64 Mr. R. 11. M. Bosanquct on the Relation between 



Now suppose a flat stopper, fitting airtight, to be applied at 

 one end of the tube. It may then, according to the ordinary 

 theory, be regarded as equivalent to the half of an open pipe 

 whose middle point, or node, coincides with the face of the 

 stopper, the effective length measured from the node being 

 Z-f-a. The length of the corresponding open pipe would be 

 double of this, or 2(1 + a). The ratio of the notes is conse- 

 quently (7 + 2a) : 2(1 + a), which may be put in the form 



1 Z + 2* 

 2 X l + u ; 



that is to say, the interval in question differs from an octave 

 by the interval whose ratio is (l + 2a) : (l + ct). 



The following experiment was made with an iron cylindrical 

 tube, 4*9 inches in length and 2 inches in diameter. The 

 notes were determined, as in my former investigations, by 

 blowing short jets of air against the edges. The tube was 

 stopped by standing it upright on a flat surface, and applying 

 a little oil round the edge in contact with the surface. The 

 notes of the pipe, open and stopped, made with one another 

 the interval of a minor seventh ; i. e. they deviated from the 

 octave by a whole tone. The ratio (9:8) was determined 

 with some slight accuracy by comparison with the notes of 

 my enharmonic organ. The tuning of this instrument is not, 

 however, sufficiently stable to base very accurate work on. 

 Then 



9 _ l+2a 



8~ 1 + *' 

 or 





1 « 

 S~ l + ct ' 



And / = 4-9 in., 



/. Z=7«. 



and R=l in., 



.♦. «:=•? in. ; 

 .-. «=-7R. 



The value of « for this tube was formerly determined at *635R 

 (Phil. Mag. vol. iv. p. 219). The tube has been shortened by 

 about -1 inch since; but this cannot affect the correction. It 

 appears then that the present process presents general cor- 

 respondence with the result of the former investigation ; but 

 the numerical values of « do not coincide very exactly. 



When I originally investigated this subject some time ago, 

 I anticipated that I should be able, by observation of the in- 



