123, 124] The Quadrant Electrometer 109 



shewing that 6 is, for small displacements of the needle, approximately 

 proportional to the difference of potential of the two pairs of quadrants. 

 The instrument can be made extraordinarily sensitive owing to the possibility 

 of obtaining quartz-fibres for which the value of k is very small. 



If the difference of potential to be measured is large, we may charge the 

 needle simply by joining it to one of the pairs of quadrants, say the pair at 

 potential F 2 . We then have v = F 2 , and equation (55) becomes 



so that 6 is now proportional to the square of the potential difference to be 

 measured. 



Writing , , = C, so that C is a constant of the instrument, we have, 

 when v is large 



........................... (56), 



when v = F 2 , 



(57). 



124. Measurement of charge. Let us speak of the pairs of quadrants 

 at potentials F l5 F 2 , as conductors 1, 2 respectively, and let the needle be 

 conductor 3. When the quadrants are to earth and the needle is at 

 potential F 3 , the charge E induced on the first pair of quadrants by the 

 charge on the needle will be given by 



where q ls is the coefficient of induction. This coefficient is a function of the 

 angle which defined the position of the needle. If the instrument is 

 adj usted so that = when both pairs of quadrants are to earth, we must 

 use the value of q l3 corresponding to = 0, say (#13)0, so that 



E = (q\V. .............................. (58). 



Now suppose that the first pair of quadrants is insulated and receives 

 an additional charge Q, the second pair being still to earth. Let the needle 

 be deflected through an angle in consequence. Since the charge on the 

 first pair of quadrants is now E + Q, we have 



On subtracting equation (58) from this we obtain 



Q = fei) F 1 + [(g 13 ),-( 

 If is small this may be written 



