the Stability of Ships . 
CASE III. 
The sides of a vessel are inclined inward above the water- 
line, and are parallel to the plane of the masts under the water- 
line. 
AH, BY, (fig. 6 .) are the sides of a vessel inclined inward 
above the water-line BA, at an angle HAQ = YBP from the di- 
rection of the sides AW, B C, under the water-line, which are 
parallel to each other, and to the plane of the masts. Suppose 
the vessel to be inclined from the upright, through an angle 
= OPQ. By the construction, (p. 220.) draw the line CH 
intersecting BA, in a point S, at an angle ASH equal to 
the given angle OPQ; so that the area ASH shall be equal 
to the area BSC. When the vessel has been inclined through 
the given angle OPQ, it will be intersected by the water's 
surface in the line CH. The construction of the line GZ, or 
measure of the vessel's stability, is the same as in the preceding 
case. 
Let the sine of ASH = 5 ; sin. SAH = a ; sin. SHA = h ; 
sin. S C B =. c to rad. = 1. Also let GE = d. 
From the rules of trigonometry, it is inferred that 
+ SB x cos. ASH -f sec. ASH. 
The area SBC or ASH = ASH , 
2 
If, therefore, the total volume immersed is made == V, the 
value of the line ET will be 
KL = A x / 1 + j > x 
1 — h x 
h x 
4s x v'l —a 2 - 
h 
1 — h z 
~1F~ 
4s X 1 — a 
h ~~ 
