MEASUREMENT OF CAPACITANCE 



435 



small enough to be neglected in all cases. The final determination of 



the shunt capacitance of R was accurate to ±lnij.f, and hence in most 



of the cases under consideration the resulting uncertainty in K was less 



than ±.001 per cent. 



4. Bridge Errors 



The principal source of error in the bridge itself lies in the inequality 

 of the ratio arms, both in magnitude and angle. Since this inequality 

 may result from sources other than the ratio arms proper, it is best to 



Fig. 2 



ascertain it by interchanging the impedances being measured rather 

 than by reversing the arms themselves. The following formulae (see 

 Fig. 2) show the errors in conductance and capacitance which may 

 arise from ratio arm inequalities. 



AG 

 2G 



Ar 

 r 



^CAcr 



AC _ Ar AcrG 

 1C~ ~T'^~C~ 



(4) 



(5) 



In the above, 



G = the conductance of the unknown. 

 AG = the change in conductance due to reversing the unknown and 

 the standard arms. 

 C = the capacitance of the unknown. 

 AC = the change in capacitance due to reversing the unknown and the 

 standard arms. 



