464 Prof. 0. Lodge on the Controversy 



and that this solution changes abruptly to another strength 

 n 2 of the same solution, the circuit being completed by another 

 metal N 2 dipping into that second solution ; then the whole 

 E.M.F. of the cell, on the above hypothesis, is 



E = EeT flog *L + ?=? , og 5 + l og £) 

 = -lH(log 10 |i + -^log.o- 2 ) volt. 



One case of this is the one we have already considered at 

 length, where only one metal is employed, that is, where 

 ^ = ^2, and the E.M.F. depends wholly on the solutions. 

 The other chief case is the ordinary simple Volta cell, where 

 n 2 — n±, and where the theoretical E.M.F. depends solely on 

 the two metals. 



But now suppose that the two liquids are different, as well 

 as the two metals ; there will now be altogether four ionic 

 velocities and four real or virtual concentrations: — 



u l9 v l ; u 2 , v 2 .; n l9 n 2 ; N l9 N a . 



So assuming that each solution acts like vacuum to the 

 other, we have intrinsic velocities u x out and v 2 in across the 

 liquid boundary of the first solution, or an E.M.F at that 

 place of 



together with 



114 ^L^hiogn. volt ; 



. lu v 1 _u 1] lt 



v x + u 2 & 



to be added to it, for the same boundary, considered from the 

 point of view of the other solution. 



Hence in this case, with two different metals, 



E . N, 2v 2 . 2«, , 



= logio *f - — -— logio wi + —7— lo gio n z- 



•114 volt felu N 2 Ul +v 2 * 1U l ' Mg + Wi 

 And the first term is usually the most important. For the 



special case where — = — = - , the two last terms reduce 

 r u x u<i r 



to the simple concentration expression already familiar, 



2 n 



log— 2 . The osmotic pressure ratio nJni for the liquids 



1 -H' n x 



may be a measure of their relative conductivities ; but the 



solution-pressure ratio N^/Ng for the metals seems to be 



