Murthy 



S and if this domain is subdivided into 

 o 



s ="s~ + S' 



o o o 



where S Q is the equilibrium configuration and Sq is the oscillating 

 strip, it is shown in Appendix V that an integral of the form 



II 



f (x, y) dxdy 



So 

 is equivalent to an integral over the known steady surface 



//[ 



I (x,y) + (x + h G 0) hi fo 7* j dxdy 



Substituting for <t> and p in (II. l) and making the above correction 

 for the domain of integration we derive finally after simplification 

 the following results. 



Longitudinal Force. 



V = ~r// dxdy L w( - Vp o*iooo » + 



C B * / * / s _ xx 



-i-jd dxdy [ 



S o 



+ t Z (-T p p o " v p *oioo I + W* ( - Vp o*noo + 



X XX I XX 



p o V 1000 ^0100 v *1000 ^0100 ' 



X x 



- v( *oio + Voio )(2 Po *1000 + Po*1000 >" 



X XX XXX 



- V (x + h 6 ) (2p <f> + P 4> ) I + 



v 100 G 100' v p o 0100 p o*0100 ') 



X XX XXX I 



2 ( 

 + ^ { p V<t> . V<i> 



) p o 1000 *1000 



I x 



- V (x + h ) (2p * + p 4> )) + 



V 100 G 100 y V P o *1000 P o 1000 '} 



X XX XXX 1 



+ W* { P„ (i»*ioio " V *1010 >" 



{ X XX 



176 



