223 
1918-19.] An Electron-Transference Hypothesis, etc. 
electrons ; s will therefore measure the electro-positive valency of atom 1 
and the electro-negative valency of atom 2. 
The total polarisation due to the displacement of the electrons of the 
two atoms is now equal to the sum of the polarisations due to each 
separately. 
For convenience in our analysis we shall suppose that the electrical 
force due to the incident electro-magnetic waves has components (X, O, 0 ), 
and that we are discussing the steady state of the atoms in the field, when 
the doublets to which they are electrically equivalent have their axes in 
the direction of the x axis. 
The main forced vibration of the negative electrons will therefore be 
in the x direction, and we shall neglect the contribution of all vibrations 
not in the direction of the axis of x. 
Our equations of motion can now be written — 
2-01 
Mjx, = XK, - , W , - £,) - <^> 1 (D)(x 1 - x 2 ), 
2-02 
2-03 
2-04 
m 
4 ^ 
M^2^2 = XF2 — -Trp.fc (x 9 — 3 r ) (fi , — x 2 ), 
6 1 
Mi ^ Ml Ml 
— X/xy — (£r ~ **i) 4* ~ % 2) ( £ > 2l(^r)) 
m 
M2 4 M2 Ma 
£ r — — " »7rp 9 e (£ r ~ ^ 9 ) 4- (£ r ~ **'i)Ai2(-^ r)j 
2-05 
2-06 
X' = X 
1 
where X = X + X', 
X' being the force due to polarisation of medium arising from displacement 
of the electrons. 
x x and x 2 = Displacements in x direction of centres of spheres of 
positive electrification. 
— 0 1 (D)(^ 1 — cc 2 ) = Force on positive electrification of 1st atom, due to 
electrical nature of 2nd atom in its vicinity. 
£ r and f ' r == Displacements in x direction of the r th electrons of the 
respective atoms. 
02i(D r X£r-®a) = Force on r th electron of 1st atom, due to electrical nature 
of 2nd atom. 
D r = Distance between centre of 2 nd atom and r th electron 
of 1st, 
and so on. 
