THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



APRIL 1893. 



XXXIL On Plane and Spherical Sound- Waves of Finite 

 Amplitude. By Charles V. Burton, D.Sc* 



Part I. — Plane Waves. 



1. rilHE subject of plane waves of finite amplitude has 

 JL been considered by Riemannf ; and so long as we 

 confine our attention to the case where velocity and density 

 are everywhere continuous, his investigation, as is well known, 

 leaves little to be desired. It will not, therefore, be necessary 

 here to make further reference to this aspect of the subject ; 

 but there is one part of Riemann's work which Lord Rayleigh 

 has clearly shown to be unsatisfactory, and it is this point 

 which we have now especially to consider. Lord Rayleigh 

 sayst:— 



" It has been held that a state of motion is possible 



in which the fluid is divided into two parts by a surface of 

 discontinuity propagating itself with constant velocity, all 

 the fluid on one side of the surface of discontinuity being in 

 one uniform condition as to density and velocity, and on the 

 other side in a second uniform condition in the same respects. 

 Now, if this motion were possible, a motion of the same kind 

 in which the surface of discontinuity is at rest would also be 

 possible, as we may see by supposing a velocity equal and 



* Communicated by the Physical Society : read February 24, 1893. 

 f " Ueber die Fortpflanzung ebener Luftwelleu you eudlicher Schwmg- 

 ungsweite," Gott. Abhandl. t. viii. (1860) ; reprinted in Werke, p. 145. 

 % Theory of Sound, vol. ii. § 253, p. 41. 



Phil. Mag. S. 5. Vol. 35. No. 215. April 1893. Z 



