STUDIES ON MAGNETIC DISTKIBUTION 115 



I have given in the first part of this paper we can deduce the physical 

 meaning of Green's approximations; 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 permea- 

 bility of the material is great. My formula, however, is far more gen- 

 eral than Green's. 



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

 tion in a steel magnet may be nearly represented by the same formula 

 that applies to electromagnets. 



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

 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 mag- 

 netic moment. While the rod is together, if we calculate its effect on 

 exterior bodies, we shall see that the ends are the only portions which 

 seem to act. Hence we may mathematically consider the whole action 

 of the rod to be due to the distribution of an imaginary magnetic fluid 

 over the ends of the rod. As any case of magnetism can be represented 

 by a proper combination of these rods, we see that all cases of this sort 

 can be calculated on the supposition of there being two magnetic fluids 

 distributed over the surfaces of the bodies, a unit quantity of which 

 will repel another unit of like nature at a unit's distance with a unit of 

 force. The surface-density at any point will then be the quantity of 

 this fluid on a unit surface at the given point; and the linear density 

 along a rod will be the quantity along a unit of length, supposing the 

 density the same as at the given point. 



Where we use induced currents to measure magnetism we measure 

 the number of lines of force, or rather induction, cut by the wire, and 

 the natural unit used is the number of lines of a unit field which will 

 pass through a unit surface placed perpendicular to the lines of force., 

 The unit pole produces a unit field at a unit's distance; hence the num- 

 ber of lines of force coming from the unit pole is 4 x, and the linear 

 density is 



' = & ....... < H > 



and the surface-density 



These really apply only to steel magnets ; but as in the case of electro- 

 magnets the action of the helix is very small compared with that of the 



