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 palæozoic 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.

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