390 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



Going back to ancient theory, let us imagine an electron revolving 

 with frequency/ in a circular orbit of radius r. It is equivalent to a cur- 

 rent ef running continuously in the circular loop. According to the old 

 theorem of Ampere, its magnetic moment is equal to the area of the 

 circle multiplied by the current-strength; but the current-strength is 

 to be expressed in electromagnetic units, so that the magnetic moment 

 M equals {e/c)fTrr^. The angular momentum p is mr times the speed of the 

 electron, and therefore equals 27rmr^/. For the ratio of the two we find: 



ijl/p = e/2mc (5) 



This is what has lately been miscalled the ''gyromagnetic ratio," a 

 name which was originally applied and ought still to be applied to its 

 reciprocal. It would be good to follow Gorter's suggestion of calling it 

 the "magneto-gyric ratio." 



I now state equation (5) in another fashion so as to introduce a symbol 

 which is really a word, and is the technical word of this field of physics: 

 it ought to be a word all spelled out, but it is just the letter g. 



(Morb/Pcrb) = g{e/2mc), 9 = ^ (6) 



Thus g is the ratio of magnetic moment to angular momentum given in 

 terms of e/2mc as unit, and its value for the orbital motion of an electron 

 is one. Note also that though we have arrived at (6) in a very 

 old-fashioned way, it is one of the results that have stood firm through 

 all the mutations of quantum theory. 



The study of what are known as "multiple ts" in optical spectra led 

 some thirty years ago to the conclusion that for the spin of the electron 

 the magneto-gyric ratio is such that g = 2: 



(M8pin/Pspin) = g{e/2mc), g = 2 (7) 



This belief was substantiated by the "Dirac theory," and was not upset 

 until measurements were made of the magnetic resonance of electrons 

 in atoms by the molecular-beam method. The first such measurements 

 were made upon atoms containing uncompensated electrons which had 

 orbital motion as well as spin. I pass them over, and come direct to the 

 most recent experiments on hydrogen atoms in their ground state, 

 where there is no orbital motion of the electron to complicate matters. 

 These are so recent that they came into print as these words were being 

 written. 



The hydrogen atom is a good example to take, not only for the reasons 

 that I have given already, but also because it may be compared with 

 the hydrogen molecule H2. The two electrons of the hydrogen molecule 

 compensate one another, and there is no electron resonance. The two 



