president's address — SECTION A. 35 



conductors charged with electricity positive or negative. The 

 potential at any point being denoted by V, the electric dis- 

 placement by D) the specific inductive capacity by K, we 



. ^ K f/V ^ „ . . 

 have always the equation D = t — • t — , where K, as in the 



heat problem, is usually independent of direction. The value 

 of D at any point of the boundaries of the body is otherwise 

 spoken of as the surface density of electricity at that point. 

 The data of the problem are : — 



(1.) The value of K in all parts of the body. 



(2.) The value at every point ot the boundaries of either 



d y 



y or K -^5 — : if, however, over any bounding 



surface V is constant, it is enough to know this 



, dV 

 value of V, or the surface integral of K -5— 



° du 



over the surface. 



Further, we have the conditions that y" ^^ = ^? and that 

 at any surface separating from one another portions of the 

 body of different specific inductive capacities, 



^.ly + ^. i^ = 0. 



47r du Air dwz 



The problem is then exactly the same as the former one, 

 and the results and diagrams spoken of before admit of anew 

 interpretation. Sources or sinks of heat become positively or 

 negatively charged bodies. Lines of flow of heat become 

 tubes of flux of electric displacement. One end of each tube 

 is on a conductor, the other end at infinity, or on another con- 

 ductor. In any case the charges at the ends of a tube are 

 equal and opposite, and so on. I need not enumerate any 

 more of the details of the analogy. It is interesting to notice 

 that one theory involves the idea of time, the other does not. 



Of course it is not usual to found the theory of electrostatics 

 on these data. It is usual to start, as Maxwell did, with the 

 law of attraction between electrified particles. The develop- 

 ment of the theory from this law leads naturally to the ex- 

 pressions involving potential and displacement or density. 

 Then the student is suddenly aware that he is using mathe- 

 matical expressions, which would have been obtained at once 

 from the consideration of a continuous action taking place in 

 the dielectric, instead of being the result ofa lengthy develop- 

 ment from the theory of action at a distance. 



