Part 7

21. =The Measuring of Weights. The Balance.=

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 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.

24. =The Meaning of Heavy and Light—Specific Gravity.=

We are in the habit of using the words =heavy= and =light= rather carelessly. We call things that are easily lifted light, and things that are hard to lift heavy. We say that sand, which is blown about by the wind, is light, and that a block of wood is heavy, and yet we have just seen that sand is heavier, bulk for bulk, than wood. In order to get rid of this double meaning, the weight of a volume of any liquid or solid, in proportion to the weight of the same volume of water at a known temperature and pressure, is called its =specific gravity=. Water being taken as 1, anything a volume of which is twice as heavy as the same volume of water is said to have the specific gravity 2; if three times, 3; if four and a half times, 4·5, and so on. Thus the specific gravity of any liquid or solid expresses its density in proportion to that of water under the same conditions. Sawdust, oil, and spirit have a less specific gravity than water, while treacle, sand, and quicksilver have a greater specific gravity. In this sense, the former three substances are =light=, while the latter three are =heavy=.

25. =Things of greater Specific Gravity than Water sink in Water; Things of less Specific Gravity float.=

Here are two tumblers of water. Throw some sand into one and some sawdust into the other. What happens? The sand sinks to the bottom, the sawdust floats at the top. We may stir them up as we like, but the sand will tumble to the bottom and the sawdust, as obstinately, rise to the top. Thus that which is lighter than the water floats, and that which is heavier (bulk for bulk) sinks. So, if we pour some oil into the water, it floats, and if we pour some coloured spirit in carefully, it also floats; while treacle and quicksilver sink to the bottom, just as the iron-filings do.

We saw that the iron-filings sank, because iron is heavier than water. Here is a piece of the thin tinned sheet-iron that they make tin boxes of. What will happen if we drop it into the water? It is heavier than water, bulk for bulk, and therefore it will sink as you see it does.

But now here is a “tin” canister made of this very same tinned sheet-iron. We drop that into the water, and you see it does not sink at all, but floats at the top as if it were made of cork. Here is a perplexity. We were sure just now that iron is heavier than water, and here is an iron box floating! Is this an exception to the law? Not at all; for what we said was that a thing would float if it were lighter, bulk for bulk, than water. Now let us weigh the tin box, and having weighed it let us next try to find out how much the same bulk of water weighs. This may be done very simply, for the walls of the box are very thin, so that the inside of the box is very nearly as large as the whole box. Consequently, if we fill the box with water, and then weigh the water, we shall find out, very nearly, what is the weight of a bulk of water as great as that of the box. But if we do this, we shall find that the water which was contained in the box, weighs very much more than the box does. So that, bulk for bulk, the box, although it is made of iron, is really lighter than water, and that is why it floats.

You will all have heard of the iron ships which are now so common, and you may have wondered how it is, that ships made of thick plates of iron riveted together, and weighing many thousand tons, do not go to the bottom. But they are nothing but our tin canisters on a great scale, and they float because each ship weighs less than a quantity of water of the same bulk does.

It is because of this property of water to bear up things lighter than itself, and because of that other property of being easily moved which the particles of water have, that the sea, and rivers, and canals, are such great highways for mankind.

For there is nothing so heavy that it may not be made to float in water, if the box which holds it is large enough to make the weight of the whole less than the weight of the same bulk of water. And then, having once got the weight to float, the particles of water are so easily moved, that the force of the winds, or of oars, or of paddles, readily causes it to slip through the water from one place to another.

26. =A Body which Floats in Water always occupies as much Space beneath the level of the Surface of the Water as is equal to the Volume of Water which weighs as much as that Body; in other words, it displaces its own Weight of Water.=

A cubic inch of water weighs about 252 grains and a half. Suppose that the tin box in the previous experiment was square, and had the bulk of 100 cubic inches, then the weight of a corresponding volume of water would be 25,250 grains. If the box weighed 8,416 grains, just a third of its bulk would be immersed; if 12,625 grains, half; if 16,832 grains, it would sink two-thirds of its volume, and so on. Or, if, when the box is floating, you make a mark upon its side at the exact level of the surface of the water, the bulk of that portion of the box which lies below the water-level can be ascertained. Suppose it to be thirty cubic inches, then the weight of the box will be 30 × 252·5 or 7575 grains. Hence it may be said that the immersed part of a floating body takes the place of the water which it displaces, and, as it were, represents it. If you press downwards upon the floating box, there is a feeling of resistance as it descends, and when the pressure is taken off, the body immediately rises again. Hence the water presses upwards against the bottom of the floating body. But it also presses against the sides, for if the sides of the box are very thin they will be driven in. If a thin empty bottle is tightly corked and lowered into deep water the cork will be driven in, or else the bottle will be crushed.

27. =Water presses in all Directions.=

Thus water presses in all directions upon things which are immersed in it.

If a long wooden or metal pipe, placed vertically, has its lower end stopped with a cork which does not fit very tightly, and water is poured into the top of the tube, the water will at first fill the part of the tube above the cork, and its weight will exert a certain =pressure= on the cork. In fact, if the end of the tube is stopped by applying the palm of the hand closely against it, the downward pressure of the water will have to be overcome by a certain amount of effort. As the water accumulates, this downward pressure will become greater and greater until the hand is driven away, or the cork is forced out, and the water falls to the ground. The pressure in this case is the same as the weight of the water, and the cork would have been driven out equally well by a rod of lead of the same weight.

Suppose the tube to be square, and that the inside of the square measures exactly one inch each way. Then an inch of height of the tube will hold exactly one cubic inch of water. Since one cubic inch of water weighs 252 grains and a half, as much water as will fill the tube about two feet three inches and a half high, will weigh a pound (7,000 grains), and fifteen pounds of water will fill such a tube between thirty-three and thirty-four feet high. And these respective weights measure the pressure of two columns of water, one twenty-seven and a half inches high, and the other nearly thirty-four feet high, on a square inch of the surface on which they rest.

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.