524 Dr. H. Stanley Allen on 



introduced into molecular models to give an account of 

 paramagnetism and ferromagnerism — namely, structure in 

 space or atom involving channels more or less definite for 

 the electrons to circulate in." On the present view such 

 channels would be provided in consequence of the discrete 

 nature of the tubes of magnetic induction. 



It may be well to state that in the following presentation 

 of the subject the historical order of development has been 

 followed. Starting from a consideration of McLaren's 

 theorem with regard to the lines of magnetic induction 

 threading the aperture of the magneton, the case of one or 

 more electrons moving in circular orbits with uniform 

 angular velocity is reached. The number of magnetic tubes 

 associated with an elliptic orbit is then discussed, and finally 

 it is shown that the results in all these cases can be obtained 

 very simply by employing the generalized statement, of the 

 quantum theory which has been used with such success in 

 explaining the fine structure of spectral lines. Readers who 

 are more interested in the general theorem than in its 

 particular applications may refer at once to this section of 

 the paper. 



I. The Physical Significance of /?, the Quantum 

 Constant. 



1. Planck's constant, A, is usually regarded as a quantum 

 of action, for it has the dimensions of energy multiplied by 

 time. The quantum theory demands spasmodic interchanges 

 of energy of amount hv, where v is a frequency. The 

 original suggestion that the atomicity required by the theory 

 was an atomicity of energy is no longer supported. "It is 

 more natural to suppose that the real atomicity, if it exists, 

 is that of the entity measured by A, or by some function of h 

 and constants of nature " *, Nicholson f, in his work on the 

 spectra of the solar corona, introduced the idea that /i/2tt 

 represents a quantum of angular momentum, and Bohr, in 

 his theory of spectral series, assigned this amount of angular 

 momentum to a "bound" electron. S. B. McLaren J 

 identified this natural unit of angular momentum with that 

 of the magneton. In a previous paper I have given a proof 

 of McLaren's theorem, according to which the angular 



* Jeans, Physical Society "Report on Radiation and the Quantum 

 Theory," p. 79 (1914). 



t Nicholson. Monthly Notices R. A. S., June 1912. 



t McLaren,' Phil. Mag. vol. xxvi. p. 800 (1913) ; < Nature,' vol. xcii. 

 p. 165 (1913). 



