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



equations must ensue : — 





Hence, if we introduce the above values for A^ and A A/(r and 

 again put 



we obtain for the ratio of brightness of two adjacent parts of the 

 spectrum, as a function of the density of the incandescent gas, 

 the following expression : — 



■E to= [l-(l-A J )']J A (8) 



E,„ [i_(i_A A /]J A , 



Since at constant temperature the value of a alters proportionally 

 to the pressure, this formula shows that with increasing pressure a 

 widening of the lines of the spectrum must take place, which gra- 

 dually passes into continuity of the entire spectrum. 



Further, it must here be remarked that these phenomena are, 

 within certain limits, independent of the particular nature of the 

 function according to which the coefficient of absorption of a 

 substance changes with its density, supposing only that this co- 

 efficient continuously increases with the density and converges 

 towards the value 1. Greater than 1 its value cannot become 

 without contradicting its definition. On this account, also, the 

 coefficient of absorption of a substance cannot continually in- 

 crease proportionally with the density, because otherwise there 

 would be a value of the latter at which the case mentioned would 

 occur. 



If now , we consider that with bodies in the liquid or solid state 

 the coefficient of absorption has extraordinarily far greater values 

 than with gaseous bodies, it is explained why the spectra of the 

 denser bodies must in general be continuous. 



When the compared parts of the spectrum are not adjacent, 

 but X and X t belong to sufficiently distant spectrum-lines, the 

 preceding formula shows that this ratio also is a function of the 

 pressure, which with continuous increase of the latter continously 



approaches the limiting value ~ • 



J A/ 



5. In order to illustrate, in an example, by numerical values 



