SPECULATIONS CONCERNING ATOMIC VOLUMES. 6l 



In the case of cadmium the observed potential is higher than the calculated 

 value ; hence either the second or third (or both) disturbing effects may be 

 supposed to predominate over the first. It will be seen that these excessive 

 values of the potentials with great concentrations are precisely parallel with 

 the excessive values of osmotic pressures in concentrated aqueous solutions, 

 observed especially by H. N. Morse and his assistants, in his very important 

 researches on this subject. Here as there, the simplest explanation seems to 

 be that a portion of the total volume is not effective as a receptacle for the dis- 

 solved cadmium ; and it becomes highly interesting to speculate as to the 

 magnitude of this useless space. 



Any calculation of this kind must involve assumptions of some kind, and 

 it is important that the assumptions should be as reasonable as possible. In 

 a preliminary trial, it may be assumed that the useless space does not vary 

 with the volume, and that there is complete absence of polymerization. 



The ratio of the values of the useful space in the two amalgams may be 

 derived at once from the following equation : 



ln v -A -^= W (i) 



v 3 ~RT {J 



when z/ 4 and v 3 are the ideal or hypothetical volumes of the useful space. 

 The actual ratio of the volumes is, however, 



found directly from the weight W x and W 2 and the densities D x and D 2 

 of the two masses of amalgam containing the same weight of cadmium. 



Now, calling the useless space b and assuming it to possess a constant 

 value (that is, assuming v 2 = v 4 -f- b and v x = v a -\- b) we have from (i) 



ln =b = RT (3) 



or from (2) and (3) 



vx b / RT 



or, 



Hence 



b\ 1 anti ln-gj- J = v x I iif ry anti In d-j-J 



anti In ~n~j- 



