4(32 Lord Rayleigh's Acoustical Observations. 



to the diameter of the pipe, the addition which must be sup- 

 posed to be made to the length is very nearly equal to, though 

 somewhat less than, -8242 R, and is certainly greater than 

 •785 R*, R being the radius of the pipe. 



It is obvious that the removal of the flange would make a 

 considerable difference, probably reducing the correction be- 

 low the lower limit above mentioned. In the absence of any 

 theoretical estimate, I thought it desirable to make an experi- 

 mental determination of the effect of a flange, and ordered 

 some years ago a pair of similar organ-pipes of circular section 

 for the purpose. My idea was to tune the pipes to unison, 

 and then to count the beats when the pitch of one of them was 

 slightly lowered by the addition of a flange ; but the experi- 

 ment lay in abeyance until last winter. Instead of tuning the 

 pipes to unison, I preferred simply to count the beats before 

 and after the addition of the flange, which consisted of a large 

 sheet of stiff millboard perforated with a hole sufficiently large 

 to allow the passage of the pipe. In this way it appeared 

 that the effect of the flange was to reduce the frequency by 

 nearly 1^ out of about 242. If we take the velocity of sound 

 at 1123 feet per second, corresponding to 60° F., the calculated 

 effective length of the pipe is about 28 inches, and the radius 

 is 1 inch. Thus the correction to the length due to the flange 

 is the same fraction of 28 inches that 1^ is of 242, or is equal 

 to about *2R. Combining this result with the theoretical esti- 

 mate above referred to, we may conclude that the whole cor- 

 rection for an open end, when there is no flange, must be 

 about # 6 R. 



Mr. Bosanquet, to whom I communicated the result at 

 which I had arrived, informs me that he has since determined 

 the correction for a flange as *25 R. 



The Pitch of Organ-pipes. 



The whole correction to the length of an organ-pipe, neces- 

 sary to make it agree with Bernoulli's theory, is considerably 

 greater than any of those spoken of under the preceding head- 

 ing. According to the rule of Cavaille-Coll, the addition for 

 an open pipe of circular section amounts to as much as 31 R, 

 whereas for a simple tube open at both ends it should be only 

 about 1*2 R. This discrepancy is, I believe, often attributed to a 

 peculiar action of the stream of air by which the pipe is excited. 

 Of course it is not to be denied that some disturbance arises 

 from this source, as is proved by the dependence of the pitch 

 on the strength of the wind ; but the near agreement between 



* See note to a paper " On the approximate Solution of certain Pro- 

 blems relating to the Potential," Math. Soc. Proc. vol. vii. No. 93, 



