F. W. Very — Sky Radiation and Isothermal Layer. 385 



Chimie et de Physique (6) ix, pp. 433-506, 1886, where, however, the wave- 

 lengths and temperatures are very imperfectly estimated. The same remark 

 applies to the "Curve Showing Movement of the Maximum," published in 

 the memoir on "The Temperature of the Moon," by S. P. Langley, assisted 

 by F. W. Very (National Acad. Sci., vol. iv, part 2, plate ix, Washington, 

 1889), but does not so much affect the curves showing " Eates of Emission 

 for Different Deviations " (op. cit. plate 5) in which the temperature-excesses 

 are limited to fairly trustworthy values, less than 200° C. The ordinates 

 (emission of approximately homogeneous radiations corresponding to given 

 rock-salt deviations) suffer somewhat from defect, because the bolometer 

 was not a complete absorbent. This instrumental deficiency was subse- 

 quently remedied by Paschen, who devised what may be called a " repeating" 

 bolometer, or thermopile, where the heat-measuring instrument is at the 

 center of a hemispherical mirror, pierced by an aperture for admitting the 

 radiation, and where those rays which are not immediately absorbed and 

 converted into heat are diffusely reflected to the mirror and come back 

 again for one or more subsequent absorptions at the sensitive surface, until 

 the last vestige of radiant energy has been utilized. 



The Allegheny measures were revised by me in 1896 and given with 

 correctly assigned wave-lengths, and on the normal scale, in a paper, 

 "Further Considerations in regard to Laws of Radiation" (Astrophysical 

 Journal, vol. iv, p. 38, June, 1896), but still with the same temperatures 

 which had been originally assigned from known melting points. These 

 temperatures, or at least the higher ones, were largely overestimated, because 

 no allowance was made for the fact that the outermost layer of a plane, 

 vertical, radiating surface, of large temperature excess, is cooled so rapidly 

 by aerial convection, that even a highly conductive metal (heated from the 

 back side) develops a very steep subsurface temperature-gradient, and all 

 ordinary methods of measuring the real temperature of the radiating surface 

 fail. Paschen first determined the true temperatures by using a radiator of 

 cavernous shape, employing a "repeating" principle in the radiator, as 

 well as in the heat-measuring instrument. This principle had been known 

 in the theory for some time, and was reasoned out mathematically by Ferrel 

 ("Recent Advances in Meteorology," p. 97, Washington, 1886), but was first 

 practically applied in these researches by Paschen, from which Wien's law 

 was confirmed in a very satisfactory way. 



The emission of homogeneous rays may be expressed by the equation 



J = CaT* 



where x = 4 to 5 for wave-lengths (A) not far from the maximum in the spec- 

 tral energy-curve of the black body at absolute temperature T, and 0% is an 

 emission constant, varying with /i, and to a still greater extent with the 

 nature of the emitting substance and the thickness of its emitting layer. 

 At much higher temperatures, for which the spectral maximum has passed 

 to wave-lengths shorter than A, the emission of wave-length a requires a 

 smaller value of x ; an( i for low temperatures where rays of wave-length A 

 are first beginning to be emitted, the rate of increase of the incipient 

 radiation is much more rapid, so that x assumes large values. To show this, 

 I will take from the Allegheny curves of plate 5 (op. cit.) ratios of the homo- 

 geneous radiation of lampblack at three temperature-excesses : 



a = 60° = T 2 - T x = 326° - 266° abs. C. 

 6 h = 120 = 386 - 266 



6 C = 180 = 446 - 266 



This eliminates any imperfection in the absorbent process, since the errors 

 are the same in the components of each series, though varying from one 

 series to the next. Radiation of wave-length Ifi is incipient for such excesses 

 as these, and the exponent of T reaches 10, but falls below 4 for the longest 

 waves. 



Am. Jour. Sci.— Fourth Series, Vol. XXXV, No. 208.— April, 1913. 



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