Velocity of Sound Waves in Tubes. 209 
ment, and are in accord with the theoretical conclusions of Helmholtz,’ 
Kirchoff,? Rayleigh,* and others who have attacked the subject. The 
equations of both Helmholtz and Kirchoff may be reduced to the form 
vi=v(l— = 
2rJcn 
where v' is the speed of sound of frequency n in a pipe of radius 7, and 
vw is the velocity in free air. According to Helmholtz c is the viscosity 
of the gas, according to Kirchoff it is a term depending on the heat 
conduction between gas and pipe walls, according to Miiller’ the equa- 
tion has no general validity, according to Schulze’ the “constant” c was 
found to range between 0.0075 and 0.025, depending on the diameter and 
nature of the tube. 
\ 
ri 
u] WL) N=s)) 
¥ Sta 
= 
To EartH 
Lifer, Phe 
Sturm’ found that Kirchoff’s formula was not valid for different 
tubes and frequencies. On the other hand Wertheim’s' results supported 
the equation, while Schneebele’ and Seebeck’ obtained results that sup- 
1 Helmholtz, Wessensch. Abhandl. B 1, s 383, 1882. 
2 Kirchoff, Pog. Ann. B 1384, s 77, 1868. 
3 Rayleigh’s Theory of Sound, Vol. —, p. —. Also Lamb’s Dynamical Theory of 
Sound, p. 190. 
4 See Table II. 
> See Table II. 
6 J. Sturm. Ann. d. Phys. B 14, s 822, 1904. 
‘ Citation in Table II. 
5Poge. Ann. B 136, s 296, 1869. 
9 See Table II. 
14—16568 
