OF THALLIUM, INDIUM, AND TIN 33 



the amalgams. The electromotive force may be looked upon as being due 

 to at least two entirely different phenomena superposed : one, the " chemi- 

 cal free energy," which manifests itself as heat on dilution, and the other 

 the " osmotic energy," due to the difference of concentration of the two 

 different amalgams. In these cells all the free energy of the essentially 

 chemical part of the change may be supposed to appear as heat, because 

 the heat capacity of the system is essentially unchanged during the reac- 

 tion ; hence the system is peculiarly well adapted for tracing the mechanism 

 of the chemical production of electromotive force. 31 This was indeed the 

 reason why the whole investigation was undertaken. The probable reasons 

 for the lack of exactness in the application of the equation of Cady will be 

 discussed in the second half of the monograph, when other results have 

 been presented. 



APPLICATION OF THE EQUATION OF HELMHOLTZ. 



The importance of the heat of dilution in the case of amalgam cells 

 leads one to inquire concerning its exact values under the conditions 

 of the present experiments. These values are most readily calculated 

 from the well-known equation of Helmholtz, whose verity is undoubted. 

 The only difficulty in the present case lies in the fact that the temperature 

 coefficients were perforce determined over a rather large range of tem- 

 perature 30 on account of their otherwise too insignificant magni- 

 tudes. Moreover, even then their determination carries with it by far the 

 largest percentage error of any part of the work. Fortunately the nearly 

 if not quite linear nature of the coefficients with these metallic cells 

 prevents the introduction of any considerable error from the large range 

 needed. 



In 1882, Helmholtz, in a paper already referred to, evolved the equation 



(5) 



an expression already given in a somewhat different arrangement as 

 equation(i). According to this expression the sum of the heat of reaction 

 and the product of the absolute temperature and the temperature coeffi- 

 cient of the change of free energy should equal the change of free energy 

 itself. 



The experimental work already described furnishes sufficient data for 

 applying this equation to the amalgam cells of thallium, indium, and tin. 



Take, for example, the thallium cell Ci-C2. Here 71-0 = 0.033897, 

 ATT = 0.003237, AT = 30.00, 7 = 273.09, v = i, and F = 96,530. 



81 Richards, Proc. Am. Acad., 38, 293 (1902) "The relation of changing heat 

 capacity to change of free energy, etc." This theorem has been recently expanded 

 mathematically by Nernst, with the help of an interesting assumption concerning 

 the extrapolation to the absolute zero. 



