OF AIR OBSERVED IN KUNDT’S TUBES. 
17 
or if we introduce the values of V, k" from (67), (68), 
• I i 7 0 70 ,b * , 1 
Since mjv is great, Ar= —=— approximately. 
Thus 
„ n 2 , k 2 n 2 f, , 1 1 
h ~ q + /( u , in\ ~ a 2 j 1 + 
Ui v r +7) 2/1 
fin r 
V r J 
and 
H-—/, 
ft i ' /2» 
2yi V 7 
If we write k=k 1 -\-ik. 2 . 
*'-±11 1 
Til . ^ Vi 
-';/i J ’ 3 a 
(73). 
(74). 
which agrees with the result given in § 347 (11) of my book on the Theory of Sound. 
In taking approximate forms for (70), we must distinguish which half of the 
symmetrical motion we contemplate. If we choose that for which y is negative, we 
replace cosh k'y and sinh k'y by \e~ Vy . For cosh k"y we may write unity, and for 
sinh k"y simply k''y. If we change the arbitrary multiplier so that the maximum 
value of u is unity, we have 
,int 
u— (— 1 -f e~^ + ^)e ilx e h 
v — —( U _j_ Q—Uy+yy\ ( ghx^.nt 
k'XVi ) ' 
(75), 
in which, of course, u and v vanish when y— — y v 
If in (75) we change k into — k, and then take the mean, we obtain 
U = ( — 1-f-C V(y+yi)^ CO g kx e mt 
v— —— -\-e~ ,i ' { y +yi) ) sin kx e int 
k \Vi j 
. . (76). 
Although k is not absolutely a real quantity, we may consider it to be so with 
sufficient approximation for our purpose. If we write as before 
k'— A/L\(l+i)-P{l+i), 
MDCCCLXXXIV. 
D 
