436 BELL SYSTEM TECHNICAL JOURNAL 



r = the resistance of the ratio arms. 

 Ar = the resistance unbalance of the ratio arms. 

 Ac = the capacitance unbalance in the ratio arms. 



These formulae are not rigorous, as second order quantities have been 

 neglected, but they are accurate to a close approximation provided the 

 ratio arm capacitance is very small, the frequency is in the audible 

 range, and the ratio of susceptance to conductance in the unknown is 

 one or larger. All of these conditions obtain in the case in point. 



By measuring direct and reversed an admittance having a Q (ratio of 

 susceptance to conductance) of approximately 1 and solving the two 

 equations simultaneously we may ascertain errors due to the differences 

 in resistance and reactance of the ratio arms. The total change in 

 capacitance of an admittance under test due to the resistance error of 

 the ratio arms was found by the above method to be approximately 

 .004 per cent ; the capacitance error due to the reactance unbalance of 



the ratio arms was found to be '- — jr-^ . Thus the combined error in 



capacitance due to both types of unbalance is a function of the Q of the 

 impedance being measured. In the case of the particular type of tests 

 being made the combined error takes the form of an error in the 

 capacitance C, i.e., the capacitance in the shunt circuit. Table I 

 contains a column showing the Q's of the impedances used for the tests, 

 which range between .2 and 3.2. The corresponding error in C due to 

 the total ratio arm unbalance varies between .014 per cent and .002 

 per cent (the error in C is obviously ]/2 of the total capacitance change 

 resulting from the impedance arm reversal). It can easily be shown, 

 however, from the relation between the capacitances Ci and C of Table I 

 that the error in K resulting from the foregoing capacitance error will 

 in general lie between limits of .003 per cent to .005 per cent except for 

 one or two extreme cases for which the limits are .002 per cent and 

 .008 per cent. Accordingly the total correction due to the bridge 

 errors was lumped at .004 as noted under "Experimental Procedure," 

 since the few cases for which the error reaches the extreme limits are 

 those for which the accuracy of the test as a whole is a minimum, aside 

 from this particular type of error. 



Final Accuracy of Result 



The standard deviation a for the individual determinations of K 

 has been worked out for the values in Tables II and III. The value of 

 a is significant in that, provided the distribution of errors is approxi- 



