 Lecture 18. Tides are due to incomplete rigidity of bodies revolving around each other under the action of gravitation and at the same time spinning on their axes. Two spheres revolving around 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 hums with it, but the pull of the other body keeps them from moving much. Hence the rotation takes place against the 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 center 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 the 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 vibration, so that it turns always the same face towards us. Moreover, that its distance from the Earth is steadily increasing. This lasts the theory of Professor Darwin. Long ago the Moon must therefore have been much nearer the Earth, and the day much shorter. The tides were then far more violent. Having the distance would make them 8 times as high. Quartering it would increase them 64-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 around it in about 3 hours. If the Earth rotated on its axis in 3 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 around them more quickly than the planet rotates. Hence with them the process is inverted, and they must be approaching him and may someday crash along his surface. The inner Moon is now about 4,000 miles away, and revolves in 7 and a half. It appears to be about 20 miles in diameter, and weighs, therefore, if composed of rock, 40 billion tons. Mars rotates in 24 and a half hours. A similar fate may possibly await our Moon ages hence, by reason of the action of terrestrial tides produced by the Sun. 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 formed 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 to 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 gullies 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 coastline, eating away into the cliffs, undermining gradually and submerging acre after acre, and making with refuse a shingly or sandy or 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. Fingals 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 mercy, for instance. But few places are so favorably 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 20 feet vertically above mean level, now 20 feet below. Making all allowance for the power of winds and waves, currents, tides and water courses 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 30 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 30 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 100 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 the past times have been formed and denuded and reformed over and over again, we get an answer not in feed but in miles. The Laurentian and Huronian rocks of Canada constitute a stratum 10 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 in as much as the time allowable since the earth was cool enough for water to exist on it except as steam, not only 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 has been the privilege of astronomy and physics within the last 10 years to discover. To this discovery I now proceed to lead up. Our fundamental standard of time is the period of earth rotation, the length of a 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 didn't go with perfect uniformity it would seem a most difficult thing to discover its error and the most puzzling piece of knowledge to utilize when found. That it doesn't 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 Caldea is in very close accordance with the result of calculation. One of these famous old eclipses was observed in Babylon about 36 centuries ago and the Caldean 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 a lecture on Laplace. The orbit of the earth was at the 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 retodding force in action too. Laplace thought that this fact accounted for the whole of the discrepancy, but recently in 1853 Professor Adams reexamined 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 course has been allowed for amounts to about one hour. The eclipses 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 36 centuries amount to one hour and this according to the corrected Laplace 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 the solar eclipse 36 centuries ago was an hour late means that this place on earth's surface came into the shadow one hour behind time, that is had lagged one 24th part of a revolution. The earth therefore had lost this amount in the course of 3600 multiplied by 365 one quarter 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 worthwhile 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 instance 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 instance. The day after it will be going slower from the beginning at the rate of two instance a day. It will lose another instant on the fresh day's own account and it started three instance late. Hence the aggregate loss by the end of the third day is one plus two plus three equals six. By the end of the fourth day the whole loss will be one plus two plus three plus four and so on. Therefore by merely losing one instant every day the total loss in end days is one plus two plus three plus n instance which amounts to one half multiplied by n multiplied by n plus one instance or practically when n is big to one half n squared. Now in 36 centuries there have been 3600 multiplied by 365 one quarter 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 one half multiplied by 3600 multiplied by 365 instance which equals one hour. Hence 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 1300th part of a second in a century to about three seconds and in 36 centuries to an hour but even at the end of the 36 centuries the day is barely any longer. It is only 3600 multiplied by 365 instance that is 180th of a second longer than it was in the beginning and even the million years ago unless the rate of loss was different as it probably was the day would only be 35 minutes shorter though by that time the aggregate loss as measured by the apparent lateness of any perfectly punctual event record 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 used to be found in the tides. Remember that the tidal humps were produced as the prolateness of a sphere world around and around the fixed center like a football world by a strain these humps are pulled at by the moon and the earth rotates on its axis against this pole 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 at the balance of energy has to be made up to it or the tides would seize 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 friction break is applied winds and ocean currents have no such effect as mr frondi and oceana supposes they have because they are all accompanied by a precisely equal current somewhere else and no internal rearrangement of fluid can affect the motion of a mass as a whole but the tides are in a 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 doesn't 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 an operation but with 80 fold greater intensity on the moon it has seized 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 it 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 20 million years ago it must have been much shorter 50 million years ago it may have been only a few hours long the earth may have spun around then quite quickly but there is a limit if it spun too fast it would fly to pieces attached shot by means of wax to the whirling earth model figure 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 a non-stable 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 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 be 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 its 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 center hence by kepler's second law the rate of description of areas by its radius vector cannot be constant but must increase page 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 this matter though it serves well enough for the case of a ball world at the end of an elastic string after having got up the world the hand holding the string may remain almost fixed at the center 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 center the speed of the world 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 doesn't obey any of kepler's laws and so it doesn't obey the one which now concerns us this the third which practically states that the further a planet is from the center the slower it goes its velocity varies inversely with the square root of its distance c page 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've 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 center and therefore always pulling the moon the way it is going should retort it and that a retorting 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 sides 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 therefore a small change of distance will produce a great difference in the tide force the moon's present distance is 240 000 miles at a time when it was only 190 000 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 have then 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 it tied 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 neighborhood till it reached the high lands of derbyshire manchester would be a seaport then with the vengeance the day was shorter then and so the interval between tide and tide was more like 10 than 12 hours accordingly in about five hours all that massive water would have swept back again and great tracks 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 geologists required they're 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 portentious thickness and the only organism suspected in them is the doubtful euzoon candidates sir robert bowell believes and several geologists agree with them that the mighty tides we are contemplating may have been co-evil with this ancient lorencia formation and others of like nature with it but let us leave geology now and trace the inverted progress of events as we recede an imagination back through the geological era beyond into the deemed vista of the past when the moon was still closer and closer to the earth and was revolving around 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 have then revolved around the earth so as just to save itself from falling in must have gone around 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 around it in the same three hour period surely the two are connected surely the moon was 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 50 million years ago and quite possibly 100 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 80 times as big as the other the bigger one will now call earth the smaller we now call moon round and round the two bodies went pulling each other into tremendously elongated or prolete shapes and so they might have gone 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 geogenic 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 begin 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 geogenic 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 24 hours long the moon 240 000 miles distant revolving in 27 and 3 days and the tides only existing at the water of the ocean and only a few feet high this is the era we call today the process doesn't 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 describe 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 and both now about 1400 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 150 million 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 uncalculable myriads of ages hence precipitating itself upon the surface of the earth once it arose such a catastrophe is already imminent in a neighboring planet mars mars's principal moon circulates around them at an absurd pace completing a revolution of seven and a half hours and it is now only 4000 miles from his surface the planet rotates in 24 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 onto 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 20 or 30 miles in diameter but it weighs some 40 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'm unable to tell you its probable date so far we've dealt mainly with the earth and its moon but is the existence of tides limited to these bodies by no means nobody in the solar system is rigid nobody 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 professor george darwin who has worked out the astronomical influence of the tides on the principles of sir william thompson it is sir robert ball who has extended mr darwin's results to the past history of our own and other worlds tides are of course produced in the sun by the action of the planet for the sun rotates in the 25 days or thereabouts while the planets revolve in much longer periods than that the principle 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 one thousand mercury one thousand one hundred and twenty one venus two thousand three hundred thirty nine earth one thousand mars three hundred and four jupiter two thousand one hundred and thirty six saturn one thousand and thirty three uranus twenty one napkin nine 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 and 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's so utterly and inconceivably minute it only produces an appreciable effect after million 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 the 12 month 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 midday 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 eons things which now seem permanent would then appear as in perpetual state of flux a continent would be sometimes dry sometimes covered with ocean the stars will 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 did not have a history a history and also a future entirely beyond our kin 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 we are compelled to recognize the existence of uncalculable eons of time and yet to perceive that these are but as drops in the ocean of eternity end of lecture 18 recording by simon dexter and of pioneers of science by sir oliver lodge