with which we could determine motion in the line of sight, the general results would probably be comparable in excellence with the results obtained by any spectroscope at present in use, including those attached to the Lick and Yerkes telescopes.

THE UNIVERSITY OF CHICAGO,

YERKES OBSERVATORY,
June 1899.

ON THE DISTRIBUTION OF THE ENERGY IN THE SPECTRUM OF THE BLACK BODY AT LOW TEMPERATURES.1

By F. PASCHEN.

My observations on the energy spectra of different solid bodies make it seem possible that the law derived by W. Wien 3 represents the emission of "the absolutely black body." In Wien's formula,

where Jd is the energy between wave-lengths λ and λ + dλ at the absolute temperature T, and c, and c, are constants, if we substitute for A-5, the value of a changing from body to body, my former observations are represented by the formulae. The value of a decreased from 6.4 to 5.2 in passing from reflecting platinum to strongly absorbing carbon.

The deviation of my former observations from the theoretical laws was such that that which was theoretically well-founded was not confirmed with certainty, while on the other hand that which was uncertain theoretically was rendered probable by the observations. The comprehensive formula of the law of emission is not supplied by theory in an unquestionable manner. If we assume the validity of the formula with the constant a derived from the experiments, then a must have the value 5, for Wien has proven that the intensity J of the maximum of energy varies as the fifth power of the temperature, which is the case in the assumed formula only when a 5. In addition to this rela

tion

'Sitzungsberichte der Berliner Akademie; Session of the physical-mathematical section on April 27, 1899.

2 Wied. Ann., 58, 455, 1896; 60, 662, 1897. (The latter will be referred to as loc. cit.)

3 Wied. Ann., 58, 662, 1896.

two further relations are firmly established by Wien, or follow from his accurate derivations, viz. :

or the wave-length of the maximum of the energy curve for temperature 7 is inversely proportional to the temperature; and (3) the relation that the ratio of the intensity J of wave-length λ to the intensity J of the energy maximum of wave-length A, or

J

Jm

λ , is a function of and for the energy curves at different

λπ

temperatures always the same function of

λ

λι

In a logarithmic

representation all the energy curves must be congruent.

I found laws (2) and (3) to be confirmed. The experiments. gave for the last relation (3) the function

which theory left indeterminate.

(4)

It was only on making certain doubtful assumptions that Wien succeeded in deducing formula I, and we may regard formula (4) with a set equal to 5 as the result of Wien's research.

We therefore have to investigate whether this function (4) holds good with the value of a = 5, if we approach closely to the radiation of the absolutely black body. This seemed probable from my experiments, since the function was valid for radiating bodies. of very different absorptive power, and since a had already taken the value 5 for the blackest body. The confirmation of relation (1), which according to theory must hold first of all, will be a crucial test whether the arrangements of the experiments sufficiently comply with the postulates of the theory; for the constant c2 of formula I can be determined from the measures with sufficient accuracy only when this relation—in my experience the most difficult to realize-also holds good.

In attempting to answer these questions I first determined the energy spectra of cavities, the sides of which were heated by

=

baths. These experiments gave a somewhat closer approximation to law I than my former observations, as the relations 2, 3, and 4 appeared to be quite fully satisfied with a 5, and as the observations were best represented by my previous formula with a value of about 5.2 for the exponent of A; but it was impossible, however, to find the intensity of the maximum of energy exactly proportional to the fifth power of the temperature without overstepping the limits of error very considerably. The discrepancy might be due to the imperfect realization of the radiation of the black body, as the cavities had openings. When these were very much reduced, however, the emergent radiation still gave the discrepant result as before. The only thing in the experimental arrangements that could be held responsible for this was a variability of the absorptive power of the exposed bolometer strip with the wave-length. It therefore remained either to determine this or to so arrange the receiver of the radiation that it should constantly absorb the incident radiation as nearly completely as possible. I adopted the latter method and beg to show in what follows how far I have been able to approach to my aim. The experiments I communicate refer to the region of low temperatures and long wave-lengths. These experiments are the best adapted for judging of the blackening of the receiver, since my ordinary bolometers deviate most from my blackest ones just at this region.

ARRANGEMENT OF THE EXPERIMENTS.

The spectroscopic apparatus employed includes a fluor-spar prism loaned me by the firm of Carl Zeiss, which I had used before, and two silver concave mirrors of 35 cm focus, with precisely spherical figure, and so arranged that the astigmatism of the image was reduced as much as possible. The spectrum thus produced was so exceedingly sharp that the two broad absorption bands of aqueous vapor in the air of the room at X 6.0 μ and 6.5μ were resolved into numerous sharply defined bands, while between them at X6.26μ was a place without appreciable absorption. The absorption band of carbon dioxide of the air

of the room appeared narrow like a line, but at its deepest part extinguished more than two thirds of the original energy.

2000

All of the bolometers with which the results below were obtained were simply strips of platinum of mm thickness and most had a breadth of 0.5mm, corresponding to an angle of 5 minutes in the spectrum. The piece upon which radiation fell had as accurate a rectangular form as possible. The slit-width was altered until the energy curve of a line (or of the image of the slit when the prism was removed) became as nearly as possible an isosceles triangle, as the correction for the impurity of the spectrum due to the width of the slit can be simply calculated for this case.' The exposed surface of the bolometer was blackened either with lampblack or according to the Lummer-Kurlbaum method with platinum black. The layer of black was given two or three times the thickness prescribed in their rule or employed in my earlier bolometers. The extremely slight thickness of the bolometer strip gives the advantage that in spite of the thick covering with black the galvanometer deflection, even with a period of six seconds, behaves just as on breaking a shunt across the branch of the bolometer if the conductors to the sensitive parts are screened by metallic diaphragms, and protected above and below from the latter for a space of some 0.5 mm.

2

To produce a further effect of blackening, the bolometer strip was placed, according to the principle proposed by myself (loc. cit. p. 722) with its middle exactly at the center of a reflecting hollow shell which had a small aperture for the admission of the radiation. Only that hemisphere of the shell was present on which the radiation reflected from the strip could fall, while the strip was so fixed that it could reflect toward all possible parts of the hemisphere. The frame of the bolometer could be moved by a micrometer until the strip covered its image. For reflecting hemispheres I used one of 45 mm diameter with poor polish and an inaccurate surface. A second one, cut exactly spherical by 'C. RUNGE, Schlömilch's Zeitschrift für Math. und Phys., 42, 205, 1897.

F. KURLBAUM, Proceedings of the Physical Society of Berlin, p. 11. June 14, 1895.