of matter, the solid, the liquid, and the gaseous; and each of these states has certain properties which serve to distinguish it.

II. Definition of Solids.-A solid body, such as a piece of iron or wood, resists any attempt to alter its shape or its size, always keeping the same size or volume and the same shape, unless it be violently destroyed.

12. Definition of Liquids.-A liquid like water, when kept in a bottle or other vessel, always spreads itself out, so as to make its surface level, but yet it will always keep its proper size or volume. You cannot by any means force a pint of water into a half-pint measure; it will insist upon having its full volume, but it is not particular as to shape.

13. Definition of Gases.-A gas again has no surface; for if you put a quantity of any gas into a perfectly empty vessel, the gas will fill the whole vessel. Nor does a gas insist so violently as a liquid upon occupying a certain space; for by means of a proper amount of force I can compress the gas which now fills a pint bottle into half a pint, or even into less space, if I use sufficient force. In fact, a gas will be persuaded to go into less space, but a liquid will not be persuaded.

PROPERTIES OF SOLIDS.

14. The peculiar distinction of a solid is that it insists upon keeping not only a certain space or size for itself, but also a certain figure or shape.

* Experiment 7.—In fig. 4 you have two vessels of different shapes, but of the same size. And it

you exactly fill the one with water and pour it into the other, you will find that the water exactly fills it also.

Here, again, you see two pieces of wood that have both the same shape or figure, but the one is much larger than the other-their size is different.

mean the same thing), Now, you cannot take

You see now what is meant by space or size or volume (for the three words and what by figure or shape. a solid which has the shape of the one bottle and force it into the shape of the other, although the size or volume of both is the same; nor can you take a solid of the size or volume of the first wooden block and squeeze it into that of the second, although the shape of both blocks is the same. A perfect solid will keep its figure, and it will also keep its size.

Bear in mind, however, that when we say we cannot do a thing, we really mean we cannot do it without very great difficulty, and then not completely, but only to a very small extent; in fact, what we

really mean is best explained by making a series of simple experiments.

* EXPERIMENT 8.-Let me take a bar of iron; I will first of all try to break it in pieces by means of a blow, but it won't be broken.

I will next try to stretch it out by hanging it up tightly by one end, and then applying to the other end a heavy weight, but it won't be stretched.

I will now, by means of two rods, fitting in to the bar at its ends, as you see in the figure, try to twist

Fig. 5.

round the one end, while I hold the other still, but it won't be twisted.

I will now set the bar endwise upon the table, and put a heavy weight above it, to try and squeeze it together, but it won't be squeezed.

And finally I will hang it up horizontally by both ends, and attach a weight to the centre, and I find it won't be bent.

Now the bar of iron which I can neither break by a blow, nor stretch, nor twist, nor squeeze together, nor bend, is a very good example of a solid body; and yet, if I applied an exceedingly great force, this bar might be stretched, or twisted, or squeezed, or bent. And in truth I did actually stretch, and twist, and

squeeze down, and bend it, in the experiments I have just described, but not enough to make it visible to you. In fact the amount by which I stretch, or twist, or squeeze down, or bend the bar, depends upon the amount of force I use; and in Physics we try to find out the relation between the force which we use and the effects which we produce. I cannot tell you all about this subject, because it would take up a great deal of time, but we may take one operation, such as bending, and endeavour to find in what way its effects depend upon the force which we employ.

15. Bending. EXPERIMENT 9.-For this purpose let us support a wooden beam in a horizontal position by both ends, and let us hang a somewhat heavy weight from its middle or centre. Then let us measure upon a scale how far the centre has been bent down by the weight. Let us now double the weight that hangs from the centre, and mark the new position of the centre of the beam under the increase of weight, and we shall find that the centre of the beam has been lowered about twice as much by the double weight as by the single weight, or

in fact the bending is nearly proportional to the weight applied.

EXPERIMENT 10.-Let us now take the very same beam of wood, and place it in edgewise, so as to give it a great depth, rather than a great flat surface, and let us apply the same force as before.

Fig. 6.

We shall find that the beam is not bent nearly so much

as it was before.

16. Strength of Materials.-Now if an architect or an engineer were using great wooden beams in the construction of a building, it would evidently be most advantageous to strength were he to place them in such a way that their depth might be as great as possible, for in such a position they would give way much less under any heavy weight.

An architect or engineer ought therefore to know all about the strength of things, and how to place them so as to get the greatest possible strength out of the least possible amount of material; in fact he ought to know how to use his wood or his iron in the best possible way.

Another point that the architect or engineer should bear in mind is to make his house or his bridge five or six times strong enough to bear the greatest load that will ever be put upon it. For sometimes a building may be strong enough to stand a heavy weight on the floor, or a bridge may be strong enough to stand the passage of a long train, without absolutely breaking down, and yet the floor of the building may be so much bent that it won't quite recover itself when the weight is taken off, or the bridge may in like manner be so much bent that it won't recover itself when the train has passed. In such a case the floor will be less strong each time the weight is put on it, and the bridge will be less strong each time the train passes. They will in fact go on bending more and more, until at last they give way. The architect or engineer must therefore take great care that his structure is never bent beyond the limits of perfect recovery.

17. Friction. Before leaving solids, let us say a few words about friction. If I put a very heavy