236 THEORY OF NEWTONIAN FORCES. [PT I. CH. V. 



Accordingly the potential at points outside of a lamellarly 

 polarized body depends only on its form and position, and on the 

 values of the potential of polarization at the surface. 



If the attracted point is within the substance of the polarized 

 body, we may integrate (9) in the other manner, interchanging < 

 and 1/r, obtaining 



which, by the theorem of 83 (5) or 84 (12) applied to </>, 

 becomes 



03) = 



In the case of lamellar polarization the induction becomes 



so that the induction, being the parameter of the function 

 F+ 47T(, is also lamellar. For both inside and outside points, 

 this function is equal, except for a constant, to the surface 

 integral 



Os) 



vn 



as we see from (13) and (n), together with the fact that outside 

 <f> is constant. 



125. Polarized Shells. The characteristic of a lamellar 

 polarization is that if we construct two infinitely near equi- 

 potential surfaces of polarization <> = fa and </> = fa, the polariza- 

 tion is normal to them at all points, inversely proportional to the 

 distance between them, and in the direction from the smaller to 

 the larger value of fa The portion of matter included between 

 the two surfaces, which need not be closed, is called a simple 

 polarized shell. If we consider the infinitesimal portion of the 

 potential due to such an unclosed shell, the surface integral (i i) is 

 taken over both sides of the shell, the portion over the edge 

 vanishing, since the width of the edge is infinitesimal. Conse- 

 quently, replacing n, the internal normal, by n-^ and n 2) away from 



