by Stationary Sound- Waves. 235 



The rate may be considered as approximately a constant for 

 all the gases, although the force producing this rotation varies 

 with the density of the gas. This can be explained by the 

 circumstance that the resistance to motion is also proportional 

 to the density. The deviation from this result in the case of 

 hydrogen is explained by the fact that the friction on the sup- 

 porting pivot was not an inconsiderable quantity compared to 

 the total resistance experienced by the cylinders, and this factor 

 is proportionately larger in the case of hydrogen. 



Prof. Halloek first suggested to me the explanation of the 

 effect described in this paper.* He pointed out that' Daniel 

 Bernoulli has shown that a gas in motion is virtually less dense 

 than the same gas at rest. The air in the capsule cylinder is 

 at rest, while that on the outside of it is in motion. The 

 energy exerted is due to the difference in density on the two 

 sides of the closed end of the cylinder. 



An inspection of the curve in fig. 3 sliows that the force is 

 approximately proportional to the square of the velocity of the 

 vibrating air. 



I have applied this effect to the problem of determining the 

 amplitude of the vibrating air particles in the middle of the 

 loop of the stationary wave. It is evident from the formula 

 given below, that if the force per unit of area on the closed 

 end of the cylinder is obtained experimentally, the change of 

 density may be found, and the amplitude of vibration calcu- 

 lated from it. 



Prof. P. S. Woodward has kindly assisted me in applying 

 the proper principles of hydrodynamics to the problem. The 

 relation between the velocity, pressure and density of a moving 

 fluid may be expressed by Bernoulli's equation, since, for this 

 case the average state of the fluid only is under consideration. 



r± = R _4 u . 



«/ p 



P is the potential due to external forces, and is negligible in 

 this case ; hence 



'dp 



Pdp 



* u' 

 P 



The adiabatic gas relation gives, p =cp r , where cis the gas con- 

 stant. 



* This effect is somewhat similar in nature to the acoustic attractions and 

 repulsions of Guthrie and the rotating mill of Dvorak that is, they all depend on 

 the change in density arising from motions of a fluid. The effect herein 

 described is of a different order of magnitude than that of the rotating resonators 

 BD. 



Air. Jour. Sci.— Fourth Sertes, Vol. X, No. 57.— September, 1900. 

 16 



