156 Whitehead and Hill — Measurement of Self -Inductance. 



differed from those obtained at a different time. The cause of 

 this variance proved to be the heating and consequent lack of 

 knowledge of the resistances. In order to secure sensibility of 

 the electrodynamometer it was the custom to make the current 

 through the fixed and hanging coils quite heavy. Sometimes the 

 current through the fixed coils was nearly T \ ampere. This was 

 unnecessarily large, as with a current of -fa ampere it is easily 

 possible to adjust the resistance to one part in fifteen hundred 

 or two thousand. If we wish to make exact measurements of 

 inductance, the method requires an accurate knowledge of the 

 resistances. To take a specific example, if in the first determina- 

 tion in Table IV we increase B or B" by 1/20 per cent, a change 

 of -1/3 per cent is introduced in the value of L; similarly 

 changing R or B/ by 1/20 per cent we alter L by +1/4 per 

 cent. In regard to r, L varies only as the first power. Fortu- 

 nately these errors in L introduced by variation of the resis- 

 tance are not all of the same sign, and since the current through 

 r must of necessity be quite small (about T fa ampere) the 

 currents through R + R and B/ + R" are nearly equal. 

 Hence if w r e assume an increase of all the resistances of 1/20 

 per cent, the value of L is increased by about one part in one 

 thousand three hundred. Therefore, to obtain the best results 

 with this method we must measure the resistances carefully and 

 avoid much heatings. To avoid heating of the resistances the 

 following plan of taking readings was adopted. The bridge was 

 first adjusted, this being done by altering R' and R / until on 

 reversing the current through the hanging coil of the electro- 

 dynamometer there was zero deflection indicating a ninety 

 degree phase difference between the fixed and suspended coils. 

 By means of the switch S (vide fig. 5) the current w T as turned 

 through the resistance X, made closely equal to the impedance of 

 the network. This was done to avoid change in the frequency. 

 After a considerable interval, sufficient to avoid the effect of 

 any slight heating in the preliminary adjustment, the current 

 was again switched through the network and R / remaining the 

 same, B' readjusted to give zero deflection, the exact time of 

 adjustment being noted in the chronograph sheet. This adjust- 

 ment when made would usually hold good for several minutes. 

 However, it was not usually necessary to run the current 

 through the network longer than twenty or thirty seconds. 

 This process was repeated a number of times with longer or 

 shorter intervals and then the resistances B' and R / measured. 

 The other arms of the bridge were measured once or twice 

 during the evening ; this time was chosen as being free from 

 various disturbances. Generally for several successive obser- 

 vations the same value of R' would give zero deflection, R / 

 remaining the same. The mean of the frequencies measured for 

 the several observations was taken as being nearest correct. 



