Murthy 



Sepe (i<r* 1001 - V* 1QQ1 + V4> 1000 . V<*> 0()01 ) 



x 



0epe 1Ot (i«r* 0101 - ViJ^ + V<t> Q100 • V* m0l } 



- d «*f>* 2l(Tt * V * 10 10- V *0001 



" fi«*Pe 21 — V *oilO- V *0001 + PgZ (HL2) 



where the argument to be used for the potentials is (x, b+, z) and 

 (x,b-, z) for p + and p~ respectively. 



To obtain the pressure in the (x',y', z') system we may 

 expand the potentials in the form of a Taylor series. In view of the 

 singularity of the potential at y 1 = b , separate expansions will have 

 to be used for the two sides. 



Thus, in the case of S 



o+ 



* + iooo (x - y ' z) =*iooo < x '' b+ '*'> + < x - x '>* 10 oo , < x, ' b+ - z '> 



X 1 



+ (y- b )^ 100 o ( x '' b+ ' z ') 

 y' 



+ (z-z')<i» 1000 (x',b+,z') 

 z' 



where 



x - x- = x + (.« + h G ) = 8r l0Q + 0t oio + ae 1£rt r 0Q1 

 y _ b = y 1 - b = 5h x (x'.z') 



and 



z . z . = z -x-a = «r' + 0r» __ + ae 



iat 



r' 



100 H 010 001 



but the normal derivative 1000 y' i. e. the velocity across the plane 

 may be considered equal to zero, so that 



188 



