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The bronze yard No. 11, which was an exact copy of the British imperial yard both in form and material, had shown changes when compared with the imperial yard in 1876 and 1888 which could not reasonably be said to be entirely due to changes in No. 11. Suspicion as to the constancy of the length of the British standard was therefore aroused.

On the other hand, the new meters and kilograms represented the most advanced ideas of standards, and it therefore seemed that greater stability in our weights and measures as well as higher accuracy would be secured by accepting the international meter and kilogram as fundamental standards.

Time has amply proved the wisdom of this action, and therefore when the Bureau of Standards was established in July, 1901, the decision made by the Office of Weights and Measures in 1893 to adopt the meter and kilogram as fundamental standards was fully accepted by this Bureau.

In conclusion I wish to state that in preparing so brief an account of so great a subject many matters of importance and interest have necessarily been omitted, but if I have succeeded in giving you an outline of the growth of our weights and measures, I shall have accomplished all that I had in mind when this paper was prepared.

WATTMETER METHODS OF MEASURING POWER EXPENDED UPON CONDENSERS AND CIRCUITS OF LOW POWER FACTOR.

By EDWARD B. Rosa.

The power factor of an alternating current flowing into and out of a good condenser, or a cable on open circuit, is so small as to make its measurement by a wattmeter somewhat difficult. Measurements made by the resonance methoda and by the calorimetric method

gave power factors for some paraffined paper condensers of less than half of 1 per cent. These methods are, however, not adapted to general laboratory work. A simple wattmeter method of measuring power involves two corrections. First, for the power expended upon the fixed coil of the wattmeter, which is measured along with that of the condenser, and, second, for the change of phase of the potential current due to the combined inductance and capacity of the potential circuit. The correction (which is chiefly due to the inductance of the coil of the instrument which carries the potential current) is made small by using a large resistance in the potential circuit. Incandescent lamp filaments have extremely small inductance and capacity, and may be employed in series with one another, as the high resistance of the potential circuit; or wire coils may be employed if wound so as to avoid both inductance and capacity. The potential current, being very small, requires a relatively delicate suspension in order to give a satisfactory deflection. I have found difficulty in securing sufficient stability and sensitiveness at once, and have hence been led to the use of a series of null methods for measuring the power factor of a condenser or cable current, thereby avoiding the measurement of a deflection, and dispensing with the requirement of so great stability. These methods were devised and employed in a long series of measurements in 1898, but the work was interrupted before its completion, and circumstances have since prevented me from resuming the work.

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

.. cos 6, =

The most obvious null method consists in using a variable inductance in the potential circuit. The difference of phase between the two currents being nearly 90°, if the potential current is slightly retarded by an added inductance the phase difference can be made 90° and the deflection reduced to zero. Knowing the value of the added inductance, the frequency of the current, and the resistance, the change of phase, and hence the power factor, can be readily computed.

USING AN AUXILIARY COIL ON THE WATTMETER.

There are, however, several other methods of getting a difference of phase of 90° and securing a zero deflection, any one of which can be employed for this purpose, according to the instruments one has available. These all depend upon the use of an auxiliary coil of fine wire wound over the fixed coil of coarse wire, having about the same number of turns as the fixed coil and made exactly equivalent to the fixed coil magnetically. This equivalence is shown by causing the same current to flow through the main coil and the auxiliary coil in opposite directions. The resulting magnetic field is then zero at the position of the suspended coil if the latter is not deflected when the current flowing through the main and auxiliary coils in opposite direction passes through the suspended coil also. Suppose, then, the condenser current is passes through the fixed coil, the potential current i, passes through the suspended coil, and a small current is in phase with ;) passes through the auxiliary coil. Then if K is the constant of the instrument, the deflection d, of the suspended coil due to current i, in the main coil and in in the suspended coil will be

de = ki,, cos , where 4, is the angular difference of phase between i, and iz.

The current iz through the auxiliary coil would by itself (supposing there is no current in the main coil) produce a deflection d, such that

d,=Kiziz.

If the current iz flows in such a direction as to make the deflection d, opposite to d,, then when the currents i, and i, flow simultaneously, the deflection is the difference between d, and d,; and when this is made zero by adjusting iz we have

i, cos ,

Another way of expressing this result is to say that the current is (which is in phase with i,, but reversed by the connections, and therefore differs in phase by 180° from iz) is added to is, and the vector sum is thereby made to differ by 90° in phase from iz. The ratio of iz to i then gives the angle through which i, has been turned, to make it differ by 90° from in. Or, again, the magnetic field of ig, added to the magnetic field of in, gives a resultant magnetic field which differs by 90° in phase from the potential current in. Hence, knowing is, we can find the power factor cos 6,. The corrections for the resistance of the fixed coil and the inductance of the suspended coil being applied, we have cos 6, the true power factor.

The auxiliary or compensation current iz may be secured by several different devices, as follows:

(1) From the terminals of a noninductive resistance r, in the main circuit a shunt circuit is carried to the auxiliary coil, having a second condenser in series with it. Thus the current iz is proportional to the main current is, to the resistance rz, to the capacity of the secondary condenser Cs, and to the frequency of the current. That is

iz=pCzir, and = cos .=pC,?'

21 Thus, knowing the capacity of the secondary condenser Cs, the frequency of the current (p=2an), and the variable resistance rz, we readily compute the power factor cos du, which, corrected as before, gives cos 0.

(2) A portion of the potential current i, is shunted off through the auxiliary coil, and the value of iz becomes known if iz and the resistances of the divided circuit are known.

(3) By transforming down from the high e. m. f. E impressed upon the condenser and shunt circuit, a small e. m. f. e, is obtained, differing in phase by 180° almost exactly. A current i;= is thus obtained, wbich differs in phase from the shunt current i, by 180°, and this is used as a compensation current. The resistance R, is varied until the deflection is zero, and e, is measured by an alternating current voltmeter; i, thus becomes known, and from it cos 6, as before.

When the capacity of the condenser is small, and therefore the main current i, is small, it may be better to pass is through the suspended coil and the potential current through the fixed coil. This gives rise to two other arrangements of the circuits. But the principle is the same in every case, the compensation current is being determined when the deflection of the wattmeter is zero, and the phase angle then found by a very simple calculation.

2214-No. 3–05—7

eg R,

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