THERMODYNAMICS OF THE VOLTAIC CELL. 81 
v, and p areall functions of h, we may differentiate 
equation (7) with respect to h, and we get 
a i. 5 p 
Sloe) ae OR 
by (6) , : 
api ERA typ 
eaereyy oe 
h=h 
peor = Bienes aie 
8s h=oo? 
Similarly, if we denote the ratio of water to salt in the second 
solution by k, we may show that— 
— dF, cee dh. 
és h=ceo” 
SF SF, 3F a ae 
: — — 2)\— ees 
B= ee = —e(= re kt ea ee 
We now have to evaluate the integral in equation (F). For 
moderate temperatures the expression may be simplified, since the 
density of saturated vapours is small at such temperatures, even 
for pure water ; we may therefore assume that the aqueous vapour 
obeys the laws of a perfect gas—an assumption which Regnault 
has shown to hold good so long as the saturation density is small. 
We have, therefore, 
Ee Viceoek Ve pe 
TM i t 
where the capital letters refer to saturated vapour overlying pure 
water, the small ones to that above a solution. 
Hence equation (I) transforms into 
meee eo 5, = oe ie 
Helmholtz determined an rane formula expressing the 
relation between p and h/ for zine chloride solutions, evaluated the 
integral by its means, and deduced the values of E at O° C. for 
pairs of solutions of various strengths; the calculated values agreed 
very closely with those subsequently obtained by experiment. 
* The analysis as given here is considerably altered from that in Helmholtz’s memoir, to 
which Raynes has justly taken exception. (See ‘‘Physical Memoirs” of the Phy sical 
Society, Vol. I, list of errata.) The final result is, however, the same in both cases. 
F 
