Section III., 1911. [47] TRANS: B.S: GC: 
The Number of Electrons in Atoms. 
By H. A. Witson, FRS; F.RSC: 
According to Sir J. J. Thomson’s theory atoms may be regarded 
as rigid spheres of positive electricity containing negative electrons. The 
total negative charge on the electrons in a neutral atom is equal to the 
positive charge of the sphere. The electrons are supposed to move 
about freely inside the positive sphere. The properties of the atoms 
of different elements are supposed to be determined by the number 
and arrangement of the electrons. 
The problem of the arrangement of n electrons inside a positive 
sphere is too complicated to be solved exactly, so Sir J. J. Thomson 
considered the simpler case in which the electrons are supposed con- 
fined to one plane. In this case the electrons arrange themselves in 
concentric rings. In the actual case of distribution throughout the 
sphere we should have concentric spherical layers instead of rings. 
Sir J. J. Thomson suggests that in a series of similar elements 
like hydrogen, lithium, sodium, potassium, rubidium, caesium, each 
element is formed from the one preceding it by the addition of another 
layer of electrons. 
The object of the present paper is to show that a simple approxi- 
mate solution of the distribution of the electrons inside the sphere 
can be obtained, which leads to results agreeing approximately with 
the atomic weights of the known series of similar elements and enables 
the number of electrons in the atoms to be easily calculated from the 
atomic weights. 
Consider an electron inside a positive sphere of uniform density 
of electrification o and let e denote the charge carried by the electron. 
Close to the electron the electric field strength is equal to e/r? where r 
is the distance from the electron. If we take the number of tubes of 
electric force per sq. cm. to be equal to the strength of the field it follows 
that 4re tubes start out from the electron. Each of these tubes of force 
will extend into the positive electricity so far as to include a positive 
charge equal to the negative charge from which the tube started. Thus 
each tube will occupy a volume 1/47 and all the 47e tubes a volume 
e/p. The field of the electron therefore occupies a volume e/p, which 
contains a positive charge equal to the negative charge on the electron. 
In a neutral atom, therefore the positive sphere will be divided up 
into as many equal volumes as there are electrons in it and each of 
these volumes will contain one of the electrons. The tubes of force 
