442 Mr. Murphy on the General Properties 

 Similarly, ^,^ —^ = 5 log. {-i) - 2T - ^fV - &c. 



4- 2< + fra + &C. 



I 



whence -J^^ ^ = S log. (- 1), 



the limits of k being — 1 and + 1. 



Again, if f (A) = e" . Ifj; e'" /r"-', 



the integral commencing when h = o, we have by the very same 

 process. 



U JT^^ = 5'l0g.(-l); 



if therefore we denote cx(p{h) + c'.(p'{h) by F{h), which function 

 contains two arbitrary constants, we get 



I 



^k h 



y . 



h 



from A = - 1 to A = + 1, such is the complete value of y; from 

 hence the value of u, namely, 



Aydt Aa.ydx' 



is known, and u will lose none of its generality by making C'= 1, 

 for the constants evidently enter u only in the form -p , which 

 may be replaced by C, without losing ought of its generality. 



