68 Prof. H. Lamb on the Theory of Electric 



the origin are 



- {Ax + By) - \{ Fa?? + '2Gxy + By 2 ) -v 

 -(Bx + Cy)-±(Gx 2 + 2Hxy + Ky 2 ) £ . . (47) 

 l-±(Ax + By) 2 -±(Bx + Cy) 2 ) 

 approximately. The condition in question therefore is 



-{A ie + By + !(F.r* + 2G^ + H/)}{ M +^.r + |S,+ ...} 

 -{B., + Cj, + i(G^ + 2H.^ + K/)f{«. + ^^ + ^ + ...} 



where the symbols u, v, w, &c, denote the values of these 

 quantities at the origin. It follows that 



w = 0, 



" X \ (48) 



*?_B«-Ct,=0 J 



d7 +A cF- Fu ~ Gv ~ 2A dx~ 2B Tv =0} 



UUi UiZ It-it' UiC 



_^_ + B — — Gif—H —A - f —B /"— + —)— C — ==0 > (M) 

 dxdy dz dy \dx dy' dx ' * ' 



dy z dz dy dy J 



Take next the dynamical boundary conditions. At the 

 origin these are* 



7 fdu . dw\ ~) 



U= \dz + d7v)> 



(50) 



i=l rdv + dw\ I 



\dz dyJ J 



* We are here considering cases where, as in §§ 4, 5, the electric 

 surface-forces may he neglected, being of the second order. 



