648 CONSTANTS OF MAGNETISATION. 



This experiment is certainly in contradiction with the hypothesis 

 of a uniform magnetisation, and we may say that there was mag- 

 netism outside the ends. But if, just as well, the same results had 

 been obtained at twice the distance, Coulomb's reasoning would not 

 be sensibly modified ; while the real magnetisation would be equi- 

 valent to masses m, situate at the centres of the two bases. 



In the case of a short cylinder, uniformly magnetised, the same 

 reasoning, applied to different magnetic filaments, would give the 

 perpendicular component on the lateral faces or rather, on the 

 surface of a concentric cylinder of somewhat greater diameter. 

 We could then apply the formulae which enable us to calculate the 

 action of a uniform circular layer (767), or the external action of a 

 cylindrical coil (768). 



1213. Let us again suppose that the surface S which surrounds 

 the magnet is an infinite plane or a spherical surface. The fictive 

 layer on this surface is the algebraic sum of those corresponding to 

 different internal masses; it is the problem of electrical images (148). 

 For a mass m, situate in a sphere of radius R, at a distance L from 



the centre, the value of the density o^ of the fictive layer at a point P, 



-n 



at the distance r from the acting mass, putting & 2 = , is 



za m 



The numerator 20, which represents the distance of this mass 

 from its external image, is 



it follows that 



R 2 - L 2 m 



(3) 



4 7rR 



If <o is the angle which the radius of the point P makes with 

 the right line L, the perpendicular component of the force is 



