CONTEMPORARY ADVANCES IN PHYSICS 



345 



The simplest form of Ewing's model * is composed of linear chains 

 of elementary magnets. To analyze this it suffices to consider a 

 system composed of two identical magnets, each so long and slender 

 that it may be visualized as a pair of poles of equal polestrength M 

 separated by the length L of the magnet, and 

 both of them pivoted around their centres at 

 points distant from one another by a spacing 

 S which is only slightly greater than L (Fig. 

 10). If there is no external field, they come 

 to an equilibrium, in which state both point 

 in the same sense along the line of centres. If 

 there is an applied field oblique to the line of 

 centres, they come to an equilibrium in which 

 both are deflected through equal angles from 

 that line. Denote their angles of deflection 

 by d, the angle between the field and the line 

 of centres by a, the fieldstrength by H, the 

 distance between the adjacent unlike poles of 

 the magnets by R. The distance R is equal 

 to {S — L) when d is zero, and in general is 

 given by the equation: 



R^ = U + 52 - 2LS cos 



(1) 



The adjacent poles attract one another with 

 forces AP/R^ directed along R, which result in 

 torques 7"' upon each magnet: 



H.P. 



Fig. 10 — ^"Illustrating 

 the elementary f magnet- 

 pair of Ewing's theory. 



T' 



M^L 



R^ 



sm (f = 



AP LS sin 9 

 2R^ 



(2) 



The remote poles likewise exert forces upon the adjacent poles and 

 upon one another, and torques upon the magnets; but it will be 

 necessary to reduce these to relative insignificance by supposing the 



* The next four pages resulted from an attempt to formulate what I take to be 

 Ewing's objection to his own early model, which he phrases in these words: "Now 

 it is known that in ordinary iron barely one per cent of the whole magnetism of 

 saturation is acquired in the quasi-elastic stage before the effects of hysteresis set in. 

 To conform to this condition the magnets of the model must have only a very narrow 

 range of stable deflexion, and consequently they have to be set very near together 

 with the result that in the old model their mutual control became excessive. A 

 calculation of the force required to break up rows of pivoted magnets, of atomic 

 dimensions, when set near enough together to satisfy the above condition, showed it 

 to be many thousands of times greater than the force which is actually required, in 

 iron to reach the steep part of the curve." 



