Formula used in Inductance Measurements. 801 



of r. : . the vectors AQ, QT, and TS, which are proportional 

 to c. 2 , are very small, and though a true balance is impossible, 

 we shall obtain the least sound by making M very small. To 

 avoid this trouble it is best to commence balancing- with r 2 

 small or even zero. 



It is fairly evident that we would not expect a very sensi- 

 tive balance if the triangle SQA is very much smaller than 

 the triangle OPA. This implies that r^ should not be very 

 much bigger than Ma>. The latter is not likely to exceed a 

 few ohms, even if we use the variable mutual inductance 

 near its major limit, as is evidently the best. On the other 

 hand, unduly reducing r x will considerably reduce the avail- 

 able P.D. OA across the condenser terminals, and may even 

 cause the current c, to become so large as to cause over- 

 heating. We must remember that OA does not represent 

 the full voltage of the generator, as the effective impedance 

 of the mutual inductance primary must be considered. 



Effect of a Small Deviation from an Exact Balance. 



It is interesting to consider the application of the geo- 

 metrical method to the calculation of the telephone current 

 caused by a slight variation from exact balance. This calcu- 

 lation becomes somewhat cumbrous if treated exactly, all the 

 factors being taken into consideration. If, however, we 

 assume, as a first approximation, that the impedance of the 

 telephone is so high that the current through it is negligible, 

 we can, in certain cases, easily find the P.D. across its 

 terminals. We thus arrive at certain conclusions as to 

 the best conditions for accuracy which are probably near 

 enough to the truth to be of use in practice, at least in cases 

 where a high-resistance telephone is used. We can then 

 consider the effect ot the current passing through the tele- 

 phone, and also the loss of voltage due to the impedance of 

 the generator. These impose further conditions which must 

 be approximately satisfied if the most sensitive arrangement 

 is required. 



The method is best suited to measurements not involving 

 mutual inductance. Two such cases are considered below. 



Comparison of Self- Inductances, 



Suppose we are measuring a self-inductance L x by com- 

 parison with a standard L 2 . We want to arrange that a 

 given error in L, should produce the maximum effect on 



