191 1.] WILSON— CONSTITUTION OF THE ATOM. 369 



addition of one more ring of electrons together with the additional 

 amount of positive electricity required to keep the atom neutral. 

 Sir J. J. Thomson has shown that many of the facts connected with 

 Mendeleeff's periodic law can be explained on this theory. 



In the atoms of course the electrons are not really confined to 

 one plane but are distributed throughout the volume of the positive 

 sphere, so that instead of concentric rings of electrons there are 

 concentric spherical layers. An atom of bromine is therefore de- 

 rived from an atom of chlorine by the addition of one more layer, 

 the inner layers remaining unchanged. 



Although the exact solution of the problem of the distribution of 

 n electrons inside a positive sphere is too complicated to be worked 

 out I find that an approximate solution can be obtained without 

 much difficulty, which enables the results of the theory to be com- 

 pared with the atomic weights of the elements. 



Consider an electron having a negative charge c inside a sphere 

 of positive electricity of uniform density of charge p per c.c. Close 

 to the electron the electric field is of strength e/r-, where r is the 

 distance from the electron, so that ^irc tubes of electric force come 

 out of the electron, if the number of tubes per sq. cm. is taken to 

 be equal to the field strength. Consider one of these tubes of force 

 and let ds be an element of its length and a its cross section at ds. 

 The charge in the length ds is pads, so that 



Fa — lFa-\- -. iyFa)ds j = ^irp'X'/s, 



where F is the electric force along ds. Hence 



— d(Fa) = ^irpads , 

 which gives 



FjCZi — Fa^ 4Trpfa.ds. 



where F^cti denotes the value of Fa. at the surface of the electron. 

 This shows that as we go along the tube Fa diminishes and when 

 Fj^ai^4-n-pfads it will be zero and the tube will end. Xow F^ = 

 c/o-, where a is the radius of the electron and a^^^a'/e, so that 

 Fiai = i, hence ^irpfads from the surface of the electron to the 

 end of the tube is equal to unity. Thus the positive charge in each 



PROC. AMER. PHIL. SOC, L. 200 X, PRINTED AUG. 4, Igll. 



