2j6 
PRELIMINARY GENERAL CATALOGUE OF STARS FOR 1900 
Nos. 5433 and 5434. 61 Cygni. Br 2744-5. 2 2758. 
The magnitudes of the components are assumed to be 5 “5 and 6 M i. Although the micrometrical 
measures of this double star are numerous and accurate, the change in position angle is so small 
that it does not suffice for the computation of an orbit that is even fairly approximate. It might be 
assumed, however, with much plausibility, that the observed arc can be accurately represented by 
a parabola, following the precedent adopted with first orbits of comets. But in the present instance 
it has been found that not even this device would be of any service, since the direction of periastron 
is still indeterminate. Accordingly, as a last resort, and in order to provide more reliable means 
for predicting the positions of the two components, the combined effect of curvature of path and 
variation of proper-motion has been computed from the meridian-observations in each coordinate, 
assuming this effect to be proportional to the square of the time-interval, r, expressed in centuries, 
from the epoch 1875. We have for \ ~ : 
dt 
R. A. 
61 1 Cygni (-H 500389 = ) 
61 2 Cygni (— .00129 =) 
Taking these as the basis of further computations, we may gain some idea of the relative masses 
of the component stars of this system in the following manner. Let the unit of mass be that of the 
brighter star, and a, the mass of the fainter star. Dr. Bergstrand determines the coefficient of the 
centennial term in r 2 for the differences in declination between the two stars to be +''0134; and 
the corresponding term in right-ascension, — V0460. (Roy. Soc. Upsala, Ser. IV. Vol. I, No. 3.) 
These values are probably far more accurate than those which are derived from the meridian- 
observations, -f "0220 and — "0612 respectively. The ratio of Dr. Bergstrand’s terms, —3.43, may 
be taken as a known quantity, therefore, so that if, for orbital effect alone, b denotes the coefficient 
of r 2 in declination-equations of the fainter star, then —3.43 b will be the corresponding coefficient 
for right-ascension. Further, let A fx 0 denote the centennial variation of the proper-motion upon a 
great circle, due to assumption of uniform rectilinear motion (see Introduction, as well as the note 
on Groombridge 1830, No. 3112), then we shall have the following equations: 
R. A. Decl. 
+ ''0460 —.0016 
— .0152 +.0204 
(A) 
From 61 1 R. A., 
61 2 R. A., 
61 1 Deck, 
61 2 Deck, 
The solution of these equations 
Aay 
~T = +'.'0163 
0.796 
A/a0 
2 
+- 3-43 a b 
= + ('0460 
0.796 
A/a0 
~ 3-43 6 
= - -0152 
0.605 
A/a 0 
2 
— 1.00 a b 
= —.0016 
(B) 
0.605 
A/Xo 
2 
+ 1.00 b 
= + .0204 
leads 
to the following values of the unknowns 
• 
a — 
+ 1 
16 b = 
+ "00841 
ab = 
-1- ''00975 
Varying the assumptions adopted in the foregoing, values of a and similar to these are 
2 
derived, and it is found that a value of a less than unity is not inconsistent with the data. One 
may rather confidently conclude that neither star has twice the mass of the other, and no great error 
wall be committed if it be assumed that the masses are equal. The comparatively small differ¬ 
ence of magnitude of the two components is favorable to this assumption; and there is always a 
probability in such cases that the mass of the brighter star is not less than that of the fainter — 
a probability which has been sustained in the computations for this Catalogue in every instance 
where the data were really adequate to a decision. Accordingly, the masses are here assumed to be 
equal. This being the case, one-half of the observed effect of perspective upon the proper motion 
of the center of gravity in a great circle will be found in the mean of the square-terms in right- 
ascension and declination respectively, already determined (A). 
