METHOD 6. SHUNT ON MAIN CIRCUIT.

This method corresponds to method 4, but the condenser is placed in the moving coil circuit, fig. 9, and a portion of i, is shunted off into

the compensation coil. Thus, i, is opposite in phase to i, and is combined with, so that the resultant of i, and i,, O C, is 90° different in phase from, fig. 10.

This method is especially adapted to small condensers, where the current, is very small and can be increased above its usual value.

Table V.-RESULTS BY METHOD V.

[E=1,260 volts=voltage on the condensers. e=45 volts-voltage on the compensation circuit.]

METHOD 7. AUXILIARY CONDENSER ON TRANSFORMER.

This corresponds to method 5, where the transformer is used as a source of i, but as in method 6, the condenser under test is placed in the moving coil circuit. In order to bring the compensation current 90° out of phase with i,, with which it is combined, an auxiliary con

denser C, is placed in the i, circuit instead of a resistance, fig. 11. The phases are shown in fig. 10. Thus:

E

R

where n is the ratio of transformation of the potential transformer.

directly by a voltmeter and, by an ammeter or electrodynamometer.

Table VI.-SUMMARY OF QUANTITIES TO BE MEASURED IN THE VARIOUS

The quantities in Table VI are as follows:

d is the deflection of the electrodynamometer in scale divisions.

Kis the constant of the electrodynamometer.

is the main current, through the condenser under test.

i, is the potential current, through the large resistance R.

p is 27 times the frequency.

I is the variable inductance added to the potential circuit.

R is the large potential resistance, as free as possible from inductance and capacity.

is the small resistance shunted by the auxiliary circuit.

C, is the auxiliary condenser, of constant value.

R, is the resistance in series with the auxiliary coil.

e, is the relatively small electromotive force supplying the auxiliary current.

Thus it appears that each method requires the determination of three or four quantities, and a choice of method will be determined in part by what instrumental facilities are available for the work. All the methods are capable of giving good results, but the null methods are more satisfactory than method 1, unless one has a wattmeter which is both sensitive and stable, and which has a nearly uniform field, so that the constant K does not vary too rapidly. All the methods require the two correction terms a and ẞ to be applied to derive the true power factor cos from the measured power factor cos 1. These two corrections are of opposite sign, as already explained, and should be small. In the experiments here described the resistance of the fixed coils of the wattmeter and the leads through which the main

current flowed that is, from P to Q with the condenser short circuited (figs. 1, 3, 5, etc.)-was 0.08 ohm. When the current is 1.6 amperes, r is 0.20 watt, and this requires a correction of about 0.0001 in the power factor. The correction for inductance in the moving coil is of the same order of magnitude and hence the results of the measurements cited above as examples are not very different from the true power factor cos 4. At the time these measurements were made I did not have facilities for measuring the various quantities involved in these several methods with sufficient accuracy to make a crucial test of the methods. The results, however, show that the various methods agree substantially, and there is no reason to doubt the entire reliability of any of them. The values given above for the power factor are somewhat larger than those found for the same condensers by the calorimetric method," but in those experiments the high electromotive force impressed upon the condensers was obtained by resonance from a lower electro-motive force and the harmonics were therefore largely suppressed. In all the work described in this article the high electro-motive force was obtained by transforming up, and hence the harmonics were retained and magnified by the condensers. Since the power factor is higher for higher frequencies, it is higher for the harmonics and therefore for the distorted wave. This is one of the subjects to be investigated when this work is resumed.

By taking careful note of the temperature of the condensers, and determining accurately the frequency of the current and the exact values of the a and ẞ corrections, we would obtain not only a crucial test of the various methods, but also data as to how the energy losses vary with the frequency, temperature, and wave form. I hope soon to repeat these measurements with improved apparatus, and hope to obtain results of sufficient precision to give valuable information of this character.

a Rosa and Smith: Phys. Rev., Jan., 1899.