On Potentials and their Application. 157 



The only interpretation Green gives to this Function is 

 that which Laplace had ah'eady given, viz. : that it is a 

 quantity such that its partial differential, with respect to 

 any co-ordinate x of a point p, will give the attraction 

 due to the mass along any line chosen for the co-ordinate 

 axis X ; that, letting x', y', z' be the rectangular co-ordi- 

 nates of a particle of any attracting or repelling mass, p' 

 its density, dx', dy', dz' its sides regarded as an elementary 

 jKirallelopipedon, r' the distance of this element of mass 

 from an attracted point p exterior to the body, then 

 Y = Potential Function of the whole mass at the point p 



_ r p^ dx' dy' dz' 



The integral comprehending every particle (or elementary 

 mass) in the entire mass. 



Green's own words, in beginning his essay on Electri- 

 city, are : '■^It is well hriown, that nearly all the attractive 

 and repulsive forces existing in nature are such, that if we 

 consider any material point p, the effect, in a given direc- 

 tion, of all the forces acting upon that point, arising from 

 any system of bodies S under consideration, will be ex- 

 pressed by a partial differential of a certain function 

 [the Potential] of the co-ordinates which serve to define 

 the point's position in space. The consideration of this 

 function is of great importance in many inquiries, and 

 probably there are none in which its utility is more 

 marked than in those about to engage our attention. In 

 the sequel we shall often have occasion to speak of this 

 function, and will, therefore, for ahridgmejit, call it the 

 Potential Function arishig from the system S. If p 5(3 « 

 particle of positive electricity under the influence of 

 forces arising from any electrified' body, the function in 

 question, as is well hioivn, will be obtained by dividing 

 the quantity of electricity in each element of the body, by 

 its distance from the particle p, and taking the total sum 



