88 ON DIELECTRICS. 



The pressure, on unit surface, at a point of the conductor where 

 the density is a-, and the force F, has the value 



/=27TO- 2 = F 2 = -F(T, 

 O7T 2 



and this pressure is always directed outwards, whatever be the sign 

 of the electricity. 



For each element of surface, the pressure /^S is the resultant of 

 the actions exerted, on the mass OY/ S of this element, by all the masses 

 external to the conductor, and by those on its own surface. The 

 resultant of all the pressures for the entire surface, is the resultant of 

 the actions exerted on this conductor, both by the external masses 

 and by its own electricity. But the resultant of the actions which the 

 various masses of the conductor exert one upon the other is almost 

 null; for as there is equilibrium, those masses may be regarded as 

 fixed on the conductor, and in this case, the elementary forces 

 taken in pairs neutralise each other ; the resultant of the pressures 

 is then simply equal to the resultant of the actions of the external 

 masses. 



101. When an electrical system is surrounded by an equipotential 

 surface S v the action exerted on this system is the resultant of the 

 pressures which would be exerted on a layer equal to the total charge 

 of the system, in equilibrium on the surface S r 



Let us suppose that an equipotential surface S x divides all the 

 acting masses into two systems, an internal one M 15 and an external 

 one M 2 . We have seen that for points external to S 15 the internal 

 masses may be replaced by a layer of the same total mass M 1 in 

 equilibrium on the surface. Conversely, the external system M 2 will 

 act on this layer Mj fixed on the surface S lf as it would act on the 

 internal masses, supposed to be connected with each other, so as to 

 form a rigid system. 



But, from the foregoing remark, the action of external masses upon 

 the layer Sj, and therefore on the system M l of the internal masses, 

 is no more than the resultant of the electrostatic pressures of this 

 layer. 



As the total action of the system M l on all the external bodies 

 is equal, and of opposite sign to the force which this system 

 experiences, it is also seen that the action of the system M 15 on 

 external bodies, is equal to the resultant of the elementary 

 pressures on the surface S 15 each of them being counted towards 

 the inside. 



