﻿718 Dr. H. Stanley Allen on an 



angular momentum with the angular momentum of the 



magneton. According to Bohr's theory * the angular 



momentum of a " bound " electron is constant and is hj2it. 



Conway f 7 using a different model, obtains the value Ji/tt. 



Let us suppose that an electron (charge e, mass m) is moving 



in a circular orbit (radius a) with angular velocity co. 



Then its angular momentum is ma 2 co, and the magnetic 



moment of the equivalent simple magnet is \ea?w. Thus the 



magnetic moment is equal to some constant multiplied by 



Jie/m. Taking the angular momentum as h/2ir, we obtain 



h e 



=92'7xl0~ 22 b.m.u. as the value of the magnetic 



A-n-m ° 



moment. This is exactly 5 times the magnetic moment of 



the magneton of Weiss. This numerical relation was first 



pointed out by Mr. Chalmers % at the discussion on Radiation 



at the Birmingham meeting of the British Association. 



The magnetic moment of the magneton is found by dividing 



the magnetic moment of the atom gram 1123*5 by Avogadro's 



constant. Weiss used the value of this constant found by 



Perrin, but if we take the more recent value given by 



Millikan (60'62 x 10 22 ) we obtain as the magnetic moment 



of the magneton 18'54x 10~ 22 , which is exactly 1/5 of the 



number given above. 



These commensurable numbers may be of significance in 



connexion with the structure of the atom. The magneton 



may arise as a difference effect. The way in which this may 



come about may be illustrated by a simple model. Suppose 



we have a uniform sphere of positive electrification of 



radius A rotating in the same sense as an electron with 



angular velocity XI. Outside this, suppose we have a single 



rino- of mean radius a containing n electrons. The remaining- 



negative electrification required to produce a neutral system 



may be supposed concentrated at the centre without rotation. 



Then the magnetic moment of the rotating sphere § may be 



* Bohr, Phil. Mag. vol. xxvi. p. 1, p. 476 (1913). 

 t Conway, Phil. Mag. vol. xxvi. p. 1010 (1913). 



X See < Nature/ vol. xcii. pp. 630, 687, 713 (1914). The same relation 

 was noticed independently by Dr. Bohr (Richardson, ' The Electron 

 Theory of Matter,' p. 395). 



§ This is a particular case of a more general theorem. Since the 

 magnetic moment arising from a charge e moving in a circular orbit of 

 radius a with angular velocity o> is ^earw, the magnetic moment arising* 

 from a volume distribution of electricity rotating about an axis is 

 £2pdvr 2 Q, where p is the electrical density and dv an element of volume. 

 Assuming p constant, the magnetic moment 



= ±p£l2)- 2 dv 

 = fpOVA- 2 

 = ±~Ek 2 Q, 



