326 Prof. G. H. Darwin. On Jacobi's Figure of [Nov. 



Approximate Solutions of the Problem — continued. 



Therefore 



+I* 2 [^-^ + (t- 322+24 )' > 



Hence from (c) and (j) 

 4tt 



whicli is the equation (22) of the text. 



Secondly, let Tc be nearly unity and g small — 



Then we require the following definite integrals :- 



1 



1 



tdy = 

 V 



Now A 2 =l-k 2 q 2 =p 2 {l+gYp- 2 ). 



dy = — q + A. 



1 _ 1/ 3 2 ^ \ 



A 3 _p 3 2 9 p h 



By (k) and (/)— 



J-Al^2^" + 2 ? -2 A -2 ^lP^-TT2^ -^ + 472 A J--- 

 3 r 1 _ „/15 l^Al 3/15 A 



Now _=1 + /(J2 

 therefore 



But J_=l + Q* 



therefore 



P 



9% - ^^ + I*t4^!*^i^)3 



