290 Mr R. F. Gwyther, On the solution of the [May 25, 



Then P rr = 0, P r ,/=0, P rz '=0) 



yy \dt\' 



This indicates a tension in the wave front in the direction of the 

 resultant of 



d% dr) d£ 



dt' di' di' 



Next, the part of the P's due to <u 3 ' is 



p.,-0 P,,-0 p ll --l\ d ±- d l. 



JTy y< — U, ± y'g> — V, J. Z 'g> — V •< , , , , 



c&s' cfo/' 



or a pressure (?) also in the wave front in the direction of the 

 resultant of 



d£ dr) di; dt, dr) d% 



dy dz ' dz dx' dx dy ' 



Whereas the part due to co 3 ' is a tension (hydrostatic) equal in 

 all directions and of magnitude 



m (dv'Y 

 2[dt) ' 



If now we complete the equations of motion by adding the terms 

 of the second order formed as in the case of Hydrodynamics and 

 Elasticity, supposing the terms of the first order satisfied, we have 



rff- d?£_ dv _d^_ dX d^ 

 dt ' dxdt dt ' dydt dt ' dzdt 



= dw Pxx+ dy PxiJ + dz Pa ' s (18) ' 



with two similar equations. 



It is plain that the expression on the left will vanish identically, 

 and the terms on the right vanish identically so far as they depend 

 upon &> 2 and &> 3 , but the terms depending upon co 5 will' remain 

 and cannot be made to vanish by any further condition respecting 

 £, 7}, £ already sufficiently restricted. The existence of such terms 

 would require a corresponding force in the medium. 



Having investigated the stresses corresponding to &> 3 and a) 3 ', 

 I shall now neglect them, supposing that m and I are absolutely 

 zero in accordance with reasons already given. 



