HYDROSTATICS. . 19 
in the spout at the same height as in the pot itself; and it must do so, for 
if the water at B, for instance, were lower than at A, 
then the pressure under A would be greater than under 
B, since (§ 2) the pressure is proportional to the depth 
of the liquid; the water, therefore, could not be at rest, 
but a flow must take place into the spout, which 
would continue till the pressure in it was the same as 
in the pot, that is, till the water stood at the same 
level. 
This principle is applied to the introduction of water 
into houses in towns. As fluids always rise to a level, 
no matter what distance the water may be conveyed 
by pipes, it will rise to the height of the source from which it is brought. 
4, A solid body, immersed in a liquid, experiences a pressure equal to the 
weight of the liquid which rt displaces, and this pressure acts vertically 
upwards through the centre of gravity of the liquid displaced. Let AB 
be a solid body immersed in watér; it is evident 
that AB occupies the place of a quantity of water 
equal in volume to itself. Now, suppose AB not 
yet placed in the water, and AB, as seen in the 
figure, to be the water about to be displaced; this 
part of the liquid is supported by the pressure of 
the rest around. The pressure on the sides has no 
effect; because it is equal all round, and may there- 
fore be disregarded : it is the pressure from below that properly supports 
the mass. And since this mass of water has a certain weight which acts 
at its centre of gravity g, the upward pressure keeping it in its place 
must be equal to that weight, and must act through its centre of gravity. 
Suppose, now, the solid to be substituted for the water, it must experience 
exactly the same pressure as acted on the water; that is, the solid AB 
is acted on by a pressure equal to the weight of the water it displaces, 
and acting vertically upward through the centre of gravity of the water 
displaced. 
It is an obvious corollary from this, that ¢f a solid be weighed in a liquid, 
at will be lighter (than its true weight) by the weight of a quantity of the 
liquid equal in volume to the solid. 
This truth was first discovered by the ancient mathematician, Archi- 
medes, and by means of it he was able to discover how much alloy the 
goldsmith, whom the king of Syracuse had commissioned to make a 
crown of pure gold, had fraudulently mixed with the metal. It is said 
that, one day. when floating in his bath, it occurred to him that what was 
supporting his body was that which would support the water displaced by 
it ; and he thought he could, by means of this principle, discover whether 









