Ill f!
! I : !
BERKELEY
LIBRARY
or
WASHINGTON OBSERVATIONS FOR 1870. APPENDIX III.
.
ON THE RIGHT ASCENSIONS
EQUATORIAL FUNDAMENTAL STARS
AND THE CORRECTIONS NKCIWSAKY TO REUUCK THE
RIGHT ASCENSIONS OF DIFFERENT CATALOGUES
MEAN HOMOGENEOUS SYSTEM
BY
SIMON NEWCOMB,
PROFESSOR OF MATHEMATICS, UNITED STATES NAVY.
PREPARED AT THE U. S. NAVAL OBSERVATORY
1!Y ORDER OF
REAR-ADMIRAL H. F. SANDS, U. S. N.,
SUPERINTENDENT.
WASHINGTON:
GOVERNMENT PRINTING OFFICE.
I S 7 2 .
TABLE OF CONTENTS.
Pape.
i I. Introduction 5
S 2. Determination of a system of corrections to the relative right ascensions of ISessel s Tabuliv Kegiomnnlana. , pre
sumed to be free from periodic errors
$3. Discussion of the probable error of these determinations .... 17
$4. Systematic discordances among the catalogues employed 21
$ 5. Determination of the common correction to the first set of positions on account of equinox 21
$ 6. Corrections for the terms multiplied by the second and third powers of the time 34
$ 7. Corrections to different catalogues to reduce them to the preceding system 39
J 8. Derivation of definitive right ascensions 47
Table of right ascensions from 1750 to 1900 53
Corrections for orbital motion of Sirius and Procyon 69
Hill s formulae for the secular variation of the annual motion of the stars 73
ON THE RIGHT ASCENSIONS
EQUATORIAL FUNDAMENTAL STARS
THE CORRECTIONS NECESSARY TO REDUCE THE RIGHT ASCENSIONS OF
DIFFERENT STAR-CATALOGUES TO A MEAN
HOMOGENEOUS SYSTEM.
INTRODUCTION.
Within the past few years very important additions have been made to the mate
rial at our disposal for an accurate determination of the positions and proper motions
of the fundamental stars. These comprise Dr. Amvers reduction of Bradley s observa
tions, the Pulkowa catalogue of 1845, an( l the continuation of the Greenwich and
Washington observations. It is not too much to say that this additional material alone
would suffice to furnish results far more accurate than any that could be obtained from
the older data.
The object of the present work is to do for the right ascensions of the equatorial
and zodiacal stars, on which the reductions of lunar and planetary observations depend,
what has been done by Dr. Auwers for the declinations, namely, to furnish the data
necessary to reduce the principal original catalogues of stars to a homogeneous system
by freeing them of their systematic differences. I think this can best be done by com
paring the catalogue-positions of the fundamental stars with a uniform set of standard
positions as free as possible from systematic error, and to consider any systematic dis
cordance between the standard and the catalogue position as due to error of the latter,
and correct it accordingly. For the reason already mentioned, it will not be admissible
to take any existing catalogue as the standard. The first step of our work is, therefore,
the preparation of a system of right ascensions of fundamental stars which shall be as
free as possible from the suspicion of systematic error.
In the formation of such a catalogue I have been guided by certain considerations
respecting the probable presence of systematic errors in the reduced right ascensions
of many modern catalogues. It has long been the custom, in the reduction of right-
ascension observations, to deduce a correction of the clock from adopted right ascen
sions of stars, and to consider the mean correction thus deduced as applicable to all the
stars observed, the clock-stai S included. On this system it is clear that if the assumed
positions of all the clock-stars used on any one night are affected by a common error,
6 RIGHT ASCENSIONS OE FUNDAMENTAL STARS.
that same error will be carried into the concluded positions. Thus any periodic error
depending- on the right ascension will tend to perpetuate itself. In a former paper I
showed that if the clock-stars observed on each night are distributed uniformly over a
period of six hours, and if the assumed positions are affected with the error
a sin 11. A. -f- 1 cos K. A. -f- a 1 sin 2 11. A. -f- ?/ cos 2 R. A.
the concluded positions will be affected with the error
8 2 ( sin R A. + & cos R A.) + -*, <y , S m 2 R A. + V cos 2 R A.)
Hence the error of single period will be cut down very slowly by successive revisions
of the catalogue, each revision reducing it by less than one-fifth. On the other hand,
the error of double period Avill rapidly disappear.
The introduction of these periodic errors is very easy, even where the greatest
care is taken in the reductions, owing to the diurnal variation of the conditions to
which the instrument, the clock, and the observer are subjected. If the pointing" of
the instrument, the rate of the clock, or the personal equation of the observer vary
during the twenty-four hours, the right ascensions deduced will be affected by a cor
responding error. It is true that if the variation continues uniform during an entire
year, and if the observations are uniformly distributed throughout the year, this error
will be eliminated from a year s work. But neither of these conditions is completely
fulfilled, the diurnal change of temperature being greater in summer than in winter,
while the annual period in the length of the night and the degree of cloudiness interferes
Avith the continuity of the system of observation.
2.
DETERMINATION OE A SYSTEM OF CORRECTIONS TO THE RELATIVE RIGHT
ASCENSIONS OF BESSEL S TABULAE REGIOMONTANvE, PRESUMED TO BE
FREE FROM PERIODIC ERRORS.
For the reasons already mentioned, it seems best to deduce the periodic error of
the standard catalogue solely from determinations which are entirely independent of
any previous hypothesis respecting the right ascensions of clock-stars, and from those
in which there is reason to believe that the periodic error has been entirely eliminated.
I have selected the following twelve original catalogues as certainly or probably fulfill
ing one of these conditions :
1. Ameers Bradley, 1755. Dr. Auwers has very kindly placed his definitive
results for relative right ascensions, which are as yet unpublished, at my disposal.
2. Piazzi, 1800. " Praecipuarum stellarum inerrantium positiones media? ineunte
saeculo XIX. Panormi, 1814."
3. Maskclync, 1805. Catalogue found in Maskelyne s Astronomical Observations
made at the Royal Observatory, Greenwich, from 1799 to 1810, p. 112 of part 2.
4. Ameers Cacciatore. "Reduction der Beobachtungen der Fundamentalsterne
am Passageninstrument der Sternwarte zu Palermo in den Jahren 1803 his l &5i un( l
Bestimmung der mittleren Rectascensionen fur 1805. Von Arthur Auwers. Publica
tion der astronomischen Gesellschaft, V. Leipzig, 1866."
DETERMINATION OF A SYSTEM OF CORRECTIONS. 7
5. Bcssd I. "Bestimmung dor geraden Aufsteigungen der 36 Maskelyneschen
Fundamental-Sterne fur 1815, auf Kb nigsberger Beobachtungen gegriindet." Berlin
Memoirs for iSiS- ig, p. 19 of part 2.
6. Besscl II. " Neue Untersuchungen iibor die geraden Aufsteigungen der 36
Fundamental-Sterne." Berlin Memoirs for 1825, p. 23 of part 2.
7. Stntcc. Catalogue found in "Positiones media 1 ," p. xxxxi.
s. Brinklcy. Catalogue found in the Astronomische Nachrichten, Band IV, S. 102.
9. Argelander. Corrections yireii ly Besscl in Astronomische NacJiricJitcn, No. 5 1 5.
These differ from the positions in Argelander s "DLX. Stellartun fixarum positiones
media 1 " only in the addition of the third decimal of seconds.
10. Ptilkoica, 1845. "Observations do Poulkova, publiees par Otto Struve, Direc-
teur de 1 observatoire central Nicolas. Saint-Petersbourg, 1869." Vol. I, p. 120.
ir. Greenwich, 1864. "New seven-year catalogue of 2760 stars deduced from
observations extending from 1861 to 1867 at the Royal Observatory, Greenwich, and
reduced to the epoch 1864." (Appendix II to the Greenwich observations for 1868.)
1 2. WasJiiiiyton, 1870. "Positions of fundamental stars deduced from observations
made at the United States Naval Observatory between the years 1862 and 1867."
(Washington observations for 1867, Appendix III.)
On this selection I remark that, I find no positive evidence that, the catalogues of
Piazzi and Brinkley are really independent of any previous determination, and that 1
have judged them to be so because the modern system of reduction had not, then come
into general use. Argelander, Greenwich, and Washington are not rigorously inde
pendent, but they arc included, because, in the case of each, there is reason to believe
that the systematic errors have been more or less completely eliminated. The follow
ing are the reasons in the case of each catalogue:
An examination of Argelander s observations shows that they were generally
widely distributed throughout the twenty-four hours, his habit being to observe both
morning and evening. From such a day s work the error of single period will be
almost entirely eliminated.
The Memoirs of the Royal Astronomical Society, vol. 34, contain a paper by Mr.
Stone, in which the stars y Pegasi, Pollux, Spica, and a. Aquila? are compared, with the
express purpose of detecting any inequality depending on the right ascension. The
resiilt is that the relative positions of these stars, as given in the seven-year catalogue
for 1860, require the following corrections:
/ Pegasi Pollux, -.001 or .014
Pollux Spica, +.029 or -(-.015
Spica - a. Aquihv, -f- .008 or .005
a Aquihc y Pegasi, +- OI 8 or +-004
The first column shows the differences independently deduced ; the second their
values when each is diminished by a constant so as to make their sum zero.
The smallness of this result indicates that the periodic error, if it exists at all, must
be very small, and it ought to be smaller still in the catalogue of 1864, which includes
still another revision.
8 RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
In the case of Washington ;i special effort was made to determine the periodic
error of Dr. Gould s right ascensions; which was of the form
a sin R. A. + b cos R A.
the details of which are given in the catalogue cited. The determination was entirely
satisfactory except in one point a large diurnal inequality showed itself during the
second year. This inequality had to be determined on the supposition that it remained
constant throughout the year, an hypothesis which, though probable, was not certain.
Having selected our data, the next question will be the mode of combining. It
was my original intention to compare each catalogue with Dr. Gould s standard, and
thus obtain a correction to the latter of the form
a sin a -\-l) cos a-\-c
A series of values of a, b, and c being thus found for the epochs of the various
catalogues, the true values of these quantities should increase uniformly with the time.
We should then determine a , a , 1 , V, c oj c , from the equations
a + ft t = n
1> + Vt - I
c + c t = c
of which we should .have as many sets as there were catalogues compared. Having
found the most probable values of a , a , etc., the residuals left after substituting them
in the equations given by each catalogue would show the systematic error of that cat
alogue.
But it has been deemed best to begin by determining each star independently of
any catalogue whatever, and of any assumed proper motion. This is done most easily
and elegantly by assigning the same weight to all the stars in any one catalogue ; this
weight being determined not by the general accuracy of the catalogue, but solely by
its probable freedom from systematic errors. It will then be unnecessary to apply any
reduction on account of eqitinox in this preliminary determination, because, if all tlie
right ascensions of any one catalogue be changed by a constant, that change will affect
all the concluded positions by the same amount, and therefore will not change the rel
ative positions at all.
From the nature of the case, it is clearly impossible to make any numerical calcu
lation of the relative weights to be assigned to the different determinations. This is
necessarily a matter of individual judgment. Without going into the consideration of
each particular case, I- may remark that the following weights assigned were founded
on considerations respecting the probable freedom of the instruments from sources of
systematic error and the care with which systematic error was avoided in the observa
tions and reductions, probable accidental errors not being taken into account, and that
they were decided on before any comparison of results. They have, therefore, no
necessary analogy with the weights to be assigned in a definitive discussion, after sys
tematic error has been allowed for.
DETERMINATION OF A SYSTEM OF CORRECTIONS.
Weights assigned to observations.
No.
Catalogue.
Year.
Weight.
I
2
Auwers Bradley . .
I iazzi
1755
1800
i
3
iSos
4
5
Auwers Cacciotorc .
Bessel I ...
1805
181=;
I
6
7
Bessel II
Struve . .
1823
iS"i
3
7
8
Brinkley
i82a
9
10
Argclander
Pulkowa
1828
i8j?
2
6
ii
1864
2
12
Washington
l87O
1
The dates here given to the catalogues are generally supposed to be about the
means of the times of observation on which they depend. The principal exceptions
are Brinkley and Washington. The mean date of the former could not be inferred
with certainty, but must be earlier than 1824. The date assigned for the latter is,
through inadvertence, that to which the catalogue was reduced, which is five years
later than the actual mean of the times of observation. The reduction to the epoch
was, however, made with Dr. Gould s proper motions, which arc so near the truth that
few or none of the results are altered the thousandth of a second by this error. I have,
therefore, not corrected it,
The results are all exhibited in the form of corrections to the mean positions and
annual variations of the Tabula; Regiomontanre for the sake of convenience, and the
principal steps of the computation are exhibited in the following tables. The first
column in each table shows the correction to the right ascension of the Tabula; Regio-
montanse given by the catalogue. Following one star through the several catalogues,
we have a series of corrections applicable at the various epochs. The true correction
being of the form x -\- y t, each catalogue result gives an equation of condition between
x and y. As an epoch near the mean leads to the most convenient computations, I
have chosen the year 1820 as the origin of time. Let us now represent by
the corrections given by the several catalogues, the subscript numbers being the same
as those of the catalogues to which they correspond in the preceding list. Taking the
century as the unit of time, the equations of condition will then be
./ 0.65 // = (\
./ O.2O1J r 2
x o. 1 5 y r ,
etc., etc., etc.
2 F s
I0 RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
The solution of these equations by least squares, using the weights in the preceding
list, will give the following values of x and y:
-\- 0.04 c. 2 - o.io f 2
+ 0.04 f;, - 0.08 C 3
+ 0.04 c 4 - 0.08 c 4
+ 0.04 r 5 - 0.03 c,
+ o. 1 1 c 6 - 0.04 c t;
+ o. 1 1 c, 0.03 c 7
+ 0.03 c e o.o i c 8
+ 0.08 r,, + o.o i c,
+ 0.19 c, +0.40 r 10
+ 0.06 r n +0.27 c n
No account is here taken of the discordant equinoxes of the various catalogues,
because, all the stars in the same catalogue having the same weight, a change of
equinox will not change the relative positions of the stars.
In the selection of stars, attention has been at first confined to the Maskelyne
fundamental stars between the limits of declination -f 40 and 30. Several stars
have to be omitted, namely, Procyon and Sirius, on account of the irregularity of
their proper motions which has been so exhaustively investigated by Auwers that no
further discussion of their positions is yet necessary ; Castor, on account of its duplic
ity, and the confusion of the observations upon it, which render it unfit for use as a
standard star ; /? Virginis, a. Librae, and a. Capricorni, because they have of late
dropped out of use.
Under each catalogue, in the following table, we have, in column c, the correction
to the Tabulae Regiomontanae given by the catalogue, from which the values of x and
y are deduced by the preceding formulae.
The value of the correction x -f t y is next computed for the epoch of each cata
logue, and subtracted from the correction given by observation. The excess of the
catalogue result thus obtained is given in the second column of the table. To correct
the residuals for discordance of equinoxes, the mean value of the numbers in this
column is taken, and subtracted from the individual numbers. The remainders repre
sent the discordances between the catalogue and the correction as finally deduced.
DETERMINATION OF A SYSTEM OF CORRECTIONS.
I I
Corrections to rig/it ascensions given by standard catalogues.
Star.
Bradley, 1755
Piaxzi, 1800.
f\
c
c"
fl
<V
<V
y Pegasi ....
+ 65
- 31
54
- 65
4- 18
a Arietis ....
- 56
+ 40
+ 9
- lOS
- 144
- 61
Ccti.
4- 1$
4- 6.1
4- T1
76
g(3
<7
~ j^
i ^4
^ J J
7
J
a Taiiri ....
12
+ 51
+ 20
- 194
- 172
89
/? Orionis.
+ 40
+ 33
4- 2
54
- 30
+ 47
i) Tauri ....
+ 152
+ 31
O
53
- TOO
17
a Orionis.
+ 30
+ 22
9
7.
13
4- 70
,3 Geminorum .
102
+ 41
+ 10
- 173
- 133
- 50
a Hydrx ....
- 139
4- 23
- 3
- 118
- So
+ 3
Lconis ....
106
+ 43
+ 12
- 170
121
38
/? Lconis ....
- 76
+ 34
+ 3 !
- 85
- 68
+ 19
Virginis
42
4- 2S
3
- S6
54
+ 29
a Bootis ....
- 36
+ 39
4- 8
- 164
- M3
- 60
a- Libra: ....
+ 190
+ 23
- 8
4- 30
- 33
+ 50
a Corona}
- 66
+ 37
4- 6
- 240
208
- 125
a Serpontis .
+ 122
+ 35
+ 4
- 56
- 86
- 3
11 Scorpii ....
+ 84
+ 4
- =7
4- 122
+ 98
4- 181
Hcrculis .
16
+ 40
+ 9
- 225
202
- 119
a Ophiuchi .
- 162
+ 44
+ 13
- If) I
- n6
- 33
a Lyrne ....
30
+ 23
- 3
- 1 = 7
108
- 25
y Aquilrc.
+ 163
+ 29
2
- 35
- 85
- 2
a Aquilic.
12
+ 18
13
- 5
37
4- 46
/} Aquilx.
+ MI
+ 26
- 5
- f>7
- -89
6
a 3 Capricorn!.
7
+ 7
24
20
4- i
+ 84
a Aquarii.
- I 5
+ 16
- 15
74
- 22
4- 61
a Pegasi ....
+ 7
4- 29
- 2
- i*
92
- 9
a Andromcdx .
- 73
+ 45
+ 14
-187
- 159
- 76
12
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Corrections /<> rig/it ascensions, &c. Continued.
Star.
Maskclync, 1805.
Auwers Cacciotorc.
Oi
(3
f-.l"
ft ft
ft"
y Pcgasi ....
~ MS
- 152
24
+ 56 +52
+ 29
a Arietis ....
- I 4 S
- 133
- 5
23 8
- 3i
a Ccti ....
228
- Ill
- 243
94
- "5
+ 34
+ 27 +12
+ 14 +31
ii
+ 8
a Tauri ....
/} Orionis.
- 139
- 159
- 31
+ 61 +41
+ 18
ft Tauri ....
- 62
IOI
+ 27
+ 110 + 71
+ 48
n Orionis.
123
- 129
I
+112 + 106
+ 83
ft Geminoi um
(i Hyclnc
189
- 133
i/3
- 161
106
- I3&
- 33
+ 22
- S
+ f 5 + 93
+ 28 +55
+ 25 +62
+ /o
+ 32
+ 39
Lconis ....
ft Lconis ....
- 98
- 88
+ 40
+ 21 +31
+ 8
ti Virginis
- 122
93
+ 35
29 o
- 23
a Bootis ....
- 97
- 82
+ 46
+22 + 37
+ M
ft- Librge ....
50 - 101
+ 27
2 53 76
Corona;
1 20
96
+ 32
74 50
- 73
Serpentis .
125
- 148
20
- 53 - 7G
- 99
a Scorpii ....
206
223
- 95
+ 69 +52
+ 29
a Herculis
- in
91
+ 37
Si - 61
4
a Ophiuchi .
- 163
- I3i
3
28 + 4 | 19
a Lyra ....
- 65
51
+ 77 - 5 +9
14
y Aquilic ....
- 7i
- in
+ 17
+ 54 + 14
- 9
<i Aquil;c ....
- 162
- 151 23
+ 44 +55
+ 32
,3 Aquilse ....
a- Capricorni. ..
- 1 20
- 148
- 135
- 126
+ 2
,+ 17 +2
2O +2
21
21
a Aquarii.
- 208 : - 164
- 36
5 +39
+ 16
Pegasi ....
- MO - 133
5 + 47 +54
+ 31
a Andromedx .
146 125
+ 3 +23 +44
+ 21
DETERMINATION OF A SYSTEM OF CORRECTIONS.
Corrections to right ascensions, & f. Continued.
Star.
Bessel I, 1815.
Bcsscl II, i825.
ft
Ct
ft"
fa
<
<"u"
y Pcgasi ....
+ 140
+ 151
+ 98
+ 22
+ 27
a Arietis ....
+ 123
+ I2O
+ 67
17 12
n Ccti
+ 126
+ IOO
+ 47
o - 35
- 3"
a Tauri .... +20
+ 27
26
o o
+ 5
,j Orionis. ... S
-. 33
- 86
- 30
- 25
,i Tauri ....
+ 32
+ 10
43
o
- 9
4
Orionis. . . . 45
5i
- 104
- 3
+ 2
/j Geminorum . . 5
J
51
o
17
12
llydne .... 78
8
I3C
o
28
00
a Lconis .... 16
2
j j
- 55
o
4
^ J
+ I
; i Lconis . . . . 1 +34
+ 21
- 32
31
26
( Virginis
- 3
+ M
39
+ 17
+ 22
a Bootis ....
+ 33
+ 4
13
- 8
- 3
+ 166
4- I3O
+ 86
o
_ s
T
a Coronx ...
+ 102
i * Jy
+ ICQ
+ 56
6
J
a Serpentis .
+ 83
+ 73
+ 20
+ I
+ 6
a Scorpii ....
+ 121
+ 118
+ 65
+ 7
+ 12
a Hcrculis
+ 53
+ 66
+ 13
o
+ 7
+ 12
a Ophiuchi .
+ 27
+ 20
- 33
- 37
- 32
a Lyric ....
+ 56
+ 61
+ 8
2
+ 3
j Aquilx ....
+ 65
+ 44
9
o
- 6
I
a Aquilx ....
+ 48
+ 55
+ 2
+ 4
+ <)
t 3 Aquilie ....
+ 63
+ 7i
+ 18
+ 26
+ 31
n- Capricorni.
+ 52
+ 76
+ 23
+ 26
+ 31
a Aquarii.
+ (>4
+ 37
16
o
+ 13
+ 18
Pcgasi ....
+ 112
+ 116
+ 63
+ 2
+ 7
Andromeda .
+ 123
+ 123
+ 70
o
17
12
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Corrections to right ascensions, &c. Continued.
Qt.-l Y
Struve.
Brinkley.
Mar.
cr
c-,
CT
<8
<"
<"
7 Pegasi . . . .
+ II
+ 35
I
- 150
126
+ 9
a Arictis ....
+ 57
+ 33
+ 2
- 93
112
+ 23
a Ccti
-f- 73
+ 37
+ I
- 150
1 86
51
a T.iuri ....
+ 22
+ 21
- 15
- 145
- 146
it
ft Orionis.
+ 119
+ 89
+ 53
- 82
- 112
+ 23
,? Tauri ....
+ 20
+ 14
22
- 152
160
25
a Orionis.
+ 28
+ 22
- 14
- 128
- 134
"+ I
/? Geminorum
+ 34
+ 13
- 23
- So
- 101
+ 34
+ 03
+ 61
+ 2 5
- 6
- 3?
+ Q7
a Lconis ....
1 j j
+ 39
+ 32
- 137
- M4
1 j i
- 9
,:) Leonis ....
+ 58
+ 24
12
- no
- 144
9
a Virginis
+ 4
+ 20
16
- 182
- 1 66
3i
a Bootis ....
+ 29
+ 19
- 17
- 139
- 149
M
4- 22
+ 17
10
126
131
+ 4
a Cororue
+ 73
+ 66
j
+ 30
- 137
j *
- 144
9
a Scrpcntis .
+ 71
+ 74
+ 33
- 156
- 153
IS
a Scorpii ....
+ 44
+ 52
+ 16
1 86
- 177
42
a llcrculis
+ 67
+ 74
+ 38
- 115
108
+ 27
Ophiuchi .
+ 118
+ 76
+ 40
- Si
123
+ 12
tt L)TDB ....
- 6
- 9
- 45
- 101
- 104
+ 31
} AquiUe ....
+ 50
+ 46
+ 10
- 146
- 150
- 15
Aquilic ....
+ 27
+ 30
6
,- MS
- MS
10
,? AquiUc ....
+ 10
+ 39
+ 3
205
- 176
41
<i~ Capricorn!.
+ 37
+ 63
+ 27
189
163
- 28
a Aquarii
+ 21
+ 33
- 3
- 127
- "5
+ 20
a. Pegasi ....
+ 5
+ 7
- 29
132
- 130
+ 5
a Andromedx .
-
- 25
- 61
- 87
- 106
+ 29
DETERMINATION OF A SYSTEM OF CORRECTION S.
Corrections to right ascension, &c. Continued.
Star
Argelander.
I ulkowa.
fa
f
Ct"
Cut
c
fu>"
Y Pcgasi ....
1C
-4- 11
CQ
ii
6
Arietis ....
* ;?
+ 2S
1^ **T
+ 2
DV
+ 62
+ 8
+ 13
n Cell
+ 26
ic
4- c i
o
-U c
* j
1 J~T
^ D
Tauri ....
+ 12
+ 8
t f
+ 6
16
II
ft Orionis.
+ 9
- 23
.
+ 3S
+ 2
+ 7
,1 Tauri ....
+ 13
+ 12
- 7
+ 10
+ 15
Orionis.
+ 17
+ II
.
13
- 17
- 12
fi Gcniinorum .
+ 44
+ 14
t t
+ 7
+ I
+ 6
n Ilydrx ....
+ 44
I
+ 90
O
+ 5
a Lconis ....
+ 12
o
+ 50
3
+ 2
/J Leonis ....
+ 42
I
.
+ 75
+ 5
n Virginis
- 26
13
+ 3
+ 2
+ 7
a Bootis ....
+ s
- 6
.
+ 38
+ 5
+ 10
n 2 Libra; ....
8
4
60
if)
ii
Corona;
+ 36
+ 22
+ 34
7
o
Scrpcntis .
2
+ 6
.
- 37
- 8
- 3
Scorpii ....
- 55
41
54
"9
M
a Hcrculis .
+ 6
+ 10
- ID
- 23
18
n Ophiuchi .
+ 73
+ If>
.
+ 94
21
1 6
a Lyrx ....
+ 6
O
+ 34
+ 12
+ 17
} Aquihe .
-1- 7
+ 10
31
+ 5
+ 10
n Aquilffi ....
_ 5
- 3
- + 7
+ I
+ f)
/} Aquihc.
34
+ 4
.
75
- 5
a- Capricorn! .
- 5S
- 31
32
7
2
Aquarii
- 26
21
+ 16
10
5
a Pegasi ....
+ 7
+ 8
ii
- 15
10
a Andromeda; .
+ 41
+ 13
-t- 63
+ I
+ 6
i6
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Corrections to right ascensions, crV. Continued.
Star.
Greenwich, 1864.
Washington.
u
CM
fti"
Cn
tii
Ca"
7 Pcgasi ....
- 124
51
- 30
- 59
+ 22 .
12
a. Arictis ....
+ 53
33
12
+ 123
+ 27
- 7
a Ceti
+ 53
13
+ 8
+ 132
+ 5 &
+ 22
a Tami ....
+ 40
+ 1 +22
+ 9i
f 48
+ 14
/? Orionis.
+ 24
18
+ 3
- 73
+ 29
5
/? Tauri ....
- 58
o
+ 21
52
+ 16
- 18
a Orionis.
+ 6
+ 3
+ 24
+ 38
+ 35
+ i
/3 Geminorum .
+ in
- 3
+ 18
+ 151
+ 23
n
a Hydrne ....
+ 129
15
+ 6
+ 185
+ 23
n
a. Leonis ....
+ 83
13
+ 8
+ 148
+ 39
+ 5
/? Leonis ....
+ no
4
+ 17
+ 160
+ 33
i
Virginis
22
- 38
17 <
+ 57
+ 37
+ 3
a. Bootis ....
+ 39
- 17
+ 4
+ 97
+ 33
i
03
5
+ 16
67
+ 34
a Coronx
+ 48
23
2
+ 98
+ 17
17
a Serpcntis .
- 79
- 25
4
- 32
+ 29
- 5
a Scorpii ....
- 91
- 32
n
- 19
+ 48
+ M
a Ilerculis
+ 12
10
+ II
+ 62
+ 35
+ i
a Ophiuchi .
+ 178
- 5
+ 16
+ 246
+ 42
+ 8
n Lyric ....
+ 9
29
g
+ 68
+ 25
9
y Aquilx ....
- 117
46
- 25
42
+ 40
+ 6
Aquilx ....
- 32
18
+ 3
+ 49
+ 34
/? Aquihc ....
- 148
39
18
- 89
+ 33
i
n 2 Capricorn i.
54
- 29
- 8
o
+ 25
9
Aquarii.
+ 6
- 53
- 32
+ "5
+ 4<J
+ 12
Pegasi ....
2O : 30
9
+ 60
+ 49
+ 15
a Andromedx .
+78 -22
I
+ 151
+ 40
+ 6
DISCUSSION OF PROBABLE ERROR.
The following are the values of x and y, in which the units are thousandths of
seconds of time:
Star.
X
y
} Peijasi
- 18
127
ft Arietis
+ 12
F- 167
Ccti .
-J- -12
-t- 89
(i Tauri
-|- n-3
ft Orionis ....
ft Tauri . . .
+ 2S
+ M
+ 32
lf 5
Orionis ....
ft Geminorum
llvdnc
Lconis .
+ 5
+ 10
+ 19
- 5
+ 236
+ 286
+ 225
ft Lconis ....
+ 2 4
+ 206
a Virginis ....
B,,otis .
if)
+ 4
+ 78
+ 121
- Librae
-4- IT
211
n Coronic ....
n Serpentis .
+ I
+ 3
+ I f)0
- 129
fi Scorpii .
3
- I2S
Keren! is ....
" Ophinclii ....
ti Lvrx
- 9
+ 2f)
+ 72
+ 357
+ 83
} Aqnil:c
+ 12
- 1 88
ft Aquilrc ...
5
+ 39
ft Aquihc .
10
206
: C apricorni
a Aquarii ....
n I t^asi
- 25
18
3
I
+ 174
+ 29
Andromcdic .
+ II
+ I W
$3-
DISCUSSION OF PROBABLE KRROK.
From these discordances we shall next deduce the probable error of the resulting 1
x and y. It is well known that results for probable error generally prove entirely
illusory. This does not arise from any defect in the theory of the subject, but from
the fact that the probable error generally has to be deduced from the discordances
among a series of results affected by some common source of error, which changes
;ill the results in the same way, and is, therefore, not eliminated from the mean. 15ut
the twelve star-catalogues here employed may be regarded as absolutely independent
of each other.
In deducing the probable error from each series of residuals, I take the mean
value of the residuals without regard to the sign. In the more elegant method of
deducing the probable error from the sum of the squares of the residuals, it seems to
me that too much weight is assigned to those large residuals the presence or absence
3 v s
jg RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
of which is a mutter of chance. The probable error being proportional to the mean
error, and only a little smaller, I shall use the latter throughout instead of the former.
The mean values of the numbers found in the third columns, taken without regard to
the sign, are as follows:
1. Auwers Bradley ... 10.7
2. Piazzi - - 49
3. Maskelyne .... 3
4. Auwers Cacciotore 36
5. Bessol I 47
6. Bessel II ^3-7
7. Struvo - - - - 211
8. Brinkley 23.3
9. Argelander 11.4
10. Pulkowa 8.2
1 1. Greenwich . 13.1
12. Washington 7-9
Had the catalogues all been entirely accordant, these residuals would all have
been zero. Let us next see in what manner they are made up. In the case of Bradley
the residual is formed by subtracting from each c t the value of x 0.65 y deduced from
the expression on page 10, substituting for c i} r 2 , etc., their values found in the preceding
table. Substituting in this expression these values of x and y in terms of (\, c y , etc.,
which have already been given, we find
x 0.65 y .68 c t + .10 c., -f .09 c,, -f .09 c 4 -f .06 c~, + .14 C R + .13 r 7
+ .04 r 8 + .07 r fl .07 r, .1 2 c n .22 f, 2
Subtracting this from r,, the difference is
.32 Ci . i o r., .09 r : , .09 r 4 .06 Cr, . 1 4 c 6 . 1 3 c- .04 r H
- .07 c a + .07 r, + .12 Cu + .22 r 12 r;
and it is this expression of which the value is given in the second column under each
catalogue in the preceding tables.
Let us now represent by
fo, e, . f 12
tlie probable errors of
c \i CM fa .... f 12
or of the star-positions in each catalogue. The square of the mean error of a sum
being equal to the sum of the squares of the individual mean errors, the square of the
mean error of the last expression, or of c , will be
.IO2 i~ + .OTO f., 2 + .OO8 :i 2 -f -OOS ,, 2 -f .OO4 * + .029 ,f -f- .OI 7 -, -(- .OO2 E^
+ -005 ,/ + .005 10 2 + .014 U 2 + .048 K "
The mean Bradley residual being 10.7, the value of this expression is 114.
A similar equation being formed for each of the twelve catalogues, we have twelve
equations of the first degree, which suffice completely to determine the twelve values of
DISCUSSION OF PROBABLE ERROR.
F, and therefore the mean error of each catalogue. These equations are as follows,
writing only the co-efficients of the unknown quantities:
*
E
*
f 6"
*
tf
, ,
^
.IO2
.010
.OOS
.008
.004
.O2O
.017
.002
.005
1
.005
.014
.048
-- 114
.109
.866
.004
.004
.OO2 .014
.014
.OOI : .OO6
.012
.O
.0
2601
.084
.002
. 902
.004
.OO2
.014
.012
.001 .OOO
.017
.000
.000
= 900
.084
.036
.002
.002
.OO4
.002
.902
.002.
.OO2
.922
.014
.OI2
.012
.OI2
.001
.001
.0
.006
.017
.032
.0
.002
.0
.006
1296
= 2209
.022
.002
.002
.002
.OO2
.792
.OI2
.001
.006
.040
.OO5
.OIO
= 196
.020
.OO2
.OO2
.002
.OO2 .012
.792
.001 .006
.044
.OO5
.012
- 441
.020
.002
.002
.002
.002 .OI2
.OI2
.940
.006
.044
.005
.012
= 529
,OI2
.001
.001
.OOI
.002 .012
.OI2
.OOI
.846
.048
.OO6
.017
= 121
.OOI
.000
.000
.OOO
.OOI
.OIO
.OIO
.001
.006
.504
.017
.044
= 6 7
.029
.000
.000
.OOO
.OOI
.008
.OIO
.001
.006
- 37
.672
.090
- 170
.048
.
.000
.OOO
.OOO
.ooS
.OIO
.OOI
.006
.152
.036
.462
= 6 3
Those equations will give the middle scries of probable errors with great, certainty ;
but those which lie near the extremes in point of time will be quite uncertain, the
necessary uncertainty of the last members of each equation being considerably exag
gerated iu the result. If we solve by successive approximation, the equations for
determining e* and F,./ will be
. 1 02 e i~ zr 1 1 4 74 40 ; f , =. o".O2O
.462 F 12 a = 63 55 = 8 ; F,, o*.oo4
We may roughly estimate the uncertainty of the second members of the. preceding
equations as equal to one-fifth of their entire amount, so that the numlx?r for which we
have found the value 1 14 might have ranged anywhere between 91 and 135, while
that which we have found to be 63 might have ranged between 50 and 76. Hence the
value of F! may, from this cause alone, range between o s .oi3 and o".O25, and that of F,.,
between zero and O 8 .oo7. In the latter case we have an independent means of esti
mating the probable error. The catalogue result actually employed is the mean of
two nearly independent determinations with different instruments. The mean differ
ence .of the results was o".oi3. Wo may therefore put o".oo6 as the inferior limit of ,.
To make the estimate too great rather than too small, I have supposed e 12 to be o*.oo8,
and hence obtained the following scries of probable errors, which nearly satisfy all the
equations except the last:
X.
F! .019
^ =-054
f. =-037
F,, = .048
F (i .014
F 7 =.023
<H =-023
F,, =.010
F 10 = .OIO
t f = 3 6l
!./ ZZ29I6
f :1 - =1 9OO
ff =1369
f,- 2304
f "ti~ = 96
v =529
529
100
100
f/ =:
f
ID
F,., .OO8
?n"= 196
,.;- = 64
20 RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
It may be remarked that the only uncertainty among these probable errors which
materially affect our final result for the probable error of the concluded positions is that
of (.
To find the probable error of a computed star-position at the time t, we must sub
stitute the values of x and y in the expression x-\- y t, which gives the correction to the
Tubitlce licyiomontance at the time t. Calling this correction ^ we have
-4 = + (.17 - .789*1
+ (.04 .I00<3
+ (.04 -.08 f)c 3
+ (.04 .03 c 5
+ (.n . 040 A;
+ (. 1 1 .03 c 7
+ (.03 .01 Of
+ (.o8 + .oiQcb
+ (.19 + .409 CM
4- (.06 + . 279 e u
+ (-09 + 479 c is
The square of the probable error of this expression will be
(. 1 7 - .78 O 2 *, s + (-04 - - iotf v + etc. = 36 - 1 25 1 + 303 f
t being, it will be remembered, the fraction of a century after 1820. This expression
would attain its minimum in 1840, when its value would be
~ = 23 or s o s .oo48
At any other time T its value will be
/T-i84oV
--- 23 4- 1,01, I
r y 100 y
Owing to the independence of the twelve determinations on which the concluded
positions rest, I conceive that this expression for the probable error is not entirely illu
sory, but is very nearly real. Of the exactness of the constant term no serious doubt
can be entertained. But the co-efficient 303 multiplied by the square of the time
depends very largely on the concluded probable error of Auwers Bradley, and we
have seen that there is some uncertainty in this determination. If this probable error
is really as great as o s .O25, which we have seen to be quite possible, we should have
/T-i8 4 iy
t- 23 + 464 ( 1
h y 100 /
The first expression will give for the probable error in 1900
zz o s .o r i
while the second will give
ZZO a .OI4
It must be understood that these results for probable error are true only on the
assumption that the proper motion of each star carries it forward on a great circle with
a uniform velocity.
SYSTEMATIC DISCORDANCES AMONG THE CATALOGUES.
21
$4-
SYSTEMATIC DISCORDANCES AMONG THE CATALOGUES.
Let us next inquire how far the outstanding residuals of the corrections to each
catalogue are of a systematic character depending either upon the right ascension or
declination. 1 have already set forth the reasons for believing that the systematic,
errors to be looked for are those depending on the sine and cosine of the right ascen
sion. Let us then suppose the residuals of each catalogue to be of the form
m cos a -f n sin a -f- c
If we put >,, r.,, etc., for the residuals corresponding to the several stars Ave shall have
twenty-seven equations of the form
m cos oc i -f- n sin <*; + c r- t
from which to determine -m, 11, and c. If these equations be solved by least squares,
the normal equations will be
m 2 cos 2 a-\-n 2 sin a cos a -f- c 2 cos a 2 r cos a
m 2 sin a cos a -(- n 2 sin 2 a -\- c 2 sin a 2 > sin a
m 2 cos ct-\- n 2 sin a. -f- 2 7 c 2 >
( )wing to the minuteness of the quantities 2 cos <x, 2 sin <*, w, and 11, and to the fact
that when we take the residuals r ;! in the third column of the table of catalogues we
have 2 r o, we may, using these same residuals, determine m and n from the first
two equations, putting c = o. Putting for 2 cos 2 a-, etc., their values derived from the
right ascensions of the twenty-seven stars in question at or near the mean epoch, these
equations become
1 1 . 74 m + 0.93 n 2 > cos a
0.93 m + 15.26 n -=.2 r$\\i a.
which give
i i .68 m 2 r (cos a .06 sin a)
i 5. 1 9 n ^ r (sin a .08 cos a)
Computing the values of m and n corresponding to each catalogue from these formula. ,
we find that the residuals in the second column, which represent the excess of the cat
alogue right ascension over that computed, nuiy be represented as follows:
No.
Catalogue.
Systematic residuals.
s. s. s.
i
Auwers Hradley .
r = + .031 .003 cos i + .007 sin a
IMazxi, (1800) ....
r= .087 +.003 cos a .001 sin a
3
Maskclync, (1805) . . .
r= .128 .019 cos a .006 sin a
4
Auwers Cacciotore
r = + .023 + .010 cos a + .033 sin a
5
Hessel I, (1815). . . .
r + .053 4- .037 cos a .037 sin a
6
Hessel II, (1825) . . .
) =; .005 +.006 cos a .010 sin a
7
Slruvc, (1825) ....
r = + .036 .007 cos a .005 sin a
S
Hiinklcy, (1825 . . . .
/= .135 .002 cosrt +.oot) sin a
g
Argelandcr, (1828). . .
r= .000 + .001 cos a +.002 sin a
10
1 ulkowa, (1845) . . .
r = .005 + .001 cos a + .002 sin a
II
Greenwich, (1864) .
>-= .021 .oil cos a +.010 sin n
12
Washington, (1870)
r +.034 + .004 cos .001 sin
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Tlie catalogues in which the periodic character of the residual is most strongly
indicated are Auwers Cacciotore, Bessel I, and Greenwich. In the case of the latter
the systematic difference, small as it is, makes up the greater part of the residual, since,
if it is subtracted, the mean value of the residual is reduced from .0131 to .0064, while
the probable error is reduced in an even larger proportion. Taking away the three
catalogues just mentioned, the co-efficients m and n are no greater than might result
from the accumulation of accidental errors ; it is therefore doubtful whether we ought
to regard them as real.
To find what discrepancies depending on the declinations arc indicated, I have
grouped the twenty-seven stars as follows:
7 stars north of + 20
1 1 stars between -f- 6 and -f- 16
9 stars south of-f 6
The mean residual from the third column corresponding to each group is
Catalogue.
North group.
s.
Bradley ....
+ .006
. 046
Maskelyne
+ .021
Cacciotore.
+ .OO5
Bessel I ....
+ .013
Bessel II ....
. OOf)
OIQ
Brinkley ....
+ .OIO
Argelantlcr
+ .008
+ .008
Greenwich. .
+ .003
Washington
.008
Middle.
South.
s.
s.
.000
.006
- .013
+ .049
.000
.022
+ .002
.006
. 006
- .004
+ .001
+ . 004
+ .004
+ .OIO
. 002
-005
+ .007
- .016
.005
.001
+ .004
. 006
+ .003
+ .003
Notwithstanding their general minuteness, these residuals depending on the decli
nation are more certainly indicated than those depending on the right ascension. The
catalogues in which they are largest, those of Piazzi and Maskelyne, have received
but a small weight in the preceding disciission. In all the others, with the possible
exception of Struve, they are so small that they may be treated as accidental errors.
Their farther consideration is therefore, for the present, omitted.
5- .
DETERMINATION OP THE POSITION AND MOTION OF THE EQUINOX.
For the determination of the common correction to the right ascensions of all stars
on account of error in the assumed equinoctial point, we are still dependent entirely on
observations of the sun. We may ultimately hope to determine some of the quantities
on which the absolute positions of the stars depend from observations and theories of
the planets, the orbit of each planet, when corrected for perturbations, being a -fixed
great circle, and the planets being susceptible of more accurate observation than the
sun, but this course is not possible at present. It is well known that the best deter
minations of the .equinox exhibit discordances far larger than can result from purely
DETERMINATION OF THE POSITION AND MOTION OF THE EQUINOX.
accidental errors of observation, and HO indicate the existence of systematic errors in
the observations of the sun, the nature and cause of which are obscure. The deter
mination of each co-ordinate of the sun seems about equally liable to them. We know
that the absolute right ascension of a star depends effectively upon two elements, to be
determined from observation, namely:
1 . The moment at which the sun crossed the equinox, from which its absolute
rig-lit ascension at any time may be obtained, the elements of its orbit being- known.
2. The difference of right ascension between the sun and a star, from which the
absolute right ascension of the latter is obtained from that of the former.
Since any error depending on the sun s zenith distance will, in the first determina
tion, be eliminated from the mean of the t\vo equinoxes, it might be supposed that
there would be a general agreement among different authorities in this determination.
Hut such is by no means the case, and I can assign no probable cause for the observed
discrepancies.
With reference to the second determination, it is well known that the personal
equation of an observer is frequently different for the sun and for a star, and this dif
ference will appear in the difference of their right ascensions. Diurnal changes in the
clock, the instrument, and the personal equation of the observer will also introduce
errors into the determination.
Under these circumstances the most we can do is to base our determination on
the widest range of material at our disposal, depending for accuracy on the number
and variety of the determinations employed rather than upon the precision of any one.
All the data at my disposal which did not involve a re-reduction of observations are
comprised in the following discussion.
The different common corrections to the preceding determination of right ascen-
siovis of stars are represented by c. We begin with an examination of those published
catalogues in which the star-positions are referred directly to the sun.
BESSEL S BRADLEY.
The right ascensions of the following stars were determined by Bessel by direct
comparison with the sun. Opposite each star is given Auwers correction to Bessel s
position, and the concluded correction already found, the signs being changed:
Star.
H. - A.
n - (i).
+ .012
4- 063
/? Orionis ....
- .040
.007
ra Orionis ....
.030
.008
f) Gcminorum .
+ .102
+ .143
a Lcnnis ....
+ . 106
+ -149
n Virginis ....
+ .042
+ .070
-4- 036
+ .075
a Lyrnc
+ .030
+ .058
a Aquilx ....
+ .012
+ .030
Mean ....
+ .030
+ .064
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
We liavo, therefore, from Bessel s determination for 1755
c =z
PlAZ/I, l8oO.
Of Piazzi s determination of tlie equinox I know nothing-. The mean correction
given by his catalogue cannot, therefore, receive much weight, although the geograph
ical position of his observatory is very favorable to its determination. The value of c,
resulting- from this and from all the other original catalogues employed in the preceding-
determination is the same with the constant terms in the systematic residuals, given on
page 21, and represented by r.
MASKELYNE, 1805.
Maskclyne states that his catalogue was "settled with respect to the equinoctial
points, from the observed declinations of the sun about the equinoxes in 1804, 1805,
and 1806." With the same catalogue he gives one for 1756, deduced from Bradley s
observations, the mean of which is o .io less than Bessel s, if we compare the twenty-
seven stars under consideration, or o". 1 5 less, if we compare only the stars which Bessel
found by direct comparison with the sun. This large difference may arise from Maske-
lyne s having used only observations of the sun very near the equinoxes, while Bessel
extended his determination to a declination of 14 on each side. An examination of
the tables of corrections corresponding to different declinations of the sun, given on
page 15 of the Fundamenta, docs, in fact, show a systematic difference depending on
the declination, but their source and nature are too obscure to admit of much discus
sion. All we can do is to suppose Maskelyne s determination an independent one,
entitled only to small weight.
BESSEL, 1815 AND 1825.
Both Bessel s catalogues are referred directly to the sun. The first depends on
three years observations with the old transit and the Cary circle, numbering 290 in
all; the second on five years observations with the Reichenbach meridian-circle, num
bering about 400 in all.
STEUVK, 1825.
Struvc s equinox depends on 216 observations of the sun, extending through a
period of four years. (Positiones Media 1 , p. xxxx.)
ARGELANDER, 1830.
From a remark in the introduction to his catalogue, page iii, it would appear that
Argelander, from his own observations of the sun, found a correction of +".072 to
the right ascensions of the Tabulae llegiomontana?. We have, therefore, on this
authority
c + o".o64; epoch, 1828.
POND, 1830.
In the introduction to his "Catalogue of 1112 stars," Pond states that the right
ascensions of Maskelyne s last catalogue have been increased by o .2O, being a quantity
determined by observations of the sun made about the equinoxes with the present
DETERMINATION OF THE POSITION AND MOTION OF THE EQUINOX. 25
transit-instrument since 1816. The mean value of e given by this catalogue is
-f-o s .o/3. Hut, as the mean epoch of the observations is about seven years earlier, we
may inquire whether the correction is different for this epoch. A correction of -f o s .2O
applied to Maskelyne s catalogue for i8o5 would leave
I infer, therefore, that the correction should have the same value for the mean epoch,
which we may consider to be 1825.
AIKV.S GREENWICH CATALOGUES.
The five catalogues published by Airy have been so carefully referred to the sun
that they do not appear to need any further discussion. The comparison of the indi
vidual catalogues with the positions already found give the following values of e:
s.
First six-year catalogue . epoch 1839, r .052
Second six-year catalogue l &45, e .003
Third six-year catalogue 1 85 1, e -}- .01 7
First seven-year catalogue 1 857, i- .005
Second seven-year catalogue . 1864, c .02 i
PULKOWA.
The Pulkowa equinox depends on observations of the sun with the transit-instru
ment and the vertical circle, extending from the year 1842 to 1850. The copious dis
cussion of these observations bv Wagner is found in "Observations de Poulkova,"
vol. Ill, pp. 41-67.
Adding Washington, 1870, this completes the list of original catalogues referred
independently to the sun. But we have still a collection of data in the form of obser
vations of the sun made and reduced at various observatories, and compared with the
tables. I have reduced all these in a sumniarv manner, which, though coarse and rude,
will, I am persuaded, lead to results differing from those of the most refined discussion
only by quantities much smaller than the unavoidable probable errors of the results.
The mean correction to the tabular right ascension and declination was taken for each
month through a series of years, all the observations made in any month of a given
name January, for instance being combined into a single mean. This mean was that
of the entire number of individual results. The correction to the sun s absolute mean
right ascension was then deduced from the observed errors of the tabular declination,
being given by the approximate formula
S R. A. (in time) . . 2 A <5 cos /
/ being the sun s longitude, and the factor cos / being the meail value of the cosine of
the sun s true longitude during each month.
The mean correction of the sun s absolute right ascension thus obtained is com
pared with the correction obtained by comparison with the stars, and the difference,
supposed to be due to error in the adopted right ascensions of the latter, gives the mean
correction to the equinox to obtain the absolute right ascension of the stars.
4 F s
26
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
PARIS, i854- 63. (Corrections to CarfniUs tables.}
No of
No. of
Month.
A a
obs.
<5
obs.
cos /
<5 cos /
s.
,,
..
January .
+ .132
56
+ 1.07
43
+ -44
+ 0.47
February .
+ .154
86
+ 2.76
73
+ .Si
+ 2.24
March .
+ .165
104
4- 2. 68
98
+ .98
+ 2.63
Apr 1 . . .
+ .209
116
+ 2.25
105
+ .89
+ 2.OO
May . . .
+ .245
So
+ 1.73
77
+ .56
4- i. oo
unc .
+ -234
Si
+ 1.20
74
+ .10
4- 0.12
July . . .
+ .207
1 20
+ o.So
84
39
0.31
August
+ .213
126
-t- 0.19
95
- -79
- 0.15
September
+ -194
98
0.31
76
- .98
+ 0.30
October .
+ -133
93
+ 0.50
6S
- -92
0.46
November
+ .196
72
4- o.n
52
- .60
0.07
December
+ .148
49
+ 1-30
40
. 10
0.13
Sum
+ 2.230
+ 7-f>4
We hence deduce
s.
Mean correction to sun s absolute right ascension -(-0.212
Mean correction. deduced from stars ... +0.186
Therefore star s right ascensions require the correction + 0.026
A comparison of the corrections to the Tabula? Regiomontanre adopted in the reduc
tion of the Paris observations with those deduced in this paper show that the latter are
greater by o".O24. We may therefore put as the result of this series of Paris obser
vations
c =r o s .ooo
PARIS, i864- 65 (Corrections to Le Verrier s tables.")
\
No. of
No. of
Month.
A a
obs.
,5
obs.
A ! cos /
s.
January .
.072
10
+ 0.20
7
+ 0.09
February .
.060
7
+ 1-35
6
+ i. II
March .
+ .028
16
4- i.oS
16
+ i. 06
April .
.030
24
+ 1-39
22
+ 1.24
May . . .
.013
21
0.05
2O
0.03
June .
.052
19
0.29
18
0.03
July . . .
.064
14
- o.SS
16
+ 0.34
August
.022
13
+ O.II
M
0.09
September
.OO6
23
+ 0.52
25
- 0.51
October .
.022
9
+ 0.45
1 6
0.41
November
+ .037
15
1.48
14
+ 0.89
December
- .017
13
- o.S6
13
+ 0.09
Sum
- 0.293
%
+ 3-75
i
DETERMINATION OF THE POSITION AND MOTION OF THE EOflNOX.
We hence deduce
s.
Mean correction to sun s absolute right ascension . . +0.104
Mean correction deduced from stars 0.024
Correction to adopted right ascensions of stars +0.128
The Paris concluded right ascensions for 1864 are less than those here deduced
by o s .oi3. The result of these two years work at Paris is therefore
r = + o s . 1 1 5
In the following two years nearly all the observations of the sun at Paris were
made by a single observer, whose results are remarkably different from those of other
observers, as may be seen by the very large and uniformly positive corrections to the
right ascension and longitude of the sun, given in the collected results of the observa
tions. This error evidently arises from the personal equation of the observer not being
the same for the sun and for a star. Such differences are known to exist, but they are
generally so minute as hardly to admit of positive detection. We have, however, one
or two cases of the differences attaining an extraordinary magnitude, and, as they do
not follow the usual law of error in their distribution -among different observers, we
must reject entirely the cases in question.
CAMBK1DGE, (ENGLAND.)
The results of the observations of the sun during the five years 1833 37 are as
follows:
Month.
da
No. 61
obs.
A,i
No.of
obs.
A (! cos /
s.
,,
,,
January
+ .203
3i
+ I . oo 30
+ o-44
February .
+ -I JS
40 ! + 0.96 ; 41
+ o.So
March . . . . -t- .175
44 + ".18 44
+ 0.18
April . . . | + .230
55 + 0-36
56
+ 0.32
May . . . i + .215
96
+ o.f)8
95
+ 0.38
June
+ .138
71 + 0.35
77
+ 0.04
July . . .
+ .2<>5
59 4- 0.66
53
0.26
August
+ .182
77 + 0-14
80
O.I I
Sepicmber .
+ . 208
65 , + 0.07
65
0.07
October . . + .180
73 + 0.46
75 <>-43
November .
+ -237
61 + 0.79 59 0.47
December . . + .175
42 + 0.93
37 0.09
Sum
+ 2.343
+ 0.73
Mean correction to sun s absolute right ascension
Correction deduced from stars .
Correction to adopted right ascension of stars .
Adopted right ascensions f/rctifcr than ours by .
Hence
c 0".03; epoch, 1835.
s.
-f- O.O2O
+ 0.195
-0.1/5
0.146
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
in subsequent years the discussion of the correction for each year in which suffi
cient observations of the sun were made is given along with the results of the obser
vations. The following are the mean values of c for series, each including five years
actual observation:
,1.
1841, r=:-fo.o6
1849, c +0.06
1856, c:zz O.oi
OXFOED.
Since 1861 the sun has been pretty regularly observed at the Ifadclifte Observa
tory, and the apparent errors of the tabular positions are given in the results of each
year s observations. They are divided into two series, the first comprising the years
i86i- 63, in which the results are compared with Carlini s tables, and the observations
are considerably scattered; the second, comprising the years i864~ 68, during which
the comparison has been made with Le Terrier s tables.
The tabular summary of the results for the years i86i- 63 is as follows:
No. of
No.of
Month. A
1
obs.
A(i
obs.
A ti cos /
s.
,,
,,
January . . -t- .18
9
+ 0.2
12
+ O.I
February . + .40
4
+ 0.6
M
+ 0.5
March ... + .34
12
+ "o . 6
15
+ 0.6
April . ! + .32
19
+ 1-4
19
+ 1.3
May . . . ; + .33
16
+ 1.5
II
+ 0.8
June ... + .16
13
+ 0.6
II
+ O.I
July . . .1 + .30
1 6
+ 0.5
17
0.2
August . . + .38
8
+ 1.4
8
I.I
September. . + -35
M
1-3
M
+ 1.3
October . . + .53
7
+ 0.8
9
- -7
November . . + .46
15
+ 0.7
15
0.4
December . . + .40
12
+ 2.3
12
O.2
Sum . . +4.15
. .
+ 2.1
8,
Mean correction to sun s absolute right ascension . -}- 0.06
The same deduced from stars +-35
Correction to adopted right ascension of stars . 0.29
These adopted right ascensions are the same as those used during the correspond
ing year in the reduction of the Greenwich observations, the mean of which corresponds
very nearly to our adopted results. We have, therefore, from these Itadcliffe observa
tions
r o".29; epoch, 1862.
The great and improbable magnitude of this result renders the question of its
introduction somewhat embarrassing.
DETERMINATION OF THE POSITION AND MOTION OF THE EQUINOX.
For the live subsequent years, i864~ 6S, we have
29
Month.
Au
No. of
obs. A<1
No. of
obs. A cos
s.
11
,,
anuary
+ .IT
36 + 2.0
36 + 0.9
"ebruary .
+ .10
37 + i.o
37 + o.S
larch .
+ .13
28 . + i.o
27 + i.o
Vpril . . .
+ .17
43 O.I
45 o.i
lay
+ -15
45 o.i
47 o.i
une
+ .o3
56 - 0.7
55 o.i
uly . .
+ .06
55 + 0.3
57 i o.i
August
+ .08
47 + 0.7
47 0.6
eptembcr .
+ .08
52 + o.i
50 O.I
)ctober
+ .10
46 0.2
47 -i- 0.2
November .
+ -12
42 + I.o
41 0.6
)ecember .
+ .10
+ 1.4
28 o.i
Sum
+ 1.28
.
+ I.I
8,
Correction to sun s absolute rig-lit ascension -f- 0.03
Correction deduced from stars . -f o. 1 1
Correction to adopted right ascension of stars -0.08
The adopted right ascensions beingstill the same as at Greenwich, this result gives
; O .OQ : epoch, 1 866.
The correction is still negative, as in the years i86i- 63, though not so great.
A comparison of the Radcliffe results with those derived from the Greenwich
observations shows that the difference* is found chiefly in the observed relative right
ascensions of the sun and stars. Tims, during the years i86i- 63, the mean correction
to the sun s right ascension deduced from the Greenwich observations is -f o". 17, while
that from the Radcliffe observations, nsing the same adopted right ascensions of stars,
is + O 8 .35, so that the Uadclifi e results are greater by o s . 18.
An examination of the Radcliffe observations shows that this great discordance
did not exist in the year 1861, but commenced in 1862, -\\ith the introduction of the
new transit-circle. It might, therefore, well give rise to the suspicion that the pointing
of the circle is affected with a diurnal change. As the clock-error is determined from
observations made at night, a constant error would thus be introduced into the results
of transits of the sun. 1 ut this explanation seems to be negatived by the fact that the
observations of the moon, though made at the same time with the stars, deviate still
more widely from the truth. In fact, the menu correction to Hansen s right ascension,
given by the observations of 1862, is -j- o".62, while all other observations show that
the right ascension was then very nearly correct. We may heilcc conclude that the
cause is to be sought for in some personal peculiarities of the observers. Though this
;o
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
explanation is made unsatisfactory by the circumstance that the observations of the
two principal observers lead to nearly the same result, it is noticeable that in the year
1863 Ave find four observations of the moon signed M., probably made by the director
of the observatory, the mean correction from which is -j- o a .O35. This seems, therefore,
to be the only admissible explanation.
EDINBURGH.
In the Edinburgh observations for the years i836- 39 the correction to the equinox
is deduced from each year s observations. The mean result is
r ^-f- s -4j fpoch, 1838.
Observations of the sun were continued till 1843. The published corrections to
the tables lead to the following mean results:
Month.
<irt
No. of
obs.
A 6
No. of
obs.
A <! COS /
j.
January
+ -17
50
+ 1-3
32
4- 0.6
February .
4- .12
37
+ 1-3
41
+ i.i
March .
+ .09
53
+ 0.4
60
+ 0.4
April
+ .08
57
+ 0.5
50
+ 0.4
May. . . .
+ .13
42
O.I
46
0. I
June
+ .11
51
+ 0.8
47
+ O.I
July. .
+ .09
37
0.2
43
4- o I
August.
+ .05
43
0.2
44
4- 0.2
September .
+ .08
44
I.O
43
4- i.o
October
+ .18
32
- 0.3
46
4- 0.3
November .
+ .05
32
+ 0.3
20
0.2
December .
+ .13
3S
- 0.3
41
0.0
Sum
+ 1.28
+ 3-9
s.
Mean correction to sun s absolute right ascension -j-- IO 8
Mean correction deduced from stars . . . . . . + o. 106
Correction to adopted right ascensions -f- 0.002
The adopted right ascensions are o s .oi less than those in this paper; therefore
- r o s .oi; epoch, 1842.
BERLIN.
/.
The introduction to the first volume of the Berlin observations, published by
Encke, gives the results of observations of the sun from 1839 to 1842. The following
are the mean results:
DETERMINATION OF THE POSITION AND MOTION OF THE EOUINOX.
Montli.
A<;
N o. of
obs. . A !
No. of
obs. A * cos
s.
January
14
4 1.4
5 0.6
February .
+ .04
20 o.o
20 o.o
March . . .
+ .12
5 +0.2 4 +0.2
April
4- .06 IS + 0.9
18 + o.S
May . . .
+ .02 14 0.4
14 0.2
June
.00 7 i.i
7 o.,
July . . .
.03
7 + 2.4
6 -0.9
August.
+ . 12
II +0.1
II 0. I
September .
+ .07
25 o.o
23 o.o
October
+ .04
13 - 1.3
10 + 1.2
November .
+ .11
14 + 0.7
14 0.4
December .
+ .11
7 + 0.2
S o.o
Sum . .
-t- -52
0. I
81
Mean correction to absolute right ascension o.oo?
\J
Correction from stars -f- 0.043
Correction to right ascension of stars - 0.046
The adopted right ascensions are those of the Tabula; Regiomontanae, which at
this time are o".oi4 less than those deduced. We have, therefore,
r = o".o6; epoch, 1841.
The Berlin observations are distributed among the months with unusual irre>-u-
larity. Had the mean by weights been taken, the result would have been
( o s .o;
WASHINGTON.
The following are the mean results of observations made with the transit-instru
ment and mural circle during the four years i862- 65:
No. of
No. of
Month.
An
obs.
A,!
obs.
A(! cos /
January
0.052
42
+ 0.17
34
+ 0.07
February .
- 0.045
42
0.30
30
- 0.24
March . . . 0.022
41
+ 0.40
31
+ 0.39
April
+ O.022
41
+ 0.70
36
+ 0.62
May. . . .
O.O2O
53
+ 0.22
53
+ 0.12
June . [ + 0.008
50
+ 0.25
66
+ 0.02
July . . . | + 0.015
5i
+ 0.30
55
- 0.12
August ... - 0.002
57
o.oo
50 o.oo
September . . 0.038
42
0.22
47
+ 0.22
October . . - 0.033
35
- 0. 10
55
+ 0.09
November . . 0.027
35
O. IO
46
+ O.o6
December . . 0.052
27
-r 0.57
32
- 0.06
Sum . 1 - 0.238
+ I.I7
3 2
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Mean correction to sun s absolute right ascension -f- 0.032
Correction deduced from stars - 0.020
Correction to adopted rig-lit ascension of stars + 0.052
The adopted right ascensions are those of Dr. Gould, the mean of which, at this
epoch, scarcely differs from that of our deduced positions. We have, therefore, from
these observations
f + o s .O5; epoch, 1864.
Since 1866 the observations have been made with the transit-circle, but the instru
ment was dismounted a part of the time. The first two years work gave the discordant
results
.S .
1866 frr-f-0.07
1867 p o.oo
Mean c + 0.035
The following are the mean results for i868- 69:
Xo.of
No. of
Month.
A a
obs.
A .5
obs.
A 6 cos /
s.
,,
,,
January .
+ o. 10
10
+- o.S
8
+ 0.4
February .
+ 0.04
20
+ 0.3
9
+ 0.2
March .
+ 0.05
20
+ 0.7
18
+ 0.7
April .
+ 0.06
15
+ 0.7
T 9
+ 0.6
May . . .
4- O.O2
22
o.o
24
0.0
June .
4- o . 06
13
0.2
13
o.o
July . . .
+ 0.07
15
- 0.3
15
+ O.I
August
+ 0.06
9
+ 0. 5
7
0.4
September
+ 0.03
9
0.7
9
+ 0.7
October .
O.O2
13
i.5
14
+ 1-4
November
+ O.OI
12
0.7
12
+ 0.4
December
+ o . 06
10
0.9
IO
+ O.I
Sum
-I- o m
+ 4- 2
<^ " J*t
S.
Mean correction to sun s absolute right ascension -f- o. 1 1 7
Correction deduced from stars -f- 0.045
Whence
c -f- o s .o7
The comparison is with Ilansen s tables, the mean right ascension of which is
about o s .o6 or o s .o7 less than that of Le Verrier s tables.
The true value of c being of the form .r -f ?/T, every separate determination of its
value gives an equation of condition between x and y . The following is the system
of equations thus obtained. I have included the mean result of the Greenwich observa
tions for 1868, 1869, and 1870, which have been published since the appearance of the
last Greenwich seven-year catalogue. The Radcliffe resiilts are omitted.
DETERMINATION OF THE POSITION AND MOTION OF THE EQUINOX.
33
The weights have generally been assigned with reference to the entire number of
observations on which each result depends, and also on the number of years over
which the observations extend. But they have not been supposed to increase propor
tionally to either the time or the number of observations, so that, although the weight
i would be assigned to the result of a single average year s work with the best instru
ments, the weight assigned to seven consecutive years work by the same observers,
and with the same instruments, is much less than 7. On the same principle, greater
proportional weight has been given to isolated determinations than to determinations
founded on lony series of observations.
Observations. Year.
Equation.
Years.
Weight.
s.
Bessel s Uradley . 1756
. . &4_r + .06
7
3
Picizzi I Soo
.v . 2OJ = .08
(>
2
V-
Maskelyne ... 1805
- .i5/= - - 3
2
I
Bessel I .... iSiy
y - .03,1- = + .05
3
2
Bessel II . . . . 1822
.v + .02/ .00
5
4
Pond . . 1823
x + .03 v -f- .07
14
A
Struve .... 1825
x + ,o$y + .04
5
4
Argelander . . . 1828
x + .08 y = -t- .06
tf .
1
Cambridge . , . 1835
x + . isy = - .03
5
2
Edinburgh ... 1838
x + . isy + .04
4
2
Airy , 1839
x + .ig/ = - .05
(,
3
Berlin . 1841
i.v + . 21 y ~ .07
4
2
Cambridge ... 1841
x -t- .2i/ = + .06
t
5
2
Edinburgh . . . 1842
.- + . 22J- = .01
4
2
Pulkowa .... 1845
x + .25; .00
8
5
Greenwich . . . 1845
x + .25/ -~ .00
6
3
Cambridge . ! 1849
x + .2<)/ = + .06
5
2
Greenwich . . . 1851
X + -3I/ + .02
6
3
Cambridge . . . 1856
.1- + . 3&y = .01
5
2
Greenwich . 1857
x + .37 y - - - oi
7
3
Paris . . 1859
x -4- 10 v .00
10
Greenwich ... 1864
i j7 j
x + .44,1 = - .02
7
3
Washington . . . 1864
x + .447 = + .05
4
4
Paris . 1865
x + .45 y = \- . 1 1
2
2
Washington ... 1867
x + .47 y - + .05
4
4
Greenwich . . . 1869
1
x + .4 9 y = - .03
3
3
Treating these equations by the method of least squares, we are led to the normal
equations
74 y + 14.9 i/ + i ".02
14.9 x + 7.4 # = 4-0*. 1 7
the solution of which gives
x = -f o .oio
]) =.
5 F
34
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
The common correction to be applied to the star-positions first dednced is there
fore
+ o".oi6 .009 T
T being the fraction of a century after 1820. Applying- these constant corrections to
the values of x and y previously found, we shall have a set of corrections to the Ta
bulae Regiomontanae which we may suppose to be free from all systematic error what
ever, at least so far as it is possible to free them with our existing data.
6 -
CORRECTIONS FOR THE TERMS MULTIPLIED BY THE SECOND AND THIRD
POWERS OF THE TIME.
We have hitherto proceeded on the supposition that the necessary corrections to
the Tabulae Regiomontanse increase uniformly with the time. But, on computing the
co-efficients of the second and third powers of the time, in the expression for the mean
right ascension of the star at any epoch, and comparing them with those found by
induction from the mean places of the TabuLe Regiomontanse, it is found that this sup
position is not correct. In fact, it appears that Bessel computed the second differential
or secular variation of the annual variation without taking any account of the effect of
proper motion, and that he considered it constant, thus neglecting the third derivative
entirely.
The following table shows, i, the secular variation of the precession actually
employed in the Tabulae Regiomontanse ; 2, the adopted secular variation of the
annual motion for 1800, computed from the co-efficients of Struve and Peters, using
Hill s formulae in the "Star Tables of the American ephemeris," page 19; 3, the
resulting correction to the first value; 4, the variation of the secular variation in one
century, or the value of pr^g > tne um * ^ r o n ^ ascension being o s .ooi, and the unit
Cl X
of T one century; 5 and 6, the corrections to # and y necessitated by the addition of
these terms to the positions of the Tabula? Regiomontanse.
These last terms are derived as follows: Representing, for brevity, by a and b the
, d* R. A. , d 3 R.A. ., . , . . ,
corrections to JJessel s assumed values ot and T-TT-PT . the right ascensions ot
dl" d T 3
the Tabulae Reiomontanse should have received the correction
for the epoch of each catalogue before the comparison with the catalogue. T being
here counted from 1 800, the values of Cj, c. 2 , etc., already given, would have been thus
changed by the following amounts:
?! O. lOrt + O.O2&
c. 3 to c 4 o.
c 5 .01 a
c 6 =- .03 a
c, .03 a
S> T^T_-L _
.03 ft
.04 a
.IO
.026
?1=-
.2Ort
.066
CORRECTIONS FOR TERMS MULTIPLIED BY SECOND AND THIRD POWERS OF TIME. 35
Substituting these values of Ci, etc., in the expressions for .rand y, (p. 10,) we find
.08 a .o i 6
. i3 .066
the values of which are given in the last two columns.
Star.
d? R A
Bessel s rv-~~
a 1
From Struve,
(1800.)
h
AJ: \y
y Pcgasi ....
+ 97
+ 953
12 + 63
O 2
a Arictis ....
4- 2010
+ 1998
12 : 4- 41
I
a Ccti
4- O7O
+ QCQ
T II
!
V>
939
1 1 "J" 1_|
4~ I 41
a Tauri ....
4- 1090
4- 1065
25 - 39
4-2 -h 6
ft Orionis.
+ 430
+ 47
23 14
4-2 +4
,3 Tauri ....
4- 890
4- 862
28 - 95
+ 3 : + 9
a Orionis.
+ 31
+ 303
7 ; 42
+ i +4
a Canis Majoris.
4- 40
64 - i
Hi ii
a Canis Minoris
440
515
75 ~ 20
ft Gcminorum
- I22O
- 1216 4-
; 64
o 4-4
a Ilydrx ....
150
157
7 + 25
o i
Lconis ....
- IO2O
- 1039
9+37
4-1 o
(3 Lconis ....
770
7&S 4-
2 ; 4- 03
I 4
a Virginis
4- 1 1 20
4 1 1 1 r
9 ; + 5<->
0-2
a Bootis ....
4- 1 20
4- 202 4-
)2 4- 44
7 - 3
a- Librae ....
+ 1550
+ 1537
3+17
4-1 +1
a Coronas
+ 240
4- 228
2 4- 17
4-1 4-1
a Serpcntis .
4- 630
4-609 - :
!I 4- 5
4-2 4-2
o Scorpii ....
+ 1570
+ 1549 :
!I 56
4- 6
re Hcrculis .
+ 37
+ 353 i
7 i n
+ 1 +3
1
a Ophiuchi .
+ 35
+ 344
6 13
4-1 4-2
a Lyras ....
4- 1 60
4- 108 i
a | - 6
+ 4 +7
7 Aquila; ....
- So
99 l
9 5
4- 2 4-3
Aquila: ....
140
180
\o 1
+ 5
ft Aquilae ....
- 150
140 4-
8
i I
2 Capricorn* .
810
834
4 IS
4- 2 ! -4-4
<z Aquarii
430
444 1
4 +35
4- i o
a Pcgasi ....
+ 530
+ 523
7+56
2
Andromcdic .
+ 1770
+ 177
1 4- 83
1
i - 5
The values of x and y, or the correction to the right ascension and annual varia
tion of the TabuLe Regiomontanae for the epoch 1820, may now be found by adding
to the values of those quantities already found (p. i 7) the constants for correction of
equinox -f- 1 6 and 9, and the corrections from the above table. After doing this we
have, for convenience of application, transferred the epoch to 1800. Adding the
co-efficients for the second and third powers of the time, we have the following values
of the corrections in thousandths of seconds of time to the right ascensions of the
Tabulae Regiomontanee, where we put T fraction of century after 1 800 :
. ,6 RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
v.7
Corrections to Tabula Rey wmontance.
y Pegasi, 4 R. A. - + 26 - 1 3 8T - 6T a + ioT 3
a. Arietis, 3 + T 57 6 +7
Ceti, +33+8i 6 +2
a Tiuiri, 3+90 -12 6
/? Orionis, +41+27 -12 2
/? Tauri, +66165 -14 -16
a Orionis +24-10 4 7
a Canis Majoris, +26+64 -52 2 + j (Auwers)
a Canis Minoris, -27+127 -38 3 + q (Auwers)
/? Geminorum, 20 + 231 + 2 -11
a Hydra, -20 + 276 4 +4
a Leonis, -29 + 216 -10 + 6
/? Leonis, 0+193 + i +10
a Virginis, -16+67 4 + 8
a Bootis 7+99 +41 +7
a 2 Libra?, +80241 6 +3
a Coronae, -12+152 6 +3
a Serpentis, + 48 J 36 - 10 + i
a Scorpii, +41 131 - i o 9
a Herculis, 5+66 8 2
a Ophiuchi, - 2 7 + 35 3 2
a Lyra, +2+86 - 26 i
y Aquila?, +69 1 94 - i o i
a Aquilo?, +7+35 ~ 2O J
13 Aquila>, +39216+5 i
a 2 Capricorni, 6 6 -12 2
a Aquarii, -34+165 7 +6
Tega.si, + 9+ 18 4 +9
a Andromeda 1 , -12 + 185 + H
We have here added the stars Sirius and Procyori to the list because Anwers has
determined their irregular proper motions with sufficient accuracy to allow of their
being used as standards of comparison fora long time to come. The following are the
details of the operations by which Auwers results have been applied in the above
table.
PKOCYON.
By his researches on the proper motion of Procyoa, Auwers has found a certain
correction, q, to its right ascension, denned as follows: Represent by f/ { , (/ 3 , etc., to q 6 , the
several corrections to be applied to the right ascension of Procyon in Wolfers "Tabula;
Reductionum," in order that the respective differences between the corrected right
ascension and the right ascensions of a Tauri, /3 Orionis, a Orionis, /? Geminorum, a
ITydrse, and a Leonis, given in the same tables, may be correct. Then Auwers puts
CORRECTIONS FOR TERMS MULTIPLIED BY SECOND AND THIRD POWERS OF TIME. 37
It follows that if we represent by ^, J.,, etc., to J e , the definitive corrections to Wolfers
positions of these six stars, the correction to Wolfers position of Procyon will be
\24 + q
But this result requires a small change arising in this way. Wolfers and Auwers have
assumed that the corrections to the mean places of the Tabula? Regiomontana? increase
uniformly with the time. In other words, it is assumed by Auwers that q is of the
form
x + yt + P
P being the purely periodic terms depending on the orbital motion. But, on examin
ing the values of the terms depending on the second and third powers of the time in
the preceding table it will be seen that the correction is really of the form
+ i s rti 1 i T ^
/// o".03i I -+ P
To determine rigorously the correction to q which would have been introduced had
Auwers taken account of the term in T s Avould be difficult. Owing to the extreme
minuteness of the correction, Ave assume that the effect of changing the term would
correspond to the effect of a similar change in the equations used in this paper, or
^lx J R. A. (1820) .08 a + o s .oo5
^y .i3 = .i3X 62 = +
The correction to Auwers will then be
T being the fraction of a century after 1 800.
The value of this correction will be only .006 in 1/55, and will not exceed
o".oo3 during the period 1 800 to 1 860.
We therefore conclude that the correction to the position of Procyon given in the
Tabula? Reductionum is
^ + 3 + 8T- 3 iT* + /
It remains to determine d. Subtracting Wolfers corrections to the positions of
the Tabula? Regiomontanae, as found in the Tabula? Reductionum, pp. xxxv, xxxvi,
from the corrections given in the preceding table, it seems that our corrections to
Wolfers 1 positions are as follows :
a Tauri
ft Orionis
a Orionis
ft Gerninorum
a Hvdra?
*/
a Leonis
Mean J- -24 - 14 T 7 T 3 T 3
The correction to Wolfers position of Procyon is, therefore,
-2i-6T- 3 8T -3T + 2
Adding Wolfers correction to Bessel s position of Procyon, which is
-6 + I33T*
25
- 7 T
- I 2
r 8 - 6 p r 3
+ 2
-61
- I 2
2
+ I
99
4
Ij
35
+ 5
+ 2
- 14
-40
+ 28
4
+ 4
-47
+ 5
- 10
+ 6
^8 RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
J
we have the result given in the table for the correction to the right ascension of
Procyon in the Tabulae Regiomontanae.
SIEIUS.
Auwers correction to the position of Sirius is given in a form similar to that
adopted for Procyon, but the stars of comparison are /? Orionis, a Orionis, and Pro
cyon. The positions adopted for comparison are those of the Tabulae Regiomontanpe,
except that the right ascension of Procyon is first corrected by the quantity
-o s .025 o s .ooi3<86 (t 1825) o a .o;o5 cos 9.oo634 (t 179557)
or by the quantity
+ 10- 139 T + P
P being the periodic term. The terms in the correction to the relative motion of Sirius
which depend on the second and third powers of the time are
. - 34 T 2 +2T 3
and, reasoning as in the case of Procyon, we conclude that Auwers q should be cor
rected by the quantity
The value of this correction for different dates is
s.
i 760 .005
1780 +.001
1 800 + .004
1820 +-004
1840 +.002
1860 --003
1880 . -.010
The correction to the right ascension of Sirius in the Tabulee Regiomontanse is,
therefore,
4 being the mean correction to the right ascensions of /? Orionis, a Orionis, and Pro
cyon, the latter star being, however, first corrected by the expression given above.
Comparing this expression with Auwers q, (A. N. No. 1382, p. 62,) the value of
which is
39 1 19 T o s .o7O5 cos n (t T)
we see that the preliminary correction to the position of Procyon is
q 29 20 T
CORRECTIONS TO DIFFERENT CATALOGUES TO REDUCE THEM TO A MEAN SYSTEM.
39
Subtracting this correction from the above correction to Procyon, taking the cor
rections to /? Orionis and a Orionis without change, and representing by z/,, J.,, and
J-i the individual corrections to Auwers assumed positions of the three stars of com
parison, we have
^ = + 41 + 27 T - i 2 T- - 2 T :i
- f o + 24- 10 4 -7
^ 3 =+ 2 + 147 -38 -3
,4 = + 22 + 55 T--l8T a - 4 T 3
Adding this to the expression which replaces Auwers g, we have the result given
in the above table.
7-
CORRECTIONS TO DIFFERENT CATALOGUES TO REDUCE THEM TO A MEAN
SYSTEM.
The preceding investigations have resulted in giving us a set of 29 right ascen
sions, which we may suppose to be free from all systematic errors whatever, and of
which we may suppose the mean accidental error to be much less than that of any one
catalogue determination. We may, therefore, suppose any systematic differences which
exhibit themselves between the right ascensions of any catalogue and those just obtained
to be due to errors of the former, and from the entire body of the differences we may
obtain the correction necessary to reduce it to the standard. This correction may be
considered to consist of three parts
1. A constant, which we may consider as a correction to the adopted equinox.
2. Periodic terms depending on the right ascension, which in all recent catalogues
we may suppose to be of the form
m cos a. + n sin a
and to which terms of double period
in cos 2 a + n sin 2 a
may be added, if it be deemed necessary. In some of the older catalogues, especially
in Bessel I, the terms of double period appear to be quite sensible, but thev ought not
to be real in any modem catalogue.
3. A term depending on the declination, which, within the limits in which the
present investigations are applicable, may be regarded as proportional to the simple
declination. In application, it might be better to suppose it proportional to the sine
of the declination. The limits in question may be considered as 40 north declination
and 30 south declination, but the correction in question will necessarily become
uncertain as we approach either limit.
These three corrections have been obtained in the order in which they are num
bered, as follows: Represent by
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
the several excesses of the standard right ascensions over those of the catalogue to be
compared. The mean value of c may then be taken as the correction for equinox,
which we may represent by e. Subtract e from each individual c, and represent the
residuals by c t , e 2 , etc, The values of m and n may then be obtained in the same
manner by which the periodic terms of the residuals of the separate catalogues have
been obtained. But the addition of Sinus and Procyon to the list of stars will make
a slight change in the equations, so that we shall have
i 1.9 in 2 c (cos a .0
sn
i 7. i n 2 c (sin a .04 cos a)
The values of the coefficients-
cos a .03 sin a and sin a .04 cos a
for each star are given in the following table.
Co-eflicient for
Star. cos . sin
n .gin 1 7 . 1 72
a
Andromcdtc . . + I.oo .00
+ i . oo .04
7
Pegasi . + i.oo + .03
+ i.oo .01
a
Arietis ... + .87 , + .50
+ .86 + .47
a
Ceti .... | + .73 + .69
+ .71 + .66
a
Tauri .....+ .39 + .92
+ ,36 + .9
P
Orionis . . . j + .22 + .97
+ .19 4- -9 6
ft
Tauri .... + .19 + .98
+ .16 + .97
n
Orionis ... + .06 ! + i.oo
+ .03 + i . oo
a
Canis Majoi is . .16 + .99
.19 + i.oo
a
Canis Minoris . .38 + .92
.41 + -93
ft
Geminorum . . : .40 -f- .91
-43 + -93
a
Hydras ... .76 + . 64
- .78 + .67
a
Leonis ... .86 + .51
.88 + .54
(3
Leonis ... i.oo + .09
I . 00 + .13
a
Virginis ... .95 .32
.94 .28
a
Bootis. . . . .85 .53
- .83 - .50
a-
Librae .... .77 .6}
.75 - .61
a
CoronacBorealis. .62 .78
- .60 .76
a
Serpentis ... .59 .81
- -57 - -79
a
Scorpii ... .43 .90
.40 .88
a
Hcrculis . . . .23 .97
. 20 . 96
a
Opbiuchi . .16 .99
.13 .98
a
Lyric . 4- n on
+ .16 I . oo
7
Aquilae . j + .41 .91
4- .44 -93
a
Aquilse . . . + .43 .90
+ .46 ,92
Aquilae . J + .45 .89
+ .48 .91
Capricorn! . . 4- .53 .85
+ .56 : -37
a
Aquarii ... -fr .86 .51
+ .88 .54
a
Pegasi ... + .96 .28
4- .97 -32
CORRECTIONS TO DIFFERENT CATALOGUES TO REDUCE THEM TO A MEAN SYSTEM. 41
Subtracting from each c the corresponding value of
m cos a -\- n sin a
the residuals ought to l>e purely accidental errors, unless they are found to depend on
the declination. In this case, if we suppose a term proportional to the simple declina
tion, we may represent it in the form
.Dec. 10
the zero of reference being 10 north for convenience, because that is nearly the mean
declination of all the adopted standard stars, and the degrees of declination being
divided by 10 in order to have a more convenient factor. We may then find d by
solving the equations of condition formed by putting the above expression equal to c"
for each star. The following is a convenient and sufficiently accurate expression for d:
60 d =1 -\- 2 c" of a Andromedac.
+ i - - a Arietis.
i . .a Ceti.
+ I . - or. Tauri.
2 . . /? Orionis.
+ 2 /? Tauri.
2 . . a Canis Majoris.
+ 2 . . /? Geminorum.
2 . . a. Hydra;.
-)- i . . /? Leonis.
- 2 . . a Virginis.
+ I . - a Bootis.
2 . .or Libra;.
-f- 2 . . a. Corona?.
2 . . a Scorpii.
+ i - - llerculis.
-f- 2 . .a Lyrse.
2 . .or Capricorni.
i . . Aquarii.
As an example of the method we may discuss the twelve-year series of Paris
observations, extending from 1856 to 1867. The different results are shown in the fol-
lowin<>- table. First we trive the mean correction to Le Vemer s fundamental cata,-
O 5
logue deduced from all the observations, using the mean results given in each volume.
Next we have the resulting corrections to Bessel. Subtracting the correction to Bessel
for the mean epoch, we have the correction to the standard of this paper, or c. The
mean value of c is found to be 32, which is the value of e. Adding this, we have c .
6 F s
42 RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
From the values oi c we find
m = + 20
n = 23
Adding 20 cos a 23 sin a, we have c". From c" we have
f?- + 9
Applying- 9 - to c" we have r, or the definitive corrections to the standard
given by the Paris observations.
Star.
Corrections to
- c
Computed
periodic
terms.
c"
r
LeVerrier.
Tab. Reg.
a Andromeda: .
- 15
+ 57
47
15
+ 20
+ 5
+ 21
7 Pcgasi
- 16
27
- 69
37
+ 20
- i?
- 13
a Arietis ... 31
+ 33 ; - 57
- 25
+ 5
20
8
a Ccti ....
+ 34
+ 53 i - 27
+ 5
i
+ 4
2
n Tauri ....
25
+ 49
+ 3
+ 35
13
+ 22
+ 27
/? Orionis
+ 52
+ 76
+ 23
+ 55
18
+ 37
+ 21
,3 Tauri . . . .
a Orionis
- 6
+ 16
- 59
+ 13
- 18
3
+ M
+ 29
19
22
5
+ 7
+ II
+ 4
a Canis Majoris
(- 228) +39 4
+ 28
26
+ 2
22
a Canis Minoris .
(+ SO
+ 37
4
+ 28
- 29
I
6
ft Geminorum .
- 6
+ 92
24
+ 8
- 29
21
- 5
a Hydra;
+ 61
+ 157
+ 12
+ 44
- 3
+ M
- 2
a Lconis
+ 20
+ 98 o
+ 32
- 29
+ 3
+ 6
ft Leonis
+ 4
+ 86 - 32
o
22
22
- 17
a Virginis .
+ 28
o
24
+ 8
II
- 3
21
o liootis . . ,
+ 7
+ 30
- 39
7
4
II
2
a 2 Librx ....
+ 23
66
+ I
+ 33
+ 33
+ 10
n Corona
25
+ IS
60
- 28
+ 6
22
7
n Serpcntis .
+ 28
74 36
4
+ 7
+ 3
o
a Scorpii
+ 46
- 36 +6
+ 38
+ 12
+ 50
+ 18
n Ilcrculis .
ii
27
- 59
27
+ IS
- 9
4
a Ophiuchi .
I
+ 146
37
5
+ 20
+ 15
+ IS
ft Lyne ....
- 63
48 -93
- 61
+ 25
- 36
10
7 Aquilic
- 5
- "3
- 3
- 3i
+ 29
2
2
a Aquilx .
24
44
- 65
33
+ 29
- 4
- 5
ft Aquilse
+ 6
- 148
60
- 28
+ 29
+ i
3
i 2 Capricorni
+ 36
49
- 33
I
+ 30
+ 29
+ 8
a Aquarii
+ 10
+ 9
- 55
- 23
+ 29
+ 6
4
n Pegasi
- 42
42
62
- 30
+ 25
" 5
1
The systematic corrections obtained in this way for a number of catalogues are
given in the following list. The year attached to each catalogue is that to which it is
reduced. Systematic corrections much smaller than the accidental errorrs of the cata
logue may generally be omitted entirely.
CORRECTIONS 1 TO DIFFERENT CATALOGUES TO REDUCE THEM TO A MEAN SYSTEM. 43
SYSTEMATIC CORRECTIONS TO BE APPLIED TO THE RIGHT ASCENSIONS OF EQUATORIAL AND ZODI
ACAL STARS IN DIFFERENT CATALOGUES TO REDUCE THEM TO A MEAN SYSTEM.
AUWERS BRADLEY, (1755.)*
4 rr o s .o I o + O S .OO3 cos a o s .OO7 sin a
The mean value of the periodic terms being- less than one-third the probable error
of the individual star-places, they may be neglected entirely.
BESSEL S FUNDAMENTA, 1755.
J zr o a .oi
DE ZACII S FIXARUM PRECIPUARUM CATALOGUS Novus EX OHSERVATIONIBUS ASTRONO-
3IICIS IN SPECULA ASTRONOMICA GoTHANA ANNIS 1787, 1788, 1789, 1790, HABITIS
ET AD INITIUM ANNI MDCCC. CONSTRUCTS.
Dec. i o
4 zz: + o".36 o s .03 -
10
PlA/ZI, l8oO.
, Dec. 10
= + o".io-fo a .02S o
MASKELYNE, (1805.)
Catalogue in vol. 4 of Ms observations, second part, p. 1 12.
Dec. 10
-|- o . 145 -|-o .019 cos tx -f- o .006 sin a o .012 -
AUWERS CACCIOTORE, (1805.)
zz O 8 .oo6 O B .O 10 cos a O 8 .O33 sin a
BESSEL S. FIRST FUNDAMENTAL CATALOGUE, (1815.)
^ o".O3 7 o s .O3 7 cos a -f- o".O3 7 sin a .
BESSEL S SECOND FUNDAMENTAL CATALOGUE, (1825.)
^ -f o".O2o o".oo6 cos a -\- o".oio sin a
STEUVE, (1825.)
, Dec. 10
zr O .O2O -f O H .OO7 cos a -{- o .005 sin a -f o .008 - o~
AuworH 1 catalogue being Htill iiiipul)li.Hli( il, tliin correction must lie uiiiU i.stood IIM ap|iliculilu only to tho [iri 1 -
limiuury catalogue, in which no correction to BcHM-l s equinox has liecn ili tcrinini-U or
44 RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
BRINKLEY, (1824.)
ARGELANDER, (1830.)
,- Dec. 10
+ o s .oi 7 o .006 -
10
G-ILLISS S FIRST WASHINGTON CATALOGUE, 1840.
{From observations made at the old Naval Observatory during the years i838- 42. Wash
ington, 1 846. . 8vo.)
A -f- O 8 .O3 2 cos a o s .O28 sin a.
POND, 1830.
J o s .o56 o s .oi5 sin a.
(For stars in south declination the additional positive correction O 8 .ooi5 X south
declination in degrees is strongly indicated.)
AIRY S CAMBRIDGE CATALOGUE.
In the Memoirs of the Royal Astronomical Society, vol. XI.
4 o s .O24 o s .oi8 sin 2 a
(The term of double period, though a priori somewhat improbable, is strongly
indicated by the comparisons.
TAYLOR, (1835.)
General catalogue of the principal fixed stars from observations made at the honorable the
East India Company s observatory at Madras in the years 1830-1843.
Dec. 10
^/ O 8 .O47 + o .023 cos a. -(- o .001 1
The last term is far within the probable error of the catalogue-positions.
GREENWICH 12-YEAR CATALOGUE.
Catalogue, for 1840.
= + o s .o67 -f o s .oi4 cos a 01034 sin a
Catalogue for 1845.
-|- o".oi9 -|-o 8 .oo7 cos a o s .o25 sin a
CORRECTIONS TO DIFFERENT CATALOGUES TO REDUCE THEM TO A MEAN SYSTEM. 45
ROBINSON S ARMAGH CATALOGUE, (1840.)
4 r= -f O".O2O.
(No positions of fundamental stars are given in this catalogue. The correction
has, therefore, been derived from a comparison of all the stars south of 45 north polar
distance which are common to Armagh and the Greenwich 6- Year Catalogue for
1 840, and observed at least five times at each observatory. The differences between
these catalogues were corrected for the error of the Greenwich catalogue, and the out
standing differences were presumed to be due to error of the Armagh catalogue.)
PULKOWA, (1845.)
4 = -f o".
RADCLIFFE CATALOGUE, 1845.
4 zz o s .oo9 -f- o".O47 cos a o s .O2o sin a
(The positions of the fundamental stars in this catalogue give the correction
z/ + o s .ooi + C/.O55 cos a o".O2 1 sin a
In the introduction to the catalogue, Mr. Main gives a comparison of this catalogue
with Greenwich, 1845, from which I derive
Greenwich Radcliffe = o".O3S + 01032 cos a -(- o".oo5 sin a
Adding the Greenwich correction, this will give, for Radcliffe,
4 =. o".oi9 + o s .O39 cos a. o".O2O sin a
The mean result has been adopted.)
GREENWICH 6- YEAR CATALOGUE, (1850.)
l o".oo3 -f- o".oi i cos a o".O23 sin a
GREENWICH 7- YEAR CATALOGUE, (1860.)
J -f o 8 .oi4 -f- o s .oi4 cos a o".oi2 sin a
GREENWICH 7-YEAR CATALOGUE, (1864.)
d + o".O33 -|-o s -Q I o cos a. o a .oio sin a
PARIS ANNUAL CATALOGUES, i856- 67.
Dec. 10
-)- o a .O32 -(- o s .O2o cos a o .023 sin a -f o .009 - r~c
WASHINGTON "POSITIONS OF FUNDAMENTAL STARS," (1870.)
(In Appendix III to the Washington Observations fur 1867.)
4 6
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
WASHINGTON ANNUAL RESULTS OF OBSERVATIONS WITH THE OLD TRANSIT-INSTRUMENT,
(i862- 6 5 .)
^/ -)- o s .oo6 -f- o s .O2 1 cos a o s .O24 sin a.
WASHINGTON ANNUAL RESULTS OF OBSERVATIONS WITH THE TRANSIT CIRCLE, (1866-72.)
A -f- o s .oo6
Those of the above corrections which form a considerable part of the probable error
of the catalogue-positions are tabulated in the following- tables. In the corrections
depending on the declinations the constant term is included, except for Paris, where it
is included in the first table.
Corrections to different catalogues depending on the right ascension.
R. A.
Airy s
Cambridge
catalogue.
Taylor s
Madras
catalogue.
AIRY S GREENWICH CATALOGUES.
V
Paris annual
catalogues,
1855-67.
Radclifle
catalo ue,
1845.
1840.
1845.
1850,
1860.
1864.
h.
s.
j.
s.
s.
S.
s.
s.
s.
s.
o
.02
.02
+ .081
+ .026
+ .008
+ .028
+ .043
+ .052
+ .04
i
- -03
.02
+ -072
+ .020
+ .002
+ .025
+ .040
+ -045
+ .03
2
- -04
- -03
+ .062
+ .013
.005
+ .O2I
-T--037
+ .037
+ .02
3
- .04
- -03
+ .053
+ .OO6
.Oil
+ .015
+ -033
+ .030
+ .01
4
- -04
- .04
+ .045
+ .001
-.017
+ .OIO
+ .029
+ .022
- .01
5
- -03
- .04
+ .038
.003
.022
+ .005
+ .026
+ .015
.02
6
.02
- -05
+ -033
.006
.026
+ .OO2
+ .023
+ .OOg
-03
7
.02
- .05
+ .030
.007
.028
.O
+ .021
+ .005
- .04
8
.01
- .66
+ .031
.007
.028
.003
+ .OIg
+ .002
-05
9
.01.
- .06
+ .033
.004
-.027
.004
+ .Oig
+ .002
.06
10
.01
- .07
+ .038
+ .OOI
.024
.004
+ .0lg
+ .003
- .06
II
.02
- .07
+ .044
+ .006
.020
.OO3
+ .021
+ .007
- .06
12
.02
- .07
+ 053
+ .OI2
.OI4
.0
+ .O23
+ .012
- .06
13
- -03
- .07
+ .062
+ .018
.008
+ .003
+ .026
+ .Dig
.05
14
.04
- -07
+ .072
+ .025
.OOI
+ .007
+ .O29
+ -027
- .04
15
- .04
- .06
+ .081
+ .O32
+ .OO5
+ .013
"+.033
+ .34
- -03
16
- .04
.06
+ .089
+ 037
+ .016
+ .018
+ .37
+ -042
.02
17
- -03
-05
+ .096
+ .041-
+ .OI6
+ .023
+ .040
+ .049
.00
" 18
.02
- .05
+ .IOI
+ .044
+ .02O
+ .026
+ .043
+ .055
+ .01
19
.02
- .04
+ .104
+ .045
+ .O22
+ .028
+ .045
+ -059
+ .02
20
.01
- .04
+ .103
+ .045
+ .O22
+ .031
+ .047
+ .062
+ .03
21
.OI
- .03
+ .IOI
+ .042
+ .O2I
+ .032
+ .047
+ .062
+ .04
22
.OI
- .03
+ . 096
+ 37
+ .018
+ .032
+ .047
+ .061
+ .04
23
.02
.02
+ .090
+ .032
+ .014
+ .031
+ .045
+ .057
+ .04
24
.02
.02
+ .081
+ .O26
+ .008
+ .028
+ .043
+ .052
+ .04
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Come/ions depending on the declination.
47
Dec.
N. P. D.
Piazzi,
1800.
Struve,
Posit. Med.
Argelander,
1830.
Paris annual
catalogues,
i856- 63.
s.
s.
s.
s.
-t-40
5
+ .18
+ . oo
- .001
+ .-027
35
H
+ -17
.000
+ .002
+ .023
30
60
+ -1C
- .004
4- .005
+ .018
25
65
+ -14
- .008
+ .008
+ .014
20
7"
+ -13
.012
+ .Oil
+ .009
15
75
+ .11
.016
+ .014
+ .004
IO
So
+ .10
.020
+ .017
.0
+ 5
5
+ .09
- .024
+ .020
- .004
o
90
+ .07
.028
+ -023
.009
5
95
+ .06
.032
+ .021
- .014
10
100
4- .04
-036
+ .029
.018
-15
105
+ .03
- .040
+ .032
.022
20
no
+ .02
- -"44
+ -035
- .027
-25
5
.OO
- .048
+ .038
.032
8..
DEFINITIVE BIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Applying these corrections to the catalogue-positions, we may deduce definitive
corrections to the individual right ascensions of the stars under consideration. If, in
doing this, we employed only the catalogues used in the first determination, and
assigned the same relative weights as in the first discussion, we should reproduce the
right ascensions already found, lint the weights were first assigned solely with respect
to the probable freedom of the catalogue from periodic errors dependent on the right
ascension, while, after elimination of these errors, they should be assigned with respect
to the purely accidental errors of the determinations, and this change of weights Avill
make a small change in the individual definitive positions. We can also add a number
of catalogues not employed in the preliminary determination, particularly the Green
wich and Paris catalogues, which will add considerably to the precision of the results.
The details of the process are shown in the following tables. Under each star is
given, in the first column, the difference of excess of catalogue-place, corrected for sys
tematic error over the standard place already deduced.
In two cases several catalogues of small weight have been combined, as the
exhibition of the individual results of each catalogue would not be of interest. The
first set are the catalogues of
1 iazzi 1800, weight i
Maskelyne .... 1805, weight 2
Auwers Cacciotore . . 1805, weight 2
Bessel T 8i5, weight i
which have been combined into a single result for the mean date 1807. The mean
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
systematic correction was so small that only the correction for equinox was actually
applied. The next case was Airy s Cambridge catalogue and Pond s general catalogue,
which were combined into a single result.
No corrections depending on the declination have been applied, except in the case
of Paris and Argelander.
Under the titles Greenwich, 1869, and Washington, 1869, are given the mean
results of the Greenwich and Washington observations for the years 1868, 1869, and
1870, without any correction for periodic error.
The weights assigned are constant for each catalogue, except in the case of
Bradley, where the weight 2 was assigned to results depending on more than 100
observations, and i to those depending on less. The adopted weights and general
solution are as follows, the time T being reckoned from 1845 :
No.
Catalogue.
Date.
Weight.
T
Cx
C x
C ,
C"y
I
Bradley
1755
i or 2
- .90
.035
.054
- .46
- -63
2
Combined catalogue .
1807
I
- -33
.029
.024
.20
- .14
-3
Bcssel II ....
1823
2
.22
.055
.048
- .24
- .16
o
A
Struvc
l82(
I
.21
.027
.023
.11
-7
*f
5
Argelander ....
1828
4
-17
.108
.95
- -39
- -24
6
Pond- and Airy .
1830
i
- -15
.026
.023
- .08
- -05
7
Greenwich ....
1839
2
- .06
.050
.048
- .08
- .05
8
Greenwich ....
1845
2
.O
.049
.048
.02
.0
l8 45
4
.O
.098
.095
.05
J
.0
10
Greenwich ....
1851
3
+ .06
.072
.071
+ .05
+ .06
it
Greenwich ....
1857
3
+ .12
.070
.071
+ .14
+ .12
12
1862
4
+ -17
.092
.095
+ -25
+ -21
13
Greenwich ....
1864
4
+ .19
.090
.095
+ -33
+ .26
14
Washington ....
1865
5
+ .20
.112
.118
+ -44
+ .35
IS
Greenwich ....
1869
2
+ -24
.044
.047
+ .21
+ -17
16
Washington ....
1869
2
+ .24
.044
.047
+ .21
+ -17
The equations given by the several catalogues, when solved by least squares, lead
to the result that
4 R. A. for 1 845 = 2 C x X >
J Ann. variation 2 C y X r
r representing the correction given by any catalogue, and C x , C y , factors constant for
each catalogue, except that there will be two systems of these factors, the one corre
sponding to the stars for which the results of Bradley s observations receive the weight
i, the other to those in which they receive the weight 2. The former are designated
by one accent, the latter by two. In the case of C x the differences are so minute that a
single mean value has been actually used.
In the column /, under each star, is given the outstanding residual after subtract
ing the concluded correction
4 x + T 4 y
Sinus and Procyon are included only for the sake of comparison. No correction
to Auwers places is indicated.
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Residual corrections given by catalogues.
49
a Androm.
}- Pegasi.
a Arietis.
a Ceti.
a Tauri.
(i Orionis.
No.
Cutnlou iic
Year
r
/
r
r
r
r
r
r
r
r
r
t>
i
Bradley ....
1755
+ 15
+ 12
- 29
- 49
+ 9
+ 4
+ 32
+ 45
+ 24
+ 17
+ 3
+ 6
2
Combined catalogue
1807
+ 9
+ 4
+ 23
+ 17
12
II
24
20
G
- IS
- 7
- 4
3
Bessel II ....
1823
12
- IS
+ 27
+ 25
12
10
- 30
- 29
+ 5
- 8
- 25
22
4
1824
- Gi
-67
- i
- 3
+ 2
+ 5
+ I
+ 2-15
- 28
+ 53
+ 56
5
Argelander
1828
+ i
- 5
+ 15
+ M
- 8
- 5
10
10
+ 2
ii
IO
- 7
6
Pond and Airy
1830
+ 27
+ 20
+ 40
+ 40
+ 2
+ 5
- 28
- 28
+ 22
+ 8
ii
8
7
Greenwich.
1839
+ 26
+ 19
o
+ 2
28
- 24
+ 4
+ 38
+ 42
+ 28
- 13
IO
8
Greenwich ....
1845
+ 6
I
- M
II
+ 23
4- 28
- 23
2G
+ 44
+ 29
- 3
o
9
1845
+ 8
+ I
- 3
+ M
+ 19
+ 4
4- I
10
- 25
+ 6
+ 9
10
Greenwich ....
1851
+ 23
+ 15
- 7
- 2
+ 6
o
- 4
+ 21
+ 6
2
o
ii
Greenwich ....
1857
+ 28
+ 20
- 2
+ 4
- 9
3
- M
- 19
+ IS
+ 2
- 26
- 24
12
Paris
1862
+ 21
+ J 3
13
_
8
. i
2
4- 27
+ 11
-4- 2T
+ 21
3
Greenwich.
1864
+ 9
+ I
- 18
10
- 6
+ i
+ 8
7
+ 2
i * l
+ 19
+ 3
T^ * *
- 4
^J
2
4
Washington .
1865
+ i
- 7
- 13
- 4
- 7
o
+ 21
+ 15
+ M
- 3
- 4
2
15
Greenwich.
1869
+ 2
- G
21
II
- 30
- 23
IO
- 16
+ 26
+ 9
- M
u
16
Washington .
1869
22
- 30
+ 9
10
T
+ 43
+ 37
+ II
- 6
+ 6
+ 8
No.
Catalogue.
Year.
/3 Tauri .
o Orionis.
a CanisMaj.
a CanisMin.
/? Gcmin.
a Hydra.
I
Bradley ....
1755
+ 4
+ 2
- 9
- 9
o
o
.
+ ii
+ 7
- 5
12
2
Combined catalogue
1807
+ 32
+ 25
+ 27
+ 26
- 4
- 6
2
- 4
Bessel II ....
1823
- 4
12
+ 2
o
.
.
12
- 13
- 23
- 24
4
Struvc . ...
1824
22
- 30
- 14
- 16
.
.
- 23
- 24
+ 25
+ 24
5
Argelander
1828
+ 3
G
+ M
+ 12
- 17
.
+ S
- i
4- 10
+ 10
6
Pond and Airy
1830
+ 15
+ G
+ 32
+ 3
+ 5
+ M
+ 10
+ 9
+ 48
4-48
7
Greenwich ....
1839
- 4
*- M
+ 4
+ 2
.
+ 2
- 24
+ II
+ ii
- 15
- 14
8
Greenwich ....
1845
+ 6
- 4
- 5
- 7
6
.
+ 13
+ 3
+ 3
+ 3
+ 4
Pulkowa ....
1845
+ 14
+ 4
13
15
+ 6
+ 6
-+ 5
+ 6
10
Greenwich.
1851
+ 17
+ 6
- S
.
+ 4
+ 2
- 3
- 3
T^ D
- 6
- 4
ii
Greenwich. .
1857
+ 34
+ 23
+ 3
o
+ 12
12
+ 7
+ 7
4
- i
12
1862
+ ii
i
+ 4
4- i
1 1
6
,
c
2
-f- i
13
Greenwich ....
1864
+ 16
+ 4
+ 16
+ 13
*
- 17
.
+ 7
D
+ G
D
+ 7
- S
r
4
Washington .
1865
- M
- 2G
+ i
2
.
+ If)
o
ii
IO
12
- 9
15
Greenwich ....
1869
+ 36
+ 24
+ 2
I
.
- 3
+ 23
+ 9
+ 10
4- 26
+ 30
16
Washington .
1869
+ 19
+ 7
+ i
- 2
+ I
+ 15
- 7
- 6
- 23
- 9
1 F S
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Residual corrections given by catalogues.
a Leonis.
ft Leonis.
a Virginis.
a Bootis.
a 2 Librae.
a Coronae.
No.
Catalogue.
Year.
r
r
r
r
r
r
r
1
r
r
r
r
i
Bradley ....
1755
+ 12
+ G!
+ i
+ ii
- 5
- 13
I
- 6
- 7
- 8
+ 5
II
2
Combined catalogue
1807
o
8
+ 10
+ 17
2
o
+ 5
+ 3
+ 3
i
- 28
- 35
3
Bessel II ....
1823
+ I
- 5
- 26
20
+ 22
+ 27
- 3
- 3
- 3
- 8
i
- 5
4
Struve
1824
- 4
10
12
7
- 16
10
- 17
- 17
- 19
- 24
+ 30
+ 26
5
Argelandcr
1828
S
- 14
2
+ 3
o
+ 6
- 9
- 9
+ 19
+ 13
+ 9
+ 6
6
Pond and Airy
1830
9
- 15
- 3
+ 2
- 15
- 8
- 6
- C
+ 26
+ 20
+ 16
+ 13
7
Greenwich ....
1839
+ 3S
+ 32
- 10
- 6
- 15
C
+ 24
+ 25
+ 28
+ 23
- 5
- 6
8
Greenwich ....
1845
+ ii
+ 5
- 30
- 26
- 15
- 5
+ 6
+ 7
+ 30
+ 24
+ 9
+ 9
Pulkowa ....
1845
+ 2
- 4
+ G
+ 10
+ 8
+ 18
+ 10
+ ii
ii
17
2
10
Greenwich ....
1851
+ 6
+ i
+ 4
+ S
- 16
+ 15
+ iG
+ 4
J /
2
+ 28
+ 28
ii
Greenwich ....
1857
+ 16
+ ii
I
+ 2
-36
- 24
+ 8
+ 10
- 9
- 15
-t- 15
+ 17
12
Paris
1862
+ f>
+ i
- 17
- 4
21
- 8
2
o
+ 10
+ 3
- 7
- 5
13
Greenwich ....
1864
5
- 10
+ 5
+ 8
22
- 9
- 6
4
+ 16
+ 9
+ .3
M
Washington .
1865
+ 5
- 3
+ I
+ 15
12
10
- 7
- 18
- 15
15
Greenwich ....
1869
+ ii
+ &
+ 12
+ 14
21
- 7
- 19
16
+ 10
+ 3
10
- 6
16
Washington
1869
+ 6
+ i
- 5
- 3
~ 14
10
- 7
+ 20
+ 13
- 25
21
No.
Catalogue.
Year.
a Serpentis.
a Scorpii.
a Herculis.
a Ophiuchi.
a Lyrx.
y Acjuiloe.
i
Bradley ....
1755
+ 5
+ i
- 25
- S
+ ii
+ 10
+ 14 + 16 i + 2
o
i
- 4
2
Combined catalogue
1807
- 44
-46
+ 27
+ 36
-38
- 40
- 19
- 23 +14
+ M
2
- 4
3
Bessel II . . . .
1823
+ 6
+ 5
+ 12
+ IS
+ 12
+ 9
- 32
- 37 4- 3
+ 4
I
2
4
Struve
1824
+ 38
+ 37
+ 16
+ 22
+ 38
J- oe
-}- 4O
-1- -5C AC
ji
+ 10
+ r\
5
Argclander
^ ~r
1828
I J^
+ ii
[ J i
+ 10
- 13
- 7
1 J^
+ 6
[ jj
+ 3
+ 10
~ JO 4 J
+ 421
f-f
20
+ M
y
+ 13
6
Pond and Airy
1830
+ 23
+ 2 3
- 35
- 30
- 29
- 32
+ 3
- 6
20
21
7
Greenwich ....
IS39
- 24
- 24
+ I
+ 5
- 4
- 7
+ 18
+ II
+ 3
+ 5
+ 3
+ 2
S
Greenwich ....
IS45
+ i
+ I
+ 28
+ 31
- 18
21
+ 12 + 5
o
+ 2
- 5
- 5
9
Pulkowa ....
1845
3
- 3
- 15
12
- 19
22
- 17 - 24
+ 18
+ 21
+ S
+ 8
10
Greenwich ....
1851
o
o
- 37
- 35
+ 22
+ IS
+ 8 o
+ 21
+ 24
- 18
- 18
ii
Greenwich ....
1857
- 4
- 3
10
- 8
+ 33
+ 29
+ 24 +15
+ 17
+ 2O
+ 10
+ 10
12
Paris
1862
o
_j- i
+ 18
-t- 10
J
8
4- rfi 4- o
JO
"7
2
2
13
Greenwich ....
1864
+ i
+ 2
- 5
*y
- 5
4
+ 18
+ M
i iu ~f y
+ 22 +13
+ 6
/
+ 9
12
- 12
14
Washington
1865
4
- 3
+ if)
+ 16
+ i
-- 3
+ f> - - 4
- 5
- 2
+ 5
+ 5
15
Greenwich ....
1869
- 6
- 5
- 13
- 13
+ 10
+ 6
4-10 026
-23
- 18
- 18
16
Washington .
1869
+ 7
+ 8
- 18
- IS
- 3
- 7
2 12 34
i
- 31
+ 19
+ 19
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Residual corrections given by catalogues.
No.
a Aquiloe.
/? Aquilsc.
- Capricorn!.
Aquarii.
a Pegasi.
r
r
r
r
r
r
r
/
r
r
i
Bradley ....
1755
- 9
II
- 1
~ 9
21
- 6
- 16
- 5
2
2
2
Combined catalogue
1807
+ 15
+ 14
- S
10
+ 10
+ 19
+ 4
+ 10
+ 2O
+ 19
3
Bessel II ....
1823
+ 9
+ 9
+ 31
+ 29
+ 31
+ 33
+ 18
+ 23
+ 7
+ 5
4
Struve
1824
- 6
- 6
- 3
+ i
+ 27
+ 34
- 3
4- 2
- 29
3i
5
Argelander
1828
- 3
- 3
-t- II
+ 9
- 17
10
- 17
12
+ 7
+ 5
6
Pond and Airy
1830
r
/
- 7
32
- 34
- 59
- 53
+ 4
+ 8
2
- 4
7
Greenwich ....
1839
+ 23
+ 23
7
- 9
- 27
22
- 4
+ 10
+ S
S
Greenwich ....
1845
- 5
- 5
+ 5
+ 3
5
i
- 13
- 10
+ 2
9
Pulkowa ....
1845
+ 7
+ 7
+ i
i
i
+ 4
- 4
I
- 9
ii
10
Greenwich ....
1851
+ 2
+ 3
+ 12
+ 9
- 28
- 24
2
+ I
+ 4
+ i
ir
Greenwich ....
1857
O
+ I
- 10
- 13
- 19
- 16
- 18
- 16
- 9
- 12
12
1862 f.
4
3
6
+ S
+ II
4
2
i
A
*t
4
Greenwich ....
1864
- 7
- 6
4
- 7
+ 10
+ 12
- 18
- If)
+ 4
+ I
14
Washington .
1865
+ 4
+ 5
- 3
- 6
- 5
3
+ ii
+ 13
+ 13
+ 10
15
Greenwich ....
1869
- S
- 7
+ 24
+ 21
+ 10
+ 12
- 3
2
- 4
- 7
16
Washington
1869
- 19
- 18
+ 7
+ 4
7
- 5
+ 25
+ 26
+ 19
+ 16
1
There are still three of Maskelyne .s fundamental stars wliich it is desirable, for
fho sake of completeness, to add, namely, a Auriga?, a Cvgni, and a. Piscis Anstralis.
Although these stars lie a little outside the limits we have set, they are frequently used
as clock-stars. The corrections to the positions of the Tabulae Regiomontanse were
obtained on the same general system with that adopted for the other stars. The;
tabular positions were corrected for the terms depending on the second and third
powers of the time, as given in the following tables, and the catalogue-positions for
systematic error given by the formulae of the last section. From the differences
the correction proportional to the time was deduced.
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
From the residuals r we derive the folloAving definitive corrections to the right
ascensions for 1 800 and to the annual variations of the first standard :
Definitive corrections to right ascensions of Tabula JKegiomontance.
Star.
A R. A.
&y
Definitive correction.
a, Andromeda; .
+ 5
+ 5
- 7 + 190 T + o 1- +14 T 3
y Pcgasi ....
+ 8
- 26
+ 34 164 - 6 +10
n Arietis ....
o
ii
- 3 +146 - 6 +7
re Ccti
5
+ 17
+ 28 +98 6 +2
a Tauri ....
+ n
+ 8
+ 8 +98 12 6
Aurigx
- 2 +26 -31 -34
ft Orionis.
- 3
+ i
+ 38 + 28 12 - 2
ft Tauri ....
+ 6
+ 9
+ 72 156 14 16
re Orionis.
+ I
+ 3
+ 25 7 - 4 - 7
re Canis Majoris .
+ 155 + 29 -52 - 2 + P
re Canis Minoris.
-15 + 8 -38 - 3 + P
ft Gcminorum
+ 2
4
18 +227 + 2 ii
+ 1
IO
17 +266 4 +4
a Lconis ....
i J
+ 6
i
23 +215 10 + 6
ft Leonis ....
7
+ 7
7 +200 + i +10
re Virginis .
i
- 19
-17 +48 - 4 +8
a Bootis ....
+ 2
7
- 5 +92 +41 + 7
a- Librie
-4- A
+ 6
-1-8 A 2^S 6 +T
a Coronic
i H
+ &
i?
I u-f ^"33 J
- 4 +135 - 6 +3
a Scrpcntis .
+ 2
- 5
+ 50 141 10 + i
re Scorpii ....
IO
+ 15
+ 31 116 10 - 9
re Ilerculis
+ 2
+ 3
-3 +69 -8 -2
n Ophiuchi .
+ 3
+ 10
24 +360 - 3 - 2
re Lyric ....
4
+ 2 +S2 26 - I
}- Aquilac ....
+ 2
3
+ 71 197 10 - i
, Aquilx ....
+ I
- 3
+ 8 +32 20 - i
ft Aquilrc ....
+ 2
+ i
+41 215 +5 - i
re - Capricorn! .
10
+ 12
16 + 6 12 3
re Cygni ....
-32 +184 -17 + 3
n Aquarii.
7
+ 8
-41 +173 - 7 + 6
n Piscis Australis .
50 152 - 6 +11
re Pcgasi ....
+ i
+ 3
+ 10 +21 - 4 +9
In the above table P signifies the periodic part of Auwers correction, which is
more convenient to use than q.
The following table gives the definitive right ascensions for every five years from
1750 to 1900.
I conceive that the mean error of these right ascensions, after correction for
equinox, will not exceed o s .oio at any time during the nineteenth century.
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS. 53
Mean right ascensions for beginning of each fiflli Bcssdlan fictitious year, \ 750-1850.
Year.
a ANUKOMEDJE.
y PKGASI.
K. A.
Ann. Var.
R. A.
Ann. Var.
//. m. s.
s.
/i. in. s.
s.
/So
23 55 31-079
3 0665
o o 23.520
3.0702
i/55
46.413
3.0674
38.872
3.0707
1760
23 56 1.752
3.0683
54- 227
3.0712
1/65
17-095
3-0691
o i 9.584
3.0716
1770
32.443
3.0700
24-943
3.0721
775
47-795
3.0709
40. 305
3.0726
1780
23 57 3- I5 1
3-0717
55-669
3-0730
1785
18.512
3.0726
2 11.035
3-0735
1790
33-876
3-0735
26. 404
3.0740
795
49. 246
3 0744
41-775
3-0745
1800
23 58 4.620
3-0/53
57- 148
3-0749
1805
19.998
3-0761
o 3 12.524
3-0754
1810
35-38i
3-0770
27.902
3-0/59
1815
50. 768
3-0779
43- 283
3.0764
1820
23 59 6. i 60
3.0788
58.666
3.0769
1825
21. 55 6
3-0797
o 4 14.052
3-0774
1830
36. 956
3 . 0806
29.440
3-0778
35
52.361
3-0815
44-830
3-0783
1840
o o 7.771
3.0824
050. 223
3.0788
1845
23- 185
3-0833
15.618
3-0793
1850
38-603
3.0842
31.016
3.0798
1855
54.026
3-0851
46. 416
3 0803
1860
o i 9.454
3 . 0860
o 6 1.819
3. 0808
1865
24.886
3 . 0869
17.224
3-0813
1870
40.323
3.0879
32.632
3.0818
1875
55-764
3.0888
48.042
3-0823
1880
O 2 I I. 2IO
3-0897
-o 7 3-455
3.0828
1885
26. 661
3.0906
18.870
3-0833
1890
42. 1 16
3-0915
34.288
3.0838
1895
57-575-
3-0925
49. 708
3-0843
1900
o 3 13.040
3-0934
o 8 5.131
3.0848
54
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Mean riyM ascensions, d c. Continued.
Year.
a ARIKTLS.
a. CETI.
R. A.
Ann. Viir.
R, A.
Ann. Vav.
//. ill. S.
S.
h. m. s.
s.
1750
i 53 8.365
3-3430
2 49 14.423
3- 1170
1755
25-083
3-3440
30. 009
3- H75
1760
41.805
3-3450
45-598
3- H79
1765
58.533
3-346o
2 50 I. 189 3. 1184
1770
i 54 15.266
3-3470
16. 782 3. 1 189
1775
32.003
3-348o
32.377 3-II94
1780
48. 746
3-3490
47-975 3-1198
1785 i 55 5-493
3-3500
2 51 3-576 3. 1203
1790
22.245
3-3510
19. 179
3. 1208
1795
39.003
3-3520
34- 784
3- 1213
1800
55-765
3-3530
50-391
3.1218
1805 i 56 12.533
3-3540
2 52 6.001
3 . 1222
1810 29.305
1815 46.082
3-3550
3-356o
21.614
37.228
3- !227
3- 1232
1820 i 57 2.865
1825 i9- 6 52
1830 36.445
3-3570
3-358o
3-3590
52.846
2 53 8.465
24.087
3- 1237
3- I2 4 2
3. 1246
1835 53-242
3.3600
39.712
3- 1251
1840 i 58 10.045
3.3610
55-338
3- 1256
1845
26.852
3.3620
2 54 10.968
3. 1261
1850
43-665
3-3630
26. 599
3. 1266
1855
i 59 0.482
3-3640
42.233
3- 1271
1860
17-305
3-3650
57-870
3-1275
1865
34- 133
3.3661 2 55 13.509
3. 1280
1870
50.966
3-3671
29- 150
3-1285
1875
2 o 7.803
3-368!
44- 794
3- I2 90
1880
24. 646
3-3691
2 56 0.440
3- 1295
1885
41.494
3-37oi
16.088
3- 1300
1890
58.347
3-37 11
31-739
3- 1304
1895
2 115. 2O6
3-3721
47-393
3- 1309
1900
32. 069
3-3732
2 57 3-049
3- i3H
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Mean right ascensions, &c. Continued.
55
Year.
a TAUKI.
a AURIGA.
11. A.
Ann. Var.
11, A.
Ann. Var.
//. III. S.
s.
li. in. ,s.
s.
i/50
4 21 36.293
3-4227
4 58 15-977
4.4004
i/55
53-408
3-4232
37-98i
4.4014
i 760
4 22 IO. 526
3-4238
59.990
4.4023
1/65
27. 646
3-4243 4 59 22.004
4.4032
1770
44- 769
3-4248 44-023
4.4042
775 4 23 1.894
3-4254
5 o 6.046
4.4051
i 780 19. 022
3-4259
28.073
4 . 4060
1785 3 6 - S3
3-4265
50. 106
4.4069
1790 53 .286
3.4270 5 i 12. 142
4.4078
1795 4 24 10.423
3-4275
34-184
4.4087
1800 27.562
3.4281
56-230
4.4096
1805 44-704
3-4286
5 218. 280
4.4105
1 8 1 o 4 2 5 i . 848
3-4291
40.335
4.4114
1815 18.995
3.4296
5 3 2.394
4.4122
1820 36.144
3-4302
24-457
4-4I31
825 53-297
3-4307
46.525
4.4140
1830 4 26 10.452
3-4312
5 4 8.597
4.4148
1835 27.609
3.43i8
30.673
4-4 57
1840 44. 769
3.4323
52.754
4.4165
1845 4 27 1.932
3-4328
5 5 14-839
4-4174
1850
19. 097
3-4333
36.928
4.4182
1855
36. 265
3-4339
59-022
4.4190
1860
53-436
3-4344
5 621.119
4.4199
1865
4 28 To. 609
3-4349
43- 221
4.4207
1870
8/5
2 7- 7 8 5
44.963
3-4354
3-4359
5 7 5-326
27.436
4-4215
4.4223
1880
4 29 2. 144
3-4364
49-550
4-4232
1885
9-3 2 7
3-4370
5 8 11.668
4.4240
1890
36.5 4
3-4375
33-790
4-4248
< S 95
53-702
3.438o
55-9I6
4.4256
1900
4 30 10.894
3-4385
5 9 18.045
4.4264
RIGHT ASCENSIONS OF FUNDAMENTAL STARS,
Mean riylit ascensions, &c. Continued.
/? ORIONIS.
/? TAUEI.
1 p ll*
-1 Cd 1
R. A.
Ann. Var.
R. A.
Ann. Var.
li. in. s.
s.
h. m. s.
8.
1750
5 2 32.084
2-8757
5 10 30.599
3-7775
1755
46.463
2-8759
49.488
3- 7779
1760
5 3 o. 843
2.8761
5 ii 8.378
3- 7784
1765
15.224
2.8763
27. 272
3-7788
1770
29. 606
2.8765
46. 167
3-7793
775
43.989
2.8767
5 12 5-064
3- 7797
1780
58.373
2. 8769
23.964
3- 7802
1785 5 4 12.758
2.8771
42. 866 3. 7806
1790
27. 144
2.8773
5 U 1-770
3.7811
T 795
4i.53i
2.8775
20. 677
3-7815
1800
55.9I9
2.8777
39.585
3./8.9
1805
5 5 10-309
2.8779
58.496
3- 7824
1810
24.699
2.8781
5 14 17.409 3. 7828
1815
39.090
2.8783
36.324
3-7832
1820
53.482
2.8785
55-24I
3.7836
1825
5 6 7.875 2.8787
5 i5 H. 160
3.7840
1830
22. 269 2. 8789
33-o8i
3- 7845
1835
36.665 2.8791 52.005
3-7849
1840
51.061 2.8793
5 16 10.930
3.7853
1845
5 7 5-458
2.8795
29-858
3-7857
1850
19.856
2.8797
48.787
3.7861
i855
34-256
2-8799 5 17 7.719
3-7865
1860
48.656
2.8801
26. 652
3-7869
1865
5 8 3.057
2.8803
45-588
3.7873
1870
17-459
2.8805
5 i 8 4-526
3.7877
1875
31.862
2.8807
23-465
3.7881
1 880
46. 267
2.8809
42.407
3-7885
1885
5 9 0.672
2.8811 5 19 1.350
3.7889
1890
15.078
2. 8813 2O. 296
3-7893
1895
29.485
2.8815
39-243
3-7897
1900
.89 3
2.8817
58. 193
3- 790,
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Mean riyJtt ascensions, cCr. Continued.
57
a OKIOXIS. a CANIS MAJOKIS.*
Year
\{. A.
f
Ann. Yiir. U. A.
Ann. Var.
//. m. s.
s.
//. m. s.
s.
1750 5 41 38.680
3.2429
6 34 7.882
2. 6446
i/55 54-895
3-2431
21- 105
2.6445
i 760 5 42 1 1 . 1 1 1
3-2432
34-327
2.6445
1765 27.327
3-2434
47-550
2-6445
!/7o 43-545
3-2435 6 35 0.772
2-6444
775 59-763
3-2437 13-994
2-6444
1780 5 43 15.982
3-2439
27. 216
2.6444
1785 32.201
3.2440
40.438
2 - 6444
1790 48.422
3.2442 53-66o
. 2.6443
1795 5 44 4-643
3-2443
6 36 6. 88 i
2-6443
1800 20.865
3-2445
2O. IO2
2-6443
1805 37-088
3- 2446
"> 1 1 *> 1
oo- j-4
2.6442
1810 53-3 11
3.2448
46.545
2. 6442
815. 5 45 9-535
3- 2449
59-766
2.6442
1820 25. 760
3- 245
6 37 12.986
2.6441
1825 41.986
3-2452
26. 207
2.6441
1830 58.212
3-2454
39-427
2.6441
1835 5 46 H-439
3-2455
52.647
2. 6440
1840 30.667
3-2456
6 38 5-867
2 . 6440
1845 46.896
3-2458
19.087
2.6440
1850 5 47 3. 125
o- 2459
32.307
2-6439
1855 9-355
3.2461
45-527
2-6439
1860 35-586
3.2462
58. 746
2.6439
1865 51-817
3.2464
6 39 11-965
2-6438
1870 5 48 8.050
3-2465
25. 184
2-6438
1875 24.282
3.2466
38-403
2.6437
1880 40.516
3.2468
51.622
2-6437
1885 56-750
3.2469
6 40 4. 840
2.6437
1890 5 49 12.985
3.2470
18.058
2-6436
1895 29. 220
*> It** *
j- -4/ -
31.276
2.6436
1900 45-457
^ "J \ *7 ^
o- -4/0
44.494
2-6436
8 F S
The corrections, P, on p. Gl>, are to l>o applied to tliese positions of a Canis Mnjoris.
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Mean right ascensions, c. Continued.
Year.
a CANIS MINORIS.*
/? G-EMINORUM.
R. A.
Ann. Var.
II. A.
Ann. Var.
/;. m. s.
s.
n. m. s.
. s.
1750
7 26 12.027
3-I507
7 29 58.793
3.6964
J 755
27.780
3- 1505
7 30 17- 274
3-6958
1760
43-532
3- J502
35-75 1
3-6952
1765
59.282
3- H99
54-225
3.6946
1770
7 27 15.031
3- H97
7 3 1 12.697
3.6940
!775
30.779
3- H94
31-165
3-6934
1780
46.525
3- H9 2
49.631
3-6928
1785
7 28 2. 271
3- 1489
7 32 8.093
3.6922
1790
18.015
3- 1487
26.553
3.6916
1795
33-757
3- 1484
45-009
3.6910
1800
49-499
3.1482
7 33 3-462
3 6904
1805
7 29 5.239
3- H79
2*1.913
3.6898
1810
20.978
3- J 47 6
40. 360
3.6892
1815
36-715
3- 1474
58.804
3.6885
1820
52-452
3- i47i
7 34 17-246
3-6879
1825
7 30 8.187
3- H69
35-684
3-6873
1830
23.920
3. 1466
54- H9
3.6867
1835
39-653
3- 1463
7 35 12.551
3.6861
1840
55-384
3- H6i
30.980
3-6855
1845
7 3i ii. H3
3- HSS
49.405
3.6848
1850
26.842
3- H56
7 36 7-828
3.6842
1855
42.569
3- H53
26.248
3.6836
1860
58.295
3- H5o
44. 664
3-6829
1865
7 32 14.019
3- 1448
7 37 3-077
3-6823
1870
29.742
3- 1445
21.487
3.6817
1875
45.464
3- H42
39-894
3.6810
1880
7 33 1-185
3.1440
58.298
3 6804
1885
1 6 . 904
3- H37
7 38 16.699
3-6798
1890
32. 622
3- H34
35-097
3.6791
1895
48.338
3- M32
53-491
3-6785
1900
7 34 4-053
3- H29
7 39 11-882
3.6778
* The corrections, P, on p. 71, arc to bo applied to these positions of a Canis Minoris.
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Mean riylit ascensions, (fr. Continued.
59
Year.
a HYDRJE.
a LEONIS.
R A.
Ann. Var.
R. A.
Ann. Var.
I/. III. S.
8.
//. m. s.
s.
1750 9 15 17.906
2.9512
9 55 1-762
3- 2148
755
32.662
2.9512
17-835
3-2143
1760 47.418
2 -95 i 33-905
3-2138
1765 9 16 2. 173
2.9510 49-973
3-2133
1770 16.928
2-9509 9 56 6.038
3.2128
1775
31.682
2.9508
22. IOO
3 . 2122
1780 46.43 6
2-9507
38. I 60
3.2II7
1785 917 i. 190
2-9507
54-217
3. 21 12
79 5-943
2.9506
9 57 10.272
3.2107
795
30. 695
2-9505
26.324
3. 2102
1800
45.448
2.9504
42-373
3. 2096
1805
918 O. 2OO
2-9503
58.420
3 . 209 i
1810
4-95 1
2-9503
9 S 8 14-465
3. 2086
.815
29. 702
2- 95O2
30-507
3. 2081
1820
44-453
2.9501
46. 546
3.2076
1825
59-203
2-9500
9 59 2.582
3- 2071
1830
9 19 3-953
2.9500
18.617
3. 2066
835
28. 703
2-9499
34.648
3. 2061
1840
43-452
2.9498
50.677
3.2056
1845
58. 2or
2-9497
10 o 6. 704
3.2050
1850
9 20 12.950
2-9497
22. 728
3-2045
855
27.698
2.9496
38.749
3.2040
1860
42.446
2-9495
54- 768
3-2035
1865
57- 93
2-9495
10 i 10. 784
3.2030
1870
921 ir. 940
2 . 9494
26.798
3.2025
i875
26.687
2-9493
42. Sio
3. 2020
1880
41-433
2.9492
58.818
3- 2015
1885
56- 179
2.9492
IO 2 14.825
3- 2OIO
1890 9 22 IO. 925
2.9491
30.829 3-2005
895
25.670
2 . 9490
46. 830 3. 2OOO
I9OO
40.416
2-9490
10 3 2.829
3- 995
6o
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Mean riff Jit ascensions, dec. Continued,
Year.
/? LEONLS.
a VIEGINIS.
R A.
Ann. Var.
R A.
Ann. Var.
Ii. m. s.
s.
/(. In. s.
s.
1750 ii 36 17.250
3.0745 13 12 3.448
3-i38i
1755 32.622 3-0741
19. 140
3-*3S6
1760 47-992 3-0737
34-834
3- 1392
1765 ** 37 3-36o 3-0733
50.531
3- *397
1770 18.7-25 3-0729
13 13 6.231
3- H03
1775
34.089 3-0725
21-934
3- 1408
1780
49-45* 3.0722
37-639
3- i4H
1785
ii 38 4.811 3-0718
53-348
3- Hi9
1790
20. 169 3. 0714
13 *4 9-059
3- H25
1795 35-5 2 5 3-07*o
24.772
3-i430
1800
50,879
3.0706
40. 489
3- *436
1805
ii 39 6.231
3. O7O2 56. 2O8
3-144*
1810
21.581 3-0699 13 15 11.930
3-*447
1815
36.929 3-0695 27.655
3- 1452
1820
52.276 3-069 1
43-382
3- H58
1825 ii 40 7.620 3.0687
59-ii3
3- *464
1830 22.963 3-0683 | 13 16 14.846
3- 1469
1835
38.304 3.0680
30.582
3-H75.
1840
53-642
3.0676
46.321
3- 1481
1845 ii 41 8.980
3.0672
13 17 2.063
3:*486
|
1850
24-315
3.0669
17.807
3- 1492
1855
39.648
3.^0665
33- 555
3- *498
1860
1865
54.980
1 1 42 10. 309
3- O66l
3.0658
49-305 3-1503
13 i 8 5.058 3-1509
1870 25.637
3-0654
20.814 3-15*5
1875 40-963
3.0650
36.573 3-1520
1880 56.288
3.0647
52-334 3-1526
1885 ii 43 11.610
3-0643
13 19 8.099 3- iSS 2
1890 26. 931
3.0640
23.866 3.1538
1895 42.250
3.0636
39-637 3-1544
1900 57-567
1
3-0633
55-4io
3-*549
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Mean right ascensions, dr. Continued.
61
Year.
a Boons.
or LIBRAE.
K. A.
Ann. Var.
R. A.
Ann. Var.
//. 111. .V.
s.
//. ill. S.
s.
i/5o
14 4 15.978 2.7320
4 37 5-726
3.2881
755
29-638 2.7321
22. I 68
3.2888
1760
43- 2 99 2.7322
38.614
3.2896
1765
56.960 2.7323
55.064
3.2904
1770
14 5 10.622 2.7324
14 38 11.518 3.2911
1/75
24.284 2.7325
27.976
3- 2919
1780
37.946 2.7326
44-437
3-2927 .
i 785
51.609 2.7327
14 39 0.902
3-2934
1790 .
14 6 5.273 2.7328
17-37I
3.2*942
795
*
l8 -937 2.7329
33.844
3- 2950
1 800
32.601 2.7330
50-321
3-2957
.805
46.266 2.7331
14 40 6. 802
3-2965
1810
59-932 2.7332
23.286
3-2973
1815
14 7 13.598 2. 7333
39- 775
3- 2980
1820
27.265 2.7334
56.267
3.2988
1825
40.932 2.7335
14 41 12. 763
3.2996
1830
54-599 2.7336
29.263
3-3004
1835
1840
14 8 8.267 2.7337
21.936 2.7338
45- 766
14 42 2.274
3-30ii
3-3QJ9
1^45
35- 6 o5
2-7339
18.785
3.3026
.850
49-275
2. 7340
35-301
3-3034
1855
14 9 2.945
2-7341
51.820
3-3042
1860
16.616
2-7342
14 43 8.343
3-3050
,865
30. 288
2- 7344
24.870
3-3058
1870
43.960 2.7345
41 . 401
3-3065
i875
57-633 2.7346
57-935
3-3073
1880
14 i o 11. 306
2-7347
14 44 14.474
3-3081
,885
24. 980
2-7348
31.016
3-3089
1890
38-654
2-7350
47-562
3.3096
895
52.329
2-7351
14 45 4- U3
3-3104
1900
14 ii 6 . 005
2-7352
20. 667
3-3"2
62
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Mean right ascensions, rfr. Continued.
a CORONA.
Yo-u-
a SERPENTIS.
J_ CCliJ. .
K A.
Ann. Var.
R. A.
Ann. Var.
/;. in. s.
s.
//. 111. S.
s.
1750 15 24 6.587
2.5360
J 5 3i 58.355
2.9431
i/55 19.267
2-5361
15 32 13-071
2-9434
1760 3I-948
2.5363
27.789
2-9437
1765 44-630
2-5364
42.508
2 . 9440
i//o 57-3 12
2-5365 57-229
2-9443
1775 J 5 2 5 9-994
2-5366 15 33 11.952
2.9446
1780 22.678
2.5367 26.675
2.9449
785 35-362
2.5368 41.401
2.9452
1790 48.046
2.5369 56.128
.2-9455
1795 15 26 0.731
2-5370 5 34 10.856
2.9458
i 800 13-416
2-5372
25-586
2. 9462
1805 26. IO2
2-5373
40.318
2.9465
1810 38.789
2-5374 55-05I
2.9468
1815 5^476
2-5375 15 35 9- 785
2.9471
1820 15 27 4. 164
2.5376 24.521
2-9474
1825 16.852
2-5377
39-259
2-9477
1830 29.541
2.5378
53.998
2. 9480
1835 42.231
2-5380 15 36 8.739
2.9483
1840 54-921
2.5381 23.481
2. 9486
1845 5 28 7-612
2-5382
38-225
2.9489
1850 20.303
2-5383
52.970
2.9492
1855 32.995
2-5384 15 37 7-7I7
2-9495
1860 45. 687
2.5386 22.465
2.9498
.865 58.380
2-5387 37-215
2.9501
1870 15 29 11.074
2-5388 5^966
2.9504
1875 23.768
2-5389 i5 38 6.719
2.9507
1880 36.463
2.5390 21.473 2.9510
1885 49-159
2.5392
36. 229
2-95 3
1890 15 30 1.855
2-5393 50-987
2.9516
1895 H.552
2-5394 15 39 5-746 2.9520
1900 27. 249
! I
2-5395
20.506 2.9523
i
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Mean rigid ascensions, (C-c. Continued.
Year.
a ScORPIl.
a HERCUIJS.
R. A.
Ann. Var.
R. A.
Ann. Var.
//. in. t>.
s.
h. in. s.
6 .
1750
1 6 14 7.423
3.6487 17 3 15.554
2.7286
! 755
1760
25.669
43.918
3-6495
3-6503
29. 198
42.842
2. 7288
2. 7290
r / 6 5
1615 2. 172
3-6511
56.487
2.7291
1770
2O. 429
3-6519
7 4 10. 133
2.7293
1775
38.690
3-6527
23.780
2- 7295
1780
56.956
3-6534
37-428
2. 7297
1785
16 16 15. 225
3-6542
51-077
2.7299
1790
33-498
3-6550
17 5 4-727
2.7300
i/95
51-775
3-6558
18.378
2.7302
1800
16 i 7 10. 056
3.6566
32.029
2.7304
1805
28.341
3.6573
45.681
2.7306
1810
46. 629
3-6581 59-335
2.7307
1815
16 18 4.922
3-6589
17 6 12.989
2. 7309
1820
23.218
3-6596
26. 644
2.7311
1825
41.518
3.6604
40. 300
2- 73 3
1830
1835
59- 822
16 19 18. 130
3. 66 i 2
3.6619
53.956
17 7 7.614
2.7314
2.7316
1840
36.442 3-6627
21. 273
2.7318
1845
54-757
3-6635
34-932
2.7320
1850
16 20 13.076
3.6642
48.592
2.7321
855
3 -399
3-6650
17 8 2.253
2.7323
1860
49- 726
3-6657
I5-9I5
2.7325
1865
16 21 8.057 3- 666 5
29-578
2.7327
1870
26.391
3-6673
43. 2 42
2.7328
875
44- 730
3.6680
56.906
2.7330
1880
l6 22 3.O72
3.6688
17 9 10.572
2.7332
1885
21.417
3-6695
24.238
2-7333
1890
39.767
3-6703
37-905
2-7335
895
58. 120
3.6710
51-573
2-7337
1900
16 23 16.477
3.6718
17 10 5. 242
2-7339
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Mean rujld ascensions, <( -c. Continued.
Year.
a OPHIUCIII.
a LYRJE.
11. A.
Ann. Var. K. A.
Ann. Var.
li. m. s.
s. li. m. s.
,5.
1750
17 23 20.430
2.7781 18 28 28.585
2. 0298
1755
34-320
2.7783
38.734
2. 0299
i 760
48. 212
2-7784
48.883
2. 0299
1765
17 24 2. 105
2.7786
59-033.
2 . O3OO
1770
15.998
2.7788
18 29 9. 183
2 . O3OO
1775
. 29.893
2.7790
19-334
2.0301
1780
43-788
2. 7791
29.484
2. O3OI
1785
57.684
2-7793
39-635
2.0302
1790
17 25 II.58I
2-7795
49.786
2.0303
1795
25-479
2-7797
59-938
2.0303
1800
39-377
2.7798
18 30 10.089
2 . 0304
1805
53-277
2. 7800
20. 241
2.0304
1810
17 26 7. 177
2.7802
30- 394
2.0305
1815
21.079
2. 7 803
40. 546
2.0305
1820
34.981
2.7805
50.699
2. 0306
1825
48.884
2.7807
18 31 0.852
2. 0306
1830
17 27 2.788
2. 7809
i i . 005
2.0307
1835 16.692
2. 7810
21. 159
2.0307
1840 30-59 8
2. 7812
3I-3I3
2. 0308
1845
44- 504
2.7814
41.467
2. 0308
1850
58.411
2.7815
51 . 621
2.0309
1855
17 28 12.319
2.7817
18 32 1.776
2. O3IO
1860
26. 228
2.7819
11.931
2. O3IO
1865-
40. 138
2. 7820
22. 086
2.03II
1870
54.049
2. 7822
32.241
2.03II
1875
17 29 7.960
2. 7 82 4
42-397
2 . 03 I 2
1880
21.872
2.7825
52.553
2.0312
1885
35-785
2. 7827
i 8 33 2.709
2.0313
1890
49.699
2. 7829
12.865
2.0313
1895
17 30 3.614
2./830
23. 022
2.0314
1900
17-530
2.7832
33- 179
2.03H
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Mean riyld ascensions, dr. Continued.
Yea r.
y AQI:IL
JE.
a AQUIL
..
K. A.
Ann. Yar.
R. A.
Ann. Yar.
//. HI. S.
s.
//. 1)1. S.
S.
750
19 54 22.396
2-8536
9 38 34-939
2.9502
1755
36.664
2-8536
49-590
2.9501
i 760
50.93 2
2 -8535
19 39 4. 240
2.9500
1/65
19 35 5- 200
2-8535
18.890
2.9299
770
19.467
2-8554
33-539
2. 9298
775
-> t ** -> \
jj>- 734
2-8534
48. i 88
2.9297
1780
48. ooi
2-8534
19 4O 2. 856*
2. 9296
-785
19 36 2. 268
2-8533
17 484
2.9295
1790
16.534
2-8533
32- 132
2.9295
795
30. 800
2-8532
46. 779
2.9294
iSoo
45.066
2-8532
19 41 1.425
2.9295
1805
59-332
2-8551
16. 071
2.9292
i 8 10
9 37 3-597
2-853
30. 7 7
2.9291
1815
27.865
2-8530
45-362
2. 9290
1820
42. 128
2-8530
1942 o. 007
2. 9289
1825
5 6 -392
2-8529
14.652
2.9288
1830
1835
19 38 10.657
24.921
2-8529
2.8528
29. 296
43-939
2.9287
2.9286
1840
39- 185
2.8528
58-582
2.9286
i*45
53-448
2-8527
9 43 13-225
2.9285
1850
19 39 7. 712
2.8527
27.867
2.9284
t855
21-975
2.8526
42.508
2.9285
1860
36. 238
2.8526
57- 150
2. 9282
1865
50. 500
2-8525
i 9 44 i i . 790
2. 9281
1870
19 40 4.763
2.8524
26.450
2. 9280
1^75
19.025
2.8524
41. 070
2.9279
1 880
33-287
2-8523
55-7 Q
2.9278
1885
47-548
2-8523
19 45 10.349
2.9277
1890
1941 i . 810
2.8522
24.987
2. 9276
1895
i 6. 071
2.8522"
39-625
2.9275
1900
** C\ "> *> T
U - JJ 1
2.8521
54.262
2.9274
9 F s
66
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
right ascensions, <fr. Continued.
/? AQUILJE.
a 2 CAPRICORNI.
1 car.
K. A.
Ann. Var.
H. A.
Ann. Var.
//. 111. S.
s.
Ji. m. s.
s.
1750 19 43 1-8/4
2. 9490
20 4 9-754
3-3439
1755 16.619
2.9490
26.473
^> ^ 1 ^ C
o J4o
1760 3i-3 6 4
2.9489
43 i 89
^ ^ 1 "> T
o 34.5 l
i 765 46. 108
1770 19 44 0.852
2.9488
2.9488
59.902
20 5 16.614
3-3426
3-3422
775 15-595
1780 30.339
2.9487
2.9486
33-324
50.032
3-34I8
3-34I4
1785 45-082
2. 9486 20 6 6. 738
3-3410
1790 59- 82 4
2.9485
23-442
3 34o6
795 T 9 45 U-567
2 . 9484
40 . 144
3-3402
1800 29.308
2.9483
56-844
"* "> ** c\
o- o o9/
1805 44.050
2.9483 20 7 13.542
"> ^ ^ /i t
o oo9o
1810 58. 791
2.9482
30-237
3-3389
1815 19 46 I3-53 2
2 . 948 I
46.931
3-3385
1820 28. 273
2.9481
20 8 3.622
1 1 1<s T
o- 33
825 43-oi3
2. 9480
20.311
3-3376
1830 57-75 2
2-9479
36.999
1 -> *7 *>
o- o j/ -
835 19 47 12.492
2-9479
53-684
-> 1 1^9
3- oo b
1840 27.231
2.9478
20 910. 367
-^ O () 1
o- oo4
1845 41.970
2-9477
27.048
*> *> ^ /Sr^
0- JO 00
1850 56. 708
2.9476
43-726
3 3355
1855 19 48 11.446
1860 26 . 184
2.9476
2-9475
20 10 0.403
17.078
*>" ^> I f T
O- JO5 *
-1 o ^> /I *
o- jo4/
1865 40. 921
2.9474
33-750
^> -l ^ -1 1
o jo4o
1870 55-658
2-9473
50.421
o ^ o o r\
j ooo9
1875 19 49 10.394
2-9473
20 i i 7. 090
3- 3334
1880 25.131
2.9472 23.756
3-3330
1885 39.866
2.9471
40. 420
3-3326
1890 54.602
2.9471
57.082
i o t o O
o o J - -
l8 95 19 50 9-337
2.9470
2O 12 13. 742
I
o " ^y T *7
D- O J j /
1900 24. 072
2 . 9469
30. 400
*> o I T ^
o- oo j o
DEFINITIVE RIGHT ASCENSIONS OF THE FUNDAMENTAL STARS.
Mean riyld ((scomions, iCc. Continued.
67
Year.
a CYGXI.
a AQKAKII.
R. A.
Ann. Yar.
R. A.
Ann. Yar.
//. III. S.
S.
//. III. S.
s.
I750 20 32 54-957
2.0414
21 52 56.049
3.0888
1 755
-o 33 5- H4 2.0415
21 55 11.492 5.0886
i 760
15.352 2.0416
26.935 3-0884
1765
25.561 2.0417
42.376
3.0881
1770
35.770 2.0418
57.816
3.0879
775
i 780
45-979
56. 189
2 . 04 i 9
2. O42O
21 54 3- 255 3-0877
28.693 3-0875
1785
20 34 6.399
2. 042 I
44-130 3-0872
1790
16.610
2. O422
59- 565
3.0870
1 795
26.822
2.0425
21 55 15.000
3 . 0868
1800
37-054
2.0424
30-433
3.0866
1805
47.246
2.0425
45-865
3-0863
18 10
57-459
2. 0426
2 I 56 1 . 296
5. 0861
1815
20 55 7-675
2. 0428
16.726
3-0859
1820
17-887
2.0429
32.155
3-0857
1825
28. 101
2.0450
47- 583
3-0855
1830
38.316
2.0451
21 57 5.010
3-0852
i835
48.532
2.0452
i8.435
5.0850
1840
58.748
2-0433
33-86o
3.0848
1845
20 56 8.965
2-0434
49- 285
3 . 0846
1850
19. l82
2.0435
21 58 4.706
3.0844
1855
29.599
2.0456
20. 127
5.0842
1860
59.618
2-0457
35-548
5 . 0840
1865
49.856
2.0458
50-967
5.0838
1870
20 57 0.056
2.0459
2 59 6.585
3-0835
i8/5
10. 276
2.0440
2 I . 8O2
3-0833
1880
20. 496
2.0441
37-218
3-0831
1885
30-7 7
2-0445
52.633
3.0829
1890
40. 959
2.0444.
22 O 8 . 048
3.0827
1895
51. 161
2.0445
25.461
3-0825
1900
20 58 ,.585
2.0446
38.873
3-0823
68
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Mean right ascensions, <c. Continued.
Year.
a PlSCIUM AUSTEALIS.
a PEGASI.
R A.
Ann. Var.
R. A.
Ann. A T ar.
ll. III. S.
s.
It. 111. S.
s.
1/5
22 43 46. 710
3-3551
22 52 19.531
2-9775
J 755
22 44 3.483
3-3540
34-4I9
2-9778
i 760
20. 250
3-3529
49- 309
2.9780
1765
37.012
3- r 35 8
22 53 4- 199
2.9783
7/o
53-768
3-3507
19. 091
2.9785
i/75
22 45 10. 518
3-3496
33-985
2.9788
1780 27. 264
3-3485
48.879
2.9790
1785 44-003
3-3474
22 54 3- 775
2-9793
1790
22 46 o. 737
3-3463
18. 672
2-9795
J 795
17.466
3-3452
33-570
2.9798
1 800
34- 189
3-3441
48.470
2. 9801
1805
50.907
3-3430
22 55 3-37
2.9803
1810
22 47 7.619
3-34 9
18.273
2. 9806
1815
24.326
3-3408
33- 177
2. 9809
1820
41 . 028
3-3397
48.082
2. 981 I
1825
57- 7 2 4
3-3387
22 56 2.988
2.9814
1830
22 48 14-4H
3-3376
17. 896
2.9817
1835
31. ioo
"* * i (~\ ^
o- oo5
32.805
2. 9819
1840
47-779
3- 3354
47-715
2. 9822
1845
22 49 4.454
3 3343
22 57 2.627
2.9825
1850
21. 123
i f\ *> -7 *5
O- J JOO
17.540
2.9828
1855
37.786
3-3322
32.455
2.9830
1860
54-445
3-33 1
47-370
2.9833
1865
22 50 II. 097
3-3300
22 58 2.288
2.9836
1870
27-745
3.3290
I 7. 2O6
2.9839
i875
44-387
3-3279
32. 126
2.9841
1880
22 51 I.O24
3-3268
47.048
2.9844
1885
17.656
3-3258
22 59 1.971
2.9847
1890
34.282
3-3247
16.895
2.9850
1895
50- 903
3-3236
31.821
2.9853
1900
22 52 7.518
T, . T.226
\.J ^J
46.748
2.9856
CORRECTIONS FOR ORBITAL MOTION OF SIRIUS AND PROCYOX.
Periodic term* to be <ij>]>//crl tu tin riyltt d-yci iisionti of Sir ins and F roc yon.
69
a CAMS MAJOKIS.
Year.
Year.
Year. P
s.
1750.6
1800. o
1849.4 4- .026
1751.6
i 80 i . o
20
1850.4 +.006
1752.6 1802.0
1851.4 -.014
1753.6 1803.0
1852.4 --031 ^
i 754. 6 1804. o
i853-4 --047
1755.6 1805.0
1854.4 -.062
i 756. 6 1806. o
1855.4 -.076_
1757.6 1807.0
1856.4 -.088
,758.6
i 808.0
1857.4 -.099
1/59-6
i 809. o
I o
1858. 4 - . 109
, 760. 6
1810. o
1859.4 -.n8_
1761.6
i 8 1 i . o
1860.4 .126
6
1762.6 1812.0
,861.4 -.132
1763.6 1813.0
,862.4
-.138
i 764. 6 1814.0
1863.4 -- 43
1765.6 1815.0
1864. 4
-.147"
i 766. 6 1816.0
1865.4
-.149"
i 767. 6 1817.0
1866.4
- - 5
1768.6 1818.0
1867.4
~ 5-
i 769. 6 1819.0
1868.4
o
5- ,
-4- i
1770.6
1820. o
1869. 4
- 5
-4- T
1771. 6
1821 . o
1870.4
- 49 ,
1772.6
1822. o
[871.4
-.i 4 6 4
"773-6
1823. o
,872.4
.142
4- c
1774.6 1824.0
873-4
> + 6
775-6
1825. o
,874.4
- 3i
1776.6
1826.0
1875-4
+ 7
* 1
1777.6
1827.0
1876.4
-" 4
-r- O
,778.6
1828.0
.877.4
-.108^
-t- 10
1779.6
1829. o
1878.4
- .098 ]
-r- I 2
1780. 6
1830.0
1879.4
-.086]
i 2
i 78 1 . 6
I 83 I .
1880.4
~~ 74 + I"
i
7 o
RIGHT ASCENSIONS OF FUNDAMENTAL STARS,
Periodic tcnns, d c. Continued.
a CANIS MAJOKIS Continued.
Year.
Year.
Year.
P
s.
1782.6
1832.0
1881.4
.061
+ 5
1783.6
1833-0
1882.4
1784.6
1834.0
1883.4
-3 + ]8
1785.6
1835-0
1884.4
.OI 2
+ 1 9
.1786.6
1836.0
1885.4
t
+ .007
+ 20
1787.6
1837.0
1886.4
+ - 27 +22
1788.6
1838.0
1887.4
+ -049 ,
1789.6
1839. o
1888.4
_1_ "7 ~
i 790. 6
1840. o
1889.4
+ - 96 +24
1791.6
1841 .0
1890. 4
+ I2 1 oi
1792.6
1842. o
1891 . 4
+ .141
1793.6
1843.0
1892.4
+ -i5 2 _
1794.6
1844. o
1893.4
+ -I47
1/95-6
1845.0
1894.4
+ -130
i 796. 6
1846.0
1895.4
+ - 7
1797.6
1847.0
1896. 4
+ .082
1798.6
1848.0
1897.4
+ -osS
1 >- 0-1
1799.6
1849.0
1898.4
J_ ~
1800. 6
1850.0
1899.4
+ - OI 4
20
i 80 i . 6
1851.0
1900. 4
.006
18
1802.6
1852.0
1901.4
.024
CORRECTIONS FOR ORBITAL MOTION OF SIRIL S AND PROCYON.
Periodic terms, ((<: Continued.
a CANIS MINORIS.
i
Year.
Year.
Year.
Year.
p
s.
1750.0
i 790. o
1830.0
1870. o
-45
8
1751.0
1791.0
1831.0 1871.0
- -53
1752.0
1792.0
1832.0 1872.0
-.060
t;
1 753-o
793-0 1833.0 1873.0
.065
1754-0
1794.0 1834.0 1874.0
.068 ~
755-0
1 795-o 1835.0 1875.0
.O7O
1756.0
1796.0 1836.0 1876.0
O
.070
757-o
1797.0
1837.0 1877.0
- .068 4
_[._ ^>
1758.0 1798.0
1838.0 1878.0
.065
i759-o 1799-0 1839.0 1879.0
- .060 +
1760.0 1 800.0 1840.0 1 880.0
--053^ I
i 761 . o
1 80 1. o
1841 . o
1881.0
~ -045 ,
1762.0
1802.0 1842.0
1882.0
.o;6
-4- TO
1763.0
1803. o
1843.0
1883.0
., TT J U
.026
1764.0
i 804 . o
i 844 . o
1884.0
/-+ I0
.Ol6
1765.0
1805. o
1845.0
1885.0
.006
1766. o
i 806 . o
1846. o
1886.0
+ I 1
1767.0
1807.0
1847.0
1887.0
+ .oist 10
1768.0
1 808.0
1848.0
1888.0 + .026~f
1769.0
1809.
1849. o
1889.0
. , + 10
+ 036
1770.0
1810. o
1850.0
1890. o
+ -045 ,
1771.0
181 1 . o
1851.0
1891 . o
+ -053 j
1772.0
I 8 I 2 . O
1852.0
1892. o
+ .o6o 4
773-0
1813.0
1853-0
1893.0
+ -065
1774.0
1814.0
1854.0
1894. o
_j_ 2
775-o
1815.0
1855-0
1895.0
+ -O7
1776.0
1816.0
1856.0
1896. o
O
+ -070
1777.0
1817.0
1857.0
1897.0
+ .068
1778.0
1818. o
1858.0
1898.0
+ .o6 5 _ *
1779.0
1819.0
1859.0
1899. o
+ .060
1780.0
1820. o
1860. o
1900. o
+ -054_
1781.0
1821.0
i 86 i . o
i 90 i . o
+ .046
9
1783.0
i 784. o
1785.0
1786.0
1787.0
1788.0
i 789. o
i 790. o
RIGHT ASCENSIONS OF FUNDAMENTAL STARS.
Periodic twins, (C c. Continued.
Your.
Yea
1782. o
1822
a CANIS MIXORIS Continued.
1823.0
1824. o
1825.0
1826.0
1827. o
1828.0 . i
1829. o
1830.0
Year.
1862.0
1863.0
1864. o
1865.0
1866. o
1867.0
1868.0
1869. o
1870. o
1902. o
1903.0
1904. o
1905.0
1906. o
1907. o
1908. o
1909. o
1910. o
s.
+ 037
+ .027
+ .017
-f- .006
-005
.015
.027
-037
.046
IO
10
- 1 1
1 1
IO
9
HILL S FORMULA FOR SECULAR VARIATION OF ANNUAL MOTION OF STARS. 73
HILL S FORMULA FOR THE SECULAR VARIATION OF THE ANNUAL
MOTION OF THE STARS.
[From Star-Tables of the American Ephcmeris, p. xix.]
These formulae, being more complete than those usually employed, are given here,
for convenience of reference, in a slightly modified form.
Put-
ju, the proper motion in right ascension, expressed in seconds of time;
//, the same in declination, expressed in seconds of arc ;
p, p , the annual precessions, expressed in the same Avay with /* and // ,
respectively.
We then have
p rr m -\- n sin a tan 8
p n cos a
da
^ = l + "
(16
~di = P+f *
10 f TT = [7-9878] n cos a. tan 8 -f- [6.81 17] n sin a sec 2 S
d u
loo- zz [9. 1640] JLI sin a
ioo = + . 00322
- [6.6338] j>
+ [7-9878] (p + 2 /() cos a tan 5
+ [6.8117] (y + 2 /O s in
-f [6.9866] n // tan 5
fl*fi on /
too - /r , - = -[6.6338] p
[9.1640] (^ + 2 /<) sin a
-[8.7367] >" a *in 2 r5
Struve s values of m rt<7 n.
Year. m n log log
s.
s.
1750
3.06987
I -33767
0.12635
20.0650
1.30244
1800
3.07082
1-33738
o. i 2626
20.0607
I -30235
1850
3.07177
I -33710
o. 12616
20.0564
1.30225
1900
3.07272
1.33681
o . i 2607
20.0521
I .30216
IO S
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