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.



The humps as so far treated are always protruding in the earth-moon line, and are stationary. But now we have to remember that the earth is spinning inside them. It is not easy to see what precise effect this spin will have upon the humps, even if the world were covered with a uniform ocean; but we can see at any rate that however much they may get displaced, and they do get displaced a good deal, they cannot possibly be carried round and round. The whole explanation we have given of their causes shows that they must maintain some steady aspect with respect to the moon—in other words, they must remain stationary as the earth spins round. Not that the same identical water remains stationary, for in that case it would have to be dragged over the earth's equator at the rate of 1,000 miles an hour, but the hump or wave-crest remains stationary. It is a true wave, or form only, and consists of continuously changing individual particles. The same is true of all waves, except breaking ones.

Given, then, these stationary humps and the earth spinning on its axis, we see that a given place on the earth will be carried round and round, now past a hump, and six hours later past a depression: another six hours and it will be at the antipodal hump, and so on. Thus every six hours we shall travel from the region in space where the water is high to the region where it is low; and ignoring our own motion we shall say that the sea first rises and then falls; and so, with respect to the place, it does. Thus the succession of high and low water, and the two high tides every twenty-four hours, are easily understood in their easiest and most elementary aspect. A more complete account of the matter it will be wisest not to attempt: suffice it to say that the difficulties soon become formidable when the inertia of the water, its natural time of oscillation, the varying obliquity of the moon to the ecliptic, its varying distance, and the disturbing action of the sun are taken into consideration. When all these things are included, the problem becomes to ordinary minds overwhelming. A great many of these difficulties were successfully attacked by Laplace. Others remained for modern philosophers, among whom are Sir George Airy, Sir William Thomson, and Professor George Darwin.

I may just mention that the main and simplest effect of including the inertia or momentum of the water is to dislocate the obvious and simple connexion between high water and high moon; inertia always tends to make an effect differ in phase by a quarter period from the cause producing it, as may be illustrated by a swinging pendulum. Hence high water is not to be expected when the tide-raising force is a maximum, but six hours later; so that, considering inertia and neglecting friction, there would be low water under the moon. Including friction, something nearer the equilibrium state of things occurs. With sufficient friction the motion becomes dead-beat again, i.e. follows closely the force that causes it.

Returning to the elementary discussion, we see that the rotation of the earth with respect to the humps will not be performed in exactly twenty-four hours, because the humps are travelling slowly after the moon, and will complete a revolution in a month in the same direction as the earth is rotating. Hence a place on the earth has to catch them up, and so each high tide arrives later and later each day—roughly speaking, an hour later for each day tide; not by any means a constant interval, because of superposed disturbances not here mentioned, but on the average about fifty minutes.

We see, then, that as a result of all this we get a pair of humps travelling all over the surface of the earth, about once a day. If the earth were all ocean (and in the southern hemisphere it is nearly all ocean), then they would go travelling across the earth, tidal waves three feet high, and constituting the mid-ocean tides. But in the northern hemisphere they can only thus journey a little way without striking land. As the moon rises at a place on the east shores of the Atlantic, for instance, the waters begin to flow in towards this place, or the tide begins to rise. This goes on till the moon is overhead and for some time afterwards, when the tide is at its highest. The hump then follows the moon in its apparent journey across to America, and there precipitates itself upon the coast, rushing up all the channels, and constituting the land tide. At the same time, the water is dragged away from the east shores, and so our tide is at its lowest. The same thing repeats itself in a little more than twelve hours again, when the other hump passes over the Atlantic, as the moon journeys beneath the earth, and so on every day.

In the free Southern Ocean, where land obstruction is comparatively absent, the water gets up a considerable swing by reason of its accumulated momentum, and this modifies and increases the open ocean tides there. Also for some reason, I suppose because of the natural time of swing of the water, one of the humps is there usually much larger than the other; and so places in the Indian and other offshoots of the Southern Ocean get their really high tide only once every twenty-four hours. These southern tides are in fact much more complicated than those the British Isles receive. Ours are singularly simple. No doubt some trace of the influence of the Southern Ocean is felt in the North Atlantic, but any ocean extending over 90 deg. of longitude is big enough to have its own tides generated; and I imagine that the main tides we feel are thus produced on the spot, and that they are simple because the damping-out being vigorous, and accumulated effects small, we feel the tide-producing forces more directly. But for authoritative statements on tides, other books must be read. I have thought, and still think, it best in an elementary exposition to begin by a consideration of the tide-generating forces as if they acted on a non-rotating earth. It is the tide generating forces, and not the tides themselves, that are really represented in Figs. 112 and 114. The rotation of the earth then comes in as a disturbing cause. A more complete exposition would begin with the rotating earth, and would superpose the attraction of the moon as a disturbing cause, treating it as a problem in planetary perturbation, the ocean being a sort of satellite of the earth. This treatment, introducing inertia but ignoring friction and land obstruction, gives low water in the line of pull, and high water at right angles, or where the pull is zero; in the same sort of way as a pendulum bob is highest where most force is pulling it down, and lowest where no force is acting on it. For a clear treatment of the tides as due to the perturbing forces of sun and moon, see a little book by Mr. T.K. Abbott of Trinity College, Dublin. (Longman.)



If the moon were the only body that swung the earth round, this is all that need be said in an elementary treatment; but it is not the only one. The moon swings the earth round once a month, the sun swings it round once a year. The circle of swing is bigger, but the speed is so much slower that the protuberance produced is only one-third of that caused by the monthly whirl; i.e. the simple solar tide in the open sea, without taking momentum into account, is but a little more than a foot high, while the simple lunar tide is about three feet. When the two agree, we get a spring tide of four feet; when they oppose each other, we get a neap tide of only two feet. They assist each other at full moon and at new moon. At half-moon they oppose each other. So we have spring tides regularly once a fortnight, with neap tides in between.



Fig. 114 gives the customary diagrams to illustrate these simple things. You see that when the moon and sun act at right angles (i.e. at every half-moon), the high tides of one coincide with the low tides of the other; and so, as a place is carried round by the earth's rotation, it always finds either solar or else lunar high water, and only experiences the difference of their two effects. Whereas, when the sun and moon act in the same line (as they do at new and full moon), their high and low tides coincide, and a place feels their effects added together. The tide then rises extra high and falls extra low.



Utilizing these principles, a very elementary form of tidal-clock, or tide-predicter, can be made, and for an open coast station it really would not give the tides so very badly. It consists of a sort of clock face with two hands, one nearly three times as long as the other. The short hand, CA, should revolve round C once in twelve hours, and the vertical height of its end A represents the height of the solar tide on the scale of horizontal lines ruled across the face of the clock. The long hand, AB, should revolve round A once in twelve hours and twenty-five minutes, and the height of its end B (if A were fixed on the zero line) would represent the lunar tide. The two revolutions are made to occur together, either by means of a link-work parallelogram, or, what is better in practice, by a string and pulleys, as shown; and the height of the end point, B, of the third side or resultant, CB, read off on a scale of horizontal parallel lines behind, represents the combination or actual tide at the place. Every fortnight the two will agree, and you will get spring tides of maximum height CA + AB; every other fortnight the two will oppose, and you will get neap tides of maximum height CA-AB.

Such a clock, if set properly and driven in the ordinary way, would then roughly indicate the state of the tide whenever you chose to look at it and read the height of its indicating point. It would not indeed be very accurate, especially for such an inclosed station as Liverpool is, and that is probably why they are not made. A great number of disturbances, some astronomical, some terrestrial, have to be taken into account in the complete theory. It is not an easy matter to do this, but it can be, and has been, done; and a tide-predicter has not only been constructed, but two of them are in regular work, predicting the tides for years hence—one, the property of the Indian Government, for coast stations of India; the other for various British and foreign stations, wherever the necessary preliminary observations have been made. These machines are the invention of Sir William Thomson. The tide-tables for Indian ports are now always made by means of them.



The first thing to be done by any port which wishes its tides to be predicted is to set up a tide-gauge, or automatic recorder, and keep it working for a year or two. The tide-gauge is easy enough to understand: it marks the height of the tide at every instant by an irregular curved line like a barometer chart (Fig. 117). These observational curves so obtained have next to be fed into a fearfully complex machine, which it would take a whole lecture to make even partially intelligible, but Fig. 118 shows its aspect. It consists of ten integrating machines in a row, coupled up and working together. This is the "harmonic analyzer," and the result of passing the curve through this machine is to give you all the constituents of which it is built up, viz. the lunar tide, the solar tide, and eight of the sub-tides or disturbances. These ten values are then set off into a third machine, the tide-predicter proper. The general mode of action of this machine is not difficult to understand. It consists of a string wound over and under a set of pulleys, which are each set on an excentric, so as to have an up-and-down motion. These up-and-down motions are all different, and there are ten of these movable pulleys, which by their respective excursions represent the lunar tide, the solar tide, and the eight disturbances already analyzed out of the tide-gauge curve by the harmonic analyzer. One end of the string is fixed, the other carries a pencil which writes a trace on a revolving drum of paper—a trace which represents the combined motion of all the pulleys, and so predicts the exact height of the tide at the place, at any future time you like. The machine can be turned quite quickly, so that a year's tides can be run off with every detail in about half-an-hour. This is the easiest part of the operation. Nothing has to be done but to keep it supplied with paper and pencil, and turn a handle as if it were a coffee-mill instead of a tide-mill. (Figs. 119 and 120.)



My subject is not half exhausted. I might go on to discuss the question of tidal energy—whether it can be ever utilized for industrial purposes; and also the very interesting question whence it comes. Tidal energy is almost the only terrestrial form of energy that does not directly or indirectly come from the sun. The energy of tides is now known to be obtained at the expense of the earth's rotation; and accordingly our day must be slowly, very slowly, lengthening. The tides of past ages have destroyed the moon's rotation, and so it always turns the same face to us. There is every reason to believe that in geologic ages the moon was nearer to us than it is now, and that accordingly our tides were then far more violent, rising some hundreds of feet instead of twenty or thirty, and sweeping every six hours right over the face of a country, ploughing down hills, denuding rocks, and producing a copious sedimentary deposit.



In thus discovering the probable violent tides of past ages, astronomy has, within the last few years, presented geology with the most powerful denuding agent known; and the study of the earth's past history cannot fail to be greatly affected by the modern study of the intricate and refined conditions attending prolonged tidal action on incompletely rigid bodies. [Read on this point the last chapter of Sir R. Ball's Story of the Heavens.]



I might also point out that the magnitude of our terrestrial tides enables us to answer the question as to the internal fluidity of the earth. It used to be thought that the earth's crust was comparatively thin, and that it contained a molten interior. We now know that this is not the case. The interior of the earth is hot indeed, but it is not fluid. Or at least, if it be fluid, the amount of fluid is but very small compared with the thickness of the unyielding crust. All these, and a number of other most interesting questions, fringe the subject of the tides; the theoretical study of which, started by Newton, has developed, and is destined in the future to further develop, into one of the most gigantic and absorbing investigations—having to do with the stability or instability of solar systems, and with the construction and decay of universes.

These theories are the work of pioneers now living, whose biographies it is therefore unsuitable for us to discuss, nor shall I constantly mention their names. But Helmholtz, and Thomson, are household words, and you well know that in them and their disciples the race of Pioneers maintains its ancient glory.



NOTES FOR LECTURE XVIII

Tides are due to incomplete rigidity of bodies revolving round each other under the action of gravitation, and at the same time spinning on their axes.

Two spheres revolving round each other can only remain spherical if rigid; if at all plastic they become prolate. If either rotate on its axis, in the same or nearly the same plane as it revolves, that one is necessarily subject to tides.

The axial rotation tends to carry the humps with it, but the pull of the other body keeps them from moving much. Hence the rotation takes place against a pull, and is therefore more or less checked and retarded. This is the theory of Von Helmholtz.

The attracting force between two such bodies is no longer exactly towards the centre of revolution, and therefore Kepler's second law is no longer precisely obeyed: the rate of description of areas is subject to slight acceleration. The effect of this tangential force acting on the tide-compelling body is gradually to increase its distance from the other body.

Applying these statements to the earth and moon, we see that tidal energy is produced at the expense of the earth's rotation, and that the length of the day is thereby slowly increasing. Also that the moon's rotation relative to the earth has been destroyed by past tidal action in it (the only residue of ancient lunar rotation now being a scarcely perceptible libration), so that it turns always the same face towards us. Moreover, that its distance from the earth is steadily increasing. This last is the theory of Professor G.H. Darwin.

Long ago the moon must therefore have been much nearer the earth, and the day was much shorter. The tides were then far more violent.

Halving the distance would make them eight times as high; quartering it would increase them sixty-four-fold. A most powerful geological denuding agent. Trade winds and storms were also more violent.

If ever the moon were close to the earth, it would have to revolve round it in about three hours. If the earth rotated on its axis in three hours, when fluid or pasty, it would be unstable, and begin to separate a portion of itself as a kind of bud, which might then get detached and gradually pushed away by the violent tidal action. Hence it is possible that this is the history of the moon. If so, it is probably an exceptional history. The planets were not formed from the sun in this way.

Mars' moons revolve round him more quickly than the planet rotates: hence with them the process is inverted, and they must be approaching him and may some day crash along his surface. The inner moon is now about 4,000 miles away, and revolves in 7-1/2 hours. It appears to be about 20 miles in diameter, and weighs therefore, if composed of rock, 40 billion tons. Mars rotates in 24-1/2 hours.

A similar fate may possibly await our moon ages hence—by reason of the action of terrestrial tides produced by the sun.



LECTURE XVIII

THE TIDES, AND PLANETARY EVOLUTION

In the last lecture we considered the local peculiarities of the tides, the way in which they were formed in open ocean under the action of the moon and the sun, and also the means by which their heights and times could be calculated and predicted years beforehand. Towards the end I stated that the subject was very far from being exhausted, and enumerated some of the large and interesting questions which had been left untouched. It is with some of these questions that I propose now to deal.

I must begin by reminding you of certain well-known facts, a knowledge of which I may safely assume.

And first we must remind ourselves of the fact that almost all the rocks which form the accessible crust of the earth were deposited by the agency of water. Nearly all are arranged in regular strata, and are composed of pulverized materials—materials ground down from pre-existing rocks by some denuding and grinding action. They nearly all contain vestiges of ancient life embedded in them, and these vestiges are mainly of marine origin. The strata which were once horizontal are now so no longer—they have been tilted and upheaved, bent and distorted, in many places. Some of them again have been metamorphosed by fire, so that their organic remains have been destroyed, and the traces of their aqueous origin almost obliterated. But still, to the eye of the geologist, all are of aqueous or sedimentary origin: roughly speaking, one may say they were all deposited at the bottom of some ancient sea.

The date of their formation no man yet can tell, but that it was vastly distant is certain. For the geological era is not over. Aqueous action still goes on: still does frost chip the rocks into fragments; still do mountain torrents sweep stone and mud and debris down the gulleys and watercourses; still do rivers erode their channels, and carry mud and silt far out to sea. And, more powerful than any of these agents of denudation, the waves and the tides are still at work along every coast-line, eating away into the cliffs, undermining gradually and submerging acre after acre, and making with the refuse a shingly, or a sandy, or a muddy beach—the nucleus of a new geological formation.

Of all denuding agents, there can be no doubt that, to the land exposed to them, the waves of the sea are by far the most powerful. Think how they beat and tear, and drive and drag, until even the hardest rock, like basalt, becomes honeycombed into strange galleries and passages—Fingal's Cave, for instance—and the softer parts are crumbled away. But the area now exposed to the teeth of the waves is not great. The fury of a winter storm may dash them a little higher than usual, but they cannot reach cliffs 100 feet high. They can undermine such cliffs indeed, and then grind the fragments to powder, but their direct action is limited. Not so limited, however, as they would be without the tides. Consider for a moment the denudation import of the tides: how does the existence of tidal rise and fall affect the geological problem?

The scouring action of the tidal currents themselves is not to be despised. It is the tidal ebb and flow which keeps open channel in the Mersey, for instance. But few places are so favourably situated as Liverpool in this respect, and the direct scouring action of the tides in general is not very great. Their geological import mainly consists in this—that they raise and lower the surface waves at regular intervals, so as to apply them to a considerable stretch of coast. The waves are a great planing machine attacking the land, and the tides raise and lower this planing machine, so that its denuding tooth is applied, now twenty feet vertically above mean level, now twenty feet below.

Making all allowance for the power of winds and waves, currents, tides, and watercourses, assisted by glacial ice and frost, it must be apparent how slowly the work of forming the rocks is being carried on. It goes on steadily, but so slowly that it is estimated to take 6000 years to wear away one foot of the American continent by all the denuding causes combined. To erode a stratum 5000 feet thick will require at this rate thirty million years.

The age of the earth is not at all accurately known, but there are many grounds for believing it not to be much older than some thirty million years. That is to say, not greatly more than this period of time has elapsed since it was in a molten condition. It may be as old as a hundred million years, but its age is believed by those most competent to judge to be more likely within this limit than beyond it. But if we ask what is the thickness of the rocks which in past times have been formed, and denuded, and re-formed, over and over again, we get an answer, not in feet, but in miles. The Laurentian and Huronian rocks of Canada constitute a stratum ten miles thick; and everywhere the rocks at the base of our stratified system are of the most stupendous volume and thickness.

It has always been a puzzle how known agents could have formed these mighty masses, and the only solution offered by geologists was, unlimited time. Given unlimited time, they could, of course, be formed, no matter how slowly the process went on. But inasmuch as the time allowable since the earth was cool enough for water to exist on it except as steam is not by any means unlimited, it becomes necessary to look for a far more powerful engine than any now existing; there must have been some denuding agent in those remote ages—ages far more distant from us than the Carboniferous period, far older than any forms of life, fossil or otherwise, ages among the oldest known to geology—a denuding agent must have then existed, far more powerful than any we now know.

Such an agent it has been the privilege of astronomy and physics, within the last ten years, to discover. To this discovery I now proceed to lead up.

Our fundamental standard of time is the period of the earth's rotation—the length of the day. The earth is our one standard clock: all time is expressed in terms of it, and if it began to go wrong, or if it did not go with perfect uniformity, it would seem a most difficult thing to discover its error, and a most puzzling piece of knowledge to utilize when found.

That it does not go much wrong is proved by the fact that we can calculate back to past astronomical events—ancient eclipses and the like—and we find that the record of their occurrence, as made by the old magi of Chaldaea, is in very close accordance with the result of calculation. One of these famous old eclipses was observed in Babylon about thirty-six centuries ago, and the Chaldaean astronomers have put on record the time of its occurrence. Modern astronomers have calculated back when it should have occurred, and the observed time agrees very closely with the actual, but not exactly. Why not exactly?

Partly because of the acceleration of the moon's mean motion, as explained in the lecture on Laplace (p. 262). The orbit of the earth was at that time getting rounder, and so, as a secondary result, the speed of the moon was slightly increasing. It is of the nature of a perturbation, and is therefore a periodic not a progressive or continuous change, and in a sufficiently long time it will be reversed. Still, for the last few thousand years the moon's motion has been, on the whole, accelerated (though there seems to be a very slight retarding force in action too).

Laplace thought that this fact accounted for the whole of the discrepancy; but recently, in 1853, Professor Adams re-examined the matter, and made a correction in the details of the theory which diminishes its effect by about one-half, leaving the other half to be accounted for in some other way. His calculations have been confirmed by Professor Cayley. This residual discrepancy, when every known cause has been allowed for, amounts to about one hour.

The eclipse occurred later than calculation warrants. Now this would have happened from either of two causes, either an acceleration of the moon in her orbit, or a retardation of the earth in her diurnal rotation—a shortening of the month or a lengthening of the day, or both. The total discrepancy being, say, two hours, an acceleration of six seconds-per-century per century will in thirty-six centuries amount to one hour; and this, according to the corrected Laplacian theory, is what has occurred. But to account for the other hour some other cause must be sought, and at present it is considered most probably due to a steady retardation of the earth's rotation—a slow, very slow, lengthening of the day.

The statement that a solar eclipse thirty-six centuries ago was an hour late, means that a place on the earth's surface came into the shadow one hour behind time—that is, had lagged one twenty-fourth part of a revolution. The earth, therefore, had lost this amount in the course of 3600 x 365-1/4 revolutions. The loss per revolution is exceedingly small, but it accumulates, and at any era the total loss is the sum of all the losses preceding it. It may be worth while just to explain this point further.

Suppose the earth loses a small piece of time, which I will call an instant, per day; a locality on the earth will come up to a given position one instant late on the first day after an event. On the next day it would come up two instants late by reason of the previous loss; but it also loses another instant during the course of the second day, and so the total lateness by the end of that day amounts to three instants. The day after, it will be going slower from the beginning at the rate of two instants a day, it will lose another instant on the fresh day's own account, and it started three instants late; hence the aggregate loss by the end of the third day is 1 + 2 + 3 = 6. By the end of the fourth day the whole loss will be 1 + 2 + 3 + 4, and so on. Wherefore by merely losing one instant every day the total loss in n days is (1 + 2 + 3 + ... + n) instants, which amounts to 1/2n (n + 1) instants; or practically, when n is big, to 1/2n^2. Now in thirty-six centuries there have been 3600 x 365-1/4 days, and the total loss has amounted to an hour; hence the length of "an instant," the loss per diem, can be found from the equation 1/2(3600 x 365)^2 instants = 1 hour; whence one "instant" equals the 240 millionth part of a second. This minute quantity represents the retardation of the earth per day. In a year the aggregate loss mounts up to 1/3600th part of a second, in a century to about three seconds, and in thirty-six centuries to an hour. But even at the end of the thirty-six centuries the day is barely any longer; it is only 3600 x 365 instants, that is 1/180th of a second, longer than it was at the beginning. And even a million years ago, unless the rate of loss was different (as it probably was), the day would only be thirty-five minutes shorter, though by that time the aggregate loss, as measured by the apparent lateness of any perfectly punctual event reckoned now, would have amounted to nine years. (These numbers are to be taken as illustrative, not as precisely representing terrestrial fact.)

What can have caused the slowing down? Swelling of the earth by reason of accumulation of meteoric dust might do something, but probably very little. Contraction of the earth as it goes on cooling would act in the opposite direction, and probably more than counterbalance the dust effect. The problem is thus not a simple one, for there are several disturbing causes, and for none of them are the data enough to base a quantitative estimate upon; but one certain agent in lengthening the day, and almost certainly the main agent, is to be found in the tides.

Remember that the tidal humps were produced as the prolateness of a sphere whirled round and round a fixed centre, like a football whirled by a string. These humps are pulled at by the moon, and the earth rotates on its axis against this pull. Hence it tends to be constantly, though very slightly, dragged back.

In so far as the tidal wave is allowed to oscillate freely, it will swing with barely any maintaining force, giving back at one quarter-swing what it has received at the previous quarter; but in so far as it encounters friction, which it does in all channels where there is an actual ebb and flow of the water, it has to receive more than it gives back, and the balance of energy has to be made up to it, or the tides would cease. The energy of the tides is, in fact, continually being dissipated by friction, and all the energy so dissipated is taken from the rotation of the earth. If tidal energy were utilized by engineers, the machines driven would be really driven at the expense of the earth's rotation: it would be a mode of harnessing the earth and using the moon as fixed point or fulcrum; the moon pulling at the tidal protuberance, and holding it still as the earth rotates, is the mechanism whereby the energy is extracted, the handle whereby the friction brake is applied.

Winds and ocean currents have no such effect (as Mr. Fronde in Oceania supposes they have), because they are all accompanied by a precisely equal counter-current somewhere else, and no internal rearrangement of fluid can affect the motion of a mass as a whole; but the tides are in different case, being produced, not by internal inequalities of temperature, but by a straightforward pull from an external body.

The ultimate effect of tidal friction and dissipation of energy will, therefore, be to gradually retard the earth till it does not rotate with reference to the moon, i.e. till it rotates once while the moon revolves once; in other words, to make the day and the month equal. The same cause must have been in operation, but with eighty-fold greater intensity, on the moon. It has ceased now, because the rotation has stopped, but if ever the moon rotated on its axis with respect to the earth, and if it were either fluid itself or possessed any liquid ocean, then the tides caused by the pull of the earth must have been prodigious, and would tend to stop its rotation. Have they not succeeded? Is it not probable that this is why the moon always now turns the same face towards us? It is believed to be almost certainly the cause. If so, there was a time when the moon behaved differently—when it rotated more quickly than it revolved, and exhibited to us its whole surface. And at this era, too, the earth itself must have rotated a little faster, for it has been losing speed ever since.

We have thus arrived at this fact, that a thousand years ago the day was a trifle shorter than it is now. A million years ago it was, perhaps, an hour shorter. Twenty million years ago it must have been much shorter. Fifty million years ago it may have been only a few hours long. The earth may have spun round then quite quickly. But there is a limit. If it spun too fast it would fly to pieces. Attach shot by means of wax to the whirling earth model, Fig. 110, and at a certain speed the cohesion of the wax cannot hold them, so they fly off. The earth is held together not by cohesion but by gravitation; it is not difficult to reckon how fast the earth must spin for gravity at its surface to be annulled, and for portions to fly off. We find it about one revolution in three hours. This is a critical speed. If ever the day was three hours long, something must have happened. The day can never have been shorter than that; for if it were, the earth would have a tendency to fly in pieces, or, at least, to separate into two pieces. Remember this, as a natural result of a three-hour day, which corresponds to an unstable state of things; remember also that in some past epoch a three-hour day is a probability.

If we think of the state of things going on in the earth's atmosphere, if it had an atmosphere at that remote date, we shall recognize the existence of the most fearful tornadoes. The trade winds, which are now peaceful agents of commerce, would then be perpetual hurricanes, and all the denudation agents of the geologist would be in a state of feverish activity. So, too, would the tides: instead of waiting six hours between low and high tide, we should have to wait only three-quarters of an hour. Every hour-and-a-half the water would execute a complete swing from high tide to high again.

Very well, now leave the earth, and think what has been happening to the moon all this while.

We have seen that the moon pulls the tidal hump nearest to it back; but action and reaction are always equal and opposite—it cannot do that without itself getting pulled forward. The pull of the earth on the moon will therefore not be quite central, but will be a little in advance of its centre; hence, by Kepler's second law, the rate of description of areas by its radius vector cannot be constant, but must increase (p. 208). And the way it increases will be for the radius vector to lengthen, so as to sweep out a bigger area. Or, to put it another way, the extra speed tending to be gained by the moon will fling it further away by extra centrifugal force. This last is not so good a way of regarding the matter; though it serves well enough for the case of a ball whirled at the end of an elastic string. After having got up the whirl, the hand holding the string may remain almost fixed at the centre of the circle, and the motion will continue steadily; but if the hand be moved so as always to pull the string a little in advance of the centre, the speed of whirl will increase, the elastic will be more and more stretched, until the whirling ball is describing a much larger circle. But in this case it will likewise be going faster—distance and speed increase together. This is because it obeys a different law from gravitation—the force is not inversely as the square, or any other single power, of the distance. It does not obey any of Kepler's laws, and so it does not obey the one which now concerns us, viz. the third; which practically states that the further a planet is from the centre the slower it goes; its velocity varies inversely with the square root of its distance (p. 74).

If, instead of a ball held by elastic, it were a satellite held by gravity, an increase in distance must be accompanied by a diminution in speed. The time of revolution varies as the square of the cube root of the distance (Kepler's third law). Hence, the tidal reaction on the moon, having as its primary effect, as we have seen, the pulling the moon a little forward, has also the secondary or indirect effect of making it move slower and go further off. It may seem strange that an accelerating pull, directed in front of the centre, and therefore always pulling the moon the way it is going, should retard it; and that a retarding force like friction, if such a force acted, should hasten it, and make it complete its orbit sooner; but so it precisely is.

Gradually, but very slowly, the moon is receding from us, and the month is becoming longer. The tides of the earth are pushing it away. This is not a periodic disturbance, like the temporary acceleration of its motion discovered by Laplace, which in a few centuries, more or less, will be reversed; it is a disturbance which always acts one way, and which is therefore cumulative. It is superposed upon all periodic changes, and, though it seems smaller than they, it is more inexorable. In a thousand years it makes scarcely an appreciable change, but in a million years its persistence tells very distinctly; and so, in the long run, the month is getting longer and the moon further off. Working backwards also, we see that in past ages the moon must have been nearer to us than it is now, and the month shorter.

Now just note what the effect of the increased nearness of the moon was upon our tides. Remember that the tide-generating force varies inversely as the cube of distance, wherefore a small change of distance will produce a great difference in the tide-force.

The moon's present distance is 240 thousand miles. At a time when it was only 190 thousand miles, the earth's tides would have been twice as high as they are now. The pushing away action was then a good deal more violent, and so the process went on quicker. The moon must at some time have been just half its present distance, and the tides would then have risen, not 20 or 30 feet, but 160 or 200 feet. A little further back still, we have the moon at one-third of its present distance from the earth, and the tides 600 feet high. Now just contemplate the effect of a 600-foot tide. We are here only about 150 feet above the level of the sea; hence, the tide would sweep right over us and rush far away inland. At high tide we should have some 200 feet of blue water over our heads. There would be nothing to stop such a tide as that in this neighbourhood till it reached the high lands of Derbyshire. Manchester would be a seaport then with a vengeance!

The day was shorter then, and so the interval between tide and tide was more like ten than twelve hours. Accordingly, in about five hours, all that mass of water would have swept back again, and great tracts of sand between here and Ireland would be left dry. Another five hours, and the water would come tearing and driving over the country, applying its furious waves and currents to the work of denudation, which would proceed apace. These high tides of enormously distant past ages constitute the denuding agent which the geologist required. They are very ancient—more ancient than the Carboniferous period, for instance, for no trees could stand the furious storms that must have been prevalent at this time. It is doubtful whether any but the very lowest forms of life then existed. It is the strata at the bottom of the geological scale that are of the most portentous thickness, and the only organism suspected in them is the doubtful Eozoon Canadense. Sir Robert Ball believes, and several geologists agree with him, that the mighty tides we are contemplating may have been coaeval with this ancient Laurentian formation, and others of like nature with it.

But let us leave geology now, and trace the inverted progress of events as we recede in imagination back through the geological era, beyond, into the dim vista of the past, when the moon was still closer and closer to the earth, and was revolving round it quicker and quicker, before life or water existed on it, and when the rocks were still molten.

Suppose the moon once touched the earth's surface, it is easy to calculate, according to the principles of gravitation, and with a reasonable estimate of its size as then expanded by heat, how fast it must then have revolved round the earth, so as just to save itself from falling in. It must have gone round once every three hours. The month was only three hours long at this initial epoch.

Remember, however, the initial length of the day. We found that it was just possible for the earth to rotate on its axis in three hours, and that when it did so, something was liable to separate from it. Here we find the moon in contact with it, and going round it in this same three-hour period. Surely the two are connected. Surely the moon was a part of the earth, and was separating from it.

That is the great discovery—the origin of the moon.

Once, long ages back, at date unknown, but believed to be certainly as much as fifty million years ago, and quite possibly one hundred million, there was no moon, only the earth as a molten globe, rapidly spinning on its axis—spinning in about three hours. Gradually, by reason of some disturbing causes, a protuberance, a sort of bud, forms at one side, and the great inchoate mass separates into two—one about eighty times as big as the other. The bigger one we now call earth, the smaller we now call moon. Round and round the two bodies went, pulling each other into tremendously elongated or prolate shapes, and so they might have gone on for a long time. But they are unstable, and cannot go on thus: they must either separate or collapse. Some disturbing cause acts again, and the smaller mass begins to revolve less rapidly. Tides at once begin—gigantic tides of molten lava hundreds of miles high; tides not in free ocean, for there was none then, but in the pasty mass of the entire earth. Immediately the series of changes I have described begins, the speed of rotation gets slackened, the moon's mass gets pushed further and further away, and its time of revolution grows rapidly longer. The changes went on rapidly at first, because the tides were so gigantic; but gradually, and by slow degrees, the bodies get more distant, and the rate of change more moderate. Until, after the lapse of ages, we find the day twenty-four hours long, the moon 240,000 miles distant, revolving in 27-1/3 days, and the tides only existing in the water of the ocean, and only a few feet high. This is the era we call "to-day."

The process does not stop here: still the stately march of events goes on; and the eye of Science strives to penetrate into the events of the future with the same clearness as it has been able to descry the events of the past. And what does it see? It will take too long to go into full detail: but I will shortly summarize the results. It sees this first—the day and the month both again equal, but both now about 1,400 hours long. Neither of these bodies rotating with respect to each other—the two as if joined by a bar—and total cessation of tide-generating action between them.

The date of this period is one hundred and fifty millions of years hence, but unless some unforeseen catastrophe intervenes, it must assuredly come. Yet neither will even this be the final stage; for the system is disturbed by the tide-generating force of the sun. It is a small effect, but it is cumulative; and gradually, by much slower degrees than anything we have yet contemplated, we are presented with a picture of the month getting gradually shorter than the day, the moon gradually approaching instead of receding, and so, incalculable myriads of ages hence, precipitating itself upon the surface of the earth whence it arose.

Such a catastrophe is already imminent in a neighbouring planet—Mars. Mars' principal moon circulates round him at an absurd pace, completing a revolution in 7-1/2 hours, and it is now only 4,000 miles from his surface. The planet rotates in twenty-four hours as we do; but its tides are following its moon more quickly than it rotates after them; they are therefore tending to increase its rate of spin, and to retard the revolution of the moon. Mars is therefore slowly but surely pulling its moon down on to itself, by a reverse action to that which separated our moon. The day shorter than the month forces a moon further away; the month shorter than the day tends to draw a satellite nearer.

This moon of Mars is not a large body: it is only twenty or thirty miles in diameter, but it weighs some forty billion tons, and will ultimately crash along the surface with a velocity of 8,000 miles an hour. Such a blow must produce the most astounding effects when it occurs, but I am unable to tell you its probable date.

So far we have dealt mainly with the earth and its moon; but is the existence of tides limited to these bodies? By no means. No body in the solar system is rigid, no body in the stellar universe is rigid. All must be susceptible of some tidal deformation, and hence, in all of them, agents like those we have traced in the history of the earth and moon must be at work: the motion of all must be complicated by the phenomena of tides. It is Prof. George Darwin who has worked out the astronomical influence of the tides, on the principles of Sir William Thomson: it is Sir Robert Ball who has extended Mr. Darwin's results to the past history of our own and other worlds.[32]

Tides are of course produced in the sun by the action of the planets, for the sun rotates in twenty-five days or thereabouts, while the planets revolve in much longer periods than that. The principal tide-generating bodies will be Venus and Jupiter; the greater nearness of one rather more than compensating for the greater mass of the other.

It may be interesting to tabulate the relative tide-producing powers of the planets on the sun. They are as follows, calling that of the earth 1,000:—

RELATIVE TIDE-PRODUCING POWERS OF THE PLANETS ON THE SUN.

Mercury 1,121 Venus 2,339 Earth 1,000 Mars 304 Jupiter 2,136 Saturn 1,033 Uranus 21 Neptune 9

The power of all of them is very feeble, and by acting on different sides they usually partly neutralize each other's action; but occasionally they get all on one side, and in that case some perceptible effect may be produced; the probable effect seems likely to be a gentle heaving tide in the solar surface, with breaking up of any incipient crust; and such an effect may be considered as evidenced periodically by the great increase in the number of solar spots which then break out.

The solar tides are, however, much too small to appreciably push any planet away, hence we are not to suppose that the planets originated by budding from the sun, in contradiction of the nebular hypothesis. Nor is it necessary to assume that the satellites, as a class, originated in the way ours did; though they may have done so. They were more probably secondary rings. Our moon differs from other satellites in being exceptionally large compared with the size of its primary; it is as big as some of the moons of Jupiter and Saturn. The earth is the only one of the small planets that has an appreciable moon, and hence there is nothing forced or unnatural in supposing that it may have had an exceptional history.

Evidently, however, tidal phenomena must be taken into consideration in any treatment of the solar system through enormous length of time, and it will probably play a large part in determining its future.

When Laplace and Lagrange investigated the question of the stability or instability of the solar system, they did so on the hypothesis that the bodies composing it were rigid. They reached a grand conclusion—that all the mutual perturbations of the solar system were periodic—that whatever changes were going on would reach a maximum and then begin to diminish; then increase again, then diminish, and so on. The system was stable, and its changes were merely like those of a swinging pendulum.

But this conclusion is not final. The hypothesis that the bodies are rigid is not strictly true: and directly tidal deformation is taken into consideration it is perceived to be a potent factor, able in the long run to upset all their calculations. But it is so utterly and inconceivably minute—it only produces an appreciable effect after millions of years—whereas the ordinary perturbations go through their swings in some hundred thousand years or so at the most. Granted it is small, but it is terribly persistent; and it always acts in one direction. Never does it cease: never does it begin to act oppositely and undo what it has done. It is like the perpetual dropping of water. There may be only one drop in a twelvemonth, but leave it long enough, and the hardest stone must be worn away at last.

* * * * *

We have been speaking of millions of years somewhat familiarly; but what, after all, is a million years that we should not speak familiarly of it? It is longer than our lifetime, it is true. To the ephemeral insects whose lifetime is an hour, a year might seem an awful period, the mid-day sun might seem an almost stationary body, the changes of the seasons would be unknown, everything but the most fleeting and rapid changes would appear permanent and at rest. Conversely, if our life-period embraced myriads of aeons, things which now seem permanent would then appear as in a perpetual state of flux. A continent would be sometimes dry, sometimes covered with ocean; the stars we now call fixed would be moving visibly before our eyes; the earth would be humming on its axis like a top, and the whole of human history might seem as fleeting as a cloud of breath on a mirror.

Evolution is always a slow process. To evolve such an animal as a greyhound from its remote ancestors, according to Mr. Darwin, needs immense tracts of time; and if the evolution of some feeble animal crawling on the surface of this planet is slow, shall the stately evolution of the planetary orbs themselves be hurried? It may be that we are able to trace the history of the solar system for some thousand million years or so; but for how much longer time must it not have a history—a history, and also a future—entirely beyond our ken?

Those who study the stars have impressed upon them the existence of the most immeasurable distances, which yet are swallowed up as nothing in the infinitude of space. No less are we compelled to recognize the existence of incalculable aeons of time, and yet to perceive that these are but as drops in the ocean of eternity.

FOOTNOTES:

[1] The following account of Mars's motion is from the excellent small manual of astronomy by Dr. Haughton of Trinity College, Dublin:—(P. 151) "Mars's motion is very unequal; when he first appears in the morning emerging from the rays of the sun, his motion is direct and rapid; it afterwards becomes slower, and he becomes stationary when at an elongation of 137 deg. from the sun; then his motion becomes retrograde, and its velocity increases until he is in opposition to the sun at 180 deg.; at this time the retrograde motion is most rapid, and afterwards diminishes until he is 137 deg. distant from the sun on the other side, when Mars again becomes stationary; his motion then becomes direct, and increases in velocity until it reaches a maximum, when the planet is again in conjunction with the sun. The retrograde motion of this planet lasts for 73 days: and its arc of retrogradation is 16 deg.."

[2] It is not so easy to plot the path of the sun among the stars by direct observation, as it is to plot the path of a planet; because sun and stars are not visible together. Hipparchus used the moon as an intermediary; since sun and moon are visible together, and also moon and stars.

[3] This is, however, by no means the whole of the matter. The motion is not a simple circle nor has it a readily specifiable period. There are several disturbing causes. All that is given here is a first rough approximation.

[4] The proof is easy, and ought to occur in books on solid geometry. By a "regular" solid is meant one with all its faces, edges, angles, &c., absolutely alike: it is of these perfectly symmetrical bodies that there are only five. Crystalline forms are practically infinite in number.

[5] Best known to us by his Christian name, as so many others of that time are known, e.g. Raphael Sanzio, Dante Alighieri, Michael Angelo Buonarotti. The rule is not universal. Tasso and Ariosto are surnames.

[6] It would seem that the fact that all bodies of every material tend to fall at the same rate is still not clearly known. Confusion is introduced by the resistance of the air. But a little thought should make it clear that the effect of the air is a mere disturbance, to be eliminated as far as possible, since the atmosphere has nothing to do with gravitation. The old fashioned "guinea and feather experiment" illustrates that in a vacuum things entirely different in specific gravity or surface drop at the same pace.

[7] Karl von Gebler (Galileo), p. 13.

[8] It is of course the "silver lining" of clouds that outside observers see.

[9] L.U.K., Life of Galileo, p. 26.

[10] Note added September, 1892. News from the Lick Observatory makes a very small fifth satellite not improbable.

[11] They remained there till this century. In 1835 they were quietly dropped.

[12] It was invented by van Helmont, a Belgian chemist, who died in 1644. He suggested two names gas and blas, and the first has survived. Blas was, I suppose, from blasen, to blow, and gas seems to be an attempt to get at the Sanskrit root underlying all such words as geist.

[13] Such as this, among many others:—The duration of a flame under different conditions is well worth determining. A spoonful of warm spirits of wine burnt 116 pulsations. The same spoonful of spirits of wine with addition of one-sixth saltpetre burnt 94 pulsations. With one-sixth common salt, 83; with one-sixth gunpowder, 110; a piece of wax in the middle of the spirit, 87; a piece of Kieselstein, 94; one-sixth water, 86; and with equal parts water, only 4 pulse-beats. This, says Liebig, is given as an example of a "licht-bringende Versuch."

[14] Draper, History of Civilization in Europe, vol. ii. p. 259.

[15] Professor Knight's series of Philosophical Classics.

[16] To explain why the entire system, horse and cart together, move forward, the forces acting on the ground must be attended to.

[17] The distance being proportional to the square of the time, see p. 82.

[18] The following letter, recently unearthed and published in Nature, May 12, 1881, seems to me well worth preserving. The feeling of a respiratory interval which it describes is familiar to students during the too few periods of really satisfactory occupation. The early guess concerning atmospheric electricity is typical of his extraordinary instinct for guessing right.

"LONDON, Dec. 15, 1716.

"DEAR DOCTOR,—He that in ye mine of knowledge deepest diggeth, hath, like every other miner, ye least breathing time, and must sometimes at least come to terr. alt. for air.

"In one of these respiratory intervals I now sit down to write to you, my friend.

"You ask me how, with so much study, I manage to retene my health. Ah, my dear doctor, you have a better opinion of your lazy friend than he hath of himself. Morpheous is my last companion; without 8 or 9 hours of him yr correspondent is not worth one scavenger's peruke. My practices did at ye first hurt my stomach, but now I eat heartily enou' as y' will see when I come down beside you.

"I have been much amused at ye singular [Greek: phenomena] resulting from bringing of a needle into contact with a piece of amber or resin fricated on silke clothe. Ye flame putteth me in mind of sheet lightning on a small—how very small—scale. But I shall in my epistles abjure Philosophy whereof when I come down to Sakly I'll give you enou'. I began to scrawl at 5 mins. from 9 of ye clk. and have in writing consmd. 10 mins. My Ld. Somerset is announced.

"Farewell, Gd. bless you and help yr sincere friend.

"ISAAC NEWTON.

"To DR. LAW, Suffolk."



[19] Kepler's laws may be called respectively, the law of path, the law of speed, and the relationship law. By the "mass" of a body is meant the number of pounds or tons in it: the amount of matter it contains. The idea is involved in the popular word "massive."

[20] The equation we have to verify is

4[pi]^2r^3 gR^2 = —————-, T^2

with the data that r, the moon's distance, is 60 times R, the earth's radius, which is 3,963 miles; while T, the time taken to complete the moon's orbit, is 27 days, 13 hours, 18 minutes, 37 seconds. Hence, suppose we calculate out g, the intensity of terrestrial gravity, from the above equation, we get

4[pi]^2 39.92 x 216000 x 3963 miles g = ————— x (60)^3R = ——————————————- T (27 days, 13 hours, &c.)^2

= 32.57 feet-per-second per second,

which is not far wrong.

[21] The two motions may be roughly compounded into a single motion, which for a few centuries may without much error be regarded as a conical revolution about a different axis with a different period; and Lieutenant-Colonel Drayson writes books emphasizing this simple fact, under the impression that it is a discovery.

[22] Members of the Accademia dei Lyncei, the famous old scientific Society established in the time of Cosmo de Medici—older than our own Royal Society.

[23] Newton suspected that the moon really did so oscillate, and so it may have done once; but any real or physical libration, if existing at all, is now extremely minute.

[24] An interesting picture in the New Gallery this year (1891), attempting to depict "Earth-rise in Moon-land," unfortunately errs in several particulars. First of all, the earth does not "rise," but is fixed relatively to each place on the moon; and two-fifths of the moon never sees it. Next, the earth would not look like a map of the world with a haze on its edge. Lastly, whatever animal remains the moon may contain would probably be rather in the form of fossils than of skeletons. The skeleton is of course intended as an image of death and desolation. It is a matter of taste: but a skeleton, it seems to me, speaks too recently of life to be as appallingly weird and desolate as a blank stone or ice landscape, unshaded by atmosphere or by any trace of animal or plant life, could be made.

[25] Five of Jupiter's revolutions occupy 21,663 days; two of Saturn's revolutions occupy 21,526 days.

[26] Excircularity is what is meant by this term. It is called "excentricity" because the foci (not the centre) of an ellipse are regarded as the representatives of the centre of a circle. Their distance from the centre, compared with the radius of the unflattened circle, is called the excentricity.

[27] A curve of the nth degree has 1/2n(n+3) arbitrary constants in its equation, hence this number of points specifically determine it. But special points, like focus or vertex, count as two ordinary ones. Hence three points plus the focus act as five points, and determine a conic or curve of the second degree. Three observations therefore fix an orbit round the sun.

[28] Its name suggests a measure of the diameter of the sun's disk, and this is one of its functions; but it can likewise measure planetary and other disks; and in general behaves as the most elaborate and expensive form of micrometer. The Koenigsberg instrument is shewn in fig. 92.

[29] It may be supposed that the terms "minute" and "second" have some necessary connection with time, but they are mere abbreviations for partes minutae and partes minutae secundae, and consequently may be applied to the subdivision of degrees just as properly as to the subdivision of hours. A "second" of arc means the 3600th part of a degree, just as a second of time means the 3600th part of an hour.

[30] A group of flying particles, each one invisible, obstructs light singularly little, even when they are close together, as one can tell by the transparency of showers and snowstorms. The opacity of haze may be due not merely to dust particles, but to little eddies set up by radiation above each particle, so that the air becomes turbulent and of varying density. (See a similar suggestion by Mr. Poynting in Nature, vol. 39, p. 323.)

[31] The moon ought to be watched during the next great shower, if the line of fire happens to take effect on a visible part of the dark portion.

[32] Address to Birmingham Midland Institute, "A Glimpse through the Corridors of Time."



INDEX

INDEX

A

Abbott, T.K., on tides, 369

Adams, John Couch, 193, 217, 302, 323, 324, 325, 327, 329, 330, 352, 385

Airy, Sir George, 193, 244, 302, 323, 324, 327, 367

Anaxagoras, 15

Appian, 218

Arabs, the, form a link between the old and new science, 9

Archimedes, 7, 8, 84, 87, 144, 177

Aristarchus, 34

Aristotle, 66, 69, 88, 94, 99, 167. He taught that the earth was a sphere, 16; his theories did not allow of the earth's motion, 34; he was regarded as inspired, 89

B

Bacon, Francis, 142, 143, 144, 145. His Novum Organum, 141

Bacon, Roger, 96, 139, 140. The herald of the dawn of science, 9

Brahe, George, uncle of Tycho Brahe, 39

Brahe, Steno, brother of Tycho Brahe, 39

Brahe, Tycho, 37, 39, 40, 44, 45, 49, 51, 53, 54, 55, 58, 63, 64, 65, 66, 68, 71, 72, 74, 75, 77, 78, 86, 94, 117, 137, 155, 165, 166, 200, 244, 281, 288. He tried to adopt the main features of the Copernican theory without admitting the motion of the earth, 37; he was a poor theorist but a great observer, 38; his medicine, 44; his personal history, 39, seq.; his observatory, Uraniburg, 47; his greatest invention, 50, note; his maniac Lep, 52; his kindness to Kepler, 63

Ball, Sir R., 391, 394; his Story of the Heavens, 377

Barrow, Dr., 165, 187

Bessel, 288, 310, 311, 313, 315, 316, 318, 323

Biela, 345, 346, 347

Bode's Law, 60, 296, 298, 299, 326

Boyle, 139, 188

Bradley, Prof. James, 233, 246, 247, 249, 252, 253, 308, 319

Bremiker, 328, 329

Brewster, on Kepler, 78

Brinkley, 308

Bruno, Giordano, 108, 127

C

Castelli, 112, 133

Cayley, Prof., 385

Challis, Prof., 328, 329

Clairut, 193, 216, 217, 219, 234, 341

Clark, Alvan and Sons, 316

Columbus, 9, 144

Copernicus, 7, 10, seq., 14, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 62, 66, 68, 70, 78, 93, 95, 100, 108, 111, 121, 122, 137, 155, 166, 223, 234, 247, 307; his De Revolutionibus Orbium Coelestium, 11, 75, 138; he proved that the earth went round the sun, 13; the influence of his theory on the Church, 13, seq.; his life-work summarised, 30; his Life by Mr. E.J.C. Morton, 31

Copernican tables, 40; Copernican theory, 59, 60, 125, 144, 167

Copernik, Nicolas; see Copernicus

Cornu, 238

Croll, Dr., his Climate and Time, 264

D

D'Alembert, 193, 234

Darwin, Charles, 134, 138, 397

Darwin, Prof. George, 367, 394

Delambre, 253

Descartes, 145, 146, 148, 151, 153, 156, 158, 164, 165, 167, 178, 181, 224, 227; his Discourse on Method, 142; his dream, 147; his system of algebraic geometry, 149, seq.; his doctrine of vortices, 151, seq.; his Principia Mathematica, 154; his Life by Mr. Mahaffy, 154

E

Earth, the difficulties in the way of believing that it moved, 34, seq.

"Earth-rise in Moon-land," 258, note

Encke, 345, 346

Epicyclic orbits explained, 23, seq.

Equinoxes, their precession discovered by Hipparchus, 27

Eudoxus, 19

Euler, 193, 234

F

Faraday, 84

Fizeau, 238, 239

Flamsteed, 215, 246, 284, 308, 319

Fraunhofer, 311

Froude, Prof.; his Oceania, 387

G

Galen, 87

Galileo, Galilei, 63, 75, 84, 88, 90, 92, 93, 97, 98, 101, 104, 106, 107, 108, 109, 110, 112, 114, 116, 117, 118, 120, 121, 122, 123, 125, 127, 133, 134, 137, 144, 145, 153, 154, 157, 165, 166, 167, 168, 177, 188, 200, 224, 227, 256, 281, 288, 309, 361; his youth, 85; his discovery of the pendulum, 86; his first observations about falling bodies, 88, seq.; he invents a telescope, 95; he adopts the Copernican theory, 94; he conceives "earth-shine," 100; he discovers Jupiter's moons, 103; he studies Saturn, 114, seq.; his Dialogues on the Ptolemaic and Copernican Systems, 124; his abjuration, 130; he becomes blind, 132; he discovered the Laws of Motion, 167, seq.; he guessed that sight was not instantaneous, 236, 237

Galle, Dr., 245, 329

Gauss, 299, 300

Gilbert, Dr., 139, 140, 157, 188; his De Magnete, 140, 144

Greeks, their scientific methods, 7

Groombridge's Catalogue, 315

H

Hadley, 185

Halley, 192, 193, 194, 195, 197, 215, 218, 219, 246, 258, 260, 261, 340, 341; he discovered the Principia, 194

Harvey, 144, 149

Haughton, Dr., 321; his manual on Astronomy, 21, note

Heliometer, described, 311

Helmholtz, 378

Helmont, Van, invented the word "gas," 141

Henderson, 310, 314

Herschel, Alexander, 275, 277, 278, 279

Herschel, Caroline, 275, 276, 279, 286, 345; her journal quoted, 277, seq.; her work with William H. described, 284

Herschel, Sir John, 283, 285, 327, 329

Herschel, William, 185, 234, 235, 244, 249, 274, 275, 280, 281, 282, 284, 288, 289, 290, 293, 295, 305, 309, 310, 318, 319, 327; he "sweeps" the heavens, 280; his discovery of Uranus, 281, 287; his artificial Saturn, 281, 282; his methods of work with his sister, described, 284; he founded the science of Astronomy, 287

Hind, 300

Hipparchus, 7, 18, 20, 27, 28, and note, 30, 40, 66, 223, 253; an explanation of his discovery of the precession of the equinoxes, 27, seq.

Hippocrates, 87

Homeric Cosmogony, 15, seq.

Hooke, 139, 188, 192, 193, 196, 197, 308

Hopital, Marquis de l', 228

Horkey, Martin, 106

Horrebow, 244

Huxley, Prof., 149

Huyghens, 86, 166, 185

K

Kant, 267, 270

Kelvin, Lord, see Thomson, Sir W.

Kepler, John, 59, 60, 63, 64, 65, 66, 70, 72, 73, 75, 77, 79, 84, 93, 94, 95, 104, 106, 107, 110, 122, 137, 145, 153, 158, 164, 165, 166, 167, 192, 200, 208, 209, 210, 211, 212, 214, 218, 224, 227, 253, 256, 259, 260, 262, 288, 295, 296, 332, 338, 361, 389; he replaced epicycles by an ellipse, 27; he was a pupil of Tycho Brahe, 54; he was a speculator more than an observer, 58; his personal life, 58, seq.; his theories about the numbers and distances of the planets, 60, 62; he was helped by Tycho, 63; his main work, 65, seq.; he gave up circular motion, 69; his Mysterium Cosmographicon, 105; his Laws, 71, 74, 173, 174, 176, 179, 180, 206, seq.

L

Lagrange, 193, 234, 255, 256, 257, 258, 263

Lagrange and Laplace, 258, 266, 395; they laid the foundations of the planetary theory, 259

Laplace, 68, 193, 218, 234, 255, 261, 262, 267, 268, 269, 270, 272, 288, 301, 317, 384, 385, 390; his nebular hypothesis, 267, 292; his Mecanique Celeste, 323

Lassell, Mr., 283, 284

Leibnitz, 192, 197, 233

Le Monnier, 319

Leonardo, see Vinci, Leonardo da

Leverrier, 193, 327, 328, 329, 330, 352

Lippershey, Hans, 95

M

Maskelyne, 281

Maxwell, Clerk, 302, 303

Molyneux, 248, 249

Morton, Mr. E.J. C, his Life of Copernicus, 31

N

Newton, Prof. H.A., 347

Newton, Sir Isaac, 7, 30, 79, 138, 139, 144, 145, 149, 153, 157, 158, 165, 166, 167, 174, 176, 184, 187, 188, 189, 191, 192, 194, 196, 198, 199, 201, 213, 216, 219, 220, 221, 224, 226, 227, 228, 233, 242, 253, 255, 256, 274, 288, 317, 340, 378; his Principia, 191, 192, 193, 194, 195, 196, 197, 207, 214, 216, 218, 228, 233, 242, 253; his early life, 161, seq.; his first experiments, 163; his work at Cambridge, 164; his Laws, 168; his application of the Laws of Gravity to Astronomy, 177, 178, 179, 185, 190; his reticence, 178; his discoveries in Optics, 181, seq.; his work summarised, 186; his Optics, 189; anecdotes of him, 191; his appearance in a Court of Justice, 195; some of his manuscripts very recently discovered, 217; his theories of the Equinoxes and tides, 223, seq., 225, 363, seq.

O

Olbers, 299, 300

P

Peters, Prof., 300, 316

Piazzi, 298, 299, 308, 313

Picard, 190, 242, 244, 247

Pioneers, genuine, 7

Planets and days of the week, 18

Poynting, 332

Printing, 9

Ptolemy, 18, 20, 27, 38, 153, 155, 166, 214; his system of the Heavens simplified by Copernicus, 11, 30; his system described, 19, seq.; his system taught, 34; his harmonies, 74

Pythagoras, 19, 20, 34

Q

Quadrant, an early, 42, 43

R

Rheiter, 107

Ricci, Ostillio, 86, 87

Roberts, Isaac, 268

Roemer, 239, 240, 242, 244, 249, 251, 308

Rosse, Lord, his telescope, 186, 268

Rudolphine tables, 65

S

Scheiner, 107

Sizzi, Francesca, an orthodox astronomer, 106

Snell, Willebrod, and the law of refraction, 65

Solar system, its fate, 265

Stars, a list of, 307

Struve, 308, 310, 311, 313

Stuart, Prof., quoted, 52

T

Tatius, 296

Telescopes, early, 96

Thales, 7, 140, 317

Thomson, Sir William, 367, 372, 373, 378, 394

Tide-gauge, described, 373, seq.

Tides, 354, seq.

Time, is not exactly uniform, 384

Torricelli, 133, 168

Tycho, see Brahe, Tycho

V

Vinci, Leonardo da, 9, 100, 144, 184

Viviani, 133, 168

Voltaire, 181

W

Watson, Prof., 300

Whewell, 227

Wren, Sir Christopher, 188, 192, 193, 197

Z

Zach, Von, 296, 299

Zone of Asteroids, 300, seq.

THE END.

RICHARD CLAY AND SONS, LIMITED, LONDON AND BUNGAY.