Faraday. 211 



inductive capacity may be seen by what follows, which is 

 substantially a translation into electrostatical language of 

 Poisson's theory of induced magnetism.* 



Let p denote volume-density of electric charge. For each 

 of Faraday's " small shot " the integral 



JJJ pdx dy dz, 



integrated throughout the shot, will vanish, since the total 

 charge of the shot is zero : but if r denote the vector (x, y, z), 



the integral 



J/J p r dx dy dz 



will not be zero, since it represents the electric polarization of 

 the shot : if there are N shot per unit volume, the quantity 



P = &!!! P r dx dy dz 



will represent the total polarization per unit volume. If d 

 denote the electric force, and E the average value of d, P will 

 be proportional to E, say 



P - ( - 1) E. 



By integration by parts, assuming all the quantities concerned 

 to vary continuously and to vanish at infinity, we have 



+ p * D * (x> y> z} ** dy ds = "Iff* ^ p ** dy dz> 



where ^ denotes an arbitrary function, and the volume-integrals 

 are taken throughout infinite space. This equation shows that 

 the polar-distribution of electric charge on the shot is equivalent 

 to a volume- distribution throughout space, of density 



P = - div P. 



Now the fundamental equation of electrostatics may in 

 suitable units be written, 



div d = p ; 



* W. Thomson (Kelvin), Camb. and Dub. Matb. Journal, November, 1845 ; 

 "W. Thomson's Papers on Electrostatics and Magnetism, 43 sqq. ; F. 0. Mossotti, 

 Arcb. des sc. phys. (Geneva) vi (1847), p. 193 ; Mem. della Soc. Ital. Modena, 

 (2)xiv(1850), p. 49. 



P 2 



