222 Dr. S. W. J. Smith on the Weston Cell 



here he of practically identical composition. But even in 

 this region the E.M.F. curve slopes upwards. 



It is thus impossible to say beforehand that the E.M.F. does 

 not rise as the percentage of CM in the amalgam increases, 

 even when the crystals are as uniform as they can possibly be. 



§ 12. The possibility of equilibrium between two amalgams 

 and the same electrolyte. — The question raised in the pre- 

 ceding section cannot be answered satisfactorily without 

 more careful consideration of the conditions of equilibrium 

 between each amalgam and the electrolyte than has been 

 so far necessary. 



It will perhaps be useful to indicate first how, neglecting 

 surface energy, the conditions of equilibrium between the 

 two homogeneous amalgams can be represented thermo- 

 dvnamically *. 



The total energy e of a homogeneous substance containing 

 masses m x and m 2 of its two components can change by 

 acquisition of heat (alteration of the entropy 77), performance 

 of external work (alteration of the volume v) and change of 

 composition (alteration of the mass of either constituent). 



For a reversible change we may write 



de = &) Jv + (P) dv + (£L) dn h + (^L) dm, 



\OV/v mi m 2 \OV/ mi m a \OWi/i,j»»2 VpnWuwn! 



The values of the first and second partial differential 

 coefficients are obviously and —p. The terms containing 

 them represent the energy variation due to change in the 

 heat content and volume of the working substance ; the 

 remaining terms indicate how the energy variation depends 

 upon the composition. The partial differential coefficients 

 which they contain are functions of the composition of the 

 working substance and we may write 



de = 6 drj —p dv + /x 2 dm x -f fi 2 dm 2 . 



For any other homogeneous mixture of the same sub- 

 stances, also capable of reversible variation, we may write 



de' = 8 drj —p dv 4- fXy dnii + fi 2 ' dm 2 . 



Now suppose that these two mixtures can coexist in 

 equilibrium. 



By hypothesis the components are independent variables. 

 We may imagine that a small quantity dm of the Wj com- 

 ponent leaves the second phase and enters the first in such a 



* Cf. Gibbs, Trans. Conn. Acad. vol. iii. pt, 1, p. 115. 



