CHAPTER XVIII.

SCIENCE OF THE SEVENTEENTH CENTURY (CONTINUED).

Newton-Fluxions and differential Calculus-Theory of Gravitation— Attraction varies inversely as the Squares of the Distance-The 'Principia.'

Newton, 1642.-We must now leave the living creation and return to physical science, for, during all those years with which we have been occupied since the time of Galileo and Kepler, a boy had been growing up into manhood, who was to become one of the greatest men of science that England has ever known. In 1642, the same year in which Galileo died, a child was born at Woolsthorpe, near Grantham in Lincolnshire, who was so tiny that his mother said 'she could put him into a quart mug.' This tiny delicate baby was to become the great philosopher Newton.

We hear of him that he was at first very idle and inattentive at school, but, having been one day passed in the class by one of his schoolfellows, he determined to regain his place, and soon succeeded in rising to the head of them all. In his play hours, when the other boys were romping, he amused himself by making little mechanical toys, such as a water clock, a mill turned by a mouse, a carriage moved by the person who sat in it, and many other ingenious contrivances. When he was fifteen his mother sent for him home to manage the farm which belonged to their estate;

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but it was soon clear that he was of no use as a farmer, for though he tried hard to do his work, his mind was not in it, and he was only happy when he could settle down under a hedge with his book to study some difficult problem. At last one of his uncles, seeing how bent the boy was upon study, persuaded his mother to send him back to school and to college, where he soon passed all his companions in mathematics, and became a Fellow of Trinity College, Cambridge, in 1667. But even before this, in the year 1666, his busy mind had already begun to work out the three greatest discoveries of his life. In that year he discovered the remarkable mathematical process called the 'Method of Fluxions,' which is almost the same as that now called the 'Differential Calculus,' worked out about the same time by Leibnitz, a great German mathematician. In that year he also made the discoveries about Light and Colour, which we shall speak of by and by; and again in that year he first thought out the great Theory of Gravitation, which we must now consider.

Theory of Gravitation, 1666.-In the course of his astronomical studies, Newton had come across a problem which he could not solve. The problem was this. Why does the moon always move round the earth, and the planets round the sun? The natural thing is for a body to go straight on. If you roll a marble along the floor it moves on in a straight line, and if it were not stopped by the air and the floor, it would roll on for ever. Why, then, should the bodies in the sky go round and round, and not straight forward?

While Newton was still pondering over this question, the 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

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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 further. 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. Το

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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 if all the mass of the earth were collected at the centre, and then as decreasing gradually 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 one-sixth greater than it should have been: but Newton was too cautious to neglect this want of agreement. He still believed his theory to be true, but he had no right to assume that it was, unless he could make his calculation agree with observation. 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 any one 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. 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. 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 at the slightest impulse; 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.

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 if they were fastened to them by invisible elastic threads. The smaller 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 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, 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.