Cylindrical Vessel containing Liquid. 387 



If p be the value of p when p = f 



From (14) or (15) we see that the effect of a finite as com- 

 pared with an infinitely small compressibility is to increase the 

 depression of pitch due to the fluid. As the velocity of sound 

 is greater in liquids than in air, it would seem that j l % K 2 a? 

 would generally be negligible. In this case, for the principal 

 mode of vibration corresponding ton = 2, (15) becomes simply 



jJ-^sS • < 16 > 



In Auerbach's recent paper upon this subject* various ob- 

 servations upon the depression of pitch due to the action of 

 liquid are given. In his notation p /p = Q. From (15) we 

 see that if G be the value of G for water, the same vessel 

 being used in both cases, 



arzi =s > ( 17 ) 



if s denote the specific gravity of the liquid, referred as usual 

 to water as a standard. AuerbacFs observations are fairly 

 accordant with (17); and there seems to be scarcely sufficient 

 warrant for attributing the discrepancies to the influence of 

 compressibility. 



In observations with different vessels of the same material 

 and filled with the same fluid, difficulty was experienced in 

 obtaining by direct measurement a sufficiently accurate value 

 of d. To meet this, d was determined indirectly from the 

 pitch. By (4) we have 



pi rt-n* pB * n „ 



p {n l + lp a-*p a 



from which it appears that G 2 — 1 is inversely proportional to 

 the pitch (before filling), as well as inversely proportional to 

 the radius of the cylinder. In AuerbacFs notation a constant 

 C is employed, whose value for the case n = 2 would be by (18) 



0=-^. ...... (19) 



O^'TT G*a 



In actual experiment the two-dimensional character of the 

 fluid motion is disturbed by the existence of a free surface at 



* Wied. Ann. Bd, xvii. p. 964. 



