Molecular Theories 



409 



477-479] 



If E is the value of SP, measured on the same scale on which SO and OP 

 represent H and D respectively, then 



2RH 



so that, on changing the variable from a to R, we must have the relation, 

 obtained by differentiation of the above equation, 



RdR = HD sin ada. 

 We also have 



cos = 

 so that equation (409) becomes 



I=mnf" ^ D ~ dR. 



In fig. 115 the limits of integration for R are R=D + H and R D H. 

 If, however, H>D, then the point 8 falls outside the circle APE and the 

 limits for R are R = D + H and R = H-D. 



On integrating, we find as the values of /, 

 when X < D, I = $mn-^, 



X > D, 



X oo , 



I = mn 1 1 

 I mn. 



~H 



FIG. 116. 



In fig. 116, the abscissae represent values of H, the ordinates of the 

 thick curve the values of /, and the ordinates of the dotted curve the 

 values of B or pH, drawn on one -tenth of the vertical scale of the graph 

 for /. 



479. It will be seen that Weber's theory fails to account for the 

 increase in the value of /-t before I reaches its maximum, and also that 



