Method of Determining Capacities, 43 



Let <?j, c/ be the inner and outer coatings o£ the condenser 

 forming the measuring system, of which the capacity C x is 

 to be determined. Let c , c f be the coatings of the standard 

 condenser o£ known capacity C , and c 2 , c 2 those of an 

 " auxiliary w condenser of capacity C 2 . The " inner " coating 

 is that which is usually connected to the measuring system, 

 the " outer " coating that which is usually connected to 

 earth. 



Perform the following observations: — (1) Connect and 

 earth c 1? c 2 ; also earth c { ' , c 2 . Insulate C\'-\-c 2 , and then 

 raise c 2 to the potential Y l5 the potential of earth being 0. 

 In virtue of the charge induced the electrometer (or other 

 measuring instrument) indicates a potential v lt The charge 

 induced on c x must be equal and opposite to that induced on 

 c 2 : hence 



C 1 » 1 + C 2 (» 1 -V 1 ) = (1) 



(2) Connect and earth c x , c 2 , c ; earth c/, c 2 \ c r . Insulate 

 c x H- e 2 -+-c , and then raise c 2 to the potential V 2 . Then, as 

 before, if v 2 is the potential indicated by the measuring 

 instrument, 



(Ci + Q,)«,+C,(»,-V0=0 ( 2 ) 



We have thus two equations to determine Ci/C and C 2 /C 

 in terms of the known quantities Y l5 Y 2 , v 1} v 2 ; and the 

 problem is solved. 



Let us now examine the accuracy of the method. For 

 the determination of Y x and V 2 , and also of the sensitiveness 

 of the electrometer (which gives rj and v 2 in terms of the 

 deflexion), a resistance-box arranged as a potentiometer will 

 doubtless be used. The potential (V) of the battery in the 

 circuit need not be known, so long as it is constant through- 

 out the observations. The error in Y 1 or V 2 will be due to 

 the deviation of the ratio of the resistances from their nominal 

 value, and need not exceed 1 part in 1000 over a range from 

 V to 1/1000 Y. The advantage of this method lies in the 

 fact that potentials, unlike times, can be measured with the 

 same instrument over a wide range with great accuracy. 

 On the other hand, the error in determining t>j or v 2 from 

 the deflexion is likely to be about 1 part in 100 for a single 

 observation. Accordingly we shall neglect the error in Vj 

 and Y 2 compared with that in V\ or r 2 . 



In practical measurements Y 1 and Y 2 will be so chosen 

 that vi and r 2 are nearly equal. If e is the probable error 

 in the observed value t% e u e 2 , e 12 those in the deduced values 

 of C'i, C 2 , C'i -f C 2; the ordinary formula 3 for the relation of 



