ELECTROSTATIC PRESSURE. 2 9 



Hence, if p be the force on unit surface, the total force exerted 

 on the electrical layer (n/S of an element of surface is 



n -- =- .~dn = - 



As -3 is zero at the point A, we have simply, 

 dn 



On the other hand, 



F = 47T(7, 



which gives 



p = - 1 67T 2 CT 2 = 27TO- 2 . 

 O7T 



It is remarkable that this expression might be obtained strictly 

 without any other hypothesis than that of an extremely small 

 thickness e, and therefore whatever be the law of distribution along 

 the perpendicular. 



The electricity spread upon each unit of surface is thus impelled 

 towards the exterior with a force equal to 27r<r 2 , proportional therefore 

 to the square of the density. This electrostatic pressure, or electrical 

 tension is counterbalanced by the resistance of the dielectric. 



When the conductors are in air, the effect of this force is 

 to diminish the atmospheric pressure on their surface. If the initial 

 pressure for unit surface be P in the neutral state, after electrification, 

 it will be 



at each point , of the surface of the conductor. 



Thus, an insulated soap bubble will increase in volume when 

 electrified, and will resume its original volume when it is restored to 

 the neutral state. Van Marum, for example, found that a balloon 

 filled with hydrogen became lighter, and that its ascensional force 

 increased, when it was electrified. 



If the density is uniform on a conductor, the same is the case 

 with the electrostatic pressure, and as this is perpendicular at every 

 point, its resultant is zero. 



If the density is variable, the electrostatic pressure is in general 

 equivalent to a single force and to a couple. The result thus obtained 



