MEASUREMENT OF CAPACITANCE 437 



mately normal, over 99 per cent of all determinations will fall within 

 limits of :^2>(x from the mean. In this discussion the accuracy of any 

 measurement (exclusive of known consistent errors) will be defined as 

 d=3(T. The standard deviation of the mean is given by the expression 



-y=, where n is the total number of observations. If the curve of 

 errors is approximately normal (and we have no reason to assume other- 



wise), the error in the determination of K is given by ± —=. In the 



■\n 



absence of any systematic errors, of which none have been detected 

 of magnitude comparable with the final accuracy of the result, the 

 limits of accuracy are therefore, from Table V, ±.003 per cent. 



This limit was not exceeded in practice as is shown by the values for 

 K at 1,000 and at 2,000 cycles in Table V. The difference between the 

 two values of K is .002 per cent. Since the calibrations at both 

 frequencies are based on the same original standard, namely, the 1,000- 

 cycle value of the bridge .01^/ air condenser, and the latter is assumed 

 not to vary with frequency over the audio range, the final result for K 

 in the two cases should be the same within the limits of accuracy of 

 the result. 



Table V contains a comparison of the values of K as determined by 

 the method of this report and by comparing the Bureau of Standards 

 calibrated values on a standard condenser box with the calibration of 

 the capacitance bridge at 1,000 cycles. The agreement between these 

 values, .004 per cent, is very close, in view of the accuracy which the 

 Bureau certifies and the precision to which their results are given. 

 Although the Bureau calibration is certified only to ±.1 per cent, the 

 values are furnished to 5 significant figures and are apparently consist- 

 ent to db.Ol per cent or better. 



It will be noted that the values of capacitance chosen for these tests 

 were all between .01 and .5ju/. It is advisable that they be kept within 

 these limits at the frequencies used in order that the resistance values 

 required in the determination may be easily secured and easily capable 

 of measurement with the required precision, and that errors in capaci- 

 tance due to slight changes in the position of leads and units may not 

 be appreciable. 



