INDUCTION ON AN INFINITELY SMALL BODY. 139 



to the flows represented by the numbers i, 2, 3, 4 . . . , we need only 

 take, on the transverse axis, lengths corresponding to the numbers 



1 >->->- an d by equation (18) draw the lines of force which 



cut the axis in these different points. 



156. INDUCTION ON AN INFINITELY SMALL BODY. The system 

 of two equal masses of opposite signs infinitely near each other, repre- 

 sents the condition of an infinitely small body, conductor or not, 

 originally in the neutral state, and placed in any given electrical field. 

 The body is in effect covered with two layers of equal masses, and 

 of opposite signs, each of which acts as if it were concentrated in its 

 centre of gravity. 



This is also the case with any body, originally in the neutral state, 

 (that is with a total charge null,) when its action at a great distance is 

 considered. 



157, POLARIZED SPHERE. LAYERS OF GLIDING.* Let us con- 

 sider two spheres S and S' of the same radius (Fig. 41), of uniform 

 densities + p and-/), and whose, centres A and A' are at an infinitely 

 small distance 8. This system is in fact equivalent to that of two 

 equal layers of opposite signs distributed on the two halves of a 

 spherical surface. 



This particular form of electrification is of great interest, and cor- 

 responds in magnetism to a very simple method of magnetisation. 

 For the sake of brevity we may apply the term layers of gliding 



* What are here spoken of as layers of gliding (couches de glissement), are the 

 result of a purely fictitious geometrical operation, which does not aim at repre- 

 senting a real phenomenon, or a particular constitution of the electrified body. 

 We shall retain the expression electrical displacement to denote the mechanical 

 modification of the medium which Maxwell had in view in his theory of dielectrics. 



