186 



frequency, and throughout { will be used to mean the inter-nodal distance 

 for the systems of standing waves. For a perfect gas the adiabatic equa- 

 tion fi)v^=rt}]sfant) must be used, whence 



dp _ pk (2) 



Substituting this vjilue in (1) 



v^pk 



V^ = = kpv = 4n2 {2. (3) 



I' 



Let equation (3) refer to the tube B, Fig. 1, in series I, which contains 

 air, and is at 0° C, and let a similar equation with subscripts apply to the 

 tube A in the steam bith. 



V\-r=k,p,v,=4:n\A^-,. (4) 



Dividing (4) by (3) and solving for the ratio 



k, 



ki /--, V (5) 



k /^'^ Vi' 



From Gay Lussaes law specific volumes are directly proportional to 

 absolute temperatures, whence 



A-i /^T (6) 



k ~/-'T,' 

 From (6) the results given in table I are calculated. 



For series II however, using nitrogen at liquid air temperature, the 

 p-v~T relation to Bestelmeyer and Valentine icas used, 



Ij r=(».27774 T— (0.03202— 0.000253 T)p (7) 



Substituting ir. the fundamental equation 



(8) 



\dv JQ \dvj' 



3p 

 the value of — for constant temperature, as determined by differen- 



d' 



tiating (7), 



\dv/' 



k p (9) 



and substituting this in (1). 



