H, A, Rowland — Studies on Magnetic Distribution. 23 



against one pole only. In an ordinary straight electro-magnet 

 the neutral point is at the center. When a paramagnetic sub- 

 stance is placed against or near one end, the neutral point 

 moves toward it ; but if the substance is diamaguetic it moves 



The same thing will happen, though in a less degree, in the 

 case of a steel magnet, so that its neutral point depends on 

 external conditions as well as on internal. 



We now come to practically the most interesting case of dis- 

 tribution, namely, that of a straight bar magnetized longitudi- 

 nally either by a helix around it, or by placing it in a magnetic 

 field parallel to the lines of force ; we shall also see that this is 

 the case of a steel magnet magnetized permanently. This case 

 is the one considered by Biot (Traite de Phys., tome iii, p. 77) 

 and Green (Mathematical Papers of the late George Green, p. 

 Ill, or Maxwell's "Treatise," art 439), though they apply 

 their formulae more particularly to the case of steel magnets. 

 Biot obtained his formula from the analogy of the magnet to a 

 Zamboni pile or a tourmaline electrified by heat. Green 

 obtained his for the case of a very long rod placed in a mag- 

 netic field parallel to the lines of force, and, in obtaining it, 

 used a series of mathematical approximations whose pbysical 

 meaning it is almost impossible to follow. Prof. Maxwell has 

 criticised his method in the following terms (" Treatise," art 

 439) :— " Though some of the steps of this investigation are not 

 rigorous, it is probable that the result represents roughly the 

 actual magnetization in this most important case." From the 

 theory which I have given in the first part of this paper we 

 can deduce the physical meaning of Green's approximation, 

 and these are included in the hypotheses there given, seeing 

 that when my formula is applied to the special case considered 

 by Green, it agrees with it where the permeability of the mate- 

 rial is great My formula is, however, far more general than 

 Green's. 



It is to Green that we owe the important remark that the 

 distribution in a steel magnet may be nearly represented by 

 the same formula that applies to electro-magnets. 



As Green uses what is known as the surface-density of mag- 

 netization, let us first see how this quantity compares with 

 those I have used. 



Suppose that a long thin steel wire is so magnetized in the 

 direction of its length that when broken up the pieces will have 

 the same magnetic moment While the rod is together, if we 

 calculate its efiect on exterior bodies, we shall see that the ends 



are the only portions which seem to act. Hence w 



e may math- 



ematically consider the whole action of the rod t 

 the distribution of an imaginary magnetic fluid o^ 



obe^dueto 



^er the ends 



