i 



160 Intelligence and Miscellaneous Articles. 



at any point whatever. It is necessarily the same if recombination 

 is produced upon a conductor. 



This is the case presented, for instance, in the discharge from a 

 Leyden jar. Let us consider a spherical jar : we will call r the radius 

 of the sphere which is formed by the interior coating, e the thick- 

 ness of the glass. If q denotes the charge of the interior coating 

 at a given instant, dq the quantity of electricity repelled from the 

 interior to the exterior coatiug when these two coatings are united 

 by a conductor, the work effected in the repulsion of the quantity 

 of electricity dq is 



' +e l$dr = (±— L„)qdq. 



The work of the repulsion which corresponds to the quantity of 

 electricity q Q originally contained on the interior coating is 



The factor contained in the parenthesis represents the potential 

 function on the interior coating. "We thus again find, in the par- 

 ticular case of the Leyden jar, the expression of the potential of 

 the electricity. 



M. Helmholtz was the first who applied the theory of the po- 

 tential to the discharge of the Leyden jar. His researches have 

 been completed by M. Clausius * ; and the theory of the experi- 

 ments of M. Riess can now be regarded as very satisfactory. It 

 still remains, however, to inquire how the discharge is produced, 

 independently of the value of its mechanical equivalent. M. Helm- 

 holtz, after explaining the heat disengaged in M. Hiess's experi- 

 ments, adds : — 



" This law is easy to understand, provided the discharge of a bat- 

 tery be not represented as a simple movement of electricity in one direc- 

 tion, but AS A SERIES OF OSCILLATIONS BETWEEN THE TWO COATINGS, 



oscillations which become less and less continually until the vis viva 

 is extinguished by the sum of the resistances " t. 



"We have just seen that the discharge may be represented by a 

 movement of the electricity directed from one coating towards the 

 other. 



From the preceding may be deduced the demonstration of a 

 theorem established by Gauss in the case of a single conductor, and 

 generalized afterwards by M. Liouville for a system of conductors : — 

 When conductors contain respectively equal quantities of the two 

 fluids, all these conductors are in the neutral state. Indeed in this 

 case the potential is nil ; consequently the external discharge of the 

 system of conductors cannot give rise to any work. — Comptes JRendus 

 de V Academic des Sciences, Nov. 24, 1873, pp. 1238-1241. 



* Theorie Mecanique de la Chaleur, trailuite par M. F. Folie, vol. ii. p. 45. 

 t Mtmoire sur la conservation de la force, traduit par L. Perard, p. 107. 



