res On the Stability of Vessels. ([Marc#, 
of these numbers or weights with the experimented number or 
weight which inclined the model, a judgment may be formed of 
the accuracy of the experiments. See example in the experiments 
with model I, in the first page of the tables. Having shown the 
manner of making the experiments, I shall proceed to examine: the’ 
first theorem. . . 
Yo find the momentum of the section of water of models 1, 2, 
3, 5, and 16, the momentums, by experiments, of these models 
were compared together. These bodies had the same length, 
breadth, and depth; except model 16, which was. only half the 
length ; and each of them were immersed in the water 4°5 inches, 
or half their respective breadths. The centre of gravity of }, 2, 3, 
was raised 2°25 inches above the bottom of the model; and of 
models 5 and 16, 3 inches; or at the same point as the centre of 
gravity of the displaced fluid. Suppose the stability to be as some 
power of the area of the horizontal section, then A™: ai: S: 8; 
A representing the area of the horizontal section of parallelopipedon 
equal to 215; and a, the area of the ellipsis equal 10 168.; 5S being 
the momentum of the parallelopipedon (when the inclination was 
5°) equal to 60°624; and s, the momentum of the ellipsis (at the 
same angle of inclination) equal to sa : se required power, or 
og. S — Log. s 
exponent, or the value, of m, 1s = Wee Rs Ra 
5° 0 102——s«*iS®™s«HP—s«-BO—-=BNP 
20605, 2°0350, 2°0115, 1°9903, 1:9705, 1°9529; mean value of exp, m, 2°0030, 
In the next place compare the rhombus with the parallelopipedon. 
It is evident the former is precisely half, the area of the latter; and 
by comparing the experiments, nearly the same result is obtained.as 
with the ellipsis; namely, when the centre of gravity of the body 
is situated in the same point as the centre of gravity of the displaced 
fluid, the stability is as the square of the surface, the momentum 
being nearly 1. of the momentum of the parallelopipedon, as ap- 
pears by the subjoined table :— j 
5° d10—i*dS™ MDD NO 
20082, 2°0038, 1°9995, 1-9955, 1-9645, 19952; mean value of exp, m, 1:9945, 
Model 16 being but half the length of model 5, the momentum 
of model. 16 must.be doubled when. compared, withimodel 5. The 
value of m.is.as follows. :-— 
5° 10° 15° 20° 250 Si FOR 
21770, 21318, 20846, 20362, 19862, 1°9334; mean value of exp. m, 2'0582, 
The momentum of model 5 is greater or less, as the centre of 
yvravity falls short or exceeds: % inches. above the bottom of the 
model. From these results of the value of m, it appears extremely- 
probable that the momentum of all figures is in proportion to the 
squares of the area. This conclusion from experiments corroborates 
rhe first theorem. 
2 
