432 BELL SYSTEM TECHNICAL JOURNAL 



assumption the frequency of a very stable vacuum tube oscillator, 



specially constructed, when measured against the standard fork on 



the cathode ray oscillograph, can be shown not to vary with respect to 



the standard over a period of several hours by more than ±.001 per 



cent. Accordingly unless the standard fork and the special oscillator 



always fluctuate in exactly the same manner, which is very unlikely, 



we may conclude that both remain constant to better than ±.001 per 



cent. The use of the cathode ray oscillograph in checking the values 



of the oscillator used against the standard frequency introduces no 



error in the determination which is appreciable from the point of view 



of these tests. 



2. Modulation Errors 



Another type of error due to the source of frequency used was the 

 masking of the true balance by oscillator harmonics affecting the 

 detector system which consisted of the double-shielded output trans- 

 former of the bridge, a vacuum tube amplifier, a telephone receiver, and 

 the human ear. The output characteristic of each of these elements is 

 linear, or practically so, for small loads. Overloading of any one of 

 them, however, results in a curved output characteristic which causes 

 an appreciable amount of modulation. This is especially true of the 

 vacuum tube amplifier. Now in a measurement of this type the bridge 

 is balanced for the fundamental only, since the equations of balance 

 contain the frequency as a parameter, and any harmonics present in 

 the input will pass through into the detector circuit practically unat- 

 tenuated. If they are appreciable in magnitude the elements of the 

 detector, particularly the amplifier, become overloaded, more har- 

 monics are generated, these harmonics are modulated in a succeeding 

 element of the detector, and the fundamental may appear as a modula- 

 tion product even though the bridge is actually balanced. Under such 

 conditions the fundamental tone in the receiver can be eliminated only 

 by unbalancing the bridge slightly. It was found during the tests that 

 if the output of the oscillator was kept small no appreciable overloading 

 occurred in the detector circuit, but that as the oscillator output was 

 increased the amplitude of the harmonics also increased, the detector 

 gradually became overloaded, and the bridge balance began to change 

 as the oscillator output was varied. This efifect was eliminated by the 

 use of a filter to keep the harmonics from the oscillator out of the 



detector circuit. 



3. Resistance Errors 



Errors in the determination of K due to uncertainty in resistance 

 values arose in four ways. The first source of error due to the resistance 

 coils lay in their temperature coefficient. This coefficient was found to 



