INTRODUCTION 
XXIII 
relative orbit. If the ratio of the major axis of the actual orbit of the principal star 
around the center of gravity to the major axis of the relative, or ordinary double¬ 
star, orbit be denoted by r, and if A 0 a and A 0 8 be the coordinates in right-ascension 
and declination respectively of the orbital motion of the fainter around the brighter 
component, then the coordinates of the motion of the principal star around the center 
of gravity will be — rA 0 a and — rA 0 S respectively. Introducing these quantities 
also into the ordinary equations for determining the position and motion of the star, 
— A 0 a and — A 0 S will be known coefficients to be computed from the adopted orbit 
of the binary, and r will be an unknown, to be determined from the equations of 
condition, along with the corrections to assumed position and motion of the center 
of gravity. If we take for the unit of mass that of the brighter star, then the mass of 
y 
the fainter star will be -. 
i — r 
Knowing r, it now becomes possible to reduce the observations of each compo¬ 
nent to the center of gravity; and it is the position and motion of this c.g. that is 
given in the Catalogue. In Appendix II there are given for each of these stars the 
quantities necessary to be added to this position of the center of gravity for a given 
date in order to have the corresponding position of either of the components for 
that date. Following is a list of the binary systems thus treated. The ratio of 
masses is given in terms of the mass of the brighter star as the unit. 
Table of Binary Stars with Adopted Ratio of Masses. 
Catalogue 
Numbers. 
Name. 
Period, 
Years. 
Magns. 
Ratio 01 
Computed. 
Masses. 
Adopted. 
Y 
M 
M 
3 
Bradley, 3210 
104.6 
6.6 
7.6 
• • . 
1.0 
168 
■ t ) Cassiop. 
233-3 
3- 6 
7-9 
•75 
•75 
I 73 2 
a Can. Maj. 
48.8 
— 2. 
8.0 
•39 
•39 
2008 
a Can. Min. 
39- 
0.2 
9.0 
•33 
•33 
2984 
£ Urs. Maj. 
60. 
4.x 
5-i 
1.1 
1.0 
33°7 
y Virginis 
194. 
3- 6 
3- 6 
1.1 
1.0 
3735 
a Centauri 
81.2 
O. 
i-5 
•85 
•85 
3798 
£ Bootis 
148.5 
4.8 
6.7 
.87 
•87 
4138 
<r Cor. Bor. 
37°- 
5-7 
6.8 
•47 
•47 
4246 
f Herculis 
34-5 
2.8 
6 -5 
•43 
•43 
457 1 
70 Ophiuchi 
88.4 
4-3 
5-8 
.82 
.82 
6172 
/ Bradley, 3198 \ 
l (85 Pegasi) J 
25-7 
6.0 
11. 
1.8 
1.0 
The determination for No. 3 is wholly assumed from analogy, and for No. 6172 
it is extremely uncertain. Those for 1732, 2008, and 3735 are quite precise, and 
those for Nos. 2984, 3307, 4246, and 4571 may be regarded as fairly satisfactory. 
There appears to be no case in which the fainter companion can be asserted with 
high probability to have a larger mass than that of the brighter component. In the 
case of No. 6172 the computation is scarcely warranted by weight of meridian- 
observations; and the result is very likely to have been seriously influenced by 
fortuitous grouping of errors. 
Notwithstanding the care exercised in the computations for binary stars, the 
uncertainty of the result for predicted, or extrapolated, position and motion of each 
