( 275 ) 



To simplify still further we put: 



Vo r ■=z n R a -^^ 1/ R, 



SO that 



h = R [/i/ — n^ 

 and 



^'^ = '^^^77=, 





The above mentioned expression for the part of segment passes into : 

 1/3 Jl^ |^„ l/(l-y^)(2/'-«-) +2 ia„-^ (^n K ^^) - 



- ?! (3— ?t-; to«-i ]/ „"-'^ 1- 



y — n" J 



(1) becomes 



(2) becomes 



SO that uur integral is now, writing everywhere .«■ for y°^ trans- 

 formed into : 



where (paying attention to dh being equal to 1/2 R —-= ) ; 



-,-—[« (3. r2_ 1/2) , g-, 3i-2+Vo.;'(l-4«2)-M2 



A^nyX- ■'■ I ^-^^;^ "- \/r - n"' + ^^^^-^^^ l/^^-V, 



B — w (3 .r — 2 w'-^) 1/1 — *• [<an-i - ~ " — 2 toi-i ^'' 1 



« (3 fi'2 — V3I , 3 ^2 + V3 a^ (1 — 4 «2) _ if-x/^a- — V4 ] 



+ — '—^^~, — ' — V — 1 X 



X [2 iaw-i (n y^^ ^) - „ (3 -«2) tan-' K "^ 1 



L v x — n^ J X — n" J 



