Motion of the Needle of a Quadrant Electrometer. 445 

 from which it follows that 



1 



= 



20-19 e-"«" 



Note. — In the above the existence of the variation of conductivity 

 which is necessary in Maxwell's theory of the residual charge is made to 

 depend on the displacement of the free electrons in the dielectric. But 

 it must be pointed out that this displacement, without any bodily charge 

 in the dielectric, ^ould gire rise to a residual charge. When the primary 

 discharge takes place, bound charges are left on both plates which are 

 gradually set free, as the displaced electrons return to the state of uniform 

 distribution. The residual charge is therefore, probably, a more compli- 

 cated phenomenon than that contemplated in Maxwell's theory. 



XL. The Motion of the Needle of a Quadrant Electrometer. 

 By W. F. G. Swann, JJ.Sc, A.R.C.S., Assistant Lecturer 

 in Physics at the University of Sheffield*. 



VERY small currents are frequently measured by 

 observing the rate of movement of the needle of a 

 quadrant electrometer as the electricity enters one of the 

 quadrants. Such currents are of course often measured by 

 connecting the quadrant to earth through a very high re- 

 sistance, and noting the steady deflexion which is produced 

 when the electricity passes into the quadrant at the same 

 rate as it leaves through the high resistance. The former 

 method is more sensitive however, and is very convenient in 

 practice, but even though the electricity passes into the 

 quadrant at a uniform rate, the needle does not move with 

 uniform velocity, owing to its inertia. This effect must 

 doubtless have been noticed by many observers, but though, 

 unless suitable precautions are taken, considerable errors may 

 result I have seen no accounts of any systematic precautions 

 of this nature. In view of the present extensive employment 

 of electrometers, the following discussion of the theory and 

 suggestion of a simple method of avoiding the error may be 

 of interest. 



If 6 is the angle of deflexion of the needle, the equation of 

 motion is 



Kg+sg+w-KO,. • • • • CD 



where the constants have the usual significance, and Y(t) is 

 the couple on the needle due to the electricity which has 



* Communicated bv the Author. 



