Theory of the Quadrant Electrometer. 



243 



that there is an 

 be made actual]^ 



ano'le between 0° and 90° for which ho mioht 



3 

 zero 



C55 



(»: 



C35 



(2) 



0: 



■2l 



e^o 



4j 



Further it is clear that 62 mnst diminish as the air-gap is 

 reduced, and hence the potential for maximum sensibility 

 increased, other things being equal. 



So far the argument is qualitative, and we have now to 

 get a quantitative estimate of the effect of the air-gap. 



Let us take the case of a quartz fibre 5 cms. long, 

 •009 mm. diameter. For this F = 8 x lO-^. Now if 

 262= 10-22, and ¥3= 100 volts, we get 252^3' = 10"^ This is 

 a quantity of the same order as F. Hence if 2^2 is only ^^ 

 of an electrostatic unit of capacity, there would in this case 

 be a maximum sensibility at about 100 volts. 



The solution of the electrical distribution for a system like 

 the quadrant electrometer is a well-nigh hopeless problem. 

 1 now propose to discuss a two-dimensional problem, which 

 in some respects corresponds to the actual case considered in 

 the preceding pages. I have succeeded in solving the 

 problem completely, and the result confirms my view that 

 the air-gap is sufficient to account for a maximum sensibility. 



We shall take four semi-infinite plates to correspond to 

 the upper and lower plates of the quadrants, and a plate of 

 finite breadth to correspond to the needle. 



A 



C 



E 



B 



D 



The cross-section of the arrangement is shown in the 

 diagram : and it is to be understood that the plates A and B 

 extend indefinitely to the left, while C and D extend in- 

 definitely to the right. The plate E is situated midway 



R2 



