403-405] Physical Phenomena 357 



magnetic particle in two, so that one pole is left on each side of the division. 

 In other words, we must suppose the magnetic particles either to be identical 

 with the molecules of which the matter is composed or else to be even 

 smaller than these molecules. At the same time, it will not be necessary 

 to limit the magnetic particle of mathematical analysis by assigning this 

 definite meaning to it : any collection of molecules, so small that the whole 

 space occupied by it may be regarded as infinitesimal, will be spoken of as a 

 magnetic particle. 



404. Axis of a magnetic particle. The axis of a magnetic particle is 

 defined to be the direction of a line drawn from the negative to the positive 

 pole of the particle. 



It will be clear, from what has already been said, that the effect of a 

 magnetic particle at all external points is known when we know its position, 

 axis and moment. 



Intensity of Magnetisation. 



405. In considering a bar-magnet, which must be supposed to have 

 breadth as well as length, we have to consider the magnetic particles as 

 being stacked side by side as well as placed end to end. For clearness, let 

 us suppose that the magnet is a rectangular parallelepiped, its length being 

 parallel to the axis of x, while its height and breadth are parallel to the two 

 other axes. The poles of this bar-magnet may be supposed to consist of a 

 uniform distribution of infinitesimal magnetic poles over each of the two 

 faces parallel to the plane of yz, let us say a distribution of poles of aggregate 

 strength I per unit area at the positive pole, and / per unit area at the 

 negative pole, so that if A is the area of each of these faces, the poles of the 

 magnet are of strengths I A. 



As a first step, we may regard the magnet as made up of an infinite 

 number of line-magnets placed side by side, each line-magnet being a 

 rectangular prism parallel to the length of the magnet, and of very small 

 cross-section. Thus a prism of cross-section dydz may be regarded as a line- 

 magnet having poles I dydz. This again may be regarded as made up of a 

 number of magnetic particles. As a type, let us consider a particle of length 

 dx, so that the volume of the magnet occupied by this particle is dxdydz. 

 The poles of this particle are of strength + I dydz, so that the moment of the 

 particle is 



I dxdydz. 



If we take any small cluster of these particles, occupying a small volume 

 dv, the sum of their moments is clearly Idv, and these produce the same 

 magnetic effects at external points as a single particle of moment 



Idv. 



