ELECTRICAL MEASUREMENTS. 269 



similar, with a force represented by this formula / = ^. 



The force is numerically equal to the product of the two 

 charges, or to the square of either of them if they are equal, 

 divided by the square of the distance between the points at 

 which they are collected, q stands for the amount of the 

 charge or quantity of electricity, r for the distance between 

 the charges and /for the force. Heading the relation differently 

 we have q = r\/f; or the measure of the charge is the 

 product of the distance into the square root of the force 

 exerted between the two charges. This formula implies 

 that the quantity of electricity which, placed at unit distance 

 from another equal quantity, repels it with unit force, is 

 taken as the standard quantity of electricity ; so that the 

 unit charge or absolute unit of electricity is the charge 

 which repels an equal charge at unit distance (say one 

 centimetre) with unit force (one dyne). The dyne is the 

 most convenient unit of foree ; it is that force which can in 

 one second give to a mass of one gramme, a velocity of one 

 centimetre per second. But that is not a matter which is 

 essential to our present discussion. You may take what unit 

 you please as the unit of force, but the unit of electricity 

 will depend on that. 



To return to what I was saying : in order to apply practically 

 a system of measurement founded upon this principle, it is most 

 convenient, although not absolutely essential, that the charges 

 that we want to measure should be situated upon spherical 

 conductors, little spheres of metal, or spheres with metal 

 surfaces. The advantage of this form of a charged body is 

 this, that the electricity distributes itself uniformly on the 

 surface of a sphere if that is- at a sufficient distance from 

 other bodies, and this uniformly spherical layer of elec- 

 tricity acts upon other electricity as though it were con- 

 centrated at the centre of the sphere ; so that we may in this 

 case regard the quantities which exist upon the spheres as 

 concentrated at their centres. If they are at a very great 

 distance apart that is strictly true ; if at a moderate distance 

 apart it is nearly true. The apparatus in most general use 

 for this purpose is the Torsion Balance which is fully 

 described in the ordinary Text-books on Electricity, and of 

 which I have an example here. In using it, a charge of 



