
+ 0.073
1107.302
O.l62
62
26 16.9
7.191
.685
.004
.516
.166
7.198
.191
63
27 16.9
6.693
7*3
.005
.526
+ -336
7.221
.083
64
Mar. 12 1 6. i
7- 2 34
655
.O2O
643
+ -130
7-396
245
65
16 15.7
7.625
.685
.02 4
.680
.284
7-370
.127
66
23 16.4
1107.603
+ 0.455
+ 0.032
0-743
+ 0.136
1107.483
O.2O9
67
27 14.8
7.024
.842
.036
.778
+ .172
7.296
.136
68
Apr. 2 15.3
7.502
.518
.042
834
+ .189
7-4 T 7
.172
69
16 14.4
7.699
5*7
053
.961
+ -173
7.481
.240
7o
19 14.6
7-875
459
055
.988
+ .018
7.419
.099
7i
20 15.0
1107.641
+ 0.422
+ 0.056
0.997
+ 0.497
1107.619
0.183
72
25 13-4
7.940
.600
.059
1.042
- -052
7-55
244
73
26 14.2
7-947
455
.060
1.052
+ -039
7-449
.127
74
29 13-8
7-834
47
.061
1.078
+ .068
7-372
.262
75
3 13-8
8.089
.472
.062
1.087
+ .012
7-548
.240
76
May 5 13.7
1108.527
+ 0.449
+ 0-064
I-I33
0.251
1107.656
0.139
77
7 J 3-o
8-373
517
.065
1.151
.200
7.604
.166
78
9 I2 -4
8.089
.626
06 5
1.169
-044
7-5 6 7
.227
79
10 12.8
8.412
522
.065
1.178
-302
7-519
193
80
13 13-0
8.708
4 6 5
.066
1.205
-372
7.662
.085
81
14 12.8
1108.447
+ 0.487
+ 0.067
1.214
0.217
1107.570
0.056
82
16 12.8
8.361
.468
.067
!-233
-035
7.626
.219
83
18 12.8
8.716
451
.06 7
1.251
.206
7-777
.138
84
20 13.1
8-443
.411
.068
1.269
+ .088
7-74i
.250
85
26 13.2
8.410
.386
.068
!-323
+ .121
7.662
.203
86
31 u.8
1108.303
+ 0.442
+ 0.067
1.369
+ 0.166
1107.609
0.097
50
Relative Parallax of 61 2 Cygni and Star (c).
TABLE XVIII.
Equations of Condition formed from the measures
of 61 2 Cygni and Star (c).
No.
Date,
1886.
Equations of Condition.
Residual.
d. h.
//
I
May 30 11.7
+ 0.065 = # -f 0-5369 7T 0.5908 dfj.
+ 0.203
2
June i 11.7
+ .300 = x + .5590 .5853
+ .008
3
4 1 1. 8
+ .240 = x + .5910 .5771
+ -071
4
8 11.9
+ .282 = x + .6310 .5660
+ .052
5
15 ii. 2
+ .203 = x + .6935 .5469
+ .160
6
16 11.7
+ 0.460 = x +0.7029 0-5442
0.093
7
23 1 1.6
+ .460 = x + .7544 .5250
- -073
8
24 1 1. 6
+ -235 = x + .7610 .5223
+ .'55
9
30 11.4
+ .250 = x + .7860 .5059
+ .149
10
July i 11.3
+ .552 = X + -8009 .5031
.147
ii
Aug. 20 i i.i
+ 0.355 = * +0.7544 -0.3653
+ 0.018
12
24 9.8
+ -334 = x + .7264 .3556
+ -015
13
26 9.3
+ .403 = x + .7105 .3501
-053
4
28 9.5
+ .295 = x + .6941 .3445
+ .048
15
2 9 9-5
+ .211 = x + .6857 -34'8
+ .128
16
30 8.9
+ 0.284 - x + 0.6775 0.3392
+ 0.052
17
31 8.8
+ .356 = x + .6687 - .3364
.024
18
Sept. 7 8.6
+ .367 = x + .6010 - .3174
.066
J 9
10 8.4
+ -337 = * + .5692 .3091
- .051
20
ii 8.5
+ .440 = x + .5586 .3064
.159
21
13 8.4
+ 0.259 = x +0.5365 0.3009
+ O.OI2
22
15 8.1
+ .287 = x + .5139 .2955
.026
23
16 9.8
+ .301 = x + .5016 .2925
.046
2 4
17 8.1
+ .243 = x + .4895 .2900
+ .006
25
18 8.0
+ -357 = * + -47^5 - -2872
.1 12
26
20 9.0
+ 0.124 = x +0.4531 0.2815
+ 0.109
27
22 9.4
+ .119 = x + .4288 .2761
+ -'03
28
27 IO.2
+ .310 = x + .3646 - .2623
- - TI 7
2 9
29 8.6
+ .235 - * + -3387 -2570
-054
30
30 8.4
+ .277 = x + .3255 .2543
.101
3"
Oct. 2 8.2
+ 0.006 = x +0.2981 0.2488
+ 0.167
32
6 9.1
+ .235 =: X + -2436 .2380
- .097
33
13 10. i
.026 = x + .1433 -2185
+ -119
34
21 7-5
.071 = x + .0294 .1969
+ ."3
35
22 7.5
.001 = x + .0148 -^942
+ -036
Equations of Condition: 61 2 Cycjni and Star (c). 51
No.
Date,
1886-7.
Equations of Condition.
Residual.
d. h.
//
//
36
Nov. 3 6.6
O.O39 = X 0.1580 7T O.l6l5 dp
O.OO2
37
5 8.8
.098 = x .1880 .1557
+ .042
38
16 7-5
.084 = x .3387 .1257
.040
39
17 8.3
.074 x .3522 .1229
.056
40
18 8.6
.127 = X .3654 .1201
.009
4 1
23 8.6
0.124 = x 0.4292 0.1064
0.041
42
29 6.9
.243 = x .5009 .0904
+ .046
43
Dec. i 7.3
.242 = x -5241 .0847
+ -034
44
2 6.8
.316 = x .5347 .0820
-f .103
45
4 6.4
.295 = x .5564 .0766
+ -073
46
7 6.3
0.301 = x 0.5879 0.0739
+ 0.064
47
9 7-2
.383 = x .6086 .0628
+ -136
48
14 6.2
.212 = X .6552 .0492
.052
49
16 6.2
.336 = a? .6724 .0438
+ .060
50
24 6.2
.276 = x .7335 .0219
.029
5i
87 Jan. 5 6.9
0.315 = x 0.7976 4-0-0118
O.O2I
52
8 6.4
.446 x .8079 + .0198
+ -105
53
10 6.7
.301 = x .8139 + - 02 53
-043
54
1 2 6.3
-375 = x -8184 + .0308
+ -029
55
20 6.4
.556 = x .8271 + .0527
+ .204
56
25 6.3
0.307 = x 0.8242 +0.0664
0.046
57
31 6.5
.293 = x .8121 -f- .0829
.056
58
Feb. 5 6.0
.401 - x .7954 + .0938
+ -059
59
8 5.9
.274 = x .7822 + .1048
.064
60
17 17.1
.259 = x .7273 + .1306
.058
61
25 17-4
0.198 = x 0.6649 -{-0.1526
0.094
62
26 16.9
.302 = x .6564 + .1553
+ -OH
63
27 16.9
.279 = x .6475 + .1581
.006
64
Mar. 12 16.1
.104 = x .5268 + .1935
.132
65
16 15.7
.130 = x .4690 + .2044
.082
66
23 164
0.017 = x 0.3823 4-0.2236
0.160
67
27 14.8
.204 = x .3308 + .2344
+ -048
68
Apr. 2 15.3
.083 = x .2498 + .2509
-039
69
16 14.4
.019 = x .0530 + .2891
-023
70
19 14.6
.081 = x .0098 + .2973
+ .048
7 1
20 15.0
-{-0.119 = x +0.0049 +0.3000
+ 0.102
72
25 J 3-4
+ .005 = x + .0757 + .3137
+ .018
73
26 14.2
.051 = x + .0907 + .3165
+ -070
74
29 13-8
.128 = x + .1330 + .3246
+ -164
75
30 13-8
+ .048 = x + .1471 + .3272
.006
52
Concluded Parallax : 61 2 Cygni and Star (c).
No.
Date,
1887.
Equations of Condition.
Residual.
d. h.
//
//
7 6
May 5 13.7
+ 0.156 x + 0.2I747T + 0.3410^
0.085
77
7 J3-o
+ .104 = x + .2445 + .3465
.022
78
9 12.4
+ .067 = x + .2717 -1- .3519
+ -027
79
10 12.8
H- .019 = x + .2853 + .3546
+ .080
80
13 i3-o
+ .162 = x + .3258 -f- .3628
.046
81
14 12.8
+ 0.070 = x +0.3389 +0.3655
+ 0.05 I
82
16 12.8
+ .126 = x + .3649 + .3710
+ .006
83
18 12.8
+ .277 = x + .3907 + .3765
.130
84
20 13.1
+ .241 = x + .4162 + .3820
- .088
85
26 13.2
+ .162 = x + .4891 + .3984
+ .O2O
86
3 ii.8
+ 0.109 = x +0.5456 +0.4120
+ 0.097
In this case the resulting- normal equation i
//
+ 2.678 = +86.0000^ 5.6824^+ 2.974671
- 3.1824= - 5- 68: *4 +7- 8 594 + 5-55*8
+ 11.4924=+ 2.9746 +5.5518 +25.3062.
The values of the unknowns are
//
x = + 0.0098
dp = 0.0969
TT = + 0.4320.
The probable error of TT is + 0".0190, and the probable error of one complete
determination of distance of this star from 6i 2 Cygni is +o".o88.
The Table containing the parallactic processes of this star with reference to
6 1 Cygni conclude, as in former cases, by exhibiting- the difference in the
measured distance for each night of the star (c) from each of the components
of 6 1 Cygni. The mean of the measures is 1 0^.247.
Test of the Accuracy of the Measures.
53
TABLE XIX.
Difference of the measured distances of Star (c)from
61j_ and 61 2 Cygni.
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
//
//
//
//
n
n
1
10.286
0.039
31
10.286
0.039
61
10.140
0.107
2
.192
055
32
234
.013
62
295
.048
3
.276
.029
33
.364
.117
63
.351
.I0 4
4
.218
.029
34
.316
.069
64
.302
055
5
.315
.068
35
.234
.013
65
175
.072
6
10.225
O.O22
36
10.223
0.024
66
10.138
0.109
7
.280
033
37
-243
.004
67
.238
.009
8
333
.086
38
.225
.022
68
.209
.038
9
333
.086
39
.204
043
69
.217
.030
10
.205
.042
40
.206
.041
70
.476
.229
ii
10.233
0.014
41
10.259
O.OI2
7i
IO.O22
0.225
12
.196
.051
42
.241
.OO6
72
.l6l
.086
13
193
.054
43
.191
.056
73
.26 9
.022
14
273
.026
44
.321
.074
74
.324
.077
15
.320
073
45
332
.085
75
.38 4
137
16
10.251
O.OO4
46
10.372
0.125
76
10.152
0.095
J 7
.367
.120
47
.138
.109
77
.316
.069
18
.121
.126
48
.095
.152
78
.148
.099
*9
.074
^S
49
.201
.046
79
.303
.056
20
.251
.004
5
234
.013
80
.028
.219
21
J0.538
0.291
51
10.288
0.041
81
10.196
0.051
22
.217
.030
52
304
057
82
IO.I63
.084
23
.436
,I8 9
53
.227
.O2O
83
9.928
-319
2 4
.470
.223
54
.321
.074
84
10.152
095
25
^S 1
.096
55
.283
.036
85
10.245
.OO2
26
10.265
0.018
56
0.190
0.057
86
10-3I3
O.o66
27
330
.083
57
.290
043
28
.194
053
58
275
.028
29
354
.107
59
.271
.024
30
.248
.OOI
60
.264
.017
PAEALLAX OF 61j CTGNI AND STAR (D).
Concluded measures of ^ Cygnifrom the comparison Star (d).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance of
Star (d) to
61i Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (d) from
61i Cygni.
Average
Devi-
ation.
d. h.
//
//
n
H
a
//
//
I
May 30 11.7
9S5-3I7
+ 0.427
+ 0.058
-2.257
0.163
953.382
0.262
2
June I 11.7
5-396
.366
.058
2-235
- .260
3.325
133
3
4 u.8
4.981
343
.058
2.205
+ .171
3348
J 57
4
8 11.9
5.029
325
057
3.163
+ .212
3.46o
159
S
15 ii. 2
4-883
339
055
2.090
+ .148
3-335
.097
6
16 11.7
955.111
+ 0.314
+ 0.055
2.o8o
0.300
953.100
0.247
7
23 11.6
4.899
.302
.052
2.006
.210
3-037
.225
8
24 ii C>
6-244
303
.051
I -995
-553
3.050
303
9
30 11.4
5-036
.297
.049
1-933
.282
3.167
.085
10
July i 11.3
4-398
.298
.048
1.922
+ -301
3.123
.162
ii
Aug. 20 1 1. 1
954.404
+ 0.282
+ 0.007
J-395
0.018
953.280
0.139
12
24 9.8
4-284
.282
.004
1.358
+ -US
3-347
.192
13
26 9.3
3-783
283
.OO2
1-337
+ -395
3.126
157
H
28 9.5
4.490
.282
.000
1.316
.171
3-285
244
'5
29 9-5
5-518
.282
O.OOI
1.306
- -197
3-296
.209
16
30 8.9
954.521
+ 0.283
O.OO2
- L295
0.036
953.471
0.250
17
31 8.8
3-993
.283
.003
1.285
+ .161
3-149
133
18
Sept. 7 8.6
3-959
.282
.OIO
1. 212
+ .226
3.245
.182
19
10 8.4
4.406
.282
.Oil
E.fSl
+ .040
3.536
.209
20
ii 8.5
4.382
.282
.014
1.170
.076
3-404
243
21
13 8.4
954-420
+ 0.282
0.016
1-150
O.OI2
953-524
0.162
22
IS 8.1
4-573
.282
.018
1.129
.154
3-554
.153
23
16 9.8
4.071
.284
.018
1.118
+ -153
3.372
.180
24
17 8.1
4-564
.282
019
1.108
.170
3-549
243
25
18 8.0
4.469
.282
.021
1.097
- .250
3-383
.292
26
20 9.0
954-47
+ 0.282
0.023
1.076
+ 0.175
953.405
0.227
2 7
22 9.4
4.400
.284
.024
1-055
- .278
3-327
.214
28
27 IO.2
4-369
2 95
.029
I.OOI
.268
3-366
139
2 9
29 8.6
4.085
.283
.030
0.982
+ .149
3-505
243
3
30 8.4
4.467
.282
.031
0.971
- .I6 7
3-579
.229
31
Oct. 2 8.2
954- 2 38
+ 0.282
0.033
-0.951
-f- O.066
953.602
0.183
32
6 9.1
4.164
.289
.036
.909
+ .104
3.612
.205
33
13 10.1
4.046
3'7
.041
.835
.012
3-475
.156
34
21 7-5
4.092
.284
047
752
-4- 004
3.53i
.147
35
22 7.5
4.171
.284
.048
.742
+ .055
3.720
.229
Concluded Distances of 61 X Cygni from Star (d). 55
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance of
Star (d) to
61i Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (d) from
61 1 Cygni.
Average
Devi-
ation.
d. h.
n
//
H
//
n
n
n
36
Nov. 3 6.6
953-926
-f- 0.284
0.053
0.617
+ 0.042
953-582
0.204
37
5 8.8
4.207
.317
.054
595
- .I 4 I
3-734
.153
38
16 7.5
3-95 1
.308
057
.480
.004
3-718
.217
39
i7 8.3
4.032
.338
057
470
-033
3.810
.083
40
18 8.6
4.072
355
.058
459
- .148
3.762
.136
4'
23 8.6
953-984
+ 0.383
0.058
0.406
0.024
953-879
0.229
42
29 6.9
3-935
309
.058
345
.002
3-839
.097
43
Dec. i 7.3
3-859
333
.058
324
+ .060
3.870
.163
44
2 6.8
3-849
.312
.058
313
+ -003
3-793
.242
45
4 6.4
3.810
.306
.058
293
+ .060
3-825
.138
46
7 6.3
954-05I
4-o.3io
0.057
0.282
0.141
953.881
0.147
47
9 7.2
3-995
355
057
.240
.050
4.003
.202
48
14 6.2
4.219
.320
055
.188
- -379
3-9 1 ?
.190
49
16 6.2
3-9 6 3
331
055
.167
- .189
3-883
-08 3
5
24 6.2
3.808
354
.051
.084
-130
3.897
T 35
5 1
87 Jan. 5 6.9
953-884
+ 0.509
0.045
+ 0.045
- 0.564
953-829
0.165
52
8 6.4
3.824
.442
.042
.076
.297
4.003
.104
53
10 6.7
3.272
532
.041
099
4- .088
3-950
.221
54
1 2 6.3
3.908
487
.039
.118
-515
3-959
073
55
20 6.4
3-725
634
033
.201
- -485
4.042
.162
56
25 6.3
952.946
+ 0.677
O.O29
+ 0.254
+ 0.130
953-978
0.290
57
3 6.5
3-139
949
.023
317
- -379
4.003
.I8 3
58
Feb. 5 6.0
2.428
-832
.OI9
358
+ -297
3.896
.240
59
8 5-9
3-020
.928
.015
.401
- .421
3-9I3
.126
60
17 17.1
3-083
.586
.OO6
.500
.288
3-875
233
61
2 5 J7-4
952.721
+ 0.427
+ O.OO2
+ 0-583
+ 0.063
953-796
0.207
62
26 16.9
2.960
497
.003
594
.142
3.912
93
63
27 16.9
2.411
517
.004
.604
+ -289
3-825
.162
64
Mar. 12 16.1
2.527
479
.017
739
+ .112
3-874
.126
65
16 15.7
2.641
497
.O2I
.780
-244
3.695
.301
66
23 16.4
952.277
+ 0.352
+ 0.027
+ 0.854
+ O.II7
953-627
0.175
67
27 14.8
2.117
543
.031
.896
+ .148
3-735
329
68
Apr. 2 15.3
2.154
391
.036
0-959
+ .162
3.702
133
69
16 14.4
1.813
39
.046
1.104
+ -MS
3-Soi
.027
/o
19 14.6
1.922
355
047
1.136
+ -015
3-475
.144
7i
20 15.0
95M77
+ o-333
+ 0.048
+ 1.146
+ 0.427
953-431
O.l62
72
25 13-4
2.052
444
.051
1.199
- -045
3-7oi
.22 9
73
26 14.2
1-959
352
.051
1.209
+ -033
3-604
.304
74
29 13-8
1.823
373
053
1.240
+ -059
3.548
143
75
30 13-8
1-955
363
053
1.250
+ .010
3-631
.250
56
Relative Parallax of Glj Cygni and Star (d).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887.
Measured
Distance of
Star (d) to
61i Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (d) from
61i Cygni.
Average
Devi-
ation.
d. h.
//
//
//
//
it
//
//
76
May 5 13.7
95' -993
+ 0.345
+ 0.055
+ I-303
0.216
953.480
0.149
77
7 i3-o
1.790
-391
.056
1.324
.172
3.389
.227
78
9 I2 -4
1.706
.46,
.056
1-345
.038
3-530
303
79
10 12.8
1.840
-394
.056
1-355
.260
3.385
.029
80
13 13-0
1.863
359
057
1.386
.320
3.345
.149
81
14 12.8
951.676
+ 0-373
+ 0-057
+ 1.396
0.187
953.315
0.085
82
16 12.8
1-653
.362
.058
1.418
.030
3.461
153
83
18 12.8
1.688
349
058
1-439
-177
3-357
.242
84
20 13.1
I-39 3
325
058
1.460
+ .076
3-3ii
.270
85
26 13.2
1.367
311
058
1.522
+ .104
3-362
.165
86
31 1 1.8
95I-235
+ 0.360
+ 0.058
+ J-574
+ 0.142
953-369
0.136
TABLE XXI.
Equations of Condition formed from the measures of
61 X Cygni and Star (d).
No.
Date,
1886.
Equations of Condition.
Residual.
d. h.
//
//
I
May 30 11.7
O.2l8 = X 0.6444 "" 0.5908 d fJi
0.090
2
June i 11.7
.275 = x .6642 .5853
.041
3
4 1 1. 8
.252 = x .6926 .5771
- -075
4
8 11.9
.140 = x .7277 .5660
- .192
5
15 u. 2
.265 = x .7806 .5469
- .088
6
16 11.7
0.500 = x 0.7876 0.5442
+ 0.135
7
23 n.6
-563 = a? -8284 -525
+ .182
8
24 11. 6
.550 = x .8332 .5223
+ -167
9
30 11.4
-433 = x .8579 .5059
+ .040
10
July I 11.3
.477 x .8611 .5031
+ -083
ii
Aug. 20 1 1 . 1
0.320 = x 0.7133 0.3653
0.005
12
24 9.8
.253 = x .6774 .3556
.056
13
26 9.3
.474 = x .6582 .3501
+ -173
14
28 9.5
.315 = x .6379 -3445
+ -023
15
29 9-5
.304 = x .6273 .3418
+ -017
Equations of Condition : 61 X Cygni and Star (d). 57
No.
Date,
1886-7.
Equations of Condition.
Residual.
d. h.
//
//
16
Aug. 30 8.9
0.129 = x o.6i737T 0.3392 dfjL
0.154
'7
31 8.8
.451 = x .6065 .3364
+ -173
18
Sept. 7 8.6
-355 = * .5265 .3174
+ .III
'9
10 8.4
.064 = x .4900 -3Q9 1
- .164
20
ii 8.5
.196 = x .4778 .3064
- .027
21
13 8.4
0.076 = x 0.4524 0.3009
0.135
22
15 8.1
.046 = x .4268 .2955
-'55
23
16 9.8
.228 = x .4130 .2925
-f -033
24
17 8.1
.051 = x .4005 .2900
-139
25
18 8.0
.217 = x .3871 .2872
+ -031
26
20 9.0
0.195 = x 0.3586 0.2815
+ 0.024
2 7
22 9.4
.273 = x .3320 .2761
+ -113
28
27 IO.2
.234 = x .2619 .2623
+ -104
29
29 8.6
.095 = x .2335 .2570
.023
30
30 8.4
.021 *= X .2182 .2543
.090
31
Oct. 2 8.2
+ 0.002 = X O.I90I 0.2488
O.IOI
32
6 9.1
+ .012 = 0? .I32O .2380
.086
33
13 10.1
.125 = x .0264 .2185
+ .096
34
21 7-5
.019 = x + .0914 .1969
+ .040
35
22 7.5
+ .120 = x + -!o63 I 94 2
.092
36
Nov. 3 6.6
0.018 = x +0.2802 0.1615
+ O.I 2O
37
5 8.8
+ .134 = x + .3098 .1557
.018
38
16 7.5
+ .118 = x + .4560 .1257
+ .060
39
17 8.3
-f- .210 = x + .4689 .1229
.026
40
18 8.6
+ .162 = X + .4815 .1201
+ .028
4 1
23 8.6
+ 0.279 x + O-54H 0.1064
0.064
42
29 6.9
+ .239 = x + .6074 .0904
+ .005
43
Dec. i 7.3
+ .270 = x + .6283 .0847
.018
44
2 6.8
+ .193 = x + .6379 .0820
+ .064
45
4 6.4
+ .225 = x + .6573 .0766
+ .040
46
7 6.3
+ 0.281 = x + 0.6849 -c>739
0.004
47
9 7.2
+ .403 = x + .7028 .0628
.118
48
14 6.2
+ .317 = x + .7424 .0492
.015
49
16 6.2
+ .283 = x + .7565 .0438
+ .026
50
24 6.2
+ .297 = x + .8043 -0219
+ -033
Si
87 Jan. 5 6.9
+ 0.229 = x +0.8458 +0.0118
+ O.I 2O
52
8 6.4
+ .403 = x + .8502 + .0198
.052
53
10 6,7
+ .350 = x + .8519 + .0253
+ .002
54
12 6.3
+ -359 = x + -8525 + -0308
.005
55
20 6.4
+ .442 = x + .8444 + .0527
-093
58
Concluded Parallax: 61 1 Cygni and Star (d).
No.
Date,
1887.
Equations of Condition.
Residual
d. h.
//
H
56
Jan. 25 6.3
-f 0.378 = X + 0.8306 7T -f- 0.0664 dfJL
0.032
57
31 6.5
+ .403 = x + .8056 + .0829
.067
58
Feb. 5 6.0
-f .296 = x + .7783 -f .0938
+ .029
59
8 5-9
+ .313 = x + .7587 + .1048
+ .005
60
17 17.1
+ .275 = x + .6842 -f .1306
+ -013
61
25 17-4
+ 0.196 = a? +0.6062 +0.1526
+ 0.060
62
26 16.9
+ .312 = x + .5958 + .1553
.060
63
27 16.9
+ .225 = # + .5851 + .1581
+ -023
64
Mar. 12 1 6. i
+ .274 = x + .4307 + .1935
.089
65
16 15.7
+ .095 = x + .3782 + .2044
+ .068
66
23 16.4
+ 0.027 = x +0.2819 +0.2236
+ 0.097
67
27 14.8
+ -135 = x + - 22 57 + - 2 344
-033
68
Apr. 2 15.3
+ .102 = x + .1384 + .2509
.036
69
16 14.4
.099 = x .0683 + .2891
+ .071
70
19 14.6
.125 = x .1127 + .2973
+ .088
7i
20 15.0
0.169 = x 0.1278 +0.3000
+ 0.125
72
25 J3-4
+ .101 = x .1997 + .3137
- .174
73
26 14.2
+ .004 = x .2148 + .3165
.083
74
29 13-8
.052 = x .2573 + .3246
.044
75
30 13-8
+ .031 = x .2714 + .3272
-133
76
May 5 13.7
O.I2O = X 0.3411 +O.34IO
O.OII
77
7 13-0
.211 = X .3677 + .3465
+ .070
78
9 I2 -4
.070 = x .3943 + .3519
.082
79
10 12.8
.215 = x .4075 + .3546
+ -057
80
13 i3-o
.255 = x .4467 + .3628
+ .082
81
14 12.8
0.285 = x 0.4592 +0.3655
+ 0.106
82
16 12.8
.139 = x .4842 + .3710
.050
83
18 12.8
.243 = x .5087 + .3765
+ .046
84
20 I3.I
.289 = x .5328 + .3820
+ .081
85
26 13.2
.238 = x .6008 + .3984
+ .002
86
31 n.8
0.231 = x 0.6523 +0.4120
0.027
The normal equation, after the usual treatment, is of the following form
2.4080= +86.0000 x 5.6824^/01 3.688977
+ 2.6588= 5.6824 +7-8594 + 5-2392
+ 11.7980=- 3.6889 +5-2392 +27.4037
whence the values of the unknowns become
x = 0.0064
dfj. = +0.0541
IT = + 0.4193.
The probable error of TT is // .0182, and the probable error in the complete
determination of distance for one night is o".o8c).
PARALLAX OF 61 2 CYGNI AND STAR (D).
Concluded measures of 61 2 Cygnifrom the comparison Star (d).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance of
Star (d) to
61z Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (d] from
61 2 Cygni.
Average
Devi-
ation.
d. h.
//
//
//
//
//
//
//
I
May 30 11.7
963.059
+ 0-445
+ 0.059
2.194
0.164
961.205
0.092
2
June i 11.7
3-163
379
.058
2.173
.262
i.i6 S
.188
3
4 n. 8
2.6o6
353
.058
2.142
+ -173
1.048
.240
4
8 11.9
2.756
335
057
2.102
+ .314
1.260
I8 3
5
15 ii. 2
2.706
349
055
2.031
+ .149
1.228
.136
6
16 11.7
963.047
+ 0.321
+ 0.055
2.O2I
0.302
961.100
0.274
7
23 n.6
2.809
.312
052
1-949
.212
I.OI2
.225
8
24 1 1. 6
3.258
3i3
.052
1.940
- 058
I.I25
243
9
30 11.4
2.992
305
.050
1.879
- -285
1.183
.211
10
July i 11.3
2.28l
35
.048
1.868
+ -304
1.070
.0 9 6
ii
Aug. 20 1 1. 1
962.410
+ 0.285
+ 0.007
1-35 6
O.OI9
961.327
0.243
12
24 9.8
2.182
.284
.004
1.320
+ .136
1.286
.164
13
26 9.3
1.803
.286
.OO2
1.300
+ -399
I.I 9
.175
H
28 9.5
2.436
.284
.000
1-279
.172
1.269
.190
15
2 9 9-5
2.483
.284
.001
1.269
-J99
1.298
.I 5 I
16
30 8.9
962.390
+ 0.286
0.002
1.259
0.036
961.379
O.206
17
31 8.8
2.175
.286
.003
1.249
+ .163
1-372
.264
18
Sept. 7 8.6
2.125
.285
.OIO
1.178
+ .228
1.450
083
19
10 8.4
2.199
.285
.OI I
1.147
+ .040
1.366
320
20
ii 8.5
2-354
.284
.014
1.138
- -077
1.409
.242
21
13 8.4
962.267
+ 0.284
0.016
1.117
O.OI2
961.406
O.I 60
22
15 8.1
2.522
285
.018
1.097
- -155
1-537
.132
23
16 9.8
1.969
.287
.019
i. 086
+ "154
'305
083
2 4
17 8.1
2.242
285
.020
1.077
.172
1.258
.125
25
18 8.0
2-537
.284
.021
i. 066
- -2 5 2
1.482
.240
26
20 9.0
961.848
+ 0.285
0.023
1.045
+ 0.177
961.242
0.203
27
22 9.4
2.245
.287
025
1.025
.281
1. 201
.132
28
27 IO.2
2.319
.297
.029
0.974
- .270
1-343
I 53
2 9
29 8.6
1.879
285
.031
0-954
+ -IS'
1-330
.129
30
30 8.4
2.383
.284
.032
0.944
.169
1.522
173
31
Oct. 2 8.2
962.004
+ 0.285
0.033
0.924
+ 0.067
961.399
0.036
32
6 9.1
1.875
.292
037
.884
+ .105
I-35I
.183
33
13 10.1
1.936
319
.042
.811
.012
1.390
.272
34
21 7-5
1.918
.289
.047
731
+ .004
1-433
.209
35
22 7-5
1.916
.287
.048
.720
+ -056
1.491
.138
60 Relative Parallax of 61 2 Cygni and Star (d).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance of
Star (d) to
61a Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (d) from
61a Cygni.
Average
Devi-
ation.
d. h.
//
n
it
//
//
//
36
Nov. 3 6.6
961.938
+ 0.287
0.054
0.6oo
+ 0.042
961.613
0.163
37
5 8.8
2-053
324
055
578
.142
1. 602
.150
38
'6 7-5
'955
.309
058
.467
.004
x -735
.274
39
17 8.3
i. 860
338
.058
456
-033
1.651
-083
40
18 8.6
2.027
353
.058
.446
- -M9
1.727
.129
4 1
23 8.6
961.854
+ 0.380
0.059
0-394
0.024
961.757
O.2OQ
42
29 6.9
1.838
.313
059
-336
.002
-754
.240
43
Dec. i 7.3
1.848
333
.059
.3H
+ .061
1.869
.130
44
2 6.8
1.830
314
059
305
+ -003
1-783
.122
45
4 6.4
i. 808
309
.059
.284
+ .061
I-835
.084
46
7 6.3
962.033
+ 0.313
0.058
0.274
0.142
961.872
0.053
47
9 7-2
1-853
354
057
233
.050
1.867
139
48
14 6.2
2.108
324
.056
-I8 3
- -383
1.810
.208
49
16 6.2
1-732
330
055
.163
- .191
1-653
.280
50
24 6.2
1-855
351
052
.081
-131
1.942
-143
5
87 Jan. 5 6.9
961.781
+ 0.501
0.045
+ 0.044
0.569
961.712
0.127
5 2
8 6.4
1.652
.448
.043
.074
-300
1.831
173
53
10 6.7
1.1*0
-526
.041
.094
+ .089
1.848
.I6 4
54
12 6.3
1.701
.476
.040
.115
- -519
1-733
.092
55
2O 6.4
1.497
.607
033
.1 9 6
- .489
1.778
255
56
25 6.3
960.854
+ 0.663
0.029
+ 0.247
+ 0.085
961.820
0.139
57
31 6. 5
1.044
931
.023
.308
- -383
1.877
.262
58
Feb. 5 6.0
0.351
.814
.019
.348
+ -300
1.794
.138
59
8 5.9
0.960
905
.015
390
-425
1-815
.083
60
17 17.1
0.920
.620
.006
.486
.290
i-73o
.170
61
25 17-4
960.675
+ 0-445
+ O.OO2
+ 0.566
+ 0.063
961.751
0.184
62
26 16.9
0.856
.522
.003
-576
- .144
1.813
.097
63
27 16.9
0.273
540
.004
.587
+ .292
1.696
205
64
Mar. 12 16.1
0.273
.501
.017
.719
+ -"3
1.624
.162
65
16 15.7
-475
-521
.O2I
759
- .246
1-530
253
66
23 16.4
960.282
+ 0.364
+ 0.028
+ 0.830
+ 0.118
961.622
0.282
67
27 14.8
60.021
574
.031
.871
+ -149
1.646
131
68
Apr. 2 15.3
60.059
.406
.036
932
+ -164
1-597
.122
69
16 14.4
59.889
.405
.046
1-073
+ .15
1-563
*73
70
19 14.6
60.005
367
.048
1.103
+ -015
1-538
.119
7i
20 15.0
959-535
+ 0.341
+ 0.048
+ i."4
+ 0.431
961.469
0.042
72
25 13-4
9.889
463
.051
1.165
-045
1-523
.130
73
26 14.2
9-738
.364
.052
1-^75
+ -033
1.362
.204
74
29 13.8
9.707
.386
.053
1.205
+ -59
1.410
.109
75
30 13-8
9.829
376
053
1.215
+ .010
1.483
-443
Concluded Distances of 61 2 Cygni from Star (d). 61
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887.
Measured
Distance of
Star (d) to
61 2 Cygni.
Refraction
Correction.
Aberration
Correction.
Proper
Motion.
Correction
to Scale.
Concluded
Distance of
Star (d) from
61 2 Cygni.
Average
Devi-
ation.
d. h.
n
//
//
//
n
//
//
7 6
May 5 13.7
960.010
+ 0.360
+ 0.055
+ 1.266
-0.218
961.473
0.260
77
7 '3-o
959.811
.412
.056
1.286
-174
I-39 1
.132
78
9 12.4
9-565
.482
057
1.306
.038
1.372
155
79
IO 12.8
9.889
.409
-057
1.316
.262
1.409
.127
80
13 13-0
9-825
370
057
1-347
.323
1.276
.208
81
14 12.8
959.701
+ 0.386
+ 0.058
+ I-357
0.188
961.314
0.242
82
16 12.8
9.616
373
.058
1-377
-030
1-394
.I6 7
83
18 12.8
9.761
.361
.058
J-397
- -179
1.398
.209
84
20 I3.I
9.412
334
.059
1.418
+ -076
1.299
.230
85
26 13.2
9.318
3 1 7
059
1.478
+ .105
1.277
154
86
31 n.8
959.164
+ 0-373
+ 0.058
+ 1-530
+ 0.144
961.269
0.205
TABLE XXIII.
Equations of Condition formed from the measures
of 61 2 Cygni and Star (d).
No.
Date,
1886.
Equations of Condition.
ResiduaL
d. h.
//
//
I
May 30 11.7
0.295 == x 0.620777 0.5908 dp
+ 0.035
2
June i 11.7
-335 = * -6421 .5 8 53
+ .066
3
4 n.8
.452 = x .6704 .5771
+ .171
4
8 11.9
.240 = x .7067 .5660
- -057
5
15 ii. 2
.272 = x .7620 .5469
.048
6
16 11.7
0.400 = x 0.7692 0.5442
+ 0.077
7
23 ii. 6
.488 = x .8127 .5250
+ -146
8
24 11.6
-375 = * -8179 -5 22 3
+ -031
9
30 11.4
.317 = x .8450 .5059
.038
10
July i 11.3
.430 = x .8486 .5031
+ -073
ii
Aug. 20 1 1. 1
0.173 = x 0.7236 0.3653
0.129
12
24 9.8
.214 = x .6899 .3556
- -074
13
26 9.3
.310 = x .6715 .3501
+ -030
'4
28 9.5
.231 = x .6519 .3445
.046
15
29 9-5
.202 = X .6420 .3418
- -055
62 Equations of Condition: 61 2 Cygni and Star (d).
No.
Date,
1886-7.
Equations of Condition.
Residual.
d. h.
//
//
16
Aug. 30 8.9
0.121 = x 0.632217 0.3392 df*
0.142
17
31 8-8
.128 = x .6219 .3364
.127
18
Sept. 7 8.6
.050 = x .5448 .3174
- - J 75
19
10 8.4
.134 = x .5094 .3091
- -075
20
ii 8.5
.091 = x .4975 .3064
-113
21
13 8.4
0.094 = x 0.4728 0.3009
0.099
22
15 8.1
+ .037 = x .4479 .2955
- .219
23
16 9.8
.195 = x .4344 .2925
+ .018
2 4
17 8.1
.242 = x .4223 .2900
+ -070
25
18 8.0
.018 = x .4092 .2872
- -158
26
20 9.0
0.258 = x 0.3814 0.2815
+ 0.104
27
22 9.4
.299 = x .3552 .2761
+ -146
28
27 10.2
.157 = x .2862 .2623
+ -044
29
29 8.6
.170 = x .2572 .2570
+ .069
30
30 8.4
+ .022 = X .2444 .2543
- .117
31
Oct. 2 8.2
o.ioi = x 0.2158 0.2488
+ 0.018
32
6 9.1
.149 = x .1579 .2380
+ -091
33
13 10.1
.110 = x .0534 .2185
+ -097
34
21 7-5
.067 = x + .0637 .1969
+ -104
35
22 7.5
.009 * x + -0786 I 94 2
+ -051
36
Nov. 3 6.6
-f 0.113 = x +0.2520 0.1615
0.006
37
5 8.8
+ .102 = X + .2823 .1557
+ -030
38
6 7-5
+ -235 = x + .4297 -257
-039
39
17 8.3
+ .151 = x + .4429 .1229
+ -050
40
18 8.6
+ .227 = X + 4556 .1201
.020
4i
23 8.6
-f 0.257 = x -1-0.5165 0.1064
0.024
42
29 6.9
-f .254 = x + .5839 .0904
+ .008
43
Dec. i 7.3
+ .369 = x + .6054 - 8 47
.098
44
2 6.8
+ .283 = x + .6152 .0820
+ -007
45
4 6.4
+ -335 = x + -6352 -07 66
.051
46
7 6.3
+ 0.372 = x +0.6637 o-o739
0.075
47
9 7.2
+ .367 = x + .6823 .0628
.063
48
14 6.2
+ .310 - x + .7205 .0492
+ .012
49
16 6.2
+ -153 = * + .7384 -0438
+ -176
So
24 6.2
+ .442 = x + .7894 .0219
.101
51 .
87 Jan. 5 6.9
+ 0.212 = X +0.8361 +O.OII8
+ o-i59
5 2
8 6.4
+ .331 = x + .8419 + .0198
+ -043
53
10 6.7
+ .348 = x + .8426 + .0253
+ .026
54
12 6.3
+ .233 = x + .8461 + .0308
+ -143
55
20 6.4
+ .278 = x + .8418 + .0527
+ .096
Normal Equations: 61 2 Cygni and Star (d).
63
No.
Date,
1887.
Equations of Condition.
Residual.
d. h.
//
//
56
Jan. 25 6.3
+ 0.320 = x +0.8305-77 + 0.0664 d /A
+ 0.050
57
3i 6.5
+ -377 = x + .8085 + .0829
.Ol6
58
Feb. 5 6.0
+ .294 = x + .7836 + .0938
+ .056
59
8 5-9
+ .315 = x + .7654 + .1048
.027
60
17 17.1
+ .230 = x + .6953 + .1306
+ .082
61
25 17-4
+ 0.251 = x +0.6207 +0.1526
+ 0.029
62
26 16.9
+ .313 = a? + .6111 + .1553
-037
63
27 16.9
+ .196 = x + .6004 + .1581
+ -075
64
Mar. 12 16.1
+ .124 = x + .4510 + .1935
+ .08 4
65
16 15.7
+ .030 = x + .3998 + .2044
+ .156
66
23 16.4
+ O.I22 = X +0.3056 +0.2236
+ 0.023
67
27 14.8
+ .146 = x + .2503 + .2344
- .02 4
68
Apr. 2 15.3
+ .097 = x + .1643 + -2509
.OI2
69
16 14.4
+ .063 = x .0405 + .2891
.066
70
19 14.6
+ .038 = x .0847 + -2973
.Ol6
7 1
20 15.0
0.031 = x 0.0997 +0.3000
+ O.o6o
72
25 J 3-4
+ .023 = x .1715 + .3137
- .083
73
26 14.2
.138 = x .1866 + .3165
+ .062
74
29 13-8
.090 = x .2291 + .3246
+ .007
75
30 J3-8
.017 = x .2432 + .3272
-073
76
May 5 13.7
0.027 = x 0.3131 +0.3410
0.093
77
7 ^-o
.109 = x .3400 + .3465
.022
78
9 12.4
.128 = x .3667 + .3519
.014
79
10 12.8
.091 = x .3800 + .3546
-057
80
13 i3-o
.224 = a? .4196 + .3628
+ .058
81
14 12.8
0.186 = x 0.4323 +0.3655
+ 0.015
82
16 12.8
.106 = x .4575 + .3710
- .0 7 6
83
18 12.8
.102 = X .4824 + .3765
.090
84
20 13.1
.201 = a? .5068 + .3820
+ .002
85
26 13.2
.223 = x - .5761 + .3984
.OIO
86
31 n.8
0.231 = x 0.6288 +0.4120
0.024
In this, the last of the determinations of the parallax of 6i 2 Cygni with
reference to the four stars of comparison, the normal equation is
//
0.6610= + 86.00000 5.6824^ 3.726471
+ 2.3869=- 5.6824 + 7- 8 594 + 5-55 l8
+ 11.5690= - 3.7264 +5.5518 +26.8793
64: Concluded Parallax of 61 2 Cygni and Star (d).
whence the values of the unknowns are
x = +0.0115
d\L = + 0.0080
TT = + 0.4303,
and the probable error of TT becomes + 0".0178, and that of the measure of
distance between this star and 6i 2 Cygni is + o".iO4.
As in the case of the stars of comparison (a), (), and (c), I append a Table
exhibiting the difference of the measures of the two components from the same
star (d). The average difference of the measures is 7".93Q.
TABLE XXIV.
Difference of the measured distances of Star (d) from
61.! and 61 2 Cygni.
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
I
7-823
0.107
21
7.882
0.048
41
7.8 7 8
0.052
2
7.840
.090
22
7.983
-053
42
7.915
.015
3
7.700
.230
23
7-933
.003
43
7-999
.019
4
7.800
.130
2 4
7.709
.221
44
7.990
.060
5
7-893
037
25
8.099
.169
45
8.010
.080
6
8.000
0.070
26
7.837
0.093
46
7.991
O.o6 1
7
7-975
045
2 7
7.874
.056
47
7.864
.066
8
8.075
145
28
7-977
.047
48
7.893
037
9
8.016
.086
29
7.825
.105
49
7.770
.160
10
7-947
.017
30
7-943
.013
5
8.045
.115
ii
8.047
0.117
31
7-797
0-133
51
7.883
0.047
12
7-939
.009
32
7-739
.191
52
7.828
.IO2
13
8.064
134
33
7-9'5
.015
53
7.898
.032
14
7.984
054
34
7.852
.078
54
7-774
.156
15
8.002
.072
35
7-771
'59
55
7.736
.I 94
16
7.908
O.O22
36
8.031
O.IOI
56
7.842
0.088
17
8.223
293
37
7.868
.062
57
7.874
.056
18
8.205
275
38
8.017
.087
58
7.898
.032
'9
7.830
.100
39
7.841
.089
59
7.902
.028
20
8.005
.075
40
7-965
-035
60
7-845
.085
Collected Results of Parallax of 61 Cygni.
65
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
No.
Difference
of
Measure.
Difference
from
Mean.
it
//
tt
//
//
/
61
7-955
0.025
71
8.038
0.108
81
7-999
0.069
62
7.901
.029
72
7-832
.098
82
7-933
.003
63
7.871
.059
73
7-758
.172
83
8.041
.on
64
7.746
.184
74
7.862
.068
84
7.988
.058
65
7-835
095
75
7-852
.078
85
7-9iS
.015
66
7-995
0.065
76
7-993
0.063
86
7.900
0.030
67
7.911
.019
77
8.002
.072
68
7-895
035
78
7-842
.088
69
8.062
.132
79
8.024
.092
7
8.063
.133
80
7-931
.OOI
Collecting the results which are given at the end of the discussion of each
of the eight determinations of parallax, we have the following results :
Probable Error
Relative
Probable
of one
Star's Name.
Mag.
Annual
Error of
Complete
Parallax.
Parallax.
Measure of
Distance.
61 X Cygni.
D.M. 4- 37, No. 4189
7-9
+ 0.4204
+ 0.0162
+ 0.091
+ 38 4336
8.8
+ 0.4414
0.0222
+ 0.115
+ 37 4*75
9.0
+ 0.4448
+ O.O2I2
+ O.IO2
+ 38 4348
9-5
+ 0.4193
+ O.OI82
+ 0.089
61 2 Cygni.
D.M. + 37, No. 4189
7-9
+ 0.4250
+ 0.0176
+ 0.099
+ 38 4336
8.8
+ 0.4508
+ O.OI9I
+ O.IOO
+ 37 4175
9.0
+ 0.4320
+ 0.0190
+ 0.088
+ 38 4348
9-5
+ 0.4303
+ 0.0178
+ O.IO4
These results taken in connection with the probable errors, point to almost
an identity of parallax, and suggest that all the four comparison stars probably
belong to a remote system not containing 61 Cygni : under this view possibly
the average of the eight results [o".437] may be a close approximation to the
absolute parallax*; but it is a point submitted to the consideration of
astronomers whether we are ever justified in adopting a mean of independent
results, referred to various stars, as representing the absolute parallax.
Assuming, however, this mean (o".437) to represent virtually an absolute
parallax, and adopting the period of revolution and the Semi-axis major,
assigned in the researches of Prof. Peters f, there results from the combination,
* This is further confirmed by the determination of the absolute parallaxes (o".5o) referred
to p. 98.
f Ast. NacJi., No. 2709.
66
Parallax of /* Cassiopeia.
a mass equal to .505 that of the Sun, for the combined mass of the components
of the star 6 1 Cygni.
There arises naturally the additional question, how far do the distances of
the two components of 61 Cygni from each other at a given epoch, as implied
in the foregoing results, agree with the same distances, at the same epoch, as
obtained by Prof. Peters in his theoretical discussion of the orbit ? On referring
for this purpose to Table XXIV, it appears that the (mean) difference of the
distances of 6i x Cygni and 6i 2 Cygni from (d) is 7"'93, for Jan. 1887. Also,
on applying obvious reductions to the results of Prof. Peters, the same quantity
for the same epoch is 7"87. The following short Table (XXV) contains the
collected results arising from the application of a similar method to Tables
VII, XII, and XIX.
TABLE XXV.
Distance of 61i to 61z
Cygni resolved in the
direction joining 61i
and 1 1 1. star.
The same dis-
tances from
Prof. Peters'
Elements.
Difference
c o.
tf
I /'
//
a 20.29
20.34
0.05
20.59
20.64
+ 0-05
c 10.25
10-33
-f 0.08
d 7-93
7.87
O.o6
Taking into account the multiplied considerations on which these com-
parisons are founded, the foregoing enquiry exhibits a satisfactory agree-
ment between the results of Prof. Peters' investigations, and those in the
preceding pages.
PARALLAX OF ft CASSIOPEIA.
The next star submitted to the photographic method is /x Cassiopeise a star
well known for its abnormal proper motion. Independently of this con-
sideration, I was influenced in the selection of the star by the fact that its
parallax had already been investigated by two eminent astronomers, Bessel and
Otto von Struve, with very different results : since, however, the stars of com-
parison are different in each case, no conclusion can be properly drawn from
the disagreement of the final results.
Having in the case of 61 Cygni given every particular requisite for the
examination of the work, it is unnecessary to introduce the same amount of
detail in the discussion of the parallax of this star. I therefore propose to
confine myself solely to furnishing such data as are necessary for tracing the
Parallax of /* Cassiopeim.
67
sequences of the operations leading to the final result. These data will embrace
the variation in the diagonals of reference (Table I), the original measures of
distance and the total amount of correction applied (Table II), and the final
equations of condition (Tables III and IV).
In the course of the observation of this star there were so many unavoidable
interruptions, owing to the rehabilitation of the De La Rue Instrument and
other causes, that it was not possible to maintain the series without considerable
breaks, and therefore it became necessary to base the parallax, in this instance
alone, on not more than two stars of comparison. The two stars of comparison
selected are
(star 0) .... D.M. + 54, No. 225, Magnitude 7.9 *
(star a) .... D.M. + 53,No. 218 8.3
North
DIAGRAM SHOWING THE RELATIVE POSITIONS OF THE STARS COMPARED WITH fJ. CASSIOPEIA.
The approximate position-angles, and distances of these two stars shown in
the diagram are respectively
o / //
(star a) .... p = 26 56 s = 755
(star b) .... p = 201 52 s = 1356
whence the expressions for computing the factors for parallax are
o /
(star a) . . ds = .S [9.96649] cos (0333 5)
(starfl) . . ds = ^[9-955^3] cos (0 156 14).
The proper motion for //, Cassiopeia has been assumed from various authorities
inRA. = +o s .388 in Decl n . -i".58i,
or 3". 741 in the arc of a great circle inclined at an angle 115 o' to the
parallel of declination.
These preliminary data will, with the explanatory detail furnished in the
case of 6 1 Cygni, permit the whole of the subsequent Tables to be easily
followed.
* These magnitudes have been determined photometrically, by the Wedge Photometer. This
remark applies to the magnitude assigned to all subsequent stars of comparison.
68
Parallax of p Cassiopeice. '
TABLE I.
Measures of the diagonal distance of Star (a) from Star (b) for tJie
determination, at the times of exposure, of the correction to
their measured distances from p Cassiopeice.
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance
of (a) to (&)
in Arc.
Sum of
Corrections of
Refraction and
Aberration.
Difference from
Assumed
Mean
(2109".80).
d. h.
H
n
n
I
86 Oct. 22 8.4
2109.048
+ 0.625
+ 0.127
2
28 8.7
08.633
.609
+ -558
3
29 8.4
08.332
.605
+ -863
4
30 8-5
09.721
.601
- -522
5
Nov. 7 7.4
09.317
579
.096
6
10 8.2
2108.890
+ 0.572
+ o-338
7
ii 8.3
09.366
574
- -137
8
13 7-4
09.581
-566
- -347
9
IS 7-4
08.905
.560
+ -335
10
16 7.9
09471
559
-230
ii
18 8.3
2I094I8
+ 0.549
0.167
12
29 6.3
09.308
524
-032
3
30 6.6
09.006
523
+ -271
14
Dec. 12 7.6
08.892
.492
+ .416
15
3 7-5
09.756
.489
- -445
16
21 6.7
2108.923
+ 0.476
-|- 0.401
17
2* 7-5
O9.6OI
.471
.272
18
87 Jan. 17 7.2
08.971
458
+ -371
19
18 7.0
09.382
454
.036
20
Feb. 2 7.4
09.110
515
+ -'75
21
4 8.1
2109.534
+ 0-589
0.323
22
9 7-4
08.699
0.561
+ -544
23
12 9-5
08.385
1.084
+ -331
2 4
25 8.3
08.912
0.908
.020
25
Mar. i 9.5
O8.OO4
1.7*1
+ -075
26
2 IO.O
2107.950
+ 2.303
o.453
2 7
17 10.7
06.455
3.870
-525
28
25 10-5
04.958
4.117
+ -725
29
Apr. 4 10.4
06.350
4.112
.662
30
6 9.9
06.130
4-253
- -583
Measures of the Diagonal Distances (a) to (b).
69
No. for
Refer-
enoe.
Date of
Exposure
of Plate.
1887.
Measured
Distance
of (a) to (b)
in Arc.
Sum of
Corrections of
Refraction and
Aberration.
Difference from
Assumed
Mean
(2109".80).
d. h.
n
H
//
31
Apr. 25 9.9
2103.713
+ 5-556
-fO-531
32
July 31 11.9
09.580
0-745
-525
33
Aug. i 10.6
08.604
775
+ -421
34
2 11.4
09.074
-751
-025
35
8 n.a
09.877
750
- .827
36
18 10.1
2108.732
+ 0.743
+ 0.325
37
20 12.2
09.288
.741
.229
38
24 11.3
09-359
734
~ -293
39
Sept. 5 1 1.0
09.527
723
- -45
40
7 9-
08.667
.716
+ -4 J 7
41
12 9.1
2108.967
+ 0.707
+ 0.126
42
22 9.2
08.839
.690
+ .271
43
28 9.8
09.044
.685
+ .071
44
Oct. 4 10.2
09.834
.670
- -704
45
ii 8.6
08.732
.651
+ -4^7
46
12 8.8
2108.619
+ 0.650
+ 0.531
47
13 9.0
09.834
.649
- .683
48
14 9.6
09.617
.647
- .464
49
15 10.4
09.447
.640
- .287
50
17 9.2
08.891
.638
+ -271
5i
20 9.2
2108.770
+ 0.623
+ 0.407
52
22 10.0
09.624
.623
-447
53
2 4 9.4
09.104
.618
+ -078
TABLE II.
Concluded measures of n Cassiopeice from the Stars of
comparison.
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886.
Measured
Distance of
Star (a) to
/, Cassiop.
Sum of
Corrections.
Concluded
Distance
of Star (a).
Measured
Distance of
Star (6) to
ju, Cassiopeise.
Sum of
Corrections.
Concluded
Distance
of Star (6).
d. h.
"
//
//
it
n
I
Oct. 22 8.4
755-393
+ 0.245
755.638
I355- 820
+ 0-443
1356.263
2
28 8.7
5.110
.385
5-495
5.607
.712
6.319
3
2 9 8. 4
4.868
505
5-373
5.280
.907
6.187
4
30 8-5
5-663
.008
5.671
6.078
.015
6.093
5
Nov. 7 7.4
5-378
'55
5-533
5-967
.280
6.247
70
Concluded Measures of p Cassiopeia
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1886-7.
Measured
Distance of
Star (a) to
fji Cassiop.
Sum of
Corrections.
Concluded
Distance of
Star (a).
Measured
Distance of
Star (6) to
M, Cassiopeise.
Sum of
Corrections.
Concluded
Distance
of Star (b>
d. h.
//
//
//
//
it
n
6
86 Nov. 10 8.2
755-23I
+ 0.307
755.538
I355.827
+ 0-545
I356.37 2
7
ii 8.3
5.242
'37
5-379
5-9 J 7
.250
6.167
8
13 7-4
S.6 7 6
.027
5-703
6.083
.049
6.132
9
15 7-4
5-371
-304
5-675
5-854
-547
6.401
10
16 7.9
5-444
.103
5-547
6.082
.183
6.265
ii
18 8.3
755-430
+ 0.242
755.672
1355-825
+ 0-435
1356.260
12
29 6.3
5-300
.189
5.489
5-844
339
6.183
13
30 6.6
5-646
.090
5-736
6.191
H3
6-334
M
Dec. 12 7.6
5- 6 54
.020
5.674
6.240
-037
6.277
15
*3 7-5
5-376
327
5-703
5-5"
.587
6.099
16
21 6.7
755-549
+ 0.023
755-572
1356.269
+ 0.043
1356.312
17
22 7-5
5-312
-273
5-585
5-851
-469
6.320
18
87 .Tan. 17 7.2
5-453
.038
5-49 i
6.12 I
.064
6.185
'9
18 7.0
5-508
.179
5.687
5.846
-323
6.169
20
Feb. 2 7.4
5-403
'35
5-538
6.116
.231
6-347
21
4 8.1
755-371
+ 0-344
755.715
1355-651
+ 0.600
1356.251
22
9 7-4
5-455
-033
5-488
6.UI
.022
6.133
23
12 9.5
5-256
.301
5-557
5.679
495
6.174
2 4
*5 8.3
5-205
364
5-569
5.700
0.617
6.317
25
Mar. i 9.5
5.009
.635
5-644
5.021
1.075
6.096
26
2 IO.O
754-445
+ 0.968
755-4^3
1354.537
+ 1.748
1356.285
27
17 10.7
4.107
J-57I
5.678
3.983
2-330
6-313
28
25 lo-S
4-498
1.205
5-703
3-849
2.283
6.132
2 9
Apr. 4 10.4
3-905
1.670
5-575
3-39 1
2.776
6.167
30
6 9.9
3-954
1.711
5-665
3.103
3.202
6-305
31
25 9-9
753-972
+ 1.481
755-453
1352.710
+ 3-428
1356.138
32
July 31 11.9
4-9I7
0.528
5-445
5-375
0-934
6.309
33
Aug. i 10.6
5-179
93
5-374
5-936
0-35
6.286
34
2 11.4
5-159
-348
5-507
5.808
0.617
6.425
35
8 II. 2
5-234
.279
5.513
5-994
0-439
6-433
36
18 10.1
755-239
+ 0.226
755465
I355.893
+ 0.404
1356.297
37
20 12.2
4.858'
.429
5.287
5-561
7S 1
6.312
38
24 11.3
5-052
-452
5-504
5-406
.791
6.197
39
.Sept. 5 n.o
4.914
507
5.421
5-474
.891
6.365
40
7 9-
5.181
193
5-374
6.105
334
6-439
4 1
12 9.1
755.241
+ 0.297
755-538
I355-857
+ 0.515
1356-372
42
22 9.2
5-324
243
5-567
5-83I
0.416
6.247
43
-28 9.8
5-174
315
5-489
5.682
0-543
6.225
44
Oct. 4 10.2
4-749
584
5-333
5427
J -035
6.462
45
ii 8.6
5.122
.184
5-306
5-823
0.527
6.35
from the Stars of Comparison (a) and (b).
71
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887.
Measured
Distance of
Star (a) to
ju Cassiop.
Sum of
Corrections.
Concluded
Distance of
Star (a).
Measured
Distance of
Star (b) to
M. Cassiopeiae.
Sum of
Corrections.
Concluded
Distance
of Star (6).
d. h.
//
//
//
//
//
//
46
Oct. 12 8.8
755-377
+ 0.142
755-5I9
I356.0S3
+ 0.232
1356.285
47
13 9.0
5.009
-577
5-586
5.216
1.013
6.229
48
14 9.6
5- I! 5
.518
5.633
5-56I
0.872
6-433
49
15 10.4
5.124
433
S-557
5.627
0-755
6.382
50
17 9.2
5-470
233
5-703
5.869
0.396
6.265
S 1
20 9.2
755-309
+ 0.179
755-488
I355- 8 90
+ 0.303
1356.193
52
22 IO.O
5.068
.486
5-554
5-475
,851
6.326
53
24 9.4
5-330
297
5.627
5-737
.512
5.249
. _ NOTES.
No. 3. A plate rejected : the film was injured in development.
No. 5. Hazy sky : exposure eight minutes.
No. 6. Images elongated. Driving-clock went too slowly.
No. 7. Sky generally cloudy. Images feeble.
No. ii. The measures on one of the plates discordant nearly 3". The plate was rejected, but
the cause of the discordance could not be discovered.
No. 15. Images faint and elongated in the direction of diurnal motion.
No. 17. Sky very foggy : exposure ten minutes ; only three plates taken.
No. 20. Images of the stars (a) and (b) faint. One plate could not be measured.
Nos. 23 to 31. The exposure was ten minutes in each case, the star being of small altitude.
No. 26. A plate rejected for discordance, the source of which could not be detected.
No. 29. Images elongated in the direction of diurnal motion.
No. 31. Images faint and blurred : it was suspected that the plate was not quite in the focus.
No. 38. A plate rejected, the film having been injured.
No. 40. Observations repeatedly interrupted by clouds.
No. 43. Sky very foggy : exposure was continued for ten minutes.
No. 46. Sky very transparent but definition very bad : the images were large and ill- defined.
No. 51. Sky generally cloudy: the durations of exposure about ten minutes, but a little
uncertain owing to passing cloud.
No. 53. Images somewhat elliptical.
It is worthy of remark that the imperfections detailed in the above notes
are not exhibited in the residuals.
TABLE III.
Equations of Condition formed from the measures of
p Cassiopeice and Star (a) Table II.
No.
Date,
1886.
Equations of Condition.
Residuals.
d. h.
//
//
I
Oct. 22 8.4
O.l62 = X - 0.4976 7T 0.1952 d(JL
0.082
2
28 8.7
.305 = x .4132 .1788
+ .064
3
2 9 8.4
.427 = x .3988 .1750
+ .187
4
30 8.5
.129 = x .3841 .1724
.110
5
Nov. 7 7.4
.267 = x .2640 .1504
+ .032
72
Equations of Condition for Star (a).
Xo.
Date,
1886-7.
Equations of Condition.
Residuals.
d. h.
//
//
6
86 Nov. 10 8.2
O.262 = X O.2I7O 7T O.I422 d/A
+ 0.029
7
ii 8.3
.421 = x .2012 .1395
+ -189
8
13 7-4
.097 = x .1700 .1340
-135
9
15 7-4
.125 = x .1382 .1285
-105
10
16 7.9
-253 = x .1218 .1257
+ .024
ii
18 8.3
0.128 = x 0.0898 0.1203
O.IOO
12
29 6.3
.311 = x .0727 .0903
+ .082
13
30 6.6
.064 = x .0565 .0875
- .164
M
Dec. 12 7.6
.126 = x + .2919 .0546
- .087
15
13 7-5
.097 = x + .3071 .0519
-"S
16
21 6.7
0.228 = x +0.4249 0.0300
+ O.O2I
i7
22 7-5
.215 = x + -4394 -0272
+ .009
18
87 Jan. 17 7.2
.309 = x + .7492 -|- .0446
+ ."5
'9
1 8 7.0
.113 = x + .7584 -f .0473
-077
20
Feb. 2 7.4
.262 = x + .8662 + .0885
+ .072
21
4 8.1
O.O85 = X +0.8762 +O.O94O
0.106
22
9 7-4
.312 = X + .8960 + .1077
+ -123
23
12 9.5
.243 = x + .9051 + .1158
+ -052
24
25 8-3
.231 = x + .9137 + .1515
+ -039
25
Mar. i 9.5
.156 = x + .9068 + .1625
-038
26
2 1 0.0
0.387 =- x +0.9043 +0.1654
+ 0.193
27
17 10.7
.122 = X + .8358 + .2064
- -077
28
25 10.5
.097 = x + .7759 + .2283
.107
29
Apr. 4 10.4
.225 = x + .6805 + .2558
+ -015
30
6 9.9
-135 = + -6592 + .2614
.078
31
25 99
0.347 = x +0.4192 +0.3134
+ O.I 2 I
32
July 31 11.9
-355 = x .8602 + .5791
+ -050
33
Aug. i 10.6
.426 = x .8659 + .5816
+ .121
34
2 11.4
.293 - x .8722 + .5844
.013
35
8 II. 2
.287 = x .9018 + .6008
.021
36
18 10.1
0.335 = * 0-9307 +0.6281
+ 0.024
37
20 12.2
-5 '3 = x .9335 + -634
+ .200
38
24 II-3
_ .296 = x .9354 + .6448
- .OI 7
39
Sept. 5 n.o
.379 = x .9158 + .6777
+ -065
40
7 9-o
.426 = x -9094 + .6829
+ -US
4i
12 9.1
0.262 = x 0.8872 +0.6968
0.051
42
22 9.2
.233 = x .8241 + .7241
.077
43
28 9.8
.311 = x -7743 -i- -7404
+ .OOI
44
Oct. 4 10.2
.467 = x .7165 + .7571
+ .160
45
ii 8.6
.494 = x .6402 + .7764
+ -189
Concluded Parallax: p Cassiopeia} and Star (a). 73
No.
Date,
1887.
Equations of Condition.
Residuals.
d. h.
//
//
46
Oct. 12 8.8
0.28l = X 0.6282 7T + 0.7788
10, a = 35 15 10,
5 = +88 49 26.1.
6 = + 88 38 45.0.
6= +88 25 21.1.
5 = + 89 2 48.0.
The position of these stars with reference to Polaris is shown on the
accompanying diagram, which also exhibits the position and eccentricity of
the parallactic ellipse.
North
West
East
Measures of the two Diagonal Distances.
77
The expressions from which the factors of parallax have been computed
are, in the case of these four stars, respectively
o /
For, ds = ^[9.96123] cos (Q- 82 39)
I, ds = ^[9.96413] cos (0-284 i)
c, ds -#[9.99906] cos (o 1 68 2,6)
d, t
0.044
2
Feb. I 8.5
+ .262 - x + .7985 .9140
+ -007
3
8 8.7
+ .285 = x + .7369 .8949
.020
4
15 8.1
+ .366 = x + .6671 - .8757
.107
5
July 31 10.0
+ .092 = x ,8509 .4209
+ .048
6
Aug. i 11.4
+ 0.115 = x 0.8372 0.4154
+ 0.626
7
3 "-7
.016 = x .8304 .4127
+ .155
8
4 12.2
+ .008 = x .8228 .4099
+ .134
9
8 11.6
+ .237 = x .7912 .3991
- -093
10
25 12.1
+ .262 = x .6216 .3525
.106
ii
Sept. 7 10.8
+ 0.285 = x 0.4505 0.3170
0.114
12
8 II. 2
+ .108 = x .4364 .3142
+ .064
13
12 11.5
+ .208 = x .3791 .3032
.032
14
17 12.2
+ .166 = x .3051 .2897
+ .016
15
22 9.9
+ .132 = x -2307 .2760
+ -036
16
24 9-5
+ 0.303 = X O.200I 0-2705
0-133
17
28 10.8
+ .098 = x .1370 .2595
+ .097
18
Oct. 10 1 1. 1
+ .262 = x + .0529 .2266
.052
19
II 10.0
+ .185 = x + .0681 .2240
+ .026
20
12 9.8
+ .271 = X + .0838 .2212
-058
86
Relative Parallax of Polaris and Star (b).
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
it
n
21
87 Oct. 13 i i.i
+ 0.244 = x + 0.1002 7T 0.2184 dp
0.030
22
14 9.0
+ .134 = x + .1148 .2157
+ .081
23
'5 9-5
+ .176 = x + .1308 .2131
+ -039
24
17 10.3
+ .181 = x + .1629 .2075
+ -036
2 5
19 10.4
+ ,l6l = X + .1937 .2021
+ -059
26
20 9.8
-f 0.145 = x +0.2086 0.1993
+ 0.076
27
21 I2.O
+ .165 = x + .2257 .1966
+ -058
28
24 II.3
+ .306 = x + .2709 .1883
.080
2 9
28 8.6
+ .263 = x + .3291 .1774
- .032
30
Nov. i 8.2
+ .360 = x + .3871 .1667
- -125
31
4 9-3
+ 0.243 = x +0.4304 0.1584
O.OO4
32
14 9.6
+ .138 = x + .5631 .1310
+ .III
33
15 7-9
+ .008 = x + .5746 .1284
+ -241
34
23 9-
+ .284 = x + .6676 .1064
.027
35
29 9-3
+ -383 = x + .7283 - .0899
.121
36
30 8.5
+ 0.316 = x +0.7374 0.0873
-53
37
Dec. 5 7.4
+ -339 - * + -7802 .0737
~ -073
38
6 9.1
+ .203 = x + .7890 .0708
+ .064
39
15 9.6
+ -323 = * + -8494 -0462
.052
40
16 7-5
+ .309 = x + .8543 .0436
.038
4i
17 8.1
+ 0-395 = x +0.8596 0.0408
0.123
42
88 Jan. 4 8.2
H- -455 = ar + .9051 + .0092
.180
43
18 9.4
+ .213 = x + .8780 + .0477
+ .061
44
27 7.8
+ -237 = x + .8325 + .0721
+ -033
45
Feb. 2 lo.a
+ .178 = x + .7896 + .0888
+ .089
46
6 n.6
+ 0.280 = x +0.7473 +0.0999
0.017
47
17 12.8
-f- .151 = x + .6454 + .1301
+ -105
48
Mar. i 10.7
+ .132 = x + .4864 + .1654
+ .in
49
8 8.5
+ .248 = x + .3907 + .1844
.013
50
14 9.1
+ .388 = x + .3023 + .2009
- .160
5i
16 n. o
+ 0.177 = x +0.2711 +0.2065
+ 0.048
52
21 10.3
+ .248 = X + .1950 + .2201
.029
S3
27 IO.2
f- .060 = x + .1017 + .2366
+ -152
54
Apr. 3 10.8
+ .208 = x .0094 + .2557
- .005
55
6 12.3
+ .092 = x .0579 + .2642
+ -107
56
ii 9.9
+ 0.127 = x 0.1349 +0.2776
+ 0.067
57
14 9-8
+ .174 = x .1816 + .2858
+ .016
58
18 ii. 2
+ .172 = x .2442 + .29^0
+ -013
59
26 10.3
+ .140 = x .3631 + .3187
+ -036
60
30 10.8
+ .144 = x .4206 + .3297
+ -027
Equations of Condition : Polaris and Star (b). 87
No.
Date,
1888.
Equations of Condition.
Residuals.
d. h.
//
H
61
May 2 12.2
+ 0.236 = X 0.4495 7T + 0.3354 dp
0.067
62
4 11.2
+ -US = X -47 6 4 + -3408
+ .032
63
8 11.5
+ .114 = x .5299 + .3516
+ .049
64
10 130
+ .089 = x - .5563 + .3574
+ .071
65
12 12. 1
+ .108 => x .5810 + .3628
+ -051
66
17 11.4
+ 0.145 = x 0.6402 +0.3762
+ 0.009
67
20 13.3
+ .247 = x .6747 + .3848
.093
68
24 13.0
+ .184 = x .7166 + .3958
- .036
69
25 I 2 -5
+ .255 = x .7264 + .3984
- .108
70
28 12.0
+ .159 = x .7642 + .4066
.014
7i
29 12.8
+ 0.100 = x 0.7734 +0.4094
+ 0.044
72
3 1 J 3-3
+ .174 = x .7826 + .4149
.031
73
June 7 n.o
+ .212 = X .8366 + .4338
-074
74
10 11.4
+ .113 = x .8570 + .4421
+ .024
75
14 12.3
+ .139 = x .8804 + .4532
.004
76
17 12.0
+ 0.185 = x 0-8953 +0.4614
0.051
77
22 II. 2
+ .138 = x .9149 + .4750
.005
78
July I 11.3
.046 = x .9344 + .4996
+ .177
79
3 "-9
+ .229 = x .9356 + .5051
.098
80
5 12-5
+ .134 = x - .9360 + .5107
- .003
81
9 10.8
+ 0.132 = x 0.9337 +0.5215
O.OOI
82
12 11.4
+ .199 = x .9290 + .5297
.068
83
17 10.6
+ .218 = x .9164 + .5434
.085
84
20 II.5
+ .117 = x .9053 + .5516
+ .016
85
23 12.2
+ .061 = x .8919 + .5599
+ .074
86
26 II. I
+ 0.300 = x 0.8768 +0.5681
0.164
Treating- these equations in the usual method, the following normal
equations result :
+ 16.921 = +86.00000 + 3.6042 d fj. 9.005471
0.093= + 3.6042 +11.6258 10.3180
+ 0.872= 9.0054 10.3180 +34.5320
whence, by solution, are obtained the values of the unknowns, viz.
x +0.205
d\L 0.0023
TT =+ 0.0780.
It further appears that the probable error of one complete measure of
distance is +o // .o84, and that the probable error of TT is +o".oi69.
PARALLAX OF POLARIS RELATIVELY TO STARS (C) AND (D).
TABLE V.
Concluded measures of Polaris from the Stars of
comparison (c) and (d).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887.
Measured
Distance of
Star (c) to
Polaris.
Sum of
Correc-
tions.
Concluded
Distance of
Star (c) from
Polaris.
Measured
Distance of
Star (d) to
Polaris.
Sum of
Correc-
tions.
Concluded
Distance of
Star (d) from
Polaris.
d. h.
//
n
//
//
//
//
I
Jan. 31 7.5
1181.633
+ 0.401
1182.034
1634.014
+ 0-474
1634.488
2
Feb. i 8.5
81.503
.524
82.027
33-952
.653
34.605
3
8 8.7
81.697
437
83.134
33.972
.540
34-512
4
15 8.1
81.672
384
82.056
34.069
.468
34-537
5
July 31 i o.o
81.806
33
82.137
33.848
.5H
34-362
6
Aug. i 11.4
1181.587
+ 0.615
1182.202
1633.563
-f 0.840
1634.403
7
3 ".7
81.588
.672
82.260
33491
.907
34-398
8
4 12.2
81.528
.704
82.232
33-312
.956
34.268
9
8 n.6
81.586
571
82.157
33-430
.770
34.200
10
25 12. i
81-734
.521
82.255
33-525
.685
34-2io
ii
Sept. 7 10.8
1181.571
-\- 0.669
1182.240
1633.586
+ 0.905
1634.491
12
8 II. 2
81.297
.784
82.081
33-249
1.071
34-320
13
12 11.5
81.625
.558
82.183
33472
0.746
34-218
'4
17 12.2
8l. 4 56
.812
82.268
33-332
1.090
34.422
IS
22 9.9
81.772
-385
82.157
33.820
0.512
34-332
16
2 4 9-5
1181.656
+ 0.658
1182.314
I633-253
+ 0.904
1634-157
i7
28 10.8
81.722
325
82.047
33-964
.425
34-389
18
Oct. 10 1 1. 1
81.793
451
82.244
33.728
594
34-322
19
II 10.0
81.672
.481
82.153
33.719
.642
34-36i
20
12 9.8
81.717
5'7
82.234
33.585
.691
34-276
21
13 II. I
1181.735
+ 0.486
1182.221
1633.893
+ 0.642
1634-535
22
I 4 9-0
81.766
.488
82.254
33-668
.657
34-325
23
ID 9-5
81.830
.469
82.299
33.856
.629
34.484
2 4
17 10.3
81.530
583
82.113
33-478
.780
34.258
25
19 10.4
81.402
635
82.037
33.676
.852
34-528
26
20 9.8
1181.544
-f 0.619
1182.163
1633-525
-f 0.735
1634.260
2 7
21 12.0
81.551
-565
82.116
33.598
747
34-345
28
2 4 11.3
81.634
.402
82.036
33.897
.518
34-4I5
2 9
28 8.6
81.905
329
82.234
33.9 8 4
.436
34.420
3
Nov. i 8.2
81.447
.689
82.136
33-642
936
34-578
Concluded distances of Polaris, from (c) and (d). 89:
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887-8.
Measured
Distance of
Star (c) to
Polaris.
Sum of
Correc-
tions.
Concluded
Distance of
Star (c) from
Polaris.
Measured
Distance of
Star (d) to
Polaris.
Sum of
Correc-
tions.
Concluded
Distance of
Star (d) from
Polaris.
d. h.
//
H
//
it
//
//
31
87 Nov. 4 9.3
1181.707
-j- 0.521
1182.228
1633-787
+ 0.697
1634.484
32
14 9.6
81.683
SIS
82.2OI
33-750
0.691
34-44 1
33
15 7.9
81.578
593
82.171
33-672
0.804
34-476
34
23 9-o
81.313
753
82.066
33402
I.OI4
34.416
35
29 9-3
81.348
732
82.080
33'344
0.983
34-327
36
30 8.5
"81.573
+ 0.530
1182.103
I633-7I7
+ 0.706
1634.423
37
Dec. 5 7.4
81.446
.658
82.104
33465
0.894
34-359
'38
6 9.1
81.366
743
82.109
33-418
I.OO2
34.420
39
15 9.6
81.765
SH
82.279
33748
0.692
34-44
40
'6 7-5
81.516
.741
82.257
33.484
I.OO4
34-488
4 1
17 8.1
1181.654
+ 0.458
II82.II2
1633.918
,+ 0.616
1634.534
42
88 Jan. 4 8.2
81.625
.498
82.123
33-74
.670
34.410
43
18 9.4
81.779
330
82.109
33.966
.458
34.424
44
27 7-8
81.921
341
82.262
33.892
465
34-357
45
Feb. 2 10.2
82.081
.049
82.130
33.255
.084
34-339
46
6 1 1.6
1181.894
+ 0.156
1182.050
1634.312
+ 0.235
I634-547
47
17 12.8
81.858
33
82.161
34-034
.426
34.460
48
Mar. i 10.7
81.632
.428
82.060
34.112
.610
34.722
49
8 8.5
81-933
154
82.087
34-444
237
34-68i
5o
14 9.1
81.984
.109
82.093
34415
075
34.490
5i
1 6 n.o
1181.671
+ 0.444
1182.115
1634.113
+ 0.625
1634-738
52
21 10.3
81.673
.424
82.097
34- I 34
.603
34-737
53
27 IO.2
81-593
444
82.037
33-904
.580
34.484
54
Apr. 3 10.8
81.370
570
81.940
33-708
797
34.505
55
6 12.3
81.632
484
82.116
33-8i3
673
34-486
56
ii 9.9
II8I.686
+ 0.373
1182.059
1634.140
+ 0.527
1634.667
57
14 9.8
81.555
577
82.132
33-751
.719
34-470
58
l8 II. 2
81.630
.404
82.034
33-86o
561
34-4 21
59
26 10.3
81.897
.277
82.174
34.060
387
34-447
60
30 10.8
81.720
.410
82.130
33.800
569
34-369
61
May 2 12.2
1181.673
+ 0.426
1182.099
1633.942
+ 0.433
i634-375
62
4 11.2
81.521
465
81.986
33.746
.645
34-39 1
63
8 11.5
81-553
.484
82.037
33.7 4
-675
34-379
64
10 13.0
81.753
.187
81.940
34.01 2
324
34-336
65
12 12. 1
81.754
370
82.124
33.869
.520
34.389
66
17 II. 4
1181.754
+ 0.405
1182.159
1633.980
0.563
I634-543
67
20 13.3
82.033
.099
82.132
34.229
.146
34-375
68
24 13-0
81.834
.292
82.126
34.H3
.421
34-534
69
25 12-5
81.776
.218
81.994
3 4 .028
.320
34.348
JO
28 I2.O
81.606
.424
82.030
33.863
.608
34-47 1
90
Relative . Parallax of Polaris and Star (c).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1888.
Measured
Distance of
Star (c) to
Polaris.
Sum of
Correc-
tions.
Concluded
Distance of
Star (c) from
Polaris.
Measured
Distance of
Star (d) to
Polaris.
Sum of
Correc-
tions.
Concluded
Distance of
Star (d) from
Polaris.
d. h.
//
n
//
//
H
|p
7 1
May 29 12.8
Il8l.8l3
4- 0.266
1182.079
1^33-993
+ 0-393
1634.386
72
31 13-3
81.913
.212
82.125
34-119
.326
34-445
73
June 7 1 1.0
81.678
.380
82.058
33.817
544
34.36i
74
10 11.4
81.695
.436
82.131
33.827
.624
34-451
75
14 12.3
81.894
.162
82.056
34-145
.261
34406
76
17 12.0
1181.683
+ 0-434
II82.II7
1633.739
+ 0.634
1634.373
77
22 II. 2
81.648
.456
82.104
33-704
.662
34'366
78
July i 11.3
81.623
.486
82.109
33-885
.510
34-395
79
3 n-9
81.637
499
82.136
33.613
-734
34-347
80
5 12-5
81.781
.462
82.243
33-585
.688
34-273
81
9 10.8
"8I.S79
4-0.489
1182.068
1634.077
+ 0.418
1634.495
82
12 11.4
81.856
.284
82.140
33.606
.718
34-324
83
17 io.(j
8l.5 9 2
Sii
82,103
33-526
755
34-281
84
20 11.5
81.597
.603
82.2OO
33.568
.889
34-457
85
23 12.2
81.539
.641
82.180
33.662
.742
34-404
86
26 II. I
1181.530
+ 0-579
1182.109
1634.051
+ 0.356
1634.407
TABLE VI.
Equations of Condition formed from the concluded distances
of Polaris from Star (c), as given in Table V.
No.
Date,
1887.
Equations of Condition.
Residuals.
d. h.
//
//
I
Jan. 31 7.5
-f-O.O34 = X 0.7880 TT 0.9168 dfJL
4- 0.074
2
Feb. i 8.5
+ .027 = x .7986 .9140
+ -079
3
8 8.7
+ .134 = x .8644 .8949
.031
4
15 8.1
+ .056 = x .9173 .8757
4- .049
5
July 31 i o.o
4- .137 = x 4- .7757 .4209
.040
6
Aug. i 11.4
+ 0.202 = X +0.7969 0.4154
0.024
7
3 H-7
4- .260 = x 4- .8065 .4127
.081
8
4 12.2
4- .232 = x 4- .8168 .4099
.052
9
8 11.6
f .157 = x + .8541 .3991
4- .024
10
25 12. i
4- .255 = x 4- .9690 .3525
.068
Equations of Condition: Polaris and Star (c). 91
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
n
//
II
87 Sept. 7 10.8
+ 0.240 = X + 1.0033 7T 0.3170 dp
0.053
12
8 II. 2
+ .081 = x + 1-0040 .3142
+ .106
13
12 II.S
+ .183 = x +1.0035 -3032
+ .004
H
I/ 12.2
+ .268 =s X +0.9963 .2897
.081
I B
22 9.9
+ .157 = x +0.9822 .2760
+ .028
16
24 9-5
+ 0.314 = x +0.9732 0.2705
0.129
17
28 10.8
+ .047 = x + .9552 .2595
+ .137
18
Oct. 10 1 1. 1
+ .244 = x + .8720 .2266
.066
J 9
II IO.O
+ .153 = x + .8636 .2240
+ .025
20
12 9.8
+ .234 = X + .8587 .2212
.056
21
13 II. I
+ 0.221 = X +0.8451 0.2184
0.044
22
14 9.0
+ .254 = x + .8364 .2157
.078
23
15 9-5
+ .299 = x + .8264 .2131
.123
2 4
17 10.3
+ .113 = x + .8061 .2075
+ .062
25
19 10.4
+ .037 = X + .7851 .2021
+ -136
26
20 9.8
+ O.I63 = # + 0-7743 0-1993
+ 0.009
27
21 I2.O
+ .116 = x + .7621 .1966
+ .056
28
24 1 1-3
+ .036 = x + .7278 .1883
+ .134
2 9
28 8.6
+ .234 = x + .6797 ,1774
- .067
3
Nov. i 8.2
+ .136 = x + .6273 .1667
+ .029
3*
4 9-3
+ 0.228 = x +0.5851 0.1584
0.065
32
14 9.6
+ .201 = X + .4356 .1310
.047
33
*5 7-9
+ .171 = x + .4211 .1284
.018
34
23 9-
+ .066 = x + .2901 .1064
+ .079
35
29 9-3
+ .080 = x + .1885 .0899
+ -059
36
30 8.5
+ 0.103 = x +0.1748 0.0873
+ 0.036
37
Dec. 5 7.4
+ .104 = x + .0867 .0737
4- -031
38
6 9.1
+ .109 <=* x + .0677 .0708
+ .025
39
15 9.6
+ .279 = x .0893 .0462
-155
40
16 7.5
+ .257 = x .1052 .0436
-133
4 1
17 8.1
+ O.I 1 2 = X O.I23I O.O4O8
+ 0.01 1
42
88 Jan. 4 8.2
+ .123. = a? .4072 + .0092
.016
43
18 9.4
+ .109 = x .6292 + .0477
.015
44
27 7.8
+ .262 = x .7413 + .0721
.175
45
Feb. 2 10.2
+ .130 = x .8072 + .0888
.046
46
6 11.6
+ 0.050 = x 0.8457 +0.0999
+ 0.032
47
17 12.8
+ .161 = x .9294 + .1301
- .084
48
Mar. i 10.7
+ .060 = x .9829 + .1654
+ .013
49
8 8.5
+ .087 = x .9915 + .1844
.015
5
14 9.1
+ .093 = x .9870 + .2009
.021
92
Relative Parallax of Polaris and Star (c).
No.
Date,
1888.
Equations of Condition.
Residuals.
d. h.
//
//
51
Mar. 16 n.o
-f O.II5 * 0.982917 -fO.2065 J/M
0.044
52
21 10.3
-f- .097 = x .9683 + .2201
.025
53
27 10.2
+ .037 = x .9410 + .2366
+ .042
54
Apr. 3 10.8
.060 = x .8962 + .2557
+ .136
55
6 12.3
+ .116 = x .8728 -|- .2642
.039
56
11 9.9
-f- 0.059 x 0.8300 + 0.2776
+ O.O2O
57
14 9.8
+ .132 = x .8010 + .2858
.052
58
iS II. 2
+ .034 = x .7584 + .2970
+ .047
59
26 10.3
+ .174 = a? .6642 + .3187
- .08 7
60
30 10.8
-|- .130 = x .6119 + .3297
.0 4 I
61
May 2 1 2.2
+ 0.099 = * 0-5837 -H 0-3354
O.OO9
62
4 11.2
.014 = x .5568 + .3408
-h -105
63
8 11.5
+ -037 = x .4992 + -35 l6
+ -057
64
10 13.0
.060 - x .4686 + .3574
-f -156
6 S
12 12. 1
+ .124 = x .4391 4- .3628
.027
66
17 11.4
4-0.159 = x 0.3622 4-0.3762
0.048
67
20 13.3
4- .132 = x .3131 + .3848
.029
68
24 13-0
4- .126 - x .2472 4- .3958
.020
69
25 12-5
.006 = x .2324 4- .3984
+ ."3
70
28 I2.O
4. .030 =* x .1664 4- .4066
+ .080
7i
29 12.8
4-0.079 = x 0.1493 +0.4094
+ 0.032
72
31 13-3
+ .125 = x .1321 + .4149
.013
73
June 7 n.o
+ .058 = x .0159 + .4338
+ .059
74
10 11.4
+ .131 = x + .0351 + .4421
.Oil
75
14 12-3
+ .056 = x + .1034 + .4532
+ .067
76
17 12.0
+ 0.117 = x +0.1534 +0.4614
+ 0.009
77
22 II. 2
+ .104 = x + .2357 + -4750
+ .026
78
July i 11.3
+ .109 = x + .3804 + .4996
+ .028
79
3 11.9
+ .136 x + .4119 + .5051
+ .002
80
5 12-5
+ .243 = x + .4429 + .5107
.103
81
9 10.8
+ 0.068 = x +0.5014 +0.5215
+ 0.074
82
12 II.4
+ .140 = x + .5450 + .5297
+ .004
83
17 ro.6
+ .103 = x + .6136 + .5434
+ -45
84
20 11.5
+ .200 = X + .6537 + .5516
.050
85
23 12.2
+ .180 = x + .6917 + .5599
.029
86
26 II. I
+ 0.109 = x +0.7273 +0.5681
+ 0.044
Equations of Condition: Polaris and Star (d).
93
Treating these equations in the usual method, the following normal
equations result :
+ 11.336= + 86.0000 # + 3.6042 d /A + 6.447677
0.062= + 3.6042 +11.6258 5.0828
+ 3-73= +6.4476 5.0828 +41.0127
whence, by solution, are obtained the values of the unknowns, viz.
#= +0.128
dfji = 0.0224
it- +0.0521.
It further appears that the probable error of one complete measure of
distance is +0^.070, and that the probable error of the determination
of TT is + o".oii4.
TABLE VII
Equations of Condition formed from the concluded distances of
Polaris from Star (d), as given in Table V.
No.
Date,
1887.
Equations of Condition.
Residuals.
d. h.
//
//
I
Jan. 31 7.5
+ 0.288 = X +0.8173 7T 0.9168 dfA
+ 0.092
2
Feb. i 8.5
+ .405 = x + .8272 .9140
.025
3
8 8.7
+ .312 = x + .8872 .8949
+ -072
4
15 8.1
+ -337 = * + .9339 ~ - 8 757
+ -051
5
July 31 i o.o
+ .162 = x .8085 .4209
+ .020
6
Aug. i 11.4
+ 0.203 = x 0.8283 0.4154
0.024
7
3 ".7
+ .198 = x .8371 .4127
.022
8
4 12.2
+ .068 = x .8466 .4099
+ -107
9
8 11.6
+ .000 = x .8808 .399 1
+ .171
10
25 12. i
+ .010 = x 0.9809 .3525
+ -MS
ii
Sept. 7 10.8
+ 0.291 = x 1.0030 0.3170
0.137
12
8 II. 2
+ .120 = x 1.0027 -3H 2
+ -033
13
12 11.5
+ .018 = x 0.9984 .3032
+ -135
14
17 12.2
+ .222 = X .9865 -2897
.070
15
22 9.9
+ .132 = x .9680 .2760
+ .021
16
24 9-5
0.043 = x 0-9587 0.2705
+ 0.197
17
28 10.8
+ .189 = x .9358 .2595
-034
18
Oct. 10 1 1. 1
+ .122 = X .8426 .2266
+ .041
'9
II 10.0
+ .161 = x .8333 .2240
+ .002
20
12 9.8
+ .076 = X .8236 .2212
+ .088
' Relative Parallax of Polaris and Star (d).
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
21
87 Oct. 13 ii. i
4-0-335 = X 0.8134 IT 0.2184^/H
O.I7O
22
14 9.0
+ .125 = x .8039 .2157
+ -041
23
J5 9-5
+ .284 = x .7930 .2131
.118
24
17 10.3
+ .058 = x .7713 .2075
+ .110
25
19 10.4
+ .328 = X .7489 .2021
- .158
26
20 9.8
+ 0.060 = x 0.7376 0.1993
+ O.III
27
21 12.0
+ .145 - x .7244 .1966
+ .028
28
24 II.3
+ .215 = x .6883 .1883
.040
2 9
28 8.6
+ .220 = X .6378 .1774
.040
3<>
Nov. i 8.2
+ .378 - * .5830 ~ -1667 "
.193
31
4 9-3
+ 0.284 = 3 0.5393 0.1584
0.096
32
14 9.6
+ .241 = x .3856 .1310
.040
33
IS 7-9
+ .276 = x .3707 .1284
.074
34
23 9-
+ .216 = x .2375 .1064
+ .002
35
29 9-3
+ .127 = * .1350 .0899
+ .096
36
30 8.5
+ 0.223 = x 0.1182 0.0873
+ 0.001
37
Dec. 5 7.4
+ .159 = x .0325 .0737
4- -073
38
6 9.1
+ .220 = x .0137 .0708
+ .016
39
15 9-6
+ .240 = x + .1426 .0462
+ -007
40
16 7-5
+ .288 = a? + .1584 .0436
.039
,41
17 8.1
+ 0.334 = x +0.1760 0.0408
0.084
.42
88 Jan. 4 8.2
+ .210 = X + .4547 + .0092
+ .065
43
1 8 9.4
+ .224 -= x + .6683 + .0477
+ .069
44
27 7-8
+ .157 = x + .7738 + .0721
4- -145
45
Feb. 2 10.2
+ .139 = X + .8352 + .0888
+ .168
46
6 1 1.6
+ 0.347 = +0.8706 +0.0999
0.037
47
17 12.8
+ .260 = x + .9443 + .1301
+ .054
48
Mar. i 10.7
+ .522 = x + .9856 + .1654
.205
49
8 8.5
+ .481 = x + .9877 + .1844
- .165
50
14 9.1
+ .290 = x + .9772 + .2009
+ .023
Si
16 ii. o
+ 0.538 = x +0.9714 +0.2065
0.226
52
21 10-3
4- -537 = x + .9521 + .2201
.228
53
27 10.2
+ .284 = x + .9196 + .2366
+ .020
54
Apr. 3 10.8
+ .305 = X + .8690 + .2557
.006
55
6 12.3
+ .286 = x + .8428 + .2642
+ .009
56
ii 9.9
+ 0.467 = x +0.7963 +0.2776
0.177
.57
14 9-8
+ .270 = x + .7651 + .2858
+ .016
58
18 n. 2
+ .221 = X + .7196 + ,2970
4- -059
59
26 10.3
+ .247 = x + .6204 + .3187
+ .021
60
30 10.8
+ .169 = x + .5660 + .3297
+ .094
Equations of Condition: Polaris and Star (d), 95;
No.
Date,
1888.
Equations of Condition.
Residuals.
d. h.
//
//
61
May 2 12.2
+ 0.175 = x -{-0.536977 -f 0.3354 d\L
+ 0.084
62
4 ii. 2
+ .191 = x + .5089 + .3408
+ .065
63
8 11.5
+ .179 = x + .4494 + .3516
+ .070
64
10 13.0
+ .136 = x + .4182 + .3574
+ .110
65
12 12. 1
+ .189 = x + .3878 + .3628
+ -054
66
17 II. 4
+ 0.343 = # +0.3092 +0.3762
0.109
67
20 13.3
+ .175 = x + -2593 + -3848
+ -053
68
24 13.0
+ -334 = a? + -I937 + -39S 8
-"4
69
25 12.5
+ .148 = x + .1776 + .3984
+ ..074
70
28 12.0
+ .271 = x + .in i + .4066
.060
7i
29 12.8
+ 0.1 86 = x +0.0939 +0.4094
+ 0.023
72
31 13-3
+ .225 = x + .0766 + .4149
.017
73
June 7 n.o
+ .161 = x .0397 + .4338
+ -033
74
10 11.4
+ .251 = x .0905 + .4421
.062
75
14 12.3
+ .206 = x .1583 + .4532
-025
76
17 12.0
+ 0.173 = x 0.2078 +0.4614
+ 0.002
77
22 II. 2
+ .166 = x .2889 + .4750
.OOO
78
July i 11.3
+ .195 = x .4306 + .4996
~ -045
79
3 n-9
+ .147 = x .4615 + .5051
.000
80
5 12.5
+ .073 = x .4914 + .5107
+ .071
81
9 10.8
+ 0.295 = x 0.5480 +0.5215
0.158
82
12 11.4
+ .124 = x .5899 + .5297
+ .008
83
17 10.6
+ .081 = x .6557 + .5434
+ .043
84
20 11.5
+ .257 = x .6939 + .5516
- .136
85
23 12.2
+ .204 = x .7298 + .5599
.088
86
26 II. I
+ 0.207 = x 0.7633 +0.5681
0.094
Treating- these equations in the usual method, the following normal
equations result :
//
+ 19.083= +86.00000+ 3.6o426?/x 4.333211
+ 1.056= + 3.6042 +11.6258 +10.8332
+ 2.235= - 4-3333 +10.8332 +40.3528
whence, by solution, are obtained the values of the unknowns, viz.
//
x = +0.230
dfjL= -0.0735
TT = +0.0998.
It further appears that the probable error of one complete measure of
distance is o".O95, and that the probable error of the determination of TT is
96
Collected Results for Parallax of Polaris.
The collected results for the Parallax of Polaris, gathered from the preceding
pages, are as follows :
Star's Name.
Mag.
Relative
Annual
Parallax.
Probable
Error of
Parallax.
Probable Error
of one Com-
plete Measure
of Distance.
D.M.+ 88 , No. 2
8.2
+ O.0837
//
0.0232
//
0.109
,,+88 9
8-3
+ O.0780
+ 0.0169
0.084
.. +88 4
6.8
+ O.0521
0.0114
0.070
+88 t. 10
9.8
+ 0.0998
0.0175
0.095
The difference of the above parallax, relatively to the stars D.M. + 88,
Nos. 4 arid 10, is so considerable, and so much greater than their probable
errors, that it will be worth while to enquire, whether the relative parallaxes
of these two stars of comparison cannot be effectually determined from
independent measurements. It will be seen that a similar remark applies in
the case of a Cephei. This practical enquiry must, however, be deferred to
some early but convenient opportunity.
II.
Parallax of Stars of the Second Magnitude, derived from
observations at selected critical epochs.
The time and labour necessarily expended on obtaining- the foregoing 1
results, although probably less than would be required by the application of
the Heliometer, are, nevertheless, so considerable, that the thought naturally
suggested itself, whether there might not exist some possible modification,
whereby the labour could be curtailed, without sensibly impairing the accuracy
of the final determination, estimated by its applicability to cosmical enquiries.
Accordingly, a selection was made of those observations of 61 Cygni, which
necessarily affect the computed amount of parallax in the most sensible degree.
Such observations are found on or about those nights, when the positions of
the earth are such as to produce the maximum difference of displacement of
the principal star in the direction of the star of comparison. Such positions
of the earth occur, for the stars (a or b) in reference to 61 Cygni, on or
about April 10 and October 10. Taking, then, the observations made during
the ten nights nearest to these dates, and treating these twenty results after
the same fashion as that adopted for the eighty-nine observations of the
whole year, the following results are obtained :
ir n
61 1 Cygni and star (a), TT = 0.3669 + 0.0264
61 2 Cygni TT = .4047+ -0238
61 1 Cygni and star (), TT = .3929+ .0319
61 2 Cygni TT = .47 J 3 -3 2 4
while for the whole eighty-nine the following values of TT have been found
(P- 63):-
// It
6 J i Cygni and star (a), TT = 0.4294+0.0163
6i 2 Cygni it = .4250+ .0176
61 1 Cygni and star (#), TT = .4414+ .0222
61 2 Cygni TT = -45 8 - Ol 9 l
Hence then it appears that the differential Parallax, with regard to the
stars of comparison, is virtually the same, whether determined from the greater
or fewer number of observations, and herein lies the justification of a curtail-
ment of the process on the lines suggested. It may further be remarked,
that while the limit of error of determination is about 0^.015, from observations
made consecutively throughout the year, the limit of error, possibly incurred
by this contracted method does not exceed 0^.03 ; an amount which appears to
be sufficiently small to warrant the adoption of the results in cosmical
enquiries, within the approximations at present available. Moreover, it is an
obvious advantage to have the means of rapidly increasing the number of
98 Parallaxes of Stars derived
stars whose parallax is sought ; the curtailment in question also has practically
received the approval of astronomers of great experience.
This contracted method, however, is not necessarily restricted to operations
connected with the photographic method, but it applies equally to the Helio-
metric process, or in fact to any other micrometrical practice : nor is it to be
regarded as the same as that so ably applied by Dr. Ball in his parallactic
investigations, made at Dunsink in 1876-8. In the case of the Dunsink
investigations, it would appear that while the number of nights devoted to the
examination of a single star is possibly sufficient to detect a parallax of ap-
proximately a second of arc, still, as a matter of fact, no such large parallaxes
were sifted out in the process, and in all probability no such contiguities, as
that implied by a parallax of a second of arc, exist in the sidereal system :
hence, the meshes of such an astronomical sieve appear too coarse for the object
intended. Independently of this coarseness of the astronomical meshes, there
is the further difference between the two processes, that the photographic
method admits the employment of a very much wider telescopic field than is
the case with an ordinary telescope, and it is thus possible to select stars of
comparison much more suitably situated for the determination of parallax,
than is the case with other telescopes, armed with an ordinary micrometer.
Moreover, the stars of comparison themselves may be selected from a much
wider range of magnitudes than is the case with object-glasses in general.
On the other hand, the curtailed method described by Dr. Gill, wherein he
proposes to confine the observations to a couple of nights, repeated at proper
intervals during two years, is more delicate than that last described, and may,
on trial, prove sufficiently so to rapidly furnish, on a large scale, parallaxes
accurate enough to afford an approximate notion of the cosmical distribution
of stars.
The recent proposition to take photographs at critical epochs, and after
retaining them in an undeveloped state, to re-expose them after intervals of six
months, seems to me to be well worth a trial, and though attended by risk
and difficulty, I propose to try it on a small scale.
Very recently, and while writing these remarks, the attention of astro-
nomers has been called to a very remarkable and valuable contribution,
emanating from the observatory at Pulkova, towards a practical improvement
in the method of obtaining stellar parallaxes of an absolute character, from
observations made on the meridian at properly selected epochs. If the
character of meridional observation be of the highest order of reliability, then it
is not too much to say that in the case of many stars, suitably situated, every
year's observation of R.A. must implicitly contain the effects of parallax, and in
most cases may permit their determination. If this be so, the data for deriving
an approximate notion of the arrangement of stars in space, already exist in the
annals of our great observatories ; and in any case we have here, from the work
of Drs. Wagner and Belopolsky, an indication of the expectations that may
be derived from improvements in meridional instruments and meridional
methods. Dr. Belopolsky's determination of the absolute parallax of 61 Cygni
as derived from eight years' consecutive transit observations at Pulkova is o".5o.
from Observations at Critical Epochs.
99
Before proceeding 1 to give the details of this curtailed method, as applied
to a Cassiopeiae and other stars of the second magnitude, it may be well here
to make a remark which more properly belongs to page 5 of the Introduction.
It is to the effect that the average amount of correction here required for the
measures of distances, owing to variations in the film, in the .focal length of
the mirror, and other causes, known and unknown, is (from a partial enquiry)
o".i6 for i coo", whereas in the case of the Cape Heliometer it appears to be
o".io for the same distance : a result probably due to the minute, but slightly
inconstant, variations of the film.
PARALLAX OF a CASSIOPEIA
Deduced from Observations at Critical Epochs.
The stars selected from comparison are
D.M. + 55, No. 14% ... Magnitude 8.7 ... Star a
D.M. + 55 , 138 ... 9.2 ... b
Anonymous ... ... 10.2 ... c
D.M. + 55 , No. 132 ...
9.3
The approximate position-angles and distances of these four stars are
Of It
for star a ... p = 96 30 ... 8=1042
b ... = 270 46 ... = 849
d ... = 234 44 ... = 1113
The accompanying figure is a diagram, showing the relative positions of
these stars with the form and position of the parallactic ellipse.
West
East
South,
100
Parallax of a Cassiopeia derived
The parallactic factors in the equations of condition have been computed
from the expressions
o /
Star a ... ds = J2 [9.94968] cos(O 273 3 1 )
b ... ds = 72 [9.96190] cos (O 98 37)
c ... ds = R [9-99957] c s (O-39 )
d ... ds = -#[9.99998] cos (O 126 27)
The proper motion of a Cassiopeise, after consulting various authorities, has
been assumed
in R.A. +o s .oo68
in Decl n . o".
These preliminary facts will, with the information already afforded, permit
the subsequent tables to be easily followed.
TABLE I.
Measures of the diagonal distances of Star (a) from Star (b), and
of Star (c) from Star (d),for the determination, at the times
of exposure of the correction to their measured distances from
a Cassiopeia.
No. for
Refer-
ence.
Date of
Exposure of
Plate.
1887-8.
Measured
Distance
of (a) to (6)
in Arc.
Corrections
for Refrac-
tion and
Aberration.
Difference
from
Assumed
Mean.
1889". 50.
Measured
Distance
of (c) to (d)
in Arc.
Corrections
for Refrac-
tion and
Aberration.
Difference
from
Assumed
Mean.
1779".90.
d. h.
//
//
H
//
//
//
I
87 Dec. 16 5.0
1888.723
4-0. 4 7 4
+ 0.303
1779.441
+ 0-439
+ 0.020
2
J7 6-3
89.339
435
-274
79-749
.413
.262
3
23 5-2
89.190
.446
- .136
79.887
.416
403
4
27 5.6
89.503
.426
-429
79.717
403
.220
5
88 Jan. 3 5.4
89.581
.424
+ -505
79.197
.392
+ -311
6
29 6.9
1889.007
4-0.522
O.O29
I779-367
+ 0469
4- 0.064
7
Feb. i 6.1
88.848
479
+ -173
79-478
431
.009
8
3 6.3
88.271
505
+ 724
78.832
.442
4- .626
9
4 6.6
88.732
525
+ .243
78.909
.476
+ -515
10
10 6.7
89.236
.582
- .318
79.640
530
.270
ii
June 22 14.0
1888.734
+ -939
-0.173
1779.139
4-0.679
4- 0.082
12
30 13-9
88.369
.887
+ -244
79.042
683
+ -175
13
July 3 13.4
88.257
934
+ -309
78.617
.687
+ -596
4
5 13-4
88.852
.913
- .265
79-S25
.686
-3"
IJ
9 13-8
89.067
-839
- . 4 06
79-383
.681
- .164
from Observations at Selected Epochs.
101
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1888.
Measured
Distance
of (a) to (6)
in Arc.
Corrections
for Refrac-
tion and
Aberration.
Difference
from
Assumed
Mean.
1889". 50.
Measured
Distance
of (c) to (d)
in Arc.
Corrections
for Refrac-
tion and
Aberration.
Difference
from
Assumed
Mean.
1779".90.
d. h.
//
//
//
//
//
ft
16
Aug. a 12.8
1888.431
+ 0.792
+ 0.277
I 779-'39
+ 0.676
+ 0.085
i?
5 1.3-2
88.379
.740
+ -381
78.728
.662
+ -510
18
6 n.8
88.514
.861
+ -125
79.242
.690
.032
'9
7 I2 -7
88.758
.771
.029
79.083
.671
+ .146
20
8 12.9
88.932
737
.169
79.520
66 S
- .285
21
Dec. 13 6.9
1888.659
+ 0.436
+ 0.405
1779.113
+ 0.415
+ 0.372
22
18 7.2
88.789
433
+ .278
79.401
403
+ .096
23
22 5.8
89.452
431
- .383
80.017
.408
.525
24
26 6.2
89.152
.422
-074
79.886
.398
- .384
2 5
28 7-2
88.817
433
+ .250
79.092
43
+ 4S
NOTES.
No. 2. Images diffused : clouds passing at intervals.
No. 4. One of the plates rejected on account of discordant measures.
No. 7. The images elongated.
No. 9. A plate rejected on account of injury to film.
No. ii. The exposure was continued for ten minutes on account of haze.
No. 13. Clouds passing : the exposures sometimes interrupted.
No. 19. The sky very variable from passing clouds : the images large and diffused.
No. 21. A plate rejected owing to large discordant measures : no cause could be detected.
No. 25. Sky foggy. Exposure continued for ten minutes.
TABLE II.
Concluded measures of a Cassiopeice from the comparison
Stars (a) and (b).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887-8.
Measured
Distance of
Star (a) to
a. Cassiopeiae.
Sum of
Corrections.
Concluded
Distance
of Star (a).
Measured
Distance of
Star (b) to
a Cassio-
peia}.
Sum of
Corrections.
Concluded
Distance
of Star (b).
I
d. h.
87 Dec. 1 6 5.0
it
1042.311
//
+ 0431
n
1042.742
//
848.906
H
+ 0-357
it
849.263
2
17 6 -3
42.551
+ -085
42.636
49.318
+ .074
49-392
3
23 5-2
42.645
+ .169
42.814
49.107
+ -HO
49.247
4
27 5-6
42.779
.004
42.775
494 J 3
.002
49.411
5
88 Jan. 3 5.4
42.113
+ -SO?
42.620
48.771
+ .412
49.183
102
Concluded Parallax of a Cassiopeia derived
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1888.
Measured
Distance of
Star (a) to
a Cassiopeise.
Sum of
Corrections.
Concluded
Distance
of Htar (a).
Measured
Distance of
Star (b) to
a Cassio-
peiae.
Sum of
Corrections.
Concluded
Distance
of Star (b).
d. h.
//
//
//
it
//
n
6
Jan. 29 6.9
1042.505
+ 0.274
1042.779
849.015
+ 0.217
849.232
7
Feb. i 6.1
42.430
.363
42.793
48.986
.288
49.274
8
3 6.3
41.919
.678
42-597
48.869
542
49.411
9
4 6.6
42.354
.288
42.642
49.001
341
49-342
10
10 6.7
42.642
143
42.785
49.060
.109
49.169
ii
June 22 14.0
1042.348
+ 0-455
1042.803
849.040
+ 0.313
849-353
12
30 13-9
42.047
.658
42.705
49.005
475
49.480
13
July 3 13.4
41.916
.7 2 3
42.639
49- OI 3
.526
49-539
H
5 13-4
42.311
392
42.703
49.004
356
49.360
IS
9 13-8
42.367
.271
42-638
49.129
.163
49.292
16
Aug. 2 12.8
1041.967
+ 0.626
1042.593
848.934
+ 0.445
849-379
! 7
5 '3-2
42.068
.653
42.721
48958
470
49.428
18
6 1 1.8
42.079
.583
42.662
49.049
.406
49-455
19
7 12.7
42.197
.446
42-643
49.041
.299
49.340
20
8 12.9
42.157
358
42.515
49.204
.225
49.429
21
Dec. 13 6.9
1042.251
+ 0.524
1042.775
849.132
+ 0-334
849.466
22
18 7.2
42.159
452
42.6ll
48.974
.265
49- 2 39
23
22 5.8
42.839
.087
42.926
49.262
035
49.297
24
26 6.2
42.452
.256
42.708
49- 2 43
.099
49-34 2
25
28 7-2
42.211
439
42.650
49- '57
247
49.404
TABLE III.
Equations of Condition formed from the concluded distances
of a Cassiopeia from Star (a), as given in Table II.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
I
87 Dec. 16 5.0
+ 0.242 = X + 0.8656 7T 0.0439 dfJi
O.OIO
2
17 6.3
+ .136 = x + .8678 .0411
+ -094
3
23 5-2
+ .314 = x + .8756 .0248
.081
4
27 5.6
+ .275 = x + .8752 .0138
- .043
5
88 Jan. 3 5.4
+ .120 = x + .8642 + .0061
+ .III
from Observations of Selected Epochs.
103
No.
Date,
1888.
Equations of Condition.
Residuals.
d. h.
//
//
6
Jan. 29 6.9
-f-O.279 = X + O.7II2 7T + O.O775 d[*>
0.054
7
Feb. I 6.1
+ .293 = x + .6834. + .0856
.070
8
3 6.3
+ .097 = x + .6636 + .0911
+ -125
9
4 6.6
+ .142 = tf + .6533 + .0939
+ .080
10
10 6.7
+ .285 = x + .5883 + .1103
- .065
ii
June 22 14.0
+ 0.303 = a? 0.9049 +0.4725
0.140
12
30 13-9
+ .205 = x .9005 + .4917
.042
13
July 3 134
+ .139 = x .8946 + .5026
+ -023
M
5 '34
+ .203 = x .8894 ' + .5081
.041
is
9 13-8
+ .138 = x .8762 -f .5191
+ .024
16
Aug. 2 12.8
+ 0.093 = x 0.7164 +0.5847
+ 0.074
i7
5 13-2
+ .221 = X .6858 + .5929
-053
18
6 n.8
+ .162 = x .6781 + .5956
+ .006
19
7 !2-7
+ .143 = x .6676 + .5984
+ -025
20
8 12.9
+ .015 = x -6571 + .6011
+ .153
21
Dec. 1 3 6.9
+ 0.275 = x +0.8596 +0.9481
0.062
22
18 7.2
+ .in = x + .8710 + .9618
+ .102
2 3
22 5 .8
+ .426 = x + .8752 + .9728
.214
2 4
26 6.2
+ .208 = x + .8754 + .9837
+ .004
25
28 7.2
+ .150 = x + .8736 + .9892
+ .062
Treating these equations in the usual method, the following normal
equations result :
n
+ 4.975 = +25.0000 x + 10.6632 dju+ 4.1324:1
+ 2.0066= +10.6632 + 7.7764 + 0.1772
+ 1.3711= + 4.1334 + 0.1772 +16.0705
whence, by solution, are obtained the values of the unknowns, viz.
H
X +0.202
dfM = 0.019
TT= +0.0337.
It further appears that the probable error of one complete measure of
distance is + 0^.09 1, and that the probable error of 77 is +o".O238.
104 Concluded Parallax of a Cassiopeia from Star (b).
TABLE IV.
Equations of Condition formed from the measures of a Cassiopeia
and Star (b), as given in Table II.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
I
87 Dec. 1 6 5.0
-|-O.l63 = X 0.8738 7T O.O439 dfJL
0.003
2
17 6.3
+ .292 = x .8778 .0411
.132
3
23 5-2
+ .147 = x .8943 .0248
+ .014
4
27 5-6
+ .311 = x .8995 .0138
.149
5
88 Jan. 3 5.4
. + .083 = x .8983 + .0061
+ .081
6
29 6.9
+ 0.132 = x 0.7755 +0.0775
+ 0.044
7
Feb. i 6. i
+ .174 = x .7506 + .0856
+ -004
8
3 6.3
-|- .311 = x .7325 + .0911
.132
9
4 6.6
+ .242 = x .7229 + .0939
.063
10
10 6.7
+ .069 = x .6624 + .1103
+ .114
ii
June 22 14.0
+ 0.253 = x +0.9249 +0.4725
+ 0.033
12
30 13-9
+ .380 = x + .9311 + .4917
.091
13
July 3 13.4
+ .439 x + .9292 + .5026
.150
4
5 J3-4
+ .260 = x + .9266 + .5081
+ .029
'5
9 13-8
+ .192 = x + .9183 + .5191
+ .0 9 8
16
Aug. 2 12.8
+ 0.279 = x +0.7844 +0.5847
+ 0.013
17
5 13-2
+ .328 = x + .7579 + .5929
.036
18
6 1 1.8
+ -355 = * + .7492 + .5956
-063
19
7 12.7
+ .240 - x + .7377 + .5984
4- -052
20
8 12.9
+ .329 = x + .7296 + .6011
.038
21
Dec. 13 6.9
+ 0.366 = x 0.8647 +0.9481
O.IO2
22
18 7.2
+ .139 = x .8837 + .9618
+ -125
23
22 5.8
+ .197 = x .8935 + .9728
+ .068
2 4
26 6.2
+ .242 = x .8993 + .9837
+ .024
25
28 7.2
+ .304 = x .9005 + .9892
-037
Treating 1 these equations in the usual method, the following normal
equations result :
//
+ 5.9210= +25.0000 #+10.6632^ 4.140417
+ 2 -9373 = + 10.6632 + 7.7764 + 0.0004
0.1093= 4 I 44 4- 0.0004 +17.6742
whence, by solution, are obtained the values of the unknowns, viz.
//
x = +0.199
d[i = +0.105
TT= +0.0403.
It further appears that the probable error of one complete measure of
distance is o".o87, and that the probable error of TT is +o".oi98.
PARALLAX OF a CASSIOPEIA RELATIVELY TO STARS (C) AND (D).
TABLE V.
Concluded measures of a Cassiopeia from the comparison
Stars (c) and (d).
tfo. for
Refer-
ence.
Date of
Exposure
of Plate. |
.1887-8.
Measured
Distance of
Star (c) from
x Cassiopeiae.
Sum of
Corrections.
Concluded
Distance of
Star (c) from
* Cassiopeise.
Measured
Distance of
Star (d) from
a Cassiopeise.
'Sum of
Corrections.
Concluded
Distance of
Star (d) from
a Cassiopeiae.
d. h.
//
//
//
//
n
n
I
87 Dec. 1 6 5.0
667.333
+ 0.170
667.503
1112.850
+ 0.289
II13.I39
2
17 6.3
7-275
.055
7--330
13.177
.095
13.272
3
23 5-2
7.206
.005
7,211
13.176
.Oil
13.187
4
27 5.6
7.326
.067
7-393
13.241
.114
13.355
5
88 Jan. 3 5.4
7.162
.264
7,426
12.862
.441
I3-303
6
29 6.9
666.899
+ 0.198
667.097
1112.894
+ 0.338
1113.232
7
Feb. i 6.1
7.168
.l6l
7-329
13.110
257
I3-367
8
3 6.3
6.790
.403
7.193
12.443
.671
13.114
9
4 6.6
6.883
.372
7.-23S
12-573
.620
I3-I93
10
10 6.7
6-333
.098
7--43I
12.241
.164
13.405
ii
June 22 14.0
666.996
+ 0.291
667.287
1112.894
+ 0.468
1113.362
12
30 13-9
6.804
.328
7-132
12.885
529
I3-4I4
13
July 3 13.4
6.808
.487
7.295
12.564
.678
13.242
H
5 I 3-4
7.226
.147
7.373
13-163
.227
13-39
IS
9 13-8
6.946
.203
7-149
12.889
.319
13.208
16
Aug. 2 12.8
666.931
+ 0.296
667.227
1112.904
+ 0.466
I"3-37
17
5 13-3
6-934
.449
7-383
12.462
.721
13.183
18
6 1 1.8
6.951
-255
7.206
12.821
.401
13.222
*9
7 12-7
6.830
317
7.I47
12.926
.501
I3.4 2 7
20
8 12.9
7.038
153
7.191
I3.225
.225
I3-450
21
Dec. 13 6.9
666.962
f 0.313
667.275
1112.891
4- 0-473
1113.364
22
18 7.2
7-137
+ .205
7-342
12-937
+ -293
13.230
23
22 5.8
7.252
.025
7.227
.13.274
-095
13.179
2 4
26 6.2
7.370
+ .023
7-393
13.166
.013
13.153
2 5
28 7.2
6.967
+ .319
7.286
12.885
+ .484
I3-369
100 Concluded Parallax of a Cassiopeia from Star (c).
TABLE VI.
Equations of Condition formed from the concluded distances of
a Cassiopeia from Star (c), as given in Table F.
No.
Date,
1887-8.
Equations of Condition.
Kesiduals.
<
d. h.
n
//
I
87 Dec. 16 5.0
+ 0.503 = X +0.701 ITT 0.0439 rf/X
0.191
2
17 6.3
t -33o = a? + -7 I 37 -4"
.018
3
23 5-2
.211 = X -\- .7809 .0248
+ -103
4
27 5.6
393 = * + .8213 .0138
.078
S
88 Jan. 3 5.4
.426 = x + .8819 + .0061
.109
6
29 6.9
+ 0.097 = a? +0.9842 +0.0775
+ 0.223
7
Feb. i 6.1
.329 = x 4- .9828 + .0856
.OIO
8
3 6.3
.193 = x + .9804 + .0911
+ .126
9
4 6.6
.255 = x + .9788 + .0939
+ .063
10
10 6.7
.431 = x + .9627 + .1103
.113
it
June 22 14.0
+ 0.287 = a? 0.8108 +0.4725
0.036
12
30 13-9
.132 -= x .8851 + .4917
+ .Ii6
'3
Jiy 3 13-4
.295 = a? .9087 + .5026
.048
H
5 13-4
373 = * - .9234 + -5081
.128
'5
9 13.8
.149 = a? 0.9495 + .5191
+ -095
16
Aug. 2 12.8
+ 0.227 = a? 1.0128 +0.5847
+ 0.015
17
5 13-2
.383 *= x 1.0095 + -59 2 9
.142
18
6 1 1.8
.206 = x 1.0077 + -5956
+ -035
19
7 12.7
.147 = x - 1.0056 + .5984
+ -095
20
8 12.9
.191 = x 1.0032 + .6011
+ -051
21
Dec. 13 6.9
+ 0.275 t= a? +0.6738 +0.9481
+ 0.017
22
18 7.2
.342 = x + .7347 + .9618
.048
23
23 5.8
.227 = x 4- .7784 -f .9728
+ .069
2 4
26 6.2
393 # + -8190 + .9837
-97
25
28 7.2
.286 = x + .8383 + .9892
+ .Oil
Treating- these equations in the usual method, the following normal
equations result :
//
+ 7.0880= +25.0000 X +10. 6652 d/X+ 3.1 157 7T
+ 3.8748= +10.6632 + 77764 I.I329
+ 1.5984=+ 3.II57 - I.I329 +19.9150
whence, by solution, are obtained the values of the unknowns, viz.
//
x = +0.287
dp = 0.019
TT = + O.0343.
It further appears that the probable error of one complete measure of
distance is + o". J 04, and that the probable error of the determination of TT is
+ o".0247.
Concluded Parallax of a Cassiopeia from Star (d). 107
TABLE VII.
Equations of Condition formed from the concluded distances of
a Cassiopeia from Star (d), as given in Table V.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
I
87 Dec. 16 5.0
-j- 0.039 = x 0.7316 TT 0.0439 d IJL
+ O.II5
2
17 6.3
.172 = x .7435 -0411
.017
3
23 5-2
.087 = x .8074 .0248
+ .066
4
27 5.6
.255 = x .8451 .0138
.104
S
88 Jan. 3 5.4
.203 = x .9009 + .0061
.054
6
29 6.9
+ 0.132 = x 0.9838 +0.0775
+ 0.015
7
Feb. i 6.1
.267 = x .9804 + .0856
.120
8
3 6.3
.014 = x .9763 + .0911
+ -133
9
4 6.6
.093 = x .9739 + .0939
+ -055
10
10 6.7
.305 = x .9533 + .1103
~ ^57
ii
June 22 14.0
+ 0.262 = x +0.8379 +0.4725
-0.045
12
30 i3-9
.314 = x + .9072 + .4917
-95
13
July 3 13-4
.142 = x + .9287 + .5026
+ .078
*4
5 !3-4
.290 = x + .9421 + .5081
.070
15
9 13-8
.108 = x +0.9654 + .5191
+ .US
16
Aug. 2 12.8
+ 0.270 = x +I.OHI +0.5847
0.046
*7
5 !3-2
.083 = x + 1.0055 + -5929
+ -HO
18
6 n.8
.122 = X +1.0030 + .5956
+ .101
19
7 12.7
.327 = X +1.0002 + .5984
.104
20
8 12.9
.350 = x + 1.9970 + .6011
- .127
21
Dec. 13 6.9
+ 0.264 = x 0.7055 +0.9481
0.097
22
18 7.2
.130 = x .7635 + .9618
+ .036
23
22 5.8
.079 = x .8048 + .9728
+ .086
24
26 6.2
.053 = x .8429 + .9837
+ .110
25
28 7.2
.269 = x .8608 + .9892
.106
Treating these equations in the usual method, the following normal
equations result:
//
+ 45300= + 25.0000 x+ 10.6633^ 3.275671
+ 2.0715= +10.6632 + 7.7764 + 1.0536
+ 0.1394=- 3.2756 + 1.0536 +20.4262
whence, by solution, are obtained the values of the unknowns, viz.
//
x +0.181
dp = +0.012
TT = +0.0352.
It further appears that the probable error of one complete measure of
distance is +o // .iO2, and that the probable error of the determination of n is
108 . Collected Results for the Parallax of a Cassiopeia.
The collected results for the parallax of a Cassiopeise gathered from the
preceding 1 pages, are as follows :
Star's Name.
Mag.
Relative
Annual
Parallax.
Probable
Error of
Parallax.
Probable Error
of one Com-
plete Measure
of Distance.
D.M. 55, No. 142
55. No. 128
8.7
9.2
JO 2
//
+ 0.0337
+ 0.0403
-f- O.0343
//
+ 0.0238
0.0198
~t~ O O2A7
tt
0.091
0.087
~t~ o 104
D.M. 55, No. 132
9-3
+ 0.0352
0.0239
0.102
There is not, so far as I am aware, any determination of the parallax of
this star by any other astronomer. The results here presented seem to be in
accordance with the hypothesis that the stars of comparison are in the same
group with each other and the principal star, a Cassiopeise.
PA&ALIAX OF ft CASSIOPEIA
Deduced from Observations at Critical Epochs.
The stars selected for the determination of the relative parallax of /3 Cassio-
peise are
D.M. + 5 8, No. I , ... Magnitude 9 . 2 ... Star a
D.M. + 58,No. 10, ... 9.1 ... b
D.M. + 58,No. 8, ... 8.3 ... c
D.M. + 58, No. 2700, ... 9.2 ... d.
The approximate position-angles and distances of these four stars, are
Of It
for star (a) ... p = 399 47 ... *= 440
W = i53 3 = 13^
(c) ... = 37 20 ... = 664
(d) ... = 229 56 ... = 1475.
The accompanying figure is a diagram showing the relative position of
these stars, with the form and position of the parallactic ellipse.
West
} East
South
The parallactic factors in the equations of condition have been computed
from the expressions-
Star (a) ... ds = R [9-90879] cos (Q - 59 29)
(b) ... ds = E [9.89878] cos (0-197 7)
(c) ... ^ = 72 [9.98634] cos (O-3^ 2)
(d) ... from
Assumed
- Mean.
1688".90.
Measured
Distance
of (c) to (d)
in Arc.
Correction
for Refrac-
tion and
Aberration.
Difference
from
Assumed
Mean.
2102".80.
d. h^ '
//
//
n
H
//
//
I
87 Oct. 22 10.3
1687.872
+ 0.517
+ 0-5II
2101.855
+ 0.600
+ 0-345
2
24 10.8
88.505
.518
.123
02.464
593
- 2 57
3
25 10.2
88.771
5"
- .382'
02.830
-591
- .621
4
Nov. 14 9.8
88.508
.488
.096
02.228
553
+ -019
5
15 10.5
87:895
0.491
+ .5H'
01.506
570
+ .724
6
88 Jan. 26 6.7
1686.297
+ 2.274
+ 0.329
2102.043
+ 0.624
+ 0.133
7
28 6.4
87-54I
1.772
.413
02.565
.482
~ .247
8
Feb. i 6.9
86. 7 8 4
2.105
+ .Oil
02.368
.561
- .129
9
3 6.4
87.115
1.817
.032
02.275
493
+ -032
10
4 6.4
87.559
1.633
.292
02.681
465
- .346
ii
Apr. ii 13.9
1689.001
+ 0.516
0.6l7
2102.734
+ 0.638
0.572
12
H 14-5
88.247
.521
+ .132
01.866
644
+ .290
13
26 13.2
88.1 1 1
543
+ .2 4 6
01746
.740
+ -3H
14
May 3 13.2
88.725
555
- .380
02.375
.697
.272
15
4 I3.S
88.247
.556
+ .097
02.153
730
-083
16
Aug. 2 13.4
1688.271
+ 0.625
+ 0.004
2102.036
+ 0.736
+ 0.028
'7
3 13-9
87.743
645
+ -52
01.636
-750
+ .4H
18
6 12.9
87.887
.633
+ .380
01.556
.741
+ -53
9
7 13-4
88.160
.618
+ .122
02.106
754
.060
20
8 12.9
88.566
.630
.296
02.376
.766
-342
21
Oct. 19 1 2.1
1688.059
+ Q-539
+ 0.302
2101.965
+ 0.624
+ 0.2II
22
30 1 1.0
88-575
530
- -20 S
02.295
.584
.079
23
Nov. 9 94
88.544
489
- -133
02.655
557
.412
24
13 io-3
88.505
.487
- .092
02.513
552
- .265
25
17 10.6
88.521
.491
.112
O2. 201
.560
+ -039
NOTES.
No. 3. The images of the comparison stars faint.
No. 5. One of the plates rejected : the measures being grossly discordant.
No. 9. Exposure 10 minutes : sky hazy.
No. ii. One of the plates not measured, the film being accidentally injured.
No. 14. Clouds passing : the exposures of unequal length.
No. 19. The sky very variable from passing clouds : the images large and diffused.
No. 21. The images elliptical from inadequate driving.
No. 23. One of the plates rejected owing to accidental injury to the film.
from Observations at Selected Epochs.
Ill
TABLE II.
Concluded measures of ft Cassiopeia from the comparison
Stars (a) and (b).
No. for
Refer-
ence.
Date of
Exposure
. of Plate.
1887-8.
Measured
Distance of
Star (a) from
/3 Cassiopeise.
Sum of
Corrections.
Concluded
Distance of
Star {a).
Measured
Distance of
Star (6) from
j8 Cassiopeiae.
Sum of
Corrections.
Concluded
Distances of
Star (&).
d. h.
n
//
it
/>
//
//
I
87 Oct. 22 10.3
439.801
+ -3 7 2
440.173
1304.882
+ 0.691
I305-573
2
24 10.8
40.021
.204
40.225
05.226
+ -203
05.429
3
25 10.2
40.108
.132
40.240
05.472
.OOI
05.471
4
Nov. 14 9.8
39.910
.172
40.082
05-384
+ .221
05.605
5
15 io-5
39.807
333
40.140
04.680
+ '.692
05-372
6
88 Jan. 26 6.7
439.728
-1- 0.504
440.232
1303.370
+ 1-959
1305.329
7
28 6.4
40.102
.247
40.349
04.447
o-997
05/444
8
Feb. i 6.9
39.926
391
40.317
03.928
1-574
05.502
9
3 6.4
39-8.S5
.328
40.183
04.051
1.267
05-318
10
4 6 -4
39-993
-f - 2 39
40.232
04.261
o.943
05.204
ii
Apr. ii 13.9
44-555
0.183
440.372
1305.291
+ O.OO2
I305.293
12
14 14.5
40-575
-f- .008
40.583
04.824
.589
05-4^3
*3
26 13.2
39.496
+ -029
40.525
04.488
.704
05.192
H
May 3 13.2
40.485
.146
40-339
05.187
.241
05.428
15
4 '3-5
40.519
.022
40.497
04.616
.6lO
05.226
16
Aug. 2 13.4
440.601
0.177
440.424
1304.762
+ 0.713
1305475
17
3 13-9
40.312
.050
40.262
04.511
I.oSl
05.59 2
18
6 12.9
40.469
.076
40-393
04.382
I. OOI
05.383
19
7 13-4
40.647
.146
40.501
04.519
0.798
05-3I7
20
8 12.9
40-539
.265
40.274
05.022
0.480
05-502
21
Oct. 19 12. i
440.423
0.221
440.202
1304.340
+ 1.129
1305.469
22
30 n.o
40.540
405
40.135
05.050
0.565
05.615
23
\ Nov. 9 9.4
40.782
.411
40-37I
04.987
.615
05.602
24
13 10.3
40.424
.402
40.022
04-777
.647
05.424
2 5
17 10.6
40.488
409
40.079
04.670
.636
05.306
112 Concluded Parallax of & Cassiopeia from Star (a).
TABLE III.
Equations of Condition formed from the concluded distances of
P Cassiopeia from Star (a), as given in Table II.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
I
87 Oct. 22 10.3
+ 0.173 = X 0.7173 7T 0.1939 dp
+ O.OO6
2
24 10.8
.225 = x .7298 .1884
.049
3
25 10.2
.240 = x .7352 .1856
.065
4
Nov. 14 9.8
.082 = x .7956 .1309
+ .O8l
.5
'5 10-5
.140 = * .7971 .I28l
+ .022
6
88 Jan. 26 6.7
+ 0.232 = x 0.3121 +0.0692
+ 0.027
7
28 6.4
.349 = x .2861 + .0747
- -085
8
Feb. i 6.9
317 = x - 3 32o + -0857
.042
9
3 6.4
.183 = x .2057 + .0913
+ .097
10
4 6.4
.232 = x .1920 + .0939
+ -051
ii
Apr. ii 13.9
+ 0.372 = x +0.6516 +0.2781
+ 0.078
12
H 14-5
583 = * + -6764 + .2863
.128
13
26 13.2
.525 = x + .7223 + .3192
.061
'4
May 3 13.2
.339 " * + .7887 + .3384
+ -137
15
4 I3-S
.497 = x + .7925 + .3411
.019
16
Aug. 2 13.4
+ 0.424 = x +0.2576 +0.5874
0.056
17
3 13-9
.262 = x + .2443 + .5902
+ -105
18
6 12.9
393 = z + -2187 + .5984
-031
19
7 i3-4
.501 = x + .1918 + .6011
-MS
20
8 12.9
.274 = x + ,1780 + .6038
+ .080
21
Oct. 19 1 2. i
+ O.2O2 = X 0.6819 +0.8009
0.021
22
30 u.o
135 = x ^489 + -8310
+ .032
23
Nov. 9 9.4
.371 = x .7865 + .8584
.211
2 4
13 10.3
.022 = X .7949 + .8694
+ .136
25
17 10.6
.079 = x .7995 + .8804
+ .078
Treating these equations in the usual method, the following normal
equations result :
+ 7.152 = + 25.000037 + 8.3720^ 4.092777
+ 2.4675=+ 8.3720 +6.0450 -0.9371
+ 0.4923= 4.0927 0.9371 +8.9803
whence, by solution, are obtained the following values of the unknowns, viz.
//
x = +0.321
d\L = 0.0047
TT= +0.2004.
It further appears that the probable error of one complete measure of
distance is + o".OQ7, and that the probable error of TT is + 0^.0336.
Concluded Parallax of (3 Cassiopeice from Star (b). 113
TABLE IV.
Equations of Condition formed from the concluded distances of
ft Cassiopeia and Star (b), as given in Table II.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
I
87 Oct. 22 10.3
+ 0.473 = X + 0.7607 7T 0.1939 d fJt,
0.068
2
24 10.8
.329 = tf + .7530 .1884
+ -075
3
25 10.2
.371 = x + .7485 .1856
+ -033
4
Nov. 14 9.8
.505 = x + .6408 .1309
.116
5
15 10.5
.272 = x + .6339 - I28z
+ .116
6
88 Jan. 26 6.7
4-0.229 = x 0.2565 +0.0692
+ 0.043
7
28 6.4
.344 = x .2824 + .0747
- -75
8
Feb. i 6.9
.402 = x .3337 + .0857
.140
9
3 6.4
.218 = x .3561 + .0913
+ -041
10
4 6.4
.104 = x .3705 + .0939
+ -155
ii
Apr. ii 13.9
+ 0.193 = x ^0.7910 +0.2781
+ 0.008
12
14 14.5
.313 = x - .7867 + .2863
.112
13
26 13.2
.092 = x .7494 + .3192
+ .II 4
H
May 3 13.2
.328 = x .7130 + .3384
.117
!5
4 !3-5
.126 = x .7068 + .3411
+ .086
16
Aug. 2 13.4
+ 0.373 = x +0.3265 +0.5874
0.032
17
3 13-9
.492 = x + .3388 + .5902
^50
18
6 12.9
.283 = x + .3744 + .5984
+ .063
J 9
7 !3-4
.217 = x + .3858 + .6011
+ ^30
20
8 12.9
.402 = x + .3977 + .6038
-053
21
Oct. 19 12. 1
+ 0.369 = x +0.7766 +0.8009
+ 0.026
22
30 ii.o
S'3 = * + .7347 + .8310
.124
23
Nov. 9 9.4
.502 = x + .6731 + .8584
.121
2 4
13 10.3
.324 = x + .6425 + .8694
+ -053
25
17 10.6
.206 = x + .6087 + .8804
+ .168
Treating- these equations in the usual method, the following- normal
equations result :
+ 7.980 = +25.0000 #+8.3720 ^ + 3.449677
+ 2.7570=+ 8.3720 +6.0450 +2.0976
+ 2.1621 = + 3.4496 +2.0976 +8.9015
whence, by solution, are obtained the following- values of the unknowns, viz.
n
x = +0.306
dp = 0.0127
TT = + 0.1277.
It further appears that the probable error of one complete measure of
distance is +o // .io6, and that the probable error of TT is io' / .o374.
PARALLAX OFp CASSIOPEIA RELATIVELY TO STARS (C) AND (D).
TABLE V.
Concluded measures of ft Cassiopeia from the comparison
Stars (c) and (d).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887-8.
Measured
Distance of
Star (c) from
8 Cassiopeise.
Sum of
Corrections.
Concluded
Distance of
Star (c).
Measured
Distance of
Star (d) from
j3 Cassiopeia?.
Sum of
Corrections.
Concluded
Distance of
Star (d).
d. h.
//
//
//
//
//
//
I
87 Oct. 22 10.3
663.387
+ 0.286
66^.673
1474.250
+ 0.717
1474.967
2
24 10.8
63.710
-h -092
63.802
74-833
.290
75-123
3
25 10.2
63-7H
.022
63.692
75-023
.031
75-054
4
Nov. 14 9.8
63-529
+ .170
63.699
74.481
.440
74.921
5
J 5 70 -5
63479
+ -394
63-873
74.098
.948
75.046
6
88 Jan. 26 6.7
663.508
+ 0.394
663.902
1474.398
+ 0.431
1474.829
7
28 6.4
63-619
.178
63797
74^47
.125
74-772
8
Feb. i 6.9
63.604
.260
63.864
74-686
.220
74.906
9
3 6.4
63-57 1
.251
63.822
74.696
-3l6
75.012
10
4 6.4
63.921
.108
64.029
75.042
.051
75-093
ii
Apr. n 13.9
663.858
+ 0.028
663.886
1474.974
+ 0.139
I475.II3
12
14 14.5
63.618
304
63.922
74.653
-339
74.992
'3
26 13.2
63-435
.336
6377I
74.7I9
.408
75-127
14
May 3 13.2
63.561
.142
63.703
74-999
.204
75-203
15
4 13.5
63.501
.212
63.713
74.738
375
75.H3
16
Aug. 2 13.4
663-358
+ 0.22S
663.583
1474.921
+ 0.244
'475-165
'7
3 13-9
63-425
.400
63825
74.696
-633
75.329
18
6 12.9
63-387
415
63.802
74.411
.682
75-093
19
7 13-4
63-274
255
63-529
75.006
.308
75-3 14
20
8 12.9
63-390
157
63-547
75-253
.095
75-348
21
Oct. 19 1 2.1
663.522
-fo.071
663.593
'474-757
+ 0.365
1475.122
22
30 n.o
63.418
.213
63.631
74-79'
+ .122
74-9 I 3
23
Nov. 9 9.4
63.650
.105
63755
75-009
- .144
74-865
2 4
13 io-3
63.622
.148
63.770
75.180
.042
75.I38
2 5
17 10.6
63.645
.2 4 8
63.893
74.909
+ .183
75.092
Concluded Parallax of @ Cassiopeia from Star (c). 115
TABLE VI.
Equations of Condition formed from the concluded distances of
} Cassiopeia from Star (c), as given in Table V.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
I
87 Oct. 22 10.3
+ 0.173 = x 0.327277 0.1939 dp.
+ 0.051
2
24 10.8
.302 = x .2948 .1884
.074
a
25 10.2
.192 = x - 2 79 2 .1856
+ .038
4
Nov. 14 9.8
.199 = * + .0033 .1309
+ .067
S
15 10.5
373 = x -\- .0206 .1281
.103
6
88 Jan. 26 6.7
+ 0.402 = x +0.9186 +0.0692
0.0l6
7
28 6.4
.297 = x + .9273 + .0747
+ .090
8
Feb. I 6.9
.364 = x + .9417 + .0857
+ .025
9
3 6.4
.322 = x + .9469 + .0913
+ .067
10
4 6.4
.529 = x + .9491 + .0939
.140
ii
Apr. ii 13.9
+ 0.386 = x +0.4780 +0.2781
0.059
12
14 J 4-5
.422 = x + .4338 + .2863
.101
13
26 13.2
.271 = x + .2499 + .3192
+ -025
14
May 3 13.2
.203 = x + .1369 + .3384
+ .079
15
4 13-5
.213 = x + .1203 + .3411
+ .067
16
Aug. 2 13.4
+ 0.083 = x 0.9651 +0.5874
+ 0.054
J 7
3 !3-9
.325 = x .9681 + .5902
.189
18
6 12.9
.302 = x .9747 + .5984
.161
19
7 13-4
.029 = x .9766 + .6011
+ .112
20
8 12.9
.047 = x .9780 + .6038
+ .094
21
Oct. 19 1 2. i
+ 0.093 = x 0.4076 +0.8009
+ 0.116
22
30 n.o
.131 = x .2345 + .8310
+ .099
23
Nov. 9 9.4
.255 = x .0683 + .8584
-003
24
13 10.3
.270 = x .0005 + .8694
- .009
25
17 10.6
393 = # + -0671 + .8804
- -125
Treating these equations in the usual method, the following normal
equations result :
+ 6.576 = +25.00000? + 8.3720^ 0.2811 TT
+ 1.8663=+ 8.3720 +6.0450 2.5107
+ 1.2690= 0.2811 2.5107 +10.1318
whence, by solution, are obtained the following values of the unknowns, viz.
x = +0.266
dp = 0.0055
TT= +0.1313.
It further appears that the probable error of one complete measure of
distance is 0^.097, and that the probable error of it is 0^.0335.
116 Concluded Parallax of IB Cassiopeia from Star (d).
TABLE VII.
Equations of Condition formed from the concluded distances of
P Cassiopeice from Star (d), as given in Table V.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
I
87 Oct. 22 10.3
+ 0.367 = x +0.0318 IT 0.1939 dfJL
+ 0.084
2
24 10.8
.523 = x .0035 .1884
.077
3
25 10.2
454 = X .0202 -1856
.Oil
4
Nov. 14 9.8
.321 = x .3092 .1309
+ .080
5
15 10.5
.446 = X .3260 .I28l
+ .046
6
88 Jan. 26 6.7
+ 0.229 = * 0.9840 +0.0692
+ 0.077
7
28 6.4
.172 = x .9822 + .0747
+ -135
8
Feb. i 6.9
.306 = x .9750 + .0857
+ .003
9
3 6.4
.412 = x .9697 + .0913
.102
10
4 6.4
.493 = x .9665 + .0939
- -183
TI
Apr. ii 13.9
+ 0.513 = x 0.1989 +0.2781
o-o73
12
14 14-5
.392 = x .1478 + .2863
+ .056
13
26 13.2
.527 = x + .0559 + .3192
-045
H
May 3 13.2
603 = x + .1746 + .3384
.102
'5
4 13-5
.513 = x +0.1917 + .3411
- .009
16
Aug. 2 13.4
+ 0.565 = x +1.0069 +0.5874
+ 0.080
17
3 13-9
.729 = x + 1.0044 -f -59 02
-085
18
6 12.9
.493 = x +0.9956 + .5984
+ .150
19
7 13-4
.714 = x + .9922 + .6011
- .071
20
8 12.9
.748 = x + .9883 + .6038
.106
21
Oct 19 12. i
+ 0.522 = X +O.I2IO +0.8009
0.004
22
30 n.o
.313 = x .0675 + .8310
+ .176
23
Nov. 9 9.4
.265 = x .2383 + .8584
+ -215
24
13 10.3
.538 = x .3053 + .8694
- .084
25
17 10.6
.492 = x .3706 + .8804
.048
Treating 1 these equations in the usual method, the following normal
equations result :
+ 11.650 = + 25.oooo# + 8.372Of/ju 1.302377
+ 4.4463=+ 8.3720 +6.0450 + 1.9454
+ 1.1330=- 1.3023 + 1.9454 +10.3753
whence, by solution, are obtained the following- values of the unknowns, viz.
//
x = + 0.456
dfji = +0.0531
TT= +0.1565.
It further appears that the probable error of one complete measure of
distance is +o // .io6, and that the probable error of?; is + 0^.036 1.
Concluded Parallax of $ Cassiopeice.
117
The collected results for the parallax of /3 Cassiopeiae, gathered from the
preceding pages, are as follows :
Star's Name,
Mag,
Relative
Annual
Parallax.
Probable
Error of
Parallax.
Probable Error
of one Com-
plete Measure
of Distance.
D.M.+ sS , No. i
9.2
it
+ 0.2004
//
0.0336
//
0.097
+ 58, No. 10
9.1
+ 0.1277
0.0374
0.106
+ 58, No. 8
8-3
+ 0.1313
0.0335
0.097
-f 58, No. 2700
9.2
+ 0.1565
0.0361
0.106
There appears to be an indication here that /3 Cassiopeise and the stars of
comparison may possibly not belong to the same group. Possibly also the
bright stars ft and a are not closely associated. The parallax also is in
accordance with the suggestions derived from the comparatively rapid proper
motion of the star. I cannot find that the parallax of this star has been
determined by any other astronomer.
PARALLAX OF y CASSIOPEIA
Deduced from Observations at Critical EpocJis.
The stars selected for the determination of the relative parallax of y Cassio-
peiae are
Anonymous ... Mag. 10.6 ... star (a)
D.M. + 59,No. 158 ... 9.4 ... (b)
Anonymous ... 10.3 ... (c)
DJM + 59 ,No. 137 ... 8.9 ... (d).
The approximate position-angles and distances of these four stars are
o n
for star a ... p = 288 6 ... #=1356
b ... = 108 47 ... = 741
c ... = 19 i ... = 464
d ... = 245 5 = i*i-
The accompanying figure is a diagram, showing the relative position of
these stars, with the form and position of the parallactic ellipse.
North
East
SoutJi
The parallactic factors in the equations of condition have been computed
from the expressions
Star (a) ... ds = E [9.92691] cos (O - 86 6)
(b) . t .ds = R [9.92540] cos ( O - 265 23)
(c) ...
8
16 6.8
.229 = x + .8285 .0437
-145
9
18 8.2
,386 = x + .8283 .0381
.OI2
10
23 74
.474 = x + .8230 .0244
.100
ii
88 Feb. 5 6.7
+ 0.262 = x +0.5220 +0.0966
+ 0.093
12
15 6.8
-55 = * + ^o^ + - I2 4o
-157
13
1 6 6.9
.391 = x + .3876 + .1265
.044
H
Mar. i 7.1
-377 = # + .1980 + .1651
.041
IS
8 7.1
.203 = x + .0978 +..1842
+ .127
16
June 7 13.9
+ 0.162 = x 0.8472 +0.4341
+ 0.1 10
'7
13 i3-o
.314 = x .8550 + .4505
.042
18
14 12.8
,362 = x .8555 + .4533
.090
19
22 13.4
.293 = x .8504 + .4752
.022
20
30 13-3
.427 = x .8300 + .4971
.155
21
Aug. 14 12.0
+ 0.383 = x 0.4626 +0.6202
0.090
22
15 II.2
.273 = x .4507 + .6229
+ .026
23
22 II.9
.134 = x .3618 + .6421
+ -l6 5
2 4
29 u.6
.405 = x .2683 + -6612
.100
25
31 12.4
.313 = x .2403 + .6667
- .007
Treating these equations in the usual method, the following 1 normal
equations result :
+ 7.980 = + 25.oooo# + 4.245od/u-i.79397r
+ 1.1978= + 4.2450 43.8515 -2-5741
-0.0458=- 1.7939 -2.5741 +8.7606
whence, by solution, are obtained the values of the unknowns, viz.
//
x = +0.325
dp = 0.0074
TT= +0.0591.
It further appears that the probable error of one complete measure of
distance is +o /r .ii5, and that the probable error of TT is o."o436.
PARALLAX OFy CASSIOPEIA RELATIVELY TO STARS (C) AND (D).
TABLE V.
Concluded measures of y Cassiopeice from the comparison
Stars (c) and (d).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887-8.
Measured
Distance of
Star (c) from
y Cassiopeise.
Sum of
Corrections.
Concluded
Distance of
Star (c).
Measured
Distance of
Star (d) from
y Cassiopeise.
Sum of
Corrections.
Concluded
Distance of
Star (d).
d. h.
n
//
ii
//
//
n
I
87 Aug. 20 IT. i
464-43S
+ 0.140
464.575
1220.481
+ 0-455
1220.936
2
24 12.9
64.578
+ -235
64-813
20.459
+ -655
21.114
3
25 12.2
64.732
+ .010
64.742
21.016
+ .046
21.062
4
31 12.6
64-393
-f- .220
64.613
20.425
+ -578
21.003
5
Sept. 6 13.1
64.659
-h .038
64.697
20.804
+ -093
20.897
6
Dec. 6 8.0
464.603
0.003
464.600
1221.170
0.166
I22I.OO4
7
7 7-2
64.413
+ .119
64.532
20.650
4- .312
20.962
8
1 6 6.8
64.764
.000
64.764
21.204
.001
2I.2O3
9
18 8.2
64-S3S
+ -204
64-739
20.475
-f -537
2I.OI2
10
23 7-4
64-757
-h -130
64.887
20.729
+ -346
21.075
ii
88 Feb. 5 6.7
464.806
+ 0.030
464.836
1220.747
4-0.136
1220.883
12
15 6.8
64.526
+ .286
64.812
20.188
+ .837
21.025
13
16 6.9
64.436
+ .269
64.705
20.405
+ .798
21.203
14
Mar. i 7.1
64.493
+ -HO
64-633
20.535
+ -529
21.064
15
8 7.1
64.728
.019
64.709
21.003
+ .106
21.109
16
June 7 13.9
464.769
0.004
464.765
1221.128
+ O.IO2
1221.230
'7
13 i3-o
64-333
+ .258
64.591
20.157
+ ./65
2O.922
18
14 12.8
64-580
4- .242
64.822
20.217
4- .721
20.938
19
22 13.4
64475
+ .108
64-583
20.715
4- .412
21.127
20
30 13-3
64.502
+ .268
64.770
20.267
+ ,826
21.093
21
Aug. 14 12.0
464-397
+ 0.310
464.707
1220.165
4- 0.899
I22I.O64
22
15 II. 2
64-437
+ -185
64.622
29.381
+ -59 2
20-973
23
22 II-9
64.316
+ -213
64.529
20.362
+ -630
20.992
24
29 ii. 6
64.643
4- .100
64.743
20.641
+ -333
20.974
25
31 12.4
64-574
+ .061
64-635
20.668
+ -215
20.883
124
Parallax of y Cassiopeice
TABLE VI.
Equations of Condition formed from the concluded distances of
7 Cassiopeios from Star (c), as given in Table V.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//-
//
I
87 Aug. 20 1 1. 1
+ 0.075 = X 0.9152 7T 0.3662 if /A
+ 0.104
2
24 12.9
.313 = X .9260 .3551
- .'34
3
25 12.2
.242 = x .9279 .3525
- -063
4
31 12.6
.113 = x .9343 .3360
+ .066
5
Sept. 6 13.1
.,97 = x .9311 .3195
.019
6
Dec. 6 8.0
+ 0.100 = x +0.0706 0.0709
+ 0.114
7
7 7.2
.032 = x + .0861 .0683
+ .182
8
1 6 6.8
.264 = x + .2291 .0437
- -045
9
18 8.2
.239 = x + .2612 .0381
.019
10
23 7-4
.387 = x + .3372 - .0244
- -163
ii
88 Feb. 5 6.7
+ 0.336 = x +0.8377 +0.0966
0.095
12
15 6.8
.312 = x + .8906 + .1240
.070
13
1 6 6.9
.205 = x + .8945 + .1265
+ -037
14
Mar. i 7.1
.133 = a? + .9192 + .1651
+ -109
15
8 7-1
.209 = x + .9101 + .1842
+ -033
16
June 7 13.9
+ 0.265 = x 0.1253 +0.4341
0.071
17
13 13-0
.091 = x .2174 + .4505
+ .099
18
14 12.8
.322 = x .2326 + .4533
-133
19
22 13.4
.083 x .3520 + .4752
+ .101
20
30 13-3
.270 - x .4652 + .4971
.092
21
Aug. 14 12.0
+ 0.207 = x 0.8950 +0.6202
0.048
22
15 II. 2
.122 = X .8993 + .6229
+ .036
23
22 II.9
.029 = x .9232 + .6421
+ .127
24
29 11.6
.243 = x .9339 + .6612
.087
25
3 I 12-4
135 = -9345 + -6667
+ .021
Treating these equations in the usual method, the following normal
equations result :
+ 4.924 = + 25.00000 + 4. 2450 dfj. 5.176617
+ 0.7427 = + 4-245 +3-8ii5 1.4176
-0.5110=- 5.1766 1.4176 +13.1758
whence, by solution, are obtained the values of the unknowns, viz.--
x = +0.209
dp = 0.0228
If +0.04IO.
It further appears that the probable error of one complete measure of
distance is + o".ioo, and that the probable error of TT is +
derived from Stars (c) and (d).
TABLE VII.
125
Equations of Condition formed from the concluded distances of
y Cassiopeia from Star (d), as given in Table V.
No.
Date,
1887-8. ....
Equations of Condition.
Residuals.
d. h.
M
u
I
87 Aug. 20 1 1. 1
+ 0.136 = x + 0.9185 TT 0.3662 d\L
+ 0.069
2
24 12.9
.314 = x + .8880 - .3551
.108
3
25 12.2
.262 = x + .8801 .3525
.056
4
31 12.6 ,
.203 = x + .8259 .3360
+ .004
5
Sept. 6 13.1
.097 = x + .7639 - .3195
+ .112
6
Dec. 6 8.0
-{-0.204 = x 0-6352 0.0709
+ 0.047
7
7 7-2
.162 = x -6477 .0683
+ .08 9
8
16 6.8
.403 = x .7551 .0437
.148
9
18 8.2
.212 = x .7775 .0381
+ -043
10
23 7-4
.275 = x .8258 .0244
.019
ii
88 Feb. 5 6.7
+ 0.083 = x 0.9546 + 0.0966
+ 0.176
12
15 6.8
.225 = x .9039 + .1240
+ -033
13
16 6.9
.403 = x .8972 + .1265
- .I 4 6
H
Mar. i 7.1
.264 = x .7770 -|- .1651
.012
15
8 7-i
.309 = x .7153 + .1842
- .0 S 8
16
June 7 13.9
+ 0.430 = x +0.6968 +0.4341
0.226
17
13 i3-o
.122 = X + .7659 + .4505
+ .079
18
14 12.8
.138 = x + .7767 + .4533
+ .062
J 9
22 13.4
.327 = x + .8557 + .4752
- .12 9
20
30 13-3
.293 = x + .9192 + .4971
~ -097
21
Aug. 14 12.0
+ 0.264 = x +0.9512 +0.6202
0.070
22
15 II. 2
.173 = x + .9458 + .6229
+ .O2I
23
22 II-9
.192 x + .8978 + .6421
+ .004
24
29 1 1.6
.174 = x + .8383 + .6612
+ .023
25
31 12.4
.083 = x + .8187 + .6667
+ .II 4
Treating these equations in the usual method, the following normal
equations result :
+ 5^548 = +25.00000 + 4.2450 d/z+ 4-85337T
+ 0.8468=+ 4.2450 +3.8515 + 2.8325
+ 0.5407= + 4.8532 +2.8325 +I7-33H
whence, by solution, are obtained the values of the unknowns, viz.
x = + 0.230
dfJL = 0.0102
77 = -0.0315.
It further appears that the probable error of one complete measure of
distance is +o".iO2, and that the probable error of TT is +o".o263.
126
Concluded Parallax of y Cassiopeia.
The collected results for the parallax of y Cassiopeise, gathered from the
preceding pages, are as follows :
Star's Name.
Mag.
Relative
Annual
Parallax.
Probable
Error of
Parallax.
Probable Error
of one Com-
plete Measure
of Distance.
Anonymous . . . . ...
10.6
//
0.0179
//
+ o.o37;
//
~f~ O.OQQ
D.M.+ 59 , No. 158
9-4
10.3
+ 0,0591
+ 0.0410
0.0436
+ 0.0280
0.115
-f-o.ioo
D.M. + 59 ,No. 137
8.9
_ 0.0315
0.0263
0.102
This is the first instance of a negative parallax met with in these
researches. Its smallness of amount, notwithstanding its algebraic significance,
seems to indicate that the principal star, and the faint stars of comparison are
in the same group, although no conclusion can be deduced therefrom as to the
comparative remoteness or proximity of the group itself in relation to the
Solar System. The brightness, however, of the principal star would in itself
indicate a probable proximity. Apart from such considerations, the nature of
its bright-lined spectrum points to a constitution quite different from that of
other stars in this constellation ; this peculiarity of spectrum, according to
Mr. Lockyer's hypothesis, may indicate an as yet unformed condition of the
star. The variability also of this spectrum is in accordance with the hypothesis
of meteoric collisions in the star, whether periodic or irregular. In making
this remark it is not to be understood that I am here adopting, without reserve,,
the bold and ingenious hypothesis of Mr. Lockyer ; nor, on the other hand, do-
I desire to express a doubt of its legitimacy. I cannot find any determination
of the parallax of this star by other astronomers.
PARALLAX OF a CEPHEI
Deduced from Observations at Critical Epochs.
The stars selected for the determination of the relative parallax of a Cephei
are
D.M. + 6i, No. 2106 ... Magnitude 9.1 ... Star a
D.M. + 62 , No. 1936 ... 9.3 ... b
D.M. + 6i, No. 2107 ... 9.0 ... c
D.M. + 62 , No. 1927 ... 9.1 ... d.
The approximate position-angles and distances of these four stars are
for star (a)
p = 211 2,2
= 47 9
= 267 25
= 81 16
= 989
= 672
= 5"
= 878.
The accompanying figure is a diagram showing the relative position of
these stars, with the form and position of the parallactic ellipse.
Hast
South
The parallactic factors in the equations of condition have been computed
from the expressions
o /
Star (a) ... ds = ^[9.99999] cos (o 103 10)
(b) ... ds = 22 [9.99843] cos (0-268 25)
(c) ... ds = ^[9.98087] cos (O 49 20)
(d) ... ds= ^[9.98400] cos (0235 23).
The proper motion of a Cephei, after consulting various authorities, has
been assumed, in
E.A. +c s .02i8
Decl n . +0^.035.
These preliminary facts will, with the information already afforded, permit
the subsequent tables to be easily followed.
128
Parallax of a Cephei derived
TABLE I.
Measures of the diagonal distances of Star (a) from Star (b), and
of Star (c)from Star (d),for the determination, at the times of
exposure, of the correction to their measured distances from
a Cephei.
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887-8.
Measured
Distance
of (a) to (6)
in Arc.
Correction
for Refrac-
tion and
Aberration.
Difference
from
Assumed
Mean
1647".50.
Measured
Distance
of (c) to (d)
in Arc.
Correction
for Refrac-
tion and
Aberration.
Difference
from
Assumed
Mean
1387". 10.
d. h.
//
//
//
//
//
I
87 Nov. 14 8.1
1647.093
+ 0.436
0.029
1386.375
+ 0.412
+ 0.313
2
15 6.8
47.426
.421
- -347
86.994
.368
.262
3
17 7-3
46.463
.424
+ -613
86.210
385
+ -SOS
4
23 6.8
47-36S
.420
- .285
86.851
379
.130
5
24 7.1
47.220
.422
- .142
86.679
392
+ .029
6
Dec. 6 6.9
1646.691
+ o-434
+ 0-375
1386.214
+ 0.412
+ 0-474
7
7 7.0
46.561
.436
+ -503
85-97I
.420
+ -709
8
15 7-5
46.861
499
+ -Ho
86.303
.489
+ -308
9
16 6.9
47-233
-474
- .207
86.650
447
+ .003
10
23 6.7
46.211
474
+ -815
86.006
469
+ .625
ii
88 May 3 12.6
1647.424
+ 0.501
0.425
1386.721
+ 0.671
0.292
12
4 "-4
47.281
494
- -275
86.718
.695
- .313
13
8 12.0
46.455
.501
+ -544
86.172
.684
+ -244
'4
IO 12.2
46.668
5"
+ -321
86.153
.672
+ -275
15
12 II.3
47.260
.502
- .262
86.374
.696
-030
16
June 30 1 2. i
1646.824
+ 0.565
+ O.III
1386.572
+ 0.541
0.013
17
July 3 10.3
46.858
559
+ .-083
86.570
592
- .062
18
5 12. i
47.181
561
.242
86.962
493
-355
19
9 11.7
46.944
563
- .007
86.475
.496
+ -129
20
12 9.6
46.629
-558
+ .313
86.337
.501
+ .262
21
Nov. 9 8.7
1647.101
+ 0.452
0.053
1386.970
+ 0-434
0.304
22
13 7-3
46.908
445
+ -147
86.685
.424
- .009
23
16 9.3
47.187
515
.202
86.816
503
.219
2 4
20 8.6
47-334
474
- .308
86.711
463
- -074
25
21 8.9
46-734
.501
+ -265
86.207
.492
+ -401
NOTES.
No. 4. The exposure continued for ten minutes owing to haze.
No. 5. The images elliptical, but measurable.
No. 9. One of the plates rejected : the measures being grossly discordant.
No. II. Clouds passing : the exposures of somewhat uncertain length.
No. 17. Clouds passing : the exposures sometimes interrupted.
No. 20. Images elliptical, but measurable.
No. 24. Exposure continued for eight minutes : the images of the comparison stars very faint.
from Observations at Selected Epochs.
129
TABLE II.
Concluded measures of a Cephei, from the comparison
Stars (a) and (b).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887-8.
Measured
Distance of
Star (a) from
a Cephei.
Sum of
Corrections
Concluded
Distance of
Star (a).
Measured
Distance of
Star (6) from
a Cephei.
Sum of
Corrections.
Concluded
Distance of
Star (6).
d. h.
//
//
//
tt
//
//
I
87 Nov. 14 8.1
989-377
+ 0.255
989.632
672.555
+ 0.152
672.707
2
15 6.8
89.549
.158
89.707
72.619
.014
72.633
3
17 7-3
88.869
635
89.504
72.336
.406
72.742
4
23 6.8
89.503
.090
89.593
72.875
.040
7 2 -9'5
5
24 7.1
89.609
.177
89.786
72.613
.104
72.717
6
Dec. 6 6.9
989.159
+ 0.483
989.642
672.491
+ 0.324
672.815
7
7 7-o
88.964
.565
89.529
72.448
379
72.827
8
15 7-5
89.454
373
89.827
72.429
.264
72.693
9
16 6.9
89.596
.146
89.742
72.801
.105
72.906
10
23 6.7
88.863
.768
89.631
72.259
533
72.792
ii
88 May 3 12.6
989.761
+ 0.004
989.765
672.486
+ 0.092
672.578
12
4 11.4
89.780
.103
89.883
72442
.200
72.642
13
8 12.0
89.207
587
89.794
72.241
.486
72.727
H
10 12.2
89.144
455
89.599
72.191
.402
72.593
15
12 11.3
89.772
.105
89.877
72.659
157
72.816
16
June 30 12. i
989.568
+ 0.346
989.914
672.390
+ 0:352
672.742
17
July 3 10.3
89-383
.322
89.705
72.295
-344
72.639
18
5 ".I
89.093
534
89.627
72.699
193
72.892
iQ
9 "-7
89.611
.272
89.883
72.425
-302
72.727
20
12 9.6
89.442
433
89.875
72.224
44 1
72-665
21
Nov. 9 8.7
989.621
4 0.141
989.762
672.454
4-0.286
672.740
22
13 7-3
89.263
+ -256
89.519
72.227
366
72.593
23
16 9.3
89.661
+ .086
89.747
72.628
-257
72.885
2 4
20 8.6
89.726
.006
89.720
72.419
.197
72.616
2 5
21 8.9
89.261
+ -352
89.613
72.427
445
72.872
130 Concluded Parallax of a Cephei
TABLE III.
Equations of Condition formed from the concluded distances of
a Cephei from Star (a), as given in Table II.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
I
87 Nov. 14 8.1
+ 0.132 = x 0.6224 TT 0.1312 dp
+ 0.032
2
15 6.8
.207 = x .6347 .1284
.044
3
'7 7-3
.004 = x .6611 - I2 3O
+ .158
4
23 6.8
.093 = x .7338 .1065
+ -063
5
24 7-i
.286 = x .7454 .1038
.130
6
Dec. 6 6.9
+ 0.142 = x 0.8632 0.0710
+ 0.006
7
7 7-0
.029 = x .8714 .0683
+ -"9
8
IS 7-5
.327 = x .9270 .0464
- -183
9
1 6 6.9
.242 = x .9324 .0437
.098
10
23 6.7
.131 = x .9636 .0245
+ .012
ii
88 May 3 12.6
+ 0.265 = x +0.5164 +0.3382
0.000
12
4 11.4
383 = x + -5304 + -3409
- .117
13
8 12.0
.294 = x + .5880 + .3518
.024
14
IO 12.2
.099 = x + .6157 + .3573
+ -173
'5
12 II.3
.377 = x + .6422 + .3628
.103
16
June 30 1 2. 1
+ 0.414 = x +1.0146 +0.4970
0.107
i7
July 3 10.3
.205 = x + 1.0167 + .5050
+ .IO2
18
5 12.1
.127 = x +1.0165 + .5107
+ .180
19
9 "-7
.383 = x +1.0144 + .5215
.076
20
12 9.6
375 = * +1.0074 + .5295
.069
21
Nov. 9 8.7
+ 0.262 = x 0.5642 +0.8580
-0.057
22
13 7-3
.019 = x .6049 + .8688
+ -183
23
16 93
.247 = x .6590 + .8770
.049
2 4
20 8.6
.220 = x .7083 + .8880
- .025
25
21 8.9
.113 = x .7205 + .8907
+ .082
Treating these equations in the usual method, the following- normal
equations result :
+ 5".376 = +25.0000 x + 7.3504^- 3.249677
+ 1.8970=+ 7.3504 + 5- 8 5 61 + i-3 8 49
+ 0.4798 = 3.2496 +1.3849 +15.4480
whence, by solution, are obtained the values of the unknowns, viz.
//
x = +0.214
dp= +0.0373
ir= +O.0729.
It further appears that the probable error of one complete measure of
distance is +o".H3, and that the probable error of TT is +o' / .O3O9.
from the Stars of Comparison (a) and (b). 131
TABLE IV.
Equations of Condition formed from the concluded distances of
a Cepheifrom Star (b), as given in Table II.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
I
87 Nov. 14 8.1
+ 0.207 = X + 0-7974 7T O.I3I2 d[L
+ 0.048
2
15 6.8
.133 = x + .8067 .1284
+ .122
3
17 7-3
.242 = x + .8260 .1230
+ .014
4
23 6.8
.415 = x + .8778 .1065
- -157
5
24 7-i
.217 = a + .8851 .1038
+ -041
6
Dec. 6 6.9
+ 0.315 = x + -95S2 0.0710
0.054
7
7 7-0
.327 = x + .9590 .0683
- .065
8
IS 7-5
.193 = a + .9802 .0464
+ .069
9
16 6.9
.406 = x + .9811 .0437
.144
10
23 6.7
.292 = x + .9813 .0245
.029
ii
88 May 3 12.6
+ 0.078 = x 0.7199 +0.3382
+ 0.128
12
4 n-4
.142 = x .7313 + .3409
+ .064
*3
8 12.0
.227 = x .7777 + .3518
.023
H
10 12.2
.093 = x .7993 + .3573
+ .III
15
12 II.3
.316 = x .8198 + .3628
.112
16
June 30 1 2. i
+ 0.242 = x 0.9972 +0.4970
0.043
17
July 3 10.3
.139 = x .9865 + .5050
+ .061
18
5 12.1
.392 = x .9784 + .5107
.192
!9
9 i-7
.227 = x .9625 + .5215
.027
20
12 9.6
.165 = x .9389 + .5295
+ .037
21
Nov. 9 8.7
+ 0.240 = x +0.7508 +0.8580
+ 0.031
22
13 7-3
.093 = x + .7943 + .8688
+ - J 79
23
16 9.3
.385 = x + .8245 + .8770
.in
24
20 8.6
.116 = x + .8598 + .8880
+ - J 59
25
21 8.9
.372 = x + .8684 + .8907
.097
Treating 1 these equations in the usual method, the following 1 normal
equations result :
+ 5.974 = +25.00000 + 7.3504^ + 4435 8< f
+ 1.7383= + 7.3504 +5-8561 - 0.9886
+ 1.7051 = + 4-435 8 -0.9886 +19.3107
whence, by solution, are obtained the values of the unknowns, viz.
H
x = +0.227
dp = +0.0181
77= +0.0371.
It further appears that the probable error of one complete measure of
distance is +o".io6, and that the probable error of TT is +o".o256.
PARALLAX OF a CEPHEI, RELATIVELY TO STARS (C) AND (D).
TABLE V.
Concluded measures of a Cephei, from the comparison
Stars (c) and (d).
No. for
Refer-
ence.
Date of
Exposure
of Plate.
1887-8.
Measured
Distance of
Star (c) from
a Cephei.
Sum of
Corrections.
Concluded
Distance of
Star (c>.
Measured
Distance of
Star (d) from
a Cephei.
Sum of
Corrections.
Concluded
Distance of
Star (d).
d. h.
//
//
//
tt
//
it
I
87 Nov. 14 8.1
510.815
+ 0.290
5II-I05
877.677
+ 0.436
878.113
2
15 6.8
10.843
+ .060
10.903
78-055
045
78.100
3
17 7-3
10.654
+ -35
II.OO4
77.360
543
77-903
4
23 6.8
10.783
-1- -109
10.892
78.046
'39
78.185
S
24 7.1
10.945
+ .173
i 1.1 iS
77.987
.212
78.199
6
Dec. 6 6.9
510.722
+ 0.340
511.062
877.509
+ 0-553
878.062
7
7 7.0
10.518
+ .429
10.947
77.614
.699
78-3I3
8
IS 7-5
10.846
+ -301
II.I 4 7
77-516
497
78.013
9
1 6 6.9
10.844
+ .174
1I.OI8
77.815
.277
78.092
10
23 6.7
10.678
+ -412
11.090
77-485
.689
78.174
ii
88 May 3 12.6
5II.CI4
+ 0.099
5II-I3
877.701
+ 0.282
877.983
12
4 "-4
10.752
+ .102
10.854
77.766
.281
78.047
13
8 12.0
10.740
+ -302
11.042
77-359
.633
77.992
H
10 12.2
10.867
4- -305
11.172
77.363
.646
78.009
15
12 11.3
JO.SlI
-f .202
11.013
77-398
.467
77.865
16
June 30 i a. i
511.063
+ O.II9
511.182
877-524
+ 0.414
877.938
!7
July 3 10.3
10.931
+ .122
"053
77.695
.412
78.107
18
5 ".I
10.995
.028
10.967
77.842
.167
78.009
19
9 n-7
11.045
+ .152
11.197
77.689
479
78.168
20
12 9.6
10.864
+ -241
11.105
77.222
.627
77-849
21
Nov. 9 8.7
5II.III
0.084
511.027
878.003
+ 0.216
878.219
22
13 7-3
11.093
-f- .O2O
11.113
77.693
399
78.092
23
16 9.3
10.915
.032
10.883
77.864
.315
78.179
2 4
20 8.6
11.004
+ -005
11.009
77.889
.386
78275
25
21 8.9
10.928
+ -194
II. 122
77.400
705
78.105
Parallax of a Cephei from Star (c).
TABLE VL
133
Equations of Condition formed from the concluded distances of
a Cephei from Star (c), as given in Table V.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
it
//
I
87 Nov. 14 8.1
+ 0.305 = X 0.9452 7T O.I3I2 dp
0.080
2
15 6.8
.103 = x .9441 .1284
+ .122
3
17 7-3
.204 = x .9408 .1230
+ .020
4
23 6.8
.092 = x .9243 .1065
+ -132
5
24 7.1
.318 = x .9204 .1038
-094
6
Dec. 6 6.9
+ 0.262 = x 0.8539 0.0710
0.039
7
7 7.0
.147 = x .8464 .0683
+ -077
8
15 7-5
.347 = x .7786 .0464
-I2 4
9
1 6 6.9
.218 = x .7690 .0437
+ .005
10
23 6.7
.290 = x .6955 .0245
- .067
ii
88 May 3 12.6
+ 0.313 a x +0.9614 +0.3382
0.044
13
4 11.4
.054 = x + .9629 + .3409
+ .215
13
8 12.0
.242 = x + .9667 + .3518
+ -027
14
IO 12.2
.372 = x + .9670 + .3573
.103
15
12 II.3
.213 = x + .9661 + .3628
+ -057
16
June 30 1 2. i
+ 0.382 = x +0.6229 +0.4970
O.III
i7
July 3 10.3
.253 = x + .5857 + -55
+ -017
18
S ".I
.167 = x + .5587 + -5107
+ -103
19
9 11.7
.397 = x + .5184 + -5215
.128
20
12 9.6
.305 = * + -4 6 37 + -5295
~ .036
21
Nov. 9 8.7
+ 0.227 = x 0.9469 +0.8580
+ 0.035
22
13 7-3
.313 = x .9454 + -8688
.051
23
16 9.3
.083 = x .9410 + .8770
+ .180
24
20 8.6
.209 = x .9315 + -8880
+ -054
25
21 8.9
.322 = x .9283 + .8907
.058
Treating these equations in the usual method, the following normal
equations result :
+ 6.138 = + 25.00000 + 7.3504^- 5.737871
+ 2.0207=+ 7.3504 +5- 8 56i - 0.2567
-1.0462= - 5.737 8 -0.2567 +18.0845
whence, by solution, are obtained the values of the unknowns, viz.
//
x +0.234
dp = +0.0518
7T = + 0.0172.
It further appears that the probable error of one complete measure of
distance is +o".ioo, and that the probable error of TT is +o".O249.
134
Parallax of a Cephei from Star (d).
TABLE VII.
Equations of Condition formed from the measures of a Cephei
and Star (d), as given in Table V.
No.
Date,
1887-8.
Equations of Condition.
Residuals.
d. h.
//
//
I
87 Nov. 14 8.1
+ 0.313 = X 4- 0.9515 7T O.I3I2 dp
4- 0.031
2
15 6.8
.300 = x 4- .9521 .1284
4- -044
3
'7 7-3
.103 = x 4- .9524 .1230
4- .242
4
23 6.8
385 = * 4- -9465 -I06S
.041
5
24 7.1
399 = * + -9442 .1038
-054
6
Dec. 6 6.9
-{-0.262 = x 4~ 0.9059 0.0710
4-0.081
7
7 7-o
5*3 = a; + -8917 .0683
- .171
8
15 7-5
.213 = x 4- .8360 .0464
4- .T2 3
9
16 6.9
.292 = x 4- .8279 .0437
4- .044
10
23 6.7
374 = + .7639 -0245
- .044
ii
88 May 3 12.6
+ 0.183 = x 0.9532 +0.3382
0.028
12
4 ".4
.247 = x .9563 4- .3409
-093
13
8 12.0
.192 = x .9672 + .3518
-039
H
IO 12.2
.209 = x .9710 4- .3573
- .056
IS
12 II.3
.065 = x .9734 4- .3628
4- .088
16
June 30 1 2. i
4-0.138 = x 0.7030 4-0-4970
4- 0.058
17
July 3 10.3
.307 = x .6691 + .5050
.106
18
5 12.1
.209 = x .6441 4- .5107
.004
19
9 11.7
.368 x .6067 4- .5215
- -158
20
12 9.6
.049 = x .5551 4- .5295
4- -158
21
Nov. 9 8.7
4-0.419 = x 4-0.9458 4-0.8580
4- 0.003
22
13 7-3
.292 = x 4- .9513 4- -8688
4- -130
23
16 9.3
.379 = x 4- -9524 4- -8770
4- -044
24
20 8.6
475 = 4- -9497 4- -8880
.051
25
21 8.9
.305 = x 4- .9484 4- .8907
4- -119
Treating these equations in the usual method, the following normal
equations result :
4-6.983 = 4- 25.00000 4- 7-354^M+ 3-i7467r
4-2.2348= 4- 7-354 4-5.^501 4- 0.0183
4-3.0530=4- 3.1746 4-0.0182 4-19.2716
whence, by solution, are obtained the values of the unknowns, viz.
//
x = 4-0.241
dp= 4-0.0785
TT = 4- O.1186.
It further appears that the probable error of one complete measure of
distance is +o".iO4, and that the probable error of TT is +O / '.O274.
Collected Results for Parallax of a Cephei.
135
The collected results for the parallax of a Cephei, gathered from the
preceding pages, are as follows :
Star's Name.
Mag.
Relative
Annual
Parallax.
Probable
Error of
Parallax.
Probable Error
of one Com-
plete Measure
of Distance.
D.M. + 6i, No. 2106
9.1
+ O.O729
0.0309
n
0.113
+62, 1926
9-3
+ 0.0371
0.0256
0.106
+61, 2107
9.0
+ 0.0172
0.0249
0.100
+62, 1927
9.1
+ 0.1186
0.0274
0.104
The comparatively great difference of one-tenth of a second between the
relative parallaxes of this star in respect of the faint stars of comparison (c)
and (d\ is very observable, and is even more marked than in the case of
Polaris, to which reference has already been made. And yet the brightness of
these comparatively faint stars is approximately the same. Moreover, the
determination of a parallax of one -tenth of a second is far within the capa-
bilities of these researches. It will therefore be a question of interest to
ascertain whether the relative parallaxes of the stars (c) and (d) cannot be
determined by a direct method. The proper motion of a Cephei calls for no
particular remark, nor can I find any other determination of its parallax.
Here arises once more the suggestion of an enquiry already partially applied
to 6 1 Cygni, viz. as to the effect of a greater or less number of sets of observa-
tions on the concluded parallax of a star. Accordingly, I made an additional
set of measures of distance during the month of July last, at which time the
co-efficient of parallax for the stars (a) and (b) is influential.
The addition of this set of five nights in July last, leads to the following
normal equations, based on the whole thirty nights : viz. six sets of five nights
each :
For the Star (a).
+ 6.916 = +30.0000 x + 14.9756 dp + 1.78597:
17.4854 + 9.0505
9-55 +20.5197.
+ 4.2466= +14.9756
+ 2.0345= + 1.7859
For the Star (b).
H
+ 7.117 = +30.00005? + 14.9756^ 0.248477
+ 3.4847 = +14.9756 +17.4854 - 8.1319
+ 0.6419= 0.2484 8.1319 +23.7027.
The results of the solution of the above equations are
// //
Star (a) ... TT = +0.0709 0.0305 ... weight 3.710
Star (b) ... TT = +0.03 74 0.0255 weight 4.158.
136 Effect of Altering the Number of Observations.
On comparing these results with those already given (page 135) deduced
from twenty-five nights, and which are here repeated for convenience
/ //
Star (a) ... TT = +0.0729 + 0.0309 ... weight 3.664
Star (b) ... IT +0.0371+0.0256 ... weight 4.027
it appears that no material alteration has arisen by increasing the number
of nights from twenty-five to thirty, either as respects the parallaxes or the
' weights ' attached to them.
On pursuing a similar line of investigation as to the effects of reducing the
number of the sets of observation, by the omission of the two sets made in the
months of November and June, when, for these stars (a) and (#), the co-efficient
of parallax was less influential, the following results were deduced :
//
Star (0) ... TT = + 0.0522 + 0.0463 ... weight 2.277
Star (#) ... TT = + 0.0375 + 0.0466 ... weight 2.444
wherein are exhibited considerable alterations both in parallax and ' weight/
From all the above details, which may be regarded as important and
decisive as to the number and distribution of the sets of measures which it is
desirable to make, the inevitable conclusion appears to be that the plan of
curtailment herein already adopted in these researches is at once economical
and satisfactory, and I am thereby encouraged to continue the method with
reference to the remaining stars of the second magnitude.
I conclude with a summary of the Results, obtained in the foregoing
investigations.
Summary of Parallactic Determinations.
137
Summary of Results.
Star's Name.
Magnitude
and (Proper
Motion) of
Star.
Designation
of
Comparison
Star.
Relative Annual
Parallax.
Photometric
Magnitude
of
Comparison
Star.
Approximate
Distance of
Comparison
Star.
H II
n
61 C ni
4.98
a
+ 0.429 0.016
7-73
1380
*T 7
(516)
b
.441 .022
8.67
1003
c
.445 .021
8.88
1118
d
.419 .018
9-34
953
6 1. Cverni ..
4.98
a
+ O.425 0.018
7-73
1360
(516)
b
.451 .019
8.67
1024
c
.432 .019
8.88
1107
d
.430 .018
9-34
961
IJL Cassiopeiae . . .
540
a
+ 0.051 0,027
7.89
756
//
(3.75)
b
.021 .023
8.38
1356
Polaris
2.05
a
+ 0.084 0.023
8.22
1285
(o'.05)
b
.078 + .017
8.30
1056
c
.052 .011
6.84
1182
d
100 .018
9-75
1634
a Cassiopeia ...
2.41
a
+ 0.034 + 0.024
8.68
1042
(o'.05)
b
.040 + .020
9.26
849
c
.034 + .025
10.19
667
d
.035 .024
9-30
1113
/3 Cassiopeia...
2.32
a
+ 0.200 0.034
9.20
440
(o!'55)
b
128 .037
9.14
1305
c
.131 .034
8-33
664
d
157 .036
9.24
H75
y Cassiopeise . . .
2 ;/ 9
a
-0.018 0.037
10.64
1356
(0.02)
b
+ .059 + .044
9-39
74i
c
+ .041 + .029
10.27
465
d
.032 .026
8-93
1221
a Cephei
2-57
a
+ 0,073 0.031
9.08
9 8 9
(016)
b
.037 + .026
9- 2 5
673
c
.017 .025
8.98
5"
d
119 .027
9.11
878
From a survey of the foregoing results an enquiry naturally arises as to
the relations between the apparent relative lustre of the stars, their parallaxes,
and their proper motions. It is true that the element here last mentioned is
imperfectly determined, so long as the motions in the line of sight remain
138 Relation of Parallax to Magnitude and Proper Motion.
unknown ; but in the long run it seems probable that the latter do not
seriously modify the amount of the final resultant motions themselves.
Even on a cursory examination of the foregoing summary, it is evident that
no relation exhibits itself between the lustre and the parallax: nor in fact
should we expect to find any such relation, if, as we have some reason to
suppose, the stars in our system are still in various stages of condensation, and of
chemical or even mechanical interactions of their component materials. The
case, however, is very different in respect to a relation between parallax, or
distance, and the apparent proper motion of a star, as seen by us. Here we
should naturally expect to find that the observed motions of stars would be
materially influenced by their distance from the point of observation, our
earth or the sun, provided there is some systematic connection, as we presume
there is, between these proper motions themselves.
Dr. Oudemans in a very valuable and interesting memoir just printed in
the Ait. Nacfi.,No. 2915, has collected all the reliable parallactic determinations
yet made (not yet amounting to fifty), and has tabulated them in five groups
of nine stars each, arranged in the order of their proper motions, and the
prominent conclusion to be drawn therefrom is, that so soon as the observed
proper motion of a star falls below one-twentieth of a second of arc, its parallax
may be expected to fall below one-tenth of a second. This concluded relation
between proper motion and parallax may indeed be somewhat modified by the
fact, that the selection of stars for the determination of parallax has hitherto
been greatly influenced by the consideration of their known large proper
motions ; nevertheless, this last observation hardly applies to those series of
stars, selected for parallactic investigations on grounds quite irrespective of
motion, such as the groups of the first and second magnitude stars submitted
to observation by Dr. Elkin and myself. It must not, however, be overlooked,
that any final conclusion on this subject is necessarily premature on account of
the small number of parallactic determinations available for discussion.
4-4
UNIVERSITY OF CALIFORNIA LIBRARY
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