Muvthy 



2 2 gG, = 0. on f =0 (V. 9) 



It will be observed that this free surface condition we have stipulated 

 for G is the same as that satisfied by the potentials in (V. 4) with 

 the difference that V is replaced by -V so that the second term on 

 the left hand side is of a different sign. The reason for this will be 

 apparent presently. 



We may also assume that 



and 



Lt G = 



f — > oo 



u ff-o 



£ — >• oo 



A suitable radiation condition is also imposed on G for 

 large ($ + f )~2~ anc * fixed T in order to obtain a unique solution 

 of the problem. 



The radiation conditions for <t> and G are fully discussed 

 in Appendix V of Reference 1. 



The Domain of Integration. 



We may subdivide the closed surface /_, into the following 

 separate regions : 



E=E + E 1 + E 2 + E 3 



where /] is a surface of small depth below the undisturbed water 

 surface which just encloses the immersed part of the side hulls of 

 the ACV in its interior and which intersects the EFS in a closed curve 

 L (see Figure 3). This curve will therefore contain in its interior 

 the actual boundary Ln of the ACV on z = , i. e. the closed curve 

 formed by the intersections of the outer surfaces of the hulls on z = 

 and the vertical projection thereon of the hemline of the skirts at the 

 bow and stern. 



Z-f is the lateral surface and 2L»_ the base of a large circu- 



220 



