Radiation Pressure, 



307 



This excess iu the compression half of a wave-train is con- 

 nected with the extra speed which exists in that half, and 

 makes the crests of intense sound-waves gain on the troughs. 



Lord Rayleigh*, using Boyle's Law, has shown that the 

 average excess on a surface reflecting sound-wares should be 

 equal to the average density of the energy just outside ; and 

 I think the same result can be obtained by his method if we 

 use the adiabatic law. But the subject is full of pitfalls, and I 

 am by no means sure that the result is to be obtained so easily 

 as it appears to be. It is perhaps worth while to note one of 

 these pitfalls, of which I have been a victim. It is quite easy 

 to obtain the pressure against a reflecting surface by supposing 

 that the motion just outside it is harmonic. But the result 

 comes out to (y -f- 1) energy-density, where 7 is the ratio 

 of the specific heats. Lord Rayleigh kindly pulled me out 

 of the pit into which I fell, pointing out that when we take into 

 account second-order quantities the ordinary sound equation 

 does not hold. In fact we cannot take the disturbance as 

 harmonic, and the simple mode of treatment is illusory. 



The pressure in transverse waves in an elastic solid is, 

 I think, to be accounted for by the fact that when a square, 



Ficr. 1. 



o//psct/o/v 



o^ ^/fOf 3 /iG^7-/o^y 



ABOD, is sheared into the position aBCd (fig. 1) through an 

 angle e, the axes of the shear, aC and Br/, no longer make 45° 



with the planes of shear AD, BC. Since ACa = -s-, the 

 -ure-line aC is inclined at 45°—-^- to the direction of 

 propagation, and the tension-line at 45°+- to that line. 

 * Phil. Map:, iii. 10O2, p. 338, " On the Pressure of Vibrations." 



