ELECTROMETERS. 167 



given charge, the electric energy at any point on a con- 

 ductor, called its surface density, is in proportion to its 

 surface area. Let Q represent the surface density, then 

 the electric force, exerted by a charged conductor on a 

 point near it, equals Q multiplied by the surface area. 



On a sphere the surface equals the square of its ra- 

 dius multiplied by 4x3.14159. If 3.14159 = ^, and 

 radius = 1, we have I 2 x 4 a = 4 n. Hence the force 

 exerted by a charged sphere on a point near it equals 

 4 7t Q ; and the force exerted by a charged hemispher- 

 ical surface equals 2?tQ. 



The hemispherical surface may be considered as 

 made up of the bases of an infinite number of small 

 cones, having their apexes at the center. Hence each 

 base subtends a solid angle : and lines of force, extend- 

 ing from surface to center, are everywhere normal to 

 the surface. 



Now if we conceive a plane surface applied to the 

 hemispherical surface, and these cones extended to 

 meet it ; we find that the lines of force, extending from 

 these bases, are oblique to the plane surface. Hence 

 each one can be resolved into two components, one 

 normal to the plane, and the other acting along it. 

 But since there are an infinite number of these cones, 

 the lines of force from whose bases may all be resolved 

 in this way; the components along the plane, all 

 around, neutralize each other, leaving only the normal 

 components; whose force equals the sum of all the 

 solid angles multiplied by the surface density, which, as 

 we have seen, equals 2 TIQ. Hence the expression is 

 the same for a plane or a hemispherical surface. 



APPLICATION OF FORMULAE TO MEASUREMENTS 

 BY ELECTROMETER. When there are two discs, at 



