EXPERIMENTAL RESULTS. The methods we have used are all dependent on the extrapolation of Wien's equation for the distribution of energy in the spectrum of a black body, J=c, λe ̄λT The researches of Lummer and Pringsheim," Paschen," Rubens and Kurlbaum, and Beckmannd have shown that this law does not hold for long wave lengths and high temperatures. The results of experiment are better represented by the equation deduced by Planck. The experiments of Rubens and Kurlbaum have shown that this equation is in most satisfactory agreement with the results of experiments throughout the widest range of measurable temperatures, -200° C. to +1,500° C., and for the longest waves of the infra red portion of the spectrum obtained by multiple reflection from fluorite (λ=24.0μ and 31.6μ) and rock salt (λ=51.2μ) surfaces. However, for the wave lengths of the visible spectrum, and even for the region of the infra red in which the largest part of the total energy of the spectrum is found, Wien's law applies with sufficient precision. Lummer and Pringsheim have shown that for values of AT less than 3000 Wien's equation represents the results of experiments to an order of accuracy of 1 per cent. For the photometric measurements in the visible spectrum where the wave length does not exceed 0.65μ, the use of Wien's equation is justified for extrapolation to temperatures exceeding 4000° C. a Lummer and Pringsheim: Verh. d. Deutsch. Phys. Ges., 1, pp. 23, 215; 1899; ibid. 2, p. 163; 1899; ibid. 3, p. 6; 1901. Lummer: Sur le rayonnement des corps noirs: Int. Cong. Rep., Paris, 1900; p. 929. Paschen: Ann. d. Phys., 4, p. 277; 1900. c Rubens and Kurlbaum: Ber. d. K. Akad. d. Wiss., Berlin, 41, p. 929; 1900; Ann. d. Phys., 4, p. 649; 1900. d H. Beckmann: Inaug. -Dissert., Tübingen, 1898. e Planck: Verh. d. Deutsch. Phys. Ges., 2, pp. 202, 237; 1900; Ann. d. Phys., 4, p. 553; 1901. We have determined the temperature of the brightest portion of the positive crater of the electric arc by means of the three pyrometers devised, respectively, by Le Chatelier, Wanner, and Holborn and Kurlbaum. The three instruments are photometers. In the Wanner a narrow spectral band in the red is used as monochromatic source, while in the other two dependence has to be placed upon colored glasses for monochromatism. In the Holborn-Kurlbaum" pyrometer the tip of a very fine incandescent lamp filament is made to disappear against the bright background observed, by varying the current through the lamp. The current is then a function of the temperature which may be found by calibration against a thermocouple. In the Wanner instrument a polarizing device permits balancing photometrically the intensities of the same spectral hues coming from a standard light and the source observed. The angle of the analyzer may be converted into degrees of temperature by calibration. In the Le Chatelier instrument the light from the source is cut down by a cat's-eye diaphragm until photometric equality is had with light from a comparison source, when from the opening of the cat's-eye the temperature may be calculated after the instrument has been calibrated. Between such a bright source as the arc and any of these instruments it is necessary, in order to render photometric comparison possible, to interpose absorbing glasses whose absorption factors (K) have to be determined for the different wave lengths used. Wien's law gives: 2 e T. T 2 where c2=14500 for a black body, where A is expressed in μ, e is the base of Naperian logarithms, J and J, are the light intensities expressed in any units corresponding to the temperatures T and T2, Tbeing the absolute black-body temperature of the source and T2 its apparent temperature when the absorbing glasses are interposed. This formula may be used with any of the above pyrometers to determine the arc temperature when Kis known and the reading of each instrument has been found for some source which can be viewed without the absorption glasses. As a convenient reference temperature, or source of constant intensity, that of the central area of a definite acetylene flame viewed normally was used. The apparent black body a Holborn and Kurlbaum: Ann. d. Phys., 10, p. 225; 1902. Le Chatelier: J. de Phys., (3), 1, p. 185; 1892. temperature of this source was 1625 abs., the different instruments agreeing to within 3° in this determination. Each of the instruments was also calibrated over a considerable temperature range in terms of a thermocouple using a Lummer-Kurlbaum black body as source, thus obtaining a whole series of comparison points. The two methods gave concordant results. The values of absorption factors (K) vary with the wave lengths of the light used, K decreasing quite rapidly for shorter wave lengths. Thus a given absorbing glass gave K=1500 for λ=0.651μ, and only 360 for λ=0.550μ. Also with these glasses the value of K for n glasses is not K", as is generally assumed, but something less than this quantity. Four glasses of the same quality and thickness gave, for A=0.651μ, the following results, as determined from a large number of observations, using all three pyrometers in this determination: The results of our determination of the arc temperature for a current of 15 amperes are given in the three following tables. The carbons were exceptionally homogeneous, prepared especially for optical projections and arcing very readily. The positive carbon (13 mm diameter) was mounted horizontally and the negative (11 mm diameter) vertically. The potential across the arc was about 65 volts. In order to prevent the formation of a deep crater on the under side of the positive carbon, the latter was occasionally trimmed down so that the hottest part of the crater could be readily viewed in a horizontal line. Although the three pyrometers give practically an identical value (3700° abs.) for the arc temperature, yet we do not consider all the observations of equal weight. The red glass λ=0.630μ is not sufficiently homogeneous for good photometric measurements; with the Holborn-Kurlbaum instrument, for instance, the filament of the lamp can not be made to disappear when using this glass. Glass A 0.651μ, on the other hand, leaves practically nothing to be desired as to its homogeneity, and the results obtained with it have the greatest certainty. The values of the equivalent wave lengths for the red glasses were verified by Dr. Nutting to an accuracy well within the limits of error from other sources. The relative temperatures obtained with the various instruments are independent of the absorption factors, the latter being dependent upon the absorption glasses, which were the same for all the pyrometers, and upon the wave length used. The absolute values we have obtained for the arc temperatures would evidently be in error if the values of the absorption coefficients are incorrect. The values chosen are the best that could be deduced from several hundred observations made with all the pyrometers. The absorption factor for green light (λ=0.550μ) is, however, less well determined. As to the pyrometers themselves and the reliance to be placed upon the results obtained with the different instruments, the greatest uncertainty seems to be with the Wanner, because it is more difficult with this instrument than with the others to be sure that one is sighting upon the desired spot, as the instrument is not a telescope; also, the extrapolation of the scale of this particular instrument is somewhat uncertain. As between the determinations with the Le Chatelier and Holborn-Kurlbaum instruments, the preference is in favor of the latter, as a smaller area is used in the photometry and there are more independent checks upon its calibration; thus, using three comparison lamps, identical results are obtained. On the whole, a better agreement among different instruments employing such varied methods of measurement could hardly be expected at such a high temperature. Our experiments with pure graphite have shown that the value, 3700 abs., would not be increased by more than 50°. The effect of material of carbons and of current density will also be considered. |