Muvthy 



with the plane z = and L and L are the vertical projections 

 of the hemlines of the skirts at the bow and the stern. All these curves 

 are to be traversed in the same direction as L, , i. e. in the counter- 

 clockwise direction. 



The surface integral over S Q may be transformed by the 

 application of Stokes'theorem : 



g // *G^ d£d7j= // *(V G^ + 2iaVGp <r G) dSdr/ 

 V A* G^dTj - V // ^^G. d^dTj + 



+ 2ia V ®* G dTj -, 2i<r Vlp G d^dr, - 



f 



So 



= v 2 





and since 



I h | G^ d|d 7? = <j> ^Gd, - II * G d|d77 



5o 1 Lc S Q 



we may combine all these integrals together and write 



yH-f- G i*- ,d{d ' -*t// <*«-*• v*,-' 2 *- 



So *o 



.2 



g *r ) g d^d,, + 4?rg j> (*g € - 



c 



- * fG+ ^-* G )d, 



where, now, L is the boundary of the IFS 



L„ = L, + L + L + L , 



C 1- B 2 + S 



L^_ and Lp+ being the intersections of the inner hull surfaces with 

 z = and L n and L c as defined previously in connection with Lm. 



224 



