312 NOTES TO BOOK VII. 



(T.) p. 271. In calculating the orbits of revolving 

 systems of double stars, there is a peculiar difficulty, 

 arising from the plane of the orbit being in a position 

 unknown, but probably oblique, to the visual ray. Hence 

 it comes to pass that even if the orbit be an ellipse 

 described about the focus by the laws of planetary mo- 

 tion, it will appear otherwise, and the true orbit will 

 have to be deduced from the apparent one. 



With regard to a difficulty which has been mentioned, 

 that the two stars, if they are governed by gravity, will 

 not revolve the one about the other, but both about their 

 common center of gravity ; this circumstance adds little 

 difficulty to the problem. Newton has shown (Princip. 

 lib. i. Prop. 61) in the problem of two bodies, the relation 

 between the relative orbits and the orbit about the com- 

 mon center of gravity. 



How many of the apparently double stars have orbitual 

 motions? Sir John Herschel in 1833 gave, in his Astro- 

 nomy, (Art. 606,) a list of nine stars, with periods extend- 

 ing from 43 years (/ Coronae) to 1200 years, (y Leonis,) 

 which he presented as the chief results then obtained in 

 this department. In his work on Double Stars, the fruit 

 of his labours in both hemispheres, which the astrono- 

 mical world are looking for with eager expectation, he will, 

 I believe, have a few more to add to these. 



Is it well established that such double stars attract each 

 ot/ier according to the law of the inverse square of the dis- 

 tance ? The answer to this question must be determined 

 by ascertaining whether the above cases are regulated by 

 the laws of elliptical motion. This is a matter which it 

 must require a long course of careful observation to de- 

 termine in such a number of cases as to prove the uni- 



