211 
1918-19.] An Electron-Transference Hypothesis, etc. 
cation throughout which are distributed negative electrons in positions of 
equilibrium, we may quote the well-known result : 
1-01 . . . . X'»|irN^Ea!-2«fr). 
with similar equations for Y' and Z' 
where N = number of atoms in 1 c.c. of substance. 
Ti — number of electrons in the atom when it is neutral. 
jUL = n — s. 
E = ne = magnitude of positive electrification. 
The equations of motion for the positive electrification and the negative 
electrons we take to be 
1-02 . . . . M* = (X + X')E-|7rpe2(*-4), 
1-03 
-(X + X')2e + f 
where M = mass of positive electrification. 
m = mass of a negative electron. 
Equations T02 and 1*03 implicitly determine the type of action which 
we are assuming to take place within the atom. 
Sir J. J. Thomson and H. A. Lorentz have assumed that the elastic 
force tending to restore a displaced electron to its position of equilibrium is 
proportional to its relative displacement. 
4 
This constant of proportionality is - 7 rpe in the case of a sphere of 
O 
uniform positive electrification, and is used in Sir J. J. Thomson’s paper in 
Phil. Mag., 1906, to establish the refractive index of a collection of atoms. 
Let 
and 
X = X+X' 
If the frequency of the electro-magnetic waves incident on the atoms is 
P, equation 1*02 and L03 become 
1-04 . . . . -Mp 2 aj = XE- #2 (*“&), 
1 
-mp 2 2,£ = |X/*e + <2(*-&)- 
1 1 
1-05 
