CHAP, v.] ELECTRICITY AND MAGNETISM. 267 



distances ; and the equipotential surfaces would 

 be a system of concentric spheres at such dis- 

 tances apart that it would require the expendi- 

 ture of one erg of work to move a unit pole up 

 from a point on the surface of one sphere to any 

 point on the next (see Fig. 97). Around any real 

 magnet possessing two polar regions the equi- 

 potential surfaces would be much more com- 

 plicated. Magnetic force, whether of attraction 

 or repulsion^ always acts across the equipotential 

 surfaces in a direction normal to the surface j the 

 magnetic lines of force are everywhere perpen- 

 dicular to the equipotential surfaces. 



311. Tubes of Force. The following proposi- 

 tion is also important : From a single magnetic pole 

 (supposed to be a point far removed from all other 

 poles) the lines of force diverge radially in all directions. 

 The space around may be conceived as thus divided up 

 into a number of conical regions, each having their apex 

 at that pole ; and through each cone, as through a tube, a 

 certain number of lines of force will pass. Such a conical 

 space may be called a "tube of force." No matter 

 where you cut across a tube of force the cross-section 

 will cut through all the enclosed lines of force, though 

 they diverge more widely as the tube widens. Hence, 

 (g) The total magnetic force exerted across any section 



of a tttbe of force is constant wherever the section 



be taken. 



In case the magnetism is not concentrated at one 

 point, but distributed over a surface, we shall have to 

 speak of the " amount of magnetism " rather than of the 

 " strength of pole," and in such a case the 



(h) Magnetic density is the amoitnt of free magnetism 

 per imit of surface. In the case of a simple 

 magnetic shell over the face of which the 

 magnetism is distributed with uniform density, 



