Chapter V: Preface: To First Edition (5)

When the comet at last returned to the earth after a cruise of three years through space, the number of hours by which it was late expressed the vehemence of the storm it experienced. The only storm that the comet would have met with, at least in so far as our present object is concerned, was the trouble that it had with Mercury. The mass of Mercury was, therefore, involved in the delay of the comet. In fact, the delay was a measure of the mass of the planet. I do not attempt to describe to you all the long work through which the mathematician had to plod before he could ascertain the mass of Mercury. It was a very tedious and a very hard sum, but at last his calculations arrived at the answer, and showed that Mercury must be a light globe compared to the earth. In fact, it would take twenty-five globes, each equal to Mercury, to weigh as much as the earth.

I dare say you will think that this was a very long and roundabout way of weighing. Supposing, however, we had to weigh a mountain, or rather a body which was bigger than fifty thousand mountains, and which was also many millions of miles away, all sorts of expedients would have to be resorted to. I have told you one of them. If you feel any doubts as to the accuracy with which such weighings can be made, then I must tell you that there are many other methods, and that these all agree in giving concordant results.

We hardly know anything as to what the globe of Mercury may be like. We can see little or nothing of the nature of its surface. We only perceive the planet to be a ball, brightly lighted by the sun, and we cannot satisfactorily discern permanent features thereon, as we are able to do on some of the other planets.

THE PLANET VENUS.

You will have no difficulty in recognizing Venus, but you must choose the right time to look out for her. In the first place, you need never expect to see Venus very late at night. You should look for the planet in the evening, as soon as it is dark, towards the west, or in the morning, a little before sunrise, towards the east. I do not, however, say that you can always see Venus, either before sunrise or after sunset. In fact, for a large part of the year, this planet is not to be seen at all. You should therefore consult the almanac, and unless you find that Venus is stated to be an evening star or a morning star, you need not trouble to search for it. I may, however, tell you that Venus can never be an evening star and a morning star at the same time. If you can see it this evening after sundown, there is no use in getting up early in the morning to look out for it again. The planet will remain for several weeks a splendid object after sunset, and then will gradually disappear from the west, and in a couple of months later will be the morning star in the east. Venus requires a year and seven months to run through her changes, so that if you find her a bright evening star to-night, you may feel sure that she was a bright evening star a year and seven months ago, and that she will be a bright evening star in a year and seven months to come. Nor must you ever expect to see her right overhead; she is always to the west or to the east.

The splendor of Venus, when at her best, will prevent you at such times from mistaking this planet for an ordinary star. She is then more than twenty times as bright as any star in the heavens. The most conclusive proof of the unrivalled brightness of Venus is found in the fact that she can be recognized in broad daylight without a telescope. Even on the brightest June afternoons the lovely planet is sometimes to be discerned like a morsel of white cloud on the perfect azure of the sky.

Venus is so brilliant that perhaps you will hardly credit me when I tell you that she has no more light of her own than has a stone or a handful of earth, or a button. Is it possible that this is the case, you will say, for as we see the planet so exquisitely beautiful, how can she be merely a huge stone high up in the heavens? The fact is that Venus shines by light not her own, but by light which falls upon her from the sun. She is lighted up just as the moon, or just as our own earth is lighted. Her radiance merely arises from the sunbeams which fall upon her. It seems at first surprising that mere sunbeams on the planet can give her the brilliancy that is sometimes so attractive. Let me show you an illustration which will, I trust, convince you that sunbeams will be adequate even for the glory of Venus.

Here is a button. I hang it by a piece of fine thread, and when I dip it into the beam from the electric lamp, look at the brilliancy with which the mimic planet glitters. You cannot see the shape of the button; it is too small for that; you merely see it as a brilliant gem, radiating light all around. Therefore, we need not be surprised to learn that the brilliancy of the evening star is borrowed from the sun, and that if, while we are looking at the planet in the evening, the sun were to be suddenly extinguished, the planet would also vanish from view, though the stars would shine as before.

Thus we explain the appearance of Venus. The evening star is a beautiful, luminous point, but it has no shape which can be discerned with the unaided eye. When, however, the telescope is turned towards Venus we have the delightful spectacle of a tiny moon, which goes through its phases just as does our own satellite. When first seen as an evening star Venus will often be like the moon at the quarter, and then it will pass to the crescent shape. Then the crescent becomes gradually thinner, and next will follow a brief period of invisibility before the appearance of Venus as the morning star. It seems at first a little strange that Venus when brightest should not be full like the moon, which in similar circumstances is, of course, a complete circle of light. The planet, however, has a very marked crescent-shaped form in these circumstances. But at this time the planet is so near us that the gain of brilliancy from the diminution of distance more than compensates for the small part of the illuminated side which is turned towards us.

You ought all to try to get some one to show you Venus through a telescope. A very large instrument is not necessary, and I feel sure you will be delighted to see the beautiful moon-shaped planet. You will then have no difficulty in understanding how the brightness of the planet has come from the sun. The changes in the crescent merely depend upon the proportion of the illuminated side which is turned towards us. Were Venus itself a sunlike body we should, of course, see no crescent, but only a bright circle of light.

In Fig. 50 you will notice an imaginary picture of a young astronomer surveying Venus with a telescope. I have not, as is obvious, attempted to show the different objects in their proper proportions. The sun is supposed to have set, so that his beams do not reach the astronomer. Night has begun at his observatory; but the sunbeams fall on Venus, and light her up on that side turned towards the sun. A part of this lighted side is, of course, seen by the telescope which the astronomer is using, and thus the planet seems to him like a crescent of light.

THE TRANSIT OF VENUS.

We might naturally think from Fig. 46 that Venus must pass at every revolution directly between the earth and the sun; and therefore it might appear that what is called the transit of Venus across the sun ought to occur every time between the appearance of the planet as the evening star and the next following appearance as the morning star. No doubt on each of these occasions Venus seems to approach the sun closely; but the orbits of Venus and the Earth do not lie quite in the same plane, and hence the planet usually passes just over or just under the sun, so that it is a very rare event indeed for her to come right in front of the sun. But this does sometimes happen. It happened, for instance, in the year 1874, and again in the year 1882; but, alas! I cannot hold out to you the prospect of ever seeing another such spectacle. There will be no further occurrence of the transit of Venus until the year 2004, though there will be another eight years later, in 2012.

It seems rather odd that one transit of Venus should be followed by another after an interval of eight years, and that then a period of much more than a century should have to elapse before there will be a repetition of a similar pair. This is in consequence of a curious relation between the motion of Venus and the motion of the Earth, which I must endeavor to explain with the help of a little illustration.

Let us suppose a clock with ordinary numbers round the dial, but so arranged that the slowly moving short hand requires 365.26 days to complete one revolution round the dial, while the more rapidly moving long hand revolves in 224.70 days. The short hand will then go round once in a year, and the long hand once during the revolution of Venus. Let us suppose that both hands start together from XII, then in 224.70 days the long hand is round to XII again, but the short hand will have only advanced to about VII, and by the time it reaches XII the long hand will have completed a large part of a second circuit. It happens that the two numbers 224.70 and 365.26 are very nearly in the ratio of 8 to 13. In fact, if the numbers had only been 224.8 and 365.3 respectively, they would be exactly in the proportion of 8 to 13. It, therefore, follows that eight revolutions of the short hand must occupy very nearly the same time as thirteen revolutions of the long hand. After eight years the short hand will of course be found again at XII; and at the same moment the long hand will also be back at XII, after completing thirteen revolutions.

We can now understand why the transits, when they do occur, generally arrive in pairs at an interval of eight years. Suppose that at a certain time Venus happens to interpose itself directly between the earth and the sun, then, when eight years have elapsed, the earth is, of course, restored for the eighth time since the first transit to the same place, and Venus has returned to almost the same spot for the thirteenth time. The two bodies are practically in the same condition as they were at first, and, therefore, Venus again intervenes, and the planet is beheld as a black spot on the sun’s surface. We must not push this argument too far; the relation between the two periods of revolution, though nearly, is not exactly 8 to 13. The consequence is that when another eight years have elapsed, the planet passes a little above the sun or a little below the sun, and thus a third occurrence of the transit is avoided for more than a century. The next transit will take place at the opposite side of the path.

We were fortunate enough to be able to see the transit of Venus in 1882 from Great Britain. Perhaps I should say a part of the transit, for the sun had set long before the planet had finished its journey across the disk. Venus looked like a small round black spot, stealing in on the bright surface of the sun and gradually advancing along the short chord that formed its track.

An immense deal of trouble was taken in 1882, as well as in 1874, to observe this rare occurrence. Expeditions were sent to various places over the earth where the circumstances were favorable. Indeed, I do not suppose that there was ever any other celestial event about which so much interest was created. The reason why the event attracted so much attention was not solely on account of its beauty or its singularity; it was because the transit of Venus affords us a valuable means of learning the distance of the sun. When observations of the transit of Venus made at opposite sides of the earth are brought together, we are enabled to calculate from them the distance of Venus, and knowing that, we can find the distance of the sun and the distances and the sizes of the planets. This is very valuable information; but you would have to read some rather hard books on astronomy if you wanted to understand clearly how it is that the transit of Venus tells us all these wonderful things. I may, however, say that the principle of the method is really the same as that mentioned on pp. 19–25. When you remember that not we ourselves, nor our children, and hardly our grandchildren, will ever be able to see another transit of Venus, you will, perhaps, not be surprised that we tried to make the most of such transits as have occurred in our time.

VENUS AS A WORLD.

Though Venus exhibits such pretty crescents in the telescope, yet I must say that in other respects a view of the planet is rather disappointing. Venus is adorned by such a very bright dress of sunbeams that we can see but little more than those sunbeams, and we can hardly make out anything of the actual nature of the planet itself. We can sometimes discern faint marks upon the globe, but it is impossible even to make a conjecture of what the Venus country is like. This is greatly to be regretted, for Venus approaches comparatively close to the earth, and is a world so like our own in size and other circumstances that we feel a legitimate curiosity to learn something more about her.

But the marks on the planet, though very faint, are still sufficiently definite to have enabled some sharp-sighted astronomers to answer a question of much interest. They have made it plain that in one most important respect Venus is very unlike our Earth. Our globe, of course, rotates on its axis once each day, but Venus requires no less than 225 days to complete each rotation. In fact, this planet rotates in such a fashion that she always keeps the same face to the sun. The inhabitants of Venus will therefore find that it is perennial day on one side of this globe and everlasting night on the other.

Venus is one of the few globes which might conceivably be the abode of beings not very widely different from ourselves. In one condition especially--namely, that of weight--she resembles the earth so closely that those bodies which we actually possess would probably be adapted, so far as strength is concerned, for a residence on the sister planet. Our present muscles would not be unnecessarily strong, as they would be on the moon, nor should we find them too weak, as they would certainly prove to be were we placed on one of the very heavy bodies of our system. Nor need the temperature of Venus be regarded as presenting any insuperable difficulties. She is, of course, nearer to the sun than we are, but then climate depends on other conditions besides nearness to the sun, so that the question as to whether Venus would be too hot for our abode could not be readily decided. The composition of the atmosphere surrounding the planet would be the most material point in deciding whether terrestrial beings could live there. I think it to be in the highest degree unlikely that the atmosphere of Venus should chance to suit us in the requisite particulars, and therefore I think there is not much likelihood that Venus is inhabited by any men, women, or children resembling those on this earth.

THE PLANET MARS AND HIS MOVEMENTS.

The path of the earth lies between the orbits of the planets Venus and Mars. It is natural for us to endeavor to learn what we can about our neighbors. We ought to know something, at all events, as to the people who live next door to us on each side. I have, however, already said that we cannot observe very much upon Venus. The case is very different with respect to Mars. He is a planet which we are fortunately enabled to study minutely, and he is full of interest when we examine him through a good telescope.

The right season for observing Mars must, of course, be awaited, as he is not always visible. Such seasons recur about every two years, and then for months together Mars will be a brilliant object in the skies every night. Nor has Mars necessarily to be sought in the early morn or immediately after sunset, in the manner we have already described for Venus and Mercury. At the time Mars is at his best he comes into the highest position at midnight, and he can generally be seen for hours before, and be followed for hours subsequently. You may, however, find some difficulty in recognizing him. You probably would not at first be able to distinguish Mars from a fixed star. No doubt this planet is a ruddy object, but some stars are also ruddy, and this is at the best a very insecure characteristic for identification. I cannot give you any more general directions, except that you should get your papa to point out Mars to you the next time it is visible. It is just conceivable that papa himself might not know how to find Mars. If so, the sooner he gets a set of star maps and begins to teach himself and to teach you, the better it will be for you both.

Mars, though apparently so like a star, differs in some essential points from any star in the sky. The stars proper are all fixed in the constellations, and they never change their relative positions. The groups which form the Great Bear or the Belt of Orion do not alter, they are just the same now as they were centuries ago. But the case is very different with a planet such as Mars. The very word planet means a _wanderer_, and it is justly applied, because Mars, instead of staying permanently in any one constellation, goes constantly roaming from one group to the other. He is a very restless body; sometimes he pays his respects to the heavenly Twins, and is found near Castor and Pollux in Gemini, then he goes off and has a brief sojourn with the Bull, but it looks as if that fierce animal got tired of his company and hunted him off to the Lion. His quarters then become still more critical. Sometimes it looks as if he desired to seek for peace beneath the waters, and so he visits Aquarius, while at other times he is found in dangerous proximity to the claws of the Crab.

Mars cannot even make up his mind to run steadily round the heavens in one direction; sometimes he will bolt off rapidly, then pause for a while, and turn back again; then the original impulse will return, and he will resume his journey in the direction he at first intended. It is no wonder that I am not able to give you very explicit directions as to how you may secure a sight of a truant whose wanderings are apparently so uncertain. Yet there is a definite order underlying all his movements. Astronomers, who make it their business to study the movements of Mars, can follow him on his way; they know exactly where he is now, and where he will be every night for years and years to come. The people who make the almanacs come to the astronomers and get hints from them as to what Mars intends to do, so that the almanacs announce the positions in which the planet will be found with as much regularity as if he was in the habit of behaving with the orderly propriety of the sun or the moon.

We must not lay all the blame on Mars for the eccentricities of his movements. Our earth is to a very large extent responsible. What we think to be Mars’ vagaries are often to be explained by the fact that we ourselves on the earth are rapidly shifting about and altering our point of view.

I was driving down a pretty country road with a little girl three years old beside me, when I was addressed with the little remark, “Look at the tree going about in the field.” Now, you or I, with our longer experience of the world around us, know that it is not the custom of trees to take themselves up and walk about the fields. But this was what this little girl saw, or rather what she thought she saw; and very often what we do see is something very different from what we think we see. We think we see Mars performing all these extraordinary movements, as the little girl thought she saw the tree moving about. But just as that little girl, when she grew to be a big girl, found that what she thought was a tree walking across the field must really have some quite different explanation, so we, too, find that what Mars seems to do is one thing, and what Mars actually does is quite another thing.

Let us see what the little girl noticed. She was looking at the tree, and first she saw it on one side of the house, and then she saw it on the opposite side (Fig. 52). If it had been a cow instead of a tree, of course the natural supposition would have been that the cow had walked. Our little friend may, perhaps, have thought it unusual for a tree to walk, but still she saw the undoubted fact that the tree had shifted to the other side of the house, and therefore, perhaps, remembering what the cow could do, she said the tree had moved.

The little girl did not stop to reflect that she herself had entirely changed her position, and hence arose the surprising phenomenon of a tree that could move about. You will understand this, at once, from the two positions of the car here shown. In the first position, as the girl looks at the tree, the dotted line shows the direction of her glance, and the other dotted line shows how the apparent places of the tree and the house have altered. It is her change of place that has accomplished the transformation. Observe also that the tree appeared to her to move in the direction opposite to that in which she is going.

Mars generally appears to move round among the stars from west to east. In fact, if we were viewing him from the sun he would always seem to move in this manner. But at certain seasons our earth is moving very fast past Mars, and this will make him appear to move in the opposite direction. This apparent motion is sometimes so much in excess of his real motion, that it may give us an entirely incorrect idea of what the planet is actually doing.

Thus, notwithstanding that Mars is moving one way, he may appear to us who dwell on the earth to be going in the opposite way. This illusion only happens for a short time, just when we are passing Mars, as we do every two years. The effect on the planet is to make the path he pursues at this time something like that shown in Fig. 53. The planet is nearest to us at the time he is moving in this loop. He is then to be seen at his best in the telescope, so that it is especially interesting to watch Mars through this critical part of his career.

I want to show you how to make a little calculation which will explain the law by which the seasons when we can see Mars best will follow each other. The period he requires for a voyage round the sun is not quite two years, for that would be 730 days, and Mars only takes 687 days for his journey. It is, however, true that 1-15/17 years is very nearly the period of Mars. Hence, every 32 years Mars will complete 17 rounds. From this we shall be able to see how long it will take after the earth once passes Mars before they pass again. I shall suppose there is a circular course, around which two boys start together to run a race. One of these boys is such a good runner that he will get quite round in 17 minutes; but the other boy can hardly run more than half as quickly, for he will require 32 minutes to complete one circle. Here then is the question. Suppose the two boys to start together: how long will it be before the faster runner gains one complete circuit on the other? By the time the good runner (A) has completed one circuit, the bad runner (B) has only got a little more than halfway. When A has completed his second circuit, he has, of course, run for twice 17 minutes--that is, for 34 minutes. This is two minutes longer than the time B requires to get round once; therefore B is only ahead by a distance which A could cover in about one minute; but B will have advanced during this minute a distance for which A will require another half-minute, during which B covers a distance for which A will need a further quarter, and so on. But all these intervals--one minute, half a minute, a quarter of a minute, one-eighth, one-sixteenth, and so on--added together amount to two minutes, and hence it follows that B will not be overtaken until about two minutes after A has completed his second round--that is, in 36 minutes altogether.

We can pass from this illustration to the case of the planet Mars and the earth. The orbit of the earth is traversed in a year, and therefore, after the earth has once passed Mars, which is then, as astronomers would say, in _opposition_, about two years and the eighth of a year--that is, two years and six or seven weeks--will elapse before Mars is again favorably placed. You will thus see that we need not expect to observe Mars under the best conditions every year. Besides, the distance of the planet from the earth at opposition varies so greatly that some oppositions are more favorable than others.

The time has come when I must tell you something about the shapes of the paths in which the earth and the other planets perform their great journeys round the sun. Perhaps you will think that I am going to contradict some of the things that I have told you before. I have often represented the orbits of the planets as circles, and now I am going to tell you that this is not correct. The fact is that the paths are nearly circles; but, still, there is some departure from the exact circular shape. Mars, in particular, moves in a path which is more different from a circle than the path of the earth, and consequently it is appropriate to introduce this subject when we are engaged about Mars.

We must first take another lesson in drawing, and the appliances I want you to use for the purpose are very simple. You must have a smooth board and some tacks or drawing-pins, besides paper, pencil, and twine.

We first lay a sheet of paper on the board, and then put in two tacks through the paper and into the board. It does not much matter where we put them in. Next we take a piece of twine and tie the two ends together so as to form a loop, which we pass round the two tacks (Fig. 54). In the loop I place the pencil, and then you see I move it round, taking care to keep the twine stretched. Thus I produce a pretty curve, which we call the ellipse. I must ask all of you to practise this experiment. Try with different lengths of string, and try using different distances between the tacks. Here are some sketches of two shapes of ellipse and a parabola (Fig. 55). Elliptic curves can be made almost circles by putting the two tacks close together, or they can be made very long in comparison with their width. They are all pretty and graceful figures, and are often useful for ornamental work. The ellipse is a pretty shape for beds of flowers in a grass-plot.

The importance of the ellipse to astronomers is greater than that of any other geometrical figure. In fact, all the planets, as they perform their long and unceasing journeys round the sun, move in ellipses; and though it is true that these ellipses are very nearly circles, yet the difference is quite appreciable.

It is also important to observe that the sun is not in the centre of the ellipse which the planet describes. The sun is nearer to one end than to the other. And the actual position of the sun must be particularly noted. Suppose that some mighty giant were preparing to draw an exact path for the earth, or for Mars, of course he would want to have millions of miles of string for producing a big enough curve, and one of the nails that he used would have to be driven right into the sun. The following is the astronomer’s more accurate method of stating the facts. He calls each of the points represented by the tacks around which the string is looped a _focus_ of the ellipse; the two points together are said to be the _foci_; and as the planet is describing its orbit, the position of the sun will lie exactly at one of the foci.

The ellipse is a curve that nature is very fond of reproducing. From an electric light, a brilliant beam will diverge. If you hold a globe in the beam, and let the shadow fall on a sheet of paper, it forms an ellipse. If you hold the sheet squarely, the shadow is a circle; but as you incline it, you obtain a beautiful oval, and by gradually altering the position, you can get a greatly elongated curve. Indeed, you can thus produce an ellipse of almost any form. The electric light is not indispensable for this purpose; any ordinary bright lamp with a small flame will answer, and by taking different sized balls and putting them in various positions, you can make many ellipses, great and small.

THE DISCOVERIES MADE BY TYCHO AND KEPLER.

It was by the observations of a celebrated old astronomer, named Tycho Brahe, that the true shape of a planet’s path came to be afterwards determined. Tycho lived in days before telescopes were invented. He had few of the excellent contrivances for measuring which we have in our observatories. We shall take a look at this fine old astronomer, as he sits amid his curious astronomical machines.

He lived on an island near Copenhagen, and he has given us a picture of himself (Fig. 56), as he is seated with his quaint apparatus, and his assistants around him, busily engaged in observing the heavens. You see the walls of his observatory are decorated with pictures; and one of the great Danish hounds which the King of Denmark had presented to him lies asleep at his feet. I do not think we should now encourage big dogs in the observatory at night. Nor do modern astronomers put on their velvet robes of state, as Tycho was said to have done when he entered into the presence of the stars, as, by so doing, he showed his respect for the heavens. Astronomers, nowadays, rather prefer to wear some comfortable coat which shall keep out the cold, no matter what may be its appearance from the picturesque point of view. In this wonderful contrivance, you see Tycho Brahe did not use any actual telescope. He observed through a small opening in the wall, and lest there should be any mistake as to what is going on, you see he is pointing towards it, and giving his three assistants their instructions. The most important work is being done by the man on the right. He is engaged in making the actual observation. But he has no aid from magnifying lenses. All he can do is to slide a pointer up or down till it is just in line with the planet or star as he sees it through the hole opposite.

On the circle a number of marks have been engraved, and there are numbers placed opposite to the marks; it is by these that the position of the object is to be ascertained. If the object is high, then the pointer will be low; and if the object is low, then the pointer will be high. The observer calls out the position when he has found it, and there, you see, is a man ready with writing materials to take down the observation. Notice also the other astronomer who is looking at the clock. He gives the time, which must also be recorded accurately. In fact, the entire process of finding the place of a heavenly body consists in two observations--one from the circle and the other from the clock; so that though Tycho had no telescope to aid his vision, yet the principle on which his work was done was the same as that which we use in our observatories at this moment.

You may think that such a concern would hardly be capable of producing much reliable work. However, Tycho compensated in a great degree for the imperfection of his instrument by the skill with which he used it. He had a noble determination to do his very best. Perseverance will accomplish wonders even with very imperfect means. A great astronomer has said that a skilful observer ought to be able to make valuable measurements with a common cart-wheel!

It was with instruments on the principle of that which I have here shown that Tycho made his celebrated observations of Mars. Week after week, month after month, year after year, did the patient old astronomer track the planet through his capricious wanderings.

Before we try to explain anything, it is of course necessary to ascertain, with all available accuracy, what the thing actually is. Therefore, when we seek to explain the irregular movements of a planet, the first thing to be done is to make a careful examination of the nature of those irregularities. And this was what Tycho strove to do with the best means at his disposal.

The full benefit of Tycho’s work was realized by Kepler when he commenced to search out the kind of figure in which Mars was moving. First he tried various circles, and then he sought, by placing the centre in different positions, to see whether it would not be possible to account thus for the irregularities of the wayward planet. It would not do; the movement was not circular. This was thought very strange in those days, for the circle was regarded as the only perfect curve, and it was considered quite impossible for a planet to have any motion except it were the most perfect. There was, however, no help for it; so Kepler sagaciously tried the ellipse, which he considered to be the most perfect curve next to the circle. He continued his long calculations, until at last he succeeded in finding one particular ellipse, placed in one particular position, which would just explain the strange wanderings of our erratic neighbor. It was not alone that the motion of the planet traced out an ellipse; it was further discovered that the sun lies at one of the foci of the curve. If the sun were anywhere else, the motion of the planet would have been different from that which Tycho had found it to be.

You must know that this discovery is one of the very greatest that have ever been made in the whole extent of human knowledge. After it had been proved that the orbit of Mars was elliptic, it became plain that the same path must be traced by every planet. There are very big planets, and there are small ones; there are planets which move in very large orbits, and there are planets whose paths are comparatively small. In all cases the high road which the planet follows is invariably an ellipse, and the sun is invariably to be found situated at the focus. It is surely interesting to find that these beautiful ellipses which we can draw so simply with a piece of twine and a pencil should be also the very same figures which our great earth and all the other bodies which revolve around the sun are ever compelled to follow.

Kepler also made another great discovery in connection with the same subject. If the planet moved in a circle with the sun in the centre, then there would be very good reason to expect that it would always move at the same speed, for there would be no reason why it should go faster at one place than at another. In fact, the planet would then be revolving always at the same distance from the sun, and every part of its path would be exactly like every other part. But when we consider that the motion is performed in an ellipse, so that the planet is curving round more rapidly at the extremities of its path than in the other parts where the curvature is less perceptible, we have no reason to expect that the speed shall remain the same all round.

We know that the engine-driver of a railway train always has to slacken speed when he is going round a sharp curve. If he did not do so, his train would be very likely to run off the line, and a dreadful accident would follow. The engine-driver is well aware that the conditions of pace are dependent on the curvature of his line. The planet finds that it, too, must pay attention to the curves; but the extraordinary point is that the planet acts exactly in the opposite way to the engine-driver. The planet puts on its highest pace at one of the most critical curves in the whole journey. There are two specially sharp curves in the planet’s path. These are, of course, the two extremities of the ellipse which it follows. The cautious engine-driver would, of course, creep round these with equal care, and no doubt the planet goes slowly enough about that end of the ellipse which is farthest from the sun. There its pace is slower than anywhere else; but from that moment onwards the planet steadily applies itself to getting up more and more speed. As it traverses the comparatively straight portion of the celestial road, the pace is ever accelerating until the sharp curve near the sun is being approached; then the velocity gets more and more alarming, until at last, in utter defiance of all rules of engine-driving, the planet rushes round one of the worst parts of the orbit at the highest possible speed. And yet no accident happens, though the planet has no nicely laid lines to keep it on the track.

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.