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THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



occurs. There is indeed such a natural frequency, not however a fre- 

 quency of vibration; it is a frequency of precession. Precession is a 

 concept well known to astronomers and to such physicists as have to 

 do with gyroscopes, perhaps not so well known as it should be to others. 

 In Fig. 5, the vertical is again the direction of the big magnetic 

 field. The arrow represents the angular momentum of the nucleus, 

 which I now denote by p. The magnetic field H exerts a torque on the 

 nucleus. I have already given an expression for this torque, but I gave 

 it in the language of the ''old" quantum-theory. To employ this ex- 

 pression with as little apparent change as possible, I introduce the 

 symbol fio for the magnetic moment of the nucleus, and reserve /x for 



PSIN0 



Fig. 5 — Illustrating the Larmor precession. 



the maximum permissible projection of juo on the field-direction. The 

 torque now appears on the right-hand side of the following, purely 

 classical, equation: 



dp/di = fjLoH sin 6 



(6) 



This is a vectorial equation, but I will endeavor to express its vectorial 

 content by words instead of symbols. Fix the attention on the tip of the 

 arrow. The torque makes it describe a circle of radius p sin d in the 

 horizontal plane, with a frequency which I denote by v. Its peripheral 

 speed in this circle is v multiplied by the circumference of the circle, 

 therefore u'2irp sin d. This speed is dp/dt. Putting its value into (6), 

 we observe with pleasure that vanishes from the scene: the result is 

 going to be the same for all orientations of the magnet: this is it: 



H = 2tpv/ho 



(7) 



