660 Miss M. Taylor on the Emission of Sound by a 



which we can make in the present problem is that the motion 

 o£ the particles of the fluid is resisted by a frictional force 

 proportional to the absolute velocity. This is of course not 

 the true law of friction, but it will serve to indicate the kind 

 of modification which dissipative forces will introduce. 



If m, v, w are the component velocities at a point in the 

 fluids parallel to coordinate axes of w, y, z, the equations of 

 motion become 



P B7 =-'|j -/»'«» Ac., &o., . . . (22) 



and the equation of continuity is 



|^ + |-%|^ + f =0, .... (23) 

 0% oy oz ot 



where s denotes the u condensation." Again, if the loss of 

 heat by radiation and conduction be neglected, we have 



p =p + c 2 ps (24) 



Now suppose that u, v, w, s, and p all vary as e ikct . We 

 have, then, 



|» |? |!?- +itM - =0 , . . . . (25) 

 0% oy o- 



while the equations (22) become 

 or, if ju/ = /tyt, 



( P ac+y)u=-!^,&c.,&c, . . . (26) 



/o(^c + /a)m=-|^, &c, &c. . . . (27) 

 Ox 



Differentiating the equations (27) with respect to a, y, z 

 in order, and adding, we get 



p(^ + 1 .)(g + | + |f)=-V^=-eVV^ (28) 



which, combined with (25), gives 



pikcs(ikc + fi) =rc 2 /oV 2 <s 5 

 or (V 2 + A 2 )s = 0, 



provided /,»=#_**£ ..... (29) 



