MAGNETIC RESONANCE. II 399 



time) and will also convey the plausible suggestion that all of the resonat- 

 ing electrons in the substance are coupled parallel, so that M can signify 

 the magnetization of the substance. We have: 



dM,/dt = -yiMyHi, - M.Hiy) 



dMy/dt = -y{M^Hi, - MMiz) (17) 



dM./dt = -y{MMiy - MyHi,) 



Now we are to make the following important substitutions, some of 

 which are approximations. 



(1) Presuming that M the magnetization of the substance will not 

 deviate far from the z-direction, we are to write M for Mz . 



(2) For Hiz , the 2;-component of the field actually operating upon the 

 electrons, we are to write {H — NzM) . Here H stands as heretofore for 

 the applied field and Nz for the "demagnetizing factor" in the 2-direc- 

 tion, which latter is a measure of the strength of the free poles on those 

 surfaces of the sample which face the pole-pieces of the magnet (Fig. 

 1). Thus —NzM is the value of the field produced in the substance by 

 these free poles. 



(3) YovHix and Hiy we are to write —NxMx and —NyMy . This means 

 that whatever applied fields there may be in the x and the ^/-directions 

 are negligible, and yet the components of magnetization in these direc- 

 tions are not neghgible, so that the free poles on the surfaces perpendicu- 

 lar to X and to y respectively are producing the internal fields of which 

 —NxMx and —NyMy are the strengths. 



(4) We are to ignore terms in which the product MxMy appears, 

 these being small. 



The fourth of these conditions makes dMz/dt vanish: we are left 

 with only two of the three equations (17), a convenience. Making the 

 substitutions allowed by the first three conditions, we find that the 

 other two assume the forais: 



dMx/dt = -yMy[H - {Nz-Ny)M] 



(18) 

 dMy/dt = -yMx[-H + {Nz-Nx)M] 



Now suppose that Mx and My are periodic functions of time, of fre- 

 quency j/. We write them as Ml exp {2Trivt) andilfy exp (2Trivt). Substituting 

 into (18), we find: 



2irivMl + y[H + {Ny -N.)M]Ml = 

 -y[H - {N, - Nx)M]Ml + 2irivMi = ^^ 



