Part 32 (1/2)

These daily pulses of the ocean have long ceased to be a mystery. It was in the earliest times perceived that there was a connection between the tides and the moon. Ancient writers, such as Pliny and Aristotle, have referred to the alliance between the times of high water and the age of the moon. I think we sometimes do not give the ancient astronomers as much credit as their shrewdness really ent.i.tles them to.

We have all read--we have all been taught--that the moon and the tides are connected together; but how many of us are in a position to say that we have actually noticed that connection by direct personal observation?

The first man who studied this matter with sufficient attention to convince himself and to convince others of its reality must have been a great philosopher. We know not his name, we know not his nation, we know not the age in which he lived; but our admiration of his discovery must be increased by the reflection that he had not the theory of gravitation to guide him. A philosopher of the present day who had never seen the sea could still predict the necessity of tides as a consequence of the law of universal gravitation; but the primitive astronomer, who knew not of the invisible bond by which all bodies in the universe are drawn together, made a splendid--indeed, a typical--inductive discovery, when he ascertained the relation between the moon and the tides.

We can surmise that this discovery, in all probability, first arose from the observations of experienced navigators. In all matters of entering port or of leaving port, the state of the tide is of the utmost concern to the sailor. Even in the open sea he has sometimes to shape his course in accordance with the currents produced by the tides; or, in guiding his course by taking soundings, he has always to bear in mind that the depth varies with the tide. All matters relating to the tide would thus come under his daily observation. His daily work, the success of his occupation, the security of his life, depend often on the tides; and hence he would be solicitous to learn from his observation all that would be useful to him in the future. To the coasting sailor the question of the day is the time of high water. That time varies from day to day; it is an hour or more later to-morrow than to-day, and there is no very simple rule which can be enunciated. The sailor would therefore welcome gladly any rule which would guide him in a matter of such importance. We can make a conjecture as to the manner in which such a rule was first discovered. Let us suppose that a sailor at Calais, for example, is making for harbour. He has a beautiful night--the moon is full; it guides him on his way; he gets safely into harbour; and the next morning he finds the tide high between 11 and 12.[45] He often repeats the same voyage, but he finds sometimes a low and inconvenient tide in the morning. At length, however, it occurs to him that _when he has a moonlight night_ he has a high tide at 11. This occurs once or twice: he thinks it but a chance coincidence. It occurs again and again.

At length he finds it always occurs. He tells the rule to other sailors; they try it too. It is invariably found that when the moon is full, the high tide always recurs at the same hour at the same place. The connection between the moon and the tide is thus established, and the intelligent sailor will naturally compare other phases of the moon with the times of high water. He finds, for example, that the moon at the first quarter always gives high water at the same hour of the day; and finally, he obtains a practical rule, by which, from the state of the moon, he can at once tell the time when the tide will be high at the port where his occupation lies. A diligent observer will trace a still further connection between the moon and the tides; he will observe that some high tides rise higher than others, that some low tides fall lower than others. This is a matter of much practical importance. When a dangerous bar has to be crossed, the sailor will feel much additional security in knowing that he is carried over it on the top of a spring tide; or if he has to contend against tidal currents, which in some places have enormous force, he will naturally prefer for his voyage the neap tides, in which the strength of these currents is less than usual.

The spring tides and the neap tides will become familiar to him, and he will perceive that the spring tides occur when the moon is full or new--or, at all events, that the spring tides are within a certain constant number of days of the full or new moon. It was, no doubt, by reasoning such as this, that in primitive times the connection between the moon and the tides came to be perceived.

It was not, however, until the great discovery of Newton had disclosed the law of universal gravitation that it became possible to give a physical explanation of the tides. It was then seen how the moon attracts the whole earth and every particle of the earth. It was seen how the fluid particles which form the oceans on the earth were enabled to obey the attraction in a way that the solid parts could not. When the moon is overhead it tends to draw the water up, as it were, into a heap underneath, and thus to give rise to the high tide. The water on the opposite side of the earth is also affected in a way that might not be at first antic.i.p.ated. The moon attracts the solid body of the earth with greater intensity than it attracts the water at the other side which lies more distant from it. The earth is thus drawn away from the water, and there is therefore a tendency to a high tide as well on the side of the earth away from the moon as on that towards the moon. The low tides occupy the intermediate positions.

The sun also excites tides on the earth; but owing to the great distance of the sun, the difference between its attraction on the sea and on the solid interior of the earth is not so appreciable. The solar tides are thus smaller than the lunar tides. When the two conspire, they cause a spring tide; when the solar and lunar tides are opposed, we have the neap tide.

There are, however, a mult.i.tude of circ.u.mstances to be taken into account when we attempt to apply this general reasoning to the conditions of a particular case. Owing to local peculiarities the tides vary enormously at the different parts of the coast. In a confined area like the Mediterranean Sea, the tides have only a comparatively small range, varying at different places from one foot to a few feet. In mid-ocean also the tidal rise and fall is not large, amounting, for instance, to a range of three feet at St. Helena. Near the great continental ma.s.ses the tides become very much modified by the coasts. We find at London a tide of eighteen or nineteen feet; but the most remarkable tides in the British Islands are those in the Bristol Channel, where, at Chepstow or Cardiff, there is a rise and fall during spring tides to the height of thirty-seven or thirty-eight feet, and at neap tides to a height of twenty-eight or twenty-nine. These tides are surpa.s.sed in magnitude at other parts of the world. The greatest of all tides are those in the Bay of Fundy, at some parts of which the rise and fall at spring tides is not less than fifty feet.

The rising and falling of the tide is necessarily attended with the formation of currents. Such currents are, indeed, well known, and in some of our great rivers they are of the utmost consequence. These currents of water can, like water-streams of any other kind, be made to do useful work. We can, for instance, impound the rising water in a reservoir, and as the tide falls we can compel the enclosed water to work a water-wheel before it returns to the sea. We have, indeed, here a source of actual power; but it is only in very unusual circ.u.mstances that it is found to be economical to use the tides for this purpose. The question can be submitted to calculation, and the area of the reservoir can be computed which would retain sufficient water to work a water-wheel of given horse-power. It can be shown that the area of the reservoir necessary to impound water enough to produce 100 horse-power would be 40 acres. The whole question is then reduced to the simple one of expense: would the construction and the maintenance of this reservoir be more or less costly than the erection and the maintenance of a steam-engine of equivalent power? In most cases it would seem that the latter would be by far the cheaper; at all events, we do not practically find tidal engines in use, so that the power of the tides is now running to waste. The economical aspects of the case may, however, be very profoundly altered at some remote epoch, when our stores of fuel, now so lavishly expended, give appreciable signs of approaching exhaustion.

The tides are, however, _doing work_ of one kind or another. A tide in a river estuary will sometimes scour away a bank and carry its materials elsewhere. We have here work done and energy consumed, just as much as if the same task had been accomplished by engineers directing the powerful arms of navvies. We know that work cannot be done without the consumption of energy in some of its forms; whence, then, comes the energy which supplies the power of the tides? At a first glance the answer to this question seems a very obvious one. Have we not said that the tides are caused by the moon? and must not the energy, therefore, be derived from the moon? This seems plain enough, but, unfortunately, it is not true. It is one of those cases by no means infrequent in Dynamics, where the truth is widely different from that which seems to be the case. An ill.u.s.tration will perhaps make the matter clearer. When a rifle is fired, it is the finger of the rifleman that pulls the trigger; but are we, then, to say that the energy by which the bullet has been driven off has been supplied by the rifleman? Certainly not; the energy is, of course, due to the gunpowder, and all the rifleman did was to provide the means by which the energy stored up in the powder could be liberated. To a certain extent we may compare this with the tidal problem; the tides raised by the moon are the originating cause whereby a certain store of energy is drawn upon and applied to do such work as the tides are competent to perform. This store of energy, strange to say, does not lie in the moon; it is in the earth itself.

Indeed, it is extremely remarkable that the moon actually gains energy from the tides by itself absorbing some of the store which exists in the earth. This is not put forward as an obvious result; it depends upon a refined dynamical theorem.

We must clearly understand the nature of this mighty store of energy from which the tides draw their power, and on which the moon is permitted to make large and incessant drafts. Let us see in what sense the earth is said to possess a store of energy. We know that the earth rotates on its axis once every day. It is this rotation which is the source of the energy. Let us compare the rotation of the earth with the rotation of the fly-wheel belonging to a steam-engine. The rotation of the fly-wheel is really a reservoir, into which the engine pours energy at each stroke of the piston. The various machines in the mill worked by the engine merely draw upon the store of energy acc.u.mulated in the fly-wheel. The earth may be likened to a gigantic fly-wheel detached from the engine, though still connected with the machines in the mill.

From its stupendous dimensions and from its rapid velocity, that great fly-wheel possesses an enormous store of energy, which must be expended before the fly-wheel comes to rest. Hence it is that, though the tides are caused by the moon, yet the energy they require is obtained by simply appropriating some of the vast supply available from the rotation of the earth.

There is, however, a distinction of a very fundamental character between the earth and the fly-wheel of an engine. As the energy is withdrawn from the fly-wheel and consumed by the various machines in the mill, it is continually replaced by fresh energy, which flows in from the exertions of the steam-engine, and thus the velocity of the fly-wheel is maintained. But the earth is a fly-wheel without the engine. When the tides draw upon the store of energy and expend it in doing work, that energy is not replaced. The consequence is irresistible: the energy in the rotation of the earth must be decreasing. This leads to a consequence of the utmost significance. If the engine be cut off from the fly-wheel, then, as everyone knows, the ma.s.sive fly-wheel may still give a few rotations, but it will speedily come to rest. A similar inference must be made with regard to the earth; but its store of energy is so enormous, in comparison with the demands which are made upon it, that the earth is able to hold out. Ages of countless duration must elapse before the energy of the earth's rotation can be completely exhausted by such drafts as the tides are capable of making.

Nevertheless, it is necessarily true that the energy is decreasing; and if it be decreasing, then the speed of the earth's rotation must be surely, if slowly, abating. Now we have arrived at a consequence of the tides which admits of being stated in the simplest language. If the speed of rotation be abating, then the length of the day must be increasing; and hence we are conducted to the following most important statement: that the _tides are increasing the length of the day_.

To-day is longer than yesterday--to-morrow will be longer than to-day.

The difference is so small that even in the course of ages it can hardly be said to have been distinctly established by observation. We do not pretend to say how many centuries have elapsed since the day was even one second shorter than it is at present; but centuries are not the units which we employ in tidal evolution. A million years ago it is quite probable that the divergence of the length of the day from its present value may have been very considerable. Let us take a glance back into the profound depths of times past, and see what the tides have to tell us. If the present order of things has lasted, the day must have been shorter and shorter the farther we look back into the dim past. The day is now twenty-four hours; it was once twenty hours, once ten hours; it was once six hours. How much farther can we go? Once the six hours is past, we begin to approach a limit which must at some point bound our retrospect. The shorter the day the more is the earth bulged at the equator; the more the earth is bulged at the equator the greater is the strain put upon the materials of the earth by the centrifugal force of its rotation. If the earth were to go too fast it would be unable to cohere together; it would separate into pieces, just as a grindstone driven too rapidly is rent asunder with violence. Here, therefore, we discern in the remote past a barrier which stops the present argument.

There is a certain critical velocity which is the greatest that the earth could bear without risk of rupture, but the exact amount of that velocity is a question not very easy to answer. It depends upon the nature of the materials of the earth; it depends upon the temperature; it depends upon the effect of pressure, and on other details not accurately known to us. An estimate of the critical velocity has, however, been made, and it has been shown mathematically that the shortest period of rotation which the earth could have, without flying into pieces, is about three or four hours. The doctrine of tidal evolution has thus conducted us to the conclusion that, at some inconceivably remote epoch, the earth was spinning round its axis in a period approximating to three or four hours.

We thus learn that we are indebted to the moon for the gradual elongation of the day from its primitive value up to twenty-four hours.

In obedience to one of the most profound laws of nature, the earth has reacted on the moon, and the reaction of the earth has taken a tangible form. It has simply consisted in gradually driving the moon away from the earth. You may observe that this driving away of the moon resembles a piece of retaliation on the part of the earth. The consequence of the retreat of the moon is sufficiently remarkable. The path in which the moon is revolving has at the present time a radius of 240,000 miles.

This radius must be constantly growing larger, in consequence of the tides. Provided with this fact, let us now glance back into the past history of the moon. As the moon's distance is increasing when we look forwards, so we find it decreasing when we look backwards. The moon must have been nearer the earth yesterday than it is to-day; the difference is no doubt inappreciable in years, in centuries, or in thousands of years; but when we come to millions of years, the moon must have been significantly closer than it is at present, until at length we find that its distance, instead of 240,000 miles, has dwindled down to 40,000, to 20,000, to 10,000 miles. Nor need we stop--nor can we stop--until we find the moon actually close to the earth's surface. If the present laws of nature have operated long enough, and if there has been no external interference, then it cannot be doubted that the moon and the earth were once in immediate proximity. We can, indeed, calculate the period in which the moon must have been revolving round the earth. The nearer the moon is to the earth the quicker it must revolve; and at the critical epoch when the satellite was in immediate proximity to our earth it must have completed each revolution in about three or four hours.

This has led to one of the most daring speculations which has ever been made in astronomy. We cannot refrain from enunciating it; but it must be remembered that it is only a speculation, and to be received with corresponding reserve. The speculation is intended to answer the question, What brought the moon into that position, close to the surface of the earth? We will only say that there is the gravest reason to believe that the moon was, at some very early period, fractured off from the earth when the earth was in a soft or plastic condition.

At the beginning of the history we found the earth and the moon close together. We found that the rate of rotation of the earth was only a few hours, instead of twenty-four hours. We found that the moon completed its journey round the primitive earth in exactly the same time as the primitive earth rotated on its axis, so that the two bodies were then constantly face to face. Such a state of things formed what a mathematician would describe as a case of unstable dynamical equilibrium. It could not last. It may be compared to the case of a needle balanced on its point; the needle must fall to one side or the other. In the same way, the moon could not continue to preserve this position. There were two courses open: the moon must either have fallen back on the earth, and been reabsorbed into the ma.s.s of the earth, or it must have commenced its outward journey. Which of these courses was the moon to adopt? We have no means, perhaps, of knowing exactly what it was which determined the moon to one course rather than to another, but as to the course which was actually taken there can be no doubt. The fact that the moon exists shows that it did not return to the earth, but commenced its outward journey. As the moon recedes from the earth it must, in conformity with Kepler's laws, require a longer time to complete its revolution. It has thus happened that, from the original period of only a few hours, the duration has increased until it has reached the present number of 656 hours. The rotation of the earth has, of course, also been modified, in accordance with the retreat of the moon. Once the moon had commenced to recede, the earth was released from the obligation which required it constantly to direct the same face to the moon. When the moon had receded to a certain distance, the earth would complete the rotation in less time than that required by the moon for one revolution. Still the moon gets further and further away, and the duration of the revolution increases to a corresponding extent, until three, four, or more days (or rotations of the earth) are identical with the month (or revolution of the moon). Although the number of days in the month increases, yet we are not to suppose that the rate of the earth's rotation is increasing; indeed, the contrary is the fact. The earth's rotation is getting slower, and so is the revolution of the moon, but the r.e.t.a.r.dation of the moon is greater than that of the earth. Even though the period of rotation of the earth has greatly increased from its primitive value, yet the period of the moon has increased still more, so that it is several times as large as that of the rotation of the earth. As ages roll on the moon recedes further and further, its...o...b..t increases, the duration of the revolution augments, until at length a very noticeable epoch is attained, which is, in one sense, a culminating point in the career of the moon. At this epoch the revolution periods of the moon, when measured in rotation periods of the earth, attain their greatest value. It would seem that the month was then twenty-nine days. It is not, of course, meant that the month and the day at that epoch were the month and the day as our clocks now measure time. Both were shorter then than now. But what we mean is, that at this epoch the earth rotated twenty-nine times on its axis while the moon completed one circuit.

This epoch has now been pa.s.sed. No attempt can be made at present to evaluate the date of that epoch in our ordinary units of measurement. At the same time, however, no doubt can be entertained as to the immeasurable antiquity of the event, in comparison with all historic records; but whether it is to be reckoned in hundreds of thousands of years, in millions of years, or in tens of millions of years, must be left in great degree to conjecture.

This remarkable epoch once pa.s.sed, we find that the course of events in the earth-moon system begins to shape itself towards that remarkable final stage which has points of resemblance to the initial stage. The moon still continues to revolve in an orbit with a diameter steadily, though very slowly, growing. The length of the month is accordingly increasing, and the rotation of the earth being still constantly r.e.t.a.r.ded, the length of the day is also continually growing. But the ratio of the length of the month to the length of the day now exhibits a change. That ratio had gradually increased, from unity at the commencement, up to the maximum value of somewhere about twenty-nine at the epoch just referred to. The ratio now begins again to decline, until we find the earth makes only twenty-eight rotations, instead of twenty-nine, in one revolution of the moon. The decrease in the ratio continues until the number twenty-seven expresses the days in the month.

Here, again, we have an epoch which it is impossible for us to pa.s.s without special comment. In all that has. .h.i.therto been said we have been dealing with events in the distant past; and we have at length arrived at the present state of the earth-moon system. The days at this epoch are our well-known days, the month is the well-known period of the revolution of our moon. At the present time the month is about twenty-seven of our days, and this relation has remained sensibly true for thousands of years past. It will continue to remain sensibly true for thousands of years to come, but it will not remain true indefinitely. It is merely a stage in this grand transformation; it may possess the attributes of permanence to our ephemeral view, just as the wings of a gnat seem at rest when illuminated by the electric spark; but when we contemplate the history with time conceptions sufficiently ample for astronomy we realise how the present condition of the earth-moon system can have no greater permanence than any other stage in the history.

Our narrative must, however, now a.s.sume a different form. We have been speaking of the past; we have been conducted to the present; can we say anything of the future? Here, again, the tides come to our a.s.sistance.

If we have rightly comprehended the truth of dynamics (and who is there now that can doubt them?), we shall be enabled to make a forecast of the further changes of the earth-moon system. If there be no interruption from any external source at present unknown to us, we can predict--in outline, at all events--the subsequent career of the moon. We can see how the moon will still follow its outward course. The path in which it revolves will grow with extreme slowness, but yet it will always grow; the progress will not be reversed, at all events, before the final stage of our history has been attained. We shall not now delay to dwell on the intervening stages; we will rather attempt to sketch the ultimate type to which our system tends. In the dim future--countless millions of years to come--this final stage will be approached. The ratio of the month to the day, whose decline we have already referred to, will continue to decline. The period of revolution of the moon will grow longer and longer, but the length of the day will increase much more rapidly than the increase in the duration of the moon's period. From the month of twenty-seven days we shall pa.s.s to a month of twenty-six days, and so on, until we shall reach a month of ten days, and, finally, a month of one day.

Let us clearly understand what we mean by a month of one day. We mean that the time in which the moon revolves around the earth will be equal to the time in which the earth rotates around its axis. The length of this day will, of course, be vastly greater than our day. The only element of uncertainty in these enquiries arises when we attempt to give numerical accuracy to the statements. It seems to be as true as the laws of dynamics that a state of the earth-moon system in which the day and the month are equal must be ultimately attained; but when we attempt to state the length of that day we introduce a hazardous element into the enquiry. In giving any estimate of its length, it must be understood that the magnitude is stated with great reserve. It may be erroneous to some extent, though, perhaps, not to any considerable amount. The length of this great day would seem to be about equal to fifty-seven of our days. In other words, at some critical time in the excessively distant future, the earth will take something like 1,400 hours to perform a rotation, while the moon will complete its journey precisely in the same time.

We thus see how, in some respects, the first stage of the earth-moon system and the last stage resemble each other. In each case we have the day equal to the month. In the first case the day and the month were only a small fraction of our day; in the last stage the day and the month are each a large multiple of our day. There is, however, a profound contrast between the first critical epoch and the last. We have already mentioned that the first epoch was one of unstability--it could not last; but this second state is one of dynamical stability. Once that state has been acquired, it would be permanent, and would endure for ever if the earth and the moon could be isolated from all external interference.