﻿Hydrogen and the Structure of the Atom. 333 



The application of the quantum theory in the calculation 

 of the effect of a magnetic field affords a very intricate 

 problem, since there are several possible ways of applying 

 the theory and each of them leads to different results. 

 The only guide on this question seems to be experiments on 

 the Zeeman effect. In the first place, it might be argued as 

 a serious objection against the method of calculation applied 

 by Dr. Allen, that an analogous calculation in the ease of a 

 homogeneous magnetic field does not give results in agree- 

 ment with measurements of the Zeeman effect. I shall not, 

 however, try here to discuss this difficult and unsolved 

 problem *, but will only consider the way in which the 

 formulae obtained in the first paper are applied in the second 

 paper to the hydrogen spectrum. In this application new 

 assumptions are involved, one of which seems hardly con- 

 sistent with the main principles of the theory. Accordino- 

 to Dr. Allen's calculations, the presence of a nuclear magnet 

 leads to a splitting up of the lines in components situated 

 symmetrically with respect to the original lines, at anv rate 

 if the square of the magnetic force is neglected. This 

 result, in itself, will not explain Mr. Curtis's observation, 

 which consists in a small systematical deviation of the 

 " centre of gravity " of the hydrogen lines from the position 

 calculated by the Balmer lawf. In comparing the theory 

 with experiments, Dr. Allen now uses only one of the two- 

 components calculated. For this, apparently, no explanation 

 is offered ; it might, however, be justified by assuming that 

 the nucleus, on account of its small moment oE inertia, will 

 always take a position such that its magnetic axes will 

 coincide with the direction of the magnetic force due to 

 the rotating electron. In order to obtain an expression for 

 the frequency of the same type as the empirical formula? 

 by which Mr. Curtis has represented his results, Dr. Allen 

 next assumes that the correction in one of the terms of his 

 formula can be neglected. This assumption amounts to the 

 neglect of the correction due to the nuclear magnet in one of 

 the " stationary states " of the atom. It seems very difficult 

 to see how this assumption can be justified ; for if the nucleus 

 is assumed to be a small magnet, it would appear neeessarv 

 to have the same magnetic properties for all the states of the 

 atom. According to the theory, these states differ only in 

 the size of the orbit of the rotating electron. It' the correction 



* In the special case of a homogeneous magnetic field the problem in 

 question is considered in some detail by K. Herzfeld (P/ii/s. Zeitschr. w.. 

 p. 193, 1914) and by the present writer (Phil. Mac:, xxvii. p. 506, 1914) 



t W. E. Curtis, Proc. Roy. Soc, A. xc. p. 614 (1914). 



