NUCLEAR MAGNETIC RESONANCE 81 



does not occur at all: the theorists know the reason why, and call it a 

 "forbidden" transition. As for the other two, the mere symmetry of the 

 picture shows that they involve equal absorptions of energy and there- 

 fore contribute coincident peaks. There is therefore only one dis- 

 tinguishable peak, and we have to find the value of H at which it appears. 

 This is easily done. Going back to equation (1), we integrate the inte- 

 grand which there appears from 0° to 90° (or from 90° to 180°) ; and so 

 we come to the analogue of equation (3) which applies to the deuteron: 



H = hv/na (4) 



In the course of this argument we have met with an example of two 

 general rules : no matter how many permitted orientations there are, transi- 

 tions occur only between consecutive ones, and these permitted transitions 

 always agree in energy-absorption, so that there is never more than one 

 peak. Yet equation (4) differs from equation (3), because in the right- 

 hand member hv/fi — and now I am using ju as the general symbol for 

 magnetic moment — is multiplied by J^ for the proton and by one for 

 the deuteron. Now, J^ is the value of the spin of the proton and one is 

 the value of the spin of the deuteron. We generalize from these two 

 instances: we use / as the general symbol for the spin; and we arrive at 

 the following: 



H = (I/f.)hv (5) 



The generalization is sound; and equation (5) is the fundamental equation 

 of nuclear magnetic resonance. 



I now have to interpret the word ''spin." Spin is a particular measure 

 of the angular momentum of the nucleus. That a magnetic nucleus has 

 angular momentum is surely not surprising. We are trained to ascribe 

 magnetism to the motion of charged bodies: an electric current flowing 

 in a loop has the same magnetic field as a bar-magnet. When a nucleus 

 is observed to have a magnetic moment and an angular momentum, it 

 is natural to correlate one property with the other: one does not quite 

 know how far the analogy may safely be pressed, but at least it is 

 helpful. 



But what sort of a measure of the nuclear angular momentum is the 

 quantity 7? The answer to this question is confused by the fact that in 

 our times there have been two forms of quantum theory: the "new" 

 quantum mechanics which is undoubtedly more competent in general, 

 and the "old" quantum theory of the nineteen-twenties which is certainly 

 more simple in the present case. Desire to be clear has led me to employ 



