NUCLEAR MAGNETIC RESONANCE 85 



Making the substitutions that have already been describe, we get: 



H = {I/n)hv (8) 



and this is none other than formula (5), the fundamental equation of 

 magnetic resonance. The precession-frequency is the resonance-fre- 

 quency. 



This precession is often called the "Larmor precession," and the 

 frequency given by (5) or (8) is called the "Larmor frequency." The 

 name is a posthumous honor; Larmor died before magnetic resonance 

 was discovered; his theory was applied to the Zeeman effect, the effect 

 of magnetic fields upon optical spectra. 



It is not hard to believe that when the applied frequency coincides 

 w4th the Larmor frequency, something drastic must happen to the 

 precession. The theory has been worked out on a classical basis. I will 

 not pursue it into its details; but at least the first step should be taken. 



I have said that the alternating field is perpendicular to the big 

 field. We take the x-direction as its direction. The magnetic field, or 

 magnetic vector as I will henceforth call it, has then Hi cos 2Tro)t for its 

 a;-component (I use co for the frequency so as to distinguish it from the 

 Larmor frequency) and zero for its ^/-component. Now imagine a 

 vector, of constant magnitude (3^)^i , lying in the a;?/-plane, pointing 

 away from the 2-axis and revolving around this axis clockwise with 

 frequency oj. Its x-component will be (K)^i cos 27rco^, its ^/-component 

 will be —Q/2)H\ sin 2iroit. Imagine another such vector revolving 

 counterclockwise. Its x-component will be Q/QHi cos 2iro)t, its y-Qovn- 

 ponent will be (}^)Hi sin 27rco^. (It is evident that we have chosen their 

 phases so as to bring about this result). The sum of these two vectors 

 has Hi cos 2T(at for its a;-component and zero for its ^/-component. But 

 this is the vector that we started out w^ith. In the language of optics, 

 we have resolved a plane-polarized wave into two circularly-polarized 

 ones. 



The foregoing is pure mathematics. Now comes the physics. Of these 

 two revolving vectors, one is whirling in exact unison with the precessing 

 magnet when co is exactly equal to the Larmor frequency, the other is 

 rushing round and round in the opposite direction. Our intuition tells 

 us that the former may be expected to produce a great effect on the 

 precession, the latter a small one. The latter is not always negligible, 

 but may be neglected here. Thus in this artful way w^e have substituted 

 a circularly-polarized field for the actual plane-polarized one. 



The theory further leads to the prediction that when resonance 

 exists, the precession will be exaggerated in such a way as to produce 



