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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 (6500 to 11509), 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.

Wannero 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 1400o absolute, and found that the results were in agreement with Wien's relation for the spectral distribution

C2 of energy for a black body, J=44-5 e-T, as was shown by the linear

1 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 (1 = 0.6563u) and green (1 = 0.5461u) 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 3700o abs. when cored carbons (Dochtkohle) are used; using retort carbons he finds for measurements with the red and green light 3875° and 3895o 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 Pringsheima made use of the relation 1m T=const., connecting the wave length 1m having maximum energy and the absolute temperature T 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




=3750° and T 0.7


=4200° abs. 0.7


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 u. This gives for the upper and lower limits between which the temperature of the positive carbon must lie


=4025° abs. 0. 73

T max

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a Lummer and Pringsheim: Verh. d. Deutsch. Phys. Ges., 1, p. 235; 1899; Verh. d. Deutsch. Phys. Ges., 3, p. 36; 1901.

o 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.

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



where t is degrees centigrade and b the intrinsic brilliancy per square centimeter measured photometrically. For the crater of the arc he found b=11000 candles per cm', 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 connection 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 65+® 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 0.631j than 0.659 u, 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.
4825—No. 1–04-8


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,

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The researches of Lummer and Pringsheim, Paschen, Rubens and Kurlbaum, and Beckmannd have sbown 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.

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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 (1=24.Ou and 31.6u) and rock salt (1=51.2u) 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 17 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 0.65j, 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.

log 10 K= log J2

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 Chatelierc 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:


1 1 (1)


T, T, where c,=14500 for a black body, where 1 is expressed in , e is the base of Naperian logarithms, J, and J, are the light intensities expressed in any units corresponding to the temperatures T, and T,, T, being the absolute black-body temperature of the source and T, its apparent temperature when the absorbing glasses are interposed. This formula may be used with any of the above pyrometers to determine the are temperature when K is 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


log 10


a Holborn and Kurlbaum: Ann. d. Phys., 10, p. 225; 1902.

Wanner: Phys. ZS., 3, p. 112; 1902.
c Le Chatelier: J. de Phys., (3), 1, p. 185; 1892.

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