Chapter XII: Part II: A Couple of Centuries' Progress (4)

The news flashed over Europe at the maximum speed with which news could travel at that date (which was not very fast); and by the 1st of October Professor Challis and Mr. Adams heard it at Cambridge, and had the pleasure of knowing that they were forestalled, and that England was out of the race.

It was an unconscious race to all concerned, however. Those in France knew nothing of the search going on in England. Mr. Adams's papers had never been published; and very annoyed the French were when a claim was set up on his behalf to a share in this magnificent discovery. Controversies and recriminations, excuses and justifications, followed; but the discussion has now settled down. All the world honours the bright genius and mathematical skill of Mr. Adams, and recognizes that he first solved the problem by calculation. All the world, too, perceives clearly the no less eminent mathematical talents of M. Leverrier, but it recognizes in him something more than the mere mathematician--the man of energy, decision, and character.

LECTURE XVI

COMETS AND METEORS

We have now considered the solar system in several aspects, and we have passed in review something of what is known about the stars. We have seen how each star is itself, in all probability, the centre of another and distinct solar system, the constituents of which are too dark and far off to be visible to us; nothing visible here but the central sun alone, and that only as a twinkling speck.

But between our solar system and these other suns--between each of these suns and all the rest--there exist vast empty spaces, apparently devoid of matter.

We have now to ask, Are these spaces really empty? Is there really nothing in space but the nebulæ, the suns, their planets, and their satellites? Are all the bodies in space of this gigantic size? May there not be an infinitude of small bodies as well?

The answer to this question is in the affirmative. There appears to be no special size suited to the vastness of space; we find, as a matter of fact, bodies of all manner of sizes, ranging by gradations from the most tremendous suns, like Sirius, down through ordinary suns to smaller ones, then to planets of all sizes, satellites still smaller, then the asteroids, till we come to the smallest satellite of Mars, only about ten miles in diameter, and weighing only some billion tons--the smallest of the regular bodies belonging to the solar system known.

But, besides all these, there are found to occur other masses, not much bigger and some probably smaller, and these we call comets when we see them. Below these, again, we find masses varying from a few tons in weight down to only a few pounds or ounces, and these when we see them, which is not often, we call meteors or shooting-stars; and to the size of these meteorites there would appear to be no limit: some may be literal grains of dust. There seems to be a regular gradation of size, therefore, ranging from Sirius to dust; and apparently we must regard all space as full of these cosmic particles--stray fragments, as it were, perhaps of some older world, perhaps going to help to form a new one some day. As Kepler said, there are more "comets" in the sky than fish in the sea. Not that they are at all crowded together, else they would make a cosmic haze. The transparency of space shows that there must be an enormous proportion of clear space between each, and they are probably much more concentrated near one of the big bodies than they are in interstellar space.[30] Even during the furious hail of meteors in November 1866 it was estimated that their average distance apart in the thickest of the shower was 35 miles.

Consider the nature of a meteor or shooting-star. We ordinarily see them as a mere streak of light; sometimes they leave a luminous tail behind them; occasionally they appear as an actual fire-ball, accompanied by an explosion; sometimes, but very seldom, they are seen to drop, and may subsequently be dug up as a lump of iron or rock, showing signs of rough treatment by excoriation and heat. These last are the meteorites, or siderites, or aërolites, or bolides, of our museums. They are popularly spoken of as thunderbolts, though they have nothing whatever to do with atmospheric electricity.

They appear to be travelling rocky or metallic fragments which in their journey through space are caught in the earth's atmosphere and instantaneously ignited by the friction. Far away in the depths of space one of these bodies felt the attracting power of the sun, and began moving towards him. As it approached, its speed grew gradually quicker and quicker continually, until by the time it has approached to within the distance of the earth, it whizzes past with the velocity of twenty-six miles a second. The earth is moving on its own account nineteen miles every second. If the two bodies happened to be moving in opposite directions, the combined speed would be terrific; and the faintest trace of atmosphere, miles above the earth's surface, would exert a furious grinding action on the stone. A stream of particles would be torn off; if of iron, they would burn like a shower of filings from a firework, thus forming a trail; and the mass itself would be dissipated, shattered to fragments in an instant.

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Even if the earth were moving laterally, the same thing would occur. But if earth and stone happened to be moving in the same direction, there would be only the differential velocity of seven miles a second; and though this is in all conscience great enough, yet there might be a chance for a residue of the nucleus to escape entire destruction, though it would be scraped, heated, and superficially molten by the friction; but so much of its speed would be rubbed out of it, that on striking the earth it might bury itself only a few feet or yards in the soil, so that it could be dug out. The number of those which thus reach the earth is comparatively infinitesimal. Nearly all get ground up and dissipated by the atmosphere; and fortunate it is for us that they are so. This bombardment of the exposed face of the moon must be something terrible.[31]

Thus, then, every shooting-star we see, and all the myriads that we do not and cannot see because they occur in the day-time, all these bright flashes or streaks, represent the death and burial of one of these flying stones. It had been careering on its own account through space for untold ages, till it meets a planet. It cannot strike the actual body of the planet--the atmosphere is a sufficient screen; the tremendous friction reduces it to dust in an instant, and this dust then quietly and leisurely settles down on to the surface.

Evidence of the settlement of meteoric dust is not easy to obtain in such a place as England, where the dust which accumulates is seldom of a celestial character; but on the snow-fields of Greenland or the Himalayas dust can be found; and by a Committee of the British Association distinct evidence of molten globules of iron and other materials appropriate to aërolites has been obtained, by the simple process of collecting, melting, and filtering long exposed snow. Volcanic ash may be mingled with it, but under the microscope the volcanic and the meteoric constituents have each a distinctive character.

The quantity of meteoric material which reaches the earth as dust must be immensely in excess of the minute quantity which arrives in the form of lumps. Hundreds or thousands of tons per annum must be received; and the accretion must, one would think, in the course of ages be able to exert some influence on the period of the earth's rotation--the length of the day. It is too small, however, to have been yet certainly detected. Possibly, it is altogether negligible.

It has been suggested that those stones which actually fall are not the true cosmic wanderers, but are merely fragments of our own earth, cast up by powerful volcanoes long ago when the igneous power of the earth was more vigorous than now--cast up with a speed of close upon seven miles a second; and now in these quiet times gradually being swept up by the earth, and so returning whence they came.

I confess I am unable to draw a clear distinction between one set and the other. Some falling stars may have had an origin of this sort, but certainly others have not; and it would seem very unlikely that one set only should fall bodily upon the earth, while the others should always be rubbed to powder. Still, it is a possibility to be borne in mind.

We have spoken of these cosmic visitors as wandering masses of stone or iron; but we should be wrong if we associated with the term "wandering" any ideas of lawlessness and irregularity of path. These small lumps of matter are as obedient to the law of gravity as any large ones can be. They must all, therefore, have definite orbits, and these orbits will have reference to the main attracting power of our system--they will, in fact, be nearly all careering round the sun.

Each planet may, in truth, have a certain following of its own. Within the limited sphere of the earth's predominant attraction, for instance, extending some way beyond the moon, we may have a number of satellites that we never see, all revolving regularly in elliptic orbits round the earth. But, comparatively speaking, these satellite meteorites are few. The great bulk of them will be of a planetary character--they will be attendant upon the sun.

It may seem strange that such minute bodies should have regular orbits and obey Kepler's laws, but they must. All three laws must be as rigorously obeyed by them as by the planets themselves. There is nothing in the smallness of a particle to excuse it from implicit obedience to law. The only consequence of their smallness is their inability to perturb others. They cannot appreciably perturb either the planets they approach or each other. The attracting power of a lump one million tons in weight is very minute. A pound, on the surface of such a body of the same density as the earth, would be only pulled to it with a force equal to that with which the earth pulls a grain. So the perturbing power of such a mass on distant bodies is imperceptible. It is a good thing it is so: accurate astronomy would be impossible if we had to take into account the perturbations caused by a crowd of invisible bodies. Astronomy would then approach in complexity some of the problems of physics.

But though we may be convinced from the facts of gravitation that these meteoric stones, and all other bodies flying through space near our solar system, must be constrained by the sun to obey Kepler's laws, and fly round it in some regular elliptic or hyperbolic orbit, what chance have we of determining that orbit? At first sight, a very poor chance, for we never see them except for the instant when they splash into our atmosphere; and for them that instant is instant death. It is unlikely that any escape that ordeal, and even if they do, their career and orbit are effectually changed. Henceforward they must become attendants on the earth. They may drop on to its surface, or they may duck out of our atmosphere again, and revolve round us unseen in the clear space between earth and moon.

Nevertheless, although the problem of determining the original orbit of any given set of shooting-stars before it struck us would seem nearly insoluble, it has been solved, and solved with some approach to accuracy; being done by the help of observations of certain other bodies. The bodies by whose help this difficult problem has been attacked and resolved are comets. What are comets?

I must tell you that the scientific world is not entirely and completely decided on the structure of comets. There are many floating ideas on the subject, and some certain knowledge. But the subject is still, in many respects, an open one, and the ideas I propose to advocate you will accept for no more than they are worth, viz. as worthy to be compared with other and different views.

Up to the time of Newton, the nature of comets was entirely unknown. They were regarded with superstitious awe as fiery portents, and were supposed to be connected with the death of some king, or with some national catastrophe.

Even so late as the first edition of the _Principia_ the problem of comets was unsolved, and their theory is not given; but between the first and the second editions a large comet appeared, in 1680, and Newton speculated on its appearance and behaviour. It rushed down very close to the sun, spun half round him very quickly, and then receded from him again. If it were a material substance, to which the law of gravitation applied, it must be moving in a conic section with the sun in one focus, and its radius vector must sweep out equal areas in equal times. Examining the record of its positions made at observatories, he found its observed path quite accordant with theory; and the motion of comets was from that time understood. Up to that time no one had attempted to calculate an orbit for a comet. They had been thought irregular and lawless bodies. Now they were recognized as perfectly obedient to the law of gravitation, and revolving round the sun like everything else--as members, in fact, of our solar system, though not necessarily permanent members.

But the orbit of a comet is very different from a planetary one. The excentricity of its orbit is enormous--in other words, it is either a very elongated ellipse or a parabola. The comet of 1680, Newton found to move in an orbit so nearly a parabola that the time of describing it must be reckoned in hundreds of years at the least. It is now thought possible that it may not be quite a parabola, but an ellipse so elongated that it will not return till 2255. Until that date arrives, however, uncertainty will prevail as to whether it is a periodic comet, or one of those that only visit our system once. If it be periodic, as suspected, it is the same as appeared when Julius Cæsar was killed, and which likewise appeared in the years 531 and 1106 A.D. Should it appear in 2255, our posterity will probably regard it as a memorial of Newton.

The next comet discussed in the light of the theory of gravitation was the famous one of Halley. You know something of the history of this. Its period is 75-1/2 years. Halley saw it in 1682, and predicted its return in 1758 or 1759--the first cometary prediction. Clairaut calculated its return right within a month (p. 219). It has been back once more, in 1835; and this time its date was correctly predicted within three days, because Uranus was now known. It was away at its furthest point in 1873. It will be back again in 1911.

Coming to recent times, we have the great comets of 1843 and of 1858, the history of neither being known. Quite possibly they arrived then for the first time. Possibly the second will appear again in 3808. But besides these great comets, there are a multitude of telescopic ones, which do not show these striking features, and have no gigantic tail. Some have no tail at all, others have at best a few insignificant streamers, and others show a faint haze looking like a microscopic nebula.

All these comets are of considerable extent--some millions of miles thick usually, and yet stars are clearly visible through them. Hence they must be matter of very small density; their tails can be nothing more dense than a filmy mist, but their nucleus must be something more solid and substantial.

I have said that comets arrive from the depths of space, rush towards and round the sun, whizzing past the earth with a speed of twenty-six miles a second, on round the sun with a far greater velocity than that, and then rush off again. Now, all the time they are away from the sun they are invisible. It is only as they get near him that they begin to expand and throw off tails and other appendages. The sun's heat is evidently evaporating them, and driving away a cloud of mist and volatile matter. This is when they can be seen. The comet is most gorgeous when it is near the sun, and as soon as it gets a reasonable distance away from him it is perfectly invisible.

The matter evaporated from the comet by the sun's heat does not return--it is lost to the comet; and hence, after a few such journeys, its volatile matter gets appreciably diminished, and so old-established periodic comets have no tails to speak of. But the new visitants, coming from the depths of space for the first time--these have great supplies of volatile matter, and these are they which show the most magnificent tails.

The tail of a comet is always directed away from the sun as if it were repelled. To this rule there is no exception. It is suggested, and held as most probable, that the tail and sun are similarly electrified, and that the repulsion of the tail is electrical repulsion. Some great force is obviously at work to account for the enormous distance to which the tail is shot in a few hours. The pressure of the sun's light can do something, and is a force that must not be ignored when small particles are being dealt with. (Cf. _Modern Views of Electricity_, 2nd edition, p. 363.)

Now just think what analogies there are between comets and meteors. Both are bodies travelling in orbits round the sun, and both are mostly invisible, but both become visible to us under certain circumstances. Meteors become visible when they plunge into the extreme limits of our atmosphere. Comets become visible when they approach the sun. Is it possible that comets are large meteors which dip into the solar atmosphere, and are thus rendered conspicuously luminous? Certainly they do not dip into the actual main atmosphere of the sun, else they would be utterly destroyed; but it is possible that the sun has a faint trace of atmosphere extending far beyond this, and into this perhaps these meteors dip, and glow with the friction. The particles thrown off might be, also by friction, electrified; and the vaporous tail might be thus accounted for.

Let us make this hypothesis provisionally--that comets are large meteors, or a compact swarm of meteors, which, coming near the sun, find a highly rarefied sort of atmosphere, in which they get heated and partly vaporized, just as ordinary meteorites do when they dip into the atmosphere of the earth. And let us see whether any facts bear out the analogy and justify the hypothesis.

I must tell you now the history of three bodies, and you will see that some intimate connection between comets and meteors is proved. The three bodies are known as, first, Encke's comet; second, Biela's comet; third, the November swarm of meteors.

Encke's comet (one of those discovered by Miss Herschel) is an insignificant-looking telescopic comet of small period, the orbit of which was well known, and which was carefully observed at each reappearance after Encke had calculated its orbit. It was the quickest of the comets, returning every 3-1/2 years.

It was found, however, that its period was not quite constant; it kept on getting slightly shorter. The comet, in fact, returned to the sun slightly before its time. Now this effect is exactly what friction against a solar atmosphere would bring about. Every time it passed near the sun a little velocity would be rubbed out of it. But the velocity is that which carries it away, hence it would not go quite so far, and therefore would return a little sooner. Any revolving body subject to friction must revolve quicker and quicker, and get nearer and nearer its central body, until, if the process goes on long enough, it must drop upon its surface. This seems the kind of thing happening to Encke's comet. The effect is very small, and not thoroughly proved; but, so far as it goes, the evidence points to a greatly extended rare solar atmosphere, which rubs some energy out of it at every perihelion passage.

Next, Biela's comet. This also was a well known and carefully observed telescopic comet, with a period of six years. In one of its distant excursions, it was calculated that it must pass very near Jupiter, and much curiosity was excited as to what would happen to it in consequence of the perturbation it must experience. As I have said, comets are only visible as they approach the sun, and a watch was kept for it about its appointed time. It was late, but it did ultimately arrive.

The singular thing about it, however, was that it was now double. It had apparently separated into two. This was in 1846. It was looked for again in 1852, and this time the components were further separated. Sometimes one was brighter, sometimes the other. Next time it ought to have come round no one could find either portion. The comet seemed to have wholly disappeared. It has never been seen since. It was then recorded and advertised as the missing comet.

But now comes the interesting part of the story. The orbit of this Biela comet was well known, and it was found that on a certain night in 1872 the earth would cross the orbit, and had some chance of encountering the comet. Not a very likely chance, because it need not be in that part of its orbit at the time; but it was suspected not to be far off--if still existent. Well, the night arrived, the earth did cross the orbit, and there was seen, not the comet, but a number of shooting-stars. Not one body, nor yet two, but a multitude of bodies--in fact, a swarm of meteors. Not a very great swarm, such as sometimes occurs, but still a quite noticeable one; and this shower of meteors is definitely recognized as flying along the track of Biela's comet. They are known as the Andromedes.

This observation has been generalized. Every cometary orbit is marked by a ring of meteoric stones travelling round it, and whenever a number of shooting-stars are seen quickly one after the other, it is an evidence that we are crossing the track of some comet. But suppose instead of only crossing the track of a comet we were to pass close to the comet itself, we should then expect to see an extraordinary swarm--a multitude of shooting-stars. Such phenomena have occurred. The most famous are those known as the November meteors, or Leonids.

This is the third of those bodies whose history I had to tell you. Professor H.A. Newton, of America, by examining ancient records arrived at the conclusion that the earth passed through a certain definite meteor shoal every thirty-three years. He found, in fact, that every thirty-three years an unusual flight of shooting-stars was witnessed in November, the earliest record being 599 A.D. Their last appearance had been in 1833, and he therefore predicted their return in 1866 or 1867. Sure enough, in November, 1866, they appeared; and many must remember seeing that glorious display. Although their hail was almost continuous, it is estimated that their average distance apart was thirty-five miles! Their radiant point was and always is in the constellation Leo, and hence their name Leonids.

A parallel stream fixed in space necessarily exhibits a definite
aspect with reference to the fixed stars. Its aspect with respect
to the earth will be very changeable, because of the rotation and
revolution of that body, but its position with respect to
constellations will be steady. Hence each meteor swarm, being a
steady parallel stream of rushing masses, always strikes us from
the same point in stellar space, and by this point (or radiant) it
is identified and named.

The paths do not appear to us to be parallel, because of
perspective: they seem to radiate and spread in all directions from
a fixed centre like spokes, but all these diverging streaks are
really parallel lines optically foreshortened by different amounts
so as to produce the radiant impression.

The annexed diagram (Fig. 105) clearly illustrates the fact that
the "radiant" is the vanishing point of a number of parallel lines.

This swarm is specially interesting to us from the fact that we cross its orbit every year. Its orbit and the earth's intersect. Every November we go through it, and hence every November we see a few stragglers of this immense swarm. The swarm itself takes thirty-three years on its revolution round the sun, and hence we only encounter it every thirty-three years.

The swarm is of immense size. In breadth it is such that the earth, flying nineteen miles a second, takes four or five hours to cross it, and this is therefore the time the display lasts. But in length it is far more enormous. The speed with which it travels is twenty-five miles a second, (for its orbit extends as far as Uranus, although by no means parabolic), and yet it takes more than a year to pass. Imagine a procession 200,000 miles broad, every individual rushing along at the rate of twenty-five miles every second, and the whole procession so long that it takes more than a year to pass. It is like a gigantic shoal of herrings swimming round and round the sun every thirty-three years, and travelling past the earth with that tremendous velocity of twenty-five miles a second. The earth dashes through the swarm and sweeps up myriads. Think of the countless numbers swept up by the whole earth in crossing such a shoal as that! But heaps more remain, and probably the millions which are destroyed every thirty-three years have not yet made any very important difference to the numbers still remaining.

The earth never misses this swarm. Every thirty-three years it is bound to pass through some part of them, for the shoal is so long that if the head is just missed one November the tail will be encountered next November. This is a plain and obvious result of its enormous length. It may be likened to a two-foot length of sewing silk swimming round and round an oval sixty feet in circumference. But, you will say, although the numbers are so great that destroying a few millions or so every thirty-three years makes but little difference to them, yet, if this process has been going on from all eternity, they ought to be all swept up. Granted; and no doubt the most ancient swarms have already all or nearly all been swept up.

The August meteors, or Perseids, are an example. Every August we cross their path, and we have a small meteoric display radiating from the sword-hand of Perseus, but never specially more in one August than another. It would seem as if the main shoal has disappeared, and nothing is now left but the stragglers; or perhaps it is that the shoal has gradually become uniformly distributed all along the path. Anyhow, these August meteors are reckoned much more ancient members of the solar system than are the November meteors. The November meteors are believed to have entered the solar system in the year 126 A.D.

This may seem an extraordinary statement. It is not final, but it is based on the calculations of Leverrier--confirmed recently by Mr. Adams. A few moments will suffice to make the grounds of it clear. Leverrier calculated the orbit of the November meteors, and found them to be an oval extending beyond Uranus. It was perturbed by the outer planets near which it went, so that in past times it must have moved in a slightly different orbit. Calculating back to their past positions, it was found that in a certain year it must have gone very near to Uranus, and that by the perturbation of this planet its path had been completely changed. Originally it had in all probability been a comet, flying in a parabolic orbit towards the sun like many others. This one, encountering Uranus, was pulled to pieces as it were, and its orbit made elliptical as shown in Fig. 107. It was no longer free to escape and go away into the depths of space: it was enchained and made a member of the solar system. It also ceased to be a comet; it was degraded into a shoal of meteors.

This is believed to be the past history of this splendid swarm. Since its introduction to the solar system it has made 52 revolutions: its next return is due in November, 1899, and I hope that it may occur in the English dusk, and (see Fig. 97) in a cloudless after-midnight sky, as it did in 1866.

NOTES FOR LECTURE XVII

The tide-generating force of one body on another is directly as the mass of the one body and inversely as the cube of the distance between them. Hence the moon is more effective in producing terrestrial tides than the sun.

The tidal wave directly produced by the moon in the open ocean is about 5 feet high, that produced by the sun is about 2 feet. Hence the average spring tide is to the average neap as about 7 to 3. The lunar tide varies between apogee and perigee from 4·3 to 5·9.

The solar tide varies between aphelion and perihelion from 1·9 to 2·1. Hence the highest spring tide is to the lowest neap as 5·9 + 2·1 is to 4·3 -2·1, or as 8 to 2·2.

The semi-synchronous oscillation of the Southern Ocean raises the magnitude of oceanic tides somewhat above these directly generated values.

Oceanic tides are true waves, not currents. Coast tides are currents. The momentum of the water, when the tidal wave breaks upon a continent and rushes up channels, raises coast tides to a much greater height--in some places up to 50 or 60 feet, or even more.

Early observed connections between moon and tides would be these:--

1st. Spring tides at new and full moon.

2nd. Average interval between tide and tide is half a lunar, not a
solar, day--a lunar day being the interval between two successive
returns of the moon to the meridian: 24 hours and 50 minutes.

3rd. The tides of a given place at new and full moon occur always
at the same time of day whatever the season of the year.

LECTURE XVII

THE TIDES

Persons accustomed to make use of the Mersey landing-stages can hardly fail to have been struck with two obvious phenomena. One is that the gangways thereto are sometimes almost level, and at other times very steep; another is that the water often rushes past the stage rather violently, sometimes south towards Garston, sometimes north towards the sea. They observe, in fact, that the water has two periodic motions--one up and down, the other to and fro--a vertical and a horizontal motion. They may further observe, if they take the trouble, that a complete swing of the water, up and down, or to and fro, takes place about every twelve and a half hours; moreover, that soon after high and low water there is no current--the water is stationary, whereas about half-way between high and low it is rushing with maximum speed either up or down the river.

To both these motions of the water the name _tide_ is given, and both are extremely important. Sailors usually pay most attention to the horizontal motion, and on charts you find the tide-races marked; and the places where there is but a small horizontal rush of the water are labelled "very little tide here." Landsmen, or, at any rate, such of the more philosophic sort as pay any attention to the matter at all, think most of the vertical motion of the water--its amount of rise and fall.

Dwellers in some low-lying districts in London are compelled to pay attention to the extra high tides of the Thames, because it is, or was, very liable to overflow its banks and inundate their basements.

Sailors, however, on nearing a port are also greatly affected by the time and amount of high water there, especially when they are in a big ship; and we know well enough how frequently Atlantic liners, after having accomplished their voyage with good speed, have to hang around for hours waiting till there is enough water to lift them over the Bar--that standing obstruction, one feels inclined to say disgrace, to the Liverpool harbour.

To us in Liverpool the tides are of supreme importance--upon them the very existence of the city depends--for without them Liverpool would not be a port. It may be familiar to many of you how this is, and yet it is a matter that cannot be passed over in silence. I will therefore call your attention to the Ordnance Survey of the estuaries of the Mersey and the Dee. You see first that there is a great tendency for sand-banks to accumulate all about this coast, from North Wales right away round to Southport. You see next that the port of Chester has been practically silted up by the deposits of sand in the wide-mouthed Dee, while the port of Liverpool remains open owing to the scouring action of the tide in its peculiarly shaped channel. Without the tides the Mersey would be a wretched dribble not much bigger than it is at Warrington. With them, this splendid basin is kept open, and a channel is cut of such depth that the _Great Eastern_ easily rode in it in all states of the water.

The basin is filled with water every twelve hours through its narrow neck. The amount of water stored up in this basin at high tide I estimate as 600 million tons. All this quantity flows through the neck in six hours, and flows out again in the next six, scouring and cleansing and carrying mud and sand far out to sea. Just at present the currents set strongest on the Birkenhead side of the river, and accordingly a "Pluckington bank" unfortunately grows under the Liverpool stage. Should this tendency to silt up the gates of our docks increase, land can be reclaimed on the other side of the river between Tranmere and Rock Ferry, and an embankment made so as to deflect the water over Liverpool way, and give us a fairer proportion of the current. After passing New Brighton the water spreads out again to the left; its velocity forward diminishes; and after a few miles it has no power to cut away that sandbank known as the Bar. Should it be thought desirable to make it accomplish this, and sweep the Bar further out to sea into deeper water, it is probable that a rude training wall (say of old hulks, or other removable partial obstruction) on the west of Queen's Channel, arranged so as to check the spreading out over all this useless area, may be quite sufficient to retain the needed extra impetus in the water, perhaps even without choking up the useful old Rock Channel, through which smaller ships still find convenient exit.

Now, although the horizontal rush of the tide is necessary to our existence as a port, it does not follow that the accompanying rise and fall of the water is an unmixed blessing. To it is due the need for all the expensive arrangements of docks and gates wherewith to store up the high-level water. Quebec and New York are cities on such magnificent rivers that the current required to keep open channel is supplied without any tidal action, although Quebec is nearly 1,000 miles from the open ocean; and accordingly, Atlantic liners do not hover in mid-river and discharge passengers by tender, but they proceed straight to the side of the quays lining the river, or, as at New York, they dive into one of the pockets belonging to the company running the ship, and there discharge passengers and cargo without further trouble, and with no need for docks or gates. However, rivers like the St. Lawrence and the Hudson are the natural property of a gigantic continent; and we in England may be well contented with the possession of such tidal estuaries as the Mersey, the Thames, and the Humber. That by pertinacious dredging the citizens of Glasgow manage to get large ships right up their small river, the Clyde, to the quays of the town, is a remarkable fact, and redounds very highly to their credit.

We will now proceed to consider the connection existing between the horizontal rush of water and its vertical elevation, and ask, Which is cause and which is effect? Does the elevation of the ocean cause the tidal flow, or does the tidal flow cause the elevation? The answer is twofold: both statements are in some sense true. The prime cause of the tide is undoubtedly a vertical elevation of the ocean, a tidal wave or hump produced by the attraction of the moon. This hump as it passes the various channels opening into the ocean raises their level, and causes water to flow up them. But this simple oceanic tide, although the cause of all tide, is itself but a small affair. It seldom rises above six or seven feet, and tides on islands in mid-ocean have about this value or less. But the tides on our coasts are far greater than this--they rise twenty or thirty feet, or even fifty feet occasionally, at some places, as at Bristol. Why is this? The horizontal motion of the water gives it such an impetus or momentum that its motion far transcends that of the original impulse given to it, just as a push given to a pendulum may cause it to swing over a much greater arc than that through which the force acts. The inrushing water flowing up the English Channel or the Bristol Channel or St. George's Channel has such an impetus that it propels itself some twenty or thirty feet high before it has exhausted its momentum and begins to descend. In the Bristol Channel the gradual narrowing of the opening so much assists this action that the tides often rise forty feet, occasionally fifty feet, and rush still further up the Severn in a precipitous and extraordinary hill of water called "the bore."

Some places are subject to considerable rise and fall of water with very little horizontal flow; others possess strong tidal races, but very little elevation and depression. The effect observed at any given place entirely depends on whether the place has the general character of a terminus, or whether it lies _en route_ to some great basin.

You must understand, then, that all tide takes its rise in the free and open ocean under the action of the moon. No ordinary-sized sea like the North Sea, or even the Mediterranean, is big enough for more than a just appreciable tide to be generated in it. The Pacific, the Atlantic, and the Southern Oceans are the great tidal reservoirs, and in them the tides of the earth are generated as low flat humps of gigantic area, though only a few feet high, oscillating up and down in the period of approximately twelve hours. The tides we, and other coast-possessing nations, experience are the overflow or back-wash of these oceanic humps, and I will now show you in what manner the great Atlantic tide-wave reaches the British Isles twice a day.

Fig. 109 shows the contour lines of the great wave as it rolls in east from the Atlantic, getting split by the Land's End and by Ireland into three portions; one of which rushes up the English Channel and through the Straits of Dover. Another rolls up the Irish Sea, with a minor offshoot up the Bristol Channel, and, curling round Anglesey, flows along the North Wales coast and fills Liverpool Bay and the Mersey. The third branch streams round the north coast of Ireland, past the Mull of Cantyre and Rathlin Island; part fills up the Firth of Clyde, while the rest flows south, and, swirling round the west side of the Isle of Man, helps the southern current to fill the Bay of Liverpool. The rest of the great wave impinges on the coast of Scotland, and, curling round it, fills up the North Sea right away to the Norway coast, and then flows down below Denmark, joining the southern and earlier arriving stream. The diagram I show you is a rough chart of cotidal lines, which I made out of the information contained in _Whitaker's Almanac_.

A place may thus be fed with tide by two distinct channels, and many curious phenomena occur in certain places from this cause. Thus it may happen that one channel is six hours longer than the other, in which case a flow will arrive by one at the same time as an ebb arrives by the other; and the result will be that the place will have hardly any tide at all, one tide interfering with and neutralizing the other. This is more markedly observed at other parts of the world than in the British Isles. Whenever a place is reached by two channels of different length, its tides are sure to be peculiar, and probably small.

Another cause of small tide is the way the wave surges to and fro in a channel. The tidal wave surging up the English Channel, for instance, gets largely reflected by the constriction at Dover, and so a crest surges back again, as we may see waves reflected in a long trough or tilted bath. The result is that Southampton has two high tides rapidly succeeding one another, and for three hours the high-water level varies but slightly--a fact of evident convenience to the port.

Places on a nodal line, so to speak, about the middle of the length of the channel, have a minimum of rise and fall, though the water rushes past them first violently up towards Dover, where the rise is considerable, and then back again towards the ocean. At Portland, for instance, the total rise and fall is very small: it is practically on a node. Yarmouth, again, is near a less marked node in the North Sea, where stationary waves likewise surge to and fro, and accordingly the tidal rise and fall at Yarmouth is only about five feet (varying from four and a half to six), whereas at London it is twenty or thirty feet, and at Flamborough Head or Leith it is from twelve to sixteen feet.

It is generally supposed that water never flows up-hill, but in these cases of oscillation it flows up-hill for three hours together. The water is rushing up the English Channel towards Dover long after it is highest at the Dover end; it goes on piling itself up, until its momentum is checked by the pressure, and then it surges back. It behaves, in fact, very like the bob of a pendulum, which rises against gravity at every quarter swing.

To get a very large tide, the place ought to be directly accessible by a long sweep of a channel to the open ocean, and if it is situate on a gradually converging opening, the ebb and flow may be enormous. The Severn is the best example of this on the British Isles; but the largest tides in the world are found, I believe, in the Bay of Fundy, on the coast of North America, where they sometimes rise one hundred and twenty feet. Excessive or extra tides may be produced occasionally in any place by the propelling force of a high wind driving the water towards the shore; also by a low barometer, _i.e._ by a local decrease in the pressure of the air.

Well, now, leaving these topographical details concerning tides, which we see to be due to great oceanic humps (great in area that is, though small in height), let us proceed to ask what causes these humps; and if it be the moon that does it, how does it do it?

The statement that the moon causes the tides sounds at first rather an absurdity, and a mere popular superstition. Galileo chaffed Kepler for believing it. Who it was that discovered the connection between moon and tides we know not--probably it is a thing which has been several times rediscovered by observant sailors or coast-dwellers--and it is certainly a very ancient piece of information.

Probably the first connection observed was that about full moon and about new moon the tides are extra high, being called spring tides, whereas about half-moon the tides are much less, and are called neap tides. The word spring in this connection has no reference to the season of the year; except that both words probably represent the same idea of energetic uprising or upspringing, while the word neap comes from nip, and means pinched, scanty, nipped tide.

The next connection likely to be observed would be that the interval between two day tides was not exactly a solar day of twenty-four hours, but a lunar day of fifty minutes longer. For by reason of the moon's monthly motion it lags behind the sun about fifty minutes a day, and the tides do the same, and so perpetually occur later and later, about fifty minutes a day later, or 12 hours and 25 minutes on the average between tide and tide.

A third and still more striking connection was also discovered by some of the ancient great navigators and philosophers--viz. that the time of high water at a given place at full moon is always the same, or very nearly so. In other words, the highest or spring tides always occur nearly at the same time of day at a given place. For instance, at Liverpool this time is noon and midnight. London is about two hours and a half later. Each port has its own time for receiving a given tide, and the time is called the "establishment" of the port. Look out a day when the moon is full, and you will find the Liverpool high tide occurs at half-past eleven, or close upon it. The same happens when the moon is new. A day after full or new moon the spring tides rise to their highest, and these extra high tides always occur in Liverpool at noon and at midnight, whatever the season of the year. About the equinoxes they are liable to be extraordinarily high. The extra low tides here are therefore at 6 a.m. and 6 p.m., and the 6 p.m. low tide is a nuisance to the river steamers. The spring tides at London are highest about half-past two.

* * * * *

It is, therefore, quite clear that the moon has to do with the tides. It and the sun together are, in fact, the whole cause of them; and the mode in which these bodies act by gravitative attraction was first made out and explained in remarkably full detail by Sir Isaac Newton. You will find his account of the tides in the second and third books of the _Principia_; and though the theory does not occupy more than a few pages of that immortal work, he succeeds not only in explaining the local tidal peculiarities, much as I have done to-night, but also in calculating the approximate height of mid-ocean solar tide; and from the observed lunar tide he shows how to determine the then quite unknown mass of the moon. This was a quite extraordinary achievement, the difficulty of which it is not easy for a person unused to similar discussions fully to appreciate. It is, indeed, but a small part of what Newton accomplished, but by itself it is sufficient to confer immortality upon any ordinary philosopher, and to place him in a front rank.

To make intelligible Newton's theory of the tides, I must not attempt to go into too great detail. I will consider only the salient points. First, you know that every mass of matter attracts every other piece of matter; second, that the moon revolves round the earth, or rather that the earth and moon revolve round their common centre of gravity once a month; third, that the earth spins on its own axis once a day; fourth, that when a thing is whirled round, it tends to fly out from the centre and requires a force to hold it in. These are the principles involved. You can whirl a bucket full of water vertically round without spilling it. Make an elastic globe rotate, and it bulges out into an oblate or orange shape; as illustrated by the model shown in Fig. 110. This is exactly what the earth does, and Newton calculated the bulging of it as fourteen miles all round the equator. Make an elastic globe revolve round a fixed centre outside itself, and it gets pulled into a prolate or lemon shape; the simplest illustrative experiment is to attach a string to an elastic bag or football full of water, and whirl it round and round. Its prolateness is readily visible.

Now consider the earth and moon revolving round each other like a man whirling a child round. The child travels furthest, but the man cannot merely rotate, he leans back and thus also describes a small circle: so does the earth; it revolves round the common centre of gravity of earth and moon (_cf._ p. 212). This is a vital point in the comprehension of the tides: the earth's centre is not at rest, but is being whirled round by the moon, in a circle about 1/80 as big as the circle which the moon describes, because the earth weighs eighty times as much as the moon. The effect of the revolution is to make both bodies slightly protrude in the direction of the line joining them; they become slightly "prolate" as it is called--that is, lemon-shaped. Illustrating still by the man and child, the child's legs fly outwards so that he is elongated in the direction of a radius; the man's coat-tails fly out too, so that he too is similarly though less elongated. These elongations or protuberances constitute the tides.

Fig. 111 shows a model to illustrate the mechanism. A couple of cardboard disks (to represent globes of course), one four times the diameter of the other, and each loaded so as to have about the correct earth-moon ratio of weights, are fixed at either end of a long stick, and they balance about a certain point, which is their common centre of gravity. For convenience this point is taken a trifle too far out from the centre of the earth--that is, just beyond its surface. Through the balancing point G a bradawl is stuck, and on that as pivot the whole readily revolves. Now, behind the circular disks, you see, are four pieces of card of appropriate shape, which are able to slide out under proper forces. They are shown dotted in the figure, and are lettered A, B, C, D. The inner pair, B and C, are attached to each other by a bit of string, which has to typify the attraction of gravitation; the outer pair, A and D, are not attached to anything, but have a certain amount of play against friction in slots parallel to the length of the stick. The moon-disk is also slotted, so a small amount of motion is possible to it along the stick or bar. These things being so arranged, and the protuberant pieces of card being all pushed home, so that they are hidden behind their respective disks, the whole is spun rapidly round the centre of gravity, G. The result of a brief spin is to make A and D fly out by centrifugal force and show, as in the figure; while the moon, flying out too in its slot, tightens up the string, which causes B and C to be pulled out too. Thus all four high tides are produced, two on the earth and two on the moon, A and D being caused by centrifugal force, B and C by the attraction of gravitation. Each disk has become prolate in the same sort of fashion as yielding globes do. Of course the fluid ocean takes this shape more easily and more completely than the solid earth can, and so here are the very oceanic humps we have been talking about, and about three feet high (Fig. 112). If there were a sea on the _moon_, its humps would be a good deal bigger; but there probably is no sea there, and if there were, the earth's tides are more interesting to us, at any rate to begin with.