1816.) On the Stalility of Vessels. 185 
tion is found by subtracting the square of the draft of water from 
the square of half the breadth, and then dividing three-eighths of 
the remainder by the draft of water. 
5. That the stability of vessels is augmented in proportion to the 
cubes of the breadths, provided that the centres of gravity of the 
vessel and of the displaced fluid coincide. 
G. That vessels having the same length and breadth, but different 
drafts of water, have equal stability when their centre of gravity, 
and the centre of gravity of the displaced water, are in the same 
int. 
7. That the altitude of the metacentre in different vessels above 
the centre of gravity of the displaced water is proportional to the 
squares of the breadths, 
The apparatus for making these experiments was simple, as 
appears from the perspective view (Plate XLIV. Fig. 1) of the whole 
together. In this AA represents a cistern filled with water, and 
mounted to a convenient height upon framed legs; B, a model on 
which the experiment was tried, by attaching a fine line, aa, to 
the top of the mast, D, and conducting it over a pulley, E. A scale, 
F, is suspended to the end of the line for the reception of the 
weights. These cause the model to incline, as the figure shows; 
and the degree of inclination of the mast from the perpendicular is 
shown by the plumb-line, /, upon a divided arch, d. ‘Yo prevent 
the body being drawn away towards the pulley, E, by the draft of 
the line, a, it is retained by two small lines (shown dotted at g, g), 
which are made fast to sliders, s, s, at the side of the cistern, and 
have hooks at the opposite ends, which take hold of pins projecting 
from the stem and stern of the model, B ; and these are previously 
adjusted, so that the centre of gravity of the model will be found 
in a line between them. ‘The manner of making this adjustment is 
shown in Fig. 2, which represents a frame of wood, H, supporting 
two small uprights, 4, . These have pieces of brass plate at the 
upper ends, with notches to receive the pins or pivots of the model, 
B. These pivots are fitted into grooves in two pieces of brass plate 
attached to the ends of the model. One of these slips of brass is 
shown separately at Fig. 3, where & is the pivot, and Z a screw 
tapped into the brass slide to which the pivot is fixed, and passing 
through the same groove by means of this screw, the pivot k can 
be fastened at any part of the groove, and raised or lowered. The 
ballast is then raised or lowered till the model will barely rest on 
the pivots without overturning, as shown in Fig. 2. It is necessary, 
in order to know exactly what weight is applied to the top of the 
mast, D, that the line, a, draw in a direction at right angles thereto. 
0 ascertain this, a ruler, m, is fixed upon the top of the mast, and 
the pulley, E, is attached to a cross rail, H, which applies against 
the uprights, and is suspended by a line, , which passes over a 
pley, and is made fast to « cleat, 0. By this means the palley, 
H, €an at pleasure be raised or lowered until the direction of the 
line, a, ie ee with the ruler, m. ‘The manner of conducting 
Vor, Vil, N° LI, 
