98 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



for the rate of change of Nu , the number of ''up" protons: 



dNu/dt = il/TO(Nou - Nu) - hHlNu (14) 



Here Nou stands for the number of ''up" protons in the condition of 

 equilibrium between the spin-temperature and the lattice-temperature. 

 If we were dealing with the rise of the peak after the alternating field 

 is shut off, the second term on the right would vanish, and we should 

 be back at equation (11). We are however dealing here with the fall 

 of the peak when the alternating field is on. One sees that eventually 

 Nu will reach a constant value — it is said to "saturate" — and the 

 peak a constant stature. If this saturation-value is measured and the 

 value of h is known, Ti can be computed. The saturation-value is meas- 

 ured, and h is determined from quantum mechanics. 



Though I have tried to avoid giving the impression that the stature of 

 the peak necessarily has its equilibrium-value ^o before the oscillating field 

 is first applied, I may not have quite succeeded. It would be a miracle if A 

 were equal to ^o at the moment when the sample is first put into the big 

 field. Time must be allowed for the nuclei to adjust themselves or "relax" 

 to the big field: it was because of this that I said at the beginning that the 

 sample was to be placed in the big field several hours (a generous allowance 

 of time, by the way) before the application of the alternating field. One 

 would expect in general to find A much smaller than Aq , when the sample 

 has just been exposed to the big field; on the other hand it could be greater 

 than i4o if the sample had previously been exposed to a field of greater 

 strength than the field of the experiment. 



Conceivably one might miss the peak altogether by looking for it too 

 soon, if the relaxation-time were long; or by looking for it too late, after 

 it had been reduced to its "saturation" stature. It may be that early 

 attempts to find magnetic resonance were frustrated in these ways. 

 Such dangers are now avoided by mixing the sample deliberately with 

 magnetic impurities in order to diminish the value of Ti : the peak of 

 Figure 2 was obtained with water mixed with ferric nitrate. There is 

 some reason also to conjecture that nuclear magnetic resonance might 

 have been sought and found some years earlier than it was, but for an 

 imperfect theory which indicated that the spin-lattice relaxation-time 

 would be so long as to make it hopeless to look for the peak. 



Students of the literature will find many allusions to another type 

 of relaxation — the "spin-spin" relaxation, with a relaxation-time de- 

 noted by T2 . Except for the bare statement that the breadth of the 

 peak varies inversely as the spin-spin relaxation-time, this topic must 

 be left for some other occasion. It may be mentioned here, even though not 



