Murthy 



and JJ p p dxdy = —<p p dy 



^ o o 2 J r o 



S x L, 



o C 



where the contour L is the boundary of the cushion 



L = L +L +L+T 

 C B 1- S 2 + 



discussed in Appendix V. Since L, and L 2 j. differ from the longi- 

 tidinal planes y = — b, by the semi -width of the hulls i. e. by 0( g ) 

 we may indeed set 



dy = + 0(g) 



along Lj_ and L. and the line integral may be taken over the bow 

 and stern sections L and L- only. 



In the case of a uniform cushion with p = constant throughout 

 the cushion, the first and last line integrals vanish. The line inte- 

 grals also vanish in the case of a non -uniform cushion with the pres- 

 sure reduced to a zero or non-zero uniform value at the front and 

 rear boundaries and generally, in the case of any non -uniform cushion 

 with fore-and-aft symmetry both in the pressure distribution and in 

 the plan form of the cushion. The line integrals will only survive 

 when the pressure along the front and rear boundaries have different 

 values, say, in the case of compartmented cushions. 



VI . 1 Sinkage and Trim 



Let us now consider (6-6) which shows that each term should 

 be separately equal to zero as the three terms are of different or- 

 ders and substituting for these terms from (5-7). 



" 2 " v f *iooo ,% *'<■'+*■»« Moo- 3t, 'ioo ,h 



S. x' L 



O 



(x' ,0) dx 1 = (6-8) 



2(S 010 + h G%10^ P o dxd ^ = ° (6 " 9) 



S l 



o 



and 



142 



