( 399 ) 



It' tlic ililforeiit constants arc known, we can caK-nlale liy tliese 

 formulae the velocity and the index of absorption for every value 

 of tlie frequency n ; in doing so, we shall also get an idea about 

 the breadth and tlie intensity of tiie absorption liand. 



^ 8. In these questions much depends on .the vahie of »/. In the 

 special case ^ := 0, i. e. if the frequency is equal to, or at least only 

 a little different from that of the free vibrations, we have on account 

 of (25) 



^ c'x' ( / 1 



n' 



From what has been said above, it may further be inferred that 



along a distance equal to the wave-length in air, i. e. , the 



n 



amplitude deci'eases in the ratio of 1 to 



2 jr ex 



Now, in the large majority of cases, the absorption along sucii a 



s^cx 



distance is undoubtedly very feeble, so that must be a small 



cV.' 

 number. The value of — - must be still smaller and this can oidv 



be the case, if »j is much larger than 1. 



This being so, the radical in (25) may be replaced by an approxi- 

 mate value. Putting it in the form 



1/ 



25 + 1 

 1 + ^ ^ 



è' + »i' ' 



we may in the first place observe, that, since »/ is large, the numerator 



2 § 4" 1 ^^'Jl' be very small in comparison with the denominator, 



whatever be the value of 5. Up to terms with the square of 



2| + 1 



——- — r, we may therefore write for the radical 



I + »J 



1 I i iï±_i _ i (- g + ^y 



^ 2 r + 7j' 8 (s' + t,')' 

 and after some transformations 



cV.' _ 4 »/' — 4 s — 1 

 ^ "" 8(5'+ riY • 

 As long as § is small in comparison with -if, the numerator of 

 this fraction may be replaced by 4jj\ On the other hand, as 



