462 
PEOFESSOE STOKES ON THE COMMUNICATION OE VIBE ATI ON 
To determine the arbitrary constants B, and B, the first belonging to the actual 
motion, the second to the motion which would take place if the fluid were confined by 
an infinite number of planes passing through the axis, we must have, as before, for r—c , 
whence 
4 _tt #i_t T 
dr~ dr~ 
cU 
U mr<? nr o' 1 ( me .tt\ /mV mV , \ ] 
B =1 2 F + 2^42-“--(r + log- 2 - + *2j (“2"- 2V + ---J 
+^- 2 S- 
mrc 
'2V4 
2 2 48 ^ 
=E 0 (mc)+» ^/ 0 (mc), suppose ; 
(30) 
Bj me 
3mc , 7m 3 c 3 llm 6 c 5 , 
2 2 ~' _ 2 2 .4 2 2 2 .4 2 .6 2 ' 
( 7 + log 
me .w\ /me 3m 3 c 3 
2" + *2 j \2~“ 2^4"+ ' 
me 3m 3 c 3 c 
+ 2 &I 2 2 4 
2 2 .4 2 »6 
S 3 — ... 
=^{ F ‘( mc )+* i/( mc )}’ suppose. 
(31) 
If I be the ratio of the intensities at a distance in the supposed and in the actual 
case, we see from (30) and (31) that I will be equal to the ratio of the squares of the 
moduli of B and B,, and we shall therefore have 
T {4F 1 (mc)} 2 + 7T 2 {/i(>»c)} 2 /onx 
m 2 c 2 [4{F 0 (mc)} 2 + w 2 {/ 0 (mc)} 2 ] ^ ' 
For a piano string corresponding to the middle C, c may be about - 02 inch, and X is 
about 25 inches. This gives mc=- 005027. For such small values of me I does not 
sensibly differ from (me) -2 , which in the present case is 39571, so that the sound is 
nearly 40000 times weaker than it would have been if the motion of the particles of air 
had taken place in planes passing through the axis of the string. This shows the vital 
importance of sounding-boards in stringed instruments. Although the amplitude of 
vibration of the particles of the sounding-board is extremely small compared with that 
of the particles of the string, yet as it presents a broad surface to the air it is able to 
excite loud sonorous vibrations, whereas were the string supported in an absolutely rigid 
manner, the vibrations which it could excite directly in the air would be so small as to 
be almost or altogether inaudible. 
I may here mention a phenomenon which fell under my notice, and which is readily 
explained by the principles laid down in this paper. As I was walking one windy day 
on a road near Cambridge, on the other side of which ran a line of telegraph, my atten- 
tion was attracted by a peculiar sound of extremely high pitch, which seemed to come 
from the opposite side of the road. On going over to ascertain the cause, I found that 
it came directly through air from the telegraph wires. On standing near a telegraph 
