THE EQUILIBRIUM OF FLUIDS. 



and entire function of x', y, z the rectangular co-ordinates of 

 the element dv, and therefore the density in question will 

 admit of being expanded in a series of the entire powers of 

 x, y, z and the various products of these powers. Hence 

 (Art. 1) V t i] admits of a similar expansion in entire powers &c. 

 of x, y, z the rectangular co-ordinates of the point p, and by 

 following the methods before exposed Art. 1 and 2, we readily 

 get 



2.4.6... 



and thence we have ultimately, 



<? 



2.4... It 



^ y . ... + 2-^ w-2.w...w + 2^- 



n 2.4... 



1 . n + 1 . . . n + 2i + 2*' - 3 



the finite integrals being taken from t' = to t' oo and T being 

 the characteristic of the well known function Gamma, which is 

 introduced when we effect the integrations relative to r by means 

 of the formula (3), Art. 1. 



Having thus V t (i) or the part of V corresponding to the term 

 // (0 , in /(#', y' 9 z) we immediately deduce the complete value 



10 



