Read Ebook: Time and Tide: A Romance of the Moon by Ball Robert S Robert Stawell

Font size: 10 px 15 px 20 px 25 px 30 px 35 px

Background color: BlackWhiteGrayLight GrayDark GrayDim Gray

Text color: BlackWhiteGrayLight GrayDark GrayDim Gray

Apply/Save settings

Ebook has 138 lines and 34987 words, and 3 pages

With reference to this Professor Darwin has offered an explanation, which seems so exceedingly plausible that it is impossible to resist the notion that it must be correct. I will ask you to think of the earth not as a solid body covered largely with ocean, but as a glowing globe of molten material. In a globe of this kind it is possible for great undulations to be set up. Here is a large vase of water, and by displacing it I can cause the water to undulate with a period which depends on the size of the vessel; undulations can be set up in a bucket of water, the period of these undulations being dependent upon the dimensions of the bucket. Similarly in a vast globe of molten material certain undulations could be set up, and those undulations would have a period depending upon the dimensions of this vibrating mass. We may conjecture a mode in which such vibrations could be originated. Imagine a thin shell of rigid material which just encases the globe; suppose this be divided into four quarters, like the four quarters of an orange, and that two of these opposite quarters be rejected, leaving two quarters on the liquid. Now suppose that these two quarters be suddenly pressed in, and then be as suddenly removed--they will produce depressions, of course, on the two opposite quarters, while the uncompressed quarters will become protuberant. In virtue of the mutual attractions between the different particles of the mass, an effort will be made to restore the globular form, but this will of course rather overshoot the mark; and therefore a series of undulations will be originated by which two opposite quarters of the sphere will alternately shrink in and become protuberant. There will be a particular period to this oscillation. For our globe it would appear to be somewhere about an hour and a half or two hours; but there is necessarily a good deal of uncertainty about this point.

We have seen how in those primitive days the earth was spinning around very rapidly; and I have also stated that the earth might at this very critical epoch of its history be compared with a grindstone which is being driven so rapidly that it is on the very brink of rupture. It is remarkable to note, that a cause tending to precipitate a rupture of the earth was at hand. The sun then raised tides in the earth as it does at present. When the earth revolved in a period of some four hours or thereabouts, the high tides caused by the sun succeeded each other at intervals of about two hours. When I speak of tides in this respect, of course I am not alluding to oceanic tides; these were the days long before ocean existed, at least in the liquid form. The tides I am speaking about were raised in the fluids and materials which then constituted the whole of the glowing earth; those tides rose and fell under the throb produced by the sun, just as truly as tides produced in an ordinary ocean. But now note the significant coincidence between the period of the throb produced by the sun-raised tides, and that natural period of vibration which belonged to our earth as a mass of molten material. It therefore follows, that the impulse given to the earth by the sun harmonized in time with that period in which the earth itself was disposed to oscillate. A well-known dynamical principle here comes into play. You see a heavy weight hanging by a string, and in my hand I hold a little slip of wood no heavier than a common pencil; ordinarily speaking, I might strike that heavy weight with this slip of wood, and no effect is produced; but if I take care to time the little blows that I give so that they shall harmonize with the vibrations which the weight is naturally disposed to make, then the effect of many small blows will be cumulative, so much so, that after a short time the weight begins to respond to my efforts, and now you see it has acquired a swing of very considerable amplitude. In Professor Fitzgerald's address to the British Association at Bath last autumn, he gives an account of those astounding experiments of Hertz, in which well-timed electrical impulses broke down an air resistance, and revealed to us ethereal vibrations which could never have been made manifest except by the principle we are here discussing. The ingenious conjecture has been made, that when the earth was thrown into tidal vibrations in those primeval days, these slight vibrations, harmonizing as they did with the natural period of the earth, gradually acquired amplitude; the result being that the pulse of each successive vibration increased at last to such an extent that the earth separated under the stress, and threw off a portion of those semi-fluid materials of which it was composed. In process of time these rejected portions contracted together, and ultimately formed that moon we now see. Such is the origin of the moon which the modern theory of tidal evolution has presented to our notice.

There are two great epochs in the evolution of the earth-moon system--two critical epochs which possess a unique dynamical significance; one of these periods was early in the beginning, while the other cannot arrive for countless ages yet to come. I am aware that in discussing this matter I am entering somewhat largely into mathematical principles; I must only endeavour to state the matter as succinctly as the subject will admit.

I must advert for a moment to the familiar conception of a maximum or a minimum. If a magnitude be increasing, that is, gradually growing greater and greater, it has obviously not attained a maximum so long as the growth is in progress. Nor if the object be actually decreasing can it be said to be at a maximum either; for then it was greater a second ago than it is now, and therefore it cannot be at a maximum at present. We may illustrate this by the familiar example of a stone thrown up into the air; at first it gradually rises, being higher at each instant than it was previously, until a culminating point is reached, when just for a moment the stone is poised at the summit of its path ere it commences its return to earth again. In this case the maximum point is obtained when the stone, having ceased to ascend, and not having yet commenced to descend, is momentarily at rest.

The same principles apply to the determination of a minimum. As long as the magnitude is declining the minimum has not been reached; it is only when the decline has ceased, and an increase is on the point of setting in, that the minimum can be said to be touched.

The earth-moon system contains at any moment a certain store of energy, and to every conceivable condition of the earth-moon system a certain quantity of energy is appropriate. It is instructive for us to study the different positions in which the earth and the moon might lie, and to examine the different quantities of energy which the system will contain in each of those varied positions. It is however to be understood that the different cases all presuppose the same total moment of momentum.

Among the different cases that can be imagined, those will be of special interest in which the total quantity of energy in the system is a maximum or a minimum. We must for this purpose suppose the system gradually to run through all conceivable changes, with the earth and moon as near as possible, and as far as possible, and in all intermediate positions; we must also attribute to the earth every variety in the velocity of its rotation which is compatible with the preservation of the moment of momentum. Beginning then with the earth's velocity of rotation at its lowest, we may suppose it gradually and continually increased, and, as we have already seen, the change in the energy of the system is to be expressed by multiplying the relative rotation into the change of the earth's angular velocity. It follows from the principles we have already explained, that the maximum or minimum energy is attained at the moment when the alteration is zero. It therefore follows, that the critical periods of the system will arise when the relative rotation is zero, that is, when the earth's rotation on its axis is performed with a velocity equal to that with which the moon revolves around the earth. This is truly a singular condition of the earth-moon system; the moon in such a case would revolve around the earth as if the two bodies were bound together by rigid bonds into what was practically a single solid body. At the present moment no doubt to some extent this condition is realized, because the moon always turns the same face to the earth ; but in the original condition of the earth-moon system, the earth would also constantly direct the same face to the moon, a condition of things which is now very far from being realized.

There is a fundamental difference between the dynamical conditions in these critical epochs--in one of them the energy of the system has attained a maximum value, and in the other the energy of the system is at a minimum value. It is impossible to over-estimate the significance of these two states of the system.

I may recall the fundamental notion which every one has learned in mechanics, as to the difference between stable and unstable equilibrium. The conceivable possibility of making an egg stand on its end is a practical impossibility, because nature does not like unstable equilibrium, and a body departs therefrom on the least disturbance; on the other hand, stable equilibrium is the position in which nature tends to place everything. A log of wood floating on a river might conceivably float in a vertical position with its end up out of the water, but you never could succeed in so balancing it, because no matter how carefully you adjusted the log, it would almost instantly turn over when you left it free; on the other hand, when the log floats naturally on the water it assumes a horizontal position, to which, when momentarily displaced therefrom, it will return if permitted to do so. We have here an illustration of the contrast between stable and unstable equilibrium. It will be found generally that a body is in equilibrium when its centre of gravity is at its highest point or at its lowest point; there is, however, this important difference, that when the centre of gravity is highest the equilibrium is unstable, and when the centre of gravity is lowest the equilibrium is stable. The potential energy of an egg poised on its end in unstable equilibrium is greater than when it lies on its side in stable equilibrium. In fact, energy must be expended to raise the egg from the horizontal position to the vertical; while, on the other hand, work could conceivably be done by the egg when it passes from the vertical position to the horizontal. Speaking generally, we may say that the stable position indicates low energy, while a redundancy of that valuable agent is suggestive of instability.

At that primitive epoch, when the energy of the earth-moon system was a maximum, the condition was one of dynamical instability; it was impossible that it should last. But now mark how truly critical an occurrence this must have been in the history of the earth-moon system, for have I not already explained that it is a necessary condition of the progress of tidal evolution that the energy of the system should be always declining? But here our retrospect has conducted us back to a most eventful crisis, in which the energy was a maximum, and therefore cannot have been immediately preceded by a state in which the energy was greater still; it is therefore impossible for the tidal evolution to have produced this state of things; some other influence must have been in operation at this beginning of the earth-moon system.

Thus there can be hardly a doubt that immediately preceding the critical epoch the moon originated from the earth in the way we have described. Note also that this condition, being one of maximum energy, was necessarily of dynamical instability, it could not last; the moon must adopt either of two courses--it must tumble back on the earth, or it must start outwards. Now which course was the moon to adopt? The case is analogous to that of an egg standing on its end--it will inevitably tumble one way or the other. Some infinitesimal cause will produce a tendency towards one side, and to that side accordingly the egg will fall. The earth-moon system was similarly in an unstable state, an infinitesimal cause might conceivably decide the fate of the system. We are necessarily in ignorance of what the determining cause might have been, but the effect it produced is perfectly clear; the moon did not again return to its mother earth, but set out on that mighty career which is in progress to-day.

Let it be noted that these critical epochs in the earth-moon history arise when and only when there is an absolute identity between the length of the month and the length of the day. It may be proper therefore that I should provide a demonstration of the fact, that the identity between these two periods must necessarily have occurred at a very early period in the evolution.

The law of Kepler, which asserts that the square of the periodic time is proportioned to the cube of the mean distance, is in its ordinary application confined to a comparison between the revolutions of the several planets about the sun. The periodic time of each planet is connected with its average distance by this law; but there is another application of Kepler's law which gives us information of the distance and the period of the moon in former stages of the earth-moon history. Although the actual path of the moon is of course an ellipse, yet that ellipse is troubled, as is well known, by many disturbing forces, and from this cause alone the actual path of the moon is far from being any of those simple curves with which we are so well acquainted. Even were the earth and the moon absolutely rigid particles, perturbations would work all sorts of small changes in the pliant curve. The phenomena of tidal evolution impart an additional element of complexity into the actual shape of the moon's path. We now see that the ellipse is not merely subject to incessant deflections of a periodic nature, it also undergoes a gradual contraction as we look back through time past; but we may, with all needful accuracy for our present purpose, think of the path of the moon as a circle, only we must attribute to that circle a continuous contraction of its radius the further and the further we look back. The alteration in the radius will be even so slow, that the moon will accomplish thousands of revolutions around the earth without any appreciable alteration in the average distance of the two bodies. We can therefore think of the moon as revolving at every epoch in a circle of special radius, and as accomplishing that revolution in a special time. With this understanding we can now apply Kepler's law to the several stages of the moon's past history. The periodic time of each revolution, and the mean distance at which that revolution was performed, will be always connected together by the formula of Kepler. Thus to take an instance in the very remote past. Let us suppose that the moon was at one hundred and twenty thousand miles instead of two hundred and forty thousand, that is, at half its present distance. Applying the law of Kepler, we see that the time of revolution must then have been only about ten days instead of the twenty-seven it is now. Still further, let us suppose that the moon revolves in an orbit with one-tenth of the diameter it has at present, then the cube of 10 being 1000, and the square root of 1000 being 31.6, it follows that the month must have been less than the thirty-first part of what it is at present, that is, it must have been considerably less than one of our present days. Thus you see the month is growing shorter and shorter the further we look back, the day is also growing shorter and shorter; but still I think we can show that there must have been a time when the month will have been at least as short as the day. For let us take the most extreme case in which the moon shall have made the closest possible approximation to the earth. Two globes in contact will have a distance between their centres which is equal to the sum of their radii. Take the earth as having a radius of four thousand miles, and the moon a radius of one thousand miles, the two centres must at their shortest distance be five thousand miles apart, that is, the moon must then be at the forty-eighth part of its present distance from the earth. Now the cube of 48 is 110,592, and the square root of 110,592 is nearly 333, therefore the length of the month will be one-three hundred and thirty-third part of the duration of the month at present; in other words, the moon must revolve around the earth in a period of somewhat about two hours. It seems impossible that the day can ever have been as brief as this. We have therefore proved that, in the course of its contracting duration, the moon must have overtaken the contracting day, and that therefore there must have been a time when the moon was in the vicinity of the earth, and having a day and month of equal period. Thus we have shown that the critical condition of dynamical instability must have occurred in the early period of the earth-moon history, if the agents then in operation were those which we now know. The further development of the subject must be postponed until the next lecture.

Starting from that fitting commencement of earth-moon history which the critical epoch affords, we shall now describe the dynamical phenomena as the tidal evolution progressed. The moon and the earth initially moved as a solid body, each bending the same face towards the other; but as the moon retreated, and as tides began to be raised on the earth, the length of the day began to increase, as did also the length of the month. We know, however, that the month increased more rapidly than the day, so that a time was reached when the month was twice as long as the day; and still both periods kept on increasing, but not at equal rates, for in progress of time the month grew so much more rapidly than the day, that many days had to elapse while the moon accomplished a single revolution. It is, however, only necessary for us to note those stages of the mighty progress which correspond to special events. The first of such stages was attained when the month assumed its maximum ratio to the day. At this time, the month was about twenty-nine days, and the epoch appears to have occurred at a comparatively recent date if we use such standards of time as tidal evolution requires; though measured by historical standards, the epoch is of incalculable antiquity. I cannot impress upon you too often the enormous magnitude of the period of time which these phenomena have required for their evolution. Professor Darwin's theory affords but little information on this point, and the utmost we can do is to assign a minor limit to the period through which tidal evolution has been in progress. It is certain that the birth of the moon must have occurred at least fifty million years ago, but probably the true period is enormously greater than this. If indeed we choose to add a cipher or two to the figure just printed, I do not think there is anything which could tell us that we have over-estimated the mark. Therefore, when I speak of the epoch in which the month possessed the greatest number of days as a recent one, it must be understood that I am merely speaking of events in relation to the order of tidal evolution. Viewed from this standpoint, we can show that the epoch is a recent one in the following manner. At present the month consists of a little more than twenty-seven days, but at this maximum period to which I have referred the month was about twenty-nine days; from that it began to decline, and the decline cannot have proceeded very far, for even still there are only two days less in the month than at the time when the month had the greatest number of days. It thus follows that the present epoch--the human epoch, as we may call it--in the history of the earth has fallen at a time when the progress of tidal evolution is about half-way between the initial and the final stage. I do not mean half-way in the sense of actual measurement of years; indeed, from this point it would seem that we cannot yet be nearly half-way, for, vast as are the periods of time that have elapsed since the moon first took its departure from the earth, they fall far short of that awful period of time which will intervene between the present moment and the hour when the next critical state of earth-moon history shall have been attained. In that state the day is destined once again to be equal to the month, just as was the case in the initial stage. The half-way stage will therefore in one sense be that in which the proportion of the month to the day culminates. This is the stage which we have but lately passed; and thus it is that at present we may be said to be almost half-way through the progress of tidal evolution.

My narrative of the earth-moon evolution must from this point forward cease to be retrospective. Having begun at that critical moment when the month and day were first equal, we have traced the progress of events to the present hour. What we have now to say is therefore a forecast of events yet to come. So far as we can tell, no agent is likely to interfere with the gradual evolution caused by the tides, which dynamical principles have disclosed to us. As the years roll on, or perhaps, I should rather say, as thousands of years and millions of years roll on, the day will continue to elongate, or the earth to rotate more slowly on its axis. But countless ages must elapse before another critical stage of the history shall be reached. It is needless for me to ponder over the tedious process by which this interesting epoch is reached. I shall rather sketch what the actual condition of our system will be when that moment shall have arrived. The day will then have expanded from the present familiar twenty-four hours up to a day more than twice, more than five, even more than fifty times its present duration. In round numbers, we may say that this great day will occupy one thousand four hundred of our ordinary hours. To realize the critical nature of the situation then arrived at, we must follow the corresponding evolution through which the moon passes. From its present distance of two hundred and forty thousand miles, the moon will describe an ever-enlarging orbit; and as it does so the duration of the month will also increase, until at last a point will be reached when the month has become more than double its present length, and has attained the particular value of one thousand four hundred hours. We are specially to observe that this one-thousand four-hundred-hour month will be exactly reached when the day has also expanded to one thousand four hundred hours; and the essence of this critical condition, which may be regarded as a significant point of tidal evolution, is that the day and the month have again become equal. The day and the month were equal at the beginning, the day and the month will be equal at the end. Yet how wide is the difference between the beginning and the end. The day or the month at the end is some hundreds of times as long as the month or the day at the beginning.

I have already fully explained how, in any stage of the evolutionary progress in which the day and the month became equal, the energy of the system attained a maximum or a minimum value. At the beginning the energy was a maximum; at the end the energy will be a minimum. The most important consequences follow from this consideration. I have already shown that a condition of maximum energy corresponded to dynamic instability. Thus we saw that the earth-moon history could not have commenced without the intervention of some influence other than tides at the beginning. Now let us learn what the similar doctrine has to tell us with regard to the end. The condition then arrived at is one of dynamical stability; for suppose that the system were to receive a slight alteration, by which the moon went out a little further, and thus described a larger orbit, and so performed more than its share of the moment of spin. Then the earth would have to do a little less spinning, because, under all circumstances, the total quantity of spin must be preserved unaltered. But the energy being at a minimum, such a small displacement must of course produce a state of things in which the energy would be increased. Or if we conceived the moon to come in towards the earth, the moon would then contribute less to the total moment of momentum. It would therefore be incumbent on the earth to do more; and accordingly the velocity of the earth's rotation would be augmented. But this arrangement also could only be produced by the addition of some fresh energy to the system, because the position from which the system is supposed to have been disturbed is one of minimum energy.

No disturbance of the system from this final position is therefore conceivable, unless some energy can be communicated to it. But this will demonstrate the utter incompetency of the tides to shift the system by a hair's breadth from this position; for it is of the essence of the tides to waste energy by friction. And the transformations of the system which the tides have caused are invariably characterized by a decline of energy, the movements being otherwise arranged so that the total moment of momentum shall be preserved intact. Note, how far we were justified in speaking of this condition as a final one. It is final so far as the lunar tides are concerned; and were the system to be screened from all outer interference, this accommodation between the earth and the moon would be eternal.

There is indeed another way of demonstrating that a condition of the system in which the day has assumed equality with the month must necessarily be one of dynamical equilibrium. We have shown that the energy which the tides demand is derived not from the mere fact that there are high tides and low tides, but from the circumstance that these tides do rise and fall; that in falling and rising they do produce currents; and it is these currents which generate the friction by which the earth's velocity is slowly abated, its energy wasted, and no doubt ultimately dissipated as heat. If therefore we can make the ebbing and the flowing of the tides to cease, then our argument will disappear. Thus suppose, for the sake of illustration, that at a moment when the tides happened to be at high water in the Thames, such a change took place in the behaviour of the moon that the water always remained full in the Thames, and at every other spot on the earth remained fixed at the exact height which it possessed at this particular moment. There would be no more tidal friction, and therefore the system would cease to course through that series of changes which the existence of tidal friction necessitates.

But if the tide is always to be full in the Thames, then the moon must be always in the same position with respect to the meridian, that is, the moon must always be fixed in the heavens over London. In fact, the moon must then revolve around the earth just as fast as London does--the month must have the same length as the day. The earth must then show the same face constantly to the moon, just as the moon always does show the same face towards the earth; the two globes will in fact revolve as if they were connected with invisible bonds, which united them into a single rigid body.

We need therefore feel no surprise at the cessation of the progress of tidal evolution when the month and the day are equal, for then the movement of moon-raised tides has ceased. No doubt the same may be said of the state at the beginning of the history, when the day and the month had the brief and equal duration of a few hours. While the equality of the two periods lasted there could be no tides, and therefore no progress in the direction of tidal evolution. There is, however, the profound difference of stability and instability between the two cases; the most insignificant disturbance of the system at the initial stage was sufficient to precipitate the revolving moon from its condition of dynamical equilibrium, and to start the course of tidal evolution in full vigour. If, however, any trifling derangement should take place in the last condition of the system, so that the month and the day departed slightly from equality, there would instantly be an ebbing and a flowing of the tides; and the friction generated by these tides would operate to restore the equality because this condition is one of dynamical stability.

It will thus be seen with what justice we can look forward to the day and month each of fourteen hundred hours as a finale to the progress of the luni-tidal evolution. Throughout the whole of this marvellous series of changes it is always necessary to remember the one constant and invariable element--the moment of momentum of the system which tides cannot alter. Whatever else the friction can have done, however fearful may have been the loss of energy by the system, the moment of momentum which the system had at the beginning it preserves unto the end. This it is which chiefly gives us the numerical data on which we have to rely for the quantitative features of tidal evolution.

We have made so many demands in the course of these lectures on the capacity of tidal friction to accomplish startling phenomena in the evolution of the earth-moon system, that it is well for us to seek for any evidence that may otherwise be obtainable as to the capacity of tides for the accomplishment of gigantic operations. I do not say that there is any doubt which requires to be dispelled by such evidence, for as to the general outlines of the doctrine of tidal evolution which has been here sketched out there can be no reasonable ground for mistrust; but nevertheless it is always desirable to widen our comprehension of any natural phenomena by observing collateral facts. Now there is one branch of tidal action to which I have as yet only in the most incidental way referred. We have been speaking of the tides in the earth which are made to ebb and flow by the action of the moon; we have now to consider the tides in the moon, which are there excited by the action of the earth. For between these two bodies there is a reciprocity of tidal-making energy--each of them is competent to raise tides in the other. As the moon is so small in comparison with the earth, and as the tides on the moon are of but little significance in the progress of tidal evolution, it has been permissible for us to omit them from our former discussion. But it is these tides on the moon which will afford us a striking illustration of the competency of tides for stupendous tasks. The moon presents a monument to show what tides are able to accomplish.

I must first, however, explain a difficulty which is almost sure to suggest itself when we speak of tides on the moon. I shall be told that the moon contains no water on its surface, and how then, it will be said, can tides ebb and flow where there is no sea to be disturbed? There are two answers to this difficulty; it is no doubt true that the moon seems at present entirely devoid of water in so far as its surface is exposed to us, but it is by no means certain that the moon was always in this destitute condition. There are very large features marked on its map as "seas"; these regions are of a darker hue than the rest of the moon's surface, they are large objects often many hundreds of miles in diameter, and they form, in fact, those dark patches on the brilliant surface which are conspicuous to the unaided eye, and are represented in Fig. 3. Viewed in a telescope these so-called seas, while clearly possessing no water at the present time, are yet widely different from the general aspect of the moon's surface. It has often been supposed that great oceans once filled these basins, and a plausible explanation has even been offered as to how the waters they once contained could have vanished. It has been thought that as the mineral substances deep in the interior of our satellite assumed the crystalline form during the progress of cooling, the demand for water of crystallization required for incorporation with the minerals was so great that the oceans of the moon became entirely absorbed. It is, however, unnecessary for our present argument that this theory should be correct. Even if there never was a drop of water found on our satellite, the tides in its molten materials would be quite sufficient for our purpose; anything that tides could accomplish would be done more speedily by vast tides of flowing lava than by merely oceanic tides.

There can be no doubt that tides raised on the moon by the earth would be greater than the tides raised on the earth by the moon. The question is, however, not a very simple one, for it depends on the masses of both bodies as well as on their relative dimensions. In so far as the masses are concerned, the earth being more than eighty times as heavy as the moon, the tides would on this account be vastly larger on the moon than on the earth. On the other hand, the moon's diameter being much less than that of the earth, the efficiency of a tide-producing body in its action on the moon would be less than that of the same body at the same distance in its action on the earth; but the diminution of the tides from this cause would be not so great as their increase from the former cause, and therefore the net result would be to exhibit much greater tides on the moon than on the earth.

Suppose that the moon had been originally endowed with a rapid movement of rotation around its axis, the effect of the tides on that rotation would tend to check its velocity just in the same way as the tides on the earth have effected a continual elongation of the day. Only as the tides on the moon were so enormously great, their capacity to check the moon's speed would have corresponding efficacy. In addition to this, the mass of the moon being so small, it could only offer feeble resistance to the unceasing action of the tide, and therefore our satellite must succumb to whatever the tides desired ages before our earth would have been affected to a like extent. It must be noticed that the influence of the tidal friction is not directed to the total annihilation of the rotation of the two bodies affected by it; the velocity is only checked down until it attains such a point that the speed in which each body rotates upon its axis has become equal to that in which it revolves around the tide-producer. The practical effect of such an adjustment is to make the tide-agitated body turn a constant face towards its tormentor.

I may here note a point about which people sometimes find a little difficulty. The moon constantly turns the same face towards the earth, and therefore people are sometimes apt to think that the moon performs no rotation whatever around its own axis. But this is indeed not the case. The true inference to be drawn from the constant face of the moon is, that the velocity of rotation about its own axis is equal to that of its rotation around the earth; in fact, the moon revolves around the earth in twenty-seven days, and its rotation about its axis is performed in twenty-seven days also. You may illustrate the movement of the moon around the earth by walking around a table in a room, keeping all the time your face turned towards the table; in such a case as this you not only perform a motion of revolution, but you also perform a rotation in an equal period. The proof that you do rotate is to be found in the fact that during the movement your face is being directed successively to all the points of the compass. There is no more singular fact in the solar system than the constancy of the moon's face to the earth. The periods of rotation and revolution are both alike; if one of these periods exceeded the other by an amount so small as the hundredth part of a second, the moon would in the lapse of ages permit us to see that other side which is now so jealously concealed. The marvellous coincidence between these two periods would be absolutely inexplicable, unless we were able to assign it to some physical cause. It must be remembered that in this matter the moon occupies a unique position among the heavenly host. The sun revolves around on its axis in a period of twenty-five or twenty-six days--thus we see one side of the sun as frequently as we see the other. The side of the sun which is turned towards us to-day is almost entirely different from that we saw a fortnight ago. Nor is the period of the sun's rotation to be identified with any other remarkable period in our system. If it were equal to the length of the year, for instance, or if it were equal to the period of any of the other planets, then it could hardly be contended that the phenomenon as presented by the moon was unique; but the sun's period is not simply related, or indeed related at all, to any of the other periodic times in the system. Nor do we find anything like the moon's constancy of face in the behaviour of the other planets. Jupiter turns now one face to us and then another. Nor is his rotation related to the sun or related to any other body, as our moon's motion is related to us. It has indeed been thought that in the movements of the satellites of Jupiter a somewhat similar phenomenon may be observed to that in the motion of our own satellite. If this be so, the causes whereby this phenomenon is produced are doubtless identical in the two cases.

So remarkable a coincidence as that which the moon's motion shows could not reasonably be explained as a mere fortuitous circumstance; nor need we hesitate to admit that a physical explanation is required when we find a most satisfactory one ready for our acceptance, as was originally pointed out by Helmholtz.

There can be no doubt whatever that the constancy of the moon's face is the work of ancient tides, which have long since ceased to act. We have shown that if the moon's rotation had once been too rapid to permit of the same face being always directed towards us, the tides would operate as a check by which the velocity of that rotation would be abated. On the other hand, if the moon rotated so slowly that its other face would be exposed to us in the course of the revolution, the tides would then be dragged violently over its surface in the direction of its rotation; their tendency would thus be to accelerate the speed until the angular velocity of rotation was equal to that of revolution. Thus the tides would act as a controlling agent of the utmost stringency to hurry the moon round when it was not turning fast enough, and to arrest the motion when going too fast. Peace there would be none for the moon until it yielded absolute compliance to the tyranny of the tides, and adjusted its period of rotation with exact identity to its period of revolution. Doubtless this adjustment was made countless ages ago, and since that period the tides have acted so as to preserve the adjustment, as long as any part of the moon was in a state sufficiently soft or fluid to respond to tidal impression. The present state of the moon is a monument to which we may confidently appeal in support of our contention as to the great power of the tides during the ages which have passed; it will serve as an illustration of the future which is reserved for our earth in ages yet to come, when our globe shall have also succumbed to tidal influence.

It is owing to the smallness of the moon relatively to the earth that the tidal process has reached a much more advanced stage in the moon than it has on the earth; but the moon is incessant in its efforts to bring the earth into the same condition which it has itself been forced to assume. Thus again we look forward to an epoch in the inconceivably remote future when tidal thraldom shall be supreme, and when the earth shall turn the same face to the moon, as the moon now turns the same face to the earth.

In the critical state of things thus looming in the dim future, the earth and the moon will continue to perform this adjusted revolution in a period of about fourteen hundred hours, the two bodies being held, as it were, by invisible bands. Such an arrangement might be eternal if there were no intrusion of tidal influence from any other body; but of course in our system as we actually find it the sun produces tides as well as the moon; and the solar tides being at present much less than those originated by the moon, we have neglected them in the general outlines of the theory. The solar tides, however, must necessarily have an increasing significance. I do not mean that they will intrinsically increase, for there seems no reason to apprehend any growth in their actual amount; it is their relative importance to the lunar tides that is the augmenting quantity. As the final state is being approached, and as the velocity of the earth's rotation is approximating to the angular velocity with which the moon revolves around it, the ebbing and the flowing of the lunar tides must become of evanescent importance; and this indeed for a double reason, partly on account of the moon's greatly augmented distance, and partly on account of the increasing length of the lunar day, and the extremely tardy movements of ebb and flow that the lunar tides will then have. Thus the lunar tides, so far as their dynamical importance is concerned, will ultimately become zero, while the solar tides retain all their pristine efficiency.

Thus the doctrine of tidal evolution has conducted us to a prospect of a condition of things which will some time be reached, when the moon will have receded to a distance in which the month shall have become about fifty-seven days, and when the earth around which this moon revolves shall actually require a still longer period to accomplish its rotation on its axis. Here is an odd condition for a planet with its satellite; indeed, until a dozen years ago it would have been pronounced inconceivable that a moon should whirl round a planet so quickly that its journey was accomplished in less than one of the planet's own days. Arguments might be found to show that this was impossible, or at least unprecedented. There is our own moon, which now takes twenty-seven days to go round the earth; there is Jupiter, with four moons, and the nearest of these to the primary goes round in forty-two and a half hours. No doubt this is a very rapid motion; but all those matters are much more lively with Jupiter than they are here. The giant planet himself does not need ten hours for a single rotation, so that you see his nearest moon still takes between two and three Jovian days to accomplish a single revolution. The example of Saturn might have been cited to show that the quickest revolution that any satellite could perform must still require at least twice as long as the day in which the planet performed its rotation. Nor could the rotation of the planets around the sun afford a case which could be cited. For even Mercury, the nearest of all the planets to the sun of which the existence is certainly known, and therefore the most rapid in its revolution, requires eighty-eight days to get round once; and in the mean time the sun has had time to accomplish between three and four rotations. Indeed, the analogies would seem to have shown so great an improbability in the conclusion towards which tidal evolution points, that they would have contributed a serious obstacle to the general acceptance of that theory.

But in 1877 an event took place so interesting in astronomical history, that we have to look back to the memorable discovery of Uranus in 1781 before we can find a parallel to it in importance. Mars had always been looked upon as one of the moonless planets, though grounds were not wanting for the surmise that probably moons to Mars really existed. It was under the influence of this belief that an attempt was made by Professor Asaph Hall at Washington to make a determined search, and see if Mars might not be attended by satellites large enough to be discoverable. The circumstances under which this memorable inquiry was undertaken were eminently favourable for its success. The orbit of Mars is one which possesses an exceptionally high eccentricity; it consequently happens that the oppositions during which the planet is to be observed vary very greatly in the facilities they afford for a search like that contemplated by Professor Hall. It is obviously advantageous that the planet should be situated as near as possible to the earth, and in the opposition in 1877 the distance was almost at the lowest point it is capable of attaining; but this was not the only point in which Professor Hall was favoured; he had the use of a telescope of magnificent proportions and of consummate optical perfection. His observatory was also placed in Washington, so that he had the advantage of a pure sky and of a much lower latitude than any observatory in Great Britain is placed at. But the most conspicuous advantage of all was the practised skill of the astronomer himself, without which all these other advantages would have been but of little avail. Great success rewarded his well-designed efforts; not alone was one satellite discovered which revolved around the planet in a period conformable with that of other similar cases, but a second little satellite was found, which accomplished its revolution in a wholly unexpected and unprecedented manner. The day of Mars himself, that is, the period in which he can accomplish a rotation around his axis, very closely approximates to our own day, being in fact half an hour longer. This little satellite, the inner and more rapid of the pair, requires for a single revolution a period of only seven hours thirty-nine minutes, that is to say, the little body scampers more than three times round its primary before the primary itself has finished one of its leisurely rotations. Here was indeed a striking fact, a unique fact in our system, which riveted the attention of astronomers on this most beautiful discovery.

You will now see the bearing which the movement of the inner satellite of Mars has on the doctrine of tidal evolution. As a legitimate consequence of that doctrine, we came to the conclusion that our earth-moon system must ultimately attain a condition in which the day is longer than the month. But this conclusion stood unsupported by any analogous facts in the more anciently-known truths of astronomy. The movement of the satellite of Mars, however, affords the precise illustration we want; and this fact, I think, adds an additional significance to the interest and the beauty of Professor Hall's discovery.

It is of particular interest to investigate the possible connection which the phenomena of tidal evolution may have had in connection with the geological phenomena of the earth. We have already pointed out the greater closeness of the moon to us in times past. The tides raised by the moon on the earth must therefore have been greater in past ages than they are now, for of course the nearer the moon the bigger the tide. As soon as the earth and the moon had separated to a considerable distance we may say that the height of the tide will vary inversely as the cube of the moon's distance; it will therefore happen, that when the moon was at half its present distance from us, his tide-producing capacity was not alone twice as much or four times as much, but even eight times as much as it is at present; and a much greater rate of tidal rise and fall indicates, of course, a preponderance in every other manifestation of tidal activity. The tidal currents, for instance, must have been much greater in volume and in speed; even now there are places in which the tidal currents flow at four or more miles per hour. We can imagine, therefore, the vehemence of the tidal currents which must have flowed in those days when the moon was a much smaller distance from us. It is interesting to view these considerations in their possible bearings on geological phenomena. It is true that we have here many elements of uncertainty, but there is, however, a certain general outline of facts which may be laid down, and which appears to be instructive, with reference to the past history of our earth.

I have all through these lectures indicated a mighty system of chronology for the earth-moon system. It is true that we cannot give our chronology any accurate expression in years. The various stages of this history are to be represented by the successive distances between the earth and the moon. Each successive epoch, for instance, may be marked by the number of thousands of miles which separate the moon from the earth.

But we have another system of chronology derived from a wholly different system of ideas; it too relates to periods of vast duration, and, like our great tidal periods, extends to times anterior to human history, or even to the duration of human life on this globe. The facts of geology open up to us a majestic chronology, the epochs of which are familiar to us by the succession of strata forming the crust of the earth, and by the succession of living beings whose remains these strata have preserved. From the present or recent age our retrospect over geological chronology leads us to look through a vista embracing periods of time overwhelming in their duration, until at last our view becomes lost, and our imagination is baffled in the effort to comprehend the formation of those vast stratified rocks, a dozen miles or more in thickness, which seem to lie at the very base of the stratified system on the earth, and in which it would appear that the dawnings of life on this globe may be almost discerned. We have thus the two systems of chronology to compare--one, the astronomical chronology measured by the successive stages in the gradual retreat of the moon; the other, the geological chronology measured by the successive strata constituting the earth's crust. Never was a more noble problem proposed in the physical history of our earth than that which is implied in the attempt to correlate these two systems of chronology. What we would especially desire to know is the moon's distance which corresponds to each of the successive strata on the earth. How far off, for instance, was that moon which looked down on the coal forests in the time of their greatest luxuriance? or what was the apparent size of the full moon at which the ichthyosaurus could have peeped when he turned that wonderful eye of his to the sky on a fine evening? But interesting as this great problem is, it lies, alas! outside the possibility of exact solution. Indeed we shall not make any attempt which must necessarily be futile to correlate these chronologies; all we can do is to state the one fact which is absolutely undeniable in the matter.

Let us fix our attention on that specially interesting epoch at the dawn of geological time, when those mighty Laurentian rocks were deposited of which the thickness is so astounding, and let us consider what the distance of the moon must have been at this initial epoch of the earth's history. All we know for certain is, that the moon must have been nearer, but what proportion that distance bore to the present distance is necessarily quite uncertain. Some years ago I delivered a lecture at Birmingham, entitled "A Glimpse through the Corridors of Time," and in that lecture I threw out the suggestion that the moon at this primeval epoch may have only been at a small fraction of its present distance from us, and that consequently terrific tides may in these days have ravaged the coast. There was a good deal of discussion on the subject, and while it was universally admitted that the tides must have been larger in palaeozoic times than they are at present, yet there was a considerable body of opinion to the effect that the tides even then may have been only about twice, or possibly not so much, greater than those tides we have at the present. What the actual fact may be we have no way of knowing; but it is interesting to note that even the smallest accession to the tides would be a valuable factor in the performance of geological work.

For let me recall to your minds a few of the fundamental phenomena of geology. Those stratified rocks with which we are now concerned have been chiefly manufactured by deposition of sediment in the ocean. Rivers, swollen, it may be, by floods, and turbid with a quantity of material held in suspension, discharge their waters into the sea. Granting time and quiet, this sediment falls to the bottom; successive additions are made to its thickness during centuries and thousands of years, and thus beds are formed which in the course of ages consolidate into actual rock. In the formation of such beds the tides will play a part. Into the estuaries at the mouths of rivers the tides hurry in and hurry out, and especially during spring tides there are currents which flow with tremendous power; then too, as the waves batter against the coast they gradually wear away and crumble down the mightiest cliffs, and waft the sand and mud thus produced to augment that which has been brought down by the rivers. In this operation also the tides play a part of conspicuous importance, and where the ebb and flow is greatest it is obvious that an additional impetus will be given to the manufacture of stratified rocks. In fact, we may regard the waters of the globe as a mighty mill, incessantly occupied in grinding up materials for future strata. The main operating power of this mill is of course derived from the sun, for it is the sun which brings up the rains to nourish the rivers, it is the sun which raises the wind which lashes the waves against the shore. But there is an auxiliary power to keep the mill in motion, and that auxiliary power is afforded by the tides. If then we find that by any cause the efficiency of the tides is increased we shall find that the mill for the manufacture of strata obtains a corresponding accession to its capacity. Assuming the estimate of Professor Darwin, that the tide may have had twice as great a vertical range of ebb and flow within geological times as it has at present, we find a considerable addition to the efficiency of the ocean in the manufacture of the ancient stratified rocks. It must be remembered that the extent of the area through which the tides will submerge and lay bare the country, will often be increased more than twofold by a twofold increase of height. A little illustration may show what I mean. Suppose a cone to be filled with water up to a certain height, and that the quantity of water in it be measured; now let the cone be filled until the water is at double the depth; then the surfaces of the water in the two cases will be in the ratio of the circles, one of which has double the diameter of the other. The areas of the two surfaces are thus as four to one; the volumes of the waters in the two cases will be in the proportion of two similar solids, the ratios of their dimensions being as two to one. Of course this means that the water in the one case would be eight times as much as in the other. This particular illustration will not often apply exactly to tidal phenomena, but I may mention one place that I happen to know of, in the vicinity of Dublin, in which the effect of the rise and fall of the tide would be somewhat of this description. At Malahide there is a wide shallow estuary cut off from the sea by a railway embankment, and there is a viaduct in the embankment through which a great tidal current flows in and out alternately. At low tide there is but little water in this estuary, but at high tide it extends for miles inland. We may regard this inlet with sufficient approximation to the truth as half of a cone with a very large angle, the railway embankment of course forming the diameter; hence it follows that if the tide was to be raised to double its height, so large an area of additional land would be submerged, and so vast an increase of water would be necessary for the purpose, that the flow under the railway bridge would have to be much more considerable than it is at present. In some degree the same phenomena will be repeated elsewhere around the coast. Simply multiplying the height of the tide by two would often mean that the border of land between high and low water would be increased more than twofold, and that the volume of water alternately poured on the land and drawn off it would be increased in a still larger proportion. The velocity of all tidal currents would also be greater than at present, and as the power of a current of water for transporting solid material held in suspension increases rapidly with the velocity, so we may infer that the efficiency of tidal currents as a vehicle for the transport of comminuted rocks would be greatly increased. It is thus obvious that tides with a rise and fall double in vertical height of those which we know at present would add a large increase to their efficiency as geological agents. Indeed, even were the tides only half or one-third greater than those we know now, we might reasonably expect that the manufacture of stratified rocks must have proceeded more rapidly than at present.

The question then will assume this form. We know that the tides must have been greater in Cambrian or Laurentian days than they are at present; so that they were available as a means of assisting other agents in the stupendous operations of strata manufacture which were then conducted. This certainly helps us to understand how these tremendous beds of strata, a dozen miles or more in solid thickness, were deposited. It seems imperative that for the accomplishment of a task so mighty, some agents more potent than those with which we are familiar should be required. The doctrine of tidal evolution has shown us what those agents were. It only leaves us uninformed as to the degree in which their mighty capabilities were drawn upon.

It is the property of science as it grows to find its branches more and more interwoven, and this seems especially true of the two greatest of all natural sciences--geology and astronomy. With the beginnings of our earth as a globe in the shape in which we find it both these sciences are directly concerned. I have here touched upon another branch in which they illustrate and confirm each other.

As the theory of tidal evolution has shed such a flood of light into the previously dark history of our earth-moon system, it becomes of interest to see whether the tidal phenomena may not have a wider scope; whether they may not, for instance, have determined the formation of the planets by birth from the sun, just as the moon seems to have originated by birth from the earth. Our first presumption, that the cases are analogous, is not however justified when the facts are carefully inquired into. A principle which I have not hitherto discussed here assumes prominence, and therefore we shall devote our attention to it for a few minutes.

Let us understand what we mean by the solar system. There is first the sun at the centre, which preponderates over all the other bodies so enormously, as shown in Fig. 4, in which the earth and the sun are placed side by side for comparison. There is then the retinue of planets, among the smaller of which our earth takes its place, a view of the comparative sizes of the planets being shown in Fig. 5.

Not to embarrass ourselves with the perplexities of a problem so complicated as our solar system is in its entirety, we shall for the sake of clear reasoning assume an ideal system, consisting of a sun and a large planet--in fact, such as our own system would be if we could withdraw from it all other bodies, leaving the sun and Jupiter only remaining. We shall suppose, of course, that the sun is much larger than the planet, in fact, it will be convenient to keep in mind the relative masses of the sun and Jupiter, the weight of the planet being less than one-thousandth part of the sun. We know, of course, that both of those bodies are rotating upon their axes, and the one is revolving around the other; and for simplicity we may further suppose that the axes of rotation are perpendicular to the plane of revolution. In bodies so constituted tides will be manifested. Jupiter will raise tides in the sun, the sun will raise tides in Jupiter. If the rotation of each body be performed in a less period than that of the revolution , then the tides will immediately operate in their habitual manner as a brake for the checking of rotation. The tides raised by the sun on Jupiter will tend therefore to lengthen Jupiter's day; the tides raised on the sun by Jupiter will tend to augment the sun's period of rotation. Both Jupiter and the sun will therefore lose some moment of momentum. We cannot, however, repeat too often the dynamical truth that the total moment of momentum must remain constant, therefore what is lost by the rotation must be made up in the revolution; the orbit of Jupiter around the sun must accordingly be swelling. So far the reasoning appears similar to that which led to such startling consequences in regard to the moon.

But now for the fundamental difference between the two cases. The moon, it will be remembered, always revolves with the same face towards the earth. The tides have ceased to operate there, and consequently the moon is not able to contribute any moment of momentum, to be applied to the enlargement of its distance from the earth; all the moment of momentum necessary for this purpose is of course drawn from the single supply in the rotation of the earth on its axis. But in the case of the system consisting of the sun and Jupiter the circumstances are quite different--Jupiter does not always bend the same face to the sun; so far, indeed, is this from being true, that Jupiter is eminently remarkable for the rapidity of his rotation, and for the incessantly varying aspect in which he would be seen from the sun. Jupiter has therefore a store of available moment of momentum, as has also of course the sun. Thus in the sun and planet system we have in the rotations two available stores of moment of momentum on which the tides can make draughts for application to the enlargement of the revolution. The proportions in which these two available sources can be drawn upon for contributions is not left arbitrary. The laws of dynamics provide the shares in which each of the bodies is to contribute for the joint purpose of driving them further apart.

Let us see if we cannot form an estimate by elementary considerations as to the division of the labour. The tides raised on Jupiter by the sun will be practically proportional to the sun's mass and to the radius of Jupiter. Owing to the enormous size of the sun, the efficiency of these tides and the moment of the friction-brake they produce will be far greater on the planet than will the converse operation of the planet be on the sun. Hence it follows that the efficiency of the tides in depriving Jupiter of moment of momentum will be greatly superior to the efficiency of the tides in depriving the sun of moment of momentum. Without following the matter into any close numerical calculation, we may assert that for every one part the sun contributes to the common object, Jupiter will contribute at least a thousand parts; and this inequality appears all the more striking, not to say unjust, when it is remembered that the sun is more abundantly provided with moment of momentum than is Jupiter--the sun has, in fact, about twenty thousand times as much.

The case may be illustrated by supposing that a rich man and a poor man combine together to achieve some common purpose to which both are to contribute. The ethical notion that Dives shall contribute largely, according to his large means, and Lazarus according to his slender means, is quite antagonistic to the scale which dynamics has imposed. Dynamics declares that the rich man need only give a penny to every pound that has to be extorted from the poor man. Now this is precisely the case with regard to the sun and Jupiter, and it involves a somewhat curious consequence. As long as Jupiter possesses available moment of momentum, we may be certain that no large contribution of moment of momentum has been obtained from the sun. For, returning to our illustration, if we find that Lazarus still has something left in his pocket, we are of course assured that Dives cannot have expended much, because, as Lazarus had but little to begin with, and as Dives only puts in a penny for every pound that Lazarus spends, it is obvious that no large amount can have been devoted to the common object. Hence it follows that whatever transfer of moment of momentum has taken place in the sun-Jupiter system has been almost entirely obtained at the expense of Jupiter. Now in the solar system at present, the orbital moment of momentum of Jupiter is nearly fifty thousand times as great as his present store of rotational moment of momentum. If, therefore, the departure of Jupiter from the sun had been the consequence of tidal evolution, it would follow that Jupiter must once have contained many thousands of times the moment of momentum that he has at present. This seems utterly incredible, for even were Jupiter dilated into an enormously large mass of vaporous matter, spinning round with the utmost conceivable speed, it is impossible that he should ever have possessed enough moment of momentum. We are therefore forced to the conclusion that the tides alone do not provide sufficient explanation for the retreat of Jupiter from the sun.

This presents the demonstration of tidal evolution in a fresh light. If the moon now departed to any considerable extent from showing the constant face to the earth, it would seem that its retreat could not have been caused by tides. Some other agent for producing the present configuration would be necessary, just as we found that some other agent than the tides has been necessary in the case of Jupiter.

But I must say a few words as to the attitude of this question with regard to the entire solar system. This system consists of the sun presiding at the centre, and of the planets and their satellites in revolution around their respective primaries, and each also animated by a rotation on its axis. I shall in so far depart from the actual configuration of the system as to transform it into an ideal system, whereof the masses, the dimensions, and the velocities shall all be preserved; but that the several planes of revolution shall be all flattened into one plane, instead of being inclined at small angles as they are at present; nor will it be unreasonable for us at the same time to bring into parallelism all the axes of rotation, and to arrange that their common directions shall be perpendicular to the plane of their common orbits. For the purpose of our present research this ideal system may pass for the real system.

In its original state, whatever that state may have been, a magnificent endowment was conferred upon the system. Perhaps I may, without derogation from the dignity of my subject, speak of the endowment as partly personal and partly entailed. The system had of course different powers with regard to the disposal of the two portions; the personal estate could be squandered. It consisted entirely of what we call energy; and considering how frequently we use the expression conservation of energy, it may seem strange to say now that this portion of the endowment has been found capable of alienation, nay, further, that our system has been squandering it persistently from the first moment until now. Although the doctrine of the conservation of energy is, we have every reason to believe, a fundamental law affecting the whole universe, yet it would be wholly inaccurate to say that any particular system such as our solar system shall invariably preserve precisely the same quantity of energy without alteration. The circumstance that heat is a form of energy indeed negatives this supposition. For our system possesses energy of all the different kinds: there is energy due to the motions both of rotation and of revolution; there is energy due to the fact that the mutually attracting bodies of our system are separated by distances of enormous magnitude; and there is also energy in the form of heat; and the laws of heat permit that this form of energy shall be radiated off into space, and thus disappear entirely, in so far as our system is concerned. On the other hand, there may no doubt be some small amount of energy accruing to our system from the other systems in space, which like ours are radiating forth energy. Any gain from this source, however, is necessarily so very small in comparison to the loss to which we have referred, that it is quite impossible that the one should balance the other. Though it is undoubtedly true that the total quantity of energy in the universe is constant, yet the share of that energy belonging to any particular system such as ours declines steadily from age to age.

I may indeed remark, that the question as to what becomes of all the radiant energy which the millions of suns in the universe are daily discharging offers a problem apparently not easy to solve; but we need not discuss the matter at present, we are only going to trace out the vicissitudes of our own system; and whatever other changes that system may exhibit, the fact is certain that the total quantity of energy it contains is declining.

Of the two endowments of energy and of moment of momentum originally conferred on our system the moment of momentum is the entailed estate. No matter how the bodies may move, no matter how their actions may interfere with one another, no matter how this body is pulled one way and the other body that way, the conservation of moment of momentum is not imperilled, nor, no matter what losses of heat may be experienced by radiation, could the store of moment of momentum be affected. The only conceivable way in which the quantity of moment of momentum in the solar system could be tampered with is by the interference of some external attracting body. We know, however, that the stars are all situated at such enormous distances, that the influences they can exert in the perturbation of the solar system are absolutely insensible; they are beyond the reach of the most delicate astronomical measurements. Hence we see how the endowment of the system with moment of momentum has conferred upon that system a something which is absolutely inalienable, even to the smallest portion.

Share on: WhatsApp @Hash Facebook Tweet