﻿254 Dr. J. W. Low on the Velocity of Sound in 



From the above figures it is plain that the method, even 

 for a tyro, makes considerable pretensions to exactness ; after 

 many months of practice, however, the limits of error became 

 still closer. 



Table showing the observed Mean Velocities in Air. 





Internal 

 diameter 



e r 



«/• 



ffr 



G„. 



Our 





of the 

 tube. 



»=266. 



»=320. 



rc=384. 



n=512. 



11= 102325. 



I 



millim. 

 28 



metre. 

 327-29 



metre. 

 327-50 



metre. 

 327-69 



metre. 

 328-33 



metre. 

 328-68 



II 



37-1 



325-24 



325-54 



326-03 



32670 



327-80 



Ill 



935 



320-60 



321-19 



321-88 



323-60 



325 29 



§ 3. KirchhofFs Formula discussed. 



In the light of these results let us test KirchhofFs* theore- 

 tical formula for the velocity of sound in tubes : — 



\ 2rVVn/ 



2rV ' irn' 

 where 



v = the observed velocity in tubes, 

 a = the velocity in unlimited space, 

 r=the radius of the tube, 

 n = the vibration-frequency of the tuning-fork, 

 and 7= a constant for friction and conduction of heat. 



For the same tube the product (a — v) V ' n must be constant, 

 as also (a—v)2r for the same tone. 



Then from two results with the same fork and different 

 tubes we get 



_ "fr 



■i\,r, 



n-r 2 



where v x and r x denote the velocity and the radius of the 

 wider tube, v 2 and r 2 the same quantities for the narrower 

 one. Thus, by combining in pairs the results contained in 

 the vertical columns of the above table, we should always get 

 the true velocity of sound in the open air. My results calcu- 

 lated in this way are as follows : — 



* Fogg. Ann czxxiv. p. 177 (1868) ; or KirchhofFs Ges. Abh. p. 54-3. 



