178, 179] DIELECTRICS AND MAGNETIZABLE BODIES. 353 



If we perform an experiment analogous to Experiment VIII 

 of Chapter I, namely, suspend two magnets so that two of their 

 poles may repel each other in the air, and then surround them 

 by another medium, for instance by a solution of a salt of iron, 

 we shall find that the magnets fall together, or the system seems 

 to lose energy. The experiment in this form would be difficult, 

 but if we introduce into only a portion of the space a different 

 medium, for instance by introducing a piece of iron between the 

 magnets, the effect is unmistakeable. We are thus led to con- 

 clude that the energy of a magnetic or electric distribution depends 

 not only on the distributions themselves but on the media which 

 surround them. Many of the mathematical developments of the 

 preceding chapters must therefore be abandoned, and all must be 

 examined in the light of this conclusion. 



179. Parallel treatment of Electrostatics and Magneto- 

 statics. Inasmuch as all the phenomena to be considered in this 

 chapter are exactly parallel, for electricity and for magnetism, 

 we shall in general not distinguish which they may be, but shall 

 consider in all cases the words magnetic or electric to be used 

 interchangeably. We shall accordingly in this chapter not in- 

 troduce different symbols for the two sorts of quantities, the 

 necessity for so doing occurring only when both sorts of pheno- 

 mena exist simultaneously. 



Experiment shows that in the general case here considered the 

 forces experienced by a point-charge are conservative, conse- 

 quently a potential exists. The law of the inverse square how- 

 ever ceases to hold in general, and the potential is not harmonic 

 in free space outside the acting distributions. 



When the charges are given, since the forces are different from 

 those previously calculated, the relation between the density and 

 the potential must be different from that given by Poisson's equa- 

 tion. Since however we suppose the force due to any element 

 to be proportional to the charge of the element, the differential 

 equation must be linear. Let us examine what conclusions are 

 true irrespective of the law of force. By the definition of potential 

 as a quantity of work necessary to bring unit charge from infinity 

 to any point, it follows, as was found in 117, that the energy of 

 any distribution is 



(I) W d = 



w. E. 23 



