Relation between the Notes of Open and Stopped Pipes. 63 



V. The effect of external pressure on a thermometer's bulb 

 is directly proportional to the pressure as far as about 140 

 atmospheres. The ascent of the zero of a thermometer on 

 keeping is consequent on a change of state in the glass, being 

 the same whether the thermometer be open or closed, and 

 therefore independent of atmospheric pressure. 



VI. When all corrections are made, every individual ther- 

 mometer has specific characters whereby it differs from all 

 other thermometers. 



VII. A number of bodies have been rigorously purified, 

 and their fusion-points determined, with a good second place 

 of decimals, in terms of the air-thermometer : these points 

 range from about 35° to 121°. The possession of these bodies, 

 which can always be preserved without risk, will enable any 

 observer to obtain standard points within that distance, and 

 save a vast amount of tedious experimentation. 



Anderson's College, Glasgow. 



VIII. On the Relation between the Notes of Open and Stopped 

 Pipes. By E. H. M. Bosanquet, Fellow of St. John's 

 College, Oxford. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



IT has long been known to practical men that, if an open 

 pipe be stopped at one end, the note of the stopped pipe 

 is not exactly the octave below the note of the open pipe, as it 

 should be according to Bernouilli's theory, but the stopped 

 pipe is somewhat less than an octave below the open pipe ; in 

 ordinary organ-pipes the difference is said to be about a major 

 seventh instead of an octave. It has occurred to me lately 

 that the theory of this phenomenon is not generally known ; 

 and the following account of it, with some of its applications, 

 may be of interest. I should mention that the investigations 

 were made some time ago, before the publication of my Notes 

 on the Theory of Sound, in the Philosophical Magazine last 

 year ; and they were not mentioned there only because the 

 methods depending on them proved of insufficient accuracy 

 for the purpose then in view. 



Consider a cylindrical tube open at both ends. Let its 

 length be I, and its diameter 2R. Then the effective (or re- 

 duced) length of the pipe is l + 2a; where a is the correction 

 for one open end, which formed the subject of the investiga- 

 tions contained in Nos. 5 and 6 of my "Notes ? ' (Phil. Mag. 

 [V.] vol. iv. pp. 25, 125, 216). 



