CONTEMPORARY ADVANCES IN PHYSICS 301 



understanding of the effects which the magnets produce outside. 

 Induction and intensity of magnetization are things which are supposed 

 to exist inside a solid magnetic body, to make it possible to predict 

 what effects that body produces in the world outside of itself — the 

 only region which can be entered with or without measuring-instru- 

 ments. 



Now if a magnet were delivered over by Nature in fixed and perma- 

 nent state, so that nothing which could be done to it would alter its 

 behavior towards surrounding objects, the problem of determining / 

 would be relatively simple. It would amount to this: to build up a 

 structure of little cubical magnets occupying the same volume as the 

 actual magnet, and producing everywhere outside that volume the 

 same field as the actual magnet is observed to produce. In other 

 words, it would consist in seeking a function / of the coordinates x, 

 y, z of the points within the volume of the magnet, fulfilling the 

 following condition: when this volume is subdivided into small cells 

 of volume dv, and each is treated as a magnet of moment Idv, and 

 the forces exerted by all these little magnets at any point outside of 

 the volume are summed together, their sum shall turn out to be the 

 same as the force which the actual magnet is observed to exert at 

 that point. 



This however is not the whole of the actual problem. The force 

 which a magnet exerts at any particular point in its vicinity depends 

 upon the magnetic fields which are impressed upon it by external 

 objects — other magnets, or electric currents, or the earth itself. It 

 becomes a different magnet when it is subjected to a different field. 

 The process of finding a function / fulfilling the condition made 

 above must therefore be carried through anew whenever the exterior 

 fields acting upon the magnet are changed. 



This variability makes the problem much more difficult. Yet in 

 some cases it can be dealt with, in the same manner as the more 

 restricted problem of analyzing an unchanging magnet into volume- 

 elements; and in dealing with it, the first foundations of a theory of 

 magnetism are laid down. 



A piece of iron is observed to become a different magnet, whenever 

 the impressed magnetic field is changed. Very well! we will try to 

 describe the difference, by assuming that each of the volume-elements 

 into which we have mentally divided the piece becomes itself a different 

 magnet. The change in the magnetism of the piece is all too likely 

 to be complicated and obscure; but we will simplify by supposing 

 that the magnetization of each of the volume-elements depends upon 

 the magnetic field prevailing in it, according to some law which is 



