94 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



through the state of resonance 60 times in a second; and it is possible 

 to record and measure A on every such passage. 



The fall and the rise of A are due to a cause so obvious that the 

 reader has probably guessed it already. The peak, we recall, is a peak 

 of absorption due to the turning of ''up" protons into the "down" 

 direction. When an up proton is turned into the down direction it goes 

 out of business as an absorber, and continues out of business so long as 

 it remains in the down direction. Since there is a fall and since there is 

 a rise, the sojourn in the down direction must be neither zero nor in- 

 finite. If it were zero there would be no fall, and if it were infinite there 

 would be no rise. The shrinkage of the peak in the presence of magnetic 

 resonance, and the growth of the peak after resonance is discontinued, 

 are signs that the sojourn of a proton in the down direction is finite 

 but not zero. We divine already that Ti is a measure of the average of 

 this sojourn. 



The foregoing may seem to imply that the height A of the peak is 

 proportional to the number of up protons in the sample; but this is not 

 so, and A is proportional to something else which I call the "margin." 

 To present it I use iV„ for the number of upward-pointing protons, 

 Nd for the number of downward-pointing protons, No for their constant 

 sum, fi in the sense defined before, k for Boltzmann's constant; and I 

 write down the fundamental theorem of Boltzmann : 



NJNd = expi2fiH/kT) (12) 



The "margin" is {Nu - Nd). We find: 



Nu- Nd = Nd [exp(2/xF//cT) - 1] 



= No (fiH/kT) approximately 



(13) 



We have approximated by^ supposing jiH to be very small compared with 

 kT, which it is indeed; and by supposing Nu and Nd each to be nearly half 

 of A^o — this second approximation is retroactively verified, for on substi- 

 tuting (for instance) 20,000 oersteds for H and room-temperature for T, 

 one finds that out of two million protons selected at random a million plus 

 seven are pointed up and a million minus seven are pointed down. The 

 margin is thus 14 in two millions; but it may also be regarded as seven in 

 two millions, since if seven protons out of two million should be turned 

 down the margin would vanish and the peak would vanish with it. 



Why is the stature of the peak proportional to the margin and not 

 to Nu ? The point is, that in addition to turning protons from the up 



