DETERMINATION OF THE FICTIVE LAYER. 651 



by the surface S' of a sphere of radius r', which is very small, having 

 its centre at the point in question. Equation (6) is exact on con- 

 dition that the integral of the second member is extended to the 

 surfaces S and S'. 



In this case, the second member contains implicitly the term 

 47rVp ; for the surface S' we have dn = - dr , dS = r' 2 du, dw being 

 the angle at the centre which corresponds to the surface d?S', and 



r ^r riw f _ , pv r r 



J to ~]r^n d r } V ( J 



When the radius r' becomes null, the first term of the second member 

 tends towards zero, and the second towards 47rVp. Equation (6) 

 reduces then to 



i 



(7) 



This condition being independent of the position of the point P, 

 it follows that the two quantities V and are a function of the 

 other ; the external field of the masses comprised within a surface S 

 is then defined if we know the potential on the surface, or the 

 perpendicular differential of the potential that is to say, the per- 

 pendicular component of the force on an indefinitely near point. 



If S is the surface of a sphere of radius R, and we take the 

 point P' at the centre, we have 



i c)V i C <)V Q 47rM 



r to Rj to R R 



Q denoting the total flow of force from the sphere, and M the sum 

 of the acting masses which it contains ; further 



fv </s= - I ws. 



to R*J 



