302 BELL SYSTEM TECHNICAL JOURNAL 



the same for all the volume-elements; that there is a fixed relation 

 between the intensity of magnetization at a point and the field existing 

 at that point, which is the same everywhere within the supposedly 

 uniform piece of iron, which is a quality of that particular kind of 

 iron. If there is no such relation, the whole procedure is likely to be 

 futile. If there is such a relation, it is the fundamental fact of mag- 

 netism; and the first business of the student of magnetism is to 

 determine it for as many substances, under as many conditions, as he 

 can. We shall presently see that most research in ferromagnetism is 

 devoted to determining this relation, by methods which would not 

 yield self-consistent results, did it not exist. 



But we shall attain nothing by merely assuming that there is such 

 a relation, unless we make another assumption concerning the field 

 prevailing within the magnet; for it is quite inaccessible, we cannot 

 enter in to measure it. Let us therefore suppose that the field pro- 

 duced at any point inside the magnet, by the objects outside — be 

 they laboratory magnets, or electric currents, or the earth itself — is 

 the same as they would produce at that point were the magnet taken 

 away, leaving them the same. The outer parts of the magnet are 

 supposed not to shield the inner parts from the magnetic influences 

 of the outer world. This is a natural corollary of the supposition we 

 have tacitly made already, that the outer volume-elements of the 

 magnet do not shield the outer world from the magnetic forces due to 

 the inner volume-elements. We assume it; and we assume that the 

 intensity of magnetization and the magnetic field, the vectors / and 

 //, are parallel to one another,* and that there is a relation between 

 their magnitudes which is the same for every point within the magnet. 



On proceeding to test this set of assumptions by the appeal to 

 experiment, we encounter results which at first sight seem to destroy 

 them. For instance, let us immerse a short rod of iron (quite de- 

 magnetized to begin with) in the uniform magnetic field produced 

 within a long cylindrical tube by an electric current flowing through 

 a coil of wire, a solenoid, evenly wrapped around the tube. The field 

 lie which the current would produce within the tube were the iron 

 not there is uniform in magnitude and direction, everywhere parallel 

 to the axis of the solenoid. By the last assumption, this is the field 

 which the current produces everywhere inside the iron. We map 

 the magnetic field produced by the rod in its vicinity, and determine 



* There are cases, neither few nor trivial, in which / and H cannot always be 

 supposed parallel; for instance, when the magnet is a large crystal, or when it is a 

 plate of metal which has been cold-rolled, or when the direction of the magnetizing 

 field is changed after the substance is already perceptibly magnetized. But if I 

 were to expound the most general actual case, this article would never come to an end. 



