Mr. Atwood’s Disquisition on 
224 
+ x cos. ASH -f sec. ASH ; in which expres- 
sion S A = - b - , and SB = ^ ac ~ ; i being = the 
v h -\-V ac v b -f v ac 
breadth B A. 
The value of ET having been thus obtained, if ER = d x 
sine ASH be subtracted from it, there will remain the val^e of 
GZ, the measure of the vessel’s stability. 
Suppose the vessel’s inclination from the perpendicular, or 
ASH, to be = 15 0 , let the inclination of the sides inward above 
the water-line, from the direction of the parallel sides under the 
water, or HAf) — 15 0 ; therefore SAH — 75 0 , and SHA = 90°, 
making BA = t, and, applying these conditions to the analyti- 
cal value just determined, it is found that KL = 65.530; the 
area ASH = 323.42 ; and the volume immersed, or V, being 
assumed = 3600, as in the preceding cases, ET ,= — - - 
= 5.89. Subtracting from this, E B — 3.36, there will remain 
GZ == 2.53, or the measure of stability. If the vessel’s weight 
should be 1000 tons, the force of stability will be 1000 tons, 
acting to turn the vessel at a distance of -f— parts of the breadth 
B A from the axis ; which is equal to a force or weight of 
iooo^x z -53 _ £ 0 5 tons, acting to turn the vessel at a distance of 
50 from the axis. 
* 
CASE IV. 
The sides of a vessel project outwards, and at equal incli- 
nations to the plane of the masts, both above and beneath the 
water-line. 
BA (Tab. IX. fig. 7.) is the breadth of the vessel, and coin- 
