50 Mr green, ON THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 

 If now we substitute this in the value of p before given, and after- 



// o ft^ __ >«'2 



wards write — and „3 in the place of their equivalents, 



dd"dnr" smO", andvV'^'^, 



clr R 



we shall obtain 



. (n-2 



p- i7^ — («^-i)^ (i-O^ /-^; 



the integral relative to da being extended over the whole spherical sur- 

 face. 



Lastly, if p^ represents the density of the reducing fluid disseminated 

 over the space exterior to A, it is clear that we shall get the corres- 

 ponding value of p by changing P into pida in the preceding expression, 

 and then integrating the whole relative to a. Thus, 



, = - !iy4 (i-..)=i^/a-«.)*-?/**£i. 



But dada = dvx\ dvi being an element of the volume of the exterior 

 space, and therefore we ultimately get 



fn — 2_ 



4— n 



. /n — 2\ 



(22) p= y5 -i^-r")'^ .fp^dv, ^ , 



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 

 Ave 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 



