308 PROCEEDINGS OF THE AMERICAN ACADEMY. 



importance. Meyer * was the first to measure carefully cells of this 

 type; but more accurate and significant measurements have been made 

 since by Richards and Lewis f and by Cady t under the direction of 

 Bancroft. 



The results of Cady are especially easy to interpret, because he worked 

 with sodium amalgam, which has a large heat of dilution, even with 

 fairly dilute solutions. He found that the electromotive energy of the 

 cell Na 20.2 Hg — Na 86.7 Hg was equal to the sum of two quanti- 

 ties, the osmotic work and the heat of dilution. Expressed mathemati- 



cally, mreo=^ HT In f- U, where ttcq is electrical energy, Cq the 



concentration of the mercury in the stronger amalgam, c that in the 

 weaker, and 1/ the heat of dilution (135 cal. per gram atom). He 

 showed that the electromotive force was independent of the nature of the 

 solvent between the amalgams and the concentration of the dissolved 

 electrolyte, and concerned the amalgams alone. U was shown to be 

 constant between 4° and 22°. 



This result is of the first importance, and taken in connection with the 

 preceding considerations concerning the heat capacity, it seems to afford 

 a new insight into the mechanism of electromotive energy. This 

 energy must be looked upon as the sum of at least two quantities ; in 

 the first place of the free energy of the chemical reaction, which hap- 

 pens to be equal to the total energy in Cady's case because the heat 

 capacities are unchanging, and in the second place of the osmotic ener- 

 gies at work. Only when the heat capacity is constant is the change of 

 free energy of the chemical reaction equal to the total energy ; hence in 

 general Cady's result, 



riTj- Cq = RT\n c^jc + U, 



is applicable only to such cases. When the heat ca[)acity diminishes 

 during the reaction the second member of the expression will be greater 

 than the first, and vice versa. This possibility was not considered by 

 Cady. 



The outcome of all this inductive logic is essentially identical with 

 the result attained deductively by Lewis. He found that from the first 

 and second laws of thermodynamics and the gas law, with the help of a 

 few assumptions, the following equation may be derived : — 



* Meyer, Zeitschr. phys. Clieni., 7, 477 (1891). 



t Ricliards and Lewis, These Proceedings, 34,87 (1898) ; Zeitschr. phys. Chera. 

 28, 1 (1899). 



t Cady, J., Pliys. Cliem., 2, 551 (1898). 



