ON THE TEMPERATURE OF THE ARC.

By C. W. WAIDNER and G. K. BURGESS.

The comparison of the methods of extrapolation that must be resorted to in the estimation of extremely high temperatures is of growing importance in establishing a satisfactory tentative scale of temperature which is already required in many scientific and industrial operations.

In a study of the possibilities of the application of optical and radiation methods of pyrometry to the estimation of extremely high temperatures we have been led to compare a number of carefully calibrated optical pyrometers at the "temperature of the arc."

The early attempts to estimate the so-called temperature of the arc, or more precisely, the temperature of the hottest portion of the positive crater, were based on the extrapolation of empirical relations connecting radiation and temperature (Newton, Dulong and Petit, Rosetti, etc.), that were only applicable through very narrow ranges of temperature, and the results to which they have led are now only of historical interest.

The first important measurement was that of Le Chatelier," who determined for a number of bodies the relation between the photometric intensity of the red light emitted and the temperature. The photometric measurements were made with his optical pyrometer, and the temperature measurements with the now well-known Le Chatelier thermocouple (platinum, platinum-rhodium 10 per cent). This empirical relation is based on experiments extending over the range 700° C. to nearly 1800° C. Le Chatelier found by the extrapolation of this relation (I=106.7 TT) for the temperature of the arc 4400° abs. The red light was obtained by passing the radiation through red glass, which probably lets through the shorter wave lengths at high temperatures, so that the measured intensity would increase more rapidly than the formula would indicate. This would act in the direction of making the result come out too high.

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a Le Chatelier: C. R., 114, p. 737; 1892; J. de Phys. (3), 1, p. 185; 1892.

a

Violle made an estimate of the temperature of the arc by a calorimetric method. A small removable button of carbon on the end of the positive crater was dropped into the calorimeter. The specific heat of carbon was measured and found to obey a linear relation for a considerable range above 1000°, and the relation thus established was assumed to hold as far as the temperature of the arc. The final value found by Violle was given as 3875° abs. Among the great experimental difficulties of this method are those due to loss of heat by the button in falling to the calorimeter and to nonuniformity of heating. Violle investigated these by varying the height of fall and size of the button. In general criticism of this method it should be noted that the specific heat of most substances increases more rapidly as the temperature corresponding to change of state is approached than at low temperatures. Although the difficulties of this method are very great-as admitted by Violle-the result is nevertheless interesting as a determination by a method widely different from those usually employed, based on the extrapolation of relations connecting radiation and temperature.

b

Wilson and Gray made an estimate of the temperature of the arc by a method in which the radiation from the positive crater falling on one junction of a differential radiomicrometer was balanced by the radiation on the other junction from a known area of incandescent polished platinum strip, whose temperature was measured by its expansion after the principle of the Joly meldometer. The relation between the radiation of polished platinum and of platinum covered with copper oxide was then determined and the assumption made that the radiation from the carbon obeyed the same law as from the copper oxide, which is very nearly the case. Knowing then the apparent areas of the two sources of radiation, and knowing the relation connecting radiation and temperature, they could at once find the temperature to which the platinum strip would have to be raised to balance the arc if the apparent areas were equal. The result to which these experimenters were led was 3600° abs. In discussing this experiment which was admirably carried out it must be remembered that it was done at a time when the laws of radiation were not so well understood as they were a few years later. The method of measuring the temperature made use of in these experiments is capable of considerable precision. Their temperature scale is probably about 20° low at 1000°, inasmuch as the melting point of gold was taken as

a Violle: C. R., 95, p. 1273; J. de Phys. (3), 2, p. 545; 1893; C. R., 120, p. 868; 1895. Wilson and Gray: Proc. Roy. Soc., 58, p. 24; 1895; Phil. Trans. A., 185, p. 361, 1894, for details of apparatus, same as used in estimation of temperature of the sun.

BURGESS.

1041° in the calibration of the platinum strip. The radiation of the bare platinum was found to increase approximately as the 4th power of the absolute temperature and of the blackened platinum about as the 3.4th power. This is not in agreement with subsequent researches of Paschen and of Lummer, Pringsheim, and Kurlbaum. The bare platinum was inclosed in a gilt case, which made it approximate more or less to a black body. The strongest criticism of this method is undoubtedly that it is based on the extrapolation of an empirical relation which was studied only through a comparatively narrow range of temperature (650° to 1150°), and the results can not therefore be given so much weight as those obtained by the extrapolation of Planck's law, which has been found to satisfy the results of experiments throughout the range from -200° C. to +1500° C.

Wanner" studied experimentally the relation connecting the temperature and the photometric intensity of monochromatic light of different wave lengths emitted by several black bodies of different construction, up to about 1400° absolute, and found that the results were in agreement with Wien's relation for the spectral distribution

of energy for a black body, J= cλ- e-λT, as was shown by the linear

1

T

relation between log J and Wanner then applied this method to an estimation of the temperature of the arc, by comparing with a spectrophotometer the intensity of the red (A = 0.6563μ) and green (λ = 0.5461μ) radiation with the intensity of the same radiation emitted by a black body (indirectly for convenience through the intermediary of an amylacetate flame whose radiation for these wave lengths had been compared with black body radiation). Using red light, Wanner finds for the temperature of the hottest portion of the positive crater 3720°, and using green light 3700° abs. when cored carbons (Dochtkohle) are used; using retort carbons he finds for measurements with the red and green light 3875° and 3895° abs., respectively. If it can be assumed that the Wien equation continues to hold for such extremely high temperatures, which will be referred to again, this determination of Wanner must be given considerable weight, as the method is capable of precision. It must be noted that inasmuch as this determination is based on the extrapolation of the Wien equation which applies to a black body, the temperature thus found is the "black body temperature," i. e., the temperature that a black body would have to emit light of the same intensity. Barring the presence

a Wanner: Ann. d. Phys., 2, p. 141; 1900.

of luminescence, this method therefore gives the lower limit of temperature, so that the true temperature of the positive crater must at least be higher, by an amount depending on how much its radiation differs from black body radiation.

Lummer and Pringsheim" made use of the relation A, T= const., connecting the wave length Am having maximum energy and the absolute temperature 7 of the radiating body, to estimate the limiting temperatures of a number of incandescent bodies, such as the Nernst filament, the Wellsbach mantle, argand gas flame, and the electric arc. The value of the constant for a black body is 2940, according to their experiments, and 2921 by those of Paschen,' a most satisfactory agreement. For the radiation from polished platinum Lummer and Pringsheim have found for the constant 2630. Assuming, then, that the "displacement law" continues to hold, and that the radiation from the crater of the arc is of the same character as from the black body and platinum, and is intermediate between these, which they have shown is very probable, these investigators concluded that the temperature of the positive crater must be between

From the flattened form of the energy curve and the effect of atmospheric absorption, it is difficult to locate the position of the maximum with precision. It must be said that the "displacement law" on which this method is based is one of the best established laws of radiation, both from the theoretical and experimental side.

By an examination of a spectral energy curve of the positive pole of an electric arc, in a paper by Abney and Festing, F. W. Veryd was led to fix the maximum at about 0.73 μ. This gives for the upper and lower limits between which the temperature of the positive carbon. must lie

a Lummer and Pringsheim: Verh. d. Deutsch. Phys. Ges., 1, p. 235; 1899; Verh.

d. Deutsch. Phys. Ges., 3, p. 36; 1901.

Paschen: Ann. d. Phys., 4, p. 277; 1901.

c Abney and Festing: Proc. Roy. Soc., 35, p. 334, Diagram II; 1883.

d F. W. Very: Astrophysical Journal, 10, p. 208; 1899.

Petavel has found that his observations on platinum radiation satisfy the formula

6.9

(t-400)=889.6✅T

where t is degrees centigrade and 6 the intrinsic brilliancy per square centimeter measured photometrically. For the crater of the arc he found b=11000 candles per cm3, which would give t=3830° C (4100 abs.) assuming that carbon and platinum obey the same radiation law. This assumption gives too high a value for t. With the constants proper to carbon in the above formula, the method might give good results.

More recently Féry' has made estimates of this temperature by two different methods. In one the radiation from the positive carbon was focused by a fluorite lens on the blackened junction of a minute ironconstantan thermocouple which was joined in circuit with a galvanometer. A preliminary calibration of this thermo-electric telescope with the radiation from an electrically heated black body as far as 1500° C showed that the observed deflections of the galvanometer were in most satisfactory agreement with those calculated from the Stefan-Boltzmann law. By this method Féry was led to the value 3763 abs. as the "black body temperature" of the arc. In this con

с

nection it is of interest to note that Lummer and Kurlbaum have found that while the energy of total radiation from iron oxide, which is, very approximately, the same as from carbon, is only 30 per cent of that from a black body at 654° abs., at 1481° abs. it has already grown to 60 per cent. This would indicate that the "black body temperature of the arc," as found by the energy of total radiation from carbon, would not differ very much from its true temperature, probably by less than 200°.

Using the photometric method and a modified form of the Le Chatelier optical pyrometer and assuming that Wien's law continues to hold, Féry finds 4140° abs. with red light and 4170° abs. using green light. As an explanation of this high value, want of monochromatism of the glass used at once suggests itself. The explanation certainly applies for the usual red glasses that are sent out by Pellin with the Le Chatelier optical pyrometer. Moreover, the "center of light" transmission of this glass is nearer to 0.631μ than 0.659μ, the value usually assumed from Le Chatelier's early determinations, probably made with a different kind of glass.

a Petavel: Phil. Trans. Roy. Soc., A 191, p. 515; 1898.

Féry: C. R., 134, pp. 977, 1201; 1902.

c Lummer and Kurlbaum: Verh. Phys. Ges., Berlin, 17, p. 106; 1898.

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