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where n is the ratio of transformation of the potential transformer. Or, the formula may be written cos 6,=pCzes


and determined

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

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The quantities in Table VI are as follows:

d is the deflection of the electrodynamometer in scale divisions.
K is the constant of the electrodynamometer.
, is the main current, through the condenser under test.
į, is the potential current, through the large resistance R.
p is 27 times the frequency.
L is the variable inductance added to the potential circuit.

R is the large potential resistance, as free as possible from inductance and capacity. 73

is the small resistance shunted by the auxiliary circuit. Cz is the auxiliary condenser, of constant value. R, is the resistance in series with the auxiliary coil.

ez 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 B to be applied to derive the true power factor cos 0 from the measured power factor cos dz. 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 with the condenser short circuited (figs. 1, 3, 5, etc.)—was 0.08 ohm. When the current is 1.6 amperes, ir 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 0. 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 bigher 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.





From an arc may be obtained a nearly pure spectrum of the electrodes, the spectrum of the surrounding atmosphere under certain conditions scarcely appearing at all. On the other hand, the light from a discharge tube may give a pure spectrum of the atmosphere about the electrodes, but no spectrum of the electrodes themselves. Various kinds of arcs, sparks, and discharge tubes under various conditions may exhibit mixed spectra in all intermediate proportions.

Arc, spark, and low-pressure discharge are but particular cases of a general case in which a gas forms part of an electric circuit otherwise metallic. It is the purpose of this paper to discuss the many conditions that may govern the preponderance of the spectrum of the electrodes over the spectrum of the intervening gas, select the predominant influences and then if possible to map out the conditions necessary for the production of a given pure spectrum with lines of a given character. To obtain coordinate data over the wide range necessary to warrant general conclusions, the spectra of twenty-one different metals were photographed each under a uniform schedule of eightyone different conditions.

The relative intensity of the spectrum of the electrodes depends primarily, of course, on the relative proportion of its vapor present in the part of the arc, spark, or discharge tube observed.

We are

a This paper is the third of a series of four on the general subject of the preponderance of one spectrum over another in a mixture of two spectra. The first of this series dealt with the conditions governing the relative intensities of the spectra of two mixed elementary gases under low-pressure discharge. (The Spectra of Mixed , Gases, Bulletin No. 1, pp. 77–81, November, 1904.) The second dealt with the relative intensities of the two different spectra exhibited by the electro-negative elementary gases. (On Secondary Spectra, Bulletin No. 1, pp. 83–93, November, 1904.) The fourth paper of the series is to be on the spectra of alloys.

concerned first with the conditions governing the amount of electrode metal vaporized and then with the laws governing spectral preponderance in mixed gases, namely; (1) increasing the relative amount of a gas present in a mixture of conducting gases increases the relative intensity of its spectrum; (2) other things being equal, in a steady discharge the spectrum of that component of a mixture having greater atomic weight will be brighter;a (3) in a disruptive or forced oscillatory discharge the atomic weight effect is less.

When the internal oscillations are free (instead of being forced) as in the arrangement used by Ramsey, Lilienfeld, and others to obtain the spectrum of argon in that of ordinary air, perhaps a fourth law would be necessary. Konen (Beibl., 1904, p. 1000) has cited the case of mixtures containing oxygen as apparent exceptions to the atomicweight law (2) above. But oxygen, it must be remembered, has only a very faint (visible) anode glow. Hence to make a fair test of the law we must either take the original faintness of the anode glow into account, or else use the cathode-glow spectrum for comparisons. I have always done the latter. In explanation of the exceptional absence of luminosity in the oxygen anode column, I would suggest that there may be the usual amount of radiation in this case, but that it is chiefly in the infra-red region. The anode column is known to be a region of frequent ionization and recombination, hence we should expect it would be a region of great chemical changes as well. In oxygen, ozone would be rapidly formed and decomposed; hence the radiation from the anode column would consist largely of the strong infra-red ozone bands recently studied by Angstrom.

The metallic or nonmetallic character of the atmosphere surrounding a spark appears to make no difference whatever with the behavior of the spectrum of the electrodes. A spark between aluminum electrodes in an atmosphere of mercury vapor shows identically the same changes on the introduction of capacity, inductance, spark in series, etc., that it exhibits in hydrogen. On the other hand, the spectrum of an iron spark preserves its invariant character as well in mercury vapor as in air, oxygen, or hydrogen.

The vaporization of the electrodes with which we are concerned in the arc, spark and vacuum tube is by no means a mere temperature effect. The amount of vaporization of an electrode appears to bear no simple relation either to vapor pressure or temperature. It does,

a The Spectra of Mixed Gases, Astrophys. J. 19, p. 107; Mar., 1904. o Thomson: Conduction of Electricity Through Gases, p. 486, 1 269.

c Arkiv, för “Matematik,” Ast. och Fysik 1, pp. 347–353; 1904. Beiblätter, 28, p. 1142; Nov., 1904.

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