These results do not agree exactly with those by the first method. The difference is partly due to errors of the experiment, and partly to a change in the temperature of the condensers and of the wave form of the electromotive force employed. For want of a suitable variable inductance, very little was done with this method.

METHOD 3. AUXILIARY CONDENSER SHUNT ON THE MAIN CIRCUIT.

In this and the following methods the auxiliary compensation coil A is employed. As already explained, this coil is of fine wire and is

wound on the outside of the main coil of the wattmeter, but thoroughly insulated from the latter. It is magnetically equivalent to the main coil, so that a current flowing in series through the two in opposite directions produces no magnetic field at the position of the moving coil.

A small variable resistance r,, fig. 5, is inserted in series with the main current, and an auxiliary condenser C, is placed in series with the com

pensation coil on the terminals of this resistance. The compensation current, is equal to pC, r, 1, and is nearly 90° in advance in phase of ; that brings it practically opposite in phase to i,, as appears in fig. 6. We may compound &, and i, just as though they were in parallel in the same wire. The resultant is OC, and when i, has such a value that there is no deflection of the movable coil, CO is exactly 90° ahead of OB. Then, since BOG=1,

cos 41 = ?=pC2r,

Thus, it is unnecessary to measure E, i, i,, or R, but only C, and r, in addition to the frequency of the current. To apply the corrections a and ẞ to obtain the value of 4, it is of course necessary to determine C, r, and R approximately, as in method 1. The results obtained with five paraffined paper condensers are given in Table III. Nos. 2, 3, and 4 have a capacity of about 1.7 microfarads and 5 and 6 have a capacity of about 3.2 microfarads. These condensers were intended for 500 volt circuits. In these experiments, however, they were subjected to voltages between 910 and 1,386, most of the readings being taken at 1,260. This is a very convenient method.

EFFECT OF THE SELF AND MUTUAL INDUCTANCE OF THE FIXED AND AUXILIARY COILS.

The self-inductance of the fixed coils of the wattmeter employed in these measurements is 0.075 millihenry, of the auxiliary coil 0.111 millihenry, and the mutual inductance of the two is 0.072 millihenry. At a frequency of 120, p = 754, and the reactance of the auxiliary coil is 0.083 ohm. This is wholly negligible in its effect upon the magnitude or phase of the compensation current . The self-inductance of the fixed coil has no appreciable effect upon the magnitude or phase of the main current 2. The mutual inductance between the coils, however, may have an appreciable effect upon the magnitude of the compensation current i, in the auxiliary coil, provided the electromotive force e, on the compensation circuit is small. Thus, the back e. m. f. in this circuit, due to the current i, in the fixed coil, is pMi,, and this is equal to 0.16 volt when i, = 3 amperes and p = 754. In methods 4 and 5, e, was usually 45 to 70 volts, and hence the correction y due to mutual inductance is only one or two units in the last decimal place of the values given for cos 4, in Tables IV and V. In method 3, however, e, was smaller and the correction is 5 to 6 in the last decimal place of the values of cos 4, in Table III.

The expression for cos 4, in which the mutual inductance of the fixed and auxiliary coils is taken into account, is

There is also a slight correction & to be made in method 3, for the potential current i,, which also passes through r; that is, the resultant of, and passes through 7. This makes a slightly larger current and shifts the phase a little. The shifting of the phase, however, does no appreciable harm. The correction y can be made insignificant by increasing r, and using an auxiliary condenser of correspondingly smaller capacity, while the correction & is reduced to an insignificant quantity by having the potential current, sufficiently small in comparison with. In fact, it is easy under most circumstances to eliminate the three corrections ß, y, d by properly proportioning the coils,

leaving only a small correction a to be applied, due to the resistance of the fixed coils and connections.

METHOD 4.-SHUNT ON POTENTIAL CIRCUIT.

In this case, fig. 7, the compensation current i, is shunted off from , the resistance r, being in the potential circuit through the moving

coil instead of the main circuit as in method 3. The compensation current is thus in phase with 2, but by reversing the terminals of the compensation coil it has the same effect as though it were opposite in phase. Thus, fig. 6 represents this method also.

METHOD 5. USING A TRANSFORMER FOR THE COMPENSATION CURRENT.

In this case the high potential winding of a transformer is joined across the terminals A B of the circuit, fig. 8, and the low potential

coil supplies the current i, to the compensation coil through a resistance R. This current is opposite in phase to i, as in methods 3 and 4.

The small electromotive force e, may be determined by the ratio of transformation, or by direct measurement. It is very convenient to put a voltmeter on the secondary of the transformer and measure e directly, and then get E by multiplying by the ratio of transformation. Some of the results obtained by this method are given in Table V.

The transformer used here is the potential transformer which was employed to get the voltage on the main condenser circuit. In these experiments it had a ratio of about 14, and hence, for 90 volts on the secondary there was 1,260 on the primary. The secondary consisted of two equal coils, and the compensation coil was joined to the terminals of one of them. The slight current used (about a hundredth of an ampere) did not alter the ratio of transformation of the transformer.