170 THE LAWS OF 



we shall obtain 



f n 2 

 Bin 



H 2^ ^ 2 ~ 1 ) 2 ( 1 ~ /2 ) * j'^ 3 > 



the integral relative to dor being extended over the whole sphe- 

 rical surface. 



Lastly, if p l represents the density of the reducing fluid dis- 

 seminated over the space exterior to A, it is clear that we shall 

 get the corresponding value of p by changing P into p^da in the 

 preceding expression, and then integrating the whole relative 

 to a. Thus, 



But do-da = dv l ; dv l being an element of the volume of the 

 exterior space, and therefore we ultimately get 



where the last integral is supposed to extend over all the space 

 exterior to the sphere and R to represent the distance between 

 the two elements dv and dv^ 



It is easy to perceive from what has before been shown 

 (Art. 7), that we may add to any of the preceding values of p, 

 a term of the form 



h being an arbitrary constant quantity: for it is clear from the 

 article just cited, that the only alteration which such an addition 

 could produce would be to change the value of the constant on 

 the left side of the 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. 



