58 AET. 10. K. IKEDA : STUDIES ON THE 



, , dG^ , dCa . . dC 



and as both — -, — and ^ are positive, —, — must be nesrative 



dx dx ^ ^ ax ° 



throughout. Hence C decreases continuously with increasing 

 values of x. At x = C is equal to unity, while at a- = 1 it is 

 reduced to zero. Again in the equation 



d-C d^C„ d-C 



dx" dx^ dx^ 



-j-^ is negative for smaller values of x, while , I , though 



d~C 

 positive, is very small. Hence -j-j must be positive for small 



values of x and the curve is convex towards the axis of x. 



With increasing values of x —r-^ becomes positive too, while -i-4 



d'^G 

 remains positive and increases in amount, so that -y-s- must turn 



negative at a certain value of x and from this point the curve 

 becomes concave. The form of the curve must therefore be like 

 that of }' in Fig. 12. 



Again from equation (35) we have by differentiation 



dG dGy 



= (v-l)(l-:r)^-{l + (v-l)(7p}. 



dx dx 



Hence at a: = 0, 



(^) = -'' (^-^^ 



that is to say the tangent to the curve at a; = is the diagonal 

 B\. At X = 1 we have 



(^).= -<i+'"-^)^'''' (^-^^ 



which says that the tangent at ic = 1 is equal to the degree of 

 association of the pure associated component taken negative. 



