Permanence of the Celestial Motions. 75 inter-planetary space. Had we been moving through an atmosphere even a hundredth part as heavy as that which we breathe, our globe would have long ago ceased its whirling, and fallen, by a spiral course, into the sun. But for this emptiness of the celestial spaces and the consequent uniformity of the earth's movements round its axis and round the sun, we should have no rational idea of time: we could have no proper conception of events in the past or anticipation of them in the future. Next year, next month, even to. morrow, would not mean the same length of time as last year, last month, or yesterday. We should have no standard to go by; no fixed stars of reference to calculate our rate of passage over the ocean of time; no foreknowledge of the happening of eclipses of the sun and moon; no regular routine of the seasons to direct the commerce and concerns of the world; nothing but unimaginable confusion. 156. In actual experience we can see only the tendency to this persistence of force in any moving body, because friction is always present in a greater or less degree to drain away the momentum of even the heaviest moving mass. When the steam is turned off in the engine of a railway train or of a steamboat, the momentum of the train or boat is gradually communicated in the shape of friction to the little particles against which the moving surfaces in each case graze. These masses are so small that it takes necessarily much longer time to transfer the momentum than if the body dashed against a large obstacle. So again, when a carriage is suddenly stopped, a man will be thrown on his face; because he had a common motion with his vehicle, and while that of the latter is given up suddenly by impact or powerful friction, only a small fraction of the person's motion— as much as can be transferred through the friction between him and the vehicle—is given up in the same time. Hence, while the vehicle is brought to rest, the person still possesses most of his motion, and falls forward in consequence. A horse stopping suddenly, thus throws his rider over his ears. Jumping from an omnibus or a railway carriage in motion is so dangerous, because while the feet soon give up their motion by friction to the ground, the upper part of the body is not brought to rest, and it is dashed to the earth round the feet as a pivot. If, however, the person run for a short distance, he may be able to bring the other parts of his body to rest simultaneously with his feet. A man or a horse, when racing, cannot at a given signal stop 76 Examples of so-called Inertia of Motion. instantly, because friction is the only means at his command for bringing him to rest. It is because this resistance is very much lessened that the skater cannot stop so readily as he could running at the same pace on a common road. If a tumbler of water or a tray of glasses come in contact with some obstacle, the contents, having no solid connection with the vessel, cannot be stopped so readily, and the water or glasses will be thrown forward on the floor. The greater momentum of the heavier greyhound cannot be so sharply counteracted as that of the hare, and this enables the hare to save itself by "doubling," or turning its course when the enemy is close at hand. The action of shaking the snow from one's feet by kicking against the doorstep; the cleaning of dusty books by striking them together; the drying of a wet mop or of a pen by shaking—are all similarly explained. A package containing any fragile articles, such as glass or eggs, if very suddenly dropped on the ground, or lifted even for a short distance, frequently has the contents damaged. On the awful occasion of a ship at full speed coming suddenly on a sunken rock, all things on board, men, guns, and loose furniture, start from their places and dash forwards; the connection between them and the ship not being sufficiently rigid to convey enough of the shock to stop their common forward motion as suddenly as the ship is stopped. The same principle explains the jolting motions felt in riding in a carriage over a rough road, or when a train passes "points" at a station. And, indeed, but for this inequality of motion in any carriage, we should not be aware that we were moving at all. In a dark night and calm sea, a person on the deck of a steamboat cannot tell if he be moving quickly or slowly, or if he be in motion at all. A ship becalmed at sea may, as numerous accidents have proved, be carried by rapid currents in any direction without one of the crew ever suspecting it; and if the suspicion do arise, the truth can be come at only by such means as the sounding line, or careful observation of the stars. A man in a balloon, going even eighty miles an hour, knows not in what direction he is moving, nor that he moves at all, but by observing distant objects within his view. This explains why we are not sensible of the motion of the earth itself, though we know that its circumference of nearly 24,000 miles Free Motion naturally Straight. 77 turns once round in twenty-four hours, and that near the equator, therefore, we are actually rushing through space at the rate of 1000 miles an hour. And the reason that a lofty spire or an obelisk stands more securely on the surface of the earth than even a short pillar stands on the bottom of a moving waggon, is not that the earth is more at rest than the waggon, but only that its motion is smooth and uniform. But, if there were any jerk or sudden change of its velocity for even the smallest moment of time, we should be instantly dashed across its surface, and our noblest edifices and our imperial cities would be strewn like so much dust over the land. 157. Lastly, this First Law of Motion asserts that absolutely free motion is uniformly straight, and, that when any motion is not straight, some external force is causing it to deviate. The tendency of a body to pursue its course in a straight line is unpleasantly illustrated by the overturning of carriages in quickly rounding corners; while the wheels are suddenly pulled round by the horses into a new direction, the persistence of the previous motion in a direction across that in which the carriage can move causes it to upset. Thus a loaded omnibus running south, may, when turned suddenly to the east or west, strew its passengers or any loose articles on the south side of the road. Where a sharp turning is unavoidable in a carriage road, or on a line of rails, the outside of the bend should be made higher than the inside, that this force, which would overturn a carriage, may be expended in raising it up on that side to which the fall would take place. The tendency of moving water to keep on its straight course is seen in the wearing away of the outside bank or a stream where it takes a sharp bend. Every turn in the course of a river indicates the action of some force which must have operated at some time, possibly ages ago, to make it deviate from the straight course. A stone revolving in a sling, the moment it is set at liberty, darts off as straight as an arrow, and it is only because the point of the circle from which it should depart cannot in practice be readily determined that the same sure aim cannot be taken with a sling as with a bow or a gun. On first approaching this subject one might suppose that a body, which for a time has been revolving in a circle, should naturally continue to do so when set at liberty. 78 Centrifugal or Central Force. We see a top whirling, and we usually imagine that there is merely one force-that of rotation-concerned in the case, and that this is of itself sufficient to keep it spinning could we eliminate friction. But since a circle may be regarded as an infinite number of minute straight lines, the course of any particle of the top is being constantly turned aside into a new direction, and this is due to the action of some interfering force in that direction. There is little difficulty in seeing how natural this is when we speak of a small body or a mere particle whirling round a point at some distance from the particle; it is only when we think of a large mass turning round itself—that is, round some direction within it as an axis, that the misconception arises. The experience of our earliest years teaches us this fact. The merest child, when he whirls his ball round his head by a string, knows that string is necessary, as well as force of arm, to keep it whirling, and that if the string break, away goes the ball. "Centrifugal force." 158. The force which the string exerts, and which is necessary to keep up the circling motion is called the centripetal, that is, centre-seeking force, or centrifugal, i.e. centre-flying force, if we consider it from the other side as straining the string; or, more generally, either is termed the central force. If we whirl a ball at the extremity of an elastic cord, this force is seer. and may be measured by the extent to which it stretches the cord; if a rapid whirling be given to it, the string may be stretched beyond its power of restraint and snap. In the case of our supposed whirling top, the strings which tie its particles to the centre or axis of motion are the invisible cohesive forces between them; and, just as with the ball and Fig. 12. elastic cord, there is the same pulling, tension, or tendency of the particles to fly outwards from the centre. If these cohesive forces were to cease for a moment, the particles of the whirling top would be instantly scattered in straight lines away from the centre in every direction, just as a pin or any loose body, laid on the surface of a flat revolving top, is instantly thrown outwards, because it has no tie to the centre. (Fig. 12.) Illustrations of Centrifugal Force. 79 159. The following examples show the reality of this central force in any case of rotatory motion of a body :— In a corn-mill the grain, passing through a hole in the upper or turning stone, falls between the stones, and moving round between them is, by the centrifugal force, gradually conveyed outwards to the circumference, where it escapes as flour. If the rotation of a heavy wheel or grindstone be made very rapid, the material near the circumference tends outward so strongly by its centrifugal force, that it may be even torn away with extreme violence. This not unfrequently happens with the grindstones used for sharpening needles, the fragments scattering destruction around like a discharge of musketry or the bursting of a bombshell. Were a man to lie down on a quickly-turning horizontal wheel, with his head near the edge, he would soon fall asleep, or might die of apoplexy from over-pressure of blood on the brain. A pail of water may be whirled round the body horizontally, or round the head vertically, without spilling a drop, the centrifugal tendency being great enough to overcome the tendency of the liquid to fall out. In feats of horsemanship at a circus, the rider is seen to lean inwards when moving fast in the ring, and if the horse be at full gallop, both horse and rider must lean nearly half towards falling on their side. This is to counteract the centrifugal force, which would otherwise throw both to the opposite side; if the horseman tends to fall inwards, he has merely to quicken his pace a little; if to fall outwards, he has to slacken it, and all is right again. The same inclining is seen when, in riding on a bicycle, a person keeps turning in a circle. A coin dropped on the floor or table often describes several turns of a spiral before falling flat on its face; it is the centrifugal part of the moving force which keeps it up until by the gradual friction on the floor it is reduced so as to be unable longer to counteract the weight of the coin. If a pair of common fire tongs, suspended by a cord attached to the top, be made to turn by the twisting or untwisting of the cord, the legs will separate from each other to an extent depending on the speed of rotation, and will again collapse when the turning ceases. The illustrious Watt adapted this simple fact most ingeniously to the regulation of the speed of a steam-engine. His steam-governor may be described as a pair of tongs or rods jointed at their top, and carrying heavy balls at the lower ends to make their opening more |