﻿198 M. F. Zollner on the Influence of Density and 



and density with, which a gas in a Geissler's tube shows such 

 simple spectra may agree not remotely with those of the nebulae, 

 because in the latter the enormous thickness of the radiating 

 layer supposes an almost infinite rarefaction of the luminous gas. 



On the other hand, it is obvious that the continuity of a ne- 

 bular spectrum is not sufficient to permit a conclusion as to the 

 density, because, according to the above-mentioned principle, the 

 same effect may also be produced by a sufficient thickness of the 

 radiating layer. 



Meanwhile the following consideration of the subject may at 

 least serve to determine the lower limit of the temperature of a 

 nebula the spectrum of which is discontinuous : — 



The expression for the brightness Ex<r of the place belonging 

 to the wave-length X in the spectrum of a gas with the density 

 cr, and at a given temperature, is 



Ex,= [l-(1-A,)']|-; 



As already remarked, this expression cannot become greater than 



E 



~; and, according to KirchhofFs theorem, this value is that 

 A\ 



brightness which, for equal temperature and wave-length, is 

 possessed by the same place in the spectrum of a perfectly black 

 bod}', and, in fact, independent of its other qualities*. Hence, if, 

 with the current from a galvanic battery, we heat a dark, opaque 

 body (one as nearly as possible corresponding to the requirements 

 stated — for example, a piece of charcoal), and produce a spec^ 

 trum from the light emitted, the temperature of the incandescent 

 charcoal will be lower than that of the luminous gas with a dis- 

 continuous spectrum, as long as the brightness of the continuous 

 spectrum, in the place corresponding to a bright line of the gas- 

 spectrum, is less than or equal to the brightness of this line. It 



E A 



is here assumed that, ceteris paribus, -~ continually increases 



with the temperature. 



If we now compare the brightness of a line in the nebular spec- 

 * It is easily seen that the above expression, when tr=oo , expresses the 

 perfect opacity of the layer of gas, since 1 — (1— A^) " expresses, in terms 

 of the incident light of the wave-length X, the quantity of light absorbed by 

 this layer, Axo-. If, then, Ax(j-=1, this signifies the complete absorption of 

 a ray incident upon the mass of gas. Remembering that all bodies, even 

 those relatively opaque, are transparent in sufficiently thin lamellae, and 

 that, by virtue of the equivalence of thickness and density, the number m 

 of the radiating and absorbing layers may be put in the above formula in- 

 stead of the density o-, we perceive the applicability of the above expres- 

 sion to opaque bodies also, since it involves at the same time the necessity of 

 the continuity of their spectra. 



