508 BEPOET— 1887. 



approximately. The condition in question therefore is 



-{Ax + By + h(Fx^ + 2Gxy + Rf)} {u + f^x + ^/^y+ . . . } 



, fd'^w „ ^ d'^w d^w „\ ) 



+'^{ciY^''+^d^/y+di^y')+}=^' 



where the symbols m, v, w, &c., denote the Talues of tLese quantities at the 

 origin. It follows that 



w=0, 



dw ^ ^ „ < 

 -,--A«— By=0 I 



— JsM — Uy=0 



dy ) 



dho .dw ^ ^ r. ,dn ^^dv 



d^w dw ^ ^_, rla -rj/du dv\ ^dv ^1 ..r.. 



.-^ + B^-G"-H-A^^-B(_ + ^^.j_cg=0 . (49) 



,— , + L liu—Kv — zB — — ^>->_=0 



dy^ dz Jy dy 



Take next the dynamical boundary conditions. At the oi'igin these are ' 



' = \d. + dy) 



\dz dxj[ .K^. 



Substituting the values of dw/dx, dwjdy from (48), we see that if we 

 neglect IK, IB, IC in comparison with unity, we have 



da \ 



t (^') 



Hence if q denote the velocity parallel to a tangent line at any point P 

 of the wall, we have at P 



? = Z^ (52) 



dn 



or if A.|, /«,,, j'l be the direction-cosines of the normal, and Xo, /a2, v^ 

 those of the tangent line, 



X2M + /t2V + i'2W = Z^A,i— + /*!—+ vii-VAgM+zxaV + Vaw) . (53) 



in which of course Xg, fX2, r^ are to be treated as constants daring the 

 differentiations. Let us apply this to the case when P is any point 



' We are here considering cases where, as in §§ 4, 5, the electric surface-forces 

 may be neglected, being of the second order. 



