482 ON CERTAIN APPROXIMATE FORMULA FOR [59 



i 



or putting Q for 1 (a. - /3) 2 [n-2 (sec y) 2 - n - 3], 



we have 



X = ^r^~ 



Similarly, if 



we have 



(cos y')"- 1 = (cos y)"- 1 -(n-l) (cos y)"-' sin y |~i P ^- (a - ft) + ^ (a - ffi tan yj ; 

 = (cos y)-' jl - ^ ^ (a - ft) tan y - ^ (a - /8)' (tan y) } ; 



and therefore 



where () has the same value as before. 



Hence the values of X, Y, and T are as stated in my postscript to 

 Mr Niven's paper. 



Although the method of finding the expressions for X and T given 

 above, is perhaps the plainest and most straightforward that can be taken, 

 the following leads to simpler operations. 



Let /(<} = ?/ (sec ()" +1 . 



Then (/(<) ety = lu l (sec <)" +1 rfc/, =f fw 1 J ^ cZ</> by equation (l) 

 J J KJ d<p 



Hence ^^.(y-. _,--.). 



