The Measurement of Small Capacities 



87 



is also earthed. Thus, the junction of the condensers is effectually 

 earthed when balance is obtained, but the capacities between the leads 

 and the sheath are now in parallel with the resistance arms of the bridge. 

 The resistance arms are of such low impedance that these capacities 

 introduce only a negligible phase shift. 



The theory of the method is better understood by reference to Fig. 3. 



Fig. 3 



Let C, C, be the capacities of two guard-ring condensers. 

 Let A be th area of their guarded plates, 



d, X, be the distances between their plates, 

 a, b, be the capacity of the leads to them, 



Ci, Ci', be the capacities of their guard-rings together with 

 small adjustable condensers in parallel with them. 



K is a two-way key, T a telephone, and V a source of alternating 

 current of frequency /, or P/2t7. 



With the key in position (1), condenser C'l is first adjusted until 

 there is silence in the telephone, and then, we have, 

 (C+a)/Ci = (C + 6)/C/ 

 Also the voltages at A and B are in phase and equal, so that the con- 

 densers act as true guard-ring condensers, and we may write, 

 C=A/47r</, 



C'=h/^-KX. 



With the key in position (2), the movable contact D is then adjusted 

 until silence is again obtained. 



