( 607 ) 



absorbed bv a layer of given thickness z, if the iiieideiit beam con- 

 tains all wave-lengths occurring in the part of the spectrnin occupied 

 by the absorption band. In treating this problem, I shall suppose 

 the energy to be uniformly distributed ovei' this range of frequencies, 

 so that, if we write Idn for the incident energy, in so far as it 

 belongs to wave-lengths between n and n -)- dii, I is a constant. 

 The total amount of enei'g.y absorbed is then given by 



A = I \{l~e-''-'''')dn (34) 







Now, if the coefficient ij and the time r were independent of the 

 density of the gas, both 'S, and i] would be inversely proportional to 

 X : this results from (10), (12) and (28). The equation (26) shows 

 that under these circumstances and for a given \'alue of n, k is 

 proportional to A'. The value of A will therefore be determined by 

 the |)roduct A':. This means that tlie total absorption would solely 

 depend on the quantity of gas contained in a layer of the given 

 thickness, wliose l)oundary surfaces have unit of area ; if the same 

 quantity were compressed within a layer of a thickness ^ z, the 

 absorption would not be altered. 



The result is diiferent, if y and r depend on the density. In order 

 to examine Uiis point, I shall take z to be so small that 1 — e~-^~ 

 may be replaced by 2/^ — 2k'' z^, so that (34) becomes 



A — 21 \z \ kdn — z' i k' 



fZ« (35) 



Let us further contine ourselves to an absorption band, so nari'ow, 

 that we may put 



I =2m'n„ («„-«) (86) 



77 = 71.o', k = — — (37) 



Introducing 5, instead of », and extending the integrations from 

 S = — 30 to § =: -f X , as may indeed be done, I find from (35) 



2cm \ icg J 



or, on account of (10), 



nl \, 1 ) 



A = -— \Ne z — -— (iVe' zf . 

 2cm. ( icg ) 



Two conclusions follow from this result. First, the absorption in 

 an inliuitely thin layer of given thickness does not depend on the 



42 

 Proceedings Royal Acad. Amsterdain. Vol. Vlll. 



