( OOI ) 



In aiiotlier sense, however, ilie absorption may be said to be 

 diminished i\y an increase of t (or a diniiinition of (j), the range 

 of wave-lengths to which it is confined, becoming narrower. This 

 follows immediately from the equation (26). Let a fixed value be 

 given to s, so that we fix our attention on a point of the spectrum, 

 situated at a definite distance from the place of maximum absorption , 

 and let ij be gradually diminished. As soon as it has come below 

 I, further diminution will lead to smaller values of k, i. e. to a 

 smaller breadth of the band. 



If g is very small, or t very large, we shall observe a \ery nar- 

 row line of great intensity. 



§ 9. The observation of the btinds or lines of absorption, combined 

 with the knowledge that has been obtained by other means of some 

 of the quantities occurring in our formulae, enables us to determine 

 the time t and the number ^\' of molecules per unit volume. 



I shall perform these calculations for two rather different cases, 

 viz. for the absorption of dark rays of heat by carbonic dioxyd and 

 for the absorption in a sodium flame. 



As soon as we know the breadth of the absorption band, or, 

 more exactly, at what distance from the middle of the band the 

 absorption has diminished in a certain ratio, the value of t may be 

 deduced from (29) ; we have only to remember that in this formula, 

 71 is the frequency for which the index of absorption is r' -j- 1 times 

 smaller than the maximum Ho- 



Angstrom ') has found that in the absorption band of carlionic 



dioxyd, whose middle corresponds to the wave-length ?. i= 2,6() f<, 



the index of absorption has approximately diminished to 4 ^o for 



A = 2,30 ft. This diminution corresponding to r = 1, we have by (29) 



1 



- = « — "o , 

 T 



if 7)j and n are the frequencies for the wave-lengths 2,G0 /t and 2,30 ;<, 

 In this way 1 find 



T = 10-14 sec. 



In the case of the absorption lines produced in the spectrum by 

 a sodium flame, we cannot say at what distance from the middle 

 the absorption has sunk to ^ Z„. We must therefore deduce the value of 

 T from the estimated breadth of the line. Though the \alue of v 

 corresponding to the border cannot be exactly indicated, we shall 



1) K. Angstrom, Beitrage zur Kenntnlss der Absorjition der Warmestrahlen 

 durch die verschiedenen Bestandtnile der Almosphare, Ann. Pliys. Ghem. 39 (18',(ü|, 

 p. 2G7 (see p. 280). 



