186 On the Stability of Vessels. f[Marcu, 
the experiments with this apparatus is as follows. The cistern is 
filled with water up to a certain mark ; and the model being put in, 
loaded with ballast, the water is added or decreased till the edge of 
the gunwhale is exactly on a level with the edge of the cistern, as 
ascertained by looking across it, or applying a straight ruler. ‘The 
plumb-line, d, cutting the zero of the divided arch, shows the 
wwessel to be upright. In this state the model is ready for making 
the experiments. ‘The hooks of the two strings, ¢, g, attached to 
the pivots, and the two sliders, s, s, are raised or lowered to make 
the strings, g, g, horizontal in the water. Weights being now put 
into the scale, F, will show what weight is requisite to incline the 
model. The pulley, E, being raised or lowered by the line 7, as is 
found necessary to make the line, a, draw parallel to the ruler, m, or 
perpendicular to the mast. ‘The inclination of the mast is shown 
by the plumb-line, 4, cutting the divisions of the arch, d; but to 
counteract the weight of the plummet, J, which tends to incline 
the mast, another counterbalancing plummet and line, 7, is applied 
on the opposite side of the model. For this purpose holes are made 
in the arch, d, at every division, and a peg is put in at the division 
opposite to that which is cut by the plumb-line. The experiment 
is tried with different weights, to produce the several inclinations at 
every 5°, until 80° from the perpendicular ; and to verify the expe- 
riment, the model is changed end for end, the strings, g, g, being 
hooked on the pivots at the opposite ends. In this way the series of 
trials are made on the opposite side, by which means, if there is 
any difference in the two sides, or in the ballast, it will be detected, 
and allowed for by taking the mean of the different trials. 
Example with Model I. (Plate XLV.)—Exper. 1. 
The total depth of the model being 7°5 inches, the height of the 
centre of gravity is subtracted in each experiment, and the length 
of the mast is afterwards added, which gives the length of lever at 
which the weight is applied to produce. the various inclinations of 
5°, 10°, 15°, 20°, 25°. The centre of gravity in Exper. 1 being 
situated two inches above the bottom of the model, 2 oz. 10 dr. in- 
clined it 5°. The model was turned end for end ; and to incline it, 
the same angle required 3 oz. 5 dr. The mean of both is 2 oz. 15 dr., 
which is considered as the true power. This number (2 oz. 15 dr.) 
being reduced to the decimals of an oz., gives 2°9687 oz., and is 
set down on the right hand in Table I. It is evident that the effort 
of the water to restore the vessel to its original vertical position is 
exactly equal to the inclining power. If, therefore, the momentum 
of the effort to incline the vessel be divided by the weight of the 
displaced fluid, the quotient will be the length of lever on which 
the water acts. 
Exper. 1.—Model 1 inclined 30°; inclining power, 20°3125 oz. 
length of lever, 24°98 inches; and weight of displaced fluid, 
eo nee 20°312 x 24-98 
659'06 559-06 
= 0:90758 parts of an inch, the length of 
4 
