ELECTROMOTIVE FORCES IN THE VOLTAIC CELL. 515 



"Whether one ought to write S0 4 or in these expressions I am not sure, 

 hut it is not essential to decide this at present. 



Another way of regarding the matter is to say that the force propelling 

 the current is that due to the difference of energies Zn,0 — M,0, but 

 that as soon as a current actually passes and hydrogen is liberated it coats 

 the cathode more or less thickly, and an extra term must be subtracted 

 from the above to represent the opposition force of this hydrogen. The 

 efficacy of this hydrogen as a current opposer must depend in some way 

 on the intensity of the current itself, since with a feeble current it will be 

 able to dissipate itself faster than it forms, and with a strong current it 

 will thoroughly coat the plate and the balance will escape. Suppose then 

 we represent the force exerted by the hydrogen as H 2 ,0/ (C) ; where 

 f (0) = 0, and/ (co )=1 or something like 1 ; then the force available for 

 urging the current forward in any of the above cells is, in volts, 

 rtfav (Zn,0-M,0-H 2 ,0/(C)}. 



There is an obvious objection to be taken to this last hypothesis, 

 viz., that it supposes the second metal M completely operative, even 

 though it be thoroughly coated with hydrogen. This is hardly reason- 

 able, and a compromise between the two preceding hypotheses is afforded 

 by one of greater generality in which the available force is symbolically 

 represented by 



Zn-M0(C) -K 2 /(C), 



where f is a function such perhaps that </>(C) = 1 + »• / (C). On this 

 hypothesis the propelling E.M.F. is 



e = 4 -,J, r ^Zn,0-M ) 0-(H 2 ,0 + «, . M,0)/(C)}. 



This is too much like miscellaneous guessing, and we will make no 

 more of such hypotheses; but if experiment could fix an empirical formula 

 for this force in any case, we could apparently at once obtain the Joule or 

 Bouty effect, 1 or rather the difference of two such effects, for that case, 

 because we should have the E.M.F. experimentally observed on the one 

 hand, and that calculated from pure energy considerations on the other ; as 



Zn,0-H 2: 



460U0 ' 



where the two B's stand for the Bouty coefficients at the zinc and the 

 other metal respectively. The only objection is that in the cells now 

 under discussion M is coated more or less with hydrogen, and hence the 

 Bouty effect obtained is nothing very easily definable. 



21. To see if the actual behaviour of such cells at all bears out a hypo- 

 thesis formed on the above plan, I have made some rough experiments on 

 the lines suggested ; that is, I passed the same current through different 

 simple cells. There are so many sources of uncertainty and of variation, 

 that it would be very difficult to get really definite and reliable l'esults. 

 Thus, for instance, the back E.M.F. will depend considerably upon how long 

 the current has been flowing:, and so the readings will differ according' to 

 the time they are taken. The metals I used were zinc-zinc, zinc-copper, 

 and zinc-platinum ; and it was found necessary to put the cathode plate 

 in a porous cell to avoid deposition of zinc on it. But it was now diffi- 

 cult to compare the cells easily when arranged in series, because different 

 porous pots had different resistances. I therefore ultimately decided to 

 use the same porous pot and the same anode ziio plate, and to substitute 



1 That is, the thermo-electric contact force at a Eee'al-lrjnid jimct'on. Sec 

 section 0. l h 2 



