202 ELEMENTARY LESSONS ON [CHAP, iv 



the forces which they exercise on P exactly neutralise 

 one another (as experiment shows they do), it is clear 

 that the electric force must fall off inversely as the 

 squares of the distances; for the whole surface of the 

 sphere can be mapped out similarly by imaginary cones 

 drawn through P. The reasoning can be extended also 

 to hollow conductors of any form. 



246. Capacity. In Lesson IV. the student was 

 given some elementary notions on the subject of the 

 Capacity of conductors. We are now ready to give 

 the precise definition. The Electrostatic Capacity of 

 a conductor is measured by the quantity of electricity 

 which must be imparted to it in order to raise its potential 

 from zero to unity. A small conductor, such as an 

 insulated sphere of the size of a pea, will not want so 

 much as one unit of electricity to raise its potential 

 from o to i ; it is therefore of small capacity while 

 a large sphere will require a large quantity to raise its 

 potential to the same degree, and would therefore be 

 said to be of large capacity. If C stand for capacity, 

 and Q for a quantity of electricity, 



C=-| and CV = Q. 



This is equivalent to saying in words that the quantity 

 of electricity necessary to charge a given conductor to 

 a given potential, is numerically equal to the product of 

 the capacity into the potential through which it is raised. 



247. Unit of Capacity. A conductor that required 

 only one unit of electricity to raise its potential from o 

 to i, would be said to possess unit capacity. A sphere 

 one centimetre in radius possesses unit capacity ; for 

 if it be charged with a quantity of one unit, this charge 

 will act as if it were collected at its centre': At the 

 surface, which is one centimetre away from the centre, 



the potential, which is measured as - , will be i . Hence, 

 as i unit of quantity raises it to unit i of potential, the 



