The specific gravity (§ 24) of lead is 11·45; in other words it is about
eleven and a half times denser than water. Therefore if a bar of lead
cut square and one inch in the side, and rather less than 1/11th of the
height of a column of water, is slipped into the tube in place of the
water, it will exert the same pressure on the bottom.
And now comes a difference between the lead and the water, which depends
on the fluidity of the latter. The lead exerts no pressure on the sides
of the tube, but the water does. If a small hole is cut in the side of
the tube close to the bottom, and stopped with a cork, the lead will not
press upon the cork. But if the column of water is high enough the cork
will be driven out with as much force as before, so that the water
presses just as much sideways as downwards. It is easy to satisfy
oneself of this by inserting a long glass tube, with its lower end bent
at right angles and fitted with a cork, into the side of the wooden
pipe. The water will at once rise in the tube to the same height as it
has in the pipe. Whence it is obvious that the pressure of the water on
any point of the side is exactly equal to the vertical pressure at that
point; for the pressure outwards is exactly balanced by that of the
vertical column in the tube inwards. The water in a watering-pot always
stands at the same level in the can and in the spout.
If a glass tube is bent into the shape of a =U=, and water is poured
into it, the water will always stand at the same level in the two legs
of the tube, whatever the shape of the bend may be, or the relative
capacities of the two legs, or the inclination of the tube.
And this must needs be so, for the force with which the water tends to
flow out of the one half of the arrangement depends on the vertical
height[2] of the surface of the water above the aperture of exit; so
that any column of equal vertical height must balance it.
Footnote 2:
Vertical height is the height measured along a line drawn from the
surface of the water perpendicularly to the surface of the earth. A
plumb-line is a string to one end of which a weight is attached and
thus hangs suspended. If the other end of the line is brought opposite
the surface of the water the direction of the string answers to the
line of vertical height.
That a column of water will stand at exactly the same level as any other
with which it communicates, may be seen still more simply by placing a
glass tube, open at each end, in a basin of water. However the tube may
be inclined or bent, whether its lower end is wide or narrow, the column
of water inside it will be at exactly the same level as the water
outside it. Yet, of course, the rigid glass walls of the tube cut off
all communication between the column of water inside it and the rest,
except at the bottom.
Public-domain text, read in full here on John Shaqi.
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