Mr GREEN, ON THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 51 



general equation of equilibrium ; and as this constant is arbitrary, it is 

 evident that the equilibrium will not be at all affected by the change 

 in question. Moreover, it may be observed, that in general the additive 

 term is necessary to enable us to assign the proper value of p, when 

 Q, the quantity of redundant fluid originally introduced into the sphere, 

 is given. 



In the foregoing expressions the radius of the sphere has been taken 

 as the unit of space, but it is very easy thence to deduce formula^ 



adapted to any other unit, by recollecting that —, -p, j^ and y^^, 



are quantities of the dimensions 0, — 1, — 1 and S — n respectively with 

 regard to space: for if h represents the sphere's radius, when we employ 



any other unit we shall only have to write, t> j, -j- > -jr- and j- in the 



place of r, r, R, dvi and a, and afterwards to multiply the resulting 

 expressions by such powers of h, as will reduce each of them to their 

 proper dimensions. 



If we here take the formula (22) of the present article as an example, 

 there will result, 



• / W-Q ^ 4-n 



(23).... p= 1-|_-I(i"-/^)^ fp,dv^-^-^, 



for the value of the density which would be induced in a sphere A, 

 whose radius is b, by the action of any exterior bodies whatever. 



When w > 2, the value of p or of the density of the free fluid here 

 given offers no difficulties, but if » < 2, we shaU not be able strictly to 

 realize it, for reasons before assigned (Art. 6. and 7.) If however n 

 is positive, and we adopt the hypothesis of two fluids, supposing that 

 the quantities of each contained by bodies in a natural state are ex- 

 ceedingly great, we shall easily perceive by proceeding as in the last 

 of the articles here cited, that the density given by the formula (23) 

 will be sensibly correct except in the immediate vicinity of A's surface, 

 provided we extend it to the surface of a sphere whose radius is 

 h—^b only, and afterwards conceive the exterior shell entirely deprived 

 of fluid: the surface of the conducting sphere itself having such a 



G 2 



