Mi GREEN. ON THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 35 



which represents the radius of the sphere when we employ the new 

 unit. In this way we obtain 



P = — V4 — - r{a'-r")~, and Q = lii — ; . V. 



Hence, when Q, the quantity of redundant flviid originally introduced 

 into the sphere is given, the values of V and of the density p are like- 

 wise given. In fact, by writing in the preceding equation for 



ry, and sin(^7r), 



their values, we thence immediately deduce 



and F= ^ ' ■ ' a'-.Q. 



\/7r 



The foregoing formulae present no difficulties where « > 2, but when 

 H < 2, the value of p, if extended to the surface of the sphere Jl, would 

 require an infinite quantity of fluid of one name to have been origi- 

 nally introduced into its interior, and therefore, 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 S, whose 

 radius is a — Sa, 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 ^'s surface, the portion 

 so condensed, if we neglect quantities of the order Sa, compared with those 

 retained, will be 



-- r f^±i) 



2* V 2 / ^, 



' V2/ 



E 2 



(1) 



QJa 



2 



