2 16 Mr . Atwood's Disquisition on 
As V : volume ASH : : EV : ET, or 
y . \ x . s ; ;i x sec. S -|- cos. S : ET ; this will give 
the value of ET = , and because 
E R : E G : : sin. S : 1, and E G = d, it follows, that 
ER ==d x sin. S ; and therefore R T, or the measure of the 
vessel's stability GZ = - *|y g — x cos. S + sec. S — d x sin. S. 
To exemplify this determination by referring to a particu- 
lar case, let the vessel's breadth at the water's surface, or BA, 
be divided into 100 equal parts, and let G E be 13 thereof ; 
so that t — 100, and d = 13. Suppose the inclination of the 
vessel from the perpendicular, or ASH, to be 15 0 , = S ; and 
let the area BCODA, representing the volume displaced, 
be equal to a square of which the side is = 60 ; so that the 
area V shall = 3600 : then, referring to the solution, we 
obtain 
cos. S -j- sec. S = 2.0012 
Alcn * 3 X tang. S ___ ioooooo tang. 15° 
24 V 24 x 3600 3 
E T = 2.0012 x 3.10190 = 6.2063 
d x sin.S — 13 x sin .15° = 3.3646 
measure of stability, or G Z = 2.8417 
It appears by this result, that when the vessel has been 
inclined from the upright through an angle of 15 0 , the direc- 
tion of the fluid's pressure, acting to restore the quiescent 
position, will pass at a distance estimated horizontally from 
the axis = 2.84, when the breadth BA = 100. And this will 
be true, whatever be the length of the axis. 
The fluid’s pressure is the weight of water displaced, the 
magnitude of which depends both on the area of the vertical 
