s 34 
Mr. Atwood's Disquisition on 
ET 
t 3 x sine S 
izV x tang, 2, | F X ^ i 
ser 
a L F 
* 2 1 
tang. 2 f Fxtang 2 S 
and the measure of the vessel's stability, expressed in general 
and known terms, will be 
* 
GZ 
t 3 x sine S 
sec. 2 i F 
1 2 V X tang. 2 \ F VT — tang. 2 £ F x tang. 2 S 
i — d x sin. S. 
When the angle of inclination S is evanescent, or in a prac- 
tical sense very small, the expression becomes 
t x sme s x s j ne a g ree i n g w ith the solution: 
GZ 
izV 
given by M. Euler in this particular case. 
If the inclination of the sides BF, AF, should be evanescent, 
the sides will become parallel to each other, and to the masts, 
both above and beneath the water-line ; a case which has al- 
ready been solved J : and consequently, the solution of case l . 
ought to agree with that which has been just given for the 
stability, when the two sides are inclined at a given angle, 
assuming that angle as evanescent. Assuming, therefore, the 
angle BFA evanescent, and S of any finite magnitude in the 
general value of GZ, above determined, we have 
vG - tang.* * * * i F x tang . 2 S == J . F: * ***' s , an d 
sec. 2 \ F 
v' i — tang. 2 |.Fx tang. 2 S 
and therefore §GZ = 
— d x sin. S. 
. 2 + 2 X tang. 2 \ F -f- tang. 2 \ F x sec. 2 \ F x tang. 2 S # 
t 3 x sine S tang. 2 £F x tang. 2 S 4-2 x tang. 2 ■§■ F 
1 2 V x tang. 2 -§• F 
* This expression for the measure of stability, is evidently more simple, and better 
adapted to practical application, than that which is inserted in page 229. The pre- 
sent result might perhaps be obtained by more concise methods : the investigation 
here given is the best that occurred to the author, after repeatedly endeavouring to 
discover some other, requiring fewer trigonometrical calculations. 
f Theory of the Construction and Properties of Vessels, chap. viii. J Case 1. 
§ ET = 
t 3 x sin. S 
24-2 x tang. 2 i F4-tang. 2 -t- F x sec. 2 £ F x tang. 2 S 
12V X tang. 2 \ F 
1, 
ET 
t 3 x sin. S 24- tang. 2 S 
1.2V 
or because sec. -J F — i» 
2 
