THE DISCOVERIES MADE BY NEWTON.
I have now some great discoveries to talk to you about, which were made by Sir Isaac Newton. He was not an astronomer who looked much through a telescope, though he made many remarkable experiments. He used to sit in his study and think, and then he used to draw figures with his pencil, and make long calculations. At last he was able to give answers to the questions: What is the reason why the planet moves in an ellipse? Why should it move in this curve rather than in any other? Why should this ellipse be so placed that the sun lies at one of the foci?
If the planet had run uniformly round its course, Newton would have found his task an impossible one. But I have already explained that the motion is not uniform. I described how the planet hurried along with extra speed at certain parts of its path; how it lingered at other parts; how, in fact, it never preserved the same rate for even a single minute during the whole journey. Kepler had shown how to make a time-table for the whole journey. In fact, just as a captain on a long voyage keeps a record of each day’s run, and shows how to-day he makes 170 miles, and to-morrow perhaps 200, and the next day 210, while the day after he may fall back to 120, so Kepler gave rules by which the log of a planet in its voyage round the sun might be so faithfully kept that every day’s run would be accurately recorded.
When Newton commenced his work, one of the first questions he had to consider was the following: Suppose that a great globe like a planet, or a small globe like a marble, or an irregular body like an ordinary stone, were to be thrown into space, and were then to be left to follow its course without any force whatever acting upon it, where would it go to?
You may say, at once, that a body under such circumstances will presently fall down to the ground; and so, of course, it will, if it be near the earth. I am not, however, talking of anything near the earth; I want you to imagine a body far off in the depths of space, among the stars. Such a body need not necessarily fall down here, for you see the moon does not fall, and the sun does not.
If you were at a great distance from our globe and from all other large globes—so far, indeed, that their attractions were imperceptible—you could try the experiment that I wish now to describe. Throw a stone as hard as ever you can, and what will happen? Of course, when you do it down here, it moves in a pretty curve through the air, and tumbles to the ground; but away in open space, what will the stone do? There will be no such motion as up or down, as we ordinarily understand it; for though the earth, no doubt, will lie in one particular direction at a great distance, yet there will be other bodies just as large in other directions; and there is no reason why the stone should move towards one of these rather than to another; in fact, if they are all far enough, as the stars are from us, their attractions will be quite inappreciable. There is, therefore, not the slightest reason why the stone should swerve to one side more than to another. There is no more reason why it should turn to the right than why it should turn to the left. Nor could you throw the stone so as to make it follow a curved path. You can, of course, make it describe a curve while it remains in your hand, but the moment the stone has left your hand, it proceeds on its journey by a law over which you have no control. As the direction cannot be changed towards one side more than towards the other, the stone must simply follow a straight line from the very moment when it is released from your hand.
The speed with which the stone is started will also not change. You might at first think that it would gradually abate, and ultimately cease. No doubt a stone thrown along the road will behave in this way, but that is because the stone rubs against the ground. If you throw a stone across a sheet of ice, then it will run a very long distance before it stops, and all the time it will be moving in a straight line. In this case there is but little loss by rubbing against the ice, because it is so smooth. Thus we see that if the path be exceedingly smooth, the body will run a long way before it stops. Think of the distance a railway train will run if, while travelling at full speed along a level line, the steam is turned off.
These illustrations all show that if you let a body alone, after having once started it, and do not try to pull it this way or that way, and do not make it rub against things, that body will move on continually in a straight line, and will keep up a uniform speed. We can apply this reasoning to a stone out in space. It would certainly move in a straight line, and would go on and on forever, without losing any of its pace.
I need hardly tell you that no one has ever been able to try this experiment. In the first place, we reside upon the surface of the earth, and we have no means of ascending into those elevated regions where the stone is supposed to be projected. There is also another difficulty which we cannot entirely avoid, and that arises from the resistance of the air. All movements down here are impeded because the body has to force its way through the air; and in doing so it invariably loses some of its speed. Out in open space there is, of course, no air, and no loss of speed can therefore arise from this cause.
Fig. 57.—The Humming-top.
There are, however, several actual experiments by which we can assure ourselves of the general truth. Set a humming-top spinning ([Fig. 57]); it gradually comes to rest, partly because of the rubbing of its point on the table, and partly because it has to force its way through the air. In fact, the hum of the top that you hear is only produced at the expense of its motion. Supposing I use a much heavier top; if I set it spinning it will keep up for many minutes, because its weight gives it a better store of power wherewith to overcome the resistance of the air. I remember hearing a story about Professor Clerk-Maxwell. He had, when at Cambridge, invented one of these large and heavy tops, which would spin for a long time. One evening the top was left spinning on a plate in his room when his friends took their departure, and no doubt it came to rest in due time. Early the next morning, Professor Maxwell, hearing the same friends coming up to his rooms again, jumped out of bed, set the top spinning, and then got back to bed, and pretended to be asleep. He thus astounded his friends, who, of course, imagined that the top must have been spinning all the night long!
If we spin a top under the receiver of an air pump ([Fig. 58]), it will keep up its motion for a very much longer time after the air has been exhausted than it would in ordinary circumstances. Such experiments prove that the motion of a body will not of itself naturally die out, and that if we could only keep away the interfering forces altogether, the motion would continue indefinitely with unabated speed. What I have been endeavoring to illustrate is called the first law of motion. It is written thus:—
“Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.”
Fig. 58.—To illustrate the First Law of Motion.
I would recommend you to learn this by heart. I can assure you it is quite as well worth knowing as those rules in the Latin Grammar with which many of you, I have no doubt, are acquainted. The best proof of the first law of motion is derived, not from any experiments, but from astronomy. We make many calculations about the movements of the sun, the moon, the stars, and then we venture on predictions, and we find those predictions verified. Thus we had a transit of Venus across the sun in 1882, and every astronomer knew that this was going to occur, and many went to the ends of the earth so that they might see it favorably. Their anticipations were realized; they always are. Astronomers make no mistakes in these matters. They know that there will be another transit of Venus in the year 2004, but not sooner. The calculations by which these accurate prophecies are made involve this first law of motion; and as we find that such prophecies are always fulfilled, we know that the first law of motion must be true also.
Newton knew that if a planet were merely left alone in space, it would continue to move on forever in a straight line. But Kepler had shown that the planet did not move in a straight line, but that it described an ellipse. One conclusion was obvious. There must be some force acting upon the planet which pulls it away from the straight line it would otherwise pursue. We may, for the sake of illustration, imagine this force to be applied by a rope attached to the planet so that at every moment it is dragged by some unseen hand. To find the direction this rope must have, we take the law of Kepler, which explains the rules according to which the planet varies its speed. I cannot enter into the question fully, as it would be too difficult for us to discuss now. I should have to talk a great deal more about mathematics than would be convenient just at present; but I think you can all understand the result to which Newton was led. He showed that the rope must always be directed towards the sun. In other words, suppose that there was no sun, but that in the place which it occupied there was a strong enough giant constantly pulling away at the planet, then we should find that the speed of the planet would alter just in the way it actually does. Thus we learn that some force must reside in the sun by which the planet is drawn, and this force is exerted, although there is no visible bond between the sun and the planet.
There is another fact to be learned about the sun’s attraction, and this time we obtain it by knowing the shape of the curve followed by the planet. The laws by which the planet’s speed is regulated prove that the force emanates from the sun. We shall now learn much more when we take into account that the path of the planet is an ellipse, of which the sun lies at the focus. Nothing has been said as yet regarding the magnitude of the pull which is being exerted by the sun. Is that pull to be always the same, or is it to be greater at some times than at other times? Newton showed that no ellipse other than a circle could be described, if the pull from the sun were always the same. Its magnitude must be continually changed, and the nearer the planet lies to the sun, the more vehement is the pull it receives. Newton laid down the exact law by which the force on the planet at any one place in its path could be compared with the force at any other position. Let us suppose that the planet is in a certain position, and that it then passes into a second position, which is twice as far from the sun. The pull upon the planet at the shorter distance is not only greater than the pull at the longer distance, but it is actually four times as much. Stating this result a little more generally, we assert, in the language of astronomers, that the attraction varies inversely as the square of the distance. If this law were departed from, then I do not say that it would be impossible for the planet to revolve around the sun in some fashion, but the motion would not be performed in an ellipse described around the sun in the focus.
You see how very instructive are the laws which Kepler discovered. From the first of them we were able to infer that the sun attracts the planets; from the second, we have learned how the magnitude of the attracting force varies.
The true importance of these great discoveries will be manifest when we compare them with what we have already learned with regard to the movements of the moon. As the moon revolves around the earth it is held by the earth’s attraction, and the moon follows a path which, though nearly a circle, is really an ellipse. This orbit is described around the earth just as the earth describes its path around the sun. That law by which a stone falls to the ground in consequence of the earth’s attraction is merely an illustration of a great general principle. Every body in the whole universe attracts every other body.
Think of two weights lying on the table. They no doubt attract each other, but the force is an extremely small one—so small, indeed, that you could not measure it by any ordinary appliance. One or both of the attracting masses must be enormously big if their mutual gravitation is to be readily appreciable. The attraction of the earth on a stone is a considerable force, because the earth is so large, even though the stone may be small. Imagine a pair of colossal solid iron cannon-balls, each 53 yards in diameter, and weighing about 417,000 tons. Suppose these two globes were placed a mile apart, the pull of one of them on the other by gravitation would be just a pound weight. Notwithstanding the size of these masses, the hand of a child could prevent any motion of one ball by the attraction of the other. If, however, they were quite free to move, and there was absolutely no friction, the balls would begin to draw together; at first they would creep so slowly that the motion would hardly be noticed. The pace would no doubt continue to improve slowly, but still not less than three or four days must elapse before they will have come together.
By the kindness of Professor Dewar, I am enabled to exhibit a contrivance with which we can illustrate the motion of a planet around the sun. Here is a long wire suspended from the roof of this theatre, and attached to its lower end is an iron ball, made hollow for the sake of lightness. When I draw the ball aside, it swings to and fro with the regularity of a great pendulum. But when I place a powerful magnet in its neighborhood ([Fig. 59]), you see that as soon as the ball gets near the magnet it is violently drawn to one side, and follows a curved path. This magnet may be taken to represent the sun, while the ball is like our earth, or any other planet, which would move in a straight line were it not for the attraction of the sun which draws the body aside.
Fig. 59.—The Effect of Attraction.