the Absurdity of Diamagnetic Polarity. 



259 



for magnetic purposes, we enter a new body when we travel 

 along the line of magnetization past the point at which the 

 discontinuity takes place. 



If the elementary volume dv be in the form of a cylinder, 

 of small length and thickness, whose generators are lines of 

 magnetization and whose ends are orthogonal sections, it is 

 evident, from what has been shown, that the external mag- 

 netic action of the volume is the same as that of layers of 

 magnetism on the ends, of surface-densities I on the positive 

 end and —I on the negative end. 



We shall now suppose the body divided into a vast number 

 of elementary cylinders such as these, and we shall examine 

 how far the magnetic layers on contiguous ends neutralize 

 one another. Let be a fixed point on a line of magnetiza- 

 tion and P, Q two other points, such that the distance OP = s 

 and OQ = s + ds. Pound the line OPQ describe a small closed 

 curve and let a line of magnetization travel round it so as to 

 trace out a thin tube in the body. Through P and Q draw 



Fia-. 7. 



normal surfaces to the line OPQ, and let da. be the area of the 

 section of the tube at P or Q. Then let the length PQ be 

 divided into an infinite number of equal parts, each of which 

 may be supposed considerable in comparison with the size of 

 a molecule, and through each of the points of division draw 

 surfaces normal to PQ, so as to divide the small cylinder PQ 

 into an infinite number of infinitely thinner cylinders. Then, 

 since each of these constituent cylinders of PQ is equivalent 

 to equal surface-layers on its ends, the densities of which vary 



uniformly from I at P to I -f -j- ds at Q, it is clear that the 

 cylinder PQ is equivalent to layers on its ends, of surface- 



densities — I at P and 



1 + ^ds 



ds 



dl 



at Q, together with a 



quantity of magnetism —^dsdcc uniformly distributed 



