to the Length of a Cylindrical Resonant Tube. 343 

 sion of vapour '389 in. Reducing to dry air at 60°, ?j = 6*000] 



T rp 



/ 2 =19'199;^= =13*199; x='6; and-^=*577. 



(Pitch =506-8 x 2 x 13*199 in.= 1114*88 ft. per second 

 at 60°, or 1084*52 at 32°.) 



ry% 



The velocity and value of -p- thus found agree remarkably 



closely with the mean of all the observations by the first 

 method. 



Begnault's experiments give a mean limiting velocity at 

 32° in a tube of 4*25 inches diameter, of 1071*74 feet; but pro- 

 bably the pipe used by him had not so smooth an interior sur- 

 face as the mandril-drawn tube used in my experiments ; 

 this would doubtless cause a difference in the loss of velocity 

 through skin-friction. 



A third method of experiment I attempted to carry out, 

 with, however, but rather uncertain results, for the purpose of 

 determining the velocity in smooth small tubes, such as are 

 used in brass wind instruments. It is possible to sound notes 

 with the lips on such cylindrical tubes without any bell-mouth; 

 I used them in this manner, both for 1| and 2$ wave-lengths. 

 Any slight inaccuracy that may possibly be due to the lips not 

 being exactly at a nodal point is eliminated by making use of 

 the difference in length only between the tubes of 1J and 2£ 

 wave-lengths ; in this way the additional length of tube re- 

 quired for 1 wave-length is obtained. The tubes used were 

 surrounded by larger tubes; and the space between the two 

 was filled with water to prevent the heating of the tubes by 

 the breath. The notes were held for ten seconds at a time ; and 

 between each trial air was fanned through to get rid as much 

 as possible of the moist breath. In all, fifty observations were 

 made with a tube of *434 in. diam., and twenty with a tube 

 of 1*043 in. diam. The different observations with each tube 

 did not agree so nearly as I had hoped ; but the mean results 

 show a rapid decrease in velocity with decreasing diameter of 

 tube, as will be seen from the following summary of all the 

 experiments. 



Diameter Velocity in 



in inches. feet at 60°. 



•434 1092*3 



1*043 1110*5 



2*080 1114*1 



The velocities as above given are deduced from Scheibler's 

 standard of pitch as explained. Konig's standard, with which 

 I have had an opportunity of comparing one of my forks du- 

 ring the last few days, would give velocities about 2 feet less. 



