344 Advance of Perihelion of a Planet. 



when combined give 



(li dr\ 2 h 2 t ", 2m 2mh 2 , . x 



and then using (i.) and neglecting terms of order higher 



(m\ 

 — ) we obtain after reduction 

 rj 



h 2 /dr^ 2 h 2 9 i Am 2m <6m* , 



—Ala) +~2=c 2 — 1 + c 2 + ,. (vn.) 



or writing m= — , and differentiating with respect i to 0, 



d 2 u . m /rt „ N . 6 



55 



+ „= (2c 2 -l)+^ M . . . . (vm.) 



7?t 2m vm 



If we identify c 2 with 1 , and note that t^t and -^-s- w 



J a a7i 2 A 2 



are second order terms, we obtain as an approximate solution : 



777, / \ 



u=jp\l + e-coB(P-<B)\ 9 .... (ix.) 



as in Newtonian mechanics, and proceeding to a second 

 approximation on the usual lines, integrating and neglecting 

 terms which will have no appreciable effect in the solution, 

 we have : 



n— -A 1 + ecos (0 — tjt) + -jj-'e.6.sm(0 — 'Gr) J 

 — -y^(l + ^cos (0 — -57 — cvsr)], 



where -n~~jY an d gives the advance in perihelion per 



revolution. 



Yours faithfully, 

 Trinity College, E. S. JPeaeson. 



Cambridge. 



