MAGNETIC RESONANCE. II 401 



words, this is the special case in which the naive approach does not lead 

 the student astray. 



A more singular special case is that of the sphere. In this case A^x and 

 Ny and Nz are all three of them equal — ■ equal to one another but not 

 to zero. Nevertheless the formula is just our old formula (3), the same 

 as though there were no magnetization at all: 



V = {fi/I){H/h) = {ge/4Trmc)H (23) 



One wonders how long it would have been before anyone set up equations 

 (18) and derived equation (21), if all experiments had been perfomde 

 with spheres. 



In the foregoing pages we have derived the resonance frequency by 

 making certain listed approximations in the basic equations (19). Among 

 these approximations was the neglect of the oscillating field, parallel to 

 the axis of x. We arrive at some interesting results by introducing this 

 field into the equations and giving it an arbitrary frequency, while con- 

 tinuing to make all of the other approximations. It shall be denoted by 

 Hi exp {2'wivt) ; Hi , it may be recalled, was the symbol used in Part I 

 for the amplitude of this field. In this passage v shall signify any fre- 

 quency that the experimenter may choose to apply, while the resonance - 

 frequency heretofore called v shall change its symbol and become vq . 



On the right-hand side of the second of the equations (19) will now 

 appear, as the reader can show for himself, —yMHi instead of zero. The 

 two simultaneous equations now^ make sense for any value of v, instead 

 of just the value vq . On solving them for Ml , one finds: 



^°/^- - H + il^- N.)M T^hM^ (^^) 



The quantity on the left, and hence also the quantity to which it is 

 equated, is the "susceptibiUty" of the substance ^\^th respect to this 

 oscillating field which, be it remembered, is imposed at right angles to 

 the big applied field. 



The quantity on the right has the well-known form of an optical dis- 

 persion-curve. Suppose the frequency to be increased from zero. The 

 susceptibility rises from a finite and non-zero value at j/ = to positive 

 infinity at the resonance-frequency vo ; here it jumps suddenly to nega- 

 tive infinity, from which value it rises asjTiiptotically to zero as the 

 frequency is increased toward infinity. 



In magnetics there are methods of measuring directly, not the sus- 

 ceptibility X itself but the sum (1 + 47rx), which is called the "per- 

 meability" and is denoted by m- It is evident that Avhile the susceptibility 



