THE EQUILIBRIUM OF FLUIDS. 159 



But it is evident from the form of these equations, that we may 

 satisfy the whole system by making 



provided we determine B Q by 



2-n _ 2 2-n.^-n 

 2 2 . 4 ' 



n-2 



Hence as in the present case, /3 = , we immediately de- 



Si 



duce the successive values 



and =l- 



In the value of p just exhibited, the radius of the sphere is 

 taken as the unit of space, but the same formula may easily be 



adapted to any other unit by writing j- and -= in the place of 



a and r' respectively, and recollecting at the same time that in 

 consequence of the equation 



, [dv.p f 

 const. = V+ V - ^-f I 



J 9 J 9 



before given, -^> , is a quantity of the dimension 1 with regard 



to space : b being the number which represents the radius of the 

 sphere when we employ the new unit. Hence we obtain for a 

 sphere whose radius is bg, acted upon by an exterior concentric 

 spherical surface of which the radius is a, 



