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



In the case first considered, for the value cr=l, the spectrum- 

 line investigated would appear 20 times as bright as its imme- 

 diate environs, and hence might, to the eye, stand out as a sharp 

 bright line from a dark ground. If, for example, the pressure 

 of 1 millim. of mercury in a Geissler's tube corresponds to the 

 value <r=l, on the pressure being increased to 500 millims. 

 the brightness of the parts of the ground immediately adjacent 

 to the line would be to that of the line in the ratio of 10 to 11 ; 

 so that the latter would be already much widened, and its edges 

 must appear indistinct. 



The second case shows that, by compression of the incandescent 

 gas, different parts of the spectrum may reverse their ratio of 

 brightness. In the example cited, at the commencement of the 

 compression the brightness E Ao . of a line belonging to the wave- 

 length X is five times that (E A/(T ) of one the wave-length of which 

 is \ With 50 times this pressure the two lines have nearly 

 equal brightness. But if the pressure is increased to 500 times 

 its original amount, the line which at first was the darker becomes 

 nearly 4 times as bright as the other. 



If the density diminishes constantly to 0, the ratio of bright- 

 ness approaches the value tt. Differentiating according to cr the 



■p 



numerator and denominator of the expression for ^~ and sup- 

 posing cr=0, we find for that limiting value 



J A log(l-A A ) 

 J A ,log(l-A A ,)' 



Referring J A and J A/ to adjacent values of X, so that ~ may be 



supposed = 1, we find that with continued diminution of cr the 

 contrast with which a bright line stands out from the ground 

 approaches asymptotically a maximum value which is expressed 

 by 



log n (l-A A ) 



For the above adopted values of A A and A A/ this value would be 

 20'8, and hence would but little differ from that taken by the 

 ratio of brightness for cr = 1 . 



6. Our considerations hitherto have extended to the changes 

 of intensity in two different parts of the spectrum ; but the de- 

 veloped formulae account for the alterations of intensity which 

 take place in one and the same place in the spectrum, at con- 

 stant temperature, by alterations of the pressure. 



According to what precedes, the expression for the brightness 



