* 
the Stability of Ships . 
235 
t 3 x sine S 
or GZ — — ^-—77 — 
24V 
or GZ = 
x tang. 2 S -j- 2 — d x sin. S, 
2 ^ v x cos. S + sec. S — d x sin. S, 
which is the measure of stability, when the inclined sides AF, 
BF, become parallel, the angle F vanishing. But this quantity 
is the measure of stability when the sides are parallel, as de- 
termined by direct investigation * ; by which agreement the 
consistency of the two solutions is evinced. 
To exemplify the general solution for the case of the sides- 
inclined at a given angle, suppose the angle BFA to be 30°= 
F, let S = 15 0 , AB = t — 100, GE = d = 13, V = 3600, 
From the analytical value of the line GZ, we obtain 
t 3 xsine S o 
= 83.44O4 
1 2V xtang 
sec. 2, -1 F 
v" x — tang. 2, |Fx tang. 2, S 
— 1 
.07457 
83.4464 X .07457 
d x sin. S 
= 6.2 23 
= 3365 
and GZ, the measure of stability = 2.838, 
precisely agreeing with the result calculated by the solution, in 
pages 229 and 230, which has no apparent similitude or rela- 
tion to the value for stability, as expressed according to this 
last investigation, which is 
GZ = 
t 3 x sin. S 
i2V xtang. \ F V 1 — tang. 2, i F x tang. 2, S 
According to the solution in page 229, the measure of sta- 
bility is 
sec. 2, - F 
1 — d x sin. S. 
GZ 
SA 3 xsa 
6 Vb 
y 
. s’xi-i ) 1 , 45 x^ 1— a 1 
4 p 1 h 
, SB 3 xs« 
+ - 6 V 7 ~ X 
y 
4 + 
s 2 X 1 — c 2 
4 SX^ 
1 — a 2 
ds , 
* Case 1. 
H h 2 
