APPENDIX II 
269 
No. 2984. | Ursae Maj. c.g. 2 1523. 
The components are of the magnitudes 4^1 and 5Y1 respectively. The orbit of this star is com¬ 
paratively determinate and is here adopted from the computations of See (Stellar Systems). The 
period is 60 years; the major axis of the apparent orbit is 4 , /8; and the minor axis is 2"7. Taking 
the mass of the brighter star as unity, that of the companion is found to be: 
from the right-ascensions, 1.43 
from the declinations, .75 
or 1.09 in the mean. The masses are thus very near equality. They are assumed to be exactly 
equal. This places the center of gravity midway between the two stars. In making these deduc¬ 
tions, however, it has been assumed that whenever the observers record the position of the “mass,” 
the pointing was approximately upon a point one-third of the distance from the brighter toward 
the fainter star. This can only be regarded as a rough approximation to the truth; and, therefore, 
the present determination of relative mass can not lay claim to precision. 
If the position of the bright star is desired, it may be obtained by adding to the catalogue-posi¬ 
tion, reduced to the required date, the quantity taken from the following table for the corresponding 
date. For the fainter companion, reverse the sign of the table and add as before. 
Date. 
Aa. 
AS. 
Date. 
Aa. 
AS. 
1800 
i860 
s 
— .110 
// 
+ - 3 6 
1836 
1896 
s 
+ .006 
n 
+ -94 
1804 
1864 
— .098 
-f .08 
1840 
1900 
-•035 
+1.00 
1808 
1868 
— .068 
— .21 
1844 
1904 
— .062 
+ .98 
1812 
1872 
— .018 
- .42 
1848 
1908 
— .084 
+ .92 
1816 
1876 
+ .040 
- .38 
1852 
1912 
— .100 
+ .78 
1820 
1880 
+ .068 
— .08 
1856 
1916 
— .110 
-f .60 
1824 
1884 
-f .068 
+ .28 
i860 
1920 
— .110 
+ - 3 6 
1828 
1832 
1888 
1892 
+ .050 
+ .022 
+ .58 
+ .80 
1864 
1924 
— .098 
+ .08 
No. 3112. Groomb 1830. 
If the proper motion of a star is assumed to be uniform in a straight line, it will not be uniform 
in circular measure upon the sky, though this deviation in any case actually presented in nature 
will be exceedingly slight. This theoretical deviation from uniformity in angular motion was long 
ago pointed out by Bessel; and Seeliger (Ast. Nach., Bd. 154, s. 67) has derived formulas express¬ 
ing this effect. Dr. Ristenpart attempted to make an application of such formulas to the case of 
Groomb 1830 (V.J.S., Bd. 3 7, s. 242), but reached a negative result. Many years ago the writer 
made such an attempt, finding the weight of observation at that time totally insufficient for even 
a nominal solution of the problem. Even now the determination of the variation of the proper 
motion of this star due to foreshortening is associated with a probable error quite comparable with 
the quantity to be determined. The foreshortening effect produces terms etc., in the 
proper motion, of which the first, only, can have any sensible effect during the period of observa¬ 
tion thus far elapsed. In other words, we may assume that the proper motion varies uniformly 
with the time. This produces in the positions a term: 
1 Vo ( T- 1873 V 
^ dt \ 100 J 
A/u, n d/x. dfx! 
-may be resolved into its components and and these latter may be determined from the 
results of meridian-observations. In the equations for determining the correction to the assumed 
place, the term, ^ V ( T ) 2 ; has been introduced to account for the perspective effect in right- 
dt 
ascension, so that the conditional equation becomes: 
Ac, + A/i (t) + £ " (r) ! 
n 
