( !i98 ) 

 formula, which may serve for tlie deleniiiiiation of q, 



c''?'-!^^-^ (21) 



Of course, q has a complex value. If, taking x and to real, we put 



1 — i X 



q = , (22) 



to 



the expression (20) becomes 



e , 



so that the real parts of the quantities representing the vibrations 

 contain the factor 



n X 



«~^~ (23) 



multiplied by the cosine or sine of 



(-0 



It appears from this that to may be called the velocity of propa- 

 gation and that the absorption is determined by x. If 



n X 

 to 

 (index of absorption), we may infer from (23) that, while the vibra- 



i 



tions travel over a distance — , their amplitude is diminished in the 



1 



ratio of 1 to — . 

 e 



In order to determine (a and x, we have only to substitute (22) 



in (2J). We then get 



cMl — ix)' 1 



to' S + * ■»! 



or, separating the real and the imaginary parts, 



c' (1 — x') _ ^ § 2c'x _ n 



to' ~ i' + n"' w' ~ I' + n" ' 



from which we derive the formulae 



24=l/<i+I|lp + ^ + ., . . . ,24, 



to' K §' -f ij' §' + ïi' 



^c^^l x rnrT? f 



w' l^ I' + n' %" + ■»]' 



in which the radical must be taken with the positive sign. 



