CONTEMPORARY ADVANCES IN PHYSICS, XXIX 291 



while for the angular momentum, we have: 



p = mvr, (2) 



and eliminating vr between (1) and (2), we get: 



M/p = e/2mc. (3) 



Here we have on the left the ratio of magnetic moment to angular 

 momentum, a very important quantity for all these categories of atomic 

 and subatomic magnets. It is equated to ejlmc, a value which is 

 correct whenever we are dealing with the magnet constituted by the 

 orbital motion (not the spin!) of an electron; this equation in fact is 

 valid for any sort of an orbit described in a central field, and is one 

 of the few that have survived unamended all of the stages in the evolu- 

 tion of Bohr's original theory into quantum mechanics. I will rewrite 

 the equation thus: 



Mlp = g{e/2mc), g = I, ■ (4) 



and this Is meant to imply that for other categories of atomic and 

 subatomic magnets, the ratio of the moments is not always equal to 

 ejlmc, which is true. In general it is the custom to characterize 

 any one of these magnets by giving Its value of g. Orbital magnets, 

 then, are characterized by the value unity for the g-factor. 



We next ascertain the energy which the orbital magnet possesses by 

 virtue of being In the applied field //. Letting a stand for the angle 

 between the direction of the field and the axis of the magnet, we find 

 for the torque exerted on the magnet by the field, 



T = - MH sin a (5) 



and integrating to obtain the energy in question, 



U = jTda = MH cos a. (6) 



This we now write as follows : 



U = {MII/p)p cos a = {gellllmc) p cos a, (7) 



and here Is as good an opportunity as any to recall a well-known 

 theorem of classical mechanics, fundamental in the theory of the 

 gyroscope. When a torque is acting upon a rotating body, the body 

 precesses around the direction of the field responsible for the torque; 

 and if the torque be equal to a constant Tq times the sine of the angle 

 between the field-direction and the axis of the rotating body, then the 

 angular velocity co of the precession is equal to the ratio between Tn 



