﻿Magnetic Field of an Atom. 41 



in spectral series. Nicholson* has been successful in calcu- 

 lating the frequencies of the lines in the nebular and coronal 

 spectra by employing Rutherford's model involving only 

 electrostatic forces. In these cases, however, only a simple 

 nucleus is dealt with. The theory put forward by Bohrj is 

 confessedly not dependent on the usual dynamical laws, 

 although it involves the calculation by ordinary mechanics 

 of the steady motion of the electron in the electrostatic field 

 of the positive nucleus. All the relations that have been 

 obtained between the lines in a spectrum involve the 

 frequency of the vibration. Lord RayleighJ has pointed 

 out that in the case of vibrations under electric or elastic 

 forces it is the square of the frequency that is involved. If, 

 however, the vibrations take place under the action of mag- 

 Detic forces, the acceleration, instead of being proportional 

 to the displacement, is proportional to the velocity of the 

 moving electrified particle, and relations involving the 

 frequency of the vibration may be obtained. A theory 

 based on this consideration has been put forward by Ritz § . 

 He assumes the existence of molecular magnets, and sup- 

 poses that the electron is describing a circular orbit in a 

 fixed plane perpendicular to the axis of the magnet. The 

 elementary magnets are the same for all elements. To get 

 the different lines of a series he supposes that a number of 

 the elementary magnets are placed end to end, so that the 

 magnetic field is due to two poles whose distance apart is 

 always some multiple of the length of the elementary magnet. 

 It is a characteristic feature of the theory of Ritz that every 

 spectral line is brought about by the difference of two 

 actions. 



Empirical Formulce for Spectral Series || . 



It will be convenient to summarize here the empirical 

 formulse that have been suggested to represent the distribu- 

 tion of the lines in a spectral series. 



If N denote the wave number (i. e. the number of wave- 

 in 1 cm.) Balmer's series for hydrogen may be written 



»-».a-») 



where N is Rydberg's " universal" constant (usually taken 

 as 109675) and m is a positive integer, 3, I, 5 ... . 



* Nicholson, Monthly Notices 11. A. S., 1912-1914. 

 t Bohr, Phil. Mag. xxvi. pp. 1, 476 (1913). 

 X llayleigh, Phil. Mag. xliv. p. oo$ (1897). 

 § Ritz, Ann. der Physik, xxv. p. 660 (1908). 

 || See Daly's ' Spectroscopy/ Chapter xvii., 1912, 



