Conditions of a Substance on its Absorption of Light. 627 



Under these assumptions the single line in the " ideal " 

 spectrum of the substance corresponding to a frequency n=n Q 

 would be broadened out into a b;md whose brightest part 

 would lie between the two positions at distances to the red 

 side of the position n = n , 



SI 9 



1 



fil 



n l + (l + Cl 8)(H-c 2 8/ 



2n l + (l + Cl S)(l + ^)' 



If we assumed that each value of a between the above 

 limits were equally probable for any one electron, the portion 

 of the band between f 2 and f 2 would be uniformly bright. 

 Inequalities in the probability of the occurrence of the various 

 values of a, which it seems more reasonable to assume, -would 

 account for differences in the intensity of the various parts of 

 the band, the brighter parts corresponding to the more pro- 

 bable values of a. A simple explanation of the constitution 

 of channelled spectra seems to be here involved ; but this 

 point is reserved for future consideration. 



The value of pi in the above formulae is also proportional 

 to the density of the substance, and so we can write 



* 



* l -* i+(i +ei axi+<*sy 



g(l-fciS)(l-fc 2 S) 



l+ii+cfixi+cjty 



and therefore the breadth of the band is 



fc=fr 



& &-f° 6 (l + , 1 8)(i + ( . 1 S) + i 



(1 + «!*)(! 



This result enables us to deduce at least a qualitative expla- 

 nation of the effect of an increase in density on the lines of 

 the spectrum. The broadening out of the line is always 

 much faster towards the side of longer wave-length. In 

 fact the broadening towards the violet side, although prac- 

 tically symmetrical with that on the other side when the 

 density is small, soon becomes very slow. This explains 

 the unsymmetrical broadening of most of the lines of ordinary 

 spectra. An explanation of some of the remarkable phe- 

 nomena discovered by Wood particularly in the mercury 

 line 2536 is also involved. 



The extension of the above ideas to include the action of a 

 foreign chemically inactive gas is of course obvious. The 



