Time and Tide by Sir Robert Stawell Ball (read with me txt) 📖

anything like the same influence in the affairs of our solar system generally which they have done in that very small part of the solar system which consists of the earth and moon. This is, as I have endeavoured to show in these lectures, the scene of supremely interesting tidal phenomena; but how small it is in comparison with the whole magnitude of our system may be inferred from the following illustration. I represent the whole moment of momentum of our system by L1,000,000,000, the bulk of which is composed of the revolutional moments of momentum of the great planets, and the rotational moment of momentum of the sun. On this scale the rotational share which has fallen to our earth and moon does not even rise to the dignity of a single pound, it can only be represented by the very modest figure of 19_s._ 5_d._ This is divided into two parts--the earth by its rotation accounts for 3_s._ 4_d._, leaving 16_s._ 1_d._ as the equivalent of the revolution of the moon. The other inferior planets have still less to show than the earth. Venus can barely have more than 2_s._ 6_d._; even Mars' two satellites cannot bring his figure up beyond the slender value of 1-1/2_d._; while Mercury will be amply represented by the smallest coin known at her Majesty's mint.

The same illustration will bring out the contrast between the Jovian system and our earth system. The rotational share of the former would be totally represented by a sum of nearly L12,000; of this, however, Jupiter's satellites only contribute about L89, notwithstanding that there are four of them. Thus Jupiter's satellites have not one hundredth part of the moment of momentum which the rotation of Jupiter exhibits. How wide is the contrast between this state of things and the earth-moon system, for the earth does not contain in its rotation one-fifth of the moment of momentum that the moon has in its revolution; in fact, the moon has gradually robbed the earth, which originally possessed 19_s._ 5_d._, of which the moon has carried off all but 3_s._ 4_d._

And this process is still going on, so that ultimately the earth will be left very poor, though not absolutely penniless, at least if the retention of a halfpenny can be regarded as justifying that assertion. Saturn, revolving as it does with great rapidity, and having a very large mass, possesses about L2700, while Uranus and Neptune taken together would figure for about the same amount.

In conclusion, let us revert again to the two critical conditions of the earth-moon system. As to what happened before the first critical period, the tides tell us nothing, and every other line of reasoning very little; we can to some extent foresee what may happen after the second critical epoch is reached, at a time so remote that I do not venture even to express the number of ciphers which ought to follow the significant digit in the expression for the number of years. I mentioned, however, that at this time the sun tides will produce the effect of applying a still further brake to the rotation of the earth, so that ultimately the month will have become a shorter period than the day. It is therefore interesting for us to trace out the tidal history of a system in which the satellite revolves around the primary in less time than the primary takes to go round on its own axis--such a system, in fact, as Mars would present at this moment were the outer satellite to be abstracted. The effect of the tides on the planet raised by its satellite would then be to accelerate its rotation; for as the planet, so to speak, lags behind the tides, friction would now manifest itself by the continuous endeavour to drag the primary round faster. The gain of speed, however, thus attained would involve the primary in performing more than its original share of the moment of momentum; less moment of momentum would therefore remain to be done by the satellite, and the only way to accomplish this would be for the satellite to come inwards and revolve in a smaller orbit.

We might indeed have inferred this from the considerations of energy alone, for whatever happens in the deformation of the orbit, heat is produced by the friction, and this heat is lost, and the total energy of the system must consequently decline. Now if it be a consequence of the tides that the velocity of the primary is accelerated, the energy corresponding to that velocity is also increased. Hence the primary has more energy than it had before; this energy must have been obtained at the expense of the satellite; the satellite must therefore draw inwards until it has yielded up enough of energy not alone to account for the increased energy of the primary, but also for the absolute loss of energy by which the whole operation is characterized.

It therefore appears that in the excessively remote future the retreat of the moon will not only be checked, but that the moon may actually return to a point to be determined by the changes in the earth's rotation. It is, however, extremely difficult to follow up the study of a case where the problem of three bodies has become even more complicated than usual.

The importance of tidal evolution in our solar system has also to be viewed in connection with the celebrated nebular hypothesis of the origin of the solar system. Of course it would be understood that tidal evolution is in no sense a rival doctrine to that of the nebular theory. The nebular origin of the sun and the planets sculptured out the main features of our system; tidal evolution has merely come into play as a subsidiary agent, by which a detail here or a feature there has been chiselled into perfect form. In the nebular theory it is believed that the planets and the sun have all originated from the cooling and the contraction of a mighty heated mass of vapours. Of late years this theory, in its main outlines at all events, has strengthened its hold on the belief of those who try to interpret nature in the past by what we see in the present. The fact that our system at present contains some heat in other bodies as well as in the sun, and the fact that the laws of heat require continual loss by radiation, demonstrate that our system, if we look back far enough, and if the present laws have acted, must have had in part, at all events, an origin like that which the nebular theory would suppose.

I feel that I have in the progress of these two lectures been only able to give the merest outline of the theory of tidal evolution in its application to the earth-moon system. Indeed I have been obliged, by the nature of the subject, to omit almost entirely any reference to a large body of the parts of the theory. I cannot bring myself to close these lectures without just alluding to this omission, and without giving expression to the fact, that I feel it is impossible for me to have rendered adequate justice to the strength of the argument on which we claim that tidal evolution is the most rational mode of accounting for the present condition in which we find the earth-moon system. Of course it will be understood that we have never contended that the tides offer the only conceivable theory as to the present condition of things. The argument lies in this wise. A certain body of facts are patent to our observation. The tides offer an explanation as to the origin of these facts. The tides are a _vera causa_, and in the absence of other suggested causes, the tidal theory holds the field. But much will depend on the volume and the significance of the group of associated facts of which the doctrine offers a solution. The facts that it has been in my power to discuss within the compass of discourses like the present, only give a very meagre and inadequate notion of the entire phenomena connected with the moon which the tides will explain. We have not unfrequently, for the sake of simplicity, spoken of the moon's orbit as circular, and we have not even alluded to the fact that the plane of that orbit is inclined to the ecliptic. A comprehensive theory of the moon's origin should render an account of the eccentricity of the moon's orbit; it must also involve the obliquity of the ecliptic, the inclination of the moon's orbit, and the direction of the moon's axis. I have been perforce compelled to omit the discussion of these attributes of the earth-moon system, and in doing so I have inflicted what is really an injustice on the tidal theory. For it is the chief claim of the theory of tidal evolution, as expounded by Professor Darwin, that it links together all these various features of the earth-moon system. It affords a connected explanation, not only of the fact that the moon always turns the same face to the earth, but also of the eccentricity of the moon's path around the earth, and the still more difficult points about the inclinations of the various axes and orbits of the planets. It is the consideration of these points that forms the stronghold of the doctrine of tidal evolution. For when we find that a theory depending upon influences that undoubtedly exist, and are in ceaseless action around us, can at the same time bring into connection and offer a common explanation of a number of phenomena which would otherwise have no common bond of union, it is impossible to refuse to believe that such a theory does actually correspond to nature.

The greatest of mathematicians have ever found in astronomy problems which tax, and problems which greatly surpass, the utmost efforts of which they are capable. The usual way in which the powers of the mathematician have been awakened into action is by the effort to remove some glaring discrepancy between an imperfect theory and the facts of observation. The genius of a Laplace or a Lagrange was expended, and worthily expended, in efforts to show how one planet acted on another planet, and produced irregularities in its orbit; the genius of an Adams and a Leverrier was nobly applied to explain the irregularities in the motion of Uranus, and to discover a cause of those irregularities in the unseen Neptune. In all these cases, and in many others which might be mentioned, the mathematician has been stimulated by the laudable anxiety to clear away some blemish from the theory of gravitation throughout the system. The blemish was seen to exist before its removal was suggested. In that application of mathematics with which we have been concerned in these lectures the call for the mathematician has been of quite a different kind. A certain familiar phenomenon on our sea-coasts has invited attention. The tidal ripples murmur a secret, but not for every ear. To interpret that secret fully, the hearer must be a mathematician. Even then the interpretation can only be won after the profoundest efforts of thought and attention, but at last the language has been made intelligible. The labour has been gloriously rewarded, and an interesting chapter of our earth's history has for the first time been written.

In the progress of these lectures I have sought to interest you in those profound investigations which the modern mathematician has made in his efforts to explore the secrets of nature. He has felt that the laws of motion, as we understand them, are bounded by no considerations of space, are limited by no duration of time, and he has commenced to speculate on the logical consequences of those laws when time of