348 BELL SYSTEM TECHNICAL JOURNAL 



beside which we may place equation (9), reshaped and with allowance 

 for the doubling: 



H. = ——^^ . (11) 



It is now obvious that, in the case of a material for which /max is 

 known, we have apparently three disposable constants N, L, and 

 (S — L). However, the ratio of (S — L) to L must be a very small 

 fraction; otherwise the assumptions from which the equations were 

 deduced would not be valid. This ratio is determined by the ratio 

 Ic/ImaK- If we take for Ic the value of magnetization somewhere 

 near the division between the first and second segments of the initial 

 curve, we find Icflnmx = -01 for soft iron (I quote Ewing) or about .05 

 for the permalloy of which the curve is exhibited in Fig. 1. Now we 

 have the ratio of {S — L) to L fixed, and ostensibly two disposable 

 constants left. However, if we assume that each elementary magnet 

 is an atom and each atom an elementary magnet, both of these are 

 determined by the crystal lattice of the metal. Nothing remains 

 adjustable; a definite value is imposed by the theory upon lie. This 

 value is enormously too great. 



It is clear that the situation could be saved by dropping the assump- 

 tion that every atom is a magnet, so that the constants N and L 

 might again become freely disposable. Ewing proposed another way 

 of escape — a modification of the model involving the introduction of 

 a fourth constant. He invented a system composed of three mag- 

 nets with their centres in a line, the two outer ones fixed and 

 pointing in opposite senses along the line of centres, the middle one 

 free to revolve. The polestrengths of the outer magnets, M' and 

 M", are supposed to differ slightly; then, when no outside force is 

 acting, the middle one comes to an equilibrium in which it points in 

 the same sense as the stronger of its neighbors. When a field is 

 applied in a direction inclined at a to the line of centres and steadily 

 increased, capsizal occurs at a certain value of fieldstrength H and the 

 corresponding value of deflection 6. When the clearances are small 

 and a is very nearly 90°, the equation for 6 is equation (8) with an 

 unimportant change in numerical factor; while the equation for H 

 is changed, in that (M' — M") now stands in the place of M. This 

 is the new constant introduced into the model. 



Ewing supposed that the pivoted magnet of his model might be 

 the analogue of an internal electron-orbit of the iron atom, while 

 the fixed neighbors might correspond to external distributions of 

 whirling electrons, in the periphery of the same atom or in neighboring 



