Part 11

If lines are necessary to save a railway train from destruction, how can we possibly escape when we have no similar assistance to keep us from flying away from the sun and off into infinite space? Kepler has taught us to measure the changes in the speed of the body with precision. He has shown that the planet must, at every point of its long journey, possess exactly the right speed; otherwise everything would go wrong. I dare say you have seen, at different points along a line of railway, boards put up here and there, with notices like, “Ten miles an hour.” These words are, of course, an intimation to the engine-driver that he is not to vary from the speed thus stated. Kepler has given us a law which is equivalent to a large number of caution boards, fixed all round the planet’s path, indicating the safe speed for the journey at every stage. It is fortunate for us that the planet is careful to observe these regulations. If the earth were to leave her track, the consequences would be far worse than those of the most frightful railway accident that ever happened. Whichever side we took would be almost equally disastrous. If we went inwards we should plunge into the sun, and if we went outwards we should be frozen by cold.

We owe our safety to the care with which the speed of the earth is prescribed. When near the sun, the earth is pulled inwards with exceptionally strong attraction. We are often told that when a strong temptation seizes us, the wisest thing that we can do is to run away as hard as possible. This is just what the laws of dynamics cause the earth to do at this critical time. She puts on her very best pace, and only slackens when she has got well away from the danger.

The peril that we are exposed to when the earth is at the other end of the orbit is of an opposite character. We are then a long way from the sun, and the pull which it can exercise upon the earth is correspondingly lessened. Care is then required lest we should escape altogether from the sun’s warmth and his guidance. We must therefore give time to the sun to exercise his power, so as to enable the earth to be recalled; accordingly we move as slowly as possible until the sun conquers the earth’s disposition to fly off, and we begin to return.

You may remember that when we were speaking about the moon, I showed you how a body might revolve around the earth in a circle under the influence of an attraction towards the earth’s centre. So long as the path is really a circle, then the power with which the earth is drawing the body remains the same. In a precisely similar way, a body could revolve around the sun in a circle, in which case also the attraction of the sun will remain the same all round. But now we have a very much more difficult case to consider. If the body does not always remain at the same distance, the power of the sun will not be the same at the different places. Whenever the object is near the sun, the attraction will be greater than when it is farther off. For example, when the distance between the two bodies is doubled, then the pull is reduced to the fourth part of what it was before.

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.

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._”

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.

THE GEOGRAPHY OF MARS.

We will now say something with respect to the geography of our fellow-planet, a subject which seems all the more interesting because Mars is so like the earth in many respects. We require a fairly good telescope for the purpose of seeing him well, but when such an instrument is directed to the planet, a beautiful picture of another world is unfolded (Fig. 60). There are many things visible on his surface, but we must always remember that even with our most powerful telescopes the planet still appears a long way off.

In the most favorable circumstances, Mars is at least one hundred times as far from us as the moon. But we know that an object on the moon must be as large as St. Paul’s Cathedral if it is to be visible in our telescopes. An object on Mars must be, therefore, at least one hundred times as broad and one hundred times as long as St. Paul’s Cathedral if it is to be discernible by astronomers on our earth. We can, therefore, only expect to see the general features of our fellow-planet. Were we looking at our earth from a similar distance, and with equally good telescopes, the continents and oceans, and the larger seas and islands, would all be large enough to be conspicuous. It is, however, doubtful whether they could ever be properly revealed through the serious impediment to vision which our atmosphere would offer.

It fortunately happens that the surface of Mars is only obscured by clouds to a very trifling extent, and we are thus able to see a panorama of our neighboring globe laid before us. Mars is not nearly so large as our earth, the diameters of the two bodies being nearly as two to one. It follows that the number of acres on the planet is only a quarter of the number of acres on the earth. Careful telescopic scrutiny shows that the chief features which we see on Mars are of a permanent character. In this respect Mars is much more like the moon than the sun. The latter presents to us merely glowing vapors, with hardly more permanence than is possessed by the clouds in our own sky. On the other hand, the entire absence of clouds from the moon enables us to see the permanent features on its surface. Most of the visible features on Mars are also invariable; though occasionally it would seem that the climate produces some changes in its appearance.

We first notice that there are differently colored parts on Mars. The darkish or bluish regions are usually spoken of as seas or oceans; though we should be going beyond our strict knowledge were we to assert that water is actually found there. Look at the horn-shaped object in the centre of the lower picture in Fig. 60. We call it the Kaiser Sea, and it is so strongly marked that even in a small telescope it can be often seen. You must not, however, always expect to notice this feature when you look at the planet through a telescope, for it turns round and round. We can make a globe representing Mars. On this are to be depicted this great sea and the other characteristic objects. But as we turn the globe around, the opposite side of the planet is brought into view, and other features are revealed like those represented in the upper figure. Mars requires 24 hours 37 minutes 22.7 seconds to complete a single rotation. It is somewhat remarkable that this only differs from the earth’s period of rotation by a little more than half an hour.

Mars contains what we call continents as well as oceans, and we also find there lakes and seas and straits. These objects are indicated in the drawings that are here represented. But the most striking features which the planet displays are the marvellous white regions, which are seen both at its North Pole and at its South Pole (Fig. 62). If we were able to soar aloft above our earth and take a bird’s-eye view of our own polar regions, we should see a white cap at the middle of the arctic circle. This appearance would be produced by the eternal ice and snow. It would increase during the long, dark winter, and be somewhat reduced by melting during the continuously bright summer. Though we cannot thus see our earth, yet we can sometimes observe one Pole of Mars and sometimes the other, and we find each of these Poles crowned with a dense white cap, which increases during the severity of its winter, and which declines again with the warmth of the ensuing summer.

Sketches of Mars have been made by many astronomers; among them we may mention Mr. Green, who made a beautiful series of pictures at Madeira in 1877. These may be supplemented by the drawings of Mr. Knobel in 1884, when the opposite Pole of the planet was turned to view. The drawings show the polar snows, and there seem to be some elevated districts in his arctic regions which retain a little patch of snow after the main body of the ice cap has shrunk within its summer limits. An interesting case of this kind is shown in Fig. 62, which has been copied from one of Mr. Green’s drawings.

It has lately been surmised that the continents on Mars are occasionally inundated by floods of water. There are also indications of clouds hanging over the Martian lands, but the inhabitants of that planet, in this respect, escape much better than we do. A certain amount of atmosphere always surrounds Mars, though it is much less copious than that we have here. As to the composition of this atmosphere we know nothing. For anything we can tell, it might be a gas so poisonous that a single inspiration would be fatal to us; or if it contained oxygen in much larger proportion than our air does, it might be fatal from the mere excitement to our circulation which an over-supply of stimulant would produce. I do not think it the least likely that our existence could be supported on Mars, even if we could get there. We also require certain conditions of climate, which would probably be totally different from those we should find on Mars.