Laplace's " Mtcanique Celeste. 



13 



rfVv 



(S) 



<£) 



dx 



+ 



(^) 



'(S) 



(^) = < 



^cy)-(|.o+cD-[(p-(i) + 

 (S)a')+(i')'[aT,)-(^) + 



Kd'T.dO '\dzj ^ \d^^/ ' \ dz Jj* 

 Hence, equation (A), or, = (-;^) + ( ^) + 

 i'd^)' becomes 



^ (^)- [(£:) + (9) + (^)] + 



(^)-[(^) + (l^) + (£)]+ 

 (^)-CQ + (il) + (£)] + 

 CJ)-[ « H.(S)+(S)]H- 



<ri*)-[0-(t)+(i)-(D+(i)'< 



(!)] + 



KS)-:" +(i)-a)+(")-a)]+ 



o=<; 



Hence, by substitulion, 



0=3 



