390 BELL SYSTEM TECHNICAL JOURNAL 



second order. With respect to the torque on the Rayleigh disc it is 

 not so obvious that such forces may be neglected as the potential 

 torque is itself of the second order. The effects of discontinuities in 

 the flow at the edges and of viscosity have not been determined theo- 

 retically. To what extent these are negligible can be found out only 

 by experiment. Strictly speaking we therefore cannot regard the 

 Rayleigh disc as an absolute means for determining sound intensities, 

 as is often implied. A number of experiments have been carried out 

 to determine the accuracy of the Koenig formula. Koenig himself, 

 in a subsequent paper, ^ made an estimate of the effect of the discon- 

 tinuous flow at the edges and reported measurements of the torque 

 exerted on a flat disc when placed in a steady stream of air of known 

 velocity. As a result of these studies he came to the conclusion that 

 the application of his simplified formula to the Rayleigh disc did not 

 provide a reliable and simple method for measuring the absolute value 

 of sound intensity. He felt that the effect of viscosity would prob- 

 ably also have to be taken into account. However, Koenig's experi- 

 ments were made under difficult conditions and it is possible that his 

 measurements were affected by eddies in the air stream. 



Greater confidence in the accuracy of Koenig's formula is derived 

 from the experiments of Zernow.^ Zernow experimented with both 

 thin true ellipsoids and flat discs; these were placed in a box attached 

 to one prong of a tuning fork, the motion of which was observed 

 microscopically. The tuning fork was driven at a frequency of 92 c.p.s. 

 and the relation between the amplitude of motion and the result- 

 ing deflection of the disc was determined. The values so found for 

 the ellipsoids agreed remarkably closely with those computed by the 

 formula. For the discs the agreement was within about 10 per cent. 

 On the basis of the values so found Zernow proposed an empirical 

 correction factor which reduces to unity for infinitely thin discs. 

 Barnes and West,^ using thinner discs, made measurements similar 

 to those of Zernow. They found almost perfect agreement between 

 the experimental and the theoretical values. They were able to show 

 also, by measurements made at audio frequencies with discs of differ- 

 ent diameters, that the torque varied as the cube of the diameter, 

 provided first, that the diameters did not exceed 1/5 wave-length, and 

 second, that the discs were sufficiently rigid to be free from resonant 

 vibrations at the measuring frequency. Mallet and Dutton * found 

 that the torque was proportional to the square of the velocity up to 



6 Wied. Ann. 50, 639 (1893). 

 Mmw. d. Physik 26, 79 (1908). 

 T Jour. I.E.E. 65, 871 (1927). 

 ^Jour. I.E.E. 63, 502 (1925). 



