246 ELECTRICAL MEASUREMENTS 



Suppose the upper plate is given a small displacement, Vi 

 and 7 2 being kept constant by connection to a source of potential 

 difference. There will be a change in the energy of the con- 

 denser which will be numerically equal to the mechanical work 

 necessary to displace the plate in the direction S. 



dE = FdS 



_dE A(V l -VS)* 

 = dS 



y _ y 2 = S^p- in electrostatic units. (2) 



A 



If (Vi - F) is in volts, P.D. = 3005. = 1,504& (3) 



\ A. \ A 



It has been assumed that all of the electrostatic lines of force 

 are straight and normal to the plane of the disc. A few lines will 

 stray into the very narrow gap between the guard ring and 

 the attracted plate. They may be assumed to divide equally 

 between the ring and the plate, so to make an approximate 

 allowance, the effective area of the plate may be taken as the 

 area of the plate plus one-half the area of the air gap. 



It is well to emphasize the fact that unless the voltages are 

 high, the forces to be dealt with in electrostatic instruments are 

 small. If 



A = 100 sq. cm. 

 S = 1 cm. 

 P.D. = 150 volts 

 then 



F = I dyne, approximately. 



That is, the force is about the same as the attraction of gravity 

 on a mass of 1 mg. To increase this force, the plates must be 

 brought very near together, or the use of the instrument re- 

 stricted to measuring high potentials. 



Before using the absolute electrometer, the spring balance must 

 be calibrated ; to do this the terminals of the instrument are short- 

 circuited and the disc brought to its zero position by means of 

 the micrometer head. Known weights are then placed upon the 

 disc and the number of turns which it is necessary to give B in 

 order to return the disc to the zero position is noted. The number 



