POINTS AND LINES OF EQUILIBRIUM. 39 



opposite signs, so that the equation of the cone is of the form 



they represent two rectangular planes. 



Let us consider, as an example, the surface of a conductor 

 charged partly with positive electricity and partly with negative; 

 the line of separation of the two layers is a neutral line. The force 

 is null in all points of the neutral line (35), and there is in the 

 dielectric another equipotential surface at the same potential as 

 the conductor, which cuts it perpendicularly along this line. It 

 will be remarked that this particular equipotential surface separates 

 the lines of force, which start from the conductor, from those 

 which terminate there. It might, therefore, be considered as a 

 limiting surface of the lines of force. 



49. If the equipotential surface consists of n sheets which 

 intersect along the same line^ the successive intersections take place at 



7T 



the same angle . 

 n 



Starting from a point P of the line of equilibrium, all the 

 functions H of the development of the potential, up to that of the 

 degree n, are identical with zero, since the tangent cone consists 

 of n sheets. In order that the equation H n = shall represent 

 n planes passing through the z axis, it must not contain any terms 

 in z, and Laplace's equation reduces to 





If r denotes the distance of a point P from the z axis, and putting 



x = r cos 6 



y = r sin 0, 



Laplace's equation becomes 



I*H 



~ 



The function of the degree , which satisfies this equation, is 



