30 -^Tt. 4. - M. Kimiyeda ; 



r 



whence it follows that, for sufficiently large fixed values of ?., the 

 equation (28) has one, and only one, root a. Thus the function 

 (f has one stationary value. 

 By (28), we have 



which proves that « > ^. 



Also we have 



(29) ç(o) = ^^^ = - f'(''^-"-f''(^-^ 



^""^ ^^^ a" {a) a'-' a" (a) 



Since /'<!' we have a-j-'Kl, 



and, from the property' of <7> <^"> — a"? 



whence it folloAvs that ^-7r-\ < ^^ /''(*) <x<l, 



so that ^ («) tends to zero as /->co . 

 Next consider the case in which 



where ^ > 0, J>>0, ]><\. 



and -^ — gives 



(30) i^^^lSUflL-a'. 



I' 



Now o'<Q), a">0, J»0, //>0, 



