VI. MOTION CAUSED BY FORCE.

111. When by our own strength we put a body in motion, or change or stop the motion which a body already has, we feel that we make some effort, that we exert force. We soon learn that we can assist the power of our own bodies by the aid of tools or machines, as of a bat to strike a ball, or of a bow to discharge an arrow. Again, we avail ourselves of the stores which nature presents to us in the services of animals to draw our burdens, and we have no difficulty in believing that the force which they put forth in their tasks resembles that which we ourselves are conscious of exerting in similar circumstances. Next we employ the resources of inanimate nature, as of the wind to waft our ships or of the falling waters of a stream to turn our mills. Finally, there are more subtle agencies, not presented by nature of her own accord, but gained from her by the inventive skill of man; such as the explosive force of gunpowder and the expansive force of steam.

112. It is the nature of man to seek for the causes of the effects which he experiences, and though in many cases his search leads to little direct result yet he gains much indirectly; for the effects become better known by the attempt to trace them to their causes, and sometimes we may ascertain many of the laws according to which a cause acts though the cause itself may remain unknown.

113. We cannot explain how the earth has the remarkable property of attracting bodies, though we are sure of the fact; see Art. 71. Indeed so familiar are we with the fact that we cease to wonder at it; and yet there is something very strange in the communication of motion by one lifeless mass, as the earth, to others, as stones and logs. The marvel will be increased when we learn from Astronomy that this power of attraction belongs apparently to all the bodies of the universe, and that it reaches through the long distances which separate the earth from the sun

and the planets. A very able man, the late Professor Vince of Cambridge, held that this wonderful power of attraction could be explained in no other way than by ascribing it to the immediate and ever present action of the Deity.

114. Although forces differ as to their origin, yet they all agree as to the way in which they produce or change motion. There are certain Laws which hold with respect to the connection between force and motion, which are called briefly Laws of Motion. These Laws are not presented in quite the same form and number by all writers, although there is in general substantial agreement among those who have carefully discussed the subject. We shall follow Newton in making three Laws of Motion, and also in the mode of stating them.

115. First Law of Motion. Every body continues in a state of rest, or of uniform motion in a straight line, except in so far as it may be compelled to change that state by force acting on it.

The law may be said to assert that every body is of itself passive and inert, and cannot of itself either begin to move or change its motion if it has any. The body is of course to be understood as inanimate; nothing is said as to the complex operation of the will and the muscles by which a man moves himself, or of the instinct and the muscles in the case of an animal.

116. We must now consider what evidence we have of the truth of the Law. That a body at rest will continue in that state unless force acts on it may be held to be obvious from observation and trial. But that a body in motion, if left to itself, will continue to move uniformly in a straight line seems not so obvious. For we cannot devise any means of preserving a body which is in motion from the action of force, and so we cannot obtain that perseverance in uniform rectilinear motion of which the Law speaks. If a stone is made to slide along the ground it is soon reduced to rest; but we can easily admit that this destruction of motion is due to the roughness of the ground. Accordingly we find that if the same stone is

started in the same manner to slide on a smooth sheet of ice it will go much further before it is reduced to rest. And we may imagine that if we could remove all obstacles arising from the roughness of the surface on which the stone slides, and from the resistance of the air, the motion might go on for ever unchanged.

117. Still it would be wrong to suppose that the Law can be readily accepted by the beginner on the ground of such rude experiments as he may make or imagine. The history of science shews distinctly that the Law is not one of those truths which present themselves obviously and are easily believed. The ancient Greeks, who made great progress in some branches of knowledge, never reached the simple Laws of Motion; and the honour of laying the foundation of this part of Natural Philosophy was reserved for Galileo.

118. Observation will however supply facts which are quite consistent with the Law. Thus, for instance, if a railway train in motion is suddenly stopped a passenger seated on the back seat of a carriage finds himself thrown forwards; this arises from the fact that he continues in his state of motion after the carriage itself is stopped. So also if a man is riding rapidly on horseback and the horse stumbles the man is thrown over the horse's head.

119. But since the direct evidence which can be produced in favour of the first Law of Motion is slight, it may be asked how can we be confident of its truth. The answer is complete and decisive. The oldest and most eminent of human sciences is Astronomy; and the theory of Astronomy rests on the three Laws of Motion as a foundation. By the aid of this theory astronomers are able to predict years beforehand the occurrence of striking phenomena in the heavens, such as eclipses of the sun and moon, and the return of a comet after an unseen journey of three quarters of a century; and these predictions are found to be fulfilled with minute accuracy. Thus, for example, it was predicted long in advance, that on December 9th, 1874, there would be the remarkable appearance called a transit of the planet Venus over the Sun's disc;

accordingly all the civilized nations of the world sent observers at great expense and trouble to various places to watch the appearance: and it occurred at the appointed day and hour. Now it is impossible to suppose that the three Laws of Motion can be false when astronomers have deduced from them numerous and various results which are found to be accurately true; and thus we may say briefly that the unfailing certainty with which the predictions of Astronomy are always verified supplies abundant evidence of the truth of the Laws of Motion. We need not repeat this remark in connection with the second and third Laws.

120. Second Law of Motion. Change of motion is proportional to the acting force, and takes place in the direction of the straight line in which the force acts.

This Law requires to be explained before the beginner will receive all that its statement includes; at present we will take only a portion of it. Suppose then that a body is moving in a straight line, and that a force acts on the body in the same direction; then the Law says that the change of motion is proportional to the acting force. This implies that the change of motion does not depend on the velocity which the body already has. Now this may be very well exemplified by the case of falling bodies which we considered in Chapter IV. Thus, for instance, according to our statement in Art. 92, the velocity of a falling body at the end of three seconds is 96 feet per second; so that if gravity were suddenly to cease the body would fall through 96 feet in the next second. But gravity continues to act, and according to the second Law of Motion it will affect the motion in the same way as if the body, instead of starting with the velocity of 96 feet per second, started from rest. Thus throughout the fourth second fresh velocity is constantly communicated to the falling body, just as it was during the first second; so that by virtue of this action 16 feet are fallen through, besides the 96 feet fallen through by virtue of the velocity at the beginning of the fourth second. Hence on the whole 112 feet are fallen through in the fourth second. This agrees with the result obtained in Art. 91.

121. The facts to which we have called attention in Arts. 106 and 107 are in agreement with the second Law of Motion. The steamer and every thing on it move from South to North; then the motion or change of motion which is produced in any thing on the steamer by the action of force is the same as that force would produce if the steamer were at rest. Newton himself deduces from the second Law of Motion the principle called the Parallelogram of Velocities which we have stated in Art. 108.

122. So long as we consider only the same body, change of motion is measured by change of velocity; then the second Law of Motion asserts that any force will communicate velocity in the direction in which the force acts, and it is implied that the amount of the velocity so communicated does not depend on the amount of the velocity which the body already has. When we consider different bodies the Law implies something more than this, as we shall see hereafter; we defer the discussion of this, and of the third Law of Motion until we have explained what is meant by Mass.

123. The beginner must not expect to become at once familiar with the full meaning of the Laws of Motion; by watching the application made of them in trustworthy books, and by reflexion, he will gradually gain a firm hold of them, and learn to use them with confidence to explain what he sees around him. One caution is necessary with respect to the kind of motion which we have in view. We mean such motion as that of a falling body, or of a body carried by a railway train; motion in which one point of the body moves just like any other point which may be on the side of it, or in the front of it, or behind it. We mean in fact to leave out of consideration the motion of rotation, such as that of the sails of a windmill, or of a child's top. The motion of rotation may exist together with the other kind of motion, as we know from the case of the earth as stated in Art. 104; and a more obvious example is furnished by the wheels of a carriage which turn round while at the same time they move forward with the body of the carriage. The motion of rotation is more difficult to treat