400 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



These two simultaneous equations will be compatible with one an- 

 other — • one might say that they make sense — only if they are ulti- 

 mately the same equation. The ratio of the coefficients of Ml and Ml 

 in the one must be the same as the ratio of the corresponding coeffi- 

 cients in the other. In words more natural to algebraists, the determinant 

 of the coefficients must vanish. It turns out that this condition deter- 

 mines a specific value of v, and this value is the resonance-frequency: 



p = {ge/Airmc) V[H + (N, - N^)M][H -f (A^, - N^)M] (20) 



For reasons deriving from the history of celestial mechanics, this pro- 

 cedure is known as ''solving the secular equation." 



In the most common experimental set-up, the sample is a thin layer 

 parallel to the 2;-direction — so thin that by comparison with its breadth, 

 the free poles at the surfaces opposite the pole-pieces of the magnet may 

 be regarded as infinitely far away. Under these conditions Nz vanishes, 

 and so does Nx if we lay the a:-axis parallel oo the surface of the thin 

 layer; but Ny does not vanish, it is in fact equal to 4^. Under the radical, 

 the first factor becomes equal to H and the second to H -\- 4x3/, which 

 latter is by definition the induction B. We have: 



V = {ge/4wmc) VHB (21) 



Note here that since B depends upon both H and M, one cannot use 

 the formula unless one knows the value of M, which is the magnetization 

 of the substance at saturation. This usually requires knowledge obtained 

 from other experiments; but we shall meet with a case in which, at least 

 "in principle," the value of B may be found from the resonance-experi- 

 ment itself. 



Equation (21) is the commonest formula for the ferromagnetic reso- 

 nance, for it fits the "geometry" of the original and of most of the 

 subsequent experiments. Yet there are other formulae corresponding to 

 other geometries, and two of these are particularly important. 



It is feasible to orient the layer at right angles to the big appHed field. 

 For this case we shall do well to turn the axis of z so that it remains 

 parallel to the big field. Now A^^ and Ny vanish and Ns becomes Air, 

 and the formula is this: 



V = {ge/4Tmc)(H - 47rM) (22) 



The quantity {H — iwM) is the internal field Hi , the field strength 

 within the magnetized body. This is the special case in which the right 

 result is obtained by going back to equation (4) and putting for H the 

 actual field strength at the scene of the resonating electrons. In other 



