38 The Rev. BriceBronwin on the Theory of Planetary DlMurbance. 



Puttiii" the above values of £, and — ,— in that of -S', after developing rela- 



tive to £. ; we have, making p" the value of p, (a function of t + 0) when <p is 

 made nothing. 



(^)-(r)(4t-*|;)-!4?('-;l)-¥^'S-'" 



We have now got rid of ^. Let (*S") and ( T") be the values of (6') and 

 ( T) when is made nothing, or ^ = t ; then, by Taylor's theorem. 



(.S) = (5») + 0^-^^+f "^^ (2) 



diT") 



neglecting higher powers of the disturbing force ; since we exclude those of the 

 fourth order. Now enters nowhere but where it appears. 



And putting -r- for — y- for convenience, 



dt dv 



d{r) _ (i(S^ en dHp";) 



dr dr hj dr^ 



Therefore, 



' /« dt dr rt, (XT n^ dT 



Put in (1) the value of (S) given by (2), and that of (2") given by (3) ; 

 and we have 



