20 STATIC ELECTRICITY 



sectors of the outer plate under w 2 . The smaller the sectors 

 and the more numerous they are, the greater will be the quantity 

 of - induced through m^ by the + on the inner plate, and it 

 may be much more in total amount than the original + 

 sufficient number of sectors pass m 1 while the inducing charge 

 near that brush. Now the -- passing round on the outer plate 

 arrives opposite w x when the + on the inner arrives at n. 2 , and, 

 meanwhile, the + given to the outer plate through m 2 arrives 

 opposite w 2 , and under these charges not only is the + on the 

 inner plate under w a neutralised, but a charge is induced on 

 it there while a + charge is given to the sectors under w r These 

 are carried on, and when under m l m 2 they induce - and + on 

 the outer plate, while when under n^i 2 they are reversed. 



FIG. 17. 



The charges on the different parts of the plates are therefore 

 as in the figure, and if the sectors are sufficiently numerous the 

 charges will mount up until the increase is balanced by leakage. 

 To understand the necessity of a number of sectors it is sufficient 

 to consider the case represented diagrammatically in Fig. 17, where 

 there are on each plate only two sectors at the opposite ends of a 

 diameter and so arranged that they meet under the brushes. Then 

 if one inner sector receives a charge + Q the most it can do is to 

 induce Q on the outer sector when the latter is under a brush, 

 the opposite sector being charged with + Q- These + an d - 

 charges cannot do more than induce Q and + Q when in turn 

 the inner plate sectors are under the brushes, and so on, so that 

 the charges do not increase however long the rotation is continued. 



The addition of the discharging circuit does not alter the nature 

 of the action ; it only leads to an earlier reversal of the charges on 

 the sectors. Thus the + on the inner plate and the + on the 

 outer plate running in opposite directions past the right-hand 



