\yt ivic^^ Electricity in Equilibrium, &i 



clear account of it, vfrhich is extracted from Pouillet's Traits de Physique : 

 — " Quand le plan d'epreuve est tangent a une surface, il se confond avec 

 1' Element qu'il touche, il prend en quelque sorte sa place relativement h. 

 I'^lectricite, ou plutot il devient lui-meme Telement sur lequel la fluide se 

 repand ; ainsi, quand on retire ce plan, on fait la meme chose que si I'on 

 avait decoupe sur la surface un element de meme epaisseur et de meme 

 etendue que lui, et qu'on I'eAt enleve pour le porter dans la balance sans 

 qu'il perdit rien de I'electricite qui le couvre ; une fois separe de la surface, 

 cet element n'aurait plus dans ses differents points qu'une epaisseur 

 €lectrique moiti^ moindre, puisque la fluide devrait se repandre pour en 

 couvrir les deux faces. Ce principe pose, I'experience n'exige plus que de 

 rhabitude et de la dexterite : apres avoir touche un point de la surface 

 avec le plan d'epreuve, on I'apporte dans la balance, oti il partage son 

 electricite avec le disque de I'aiguille qui lui est egale, et I'on observe la 

 force de torsion a une distance connue. On repete la meme experience en 

 touchant un autre point, et le rapport des forces de torsion est le rapport 

 des repulsions electriques; on en prend la racine carree pour avoir le 

 rapport des epaisseurs. Ainsi le genie de Coulomb a donne en meme 

 temps aux mathematiciens la loi fondamentale suivant laquelle la matiere 

 electrique s'attire et se repousse ; et aux physiciens une balance nouvelle, 

 et des principes d' experience au moyen desquels ils peuvent en quelque 

 sorte sonder Tepaisseur de I'electricite sur tous les corps, et determiner les 

 pressions qu'elle exerce sur les obstacles qui I'arretent." 



To this explanation it should be added, that, when the proof plane is still 

 very near the body to which it has been applied, the effect of mutual influ- 

 ence is such as to make the intensity be insensible at every point of the 

 disc on the side next the conductor, and at each point of the conductor 

 which is under the disc. It is only when the disc is removed to a consi- 

 derable distance that the electricity spreads itself symmetrically on its two 

 faces, and that the intensity at the point of the conductor to which it was 

 applied, recovers its original value. It was the omission of this considera- 

 ^on that qaused Coulomb to fall into the error alluded to above. 



Note III. 



This memoir of Green's has been unfortunately very little known, either 

 in this country or on the continent. Some of the principal theorems in it 

 have been re-discovered within the last few years, and published in the 

 following works : — 



Comptes Rendus for Feb. 11 th, 1839, where part of the series of theorems 

 is announced without demonstration, by Chasles. 



Gauss's memoir on " General Theorems relating to Attractive and Re- 

 pulsive Forces, varying inversely as the square of the distance," in the 

 Result ate aus den Beohachtungen des magnetischen Vereins imJahre, 1839, 

 Leipsic, 1840. (Translations of this paper have been published in Taylor's 

 Scientific Memoirs for April 1842, and in the Numbers of Liouville's 

 Journal for July and August, 1842.) 



Mathematical Journal, vol. iii. Feb. 1842, in a paper " On the Uniform 

 Motion of Heat, &c." 



Additions to the Connaissance des Terns for 1845 (published June 1842), 

 where Chasles supplies demonstrations of the theorems which he had pre- 

 viously announced. 



I should add that it was not till the beginning of the present year (1845) 

 that I succeeded in meeting with Green's Essay. The allusion made to 

 his name with reference to the word " potential" (Mathematical Journal, 

 vol, iii. p. 190), was taken from a memoir of Murphy's, " On Definite 



