426 BELL SYSTEM TECHNICAL JOURNAL 



dials of the standard capacitance until a balance is obtained and the 

 value is then read from the dial settings and the reading of the air 

 condenser, which has a minimum scale division of .2 /x/i/. 



The bridge condensers cannot be made exactly direct reading, and 

 for accurate work the bridge must be calibrated. This calibration 

 may be made very simply due to the fact that the maximum setting 

 on any dial is approximately equal to one step on the next higher dial. 

 By the use of an auxiliary external condenser it is possible to get a 

 balance with any desired setting of the bridge. Thus the maximum of 

 one dial may be compared with each individual step of the next higher 

 dial by balancing the bridge first with the maximum setting of the 

 lower dial and then with that dial set at zero and the next higher dial 

 moved up one step, no change being made in the auxiliary condenser. 

 The change in capacitance required for balance, that is, the difference 

 between the dial settings, is read on the air condenser. Since the con- 

 densers in each decade are completely shielded from those in the other 

 decades this procedure gives an accurate comparison of the ten steps 

 of any dial with one another, and with the maximum setting of the next 

 lower dial. Evidently an extension of this method will furnish a 

 precise comparison of any bridge setting with any other, although it 

 gives no information as to the absolute values of any of the settings. 



In practice after the above "step-up" calibration, as it is called, is 



performed the values of all the bridge condensers are computed in 



terms of an assumed value of a single one. This furnishes a bridge 



calibration of which the consistency is dependent only on the accuracy 



of the "step-up" and of which the accuracy is dependent only on the 



value of the single calibrating standard. In general the assumed 



value of the calibrating standard will be in error, its true value being a 



constant, K, times its assumed value. Any reading on the bridge using 



the calibration will, therefore, require a correction by this same factor 



K. Now let us suppose that this bridge has exactly equal ratio arms, 



is calibrated as described above and is used to measure successively two 



capactitances whose measured values are found to be C and Ci. Their 



C 

 true values will then be KC and KCi and their ratio will be 7^ , which 



is the true ratio between the capacitances irrespective of the value of 

 K, that is, irrespective of the absolute accuracy of the measured 

 values. By means of this type of precision capacitance bridge the 

 ratio between any two capacitances may thus be obtained regardless 

 of the absolute accuracy with which the capacitance of either is known. 

 Actually the best known value is always assumed for the capacitance 

 used as the standard in computing the calibration of the bridge, and 



