72 PROFESSOR A. R. FORSYTE ON THE INTEGRATION OF 



d-iv dw 



., 



4 T - 



-l^/ rty 2 B .\ /S 8W . H\ 



= (y - hWJ - ( & + ^J ^ - 4 -^ j 



But 



yji Bs' *f[> 

 and therefore 1 



Now we must li.ive 



^?; 



- 

 (In 



that is, 



(! + "30 (f 



and so 



But, because r = ff>, .<? = 2 -f ?)/, *' z -- iy, we have 





that is, the foregoing value of n is the s-derivative of v. Further, comparing the 

 values of n, we find 



*v/ - 



whence 



<f> == "A. (Uj, 



A being an arbitrary function ; hence 



the explicit value of w. 



Next, for the value of I, we have 



from the value of to, just obtained ; and 



