238 MAGNETISM 



When we compare the foregoing investigations with the 

 corresponding investigations in electricity we see that magnetic 

 intensity corresponds to electric intensity, and magnetic induction 

 corresponds to electric strain. The magnetic equation 



corresponds to the electric equation 



so that /UL corresponds to K/4-7T. 



The introduction of 4?r in one of these is very unfortunate, for 

 it destroys the exact correspondence of formulae in the two CUM ->. 

 It arises from the fact that the units are so chosen that unit quantity 

 of electricity sends out one tube of strain, while unit quantity 

 of magnetism sends out 4?r tubes of induction. Ileavisidr* has 

 introduced a system of "rational units " in which unit magnetic 

 pole, like unit quantity of electricity, sends out one tube. But tilt- 

 difficulty in the way of change in the practical units has not yet 

 been faced. 



Representation of induced magnetism by an 

 imaginary distribution of magnetic poles acting ac- 

 cording to the inverse square law. We have seen that 

 the intensity changes when we pass from air into iron, or more 

 generally when we pass across a surface at which the permeability 

 changes. For purposes of calculation we can imagine the ch, 

 of field to be produced by a layer of magnetism, a layer of poles 

 distributed over any surface where /u changes from one con- 



stant value to another, or distributed 

 through the volume if the change in /UL 

 is gradual. These poles are supposed 

 to act according to the inverse square 

 law and as if the whole space \\ere of 

 unit permeability. 



Let us consider a change of per- 

 meability at a surface PQ, Fig. 184, 

 from 1 to /z, and let the figure represent 

 the section of a tube of induction by a 

 plane containing H x and H 2 , and let 

 the tube stamp out an area a on the 

 surface, represented in section by \\). 

 FlG - 184 - Let <r be the surface density of the 



imagined magnetic poles. Since our supposition is that the surface 

 magnetism would, in combination with the external poles, produce 

 the observed intensities if it acted in air on both sides, we may 

 apply Gausses theorem to the surface PRQS. The theorem states 



* Wx&ricaL Papert, i, 262; ii. 543. 



