154 THE LAWS OP 



w-2 



sin 



Hence, when Q, the quantity of redundant fluid originally in- 

 troduced into the sphere is given, the values of Fand of the 

 density p are likewise given. In fact, by writing in the pre- 

 ceding equation for 



, . fn-2 \ 

 and sin f - ?rk 



their values, we thence immediately deduce 



and F=-- a - Q. 



VTT 



The foregoing formulae present no difficulties where n > 2, 

 but when n < 2, the value of p, if extended to the surface of the 

 sphere A, would require an infinite quantity of fluid of one name 

 to have been originally introduced into its interior, and there- 

 fore, agreeably to a preceding observation, could not be strictly 

 realized. In order then to determine the modification which in 

 this case ought to be introduced, let us in the first place make 

 n > 2, and conceive an inner sphere B whose radius is a $a, 

 in which the density of the fluid is still defined by the first of 

 the equations (12) ; then, supposing afterwards the rest of the 

 fluid in the exterior shell to be considered on JL.'s surface, the 

 portion so condensed, if we neglect quantities of the order 8a, 

 compared with those retained, will be 



O / 2 n ~* 



^ " 5 " 



n 



2 



