the Stability of Ships . <2 i y 
sections, and length of the axis : suppose this weight to be 
1000 tons ; according to the preceding determination, the sta- 
bility of the vessel, when inclined from the upright to an angle 
of 15 0 , will be a pressure equal to the weight of 1000 tons, act- 
ing at a distance of parts of the breadth B A from the 
axis, to restore the vessel to the position from which it has 
been inclined. This force is the same as if a pressure of 
""°°° - * 2 — = 56.8 tons, should be applied to turn the vessel at 
the distance of 50 from the axis : if therefore the wind, or other 
equivalent power, should act on the sails of the vessel with a 
force of 56.8 tons, at the mean or average distance of 50, or ~ 
the breadth BA from the axis, to incline the ship, the force of 
stability will just balance it, so as to preserve an equilibrium ; 
the vessel continuing inclined from the upright at the angle of 
15 0 . If the wind's force should be less, the inclination must 
necessarily be diminished ; if greater, it must be increased, 
until the two forces balance each other. Here it is to be ob- 
served, that the force of the wind is estimated in a direction 
which is perpendicular to the plane of the -masts.* 
* In this and the following numerical examples, in order to bring into comparison 
the effect of giving different forms to the sides of vessels, their weights, and all the 
other conditions (the figure of the sides excepted) on which the stability depends, are 
assumed to' be the same. The measures of stability are compared, both by the relative 
distances from the axis at which, a given pressure, equal to the vessel’s weight, acts to 
turn the ship round the longer axis, and by the relative equivalent weights which act 
at a given distance from the axis. By the latter method,, the proportions of stability 
are perhaps more distinctly expressed than by tho former, although both are essen- 
tially the same. 
The mechanical force employed to incline a vessel from the upright, through any 
given angle, for the purpose of examining and repairing -the bottom of a ship, is to 
be ascertained from the theorems here given for expressing the measures of stability, 
jMDccxevm, F f 
