322 BELL SYSTEM TECHNICAL JOURNAL 



the question of angular momentum. Is angular momentum an 

 attribute of these whirling intra-atomic currents, or is it not? You 

 may think that the answer to this question is self-evidently "yes!" 

 but remember that for many generations of our forefathers electricity 

 was an imponderable fluid. Weber, however, did consider the affirma- 

 tive answer, and Maxwell even attempted to ask the question of 

 Nature by experiment — vainly, as it turned out. Not till the electron 

 was discovered did the mass of electricity become a prominent part 

 of experience. A moment ago I divided Ampere's achievement into 

 three parts ; similarly I wish now to divide the discovery of the electron 

 into three. Those who isolated and identified and measured the 

 electron were proving three things: first, that negative electricity 

 consists of corpuscles of a definite charge, e; second, that these cor- 

 puscles have a mass, m; and following from these two, the principle 

 which I have called the third part of the discovery, viz. that an electron 

 revolving in an orbit has an angular momentum. 



I will designate angular momentum in general by the letter p, and 

 now I will show you a formula for the ratio oi fx to p in an atom in 

 which an electron is running around in an orbit and constituting an 

 Amperian whirl. The formula, like this other one, for ^l, is valid for 

 an orbit of any shape, but to get it quickly I will simplify by postulating 

 a circular orbit. The radius of the circle being r, the area A is irr^; 

 the current around it is equal to the electron-charge e, multiplied by 

 the number of times per second that the electron runs around the 

 orbit; if I denote the velocity of the electron by v, this number is v/lwr; 

 hence the product iA/c is equal to evrjlc. Now the angular momentum 

 p of the electron, as you all know, is mvr; and hence for the ratio 

 I derive: 



^llp = e/2mc, ^ 



which is one of the most important formulae in the whole of atomic 

 physics. You notice that it does not involve in any way the size or 

 shape of the orbit or the frequency with which the electron travels 

 around it. It is the same for any or all of the revolving electrons of 

 any atom of any kind. 



Now let us see how this formula may be tested. Imagine a rod 

 of some highly magnetizable metal, iron for instance, and imagine it 

 to be unmagnetized at the start. This means, that at the start the 

 little atomic magnets are pointing at random in all directions; that is 

 to say, the vectors which represent their magnetic moments are 

 pointing every way, and so are the vectors which represent their 

 angular momenta, the latter being parallel to the former. Since these 

 atomic vectors of angular momentum are pointing every way at 



