58 ENERGY CHANGES INVOLVED IN DILUTION OF AMALGAMS. 



Selecting the cell 1-7 (see page 34) as representing the dilution in question, 

 we have the following data: ?r = 0.00828, T = 273.09 -f- 23.01 = 296.1 ; 



therefore, = = 0.00002706 and -^| =, = 0.00000099. Hence -J, 



T ' J 2 X 96,580 x r yy JT 



= 0.00002892. From this it is easily calculated that rr at o is 0.00762 and 



An 

 -r-=, is 0.00379. It 1S interesting to note that through a partial compensa- 



7T J 1 



tion of opposite effects this temperature-coefficient of electromotive force 

 should be brought to within about 3 per cent of the temperature-coefficient 

 of pressure-increase in a perfect gas (0.00366). Previous experiments" 

 were not accurate enough to detect any difference at all between these 

 values. The present values are more trustworthy, because the most doubtful 



quantity, the last term above ( x ^ g s/ T I can nar( ^y De * n error by an 

 amount which would affect the result 0.3 per cent. 



THE APPLICATION OF THE FORMULA OF CADY. 



While there is thus every reason to believe that the Helmholtz equation 

 applies with great exactness to the phenomena under consideration, the case 

 is very different with equation of Cady, 



F = RTln^ + U,or*-~ ln^ = -^ 

 Vi V F v x V F 



This equation is now to be considered. 



Selecting again similar cells for this comparison, we have for the cadmium 

 cell 1-5 from the table on p. 47. 



7T ^T i n h. = + 0.000375 volt 



and from p. 56 - = L= ^ ^- = 0.00000s volt 



F vF 2 X 96,580 J 



Difference = -f- 0.00038 volt 



This difference corresponds to about forty times the probable error of the 

 potential readings, and nearly eighty times the probable error in the estimation 

 of the heat of dilution ; moreover, the quantities are actually different in sign. 



The deviation in the case of zinc is even more marked, although in this 

 case the two members of the Cady equation at least have the same sign. 

 The figure for the potential of a cell made from amalgam 3 and one only 

 half as concentrated are less by 0.00085 than the theoretical value based on 



63 Richards and Lewis, Proc. Am. Acad., 34, 94 (1898). 



