138 
MR. A. E. OXLEY ON THE INFLUENCE OF MOLECULAR 
In addition to the forces due to external sources acting on the electrons contained 
in a given molecule, there will be internal forces having components X, Y, Z, which 
are determined by the configuration of the molecule. If the origin move with 
velocity (u, v, iv) the velocity of any electron will be ( u+x , v + y, w + z), and Langevin 
writes the equations of motion in the form 
mg = X + eEj + eH, (v + y) — eH y ( w +2) —rad—mu 
my = Y + eE y + eHj (w+z)—eH 2 (u+x) — mb—mv 
where E and H are the electric force and magnetic force and on is the mass of an 
electron. 
If we wish to take into account the forces due to neighbouring molecules, when 
crystallization takes place, we must add the term e/(P) to these equations. Now, in 
a crystalline structure, the motion of a molecule will consist of oscillations about a 
centre, and, therefore, if we take a mean value of this polarisation term and add it to 
the equations (4) we shall include the effect of the presence of neighbouring molecules. 
Assuming that the medium is isotropic (which is permissible since the crystals will 
have all kinds of orientations, and we are seeking the effect of close approach of the 
molecules only and not any particular property in a specified direction) the new 
equations are 
mg — X + e[E z + /(P x )] +eS. z (v + y) — eH y (w+z) — md—mu 
my = Y + e [E + f (P )] + eH, (w + z) — eH, (u + x) —mb—mv_ 
(4)' 
On account of the small dimensions of the elementary system considered, the 
electric force E and the electric polarisation term f (P) will be nearly constant 
throughout its extent, so that denoting the value of E and ,/(?) at the centre of the 
elementary system by E 0 and f (P 0 ), we have, expanding and neglecting higher powers 
than the first, 
E 2 = E 0J + x 
0E, 
dx /o 
+y{ 
/.se; 
and 
V dy 
+ z 
f(P,)=f(PJ+X 
MM 
dx 
+y 
~ d/(PJ 
. 3 y ^ 
aE 
02 
+ 2 
m pj 
02 
(5) 
Calculating from (3), (4)', and (5), and using the relations given on p. 137 for an 
isotropic medium, we find (writing = 2(' 2 = A/2) 
M, = 
A 
4 m 
— A jw 
3E, 
dx 
0H, 
dx 
+v 
0E, 
dy /o 
0H 
dy 
+ iv A 
0H 
dx /o 
dA 
H °' at 
a FMD'i _ /MM) 
IV 3x A \ dy 
