Definite Integrals, with Physical Applications. 357 



When a sphere, already electrised, is subjected to the influence 

 of an electrical point without it, the law of accumulation is simple ; 

 for the quantity of fluid which must be superposed to that already 

 accumulated on each annulus, to make it every where equal to 

 a certain constant, is always inversely proportional to the cube 

 of the distance from the influencing point*. 



As the application to the theory of developed electricity, offered 

 a sufficient illustration to the principles of this part; at the same 

 time that it conducted to new and remarkable results, it seemed 

 unnecessary, considering the convenient limits of this paper, to 

 insert other jmysical applications which I have made, particularly 

 on the subjects of heat and magnetism. 



* The electrical action in the third Section, is measured by the tension of the fluid 

 which would be produced in an infinitely thin rod, communicating with the electrical 

 body, by the attraction or repulsion of the latter; it is what Mr Green, of Nottingham, 

 in his ingenious Essay on this subject, has denominated the Potential Function. 



ZZ 2 



