MEASUREMENT OF CAPACITANCE . 423 



Since this ratio as measured is the true ratio, both of the measured 

 values must be multipHed by the same factor to give the true values, 

 and the following substitutions may be made in formulae (1) and (2): 



KC, for Ci 

 and 



KC for C, 



where K is the correction factor necessary to reduce the values meas- 

 ured on the bridge to their true values. The formulae now become 



Ci R 



and 



K'CC, =~, 

 rRoP' 



C 

 from which, eliminating R by the use of the ratio -yr 



K ^ '- - C* 



1 /G 



c 



In the foregoing C and d are assumed to be pure capacitances, and 

 r and R pure resistances. Of course in practice neither pure capaci- 

 tances nor pure resistances are obtainable. The former will have 

 some slight conductance and the latter some slight reactance. It we 

 use condensers having small losses, and resistances having small phase 

 angles, the conductance of the condenser C (Fig. 1) may be considered 

 as a resistance in parallel with R, and that of Ci as a resistance, ri, in 

 series with r. Similarly, the reactance of R may be considered as a 

 capacitance C, either positive or negative, in parallel with C, and the 

 reactance of r as a capacitance, Ci', in series with Ci. Of these quanti- 

 ties the conductance of C may be neglected, since the use of co, r, and 



C 

 the ratio -^ as parameters eliminates R from the formula for K, and 



hence it is unnecessary to know it exactly. Including these second 

 order quantities the formula for K becomes, using the notation above, 



^ ^ 1 / Ci + Ci 



^^^^'--(C-fC) 



^^ + ^^Kc^') 



c+ c 



Now in the range of impedances actually used in the following determ- 

 inations of K it was readily possible to obtain resistance units for r in 

 28 



