56 



AKT, 10. — K. IKEDA : STUDIES ON THE 



both Cx and Oi are small and 



ax- 



is neo-ative. But for lar^e 



values of x it becomes positive, and at x = 1 we have 



which is of course positive. 



Hence, when we represent 

 the relation between C« and x in 

 a diagram, we get a curve like 

 a in Fig. 12. The curve has 

 for its tangent at x = the 

 diagonal OA which lies com- 

 pletely above it. The curve is 

 concave towards the axis of x for 

 small values of x, and turns 

 convex as x approaches unit}', 

 straight line which passes through the origin 0. 



From equation (34) we get by differentiation 



dc,, {i+{v-\)c\,Y 



Fiir. 12. 



The tangent at x = 1 is a 



dx 



1 1-1 



,j^±^^'G<^" 



■^^^^:^R'c\r 



1 i^ 



1 V 



{1 + (V-I)(7r,}^ 



a 



.(39) 



and 



dHJ^ 

 dx' 



1 1 



= (y-1) (2 V+-4- 5^-' Cy V4 ^" C'a 



1 1-1 



1 1 



l+(v-l)6V^ 



V o, 



