646 CONSTANTS OF MAGNETISATION. 



and determine, for instance, the components in three rectangular 

 directions, which would give the true force at each point. 



Finally, when the magnet is one of revolution, the magnetic 

 images produced by iron filings in a meridian plane give very 

 sensibly the direction of the lines of force, and we could deduce 

 from them the relative magnitudes of the forces. Suppose that, 

 at a point P at a distance r from the axis of revolution, the force 

 is F, and the perpendicular distance of two adjacent lines of force 

 is /; the section of the tube of force determined by these two lines, 

 and by the corresponding lines of a meridian plane which makes the 

 angle with the first is / x rO, and the corresponding flow is FtrB. 

 For another section I'r'B of the same tube, where the force is F', 

 the value of the flow of force is the same, which gives 



F I'r' 

 F/r=F7V, or = y-- 



1212. DETERMINATION OF THE FICTIVE LAYER. We have 

 often considered the curve of normal components as representing 

 the law of the distribution of magnetism ; but the reasonings by 

 which Coulomb attempted to justify this mode of view are quite 

 insufficient. There is really no simple relation between (418) the 

 real distribution, nor even between the distribution of the fictive 

 layer, and the external field of the magnets. It may not be without 

 use to show this in greater detail by a few instances. 



Let us again take the case of a uniform linear magnet, which 

 is equivalent to two isolated masses m situate at a distance 2L; 

 the potential at a point P (1152) at the distances r and r' from 

 the masses + m and - m, is 



If y be the distance of the point P from the right line 2L, 

 (u and to' the angles of the radii vectores r and r' with this same 

 right line measured in the direction of the magnetisation, the com- 

 ponent of the force parallel to y is 



m 



This would be the expression for the component perpendicular 

 to the surface of a cylinder of radius y concentric with the magnet. 

 If this radius is very small compared with the distance 2L of the 



