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



only slightly different values \ and \ t , can likewise be but little 

 different from each other. 



Now, as in the above expression (2) the magnitudes A A and 

 A*,, by their definition, can only be positive and never greater 

 than unity, and therefore 1— A x and ■! — A K must always be 

 proper fractions, that expression is convergent for increasing 

 values of m or of A to a limiting value which is reached when 

 ?rc=oo or when A*=A A/ =1. In both these cases we have 

 simply 



E^ m J A, 



This may be verbally expressed as follows :— The ratio of bright- 

 ness of two adjacent parts of a discontinuous spectrum constantly 

 diminishes with the multiplication of the luminous layers, or as the 

 coefficient of absorption of the same layer becomes greater, to that 

 value which, for the same wave-length and the same temperature, 

 corresponds to the continuous spectrum of a body which at the 

 given thickness is perfectly opaque and black. 



This diminution of the ratio of brightness of two immediately 

 adjacent parts of the spectrum with simultaneous increase of 

 their brightness must necessarily make itself perceptible to the 

 eye, first, as a widening of the lines by diminishing sharpness of 

 their borders, and then gradually as incipient continuity of the 

 entire spectrum. 



4. It can now be shown that, cseteris paribus, increase of the 

 density of a luminous gas must produce precisely the same effect as 

 the above-considered multiplication of the layers; for if we regard 

 the weakening produced by absorption upon a ray as the effect 

 of a definite sum of particles which the ray meets with in its 

 passage through the absorbing medium, it follows that the mag- 

 nitude of the absorption thus produced is dependent only on the 

 numbei % and not on the distribution of the operative particles, pro- 

 vided we may assume that their absorptive effect is independent of 

 their distance*. This assumption becomes the more probable the 



* In order to prove by experiment the admissibility of assuming this in 

 in a given case, (for example, the solution of a colouring substance in va- 

 rious quantities of the solvent), only homogeneous light, obtained by using 

 the narrow bands of a spectrum, can be employed in the requisite photo- 

 metric measurements. The employment of coloured glass must a priori 

 be regarded as inadmissible for this purpose, since, strictly speaking, it 

 always transmits all the rays, only in different degrees of intensity, so that 

 when the quantity of light is sufficiently small, or the glass thick enough, 

 the rays most weakened are almost or quite imperceptible to the eye. 



If J A denotes the intensity belonging to the wave-length X in a given 

 spectrum, A A the coefficient of absorption of a coloured medium for the 

 same wave-length and the unit of density, the quantity of light emitted 



