182 Lord Kelvin on the Motion of Ponderable Matter 



the atom acts on every infinitesimal volume B of the ether 

 with a force in the line PQ joining the centres of these two 

 volumes, equal to 



A/(P, PQ) P B (1), 



where p denotes the density of the ether at Q, and/(P, PQ) 

 denotes a quantity depending on the position of P and on the 

 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 rect- 

 angular components of this resultant as follows : — 



x = p B j x ^y- z) '> Y = p B jy < t > ( !v >y' z )'> I 



d 



> • (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 sum- 

 mation as follows : — 



^"i^jpQ^ 7 ^' 90 * • ' ' (3) ' 



where jjT 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 



/(P,PQ) = p^i (4), 



L drjiP ' r) =m (5) ' 



where a is a coefficient specifying for the point, P, of the 

 atom, the intensity of its attractive quality for ether. Using 



