C 5 775
FIVEYEAR CATALOGUE
OF
258 FUNDAMENTAL STARS
DEDUCED FROM
OBSERVATIONS
EXTENDING FROM 1887 TO 1891,
MADE AT THE
ROYAL OBSERVATORY, GREENWICH,
UNDER THE DIRECTION OF
WILLIAM HENRY MAHONEY CHRISTIE, M.A., F.R.S.,
ASTRONOMER ROYAL,
REDUCED TO THE EPOCH
18900.
(Forming Appendix to the Greenwich Observations for the Year 1891.)
L N D N :
PRINTED FOR HER MAJESTY'S STATIONERY OFFICE,
BY DARLING & SON, ITD., 1,2,3, & 5, GREAT ST. THOMAS APOSIT.E, E.G.
1893.
INTRODUCTION
TO THE
GBEENWICH FIVEYEAR CATALOGUE
OF
258 FUNDAMENTAL STARS, .
DEDUCED B^ROM OBSERVATIONS EXTENDING FROM 1887 TO 1891,
AND REDUCED TO THE EPOCH
18900.
This Catalogue has been formed to supply revised places of Fundamental Stars,
available for determination of instrumental and clock errors, and for use in the
Nautical Almanac, in the interval between two' successive Greenwich General Catalogues,
which it is proposed to form at intervals of ten years, so that a sufficient number of
observations of each star may be accumulated. In the case of the Fundamental Stars,
however, there are usually a sufficient number of observations in the course of five
years to give trustworthy positions, and it has, therefore, been thought advisable, in
view of possible uncertainty of proper motion when applied for more than ten years, to
publish the present provisional Catalogue of Fundamental Stars based on the five
years' observations 18871891, strengthened, where necessary, by combining with
them the places of the Ten Year Catalogue (188OO).
The stars whose places are given in this Catalogue are
1. Those contained in the Greenwich Clock Star Lists.
2. Circumpolar stars whose Ephemerides are published in the " Connaissance des
Temps," or in the " Ephemerides des Etoiles de Culmination Lunaire et de Longitude,
par M. M. Loewy."
3. Stars in the Nautical Almanac, but not in the Greenwich Clock Star Lists.
The following is the process of formation of the star places in this Catalogue.
2990
SO 114268008/93 Wt , D & S. GREENWICH FIVEYEAR CATALOGUE POH 1890. a 2
4 GREENWICH FIVEYEAR CATALOGUE OF FUNDAMENTAL STARS FOR 1890.
I. FORMATION OF RIGHT ASCENSIONS.
The determinations of Right Ascension of each star, which are to be combined in
order to form the Right Ascensions in this Catalogue, are those given in the Annual
Catalogues printed in the successive volumes of Greenwich Observations from 1887
to 1891.
The Right Ascensions of each Annual Catalogue depend essentially upon the Right
Ascensions assumed for the stars whose transits are employed in each year to ascertain
the errors of the TransitClock ; it is necessary, therefore, in the first instance to
ascertain the amount of correction required for the assumed Right Ascensions of the
Clock Stars. Now it appears from the discussions of the Observations for the Position
of the Ecliptic in the Greenwich Observations 18871891, that the Right Ascensions
of the Clock Stars used in those years require the following corrections :
8.
1887 ... 0059.
1888 ... +0072.
1889 ... + 0*024.
... + 0092.
... +0088.
The mean of these is + 9 043 ; but it was considered advisable to wait for further
information before making such a large correction to the Right Ascensions, and no
correction for Epoch has therefore been applied to the Right Ascensions taken from the
Greenwich Observations 1887 to 1891. The present Catalogue is thus referred to the
Epoch of the Standard Right Ascensions of the Ten Year Catalogue (1880'0) ; and
also of the Nine Year Catalogue (1872'0) ; for it is shown on page 9 of the
Introduction to the former, that the mean difference between the two sets of Standard
Right Ascensions is only 9 '0001, which is practically insensible. It should be
remarked that the Mean R.A.'s of Clock Stars used during 1887 and 1888 were taken
from the Standard R.A.'s of the Nine Year Catalogue ; during 1889, 1890, and 1891,
from those of the Ten Year Catalogue.
The results for the separate years as given in the Annual Catalogues were reduced
to 1890*0 by using the elements given in the Ten Year Catalogue, where Struve's
Constant of Precession, and Prof. Auwers' Proper Motions are used. In the case of
Sirius and Procyon, corrections for orbital motion deduced from Prof. Auwers' Papers
(Publ. Astr. Gesellschaft, No. VII., and Astr. Nachr., Nos. 1H73 and 3085) have
been applied to the separate years in forming the Mean R.A. 1890'0.
\
INTRODUCTION. 5
A separate determination of the Right Ascensions of Clock Stars was made in
which only those observations were included where the group of Clock Stars
extended over 12 hours at least, in a similar manner precisely to that described in the
Introductions to the Nine Year and Ten Year Catalogues, though the number of such
groups is, of course, not so large. The excess of R. A. from the 12hour groups above
that of the Five Year Catalogue was tabulated for each star and the mean formed for
each hour of R.A. by combining the individual excesses with weights = , where
m+w
m and n are the munbers of observations in the TwelveHour Groups, and in
the Catalogue respectively. Similarly the corrections to the R.A.'s of the Five Year
Catalogue, as depending on the N.P.D. of the star, were formed for each 10 of N.P.D.
Both sets of corrections are given in the following tables, the Resultant Corrections
applicable to the R.A.'s of the Five Year Catalogue being the algebraic sums of the
two. The mean of all the corrections is less than s 0005, and though it enters into
both sets, no sensible error is thus introduced by adding the two sets together.
MEAN CORRECTIONS TO EIGHT ASCENSIONS OF FIVE  YEAR CATALOGUE,
DERIVED FROM A COMPARISON WITH R.A.'s OF 204 CLOCK STARS FROM
izHOUR GROUPS.
Limits
of
Correction.
i
Limits
of
Correction.
m
Limits
of
Correction.
4
Limits
of
Correc
a
B.A.
a
B.A.
8
B.A.
9
N.P.D.
i
h li
OI
8 8
4 8
h h
89
8 8
23
h h
1617
+ 'OO5 '007
30
50 60
8
'OO2
67
12
oo7f*oo5
56
910
009'0o8
20
I7I8
005'O05
44
60 70
+ 'O02
176
23
"OO2 ~(~*OOs
45
IOI I
009 'OO7
26
1819
OOlHt'OO4
63
70 80
ooo
192
34
*oo c t '006
33
I II2
+ '01 2 '009
16
1920
+ 'OO2 + 'C04
68
80 90
003
221
*OO I ~f~ *OO C
47
1213
+  oo 5 008
20
2021
+ 'oi4  oo6
37
90100
ooi
146
56
+ *oio'oo6
32
1314
004 '005
46
2 122
oio  oo6
36
IOOI 10
'OOI
80
67
+ *oio'oo6
35
1415
*oo 5 ~^~ *ooo
37
2223
000+ 005
53
1 10124
+ 006
35
78
oiioo6
39
I5l6
 *OO2 ~f~ *OC'6
32
2324
+ 002 006
3i
The probable errors appended with the sign have been computed by taking the
probable error of a single determination of R.A. as O s '034.
It appears that the errors of the assumed places of the Clock Stars, originally derived
from Pond's Catalogue, have been greatly diminished and are now very small.
II. FORMATION OF MEAN NORTH POLAR DISTANCES.
The determinations of N.P.D. of each star, which are to be combined in order to form
the N.P.D. in this Catalogue, are those given in the Annual Catalogues printed in the
successive volumes of Greenwich Observations, 1887 to 1891, to which the sam
6 GREENWICH FIVEYEAR CATALOGUE OF FUNDAMENTAL STARS FOR 1890.
statements apply generally as have been made for K.A., omitting all that relates to
Correction for Equinox. The adopted colatitude is 38 31' 21"'90 throughout. The
corrections required for orbital motion, in the case of Sirius and Procyon, have been
deduced from Prof. Auwers' papers referred to before.
III. EXPLANATION OF THE SEPARATE COLUMNS OF THE PRINTED CATALOGUE.
The " No." is the ordinal number of this Catalogue, the stars being arranged in order
of R.A. 18900.
The " Star's Name " is taken from one of the following authorities, the order of
preference being the order of mention of the authority below :
1. Flamsteed's Constellation No. and Constellation, with Bayer's Letter, taken from
Baily's Edition of Flamsteed, or the British Association Catalogue.
2. The No. in Bessel's Fundamcnta Astronomice deduced from Bradley's Observations,
referred to as " Bradley."
3. The Hour and No. in Piazzi's Catalogue, Edition 1814.
4. The No. in Groombridge's Catalogue.
For Circumpolar Stars the result of observations below the pole is shown separately.
The " Magnitude " is taken from the Harvard Photometry for stars contained in that
work, and for other stars (marked *) from the Bonn Durchmusterung. The magnitude
in the Uranometria Nova Oxoniensis is given in the Notes for all cases in which it
differs by more than 0'2 magnitude from that in the Harvard Photometry. The
magnitudes of the components of double stars, taken from Struve's Mensurcn Micrometricce
or other authority, are given in the Notes. In the case of Variable Stars, the limits of
magnitude and the period given' in the Notes are taken from Mr. Chandler's Catalogue
in the Astronomical Journal, Nos. 179, 180.
The next six columns consist of three pairs, the first of each pair referring to the
observations in 18871891, immediately under discussion, and the second to the
Ten Year Catalogue.
The first pair gives the "Mean Date " expressed in years and decimals of a year
reckoned from 1800.
INTRODUCTION. 7
The .second pair (columns 6 and 7) gives the "Number of Observations," being the
aggregate of all the observations in the different years, above and below the Pole
respectively, in column 6, and the aggregate of all observations in column 7.
The third pair (columns 8 and 9) gives the seconds of Mean R.A. formed in the
manner already described.
In forming the adopted Mean R.A. 1890'0 the following rules have been observed :
(1.) In all cases where the total number of observations in the years 18871891
is ten or more, the mean of these observations is the adopted Mean R.A., equal weight
being assigned to observations above and below the Pole.
(2.) When there are five to nine observations in the period 18871891, the adopted
Mean R.A. is formed by combining these with the result brought up from the
TenYear Catalogue, giving weight to each observation in the latter.
(3.) When there are less than five observations in the period 18871891, weight ^ is
given to each observation in the Ten Year Catalogue in combining the two means.
Assuming that there are on the average twice as many observations of a star in the
Ten Year Catalogue as in the Five Year Catalogue, this is equivalent to giving the
Ten Year Catalogue weight ^ on the average when there are from five to nine observa
tions in the Five Year Catalogue, and to taking the simple mean between the Five Year
and Ten Year (on the average) when there are less than five observations in the
former. If we assume that the probable error of one observation of R.A. is 8 034,
and that the Ten Year Catalogue deduced place for 1890'0 is affected by a probable
error of proper motion, or other systematic error represented by a, and express the
condition that the result of seven observations in the Five Year Catalogue should have
double the weight of 14 observations in the Ten Year Catalogue ; then x = 8 016 ;
or the method of combination adopted is equivalent to assuming that the results of
the Ten Year Catalogue reduced to 1890'0 are affected by a probable error of proper
motion or other systematic error amounting to S '016.
*
The " Annual Precession 1890'0 " for stars beyond 5 from the Pole has been
formed by applying to the Precession in the Ten Year Catalogue the proportional
part of the " Secular Variation 188OO " to reduce it to 189OO.
The " Secular Variation 189OO " is the same as that given in the Ten Year Catalogue,
except for stars within 5 of the Pole. For these latter stars both the Annual
8 GREENWICH FIVEYEAR CATALOGUE OF FUNDAMENTAL STARS FOR 1890.
Precession and the Secular Variation have been computed by the help of Folie's
" Douze Tables pour le calcul des reductions stellaires," in which Struve's Constant
of Precession is used. The Precession is given by the formula
+ i s 3369 [log. = 012611] sin R.A. cot. N.P.D.
and the Secular Variation by the formula
A + B cot. N.P.D. + C cot. 2 N.P.D.
where
A = o s ooi9o + o'oo65o sin 2 R.A.
B = o s ooo57 sin R.A. + o"o2987 cos. R.A.
C = + o"oi3oo sin 2 R.A.
The second term of the precession is readily computed from these tables, and the
quantities A, B, C, are therein tabulated for every minute of R.A. These formulae
correspond essentially with those used in previous Catalogues, but the method of
computation is simpler.
The " Annual Proper Motion 1890'0 " has been taken from Prof. Auwers' " Neue
Reduction der Bradleyschen Beobachtungen," or his " Catalog der Fundamental
Sterne," for stars contained in either of those works. The authority for other Proper
Motions is given in the Notes.
To the columns relating to N.P.D. the same remarks generally apply as in the case
of R.A., except that in combining observations above and below Pole the weights
mentioned below were used in forming the means. For stars whose N.P.D does not
exceed 15 the observations above and below Pole are considered equally good ; from
N.P.D. 15 to N.P.D. 36, those below Pole have the weight f for each observation ;
from N.P.D. 36 to N.P.D. 41 those below Pole have the weight : beyond 41
N.P.D. the observations below Pole are not used, and in the case of those stars
observed below Pole only the mean result is enclosed within brackets.
i
The Annual Precession and Secular Variation for stars not within 5 of the Pole
have been formed as explained above ; for the stars within 5 of the Pole they have
INTRODUCTION. 9
been computed by the help of Folie's Tables referred to above. The Precession is
given by the formula
2o"  o53O cos R.A.
which is taken directly from the Tables, and the Secular Variation by the formula
A 1 + B 1 cot. N.P.D.
where
A 1 = + o"oo86 cos R.A. + o'^So sin R.A.
B 1 = + o"i95o sin 8 R.A.
The quantities A 1 and B 1 are given directly in the Tables for every minute of R.A.
IV. COMPARISON OF THE PLACES OF CLOCKSTARS IN R.A. AND N.P.D. FROM
OBSERVATIONS MADE IN THE YEARS 18871891 WITH THOSE OF THE TEN
YEAR CATALOGUE.
The following tables give the mean excess of R.A. and N.P.D. from the FiveYear
Catalogue over those deduced from the Ten Year Catalogue, for each hour of R.A.,
and for every 10 of N.P.D. , weights being assigned to the individual excesses
according to the formula , where ? and n are the numbers of observations
m + rv
in the two Catalogues respectively.
EXCESS OF R.A.'S OF CLOCK STARS FROM FIVEYEAR CATALOGUE ABOVE THOSE
OF THE TEN YEAR CATALOGUE REDUCED TO 18900 FOR EVERY HOUR OF R.A.
AND EVERY 10 OF N.P.D.
Limits
of
Correction.
M
be
Limits
of
Correction.
be
Limits
of
Correction.
3U
Limits
of
Correc
s
.s
E.A.
'S
B.A.
R.A.
'
N.P.D.
tion.
f
b b
s s
h h a
b h
o o
_
01
f *oo s f '003
'47
89
OI4+005
55
l6I7
'OO8 '004
74
50 60
+005
156
12
*ooof *oo3
133
910
'006+: '004
68
I7I8
009 '003 j 95
60 70
+ 'OOI
461
23
+ '005 '003
1 1 1
10 1 I
+ '007 004
87
1819
{003^*003  IjO
70 80
ooo
525
34
'007 ~^~ '003
95
I II2
'005 '004
74
1920
+ oo6'oo3
157
8090    ooi
60 1
45
*ooo f '004
88
1213
+ '004+ '004
75
2021
+ '004+ '003
109
90100
005
339
56
+ '004 + 004
87
'3H
+ 001 +003
117
2122
*oi of "004
90
IOO I IO
'OO2
227
6 r j
'O02 + 003
99
1415
+ 008 004
89
2223
*oi 61 '003
125
1 10124
'006
8 9
78
f'ooi '003
107
I5l6
ooo '004
87
2324
+ '002 'OO4
79
SO 11426. GREENWICH FIVE YEAR CATALOGUE FOR 1890.
10 GREENWICH FIVEYEAR CATALOGUE OF FUNDAMENTAL STARS FOR 1890.
EXCESS OF N.P.D.'s OF 211 CLOCK STARS FROM FIVEYEAR CATALOGUE ABOVE
THOSE OF THE TENYEAR CATALOGUE REDUCED TO 18900 FOR EVERY
HOUR OF R.A. AND EVERY 10 OF N.P.D.
Limits
limits
Limits
Limits
of
Correction.
I
of
Correction.
A
of
Correction.
bo
of
Correction. U
B.A.
ffl
E.A.
JD
E.A.
9
N.P.D.
2
h h
I
//
009
113
h h
8 9
it
+013
47
h h
16 17
+ o"i3
87
, o
50 60
+ O*I3
137
12
O'OO
90
9 10
004
74
17 18
0'22
130
60 70
018
407
23
014
9 1
10 II
009
78
18 19
+ 0'!2
148
70 80
o'og
499
34
018
76
I I 12
+003
93
19 20
O'O7
147
80 90
004
53 1
45
015
64
12 13
0*05
66
2O 21
OTO
93
90 100
0'02
327
56
029
65
1314
+ O'I I
96
2122
013
84
100 110
+ 0'OI
205
67
015
79
1415
+005
129
22 23
0'20
103
1 10 124
+ 013
79
78
+ 005
81
1516
O'OO
94
2324
0*07
57
V. COMPARISON OF THE PLACES OF CIRCUMPOLAH STARS AS OBSERVED ABOVE AND
BELOW THE POLE FROM OBSERVATIONS MADE IN THE YEARS 18871891.
The following tables show the mean, excess of R.A. and of N.P.D. above Pole for
all stars in the FiveYear Catalogue, of which observations were made both above and
below the Pole. The star is designated by its No. taken from the Five Year
Catalogue. The figures on the same line as the No. refer to the observations above
the Pole, those on the next line to the observations below. The excess of R.A. is
multiplied by sin N.P.D. in all cases, to reduce it to equatorial interval. The weights
assigned to each star are computed as follows : For R.A. if m and n be the number of
observations above and below the Pole respectively, the weight assigned is
. The maximum weight for any star is thus 20, which corresponds to
m + n + 5 mn J
an infinite number of observations above and below the Pole, and the expression is
equivalent to that for N.P.D. for stars at about 30 from the Pole. For N.P.D. the
weights used are determined by use of the " Probable Errors of Greenwich Observa
tions in Zenith Distance," given by Mr. Stone in the Monthly Notices of the Royal
Astronomical Society for 1869 June 11, page 324. Putting n for the number of observa
tions of a star above Pole, e for the probable error of one observation ; HI and c\ the
similar quantities for the observations below Pole ; e the probable systematic error
affecting all observations of the same star, and depending on outstanding division error,
Uncertainty in the constant of refraction, &c. ; the formula employed to determine the
INTRODUCTION.
11
weight to be given to that star is
would make e =*0"'16, the weight becomes
for use in this investigation.
2?i "l 2 I,' 1
, 5 o , or assuming ft *& e, which
,*>' 4 )^ J I A nn <>' o ~ lw
/tC i /CGI T^ /t/tiC n
2 nHj
 + ne* + %
^ which has been adopted
TABLE OF THE EXCESS OF MEAN K.A. AND MEAN N.P.D. ABOVE POLE, ARRANGED
IN ORDER OF RIGHT ASCENSION.
s ir'<
So,
Moan 11. A.
1 8900.
Beta
Data.
1800 +
No. of
Ota
ExeC93 Of
11. A.
above Pole
x sin N.P.D.
Wuight.
Mean N.P.D.
i S^o'o.
Mean
Dite,
1800 t
No. of
Obs.
Excess of
N.P D.
above Pole.
Weight.
h in B
,
o / i
7
o. 34. 16000
15940
893I
8998
2
3
+ 0033
4
34 35828
5907
8981
8998
3
3
 079
5
12
o. 53.48194
48153
8983
9013
34
38
+ 0003
16
4. 2O. O'2I
042
8966
9025
35
34
0'2I
29
16
i. 18. 30679
30680
8925
8948
230
224
O'OOO
'9
i. 16. 4130
4176
8?53
296
33=
046
38
22
i. 46. 28909
28952
9136
9''45
3
i
0019
3
26. 52. 1950
1846
9151
9077
4
3
+ 104 6
37
3. 16. 28097
2
rvnfiS
40.31. 5136
9100
2
' l
*
28202
8835
I
<) \J\JO
5151
8835
I
46
4. 2. 13562
13233
9024
9035
34
47
+ O027
16
4.44. 837
886
9059
9035
13
47
 049 25
56
5 8.33578
9138
3
0188
c
44 6.5393
9108
2 + 006
2
33847
8812
3
J
53'87
8812
3
76
6. 48. 46624
46016
8984
8910
25
46
+ 0031
15
2.46.5440
5488
8938
8949
88
177
048
36
90
7.46.51175
51670
9030
9048
49
104
0009
17
i. 2.2581
2631
9013
9056
36
79
050
32
98
8. 51.40489
8819
3
_ , o*n i o
4' 3i 37'22
8819
3
177
]
40504
8764
I
\J \J 1 W
38'99
8764
i
77
IO2
9 21. 21791
21678
8992
9088
'.I
+ 0016
'3
8. 1 1. 1796
1778
8997
9090
23
22
+ 018
25
117
10. 56. 56212
8961
8980
I
0*0 10
4
27. 39. 1964
2016
8940
8980
. 8
2
 052
5
122
I 1. 24. 52078
522O8
.8837 ! i
8980 3
 0045
3
20. 3. 4330 ,
4263
8932
8980
8
9
+ 067
'4
126
I I. 48. 2568
2  6l I
9130 , 2
0025
4
35.4I.3728
3728
9031
9130
5
2
O'OO
4
,3,
12. 14. 22I57
208I5
90*07 48
8996 i 54 ;
'1.41.2497 9009
2545 8989
4'
44
 048
3'
151
14. I. 24658
24776
8801
0050 v
9069 3
2 5 . 55386
8778
8927
'4
9
+ 003 15
'59
I 5. 23. 4161 8940
'7
053 11
4214 8893
4
J J
'164
15. 12. 502O3
9024
'3 i QO32 1 6
2.20.4143 9017
43
O'l I
28
49'427
9047 30
4'"54
9045
22
170
15.47. 59665
59942
8922
8878
J  0057 6
1 1. 52. 260
2'33
8946
8901
12
7
+ 027
'5
'75
28. 14. 1229
8836
3
+ 051
4
1178
9088
2
GREENWICH FIVEYEAR CATALOGUE OF FUNDAMENTAL STARS FOR 1890.
TABLE OF THE EXCESS OF MEAN R.A. AND MEAN N.P.D., &C. continued.
Star's
No.
Mean E A.
I Sijo'o.
MOOD
Date.
1800 +
No. of
Obs.
Excess of
H.A.
above Pole
x sin N.P.D.
Weight.
MeanN.RD. ^f"
"^ f+
No. of
Obs.
Excess of
K.P.D.
above Pole.
Weight.
j

o / "
"
h in s
182
16. 57. 14900
15639
8794
giO}
3 oioo
2
4
7.46.5753
5706
8932
8940
'9
6
.
+ 047 1 6
I8 7
17. 27. 56806
56708
8853
8796
8 ,
+ 0060
3
3737 i39
138
8847
8796
8
i
+ oo i
2
195
18. 7 47'59 8
4732I
8898
9003
59
3
+ 0015
16
3.23. 1792
1841
8932
8926
'7 1
61
 '49
34
209
I933 353i8
337>5
8939
8979
65
18
+ 0029
15
i. 1.5902
5951
8929
8927
'45
82
 '49
35
220
20.33.44984
45276
9004
901 1
59
'9
0044
15
8. 56. 2406
2418
8997
900^
65
24
0'12 28
230
21. 15.57172
57I3I
8921
8871
10
8
+ 0019
9
27. 52.4900
4996
8917
8883
16
8
096 13
232
21. 21. 28509
28OI2
8993
9018
43
7
+ 0030
1 1
3.25. 919
9'94
8992 28
9016 6
 o75 '7
2 34
21. 27. 14281
I4455
8892
8982
2
3
 0059
4
19. 55. 1951
1947
8877
9009
6
6
+ 004 1 1
243
22. 21. 58914
58833
9021
9021
56
2 7
+ o'ooS
16
4.26.4509 ' 8.994
4561 8978
36
i?
 052 25
253 23.27.49643
493I5
9023
8994
56
35
+ 0019
16
3 i757'4 2
5750
8992 45
8975 '< 35
008 30
255
23 34 49'74
50078
9086
8734
2
I
0076
2
12. 58. 5263
5 2 '95
8942
8890
9
*$
032
19
The weighted means for each 6 h  of R.A. are shown in the following table, the
corresponding numbers for the Ten Year Catalogue, as found from the table on page 46
of its Introduction, being added for comparison.
Limits of
RA.
Mean Excess of R.A. above