On the Conduction of Electricity in Electrolytes. 95 



determined in exactly the same manner as in my former memoir, 

 so that it will suffice to give the final result without here enter- 

 ing into particulars. Conceive any portion, bounded by a closed 

 surface, of the interior of a conductor to be selected for con- 

 sideration ; let dco represent any element of this enclosing sur- 

 face, V the value, at this clement, of the potential function of 

 the free electricity, N the normal to the element, considered po- 

 sitive outside the enclosed portion, and lastly, k the conducti- 

 bility of the mass ; the work W performed in this portion of the 

 conductor during the unit of time will then be determined by 

 the equation 



■-I^S 



wherein the integration is to be extended over the whole surface 

 enclosing the portion of the conductor undei" consideration. 



3. At first sight it might perhaps appear that, with respect to 

 the determination of the heat generated by the current, a diff'er- 

 ence should exist between conductors of the first and those of 

 the second class. In conductors of the first class the molecular 

 masses remain unchanged in position, and the electricity alone 

 moves; whereas in conductors of the second class the constituents 

 of these molecules are also set in motion, and decompositions 

 and recombinations take place, during which, without doubt, a 

 considerable activity is developed by the molecular forces with 

 which the constituents act i^pon each other. On closer exami- 

 nation, however, it is easily seen that in determining the gene- 

 rated heat, it is not necessary to take into consideration the 

 quantities of work done by these molecular forces, however great 

 the same may be individually, inasmuch as they mutually and 

 completely cancel each other. 



If, during the passage of a stationary current through the 

 conductor, we examine, at the commencement and at the close of 

 a unit of time, the portion before separated and enclosed by a sur- 

 face, we shall find that during the interval the condition of this 

 portion has suffered no material change. Of course the electro- 

 positive constituents of many molecules will have separated 

 themselves from the electro-negative ones with which they were 

 hitherto united ; but to compensate this, they have united them- 

 selves again with other perfectly equal constituents, and the work 

 perfoi'med by the molecular forces during such a combination is 

 undoubtedly just as great as that which they suffer or perform ne- 

 gatively during such a separation. Similarly, the particles leaving 

 the enclosed space on the one side are re])laced by an equal 

 number entering on the other, so that at the end of the time 

 under consideration the whole mass in this space has the same 



