Bambaut — Detei mining Distance of a DouJ)Ie Slur. 663 



XLI. — On the possibility of determining the Distance of a Double 

 Stab, by Measubes of the Relative Velocities of the Com- 

 ponents IN THE Line of Sight. By Akthur A. Rambaut. 



[£ead, May 24, 1886.] 



Satary, in his memoir on double stars, in view of the difference of the 

 times that light takes to reach us from the two components of a double 

 star, on account of their unequal distances from our solar system, con- 

 cludes the existence of an inequality in their relative apparent motion, 

 and indicates the possibility of deducing thence an inferior limit of 

 their parallax. " In fact," he says, " if light required, to traverse the 

 orbit of a double star, a time equal to that in which the star moves 

 through a measurable angle, we should see this star as much behind 

 its real position, relatively to the star considered as the centre of mo- 

 tion, as it was in a part of its orbit more distant from us. . ." 



M. Arago developed this idea of Savary's, and drew the attention 

 of astronomers to the question in P Anntmire du Bureau des Lo7igitudes ; 

 and some years later M. Struve, in his great work on double stars, 

 examined to what extent this inequality, which he termed the 

 "equation of light," could become sensible. 



There had been up to this time no mathematical theory of the 

 equation of light, and M. Houzeau, who had met with considerable 

 anomalies in the measures of 70 p Ophiuchi, attempted to attribute 

 them to relative aberration, arising from the relative motion of the 

 stars. This supposition of M. Houzeau's was attacked by Sir John 

 Herschel, who denied positively that the motion could have any 

 influence. 



The question was in this condition when M. Villearceau took it up 

 and examined it in his elaborate memoir on the Theorie Analytique des 

 InegaliUs de Lumiere des Etoiles Doubles, published in the Coimaissances 

 des Temps for 1878. 



In summing up the results of his investigation he finds four dif- 

 ferent effects of aberration. Of the first three he says : "All the effects 

 of the aberration, indicated up to this, are represented by the elliptic 

 motion, whose elements, with the exception of two, the major axis and 

 the eccentricity, are effected with inequalities, on account of the dis- 

 tance of the Sun, the velocity with which this distance varies, and the 

 angular motion of the components. The inequalities produced in the 

 elements offer an interest merely speculative." Of the fourth, which 

 depends on the ratio of the masses, he says : " The introduction of the 

 inequality depending on the ratio of the masses . . . would permit us 

 to obtain an unknown containing this ratio associated with the paral- 

 lax, if this inequality could acquire a sensible value. The parallax 

 could be deduced from this if the ratio of the masses was known. But 



3 K 2 



