152 THE LAWS OF 



whole of the electrical actions exerted upon any pointy, situated 

 at will* in the interior of the conducting bodies may exactly 

 destroy each other, and consequently p have no tendency to 

 move in any direction. For the electric fluid itself, the ex- 

 ponent n is equal to 2, and the resulting value of p is always 

 such as not to require that a complete decomposition should take 

 place in the body under consideration, but there are certain 

 values of n for which the resulting values of p will render fpdv 

 greater than any assignable quantity ; for some portions of the 

 body it is therefore evident that how great soever the quantity 

 of the fluid or fluids may be, which in a natural state this body 

 is supposed to possess, it will then become impossible strictly 

 to realize the analytical value of p, and therefore some modifi- 

 cation at least will be rendered necessary, by the limit fixed to 

 the quantity of fluid or fluids originally contained in the body, 

 and as Dufay's hypothesis appears the more natural of the two, 

 we shall keep this principally in view, when in what follows it 

 may become requisite to introduce either. 



7. The foregoing general observations being premised, we 

 will proceed in the present article to determine mathematically 

 the law of the density p, when the equilibrium has established 

 itself in the interior of a conducting sphere A , supposing it free 

 from the actions of exterior bodies, and that the particles of fluid 

 contained therein repel each other with forces which vary in- 

 versely as the 7i th power of the distance. For this purpose it 

 may be remarked, that the formula (1), Art. 1, immediately 

 gives the values of the forces acting on any particle p, in virtue 

 of the repulsion exerted by the whole of the fluid contained in 

 A. In this way we get 



1 dV 



I __ . -7 = the force directed parallel to the axis X, 



I 



_ n ~j~ the force directed parallel to the axis Y, 



1 dV 



_ n ~j- the force directed parallel to the axis Z. 



