CH. XVIII. NEWTONS STUDIES. 149 plague broke out in Cambridge in the year 1665, and he was forced to go back to Woolsthorpe. Here he was sitting one day in the garden, meditating as usual, when an apple from the tree before him snapped from its stalk and fell to the ground. This attracted Newton's attention; he asked himself, Why does the apple fall? and the answer he found was, Because the earth pulls it. This was not quite a new thought, for many clever men before Newton had imagined that things were held down to the earth by a kind of force, but they had never made any use of the idea. Newton, on the contrary, seized upon it at once, and began to reason farther. If the earth pulls the apple, said he, and not only the apple but things very high up in the air, why should it not pull the moon, and so keep it going round and round the earth instead of moving on in a straight line? And if the earth pulls the moon, may not the sun in the same way pull the earth and the planets, and so keep them going round and round with the sun as their centre, just as if they were all held to it by invisible strings? You can understand this idea of Newton's by taking a ball with a piece of string fastened to it, and swinging it round. If you were to let the string go, the ball would fly off in a straight line, but as long as you hold it, it will go round and round you. Thus Newton imagined that everything near the earth is pulled towards it by an invisible force, as you would pull the ball by the string; but the ball does not come to you, although the string pulls it, because of the other force which is carrying it onwards; and in the same way the moon would not come to the earth, but would go on revolving round it. Newton felt convinced that this guess was right, and that the force of gravitation, as he called it, kept the moon going round the earth, and the planets round the sun. But a mere guess is not enough in science, so he set to work to prove by very difficult calculations what the effect ought to be if it was true that the earth pulled or attracted the moon. To make these calculations it was necessary to know exactly the distance from the centre of the earth to its surface, because the attraction would have to be reckoned as strongest at the centre of the earth, and then as gradually decreasing till it reached the moon. Now the size of the earth was not accurately known, so Newton had to use the best measurement he could get, and to his great disappointment his calculations came out wrong. The moon in fact moved more slowly than it ought to do according to his theory. The difference was small, for the pull of the earth was only onesixth greater than it should have been: but Newton was too cautious to neglect this error. He still believed his theory to be true, but he had no right to assume that it was, unless he could work it out correctly. So he put away his papers in a drawer and waited till he should find some way out of the difficulty. This is one of many examples of the patience men must have who wish to make really great discoveries. Newton waited sixteen years before he solved the problem, or spoke to anyone of the great thought in his mind. But more light came at last; it was in 1666, when he was only twentyfour, that he saw the apple fall; and it was in 1682 that he heard one day at the Royal Society that a Frenchman named Picart had measured the size of the earth very accurately, and had found that it was larger than had been supposed. Newton saw at once that this would alter all his calculations. Directly he heard it he went home, took out his papers, and set to work again with the new figures. CH. XVIII. THE LAW OF GRAVITATION. 151 Imagine his satisfaction when it came out perfectly right! It is said that he was so agitated when he saw that it was going to succeed, that he was obliged to ask a friend to finish working out the calculation for him. His patience was rewarded; the attraction of the earth exactly agreed with the rate of movement of the moon, and he knew now that he had discovered the law which governed the motions of the heavenly bodies. This law of Newton's is called the 'Law of Gravitation,' and we must now try to understand what it is. Gravitation means the drawing of one thing towards another, or towards a centre. All the objects upon our earth are held there by gravity, which pulls or attracts them towards the centre of the earth. If there were no such thing as gravity there would be nothing to prevent our chairs and tables, and even ourselves, from flying into space; but they are all held to the earth by gravity, and if you dig a hole under them they fall directly nearer to the centre. if they were Now let us see how this attraction of gravitation affects the planets. Every one of the bodies in the heavens pulls or attracts all the other bodies, just in the same way as the earth attracts the apple on the tree. But as they are all moving rapidly along (like the ball swung round your head) they do not fall into each other, but the smaller bodies move round the larger ones which are near them, just as fastened to them by invisible elastic threads. ones move round the larger one, because it is not only each body as a whole which pulls the other bodies, but every tiny atom of matter in each planet is pulling at all the atoms in all the other planets; so that the bigger a body is, and the more atoms it has in it, the more it will draw other bodies towards it. Our sun pulls the planets, The smaller and the planets pull the sun; but our sun has 700 times more atoms in it than all the planets put together, and so it keeps them moving round it. In the same way our earth has eighty times more atoms in it than our moon, and so it keeps the moon moving round it. In this way the force of gravity keeps all the different planets in their paths or orbits. It does not set them moving; some other force unknown to us first started them across the sky-gravitation is only the force which determines the direc tion in which they move. It was a grand thing to have discovered this force, but it would have been of little value to Astronomy to know that the heavenly bodies attracted each other unless it could also be known how much influence they have upon each other. This also Newton worked out accurately. You will remember that Kepler had shown that planets move in ellipses, having the sun in one of the two foci (see fig. 10, p. 99). Knowing this, Newton was able to calculate how much the sun attracts a planet when it is near, and how much when it is far off, so as to make it move in an ellipse; and he found a FIG. 24. 10 11 that exactly as much as the square of the distance increases, so much the attraction decreases; that is, the attraction grows less and less at a regular rate as you go farther away from the body that is pulling. For instance, suppose that at the point 1, fig. 24, a planet was one million of miles away from the sun, and was being attracted with immense force. When it arrived at the point CH. XVIII. THE PRINCIPIA. = 153 3 it would be about twice as far, or two millions of miles distant; and the square of 2 being 4 (2 × 2 = 4), the attraction of the sun at this point will be only one-fourth as much as it was at the point 1. At the point 7 the planet would be about three times as far, or three millions of miles from the sun, and as the square of 3 is 9 (3 × 3 9), the attraction here will be only 4th of the attraction at the point I. And so the calculation goes on; if the planet went 12 millions of miles off, the attraction would be what it was at first, and at 92 millions of miles the attraction would be 8464, so that when the planet is very far away the attraction becomes very slight indeed, but it will never entirely cease. In scientific language this law is expressed by the words, The attraction varies inversely as the square of the distance. When once this law was known, it explained in a most beautiful and complete way not only the three laws of Kepler, but all the complex movements of the heavenly bodies. These Newton worked out with the greatest accuracy by the help of his Method of Fluxions,' which enabled him to calculate all the varying rates at which the planets move in consequence of their mutual attraction; and he showed that whenever we know clearly the position and mass of all the bodies attracting a planet, the law of gravitation exactly accounts for the direction in which it moves. If you will consider for a moment what a labour it must be to calculate how much all the different planets pull each other at different times-when they are near together and when they are far off, when they are near each other and near th sun, or near each other and far from the sun, in fact in all the different positions you can imagine-you may form some idea of the tremendous work he did. When he published his great book, the 'Principia,' in 1687, there were |