156 THE LAWS OF 



If now when n is supposed less than 2, we adopt an hypo- 

 thesis similar to Dufay's, and conceive that the quantities of fluid 

 of opposite denominations in the interior of A are exceedingly 

 great when this body is in a natural state, then after having 

 introduced the quantity Q of redundant fluid, we may always by 

 means of the expression just given, determine the value of Ba t 

 so that the whole of the fluid of contrary name to , may be 

 contained in the inner sphere I?, the density in every part 

 of it being determined by the first of the equations (12). If 

 afterwards the whole of the fluid of the same name as Q is 

 condensed upon A's surface, the value of V in the interior of 

 B as before determined will evidently be constant, provided we 



n 



neglect indefinitely small quantities of the order Sa*. Hence all 

 the fluid contained in B will be in equilibrium, and as the shell 

 included between the two concentric spheres A and B is entirely 

 void of fluid, it follows that the whole system must be in equi- 

 librium. 



From what has preceded, we see that the first of the formulas 

 (12) which served to give the density p within the sphere A 

 when n is greater than 2, is still sensibly correct when n re- 

 presents any positive quantity less than 2, provided we do not 

 extend it to the immediate vicinity of A's surface. But as the 

 foregoing solution is only approximative, and supposes the 

 quantities of the two fluids which originally neutralized each 

 other to be exceedingly great, we shall in the following article 

 endeavour to exhibit a rigorous solution of the problem, in case 

 n > 2, which will be totally independent of this supposition. 



8. Let us here in the first place conceive a spherical surface 

 whose radius is a, covered with fluid of the uniform density P', 

 and suppose it is required to determine the value of the density 

 p in the interior of a concentric conducting sphere, the radius 

 of which is taken for the unit of space, so that the fluid therein 



