﻿Magnetic Field of an Atom. 43 



Ritz * has obtained remarkable agreement between the 

 observed and the calculated results by taking 



/8 



D = m + fji -}- film 2 or D = m -f fi + 



(m + ^) 2 



Several investigators have made use of the form suo-gested 

 bv Moooe nc jorf and Hicks, in which 



-- 



D = m-\-fji -\- a/m. 



The value of the expression N /D 2 for integral values of 

 m has been called a sequence. Four sequences exist, and it 

 has been shown by Hicks, van Lohuizen t, and others that the 

 majority of the lines in spectral series can be determined by 

 the difference between two sequences. 



The Magnetic Field of the Atom in the Quantum 

 Theory of Spectral Series. 



In a letter to 'Nature' (vol. xcii. p. 630, 1914) I have 

 drawn attention to the important work of Professor Carl 

 Stunner on the path of an electron in the magnetic field of 

 an elementary magnet. He has investigated the motion of 

 an electron when it is subject to the action of a central force 

 varying inversely as the square of the distance from the 

 centre of the magnet. Such a case would arise if the atom 

 consisted of a magnetic core, electrically charged and sur- 

 rounded by one or more electrons. St^rmer finds certain 

 remarkable periodic trajectories in the form of a circle whose 

 plane is perpendicular to the axis of the magnet, and whose 

 centre is at some point on that axis. If this point coincide 

 with the centre of the magnet we obtain circular orbits in 

 the equatorial plane of the magnet. Further there are other 

 trajectories which never get outside closed toroidal spaces, 

 in the case of stability, or which approach asymptotically 

 the circle in question in the case of instability. 



Let the magnetic moment of the core, considered as an 

 elementary magnet, be M and its positive charge be E, 

 electrostatic units being employed throughout. The equation 

 of motion of an electron (charge e, mass m) moving, with 

 angular velocity w, in a circular orbit of radius r in the 

 equatorial plane is 



mr 3 (o 2 = Meeo-{-¥,e (1) 



It must be noticed that there are two possible directions 



* IWiz, Phjs. Zeitschr. vol. iv. p. 400 (1003): vol. ix. pp. 244,521 

 (1908). 



t van Lohuizen, Science Abstracts, vol. xvi. no. 1T9 (1913). 



