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distance of 2 cm. The results of the measurements on platinum are given in the following table:

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From the above table it will be seen that if the temperature of a platinum surface is measured with a polarizing pyrometer large errors may result if the effect of polarized light is neglected. Thus, if the surface be viewed at an angle of 50° with the normal, two readings may be obtained differing from one another by 80° C. at 1450° C., i. e., the reading may differ from the actual temperature hy 40° or thereabouts.

As the light emitted in a direction perpendicular to the surface is not polarized, this source of error can always be avoided by viewing the surface normally. For most substances on which optical py rometers are used in industrial operations, the amount of polarized light is very feeble compared with platinum, so that its effect is entirely negligible. In some experiments where the incandescent surface of iron was viewed at an angle of 75° the effect was less than 5°C.

In any case,

sources.

the effect may be eliminated by taking readings in four azimuths at intervals of 90°.

Effect of diffuse and reflected light.The ordinary diffuse daylight or light from other sources which is not reflected directly into the pyrometer exerts a comparatively negligible effect on the indications of these instruments, not exceeding 5° C. for a change from a darkened room to bright daylight.

The magnitude of the effect of directly reflected light is very variable, depending upon the reflecting power of the incandescent body observed, and on the temperature, size, and location of the disturbing

With a good reflecting surface like polished platinum, which remains a good reflector at high temperatures, the effect may be very great, wbile with a substance like iron (oxide) it is very much less for the same surrounding sources of light. Again, the greater the difference in temperature between the object viewed and the disturbing light the greater will be the effect.

Some of the effects noted with platinum were as follows: A platinum strip at 800° C. had its temperature apparently increased 15° C. by direct reflected light from an incandescent lamp, 120° C. by a large gas flame, and with the strip mounted within a ring of gas flames an apparent rise of over 300° C. was observed.

With a sheet of iron at 725° C., within the ring and with the gas flames burning low, a change of 35° C. was noted in the indications of the pyrometer, while with the flames burning brightly no measurements could be taken. When the iron was at 1100° C., however, turning off and on the flames made practically no difference in he temperature readings.

The arrangement with the ring burner approximates a number of industrial operations, where heating is done by radiation from flames. The above results would seem to show that even for poor reflectors, such as iron, clays, etc., considerable errors may be introduced at temperatures below 800°, and that the error becomes small above 1100°

This source of error may be very nearly eliminated by viewing the object through a tube which cuts off most of the light from surrounding flames. Thus in the instance cited above for iron the error of 35° C. was reduced to 5° C. by this means.

The measurement of very high temperatures.— The temperatures that have been discussed thus far are within the range controlled by thermocouples, calibrated to agree with the gas scale to about 1150° C., which marks at present the upper limit of satisfactory gas thermometry. The thermocouple scale is then extrapolated for 500° or 600° more.

Already there are many operations, such as those carried out in the Moissan furnace, the Goldschmidt thermite process, the production of carbides and metallurgical products in electric furnaces, and many pyrochemical reactions that involve temperatures of 20000 or over. It therefore becomes necessary to establish at least some tentative scale that can be used at these extreme temperatures.

Attempts are being made by Nernst and others to estimate these high temperatures by means of chemical phenomena taking place at high temperatures, but this work is still in a preliminary state. For this purpose, therefore, recourse must be had alone to the extrapolation of the laws of radiation which have been verified throughout the range of measureable temperatures.

Lummer and Pringsheim" have recently taken a single set of observations on an electrically heated carbon tube in an atmosphere of nitrogen, using three radiation methods: Photometric (Wien's law), spectrophotometric (. T=A), and total radiation (Stefan's law), the results agreeing to 200 at 2300° C. absolute.

From our own work it would seem that the radiation laws are still in agreement at the temperature of the arc. Our measurements have given as the black body temperature of the hottest part of the positive crater 3690°, 3680°, and 3720o absolute, as determined with the Holborn-Kurlbaum, Wanner, and Le Chatelier pyrometers, based on the extrapolation of Wien's law. Féry gets for this temperature 3760° by a method based on Stefan's law.

On the basis of these experiments it would seem that the several laws of radiation are in quite satisfactory agreement at the highest attainable temperatures, and thus serve to define the same scale of temperatures.

a Lummer and Pringsheim: Verh. d. Deutsch. Phys. Ges., (5) 1, p. 3; 1903. b Waidner and Burgess: Bulletin No. 1, Bureau of Standards; 1904. c Féry: Comptes Rendus, 134, p. 977; 1902.

ON THE THEORY OF THE MATTHEWS AND THE RUSSELLLÉONARD PHOTOMETERS

PHOTOMETERS FOR THE MEASUREMENT OF MEAN SPHERICAL AND MEAN HEMISPHERICAL INTENSITIES.

By EDWARD P. HYDE.

I. INTRODUCTION.

Much attention has been given in the last few years to the development of photometers designed for the measurement of mean spherical and mean hemispherical intensities of light sources. Among other instruments of this type that have appeared may be mentioned particularly the two instruments a designed by Matthews, and the more recent instrument of Léonard, based on theory first given by Russell. In each of these photometers mirrors are employed in order to project upon the photometer screen light emitted by the source at various inclinations to the vertical axis, but in each instrument a different method is used for weighting the light from each mirror, so that in the summation the light from each mirror shall be diminished in proportion to the area of the zone in which the mirror lies and for which it is supposed to give the mean value.

In the Matthews integrating photometer for incandescent lamps the light from each mirror falls upon the screen at an angle of incidence, 90° –4, which is the same as the angle between the horizontal direction and the line joining the mirror in question with the light source. The area of a zone of latitude 90° — O is proportional to sin 0, and the intensity of illumination produced by light incident at angle 90°-A is

« Trans. Amer. Inst. of Elec. Eng., 18, p. 677, 1901; 24 p. 1465, 1902. "L'Éclairage Électrique, 40, p. 128, 1904.

19 (Jour. Inst. of Elec. Eng., 32, p. 631, 1903.

d In order to make the use of “” in this connection consistent with its subsequent use in the paper, it is necessary to denote the angle of incidence by “90°—g” instead of by “G."

cut down in the ratio of 1:sin 8; therefore, the light from each mirror produces an illumination of the screen proportional to the area of the zone in which the mirror lies, and hence receives its proper weight in the summation. In the integrating photometer for are lamps, however, the ligbt from each mirror is incident upon the screen at the same angle, but between the screen and the circle of mirrors is interposed a circular glass disk divided into as many sectors as there are mirrors, and having each sector so smoked that its coefficient of transmission is proportional to the cosine of the angle, 90°—A, between the horizontal direction in the plane of the mirrors and the line joining the light-source with the mirror to which the sector in question corresponds. In this way the light from each mirror is cut down in the ratio of 1: sin 8, and therefore receives its proper weight in the summation for the mean spherical intensity.

It is to be especially noted that in the theory of each of the above instruments the surface of the unit sphere is divided into an integral number of zones, not of equal area, but of equal arc, so that the area of each zone is proportional to sin H, and to each zone a mirror is assigned. Suppose, now, that instead of dividing the surface of the sphere into zones of equal arc we divide it into zones of equal area, and in each zone place a mirror in such a position that it gives the mean value of the intensity for the zone in which it lies. C'nder these circumstances the light from each mirror, since it stands in every case for a zone of the same area, is to be given the same weight in the summation for mean spherical intensity, and consequently no further weighting is necessary.

This principle is made use of in the instrument of Léonard, though it was Russell who first suggested that in the determination of mean spherical and mean hemispherical candle-power by a number of readings at intervals in the vertical plane, the readings be made, not at equal angular intervals, as is ordinarily done, but at intervals corresponding to the middle points of successive zones of equal area, so that the unweighted arithmetical mean of the various readings may be taken as the mean spherical intensity of the source.

It was the original intention of this paper to present a more complete theoretical discussion of the Matthews integrating photometers, particularly of the instrument intended for incandescent lamps and sources of like intensity, as it was in connection with the design of such an instrument for the Bureau of Standards that this investigation was undertaken. Since, however, the Russell-Léonard instrument may be treated in an entirely similar manner, we shall conclude the paper with a brief theoretical discussion of this new type of photo

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