498 Mr. W. J. Harrison on the Stability of 



§6. The conditions at the interface are 



B# ~dx 

 B^ = B^' 



^ By 



Vyy = P w' . 



where p^, p yy are the tangential and the normal tractions 

 at the interface. 



From the first three we have 



^y = o, 



L + N = I/ + N', 



&L + (X + Ni)N = -H/ + (- V + N/)N', . 



jw[2*«L +N(P + X 2 + 2XN X + 2N 2 )] 



= pV[2PL' + N^ + X' 2 -2X'N/ + 2N 2 ')] 



From the two equations of motion 



Bw dr< Bw 1 "dp _ 2 



o* o# oy p o% 



"dv Bv B*> 1 Bp 2 



3* B^ By p^y 



we find 



(4) 

 (5) 



(6) 



t*(2) =-^77-(a + ^B)(^L+XN4-NN 1 ) + ^C(L + N) 



+ v [x(X 2 -P) + 3X 2 Ni - PNi + 6XN 2 + 6N 3 ], 

 where rj is the elevation of the interface, 



77 = -fc/fc(L+N)/(a + *&B) 



= -^(L / + N / )/(« + ^B). 



B^ 



Now 



\ p / y= o W \dy/o 



= -P) -2W/fc(*L + XN + NN,; 

 \p/o 



