II. MATERIAL OBJECTS.—A. MINERAL BODIES.

One of the commonest of common natural objects iswater; everybody uses it in one way or another every day; and consequently everybody possesses a store of loose information—of common knowledge—about it. But, in all probability, a great deal of this knowledge has never been attended to by its possessor; and certainly, those who have never tried to learn how much may be known about water, will be ignorant of a great many of its powers and properties and of the laws of nature which it illustrates; and consequently will be unable to account for many things of which the explanation is very easy. So we may as well make a beginning of science by studying water.

13.A Tumbler of Water.

Suppose we have a tumbler half-full of water. The tumbler is an artificial object (§ 5); that is to say, certain natural objects have been brought together and heated till they melted into glass, and this glass has been shaped by a workman. The water, on the other hand, is a natural object, which has come from some river, pond, or spring; or it may be from a water-butt into which the rain which has fallen on the roof of a house has flowed.

Now the water has a vast number of peculiarities. For example, it is transparent, so that you can see through it; it feels cool; it will quench thirst and dissolve sugar. But these are not the characters which it is most convenient to begin with.

The water, we see, fills the cavity of the tumbler for half its height, therefore it occupies that muchspace, or has that bulk orvolume. If you put the closed end of another tumbler of almost the same size into the first, you will find that when it reaches the water, the latter offers a resistance to its going down, and unless some of the water can get out, the end of the second tumbler will not go in. Any one who falls from a height into water will find that he receives a severe shock when he reaches it. Water therefore offersresistance.

If the water is emptied out, the tumbler feels muchlighter than it was before; water, therefore, hasweight.

And, finally, if you throw the water out of the tumbler at any slightly supported object, the water hitting against it would knock it over. That is to say, the water being put in motion is able totransferthat motion to something else.

All thesephenomena, as things which happen in nature are often called, are effects of which water, under the conditions mentioned, is the cause, and they may therefore be said to be properties (§ 4) of water.

All things which occupy space, offer resistance, possess weight and transfer motion to other things when they strike against them, are termedmaterial substancesorbodies, or simplymatter. Water, therefore, is a kind, or form, of matter.

You will easily observe that, though water occupies space, it has no definite shape, but fits itself exactly to the figure of the vessel which holds it. If the tumbler is cylindrical, the contour of the surface of the water will be circular when the tumbler is held vertically, and will change, without the least break or interruption, to more and more of an oval when the tumbler is inclined, and whatever the shape of the vessel into which you pour it, the sides of the water always exactly fit against the sides of the vessel. If you put your finger into the water you can move it in all directions with scarcely any feeling of obstacle. If you pull your finger out there is no hole left, the water on all sides rushing together to fill up the space that was occupied by the finger. You cannot take up a handful ofwater, for it runs away between your fingers, and you cannot raise it into a permanent heap. All this shows that the parts of water move upon one another with great ease. The same fact is illustrated if the tumbler is inclined so that the level of the surface rises above the edge of the tumbler on one side, and the water is therefore to some extent unsupported by the tumbler at this point. The water thenflowsover in a stream and falls to the ground, where it spreads out and runs to the lowest accessible place, or gradually soaks up into crevices.

Nevertheless, although the parts of the water thus loosely slip and slide upon one another, yet they hold together to a certain extent. If the surface of the water is just touched with the finger, a little of it will adhere; and if the finger is then slowly and carefully raised, the adjacent water will be raised up into a slender column which acquires a noticeable length before it breaks. So, in the early morning, after heavy dew, you may see the water upon cabbage-leaves and blades of grass in spherical drops, the parts of which similarly hold together.

Material substances, the parts of which are so movable that they fit themselves exactly to the sides of any vessel which contains them, and which flow when they are not supported, are calledfluids, and fluids the parts of which do not fly off from one another, but hold together as those of water do, are calledliquids.

Water therefore is a liquid.

It has been seen that water, like every othermaterial substance, resists the intrusion of other matter into the place which it occupies. But many things, though they resist, can be easily squeezed orcompressedinto a smaller volume. This, however, is not the case with water, which like other liquids, is almostincompressible; that is to say, an immense pressure is needful to cause its volume to diminish to any appreciable extent. It may seem strange that anything so apparently yielding as water should yet be almost as difficult to squeeze as so much iron; but the apparent yieldingness of water is due to the ease with which it changes its shape; and, if water is prevented from changing its shape, it is very difficult to drive its parts closer together. It has been ascertained that if water is confined in a closed space, a pressure amounting to fifteen pounds on the square inch diminishes its volume by only120000th part. Take a common syringe, and having seen that the plug orpistonfits thecylinderof the syringe well, put the nozzle into water and draw the piston up. Then turn the nozzle upward and push upon the piston till a little of the water squirts out, so as to make sure that the cylinder contains nothing but water. Now put your finger on the opening of the nozzle firmly, so as to stop any water from passing out, and then try to push the piston down. You will find that you cannot make it stir without great force; and, if the piston moves appreciably, it will be because some of the water has escaped by the sides of the piston. In fact, if the piston presented a square inch of surface, and fitted accurately, and the column of water in the cylinder were one inch long, it must be pressed down by a weight of 30,000 pounds (about thirteen tons) to make it move one-tenth of an inch.

17.The Meaning of Weight.

Let us next consider the property of weight. We say that anything has weight when, on trying to lift it from the ground, or on holding it in the hand, we have a feeling of effort. Or again, if anything which is supported at a certain height above the ground, falls when the support is taken away, we say that it has weight. Now the ground merely means the surface of the earth; and, as all bodies which possess weight fall directly towards the surface of the earth when they are not kept away from it by some support, we may say that all bodies which have weight tend to fall in this way. And it does not matter on what part of the surface of the earth you make the experiment. Rain consists of drops of water, and it does not matter whether we watch a shower in calm weather here, or in New Zealand; the drops fall perpendicularly towards the ground. But we know that the earth is a globe, and that New Zealand is at our antipodes, or on the opposite side of the globe to England. Hence if two showers are falling at the same time, one in New Zealand and one here—the drops must be falling in opposite directions, towards one another; that is, towards the centre of the earth which lies between them. In fact, all bodies which have weight tend to fall towards the centre of the earth—that is to say they fall in this way if there is nothing to prevent them; and when we speak of weight we mean this tendency to fall. To call anything heavy, is the same as saying that we fully expect that, if there is nothing to support it, it will fall to the ground; or that if we support it ourselves we shall be conscious of effort.

18.Gravity and Gravitation.

The wordgravity, when it was first used, had exactly the same meaning as weight; and a body which has weight is said togravitatetowards the center of the earth. But gravity has now acquired a much wider sense than weight. For an immense number of careful observations and experiments have established the general rule, or law of nature, that every material substance, tends to approach every other material substance, just in the same way as a drop of rain falls towards the earth; and, in fact, that any two portions of matter, whatever the nature of that matter may be, will move towards one another if there is nothing to prevent them from doing so.

To make this clear, let us suppose that the only material bodies in the universe were two spherical drops of water, each a tenth of an inch in diameter. Each of these drops would have the same bulk as the other, and would be a quantity of matter exactly equivalent to the other. Then, however great the distance which separated these two drops, they would begin to approach one another; and, each moving with gradually increasing swiftness, they would at length meet in a point exactly half-way between the positions which they at first occupied. But if the bulk of one drop were greater than that of the other drop, then the larger would move more slowly, and the point of meeting would be by so much nearer the larger drop. It follows that, if the one body of water were as big as the earth and the other remained of its original size, no bigger than a rain-drop—the motion of the large mass towards the small one would be an inconceivably minute fraction of the totaldistance travelled over. It would appear as if the large body were perfectly still and drew the small body to itself.

This is just what happens when a single drop of water falls from a cloud, say through a distance of a mile, to the earth. The earth really moves towards it, just as it moves towards the earth, on the straight line which joins the centres of the two. But the length of this line which each travels over isinversely proportionalto the quantity of matter in each, that is to say is the less the bigger the quantity. So that we have a rule-of-three sum. As the quantity of matter in the earth is to that in a rain-drop, so is a mile to the distance travelled over by the earth. And if any one worked out this sum, he would find that the fourth term of the proportion would be an inconceivably minute fraction of an inch. For all practical purposes, therefore, we may consider the earth to be at rest in relation to all falling bodies, inasmuch as the quantity of matter in any falling body is insignificant, in comparison with that contained in the earth.

What is true of water is true, so far as we know, of all kinds of matter, and we therefore say that it is a law of nature that all kinds of matter possess gravity; that is to say, that of any two, each tends to move towards the other, at a speed which is the slower the greater the quantity of matter it contains in proportion to that which the other contains; and this speed gradually becomes quicker as the two bodies approach.

What is usually called thelaw of gravitationis a statement of the same observed facts in another and more complete fashion. (SeePhysics Primer.)

19.The cause of Weight: Attraction: Force.

We know nothing whatever of the reason why bodies possess weight. Bodies do not fall on account of the law of gravitation (§ 9); nor does their gravity explain why they fall. Gravity, as we have seen, is only a name for weight, and the law of gravitation is only a statement ofhowbodies approach one another, notwhythey do so.

It is often said that gravitation isattraction, and that bodies fall to the earth because the earth attracts them. But the word “attract” simply means to “draw towards,” and “attraction” means nothing but “drawing towards;” and to say, when two bodies move towards one another, that they are “drawn towards” one another, is simply to describe the fact and makes us no whit wiser than we were before. On the contrary, unless we take great care, it may make us a little less wise. For the words “drawing towards” are so closely associated with ropes and hooks and the act of pulling, that we are easily led to fancy the existence of some analogous invisible machinery in the case of mutually attractive bodies.

Again, gravitation is spoken of as aforce; and as the word force is in very common use, let us try to make out what we mean by it. A man is said to exert force when he pushes or pulls anything so as either to exert pressure upon it or to put it in motion. A wrestler’s force is proved by his hug; a bowler’s force is shown by the swiftness of motion of the ball.

Force, then, is the name which we give to that which causes or, in the case of pressure, tends to cause, motion. The force of gravity therefore meansthe cause of the pressure which we feel when bodies which possess gravity are supported by our bodies, and the cause of their movement towards the centre of the earth, when they are free to move. But it is exactly about the cause of these phenomena that we know nothing whatever.

A good deal of mischief is done by the inaccurate use of such words as attraction and force, as if they were the names of things having an existence apart from natural objects, and from the series of causes and effects which are open to our observation; while they are, in reality, merely the names of the unknown causes of certain phenomena. And it is worth while to take pains to get clear ideas on this head at the outset of the study of science.

Let us remember then that, so far as we know, it is a law of nature, that any two material bodies, if they are free to move, approach one another with gradually increasing swiftness; and that the space over which each travels before the two meet, is inversely proportional to the quantity of matter which it contains.Attraction of gravitationis a name for this general fact;weightis the name for the fact in the case of terrestrial bodies;forceis a name which we give to the unknown cause of the fact. The fact is that which it is important to know. The names are of no great consequence so long as we recollect that they are merely names and not things.

We must next consider, not weight in general, but the weight of water. We say that a tumbler full ofwater is heavier than an empty tumbler, because the full tumbler gives us a greater feeling of effort when we lift it than the empty tumbler does. The more water there is in the tumbler the greater is the effort. A pail full of water requires still more effort, though the empty pail feels quite light; and, when we come to deal with a large tub full of water, we may be unable to stir it, though the empty tub could be lifted with ease. Thus it seems that the greater the bulk of water the more it weighs, and the less the bulk the less it weighs. But then a single drop of water in the palm of the hand seems to weigh nothing at all. However, this clearly cannot be, for the drop falls to the ground readily, and therefore it must have weight. Moreover, a few thousand drops would fill the tumbler, and if a thousand drops weigh something, each drop must have a thousandth of that weight. The fact is that our feeling of effort is a very rough measure of weight, and does not enable us to compare small weights, or even to perceive them if they are very small. To know anything accurately about weight we must have recourse to an instrument which is contrived for the purpose of measuring weights with precision.

Such an instrument is thebalanceorscales, 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 hasweight 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.

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 ofwater 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 thatthe 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. Theproportion of its weight to its volume gives us thedensityof a body.

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 calledweightsin 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.

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 orvolumeof thatweight 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 aredenserthan 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.

We are in the habit of using the wordsheavyandlightrather 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 itsspecific 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 arelight, while the latter three areheavy.

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 poursome 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 itis, 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.

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; if12,625 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.

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 certainpressureon 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 downwardpressure 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 than111th 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 enoughthe 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 aU, 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.

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 iswide 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.

In a well-ordered town, water is supplied to every house and can be drawn from taps placed in the highest stories. These are fed by pipes which lead from a cistern at the top of the house. This water is brought from a large pipe, ormain, in the street, by a smaller house-pipe, which is often made to twist about in various directions before it reaches the cistern at the top of the house into which it delivers the water. If you followed the main, you would find that it took a long course up and down, beneath the pavement of the streets, until at last it reached the water-works. Here you would find that the main was connected with a reservoir; and either this reservoir is at a greater height than any of the cisterns into which the water is delivered, or there is some means of pumping the water from it to that height on its way to the main. Thus the reservoir, the main, and the house-pipe form one immenseU-tube, and the water in the house-pipe tends to rise to the same level as that of the water in the reservoir, and hence flows into the cistern when the supply-pipe is open.

Suppose a wooden vat with a horizontal tap, the sectional area[3]of the tube of which is one square inch,inserted close to the bottom, to be filled with water up to 100 inches above the tap. Then supposing the tap to be shut, the pressure upon its sectional area will be 25,250 grains, or rather more than three pounds and a half—and there is the same pressure on every square inch of the bottom of the vat.

3. The sectional area of a tube is the surface occupied by its cavity when it is cut across. It would be represented by the surface of a piece of cardboard, like the wad of a gun, just large enough to go into the tube.

If the tap is now turned, the water nearest to it being unsupported on its outer side, the pressure on the inner side sets it in motion, and it flows out in a stream. At first the stream shoots out violently and the water is carried to a long distance. That is to say, the weight of the column of water 100 inches high acts as a force, or cause of motion, upon the water nearest the tap, and this water is forced out with a velocity depending on that force in a horizontal direction. Now suppose that you take a common toy cup-and-ball and bring the ball into the way of the stream of water. The stream will at once strike the ball and drive it in the same direction as that which it is itself taking. The power which the moving water has of transferring or communicating motion to a body which is at rest, but free to move as the ball is, is due to itsmomentum. The greater the mass of the stream and the more rapidly it moves, the more motion will it communicate to the ball, or the heavier the ball it will move. Close to the mouth of the tap the direction of the stream is horizontal; but it very soon begins to bend downwards, and describing a rapid curve, comes to the ground. It does this for just the same reasons that a stone thrown horizontally describes a curve; and atlength strikes the ground; and, in fact, the stream may be regarded as so much water thrown horizontally.

These reasons are two: firstly, as soon as the water has left the tap it is an unsupported heavy body; and, as such, it begins to fall to the ground. Secondly, the momentum of the water is continually being diminished by the resistance of the air through which it passes. For, although the air which surrounds us is so thin and movable a body that we ordinarily take no notice of it—the fact that it offers resistance to bodies which move through it is easily observed; as, for example, in using a fan. The water has to overcome this resistance, and its momentum is proportionally diminished.

If, when the water leaves the tap, the air and gravitation were alike abolished, the water, keeping its momentum, would travel for ever in the same direction.

As the water runs out, it will be observed that the velocity of the stream becomes less and the curve which it describes sharper, so that it comes to the ground sooner; and finally, when the vat is nearly empty, the stream falls nearly vertically downwards. The reason of this is that the level of the top of the water is gradually lowered; consequently, the height of the column which presses on the water close to the tap is gradually lessened, and therefore its weight is diminished. But this weight or pressure is the cause of the motion of the water, and as the cause diminishes the effect of that cause must diminish. Therefore the momentum of the water is gradually lessened and it is carried less and less far horizontally in the time which it takes to fall to the ground:until finally, it acquires no appreciable horizontal motion at all, and so falls vertically downwards from the mouth of the tap.

If a short pipe bent at right angles like the letterLis fitted by one arm on to the end of the tap, while the other is turned vertically upwards, and the vat is full as before; when the tap is turned, the water will shoot up into the air, and after rising for a certain distance will stop, and then fall. In fact we shall have a fountain.

Observe the difference between the vertical jet of water and the horizontal jet. If we leave the resistance of the air out of consideration, the water in the horizontal jet has no obstacle to overcome; and it might go on for ever, if its weight did not gradually cause its path to become more and more bent towards the earth, against which it eventually strikes.

When the jet is vertical the case is altered. The water thrown up vertically constantly tends to fall down vertically, as any other heavy body would do, and its momentum has to overcome the obstacle of its gravity. Any given portion of the water is, in fact, acted upon by two opposite tendencies, momentum urging it up, and gravity pulling it down. Now if two equal tendencies exactly oppose one another, the body upon which they act does not move at all; while, if one is stronger than the other, the body moves in the direction of the stronger.

Thus a portion of water which has just left the spout shoots up, because the velocity with which it is impelled upwards is sufficient to carry it through agreater space in a given time, say a second, than that through which its gravity would, in the same time, impel it downwards.

But the distance which the water will travel during this second will be the difference between the distance which it would have ascended if there had been no gravity forcing it down, and the distance which it would have descended if there had been no momentum driving it up; and, at the end of the second, the rate of its motion upwards, or its velocity, will be proportionally slower. Thus, at the end of the first second, the water has spent a certain portion of its momentum in overcoming its gravity. And as there is nothing to make good the loss, it would, if left to itself, travel more slowly, or over a less distance, in the second second than it tended to do in the first. But though the momentum of the water is diminished, its gravity, weight, or tendency to fall downwards, for a given distance in a second, remains exactly what it was, and operates in the course of the second second to exactly the same extent as in the first. Hence, at the end of the second second, the distance through which the water travels upwards is still smaller, and its velocity is still more diminished. It is obvious that, however great the disproportion between momentum and gravity to start with, gravity must gain the day in the long run under these circumstances. The store of momentum will be used up; and, after a momentary rest, the water, reduced to the condition of a body without support, will begin to be carried downwards by the unopposed action of gravity.

The case is similar to that of a boy sculling a boat, the bows of which are suddenly seized and the boatthrust violently backwards by a strong man. The boat will go stern-foremost rapidly, at first, but every stroke of the boy’s oar at the stern will retard its backward motion; until, at length, the stock of momentum conferred upon it by the man’s thrust will be completely exhausted in working against the boy, and the boat, after a momentary rest, will resume its onward course. The distance to which the boat will be propelled backwards will evidently depend upon the amount of muscular power which the man, as it were, suddenly capitalizes in the boat, and which the boat then slowly pays out.

We call people who possess much muscular or other power energetic; and we estimate theirenergyby the obstacles they overcome, or, in other words, by theworkthey do. In the present illustration the man’s energy would be measured by the distance to which the boat was propelled before it stopped.

It is easy to transfer this conception of energy, as the power of doing work, to inanimate things; and thus when a body in motion overcomes any kind of obstacles in its way, parting with its momentum and more or less coming to rest in the process, we say that it hasenergyand that it doeswork.

The energy of moving water is thus measured by the intensity of the opposing forces which it can overcome multiplied into the distance which it can travel before that energy is exhausted; that is to say, by the work it does before it is itself reduced to a state of rest. In the case under consideration, the energy by which gravity is overcome, for a greater or less time, depends upon the velocity of the stream; and this again depends upon the height of the water in the vatabove the tap. Just as the energy of the horizontal stream diminished as the level of the water became lower, so does the energy of the vertical stream diminish. Hence, as the vat empties, the jet becomes shorter and shorter, until at last it sinks down to nothing.

The energy of moving water makes it, under some circumstances, one of the most destructive of natural agents; and, under others, one of the most useful servants of man. A stream is water falling down hill with a velocity depending upon the inclination of its bed. As it falls it acquires momentum and, hence, energy; and thus a mountain stream, suddenly swollen by rain or melting snow, will tear away masses of rock and sweep everything before it. Nothing can look softer or more harmless than a calm sea, but if the wind sweeping over its surface puts the water in motion, it strikes upon the shore with terrific force; and its energy is expended in throwing up great waves, which lift vast blocks or drive masses of shingle up the beach.

In all kinds of watermills it is the energy of more or less rapidly falling water which is turned to account. The water is made to flow against buckets or floats attached to the circumference of a wheel. Each bucket or float is therefore an obstacle to which the water transfers some of its own motion; it moves away and thus makes the wheel to which it is fastened turn. But the turning of the wheel brings a new obstacle in the way of the stream. This is treated in the same fashion, and the wheel turns still further, thus introducing another obstacle in the way of the stream upon which the same effect is produced. Thus each float, or bucket, is a means by which some of the momentumof the stream is, as it were, caught and transferred to the water-wheel, which consequently turns round with a certain velocity.

But this water-wheel is now a mass of matter in motion, and therefore itself contains a store of energy or power doing work. If a cord with a weight at the end of it were fastened to the axle of the wheel, the cord would be wound upon the axle, and the weight could be raised, or, in other words, so much work would be done by the turning of the wheel and we should thus have a rough measure of the amount of energy which had been given up by the stream to the wheel.

The machinery of the mill is simply a set of contrivances for transferring the energy stored up in the water-wheel to the place in which work has to be done. In a flour-mill, for example, a series of wheels carries it from the water-wheel to the grindstones, which it sets in motion.

If, whenever there is a shower, you catch some rain-water, you will find that it possesses all the properties which have been described. It will be found to be an almost incompressible liquid, an imperial pint of which weighs about a pound and a quarter. It would make no difference if the rain-water were collected in Africa or in New Zealand; or if it had been obtained centuries ago and kept bottled up ever since. And there is every reason to believe that rain-water will have exactly the same properties a hundred or a thousand years hence. So far as the properties ofrain-water are concernedthe order of nature is constant.

This, however, is by no means the same thing as saying that the properties of water are always the same. In fact the properties of the substance, water, vary immensely according to the conditions to which it is exposed; but, under the same conditions, they are the same, so that we may still say that so far as water is concerned, the order of nature is constant.

It has been seen that a certain weight of water always has the same volume under the same conditions. The most important of these conditions is the heat or cold to which it is exposed. Water which has stood for some time in a warm room becomes less in volume, orcontracts, if it is taken into a cool place; while its volume increases, or itexpands, if it is made hot. The same thing is true of quicksilver, of spirit, and of liquids in general. Athermometeris simply a small flask—the bulb—with a long and narrow neck—the tube—filled with as much mercury or spirit as will rise a short distance into the neck. If the liquid in the bulb is warmed, its volume is increased and it overflows into the tube, increasing the height of the column of liquid in the tube. If, on the other hand, the liquid in the bulb is cooled, its volume is diminished; and, as it shrinks, the column of liquid in the tube flows back into the bulb, and the level of the top of the column is lowered.

If a mark is made on the tube, or on a scale fixed to it, at the point which the liquid reaches when thebulb is placed in boiling water; and another mark at the point to which it sinks when the bulb is in melting ice; and the space between the two marks is divided into 180 equal parts, each of these parts is what is called a “degree” in the thermometers ordinarily used in this country (called Fahrenheit). And if the boiling-point is counted as 212° the freezing-point must be 32° (212 - 32 = 180). With the same amount of heat the fluid in the tube always stands at the same degree, and hence the instrument measurestemperature.

That hot water is lighter than cold is easily seen when a bath is filled from two taps, one of hot and one of cold water, which run at the same time. Unless care is taken to stir the water, the top of the bath will be very much hotter than the bottom. Thus, an imperial pint of water weighs a pound and a quarter only at a certain temperature or degree of warmth, namely at 62°; if it is made hotter its volume increases, and therefore its specific gravity diminishes.

It was for this reason that in § 22 the weight of the same volume of water was said to be constantunder the same conditions; and, of course, the same qualification must be borne in mind when we speak of the weight of a cubic inch of water being about 252 and a half grains. Its weight is in fact 252·45 grains only when Fahrenheit’s thermometer stands at 62°—but as this is the temperature of ordinary mild weather, and the expansion or contraction of water for a degree about this temperature amounts to less than13000th of its volume, the weight of a cubic inch may for all practical purposes be taken as 252 and a half grains.

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