the result is produced, but we cannot doubt the fact that the earth does draw the moon. It is found also that this attraction is universally a property of matter; that the moon also attracts the earth, and that the earth and the moon attract the sun. The earth's attraction moreover gives rise to the weight of a body which is supported, and to the fall of an unsupported body: these two results are in a slight degree modified by the earth's rotation on its axis, but in the main they depend on the earth's attraction. This attraction, which, as far as we can see, prevails throughout the universe, is called attraction of gravitation, or simply gravitation.

72. Another kind of attraction is that which exists between the particles of a solid body. We know that if we want to break up a solid body we must make an effort to separate the parts, and it may happen that a very considerable effort is necessary; hence we are led to ascribe the union of the parts to the existence of some mutual attraction between them. This is called the attraction of cohesion, or simply cohesion.

73. If the surfaces of two bodies are made smooth, and pressed together with a moderate force, they will sometimes stick very closely. For example, let two cylinders of lead have their ends scraped very smooth, and let the ends be pressed and turned against each other until they are in close contact; then it will require some effort to separate the cylinders. Glass plates can be made so even that when once in contact they cannot be separated without breaking. Contact is frequently ensured by putting some soft substance between the surfaces to be joined; when this dries it is in close contact with both surfaces, and much effort is required to effect a separation. This kind of attraction is called adhesion; and in accordance with this and the definition of the preceding Article we may say that particles of the same body cohere, and that particles of different bodies in suitable circumstances adhere.

74. Again in Chemistry we often find that if two substances of different kinds are brought together under favourable conditions they will unite and form a new sub

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stance. This is spoken of as chemical attraction, or sometimes as chemical affinity. A large part of chemistry consists of illustrations of this kind of attraction. For an example: Sulphuric acid will unite with copper and water, and form a beautiful translucent blue salt; and if a piece of iron be thrown into a solution of the copper salt, the acid will immediately let fall the copper, and take up or dissolve the iron. Sulphuric acid will not unite with or dissolve gold at all."

75. Capillary attraction is the name given to the action between fluids contained in slender glass-tubes and those tubes themselves; the term has been extended to include some other cases of action between fluids and solids, as we shall see hereafter.

76. Electrical attraction is the name given to some cases resembling magnetic attraction, in which electricity is the agent.

77. Of the various kinds of attraction which we have mentioned that called gravitation is the one which has been most carefully studied, and of which we know the most. Here we have that very important principle or law called the law of gravitation, which tells us how the amount of the attraction changes when the distance of the attracting bodies changes. Suppose we have a sphere composed of one substance, as lead or iron; and suppose we have also another sphere composed of one substance, which may be the same as that of the first sphere or different. Each sphere may be of any size we please. By the distance between the spheres let us understand the distance between their centres. Put the spheres at any distances apart; then there is a certain attraction exerted between them, so that unless the spheres were in some way kept apart they would move towards each other. Now suppose that the spheres are put at double the former distance, then the attraction will be only a quarter of what it was at first; suppose the distance is made three times as great as at first, then the attraction will be only of what it was at first; suppose the distance is made four times as great as at first, then the attraction will be only

of what it was at first; and so on. This principle or law is easily understood for all cases; it is technically expressed by saying that the attraction varies inversely as the square of the distance: thus, if the distance is made ten times as great, since the square of 10 is 100, the attraction will be only of what it was before.

78. The law stated in the preceding Article is true of the spheres whatever be the size and the substance of each. It is not strictly true of other bodies; but there are cases in which it may be extended to bodies not spherical. Thus, if the bodies are excessively small it will be true without regard to the shape of them; and therefore it is frequently given as the law of attraction of particles. If the bodies are not particles, still, if the distance between them is very great compared with the size of the bodies, the law will be practically true.

79. As to the kind of attraction called cohesion we do not know accurately in what way the change of distance is connected with the change in the amount of the attraction. The attraction appears to be very intense between particles that are very close together, and to become feeble as soon as the distance between the particles is large enough to be practically sensible. It is possible that science may hereafter shew that cohesion and gravitation are really attractions of the same kind; the law being that established by Newton when the particles are at a sensible distance, and taking some other form when the particles are extremely close.

80. Many substances which occur in nature present themselves under three forms, namely, the solid, the liquid, and the aeriform. Thus it is one and the same substance with which we are familiar under the names of ice, water, and steam. Mercury also, which is usually a liquid, can be frozen, and can be turned into a vapour. There are grounds for believing that every substance can take these three forms, and that the change from the solid state to the liquid state is produced by the application of heat, and the change from the liquid state to the aeriform state by the further application of heat.

81. In solids the cohesion is strong, aud keeps the particles in contact; in liquids the cohesion is very weak, and indeed scarcely sensible, so that the particles may be separated by the slightest effort; in aeriform bodies there is no cohesion whatever, but on the contrary the particles repel each other, and some external force is required in order to keep them near each other. The distinction between the three forms of matter is sometimes expressed with technical precision as follows. Solid bodies have an independent volume and an independent shape. Their parts do not move easily among themselves; it requires always more or less effort to disturb them or to separate them. When once separated they do not unite by being merely placed again in contact. Liquids have an independent volume, but not an independent shape. They take the shape of the vessel in which they are placed. The least effort can move or separate the parts; but after separation the parts unite again when placed in contact. Aeriform bodies have neither an independent volume, nor an independent shape; they spread themselves through any space open to them, until restrained by some external obstacle.

82. It is, as we have said, by the application of heat that the cohesion of solid bodies is destroyed and the liquid state assumed; and by a further application of heat the cohesion is changed into repulsion and the aeriform state assumed. Hence some writers have been inclined to consider heat mainly as a repulsive power opposite in character to that attractive power of which we have already spoken.

After this general notice of our subject, of its connection with other parts of science, and of the necessary preliminary mathematical knowledge, we proceed in this volume to treat in detail of the various mechanical properties of solid and fluid bodies; that is of properties which belong to all such bodies, connected with the operation of force.

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IV. MOTION.

FALLING BODIES.

83. Objects in motion present themselves readily to our notice as we look around us; and moreover we soon learn that motion is a thing which may be measured. Thus we are told that a man whom we know walks four miles an hour, that a certain horse trots nine miles an hour, and that a railway train in which we made a journey moved through thirty miles in an hour. In these cases we understand that the motion is uniform, that is the motion is kept up steadily, not becoming sometimes faster and sometimes slower. It will then be an easy question in arithmetic to find the distance moved through by any of these bodies in whatever interval of time may be mentioned; as, for instance, to find the distance moved through by the railway train in one second. In 30 miles there are 30 times 5280 feet, that is 158,400 feet; and in an hour there are 60 times 60 seconds, that is 3600 seconds. Divide 158,400 by 3600; the quotient is 44: so that the railway train moved through 44 feet in one second.

84. There are two words much used when we speak and write about motion, of which the meaning is perhaps familiar, but for clearness should be mentioned; these words are space and describe. The word space is used as equivalent to length or distance; thus we talk about a space of 44 feet, meaning a length or distance of 44 feet. The word describe is used in the sense of moving through; thus we say a body describes a space of 44 feet, meaning that it moves through a space or distance of 44 feet. Sometimes we omit the word space and say that a body describes 44 feet.

85. When a body describes 44 feet in a second we say that its rate of motion is 44 feet a second; or we may say that its velocity is 44 feet a second: it is very customary to employ a Latin preposition and say 44 feet per second. We see that velocity is a thing which admits of exact measurement. Thus, if a child can walk at the rate of one mile in an hour, and his father at the rate of four miles in an hour, the velocity of the father is four times that of the child. If a railway train goes 45 miles in an hour, and a