

532 Prof. J. J. Thomson on the Relation between the 



and Q the charge, this part of the Lagrangian function will 

 be equal to 



1Q 2 



20 * 



Thus the total variable part of the Lagrangian function, which 

 we shall denote by H, is given by the equation 



H = mjZi — 0(n2 2 R 2 log m 2 + m^R 3 log m 3 + w 4 R, 4 log m A ) 



* 1 2 

 -f [?n 2 iv 2 + m z iv$ + 7n 4 w 4 ) — T.jv* 



When things are in a steady state the value of this function 

 is stationary,, hence 



dK «, dK ~ dK z , dK ~ dK ~~ A .,. 



_ gmi+ ^8m 2 + — Sm8+ _Sm 4 + ^SQ=0, . (1) 



for all consistent values of Sm l5 Sm 3 , Sm 3 , 6?m 4 , SQ. 



One possible change in the system is for n atoms of zinc in 

 the rod to combine with 2n atoms of CI to form n molecules 

 of ZnCl 2 . Q will, if we take as unit charge the charge carried 

 by a monad atom, be increased by 2n, since zinc is a dyad. 



Hence 



0^=— n, hm 2 = +n, Sm 3 = 0, Bm i = — 2n J SQ = 2n; 

 so that by (1) we have 



dR dK 2dK 2dK 



dnii dm 3 dm A <iQ 



Since -^ = — ^ = — V, where V is the potential difference 

 dQ, O 



between the plates of the condenser, we have 



1 f^H dK 2dK | 

 ~ 2 \ dm 2 dnii dm 4 J ' * ' 



Another change that could take place in the system is for n of 

 the atoms of zinc in the solution to combine with 2n of the 

 chlorine atoms to produce n molecules of ZnCl 2 . In this case 



gm 1 = 0, hm 2 = n, $m 3 = — n, Sm 4 =— 2w, SQ=0. 



Thus equation (1) becomes 



dK dK 2dK 



dm 2 dm 3 din 4 

 hence from (3) and (4) we have 



=0; (3) 



