398 



Prof. J. H. Poynting on 



Fig. 2. 



The result is a small pressure perpendicular to the planes of 

 shear, that is, in the direction of propagation ; and this small 

 pressure is just equal to the energy-density of the waves. 



For let PQR (fig. 2) be a small triangular wedge o£ the 

 solid, PQ being a plane o£ shear perpendicular 

 to the direction of propagation. Let this 

 wedge have unit thickness perpendicular to 

 the plane of the figure. Let PR be along a 

 pressure-line and QR along a tension-line, 

 and let pressure and tension each be P. 

 Resolve the forces on PR and QR perpen- 

 dicular to PQ. Then we have a force from 

 right to left, 



P. QR cos PQR-P. PR cos QPR 



= P.PQ(cos 2 (45 -|)-- 

 =P.PQ.e. 



COS' 



(«'+!)) 



Thus, to prevent motion in the direction of propagation 

 there must be a pressure on PQ equal to ~Pe = ne 2 , where n is 

 the rigidity modulus. But the strain-energy per unit volume 



ne 



is — , and the kinetic energy is equal to it. The total energy- 



density is therefore ne 2 ^ and the pressure is equal to this. 



The pressure of elastic solid waves appears to be beyond 

 experimental verification at present. But that of sound- 

 waves has been demonstrated most successfully by Altberg*, 

 working in Lebedew's laboratory at Moscow. 



A small wood cylinder, 21 mm. diameter, was suspended 

 at one end of a torsion arm, with its axis horizontal and 

 transverse to the arm. One end of the cylinder occupied a 

 circular hole in the middle of a board, there being just 

 sufficient clearance to allow it to move ; and the plane end 

 was flush with the outer surface of the board. When very 

 intense sound-waves 10 cm. in length, from a source 50 cm. 

 distant, impinged on the board, the cylinder was pushed back, 

 the pressure sometimes rising to as much as 0*24 dyne/sq. cm. 

 The intensity of the sound was measured independently by 

 the vibrations of a telephone-plate, in a manner devised 

 by M. Wien ; and through a large range it was found that 

 the pressure on the cylinder was proportional to the intensity 

 indicated by the telephone manometer. 



Just lately Professor Wood f has devised a strikingly 



* Ann. der Physik, xi. 1903, p. 405. 

 t JPhjs. Zeitschrift, 1 Jan. 1905, p. 22. 



