420 Prof. Stokes on the Communication of Vibration 



cXJ 1 _ 1 3mc 7m 3 c 3 _ \\m b c b 

 "B7 " ~ m~~c " "2^ + 2 2 . 4 2 2 2 . 4 2 . 6 2 + ' * * 



(, mc . 7r\ (mc Sm 3 c 3 \ 

 y+ 1 °g 1 i +i <i)\ii-iKi + "){ 



+ ~2 1_ "W 2+ 2 2 .4 2 .6 3 "• 



= m\ ¥ i( mc ) + z '|/i Wp suppose. 



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 1? 

 and we shall therefore have 



{4$,{mc)y + ^{fMc)Y (32) 



m^^F {mc)}^+7r^f {mc)Yy 



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 mc I does not sensibly 

 differ from (mc)~ 2 , which in the present case is 39571, so that 

 the sound is nearly 40000 times as weak as 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 im- 

 portance 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 5 it is able to 

 excite loud sonorous vibrations, whereas, were the string supported 

 in an absolutely rigid manner, the vibrations which it could ex- 

 cite directly in the air would be so small as to be almost or alto- 

 gether 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 Cam- 

 bridge, on the other side of which ran a line of telegraph, my 

 attention 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 di» 

 rectly through the air from the telegraph-wires. On standing 

 near a telegraph-post, the ordinary comparatively bass sound with 

 which we are so familiar was heard, appearing to emanate from 

 the post. On receding from the post the bass sound became 

 feebler, and midway between two posts was quite inaudible. 

 Nothing was then heard but the peculiar high-pitched sound, 

 which appeared to emanate from the wires overhead. It had a 

 peculiar metallic ring about it which the ear distinguished from 

 the whistling of the wind in the twigs of a bush. Although the 



