of Small Differences of Phase, 16*3 



to be 2"2S when the instruments were shunted to a portion 

 of a non-inductive resistance connected with two slip-rings 

 of the rotary. These ratios were the same whatever instru- 

 ments were used, and for different resistances put in series 

 with the direct-current instrument, provided due allowance 

 was made for these resistances when interpreting in volts 

 the reading of the latter instrument. But although the ratio 

 of the reading of the alternate-current voltmeter to the 

 maximum reading of the direct-current instrument was always 

 found to be 2*28 when only noninductive resistances were 

 included in the circuit connecting two slip-rings of the rotary, 

 this number was found to vary with the inductiveness of the 

 load current taken from these slip-rings. Thus the parallel 

 arrangement of instrument just described, when shunted to 

 a suitable noninductive resistance traversed by the current 

 passing through an iron-cored choking-coil consisting of one 

 of the coils of an old hedgehog transformer, yielded a ratio of 

 2*36 for the readings of the two voltmeters when the current 

 was 10*6 amperes, and the frequency 43 cycles per second. 

 A similar experiment on a hand-regulated alternating-current 

 arc for a current of 11 amperes of the same frequency, yielded 

 a ratio of 2*55. In each case about a dozen different observa- 

 tions were taken, and the individual values of the ratio found 

 in each set of tests agreed with each other as accurately as it 

 was possible to read the instruments observed. Since the 

 ratio between the two readings is '2/ where / is the form 

 factor of the voltage, or the ratio of the square root of mean 

 square of the voltage to its arithmetical mean value, it follows 

 that the form factor of the slip-ring voltage is 1*14, that of 

 the current through the choking-coil is 1*18, and that of the 

 alternating-current arc is 1*275, the theoretical value for sine- 

 currents being 1*11. The wave-forms of the alternating- 

 current through an arc, or through a large choking-coil with 

 a strongly magnetized iron core, are quite exceptional. For 

 ordinary currents produced by the rotary, it was found 

 sufficiently accurate to take a constant of 2*3 for direct- 

 current voltmeters used with the commutator. 



It now became possible to measure the voltages represented 

 by the lines in tigs. 1 and 3, even when some of these voltages 

 were small compared with a millivolt. Moreover, as the angles 

 to be measured are determined from the ratios of voltages, and 

 not from their actual values, it was possible, by measuring 

 each voltage by the commutator method, to eliminate the 

 constant of the instrument, assuming only that the form 

 factor is the same for all the voltages measured. 



Thus the inductiveness of a pair of lead plates in slightly 

 acidulated water was tested by the method shown in tig. 3. 



M 2 



