APPENDIX. 



Note to Art. 6, p. 36. 



THE important theorem of reciprocity, established in Art. 6, 

 may be put in a clearer light by the following demonstration, 

 which is due to Professor Maxwell. 



Let A, B be any two points on a closed conducting surface, 

 and let a unit of positive electricity be placed at a point Q, 

 within the surface, then a unit of negative electricity will be so 

 distributed over the surface that there will be no electrical 

 force outside the surface, and the potential outside it will be 

 everywhere zero. The potential at any point P within the 

 surface, due to the electricity on the surface, is a function of 

 the positions of P, Q, and of the form of the surface. 



Denoting this by G it is required to shew that #/>= G*\ 

 or that the potential at P, due to the distribution on the surface 

 caused by a unit of positive electricity at Q, is equal to the 

 potential at Q, due to the distribution on the surface caused by 

 a unit of positive electricity at P. 



Let X be any point outside the surface. The potential there 

 is zero, hence 



..................... (i), 



where p A is the density and dS A the element of surface, at any 

 point A of the surface, and the integration is extended over the 

 whole surface. 



Also, by definition, 



ey .................... (2). 



