Newton-Einstein Planetary Orbit. 147 



*%Then in G-. C. Darwin's investigation in the Phil. Mag. 

 May 1920, the influence of both additional terms together is 

 considered, by taking physical quantities a and @, making 



P=^w a +j8AV+3oAV, .... (20) 

 so that his a. is our 2m : and then, changing his 8 into n. 



-« r> 



72 1 



-^2 -\-u = 3mu u + nu+ y, . . . . (21) 



tTtfJ =2m(M-a.«- i 8.w-7) ; . (23) 



making the orbit, as before, in (11), 



u = ycii 2 ip0 + /3sn 2 ip0, . . . . (24) 

 but with 



Here with m small, but n unrestricted , 

 m->0, 2ma.= l — n— 2m(j3 + y)->l—n, 



/ = 2,, H «- 7 )-Jl-?)(l-n), ^l-^l -^ '» 



\ «/ 4a Umw l{l — n) £ 



. . . (26) 



^ = 2K_ > 1 / ff + 7 \ > 1 m 



t *p ^'(l-»)\ 4a / v"(l— n) Z(l_ n )S' 



... (27) 

 reducing to the (15) above for n = 0. 



Add a further term to P, 2Sh?u 5 , varying as co%, 



-jjr 2 +u = 28u* + 3mit 2 + nu+ y, , . . {28) 



™\ +i<? = Su i + 2mi l !i-nu 2 +--f +C, . (29) 

 (gy=S(«,l) 4 ; (30) 



and further progress in the elliptic integral requires some 

 knowledge of the factors of the quartic. 



Then there is the memoir of \V. J. Harrison in the Proc. 

 Cambridge Phil. Society (C. P. S.) Nov. 1919, on the 

 pressure in a radiating current of viscous liquid, and a 



L 2 



