THERMODYNAMICS OF THE VOLTAIC CELL. 83 
only a theoretical value—if that. The net result of the discussion 
is a determination of the effect of pressure on the e. m. f. of a 
Grove’s gas-battery ; as Helmholtz’s analysis is very cumbrous, 
and as this is merely a special case of the problem discussed in 
section 10—-where the whole question is shown to be susceptible 
of very simple treatment—only the results are given here. 
Let E, = e. m. f. under pressure p, of the mixed gases. 
” EK, = e. m. f. ” P2 ” ” 
= P, + po. 3 where 
~ 
sS 
S 
~] 
Pr = partial pressure due to hydrogen. 
| - . oxygen. 
Let a,, a, denote the atomic weights of hydrogen and oxygen. 
» Un » Specific volumes % re 
» € = electrochemical equivalent of water. 
ee ie _— Po Vo 
» R= ;R, => 
th, t 
Then Helmholtz finds 
B,—E,=10~%e. T{ Ry = tog eae “be, a (G) 
20, a, FD Tern 
In a fourth memoir* Helmholtz compares this Cane with the 
results of his own experiments. The agreement is, to all appear- 
ance, satisfactory ; but is in reality illusory, being due to an error 
in computation. He shows that the formula simplifies into 
5x10 —7 x 000009319 x Tx R, x log, (”") 
Pi 
BK, — E, 
— 0-018868 log. (7) 
L 
and gives as the result of the calculation, when p,=10 mm. of 
mercury, p,= 742 mm., 
EK, — E,=0°1305. 
This agrees fairly well with his experiments; but it is not 
correctly calculated. If we substitute the values of the logarithms 
and work out the result we obtain— 
E, — E,=0:0813, 
which is not in agreement with Helmholtz’s observations, but 
agrees well, as we shall tind in section 10, with the much more 
extended researches of Gilbault. 
* Sitzungsb. d. Akad. der Wiss., Berlin, 1887, p. 749 ; ‘‘ Physical Memoirs” of the Physical 
Society of “London, Vol. i, p. 98. 
