191 
The stability of floating bodies depends entirely on the action 
of couples. Take a block of wood and hold it in water in the 
position represented in Figure 2: it will not stay in this position 
unless held, and, if released, will turn about without moving from 
its place till the upper and lower sides become horizontal. The 
forces which act upon it constitute in fact a couple. What are 
these forces? There are but two of them: its own weight acting 
vertically downwards through its centre of gravity ; and the pressure 
of the water upon it, which is equal to the weight of the water 
displaced, and acts upwards through the centre of gravity of the 
water displaced. Itis necessary to be very clear about these forces. 
The first is familiar to us from hourly experience. The second 
may be less generally understood; it is, however, a main 
principle of hydrostatics, and may either be deduced as a 
conclusion of pure reason, or established directly from experiment, 
that the resultant pressure on the immersed surface of any body 
is equal to the weight of the fluid displaced, and acts vertically 
upwards through the centre of gravity of the fluid displaced. This 
centre of gravity of the fluid displaced is, in the case of vessels, 
called the Centre of Buoyancy, a term of constant use. Returning 
to our block of wood, we may now say that it is acted on by 
two equal and opposite forces, its own weight acting downwards 
through its centre of gravity, and the resultant pressure of the water 
upon it acting upwards through its centre of buoyancy. It is to be 
observed that the position of the centre of gravity of the block is 
_always the same, but that of the centre of buoyancy will be changed 
with every motion of the block. One position of the centre of 
_ buoyancy should especially be noted: when the block is at rest, 
_ the centre of buoyancy will be found to be directly under the 
centre of gravity, so that the two forces now act in the same line, 
though in contrary directions, and completely neutralize each other. 
To apply these notions exactly to the case of boats is some- 
what difficult, as it requires long and careful calculation to find 
the centre of gravity of a boat, and for every position of the 
centre of buoyancy a fresh calculation must be made. 
Approximate results sufficient for practical purposes may, 
