100 BELL SYSTEM TECHNICAL JOURNAL 



The "pfi^^'iple of quantization" is, that the permitted orbits are 

 marked out from all others in that they fulfil these conditions, which 

 are the Quantum Conditions: 



jprdr=kh, (2) 



jpr dr-\-jp4>d4> = nh. (3) 



In these equations each integral is taken around one complete cycle 

 of the corresponding variable; h stands for Planck's constant, and 

 n and k take the values of all positive integers, k never surpassing n. 

 There is an alternative way of phrasing these quantum-conditions, 

 which is much easier to visualize; but it emphasizes what are probably 

 accidental features of the permitted rosettes, rather than fundamental 

 ones. The rosettes are, as I have said, precessing ellipses; the major 

 axes 2a and the minor axes 2b of these ellipses are, for the permitted 



rosettes 



2a = w2/iV27r2e2w, (4) 



2b = {k/n)2a = knh^/2T^e^m, (5) 



in which n and k take as before the values of all positive integers, 

 k not surpassing n. 



Exactly the same principle governs the permitted orbits of an 

 electron revolving in a perfect inverse-square central field, but varying 

 in mass when its speed varies, as the theory of relativity requires. 

 In this case also the orbits are rosettes, and the permitted orbits 

 are particular rosettes set apart from all the others in that they fulfil 

 (2) and (3), therefore automatically (4) and (5). The energy-values 

 of these permitted orbits agree closely with those of the observed 

 Stationary States of hydrogen and of ionized helium, the atoms of 

 which are the only atoms believed to consist of a nucleus and one 

 electron. Inversely, the orbits required to interpret the observed 

 Stationary States are set apart from all the other conceivable orbits 

 by the features expressed by (2) and (3), and by (4) and (5). On 

 these close numerical agreements for hydrogen and ionized helium, 

 and on other numerical agreements for the same atoms arising when 

 external fields are applied, the prestige of Bohr's atom-model is 

 founded. 



The integers n and k, the total quantum number and the azimuthal 

 quantum number, are used as indices to symbolize the various Station- 

 ary States of hydrogen and ionized helium to which they correspond. 

 Thus the symbol "82" stands for the Stationary State of either atom, 



