﻿Temperature on the Spectra of Incandescent Gases. 193 



more widely the individual particles of the absorbent medium are 

 separated — that is, the less its density is. Accordingly, if the 

 density of such a medium is altered, the ray passing through it 

 has a different number of absorbent particles to pass in an equal 

 length of its path ; and it is easily seen that, on the assumption 

 made, the number must change proportionally to the density. 

 ^ If, then, the values of A A and A A/ in the above expressions are 

 simultaneously referred to the unit of density, the quantity of 

 light transmitted by the same layer of density a is expressed, in 

 parts of the incident light, by (1— Aj* and (1— A A/ ) ff ; con- 

 sequently the quantity of light absorbed is expressed by: — 



i-(i~A,r=A /V , 



l-(l-A x / = A A/ff . 



Analogously to the absorption let E x and E A/ be referred to the 

 quantity of light emitted at the unit of density ; and accordingly 

 let E A(r and E A/0 . denote the quantity of light of that layer corre- 

 sponding to the density cr. As the temperature and wave-length 

 are supposed to be constant during these alterations, from the 

 above-mentioned properties of KirchhofFs function the following 



from the whole spectrum can be represented as the value of the following 

 integral, 



J«*XJx(1-Aa), 



in which J A and A A are functions of X, and the integral is to be extended 

 to all the values corresponding to the spectrum. 



With another density cr of the absorbent medium, on the assumption of 

 the law of absorption, this integral is transformed into the following, 



j\aj A (l-A;0<7. 



For a definite value of a- the value of a mean coefficient of absorption B 

 can now indeed always be found, by virtue of which we have the following- 

 equation, 



jaj A (l-A A ) a =(l-B) ,T j , c/XJ A ; 



but it is evident that this equality cannot exist for other values of cr with 

 the value of B constant. On this account it is inadmissible to calculate, 

 by means of such a mean coefficient of absorption, and applying the above 

 law of absorption, the quantities of light transmitted through a coloured 

 liquid in different degrees of concentration, and to found conclusions on 

 the difference between calculation and observation. Such conclusions 

 would only be valuable if the change of thickness of the layer passed through 

 by the rays, with constant concentration, produced a different effect from 

 that produced by the concentration being altered in the sarne ratio, the 

 thickness of the layer remaining constant. In this kind of experiments it 

 would be simplest to decide by observations alone -whether the absorbent 

 effect of the individual elements of an absorbent medium is dependent or 

 not on their distance (compare Pogg. Ann. vol. cxli. p. 69 et seqq.). 



Phil Mag. S. 4, Vol. 41. No, 272. March 1871. 



