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With the cylinder in position to receive the rays, the galvanometer showed a positive deflection of about 300 mm as soon as the discharge was started; the deflection dropped at once to 5 mm when the cathode rays were deflected by a magnet, so that the canal rays could not pass the diaphragms. The original deflection appeared again as soon as the magnet was removed. When the cylinder was turned back so that the canal rays just grazed it as they passed through B, the deflection was about 15 mm, probably due to diffuse rays from the main stream. The exact position of the rays could be easily determined by the bright fluorescence of the gas.

This experiment was performed with a potential difference between the electrodes of the tube of 8,000 volts, as measured on a Braun electrometer.

aJ. J. Thomson: loc. cit. E. Rutherford: Address before the International Congress of Arts and Sciences, St. Louis, 1904. G. C. Schmidt: Die Kathodenstrahlen,

p. 110.



The study of the emissive properties of substances which can be brought to high temperatures without undergoing chemical or physical changes of surface is important in optical pyrometry for the practical realization and measurement of high temperatures; for a knowledge of the emissive properties of platinum, for instance, at various temperatures, gives a ready means of obtaining true temperatures from observations of the “black-body temperatures" as measured by an optical pyrometer. A platinum strip may replace to advantage an experimental black body, especially at temperatures above 1,500° C., and may conveniently serve as a luminous source for the comparison or calibration of optical pyrometers.

It is the object of this paper to interpret the observationsa of Dr. Waidner and the author on the departure of platinum from blackbody radiation for red, green, and blue light, in terms of the now better known values of the higher temperatures involved, and as expressed by Wien's law as applied in a form first suggested by Lucas.

For a black body, Wien's law for the distribution of energy in the spectrum may be written

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where E is the energy radiated between wave lengths 1 and 1+d1, ar the reciprocal of the absolute temperature, C and C, constants, and E, the logarithmic base.

For any other substance at the same photometric brightness we have

a C. W. Waidner and G. K. Burgess: Optical pyrometry; Bull. Bureau of Standards, 1, p. 189; 1904. bR. Lucas: Phys. ZS., 6, pp. 19, 418; 1905.

log E=log C;'-n log 1 e ,



in which n>5, C;">C, and 6,>. Thus, for platinum n=6.42 according to Paschen, and n=6 from Lummer and Pringsheim's work. The largest value of C, for the visible spectrum is that deduced from the measurements of Lummera and Pringsheim: Ce=51,T=5 X 2940 =14700, and the smallest value of Cis Co61 mT=6.2600=15600.

That 0,>,, follows from the definition of a black body. C, and C; are both small and the difference of their logarithms is negligible in most of what follows.

We may shorten the expressions by grouping the various constants, as follows:

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slog C, -5 log 1=K,

log &

12 (B)

log &

C, llog C'-n log 1=K,

λ Whence, by equating (1) and (2),

K-K,9,=K,'K,'8, Or, more simply, 0,=a8,+B

(3) Where

K, C,
by (B)

(4) And

K,-K,_1 (log C; – log C'+(n—5) log 1) by (A) and (B) (5) B= K,

C, log &


B=K1 log 1

(5a) where K is a constant, characteristic of the substance.

Furthermore, the constants a and ß must lie within well-defined limits, as follows: a >1 since C,' > C,



That is, a is always greater than unity, but approaches unity as the substance examined is more nearly a black body; a=1.06 from

a A discussion of the values of these constants is given by Lummer in Reports to Congress of Physics, Paris, 1900, vol. 2, p. 41.

the data cited above. Again, a is independent of the wave length 1 to a first approximation, by (4). Since experiment shows n > 5, we have B> 0


or B approaches zero as the black body condition is approached, and equation (5a) shows the dependence of ß upon the wave length, namely, that B increases as the product of the wave length into its logarithm. The constant n can evidently be computed by (5) if B and C, are known, or conversely, ß may be calculated; but then, in these computations log C, -log Ci' is no longer negligible.

Equation (3) was deduced by Lucas, although he does not show completely the interrelations of the constants involved nor the necessary limitations as to the numerical values of a and ß.

Equation (3) with the above corollaries is fundamental and completely expresses the departure of any substance from a black body in terms of the temperature and two constants whose values are a measure of its emissive properties, and states that the reciprocals of the temperatures of a black body and any substance having the same photometric brightness are directly proportional.

As the equation is linear, a knowledge of the black body temperature and true temperature at two points only is sufficient to completely define the departure of the radiation of a given substance from that of a black body throughout the entire temperature scale, provided the substance undergoes no chemical change; and since a is a contant independent of 1, when equation (3) is determined for any single value of 1, that for any other value of 1 in the visible spectrum is had by an observation of 0, at a single temperature. These facts are expressed by writing (3) in the form: 0,=a 0,+K1 log 1

(8) Experimetal verification of the above conclusions is had in the observations of Dr. Waidner and the author on the relation between the black body temperature and the true temperature of platinum for wave lengths 1=0.651 j (red), 1=0.550 u (green), and 1=0.474 u (blue). The observations were taken on a platinum strip mounted on a Joly meldometer, and the scale defined by melting points, that of platinum being assumed as 1,715° C. and palladium (slightly impure) as 1,525° C.

a Lucas, I. c.
6 Waidner and Burgess, I. c.

c Holborn and Henning: Sitzungber., Berlin Akad., March 2, 1905, p. 311. Harker: em. News, 91, pp. 262, 274; 1905.

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