( 562 ) 
wave-length, and we shall suppose this to be a very small fraction. 
We shall also omit all terms containing such factors as 
r é r 
cos 2 nk or sin 2 dary (& a moderate number). These reverse 
their signs by a very small change in #; they will therefore disappear 
from the resultant force, as soon as, instead of single particles P 
and Q, we come to consider systems of particles with dimensions 
many times greater than the wave-length. 
From what has been said, we may deduce in the first Mass that, 
in applying the above Pine to the ion P, it is sufficient, to take 
for » and 6 the vectors that would exist if P were removed from 
the field. In each of these vectors two parts are to be distinguished. 
We shal} denote by >; and $; the parts existing independently of 
Q, and by 2 and Ps the parts due to the vibrations of this ion. 
Let Q be taken as origin of coordinates, QP as axis of 2, and 
Jet us begin with the terms in (2) having the coefficient a. 
To these corresponds a force on P, whose first component is 
dx 
bv? da (5 = hd y af, B) par bs — br 0) o> ee (5) 
Since we have only to deal with the mean values for a full 
period, we may write for the last term 
— a (dy Dr — bs Dy), 
and if, in this expression, Hy and 5: be replaced by 
ar) and sare (GED) 
(5) becomes 
2nV2ea 
0(d*) 
am May a ee eS 
where > is the numerical value of the dielectric displacement. 
Now, »? will consist of three parts, the first being 5°, the second 
Do? and the third depending on the combination of dj and ds. 
Evidently, the value of (6), corresponding to the first part, will 
be 0. 
As to the second part, it is to be remarked that the dielectric 
displacement, produced by Q, is a periodic function of the time. At 
; : c Ae 
distant points the amplitude takes the form —, where c is indepen- 
U hd 
