On the Orbit of a Planet. L99 



momentarily stationary in space, 1 lie average energy density 



e 2 

 which is required for this is— ; the total stationary energy 



thus present in the spheroidal nucleus at any moment 

 is given by multiplying this expression by the volume 

 |7ra 3 (l— j3 2 )^, and it is precisely the same in amount as 

 that (1) which is required to satisfy the mechanical and 

 also the relativity theory. 



The University, Sheffield. 

 8 th June,' 1920. 



LVL On the Orbit of a Planet. By Prof. A. Anderson *. 



IF we equate the space-time interval ds in a central gravi- 

 tational field to (7 — cc d \r — j3 d0 2 )% where 7, «, ft are 

 any functions of r that, when ?», the astronomical mass of 

 the body to which the field is due, is zero, become, respec- 

 tively, 1, 1, and r 2 , we have 



and s = C\ry-av 2 -/36 2 )hlt. 



J to 



Making the variation of this integral between two fixed 

 points zero, the time limits being given, we have 



d'ht (du\r[l_ dy 1_ d* _ 1 d& __ 21 

 d6 2 + \dd) [Tj ' du + 2« ' du /3 du u\ 



+ 2«U 2 7V PJdu du] U ' 



where Ji = /30f -r = constant, and w=l/r. 



(7 \ 2 

 -. -J vanish, we must ha 



ve 



— '— = constant = 1, 



and then the equation becomes 



d 2 n Ulcly d(y^ = 



* Communicated bv the Author. 



