93 



''•Let l + ig= X, 1 + i (f ) = (*) and jii^ = / 

 Then equat. (2) of art. 1 gives 

 ]^ _ — XX sin. 6 (x) ^ 



2 {x) -^ x\/ x--(llflL sin.' S 



2/- 3 



— XX Sin. t* 



(x)^^ 



-i£=iiW ; 2/-1 



This by integration gives 



R = L_ (Circ. Arc. rad. 1 and sin. = (^)««.« ) + 



constant. 

 When R = 0, ? = (e) 

 Therefore constant = ^yr-^ 6. 



Hence the integral from ^ = (f) to ^ = o gives 



13 _ ^ & — -L- CCirc. Arc. rad. 1 and sin, = 



( i+Mp))-' 

 or nearly 



""•! — = sin. (^ — (2/— 1) R) 



This is equivalent to Simpson's Rule, page 58, Math. 

 Dissert. 



