1 8 ON POTENTIAL. 



that is to say, that the total flow of force which starts from the surface 

 is equal to zero. 



If the acting mass m is within the closed surface S (Fig. 5), the 

 elements dS and ^S', cut by a cone of aperture d^ starting from the 

 mass m, always gives the ratio 



But in the present case, the perpendicular components f n and/' n 

 are of the same sign. We have thus for the whole surface, 



/ n d?S = w du = 



The flow of force which proceeds from a surface S, enclosing an 

 acting mass, is thereby equal to ^irm. In other words, we may say 

 that the total flow of force which issues from a mass m t in all 

 directions^ is equal to 



Fig. 6. 



It is clear that if each sheet of the cone meets the surface more 

 than once, it meets it an uneven number of times, for which the 

 values off n dS should be taken alternately of opposite signs, and the 

 final result is still the same. 



30. Let us now suppose that there are masses m, m', m", . . . com- 

 prised within the surface S (Fig. 6), and other masses m v m^ m 3 , . . . 

 on the outside. 



At each point of the surface, the perpendicular component F* of 

 the resultant force F, is equal to the algebraical sum of the perpen- 

 dicular components of the forces proceeding from all the acting 

 masses, both internal and external. 



Calling 2 fn tne sum J at a P ^ of the perpendicular com- 

 ponents which arise from the external masses, and fn> tne sum 



i 



