Such an instrument is the _balance_ or _scales_, which you may see in
every grocer’s shop. It is composed of a beam which moves easily on a
pivot fixed to its middle, and which has a scale-pan attached to each
end. So long as both scale-pans are empty the beam is horizontal; but if
you put anything which has weight into one, that one goes down and the
other rises. If now you either pull or push the empty scale downwards,
the beam may be brought into the horizontal position again, and the
effort required to bring it into the horizontal position will be the
greater, the greater the weight of the body in the opposite scale. An
ounce in the one scale is easily raised by the pressure of a finger in
the other. A pound requires more effort; ten pounds needs putting out
the strength of the arm; to raise fifty pounds involves still more
exertion; while a couple of hundredweight will not be stirred by the
strongest push or pull upon the empty scale.
Suppose that, instead of pressing down the empty scale, you put
something that has weight into it; then, as soon as this weight is equal
to that in the other scale, the beam will become horizontal. In fact,
one scale has just as much tendency to move towards the centre of the
earth as the other has, and as neither can go down without pulling the
other up, they neutralise one another. It comes to the same thing, as if
two boys of equal strength were pulling one against the other; so long
as the pulls in opposite directions are equal, of course neither boy can
stir; while the smallest addition of strength to one enables him to pull
the other over.
22. =The Weight of the same Bulk or Volume of Water is Constant under
the same conditions. Mass. Density.=
Now let two graduated thin glass measures be put into the two scales,
and made to counterpoise one another exactly. Then, if even a single
drop of water is put into the one measure the scale will descend, if the
balance is a good one; showing that the drop has weight. If the measures
are graduated accurately, then whatever volume of water is put into one,
an exactly similar volume of the same water must be put into the other
to make the beam level. This obviously means that =the same volume of
water under the same circumstances always has the same weight=.
In § 18 it was said that bodies tend to move towards one another with a
relative velocity[1] which is inversely proportional to the quantity of
matter which they contain. But how are we to measure quantity of matter?
Is it to be estimated by the space which it occupies; that is, by its
volume? or are we to estimate the quantity of matter in a body by its
weight? You will soon learn that the volume of all bodies is constantly
changing in correspondence with the changes in the pressure exerted by
other bodies, but more especially in correspondence with the changes of
temperature to which they are subjected; while the weight of the same
body, at the same point on the earth’s surface, never alters. Hence we
may take the weight of a body as a measure of the quantity of matter
which it contains; and it follows that, for the same weight, the larger
the volume of a body the less matter it contains proportionally to its
volume, and the less the volume, the more matter it contains. The
proportion of its weight to its volume gives us the =density= of a body.
Footnote 1:
Velocity, or swiftness, is measured by the distance over which a body
travels, in a given time. Of two bodies, one of which travels through
one foot in a second, while the other travels through two feet, the
latter has the greater relative velocity.
Now what is true of water is true of all other bodies or material
substances. Suppose that one of the measures is emptied and replaced,
the beam may be brought to the horizontal position again by means of a
piece of lead cut to exactly the right size. The piece of lead will
thenceforth furnish an exactly corresponding or equivalent weight for so
much water; and pieces of iron or brass, which counterpoise the lead,
will also be equivalents of the weight of the water, or of the lead, or
of one another. But the pieces of lead, iron, or brass will obviously be
of much less volume or bulk than the water which they counterpoise. Here
it follows that the densities of these metals, or the quantity of matter
contained in the same volume, must be much greater than in the case of
water.
What are called =weights= in commerce are pieces of lead, or iron, or
brass exactly equivalent in weight to a certain bulk of water under
certain conditions. =An imperial gallon of water thus weighs ten pounds,
and therefore an imperial pint weighs a pound and a quarter.=
23. =Equal Volumes of Different Things under the same circumstances,
have Different Weights: the Density of Different Bodies is Different.=
The important fact which has just been alluded to must be considered
more fully. We have seen that an imperial pint measure gives us the
space which is taken up by as much water as weighs a pound and a
quarter; and this space is the bulk or =volume= of that weight of water.
But if you take an ordinary pound weight and a quarter-pound weight, and
put them into an imperial pint measure, you will find that instead of
filling it, they take up only a very small portion of the space in its
interior, or in other words, of its capacity. Thus the volume of a pound
and a quarter of lead, or of iron, or of brass, is very much less than
the volume of the same weight of water; that is to say, the metals are
=denser= than water; the same volume has greater mass or more gravity.
Or, to put the case in another way, fill the tumbler with which we began
half full of water, making a mark on the side exactly at the level of
the top of the water. Then place it in one scale of a balance, and
counterpoise it with weights in the other. Next, pour out the water, and
after drying the tumbler, fill it with fine sand carefully up to the
mark. The volume of sand will be equal to the volume of water. But now
the same weights will no longer counterpoise it, and you will have to
put more weights in the opposite scale. Volume for volume, therefore,
sand is heavier than water. Throw out the sand, and put in sawdust in
the same way, and you will find that a less weight than was necessary to
counterpoise the water counterpoises the sawdust. Volume for volume,
therefore, sawdust is lighter than water. Experiment in the same way
with spirit and oil, and they will be found to be lighter than water,
while treacle will be heavier, and quicksilver very much heavier than
water.