Chapter V: Part 5

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 indefinite duration is assumed to be at his disposal. From the very nature of the case, observations for confirmation were impossible. Phenomena that required millions of years for their development cannot be submitted to the instruments in our observatories. But this is perhaps one of the special reasons which make such investigations of peculiar interest, and entitle us to speak of the revelations of Time and Tide as a romance of modern science.

INDEX.

Aberdeen, tides at, 23 Action and reaction, 69 Adams, discoverer of Neptune, 186 Admiralty Manual of Scientific Inquiry, 30, 31, 34 Admiralty tide tables, 29 Africa, Krakatoa dust over, 84 Analysis, harmonic, of tides, 34 Analysis of tide into its constituents, 33 Ancient tides on moon, 136 Annus Magnus of solar system, 72 Areas, conservation of, 61 Arklow, tides at, 23 Ascension, tides at, 24 Astronomical chronology, 147 Atlantic, Krakatoa dust over, 84 Atlantic, tides in, 38 Atmosphere, tides in, 40 Avon, tides in, at Bristol, 39

Ball-room, illustration, 62 Barometric records of Krakatoa airwave, 82 Batavia, Krakatoa heard at, 83 Bath, hot waters at, 89 Bay of Fundy, 39 Beds of rock, how formed, 149 Birmingham, lecture at, 148 Birth of moon, 118 Blast iron furnace, 87 Blue sun produced by Krakatoa, 84 Bodily tides of moon, 131 Brake illustrating friction, 68 Brickwork as a non-conductor, 87 Bristol Channel, 39 Bucket of water, oscillations in, 98

Cambrian rocks, 153 Cannon-ball, energy of, 51 Cardiff, tides at, 39 Caspian Sea, tides in, 38 Casting, cooling of, 79 Celebes, Krakatoa heard at, 83 Central America, 86 Change and full, tides at, 22 Chemical action in earth, 81 Chepstow, tides at, 39 Chronology, the two systems of, 147 Clifton, tides in Avon at, 39 Clock, illustration of, 49 Coal, 11 Coincidence of moon's rotation and revolution, 134 Combustion, heat of, 92 Cones, volume of, 151 Conservation of spin or areas, 64 Constituent tides, 35 Consumption of energy by tides, 48 Cooling, laws of, 79 Cooling of earth from primitive heat, 87 Crane, brakes on, 69 Craters of moon, 94 Critical epoch in earth's history, 75

Darwin, 12 Darwin, G. H., in Admiralty Manual, 34 Darwin, G. H., on tidal evolution, 97, 118, 122, 151, 185 Day and month equal, 107 Day at present increasing, 68 Day of 1400 hours, 121 Day of 3 or 4 hours, 75 Decline of earth's heat, 90 Diagram showing why moon recedes, 70 Diego Garcia, Krakatoa heard at, 83 Difficulties of tidal evolution, 48 Dives and Lazarus, 161 Dust clouds, 84 Dynamical principle, 65 Dynamical stability, 110

Earth and moon as rigid body, 107 Earth a fly-wheel, 57 Earth, fusion of, 12 Earth, heat of, 80 Earth in highly heated early state, 92 Earth's crust, Lyell on, 12 Earth's history, 12 Earth-moon system originally, 107 Earthquakes, 80 Eccentricity of moon's path explained, 184 Ecliptic, obliquity of, explained, 184 Economic aspects of tides, 45 Egg on end, 108 Elliptic orbit of moon, 113 Endowment of moment of momentum, 167 Energy for tides, whence, 67 Energy lost by tides, 60 Energy of moon's position, 50 Energy of motion, 51 Energy of separation, 50 Energy, sources of, 49 Equality of day and month, 122 Equilibrium, stable and unstable, 108 Equinoxes, precession of, 72 Eruption of volcanoes, 80 Establishment, 30 Estuary, tides in, 152 Explosion of Krakatoa, 83 Extinct season, moon, 129

Fiji, 24 Fishes, periods of fossil, 12 Fitzgerald, Prof., on Hertz' experiments, 101 Floating log, 109 Fortnightly tide, 34 Friction brake, 69 Friction, tidal, 40, 47 Full and change, tides during, 22 Fundy, Bay of, tides in, 39

Gauge for tides, 31 Geological chronology, 146 Geology and tides, 144 Geometric series, 92 Geysers, 85 Gibraltar, Straits of, tides in, 38 Glimpse through the corridors of time, 148 Glorious sunsets from Krakatoa, 85 Greatest length of day, 121 Greatest length of month, 122 Greatest tides, 39 Green moons from Krakatoa dust, 84 Greenock, tides at, 22 Grindstone, rupture of, 76 Gunpowder, energy from, 51

Hall, Prof. A., discovers satellites of Mars, 142 Harmonic analyzer, 35 Heated body, cooling of, 79 Height of tide, how to measure, 29 Helmholtz explains the constant face of the moon, 136 Hertz, undulations of ether, 101 High water, is it under the moon? 21 High water, simple rules for, 26 High water twice a day, 18 Hot springs, 85 Hot waters of Bath, 89 Hour of high water, how found, 26 Howth, 25 Hull, tides at, 23

Ichthyosaurus, 148 Impulse, effect of timed, 101 Incandescence of earth's interior, 85 Incandescence of moon, 94 Indian ocean, 84 Initial condition of earth and moon, 76 Instability, dynamical, 110 Interval, luni-tidal, 30 Iron, machine for punching, 55 Iron smelting, 87

Java, 82 Jupiter, 141, 156

Kepler's Law, 53, 114 Kerguelen Island, 24 Kingstown, 21 Krakatoa, 58

Lagrange, 186 Language, origin of, 12 Laplace, 186 Laurentian rocks, 148 Law of tides, 15 Lazarus and Dives, 161 Leakage of heat, 86 Length of day increasing, 68 Leverrier discovers Neptune, 186 London, tides at, 23, 27 Lunar and solar tides compared, 15 Lunar diurnal tide, 34 Luni-tidal interval, 30 Lyell, 12

Macassar, explosion of Krakatoa heard at, 83 Machine for analyzing tides, 35 Machine for predicting tides, 35 Machine for observing tides, 32 Malahide estuary, 152 Mars, moons of, 142 Mass of moon found from tides, 16 Max Müller, 12 Maximum and minimum, 104 Mediterranean, tides in, 38 Meridian position of moon at high water, 26 Mills, tidal, 43 Mines, heat in, 86 Moment of momentum, how estimated, 170 Month equals day, 122 Month of 1400 hours, 122 Month with greatest number of days, 118 Moon and tides connected, 13 Moon, constant face of, 136 Moon-energy, 54 Moon, volcanic activity on, 94 Moons of Mars, 142 Motion, perpetual, 48

Nautical almanac, 26 Neap tides, 16 Needles, tides at, 23 Niagara, utilization of, 47 Noise from Krakatoa, 83 Numerical data of tidal evolution, 127

Obliquity of ecliptic and tides, 184 Observations of tides, 29 Ocean tides, 38 Orbit of earth, changes in, 72 Orbit of moon explained by tides, 184 Origin of moon, 100 Oscillations of water, 98

Pacific, 84 Paradox of geometric series, 92 Pendulum, motion of, 49 Periodic phenomena, 71 Periods of rotation and revolution of moon equal, 43 Periods of tides, 34 Perpetual motion, 48 Planets and tides, 155 Precession of equinoxes, 72 Prediction of tides, 35 Principal tides, 33 Punching-engine, 55 Purser, Professor, 61

Railway brakes, 68 Reaction and action, 69 Relative rotation, 104 Relative tides on earth and moon, 131 Reptiles, fossil, 11 Retreat of moon explained, 69 Retrospect of moon's history, 77 Rhine, mills on, 43 Ring theory of moon's origin, 96 Rivers, 149 Rocks, formation of, 150 Rodriguez, Krakatoa heard at, 83 Rolling mills, 56 Rotation of moon on its axis, 133 Rupture of earth, 76 Rupture of grindstone, 75

St. Helena, tides at, 38 Santa Cruz, 24 Satellites of Jupiter, 135 Saturn, 141 Seasons, 72 Seas, so called, on moon, 129 Secondary ages, 11 Sligo, tides at, 23 Small tides, 38 Smelting of iron, 87 Solar and lunar tides compared, 15 Solar system, 155 Solar tides, 14 Solar tides, ultimate importance of, 139 Sounds from Krakatoa, 83 Source of tidal energy, 67 Spring tides, 16 Stability, dynamical, 110 Stable equilibrium, 108 Stages of special importance, 117 Stalactites, 73 Steam engine and tides compared, 45 Strata, formation of, aided by tides, 154 Sumatra, 82 Sun, rotation of, 134 Sunbeams stored, 11 Sunda, 82 Sunsets, Krakatoa, 85

Table of luni-tidal corrections, 30 Telescope at Washington, 143 Temperature of space, 91 Tertiary ages, 11 Thames, tides in, 125 Thomson, Sir W., 36, 44 Tidal currents used in making rocks, 153 Tidal efficiency, how estimated, 14 Tidal evolution, to whom due, 97 Tide gauge, 31 Tide mills, 44 Tide predicting engine, 36 Tides and geology, 144 Tides at London bridge, 28 Tides, change and full, 22 Tides, commercial value of, 47 Tides, due to moon, 13 Tides, how to observe, 29 Tides in Jupiter, 138 Tides in moon, 128 Tides, small, 38 Tides, solar and lunar compared, 15 Tides varying inversely as cube of distance, 15 Time and tide, 12 Timor, Krakatoa heard at, 83 Tralee, tides at, 23 Tyndall, 73 Tynemouth, 23

Undulations of a fluid globe, 99 Undulations of air from Krakatoa, 82 Unintermitting phenomena, 71 Unstable equilibrium, 108 Uranus, 142

Vast tides, 39 Volcanoes, 80 Voyage of Krakatoa dust, 84

Washington reflector, 142 Water absent from moon, 129 Water-wheels under London bridge, 43 Waves of air from Krakatoa, 82 Whewell on tides, 30 Work done by tides, 42, 47 Work of tides, 42

Yarmouth, tides at, 23

THE END.

_Richard Clay & Sons, Limited, London & Bungay._