554 RATIO OF UNITS. 



historical importance. The charge of a Leyden jar is measured in 

 electrostatic units, by determining the repulsion of two balls of a 

 Coulomb's electrometer when they had received a known fraction 

 of the total charge ; the measurements in electromagnetic units was 

 given by discharging the jar through a ballistic galvanometer. 



In the electrostatic measurement, when once the jar is charged, 

 the knob is touched with a conducting sphere of radius R, and this 

 with a ball of radius r^ which is then insulated, and which serves as 

 fixed ball in a Coulomb's balance. The movable ball is electrified 

 by contact with the first, and their repulsion at a given distance is 

 determined. 



A preliminary experiment gives the fraction of the total charge 

 worked with. After having electrified the jar, an insulated sphere R 

 is put successively four times in contact with the knob, being each 

 time reduced to the neutral state. Before the first contact, and 

 after the last, the jar is connected with an electrometer which is 

 systematically graduated a sine electrometer, for instance which 

 gives the ratio of the potentials in the two cases. Let C be the 

 capacity of the jar, C' that of the sphere at the moment of contact, 

 V, V 1? V 2 , V 3 , and V the successive potentials ; we have 



+ C / _V_V 1 _V 2 _V 



C 



and consequently, 



/ C'\ 4 V 

 ( x + I 



V c/ v 



c 4 /v 



or = A 4 / i. 



Two observations made on the electrometer before the contacts, 



and two others afterwards, enable us to allow for the leakage. The 



C' 



ratio was found equal to 0-03276. 



\~r 



The electrostatic capacity C' of the sphere in the conditions of 

 the experiment is not equal to its radius, but it need not be known 

 exactly; and it may be admitted, without any great error, that the 

 division of the electricity between this sphere and the small knob is 

 in the same ratio as if the system were withdrawn from any external 

 influence ; this ratio is given by Plana's tables,* calculated from the 

 formulae of Poisson. 



* See MASCART. Traite d" Electricite Statique, Vol. I., p. 281. 



