velocity to be reduced, and consequently we believe that the body could journey on for ever with unabated speed. No doubt such a statement seems at variance with our ordinary experience. A sailing ship comes to rest on the sea when the wind dies away. A train will gradually lose its velocity when the steam has been turned off. A humming-top will slowly expend its rotation and come to rest. In these instances we seem to have proof that when the force which has imparted motion has ceased, the motion itself will gradually wane and ultimately cease entirely. But in all these cases it will be found, on reflection, that the decline of the motion is to be attributed to the action of resisting forces. The sailing ship is retarded by the rubbing of the water on its sides; the train is retarded by the friction of the wheels, and by the fact that it has to force its way through the air; and the resistance of the air is mainly the cause of the stopping of the humming-top, for if the air be withdrawn, by making the experiment in a vacuum, the top will continue to spin for a greatly lengthened period. When we duly weigh these considerations we shall find it possible to admit that a body, once projected freely in space and acted upon by no external resistance, will continue to move on for ever in a straight line, and will preserve unabated to the end of time the velocity with which it originally started. This principle is known as the first law of motion.

Let us apply this great principle to the important question of the movement of the planets. Take, for instance, the case of our earth, and discuss the consequences of the first law of motion. Our earth is every moment moving with a velocity of about eighteen miles a second, and the first law of motion assures us that if the earth were submitted to no external force, it would for ever pursue a straight track through the universe, and never depart from the precise velocity which it has at the present moment. But is the earth moving in this manner? Obviously not. We have already found that the earth is moving round the sun, and the beautiful laws of Kepler have given to that motion the most perfect distinctness and precision. The consequence is irresistible. The earth cannot be free from external force. Some potent

influence on the earth must be in ceaseless action. That influence, whatever it may be, constantly deflects the earth from the rectilinear path which it tends to pursue, and constrains the earth to trace out an ellipse instead of a straight line.

The great problem to be solved is now easily stated. There must be some constant influence on the earth. What is that influence, from whence does it proceed, and to what law is it submitted? Nor is the question confined to the earth alone. Mercury and Venus, Mars, Jupiter, and Saturn proclaim aloud that, as they are not moving in rectilinear paths, they must be exposed to some force. What is this force which guides the planets in their paths? Before the time of Newton this question might have been asked in vain. It was the mighty genius of Newton which supplied the answer, and thus revolutionised the whole of modern science.

Where lie the data from which the answer to the question is to be elicited? We have here no problem which can be solved by mere mathematical meditation. Mathematics is no doubt a useful, indeed an indispensable instrument in the inquiry; but we must not attribute to mathematics a potency which it does not possess. In a case of this kind, all that mathematics can do is to interpret the results obtained by observation. The data, then, from which Newton proceeded, were the observed facts in the movement of the earth and the other planets. Those facts had found a most beautiful expression by the aid of Kepler's laws. It was, accordingly, the laws of Kepler which Newton took as the basis of his labours, and it was for the interpretation of Kepler's laws that Newton invoked the aid of that celebrated mathematical reasoning which he created.

The question is then to be approached in this way: A planet. being subject to some external influence, we have to determine what that influence is, from our knowledge that the path of each planet is an ellipse, and that each planet sweeps round the sun over equal areas in equal times. The influence on each planet is what a mathematician would call a force, and a force must have a line of direction. The most simple conception of a force is that of a pull

communicated along a rope, and the direction of the rope is in this case the direction of the force. Let us imagine that the force exerted on each planet is imparted by an invisible rope. What do Kepler's laws tell us with regard to the direction of this rope and to the intensity of the strain which is transmitted along it?

The mathematical analysis of Kepler's laws would be beyond the scope of this volume. We must, therefore, confine ourselves to the results obtained by them, passing by the details of the reasoning. Newton first took the law which asserted that the planet moved over equal areas in equal times, and he showed by unimpeachable logic that this at once gave the direction in which the force acted on the planet. If for the sake of illustration we regard as before the force to be exerted by the medium of a rope, Newton showed that that rope must be invariably directed towards the sun. In other words, that the force exerted on each planet was at all times directed exactly from the planet towards the sun. It still remained to explain the intensity of the force, and to show how the intensity of that force varied when the planet was at different points of its path. Kepler's first law enables this question to be answered. If the planet's path be elliptic, and if the force be always directed towards the sun at one focus of that ellipse, then mathematical analysis obliges us to say, that the intensity of the force must vary inversely as the square of the distance from the planet to the sun.

The movements of the planets in conformity with Kepler's laws would thus be accounted for even in their minutest details, if we admit that an attractive power draws the planet towards the sun, and that the intensity of this attraction varies inversely as the square of the distance. Can we hesitate to say that such an attraction does exist? We have seen how the earth attracts a falling body; we have seen how the earth's attraction extends to the moon, and explains the revolution of the moon around the earth. We have now learned that the movement of the planets round the sun can be also explained to be the consequence of this law of attraction. But the evidence in support of the law of universal gravitation is, in truth, much stronger than any we have yet presented. We

shall have occasion to dwell on this matter further on. We shall show not only how the sun attracts the planets, but how the planets attract each other; and we shall find how this mutual attraction of the planets has led to remarkable discoveries which have raised the truth of the law of gravitation beyond the possibility of doubt.

Admitting the law of gravitation, we can then show that the planets must revolve around the sun in elliptic paths with the sun in the focus. We can show that they must sweep over equal areas in equal times. We can prove that the squares of the periodic times must be proportional to the cubes of their mean distances. Still further we can show how the mysterious movements of comets can be accounted for. By the same great law we can explain the revolutions of the satellites. We can account for the tides, and for numerous other details throughout the Solar System. Finally, we shall show that when we extend our view beyond the limits of our Solar System to the beautiful starry systems scattered through space we find even there evidence of the great law of universal gravitation.

CHAPTER VI.

THE PLANET OF ROMANCE.

Outline of the Subject-Is Mercury the Planet nearest the Sun?-Transit of an Interior Planet across the Sun-Has a Transit of Vulcan ever been seen ?Visibility of Planets during a Total Eclipse of the Sun--Professor Watson's Researches in 1878.

PROVIDED with a general survey of the Solar System, and with such an outline of the law of universal gravitation as the last chapter has afforded us, we commence the more detailed examination of the planets and their satellites. We shall begin with the planets nearest to the sun, and then we shall gradually proceed outwards to one planet after another, until we reach the confines of the system. We shall find much to occupy our attention. Each planet is itself a globe, and it will be our duty to describe what is known of that globe. The satellites by which so many of the planets are accompanied possess many points of interest. The circumstances of their discovery, their sizes, their movements, and their distances, must all be duly considered. Then, too, it will be found that the movements of the planets present much matter for reflection and examination. We shall have occasion to show how the planets mutually disturb each other, and what remarkable consequences have arisen from these disturbances. We must also occasionally refer to the important problems of celestial measuring and celestial weighing. We must show how the sizes, the weights, and the distances of the various members of our system are to be discovered. A great part of our task will lead us over ground which is thoroughly certain, and where the results have been confirmed by frequent observation. It happens, however, that at the very outset of our course we are obliged to deal with observations which are far