28. =Hardness.=--This property seems to depend upon some peculiar arrangement of the particles of matter. We should suppose that the densest substances would be the hardest. But it is not so. Iron is the hardest of the metals, but its particles are not so close together as those of gold, which is quite a soft metal. And gold is five times as heavy as the diamond, which is so hard as to cut glass easily. Common flint is hard enough to scratch glass, but will not cut it like the diamond. [Illustration: Fig. 2.] 29. =Flexibility and Brittleness.=--If you bend a flexible body as a piece of wood, as represented in Fig. 2, it is obvious that the particles on the upper or convex side must be put a little farther apart, while those on the under or concave side are brought a little nearer together. But the wood does not break, because the particles that are thus moved a little apart still retain their hold upon each other. This is the explanation of what we call flexibility. On the other hand, the particles in a rod of glass can not be put farther apart in this way. They are not actually in contact any more than the particles of the wood are (§ 20), but they are in a _fixed_ relative position; that is, a position which can not be disturbed without a _permanent_ separation of particles. If you attempt to bend the rod there is no slight separation of many particles, as in the bent wood, but a full and permanent separation in some one part of the rod. We call the property on which this result depends brittleness. Brittle substances are generally hard. Glass, while the most brittle of all substances, is hard enough to scratch iron. Brittle substances also have much tenacity. A rod of glass can hold up a heavy weight, although a slight blow suddenly given would break it. 30. =Flexible and Brittle Steel.=--There are two kinds of steel, flexible and brittle. The steel of most cutting instruments is brittle. The steel of a sword-blade is quite flexible, and that of a watch-spring is so much so that we can wind it up in a coil. This difference is owing to a difference in the mode of cooling the steel. If it be cooled suddenly, it is brittle; if slowly, it is flexible. The process by which it is cooled slowly is called _annealing_. The explanation of all this is quite plain. The steel being expanded by heat--that is, its particles being put farther apart than they usually are--when they are suddenly brought together again they have not time to arrange their relative position properly. Brittleness is therefore the result. But, on the other hand, when the cooling is effected gradually, time is given for the arrangement.