Lord Rayleigh's Acoustical Observations. 463 



theory and measurements by Wertheim and others, on the pitch 

 of resonators caused to speak by a stream of air, has always 

 seemed to me to prove that a comparatively small part only of 

 the whole discrepancy is to be explained in this way. On the 

 other hand, it is obvious that the " open " end at the base of 

 the pipe is very much contracted, and that the correction 

 thence arising may be several times as great as that applicable 

 to the upper end, where the pipe retains its full section. I was 

 therefore anxious to ascertain what was the proper note of an 

 organ-pipe, regarded as a freely vibrating column of air, and 

 thus to estimate in what proportion the two causes of disturb- 

 ance contribute to the final result. 



There are two methods by which the pitch of a resonator 

 may be determined without the use of a stream of air. The 

 simplest, and in many cases the most accurate, method con- 

 sists merely in tapping the resonator with the finger or other 

 hammer of suitable hardness, and estimating with the aid of a 

 monochord the pitch of the sound so produced. In attempting, 

 however, thus to determine the pitch of the organ-pipe, I 

 found a difficulty arising from the uncertain character of the 

 sound, and the results were by no means so accordant as I 

 desired. Possibly an observer gifted with a more accurate 

 ear than mine would have been more successful. The other 

 method is one of which I have had a good deal of experience, 

 and which I can generally rely upon to give results of mode- 

 rate accuracy. It consists in putting the ear into communi- 

 cation with the interior of the resonator, and determining to 

 what note of the scale the resonance is loudest. I have gene- 

 rally found it possible thus to fix the pitch of a resonator to 

 within a quarter of a semitone. In the present case a small 

 hole was made in the side of the pipe near the centre ; and over 

 the hole a short piece of tube was cemented, which could be 

 put into communication with the ear by means of a rubber 

 tube. In this way the effective length of the pipe was deter- 

 mined to be 2 8* 7 inches, 4' 7 inches more than the actual 

 length. As a check upon this estimate, I closed the upper 

 end of the pipe with a plate of wood and again determined the 

 note of maximum resonance. The effective length of the pipe 

 was now 29*1 inches, so that the correction due to want of 

 openness at the lower end amounted to 5 e l inches. If we add 

 •6 as a correction for the upper end, we obtain as the corrected 

 length of the pipe in its ordinary condition 29' 7 inches. The 

 difference between this and 28*7, obtained directly, is greater, 

 I think, than can be ascribed to errors of experimenting, and 

 is possibly connected with the excessive magnitude of the cor- 

 rection in relation to the wave-length of the sound. The 



