the Notes of Open and Stopped Pipes. 6o 



terval between open and stopped pipes, to determine « in an 

 accurate manner. For this purpose I constructed many pipes, 

 in which the interval in question was as nearly as possible of 

 definite magnitude, generally a semitone less than the octave ; 

 but the method proved too inaccurate to be of any real use. 

 An excellent and perfect tonometer is required to measure the 

 intervals accurately ; and if we have that, it can be applied to 

 the solution of the problem with greater advantage in other 

 ways. The present method, however, is quite sufficient for the 

 approximate demonstration of the value of a. 



There are difficulties in the way of the exact application of 

 these principles to ordinary organ-pipes. First, it is impos- 

 sible to blow an open and stopped pipe in a similar manner 

 with the same mouthpiece. The pitch varies considerably 

 with the force of the blowing ; and the two notes produced 

 with different blowing are not comparable. Again, there is a 

 considerable correction of unknown amount to be taken ac- 

 count of, due to the closing-in of the mouth-end of the pipe. 



We may, however, partly get over these difficulties. In the 

 first place, it is possible to arrange a pipe so as to blow the 

 fundamental when open and the twelfth when stopped, without 

 variation of the wind. Secondly, the correction due to the 

 closing-in of the parts round the mouth can be determined for 

 pipes of given shape by sawing one of them across so as to 

 leave a plain circular end. The correction due to the differ- 

 ence in pitch + a (correction for circular end) gives the total 

 value of the correction for the mouth. 



The following is an example : — Organ-pipe 9*5 inches from 

 upper lip to open end ; diameter '95 inch. When arranged so 

 as to blow the fundamental when open and twelfth when 

 stopped, the twelfth was 2 commas of the enharmonic organ 

 sharper than the note corresponding to the fundamental. 

 Taking these to be true commas, which they are very nearly, 

 we may take the resulting interval to be 40 : 41. 



The correction for the mouth was determined by sawing 

 across a similar pipe ; it is roughly 



Then 



h- 



41 l + \ + u 



40 l + X 



u = -2S in. ; 

 Phil. Mag. S. 5. Vol. 6. No. 34. July 1878. 



