THE EQUILIBRIUM OF FLUIDS. 163 



The last of these expressions may readily be exhibited under 

 a finite form, by remarking that 



- ( ' 



"' 2.4.6 ...... 27~ ' a 2 ' 



-2 r* V 2 



l\ /4-n\ 

 J \ 2 J 



<0 2. 4 . 6 25 'a 2 ' 



2 



rfl ~ "4. 5 . 6 ... 25+3 



Hence, since T () = VTT? the value of the repulsion arising 

 from J.'s surface becomes 



Now by adding the repulsion due to the inner sphere which 

 is given by the formula (16), we obtain, (since it is evidently 

 indifferent what variable enters into a definite integral, provided 

 each of its limits remain unchanged) 



4-7T 



112 



