114 



HENRY A. EOWLAND 



where x is the distance of the neutral point from the end. Making 

 b = 12, we have from this : 



By experiment we find that the neutral point is, in all the cases we 

 have given in Table X, between 7-5 and 8-1 inches, which are quite 

 near the points indicated by theory for the proper values of r, though 

 we might expect curve D to pass through the point x = 9, except for 

 the disturbing causes we have all along considered. 



Our formulae, then, express the general facts of the distribution in 

 this case with considerable accuracy. 



These experiments and calculations show the change in distribution 

 in an electromagnet when we place a piece of iron against one pole only. 

 In an ordinary straight electromagnet the neutral point is at the 

 centre. When a paramagnetic substance is placed against or near one 

 end, the neutral point moves toward it; but if the substance is diamag- 

 netic it moves from it. 



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 distribution, 

 namely that of a straight bar magnetized longitudinally 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 mag- 

 netized permanently. This case is the one considered by Biot (Traite 

 de PJiys., 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 formula? 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 magnetic field parallel to the lines 

 of force, and, in obtaining it, used a series of mathematical approxima- 

 tions whose physical 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 



