INTRODUCTION 
XXVII 
For the convenience of the reader a table of constants is here given adapted for 
reducing a star-place given for 1900 to other dates preceding and following. 
Tables for Trigonometrical Computation of Precessions. 
Newcomb’s Constants. 
1900 TO T' 
Date T' 
?o 
Z 
log sin 0 
log tg - 
2 
e 
1755 
- 55 ' 
// 
40.58 
- 55 ' 
n 
38.92 
8.149089 n 
7.848080?! 
-48' 
// 
27-55 
1790 
- 42 
14-33 
- 42 
13-38 
8.029096 n 
7.728078?? 
- 36 
45 - 6 i 
1800 
-38 
23.96 
-38 
23.17 
7.987696 n 
7.686676?! 
-33 
25.06 
1805 
- 3 6 
28.78 
- 36 
28.07 
7-965259 n 
7.664238?? 
— 3 1 
44.10 
1810 
“34 
33-59 
-34 
32-97 
7.94193m 
7.640910?! 
-30 
4-52 
1815 
-32 
38.40 
-32 
37-83 
7.917106M 
7.616083?! 
-28 
24.26 
1820 
“ 3 ° 
43 - 2 i 
- 3 ° 
42.71 
7.890774 n 
7.589750?! 
— 26 
44.00 
1825 
— 28 
48.02 
- 28 
47-58 
7.86274m 
7.561717 n 
-25 
3-73 
1830 
— 26 
52-83 
— 26 
52-45 
7-832775» 
7 - 53 I 75 on 
-23 
23-47 
1835 
- 24 
57- 6 4 
- 24 
57 - 3 ° 
7.800587^ 
7.49956m 
— 21 
43-21 
1840 
- 23 
2.44 
- 23 
2.16 
7.765820 n 
7.464794?! 
— 20 
2-95 
1845 
— 21 
7-25 
— 21 
7.01 
7.72802811 
7.427001?! 
- 18 
22.70 
1850 
- 19 
12.05 
- i 9 
11.85 
7.686632 11 
7.385605?! 
— 16 
42.44 
1855 
- 17 
16.85 
- 17 
16.69 
7.640870 n 
7 - 339843 W 
- i 5 
2.19 
i860 
- 15 
21.65 
- 15 
21.52 
7.589714M 
7.288685 ?! 
- i 3 
21-94 
1865 
“ J 3 
26.45 
“ r 3 
26.35 
7 - 53 i 7 i 8 « 
7.230689 ?! 
— 11 
41.69 
1870 
— 11 
3!-25 
— 11 
3 x -i 8 
7.46476771 
7.163738?! 
— 10 
1.44 
187S 
“ 9 
36.04 
- 9 
35-99 
7.38558m 
7.084552?! 
- 8 
21.20 
1880 
- 7 
40.84 
- 7 
40.81 
7.288668 n 
6.987638?! 
— 6 
4°-95 
1885 
“ 5 
45-63 
- 5 
45-6i 
7.163726 n 
6.862696?! 
- 5 
0.71 
1890 
- 3 
50.42 
- 3 
50-4I 
6.987628 n 
6.686598?! 
- 3 
20.47 
1895 
— 1 
55 - 2 i 
— I 
55-21 
6.686595?! 
6.385565?! 
— 1 
40.24 
1900 
0.00 
0.00 
-00 
— 00 
0.00 
1905 
+ 1 
55 - 2 i 
+ 1 
55-22 
6.686586 
6.385556 
+ 1 
40.23 
1910 
+ 3 
5°-43 
+ 3 
5°-44 
6.987606 
6.686576 
+ 3 
20.46 
I 9 I 5 
+ 5 
45-64 
+ 5 
45.66 
7.163697 
6.862667 
+ 5 
0.69 
1920 
+ 7 
40.86 
+ 7 
40.89 
7.288632 
6.987602 
+ 6 
40.92 
1925 
+ 9 
36.08 
+ 9 
3613 
7-385535 
7.084506 
+ 8 
21.14 
FORMULAS OF APPLICATION. 
Let a! and S' be the right-ascension and declination whose values for the epoch, 
T', are sought; a and 8 the corresponding coordinates for 1900; /a and /x' the coordi¬ 
nates of proper-motion for 1900; t—T' — 1900, in years. Then 
a 0 = a + r/x 8 0 =S-fT/4' A 0 = a 0 + £ 0 
0 
p = sin 6 ^tan 8 0 + tan - cos 
r a a \ P sin A 0 
tan (A - A 0 ) = 
1 - p cos A 0 
A + Aq 
, S'-80 cos 2 f 0 
tan-- =-tan- 
2 A-A 0 2 
cos-- 
a = A + z 
