in relation to Sound. 185 
re 2 applicable when the diameter (2r) is very small, 
**=- 8 #', (10) 
fjj being the kinematic coefficient of viscosity. The wave 
propagated into the channels is thus proportional to 
eP* cos (nt+ pas + e), (11) 
where 
_ re _ 2 s/ (V) _ 2 V (rvYfi') 
^~ 1—i br ar ' 
(12) 
7 being the ratio of the specific heats, equal to 1*41. In the 
derivation of (10), nr 2 /(Sv), v being the thermometric coeffi- 
cient of conductivity, is assumed to be small. 
To take a numerical example, suppose that the pitch is 256 
(middle c of the scale), so that n-=2 r jrx 256. The value of // 
for air is '16 C.Q-.S. (Maxwell), and that of v is -256. If we 
take r=j^QQ centim., we find nr 2 /8v equal to about xoW ^ 
r were 10 times as great, the approximation would perhaps 
still be sufficient. 
From (12), if n=27rx256, 
1-15x10-' , 1Q , 
P= ~ > (13) 
so that if r =yoVo> p=l"15. In this case the amplitude is 
reduced in ratio e : 1 in passing over the distance p~* — that is, 
about one centimetre. The distance penetrated is proportional 
to the radius of the channel. 
The amplitude of the reflected wave is, by (8), 
p(l + (/)(! -i)-K 
p(l+g)(l-i) + Ko > 
or, as we may write it, 
D ~p f (l-i)'+l~p f + l-ip /f ' ' W 
where 
p'=(l+ g )p/ Ko (15) 
If I be the intensity of the reflected sound, that of the incident 
sound being unity, 
V-2J/ + 1 
1 2p /2 + 2p' + l W 
The intensity of the intromitted sound is given by 
r-^- V+y+i < 17 > 
