NUCLEAR MAGNETIC RESONANCE 79 



admitted the existence of only two values of 6, viz. the values 0** and 

 180°; more will be said about this later; but for the duration of this 

 particular argument we shall have to admit all values of 6 from 0° to 

 180°. The value of W which we are seeking is the integral of iipH sin 

 from 0° to 180°, from the up orientation to the down one. It is easily 

 obtained : 



/.ISO" 



TT = - / iXj,H sin BdB = 2^j,H (1) 



Having arrived at equation (1) by strictly classical reasoning, we 

 must now approach equation (2) by a starkly quantal argument. 

 Immense amounts of evidence have sho\\Ti that when energy is absorbed 

 from electromagnetic waves of frequencies v in the optical range of the 

 spectrum and in the X-ray range, not to speak of other ranges, it is 

 invariably absorbed in parcels or quanta equal to hv, h standing as 

 always for Planck's constant. If this doctrine is sometimes difficult to 

 assimilate when applied to the optical spectrum, how much more 

 difficult it is to accept w^hen applied to waves of radio frequencies! 

 Yet here also it is to be accepted, so we put: 



W = hv (2) 



Now we transfer the value of W from equation (1) to equation (2), 

 and arrive at the destination: 



H = y2hv/f.^ (3) 



In this equation h is kno^^^l with very great accuracy, and /ip had 

 also been measured when the first experiments upon magnetic resonance 

 were made, though not with nearly the accuracy that physicists now 

 claim for it. It remains only for the experimenter to insert for v the 

 value of the frequency in his experiment and for H the value of the 

 fieldstrength at which the peak appears. The test is whether the two 

 sides of the equation agree. Needless to say, the test has been brilliantly 

 passed. 



Quantum-theory has entered into this argument in more ways than 

 the one which led to equation (2). I return now to the fact that we 

 have arrived at equation (3) by postulating two, and only two, ''per- 

 mitted" orientations of the protonic magnets in the steady field. This is 

 illustrated by the presence, in Fig. 1, of arrows pointing up and arrows 

 pointing do\Mi but no arrows pointing slantwise. We might have assumed 

 that there are protons, and therefore arrows, pointing in every direction. 

 We might have assumed that there is a proton pointing, say, at angle 



