Mh green, on the laws of the equilibrium of fluids. 37 



-)„=. 





If now when w is supposed less than 2, we adopt an hypothesis 

 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 Sa, so that the whole of the fluid of 

 contrary name to Q, may be contained in the inner sphere S, the 

 density in every part of it being determined by the first of the equa- 

 tions (12). If afterwards the whole of the fluid of the same name as 

 Q is condensed upon A's svirface, the value of V in the interior of S 

 as before determined will evidently be constant, provided we neglect 



n 



indefinitely small quantities of the order ht'\ Hence all the fluid con- 

 tained in J3 will be in equilibrium, and as the shell included between 

 the two concentric spheres, A and S is entirely void of fluid, it follows 

 that the whole system must be in equilibrium. 



From what has preceded, we see that the first of the formulae (12) 

 which served to give the density p within the sphere A when n is 

 greater than 2, is still sensibly correct when n represents 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 approxi- 

 mative, and supposes the quantities of the two fluids which originally 

 neutralized each other to be exceedingly great, we shall in the follow- 

 ing article endeavour to exhibit a rigorous solution of the problem, 

 in case w < 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 contained, may be in equi- 

 librium in virtue of the joint action of that contained in the sphere 

 itself, and on the exterior spherical surface. "• 



