INDUCTANCE AND CAPACITY 



349 



In any experimental work with such a very small capacity, it 

 is necessary to make allowances for the capacity of the wire by 

 which the charge is imparted to the ball, for the capacity of all 

 leads and' of the commutator by which the charging and dis- 

 charging is effected. 



The capacity of an air condenser with coaxial cylindrical 

 electrodes, if the charge be uni- 

 formly distributed, is given in 

 electrostatic units bv 



I 



C = 



where I is the length of the cylin- 

 der and R and r are the radii 

 bounding the dielectric. For pre- 

 cision work, on account of the 

 effect of the ends of the condenser, 

 the assumption of a uniform den- 

 sity of charge is not tenable, so re- 

 course is had to guard cylinders, 

 shown in Fig. 207 at G. The effect 

 of the ends is thus removed from 

 the central section, which is the 

 one connected to the measuring 

 apparatus, to the guard cylinders 

 where it does no harm. In order 



to make practically all the lines of force radial the air gaps be- 

 tween the main section and the guard cylinders must be made 

 as small as possible, . and the measuring apparatus so arranged 

 that the guard cylinders are always at the same potential as 

 the main or central section. 



For one of the condensers used by Rosa and Dorsey, 



I = 20.00768 cm. 



R = 7.23831 cm. 



r = 6.25740 cm. 



FIG. 207. Section of cylin- 

 drical air condenser with guard 

 cylinders. 



Then, as a first approximation, C = - 



20.00769 



electrostatic units. 



2 log. 



7.3831 

 6.25740 



= 68.696 



