1899-1900.] Lord Kelvin on the Motion in an Elastic Solid. 219 
distance PQ. The whole force exerted by the atom on the portion 
pB of the ether at Q, is the resultant of all the forces calculated 
according to (1), for all the infinitesimal portions A into which we 
imagine the whole volume of the atom to be divided. 
§ 3. According to the doctrine of the potential in the well- 
known mathematical theory of attraction, we find rectangular 
components of this resultant as follows : — 
X - pB J-<A(z, y, z ) ; Y - pB y, *) ; 
d 
Z = pB lz^ X ’ y ’ Z ^ j 
• • ( 2 ), 
where x, y, z denote co-ordinates of Q referred to lines fixed 
with reference to the atom, and </> denotes a function (which we 
call the potential at Q due to the atom) found by summation as 
follows : — 
drf(P , r) (3), 
where fff A denotes integration throughout the volume of the 
atom. 
§ 4. The notation of (1) has been introduced to signify that no 
limitation as to admissible law of force is essential; but no 
generality that seems to me at present practically desirable, is lost 
if we assume, henceforth, that it is the Newtonian law of the 
inverse square of the distance. This makes 
and therefore 
• ( 4 ), 
• ( 5 ). 
where a is a coefficient specifying for the point, P, of the atom, 
the intensity of its attractive quality for ether. Using (5) in (3) 
we find 
( 6 ). 
and the components of the resultant force are still expressed by 
(2). We may suppose a to be either positive or negative (positive 
for attraction and negative for repulsion); and in fact in our first 
