It is my privilege to address you this afternoon on a subject in which
science and poetry are blended in a happy conjunction. If there be a
peculiar fascination about the earlier chapters of any branch of
history, how great must be the interest which attaches to that most
primeval of all terrestrial histories which relates to the actual
beginnings of this globe on which we stand.
In our efforts to grope into the dim recesses of this awful past, we
want the aid of some steadfast light which shall illumine the dark
places without the treachery of the will-o'-the-wisp. In the absence
of that steadfast light, vague conjectures as to the beginning of
things could never be entitled to any more respect than was due to
mere matters of speculation.
Of late, however, the required light has been to some considerable
extent forthcoming, and the attempt has been made, with no little
success, to elucidate a most interesting and wonderful chapter of an
exceedingly remote history. To chronicle this history is the object of
the present lectures before this Institution.
First, let us be fully aware of the extraordinary remoteness of that
period of which our history treats. To attempt to define that period
chronologically would be utterly futile. When we have stated that it
is more ancient than almost any other period which we can discuss, we
have expressed all that we are really entitled to say. Yet this
conveys not a little. It directs us to look back through all the ages
of modern human history, through the great days of ancient Greece and
Rome, back through the times when Egypt and Assyria were names of
renown, through the days when Nineveh and Babylon were mighty and
populous cities in the zenith of their glory. Back earlier still to
those more ancient nations of which we know hardly anything, and
still earlier to the prehistoric man, of whom we know less; back,
finally, to the days when man first trod on this planet, untold ages
ago. Here is indeed a portentous retrospect from most points of view,
but it is only the commencement of that which our subject suggests.
For man is but the final product of the long anterior ages during
which the development of life seems to have undergone an exceedingly
gradual elevation. Our retrospect now takes its way along the vistas
opened up by the geologists. We look through the protracted tertiary
ages, when mighty animals, now generally extinct, roamed over the
continents. Back still earlier through those wondrous secondary
periods, where swamps or oceans often covered what is now dry land,
and where mighty reptiles of uncouth forms stalked and crawled and
swam through the old world and the new. Back still earlier through
those vitally significant ages when the sunbeams were being garnered
and laid aside for man's use in the great forests, which were
afterwards preserved by being transformed into seams of coal. Back
still earlier through endless thousands of years, when lustrous
fishes abounded in the oceans; back again to those periods
characterized by the lower types of life; and still earlier to that
incredibly remote epoch when life itself began to dawn on our
awakening globe. Even here the epoch of our present history can hardly
be said to have been reached. We have to look through a long
succession of ages still antecedent. The geologist, who has hitherto
guided our view, cannot render us much further assistance; but the
physicist is at hand--he teaches us that the warm globe on which life
is beginning has passed in its previous stages through every phase of
warmth, of fervour, of glowing heat, of incandescence, and of actual
fusion; and thus at last our retrospect reaches to that particular
period of our earth's past history which is specially illustrated by
the modern doctrine of Time and Tide.
The present is the clue to the past. It is the steady application of
this principle which has led to such epoch-making labours as those by
which Lyell disclosed the origin of the earth's crust, Darwin the
origin of species, Max Müller the origin of language. In our present
subject the course is equally clear. Study exactly what is going on at
present, and then have the courage to apply consistently and
rigorously what we have learned from the present to the interpretation
of the past.
Thus we begin with the ripple of the tide on the sea-beach which we
see to-day. The ebb and the flow of the tide are the present
manifestations of an agent which has been constantly at work. Let that
present teach us what tides must have done in the indefinite past.
It has been known from the very earliest times that the moon and the
tides were connected together--connected, I say, for a great advance
had to be made in human knowledge before it would have been possible
to understand the true relation between the tides and the moon.
Indeed, that relation is so far from being of an obvious character,
that I think I have read of a race who felt some doubt as to whether
the moon was the cause of the tides, or the tides the cause of the
moon. I should, however, say that the moon is not the sole agent
engaged in producing this periodic movement of our waters. The sun
also arouses a tide, but the solar tide is so small in comparison with
that produced by the moon, that for our present purpose we may leave
it out of consideration. We must, however, refer to the solar tide at
a later period of our discourses, for it will be found to have played
a very splendid part at the initial stage of the Earth-Moon History,
while in the remote future it will again rise into prominence.
It will be well to set forth a few preliminary figures which shall
explain how it comes to pass that the efficiency of the sun as a
tide-producing agent is so greatly inferior to that of the moon.
Indeed, considering that the sun has a mass so stupendous, that it
controls the entire planetary system, how is it that a body so
insignificant as the moon can raise a bigger tide on the ocean than
can the sun, of which the mass is 26,000,000 times as great as that of
our satellite?
This apparent paradox will disappear when we enunciate the law
according to which the efficiency of a tide-producing agent is to be
estimated. This law is somewhat different from the familiar form in
which the law of gravitation is expressed. The gravitation between two
distant masses is to be measured by multiplying these masses together,
and dividing the product by the _square_ of the distance. The law for
expressing the efficiency of a tide-producing agent varies not
according to the inverse square, but according to the inverse _cube_
of the distance. This difference in the expression of the law will
suffice to account for the superiority of the moon as a tide-producer
over the sun. The moon's distance on an average is about one 386th
part of that of the sun, and thus it is easy to show that so far as
the mere attraction of gravitation is concerned, the efficiency of the
sun's force on the earth is about one hundred and seventy-five times
as great as the force with which the moon attracts the earth. That is
of course calculated under the law of the inverse square. To determine
the tidal efficiency we have to divide this by three hundred and
eighty-six, and thus we see that the tidal efficiency of the sun is
less than half that of the moon.
When the solar tide and the lunar tide are acting in unison, they
conspire to produce very high tides and very low tides, or, as we
call them, spring tides. On the other hand, when the sun is so placed
as to give us a low tide while the moon is producing a high tide, the
net result that we actually experience is merely the excess of the
lunar tide over the solar tide; these are what we call neap tides. In
fact, by very careful and long-continued observations of the rise and
fall of the tides at a particular port, it becomes possible to
determine with accuracy the relative ranges of spring tides and neap
tides; and as the spring tides are produced by moon plus sun, while
the neap tides are produced by moon minus sun, we obtain a means of
actually weighing the relative masses of the sun and moon. This is one
of the remarkable facts which can be deduced from a prolonged study of
the tides.
The demonstration of the law of the tide-producing force is of a
mathematical character, and I do not intend in these lectures to enter
into mathematical calculations. There is, however, a simple line of
reasoning which, though it falls far short of actual demonstration,
may yet suffice to give a plausible reason for the law.
The tides really owe their origin to the fact that the tide-producing
agent operates more powerfully on those parts of the tide-exhibiting
body which are near to it, than on the more distant portions of the
same. The nearer the two bodies are together, the larger
proportionally will be the differences in the distances of its various
parts from the tide-producing body; and on this account the leverage,
so to speak, of the action by which the tides are produced is
increased. For instance, if the two bodies were brought within half
their original distance of each other, the relative size of each body,
as viewed from the other, will be doubled; and what we have called the
leverage of the tide-producing ability will be increased twofold. The
gravitation also between the two bodies is increased fourfold when the
distance is halved, and consequently, the tide-producing ability is
doubled for one reason, and increased fourfold again by another;
hence, the tides will be increased eightfold when the distance is
reduced to one half. Now, as eight is the cube of two, this
illustration may be taken as a verification of the law, that the
efficiency of a body as a tide-producer varies inversely as the cube
of the distance between it and the body on which the tides are being
raised.
For simplicity we may make the assumption that the whole of the earth
is buried beneath the ocean, and that the moon is placed in the plane
of the equator. We may also entirely neglect for the present the tides
produced by the sun, and we shall also make the further assumption
that friction is absent. What friction is capable of doing we shall,
however, refer to later on. The moon will act on the ocean and deform
it, so that there will be high tide along one meridian, and high tide
also on the opposite meridian. This is indeed one of the paradoxes by
which students are frequently puzzled when they begin to learn about
the tides. That the moon should pull the water up in a heap on one
side seems plausible enough. High tide will of course be there; and
the student might naturally think that the water being drawn in this
way into a heap on one side, there will of course be low tide on the
opposite side of the earth. A natural assumption, perhaps, but
nevertheless a very wrong one. There are at every moment two opposite
parts of the earth in a condition of high water; in fact, this will
be obvious if we remember that every day, or, to speak a little more
accurately, in every twenty-four hours and fifty one minutes, we have
on the average two high tides at each locality. Of course this could
not be if the moon raised only one heap of high water, because, as the
moon only appears to revolve around the earth once a day, or, more
accurately, once in that same average period of twenty-four hours and
fifty-one minutes, it would be impossible for us to have high tides
succeeding each other as they do in periods a little longer than
twelve hours, if only one heap were carried round the earth.
The first question then is, as to how these two opposite heaps of
water are placed in respect to the position of the moon. The most
obvious explanation would seem to be, that the moon should pull the
waters up into a heap directly underneath it, and that therefore there
should be high water underneath the moon. As to the other side, the
presence of a high tide there was, on this theory, to be accounted for
by the fact that the moon pulled the earth away from the waters on the
more remote side, just as it pulled the waters away from the more
remote earth on the side underneath the moon. It is, however,
certainly not the case that the high tide is situated in the simple
position that this law would indicate, and which we have represented
in Fig. 1, where the circular body is the earth, the ocean surrounding
which is distorted by the action of the tides.
[Illustration: FIG. 1.]
We have here taken an oval to represent the shape into which the water
is supposed to be forced or drawn by the tidal action of the
tide-producing body. This may possibly be a correct representation of
what would occur on an ideal globe entirely covered with a
frictionless ocean. But as our earth is not covered entirely by water,
and as the ocean is very far from being frictionless, the ideal tide
is not the tide that we actually know; nor is the ideal tide
represented by this oval even an approximation to the actual tides to
which our oceans are subject. Indeed, the oval does not represent the
facts at all, and of this it is only necessary to adduce a single fact
in demonstration. I take the fundamental issue so often debated, as to
whether in the ocean vibrating with ideal tides the high water or the
low water should be under the moon. Or to put the matter otherwise;
when we represent the displaced water by an oval, is the long axis of
the oval to be turned to the moon, as generally supposed, or is it to
be directed at right angles therefrom? If the ideal tides were in any
degree representative of the actual tides, so fundamental a question
as this could be at once answered by an appeal to the facts of
observation. Even if friction in some degree masked the phenomena,
surely one would think that the state of the actual tides should still
enable us to answer this question.
But a study of the tides at different ports fails to realize this
expectation. At some ports, no doubt, the tide is high when the moon
is on the meridian. In that case, of course, the high water is under
the moon, as apparently ought to be the case invariably, on a
superficial view. But, on the other hand, there are ports where there
is often low water when the moon is crossing the meridian. Yet other
ports might be cited in which every intermediate phase could be
observed. If the theory of the tides was to be the simple one so often
described, then at every port noon should be the hour of high water on
the day of the new moon or of the full moon, because then both
tide-exciting bodies are on the meridian at the same time. Even if the
friction retarded the great tidal wave uniformly, the high tide on the
days of full or change should always occur at fixed hours; but,
unfortunately, there is no such delightful theory of the tides as this
would imply. At Greenock no doubt there is high water at or about noon
on the day of full or change; and if it could be similarly said that
on the day of full or change there was high water everywhere at local
noon, then the equilibrium theory of the tides, as it is called,
would be beautifully simple. But this is not the case. Even around our
own coasts the discrepancies are such as to utterly discredit the
theory as offering any practical guide. At Aberdeen the high tide does
not appear till an hour later than the doctrine would suggest. It is
two hours late at London, three at Tynemouth, four at Tralee, five at
Sligo, and six at Hull. This last port would be indeed the haven of
refuge for those who believe that the low tide ought to be under the
moon. At Hull this is no doubt the case; and if at all other places
the water behaved as it does at Hull, why then, of course, it would
follow that the law of low water under the moon was generally true.
But then this would not tally with the condition of affairs at the
other places I have named; and to complete the cycle I shall add a few
more. At Bristol the high water does not get up until seven hours
after the moon has passed the meridian, at Arklow the delay is eight
hours, at Yarmouth it is nine, at the Needles it is ten hours, while
lastly, the moon has nearly got back to the meridian again ere it has
succeeded in dragging up the tide on which Liverpool's great commerce
so largely depends.
Nor does the result of studying the tides along other coasts beside
our own decide more conclusively on the mooted point. Even ports in
the vast ocean give a very uncertain response. Kerguelen Island and
Santa Cruz might seem to prove that the high tide occurs under the
moon, but unfortunately both Fiji and Ascension seem to present us
with an equally satisfactory demonstration, that beneath the moon is
the invariable home of low water.
I do not mean to say that the study of the tides is in other respects
such a confused subject as the facts I have stated would seem to
indicate. It becomes rather puzzling, no doubt, when we compare the
tides at one port with the tides elsewhere. The law and order are,
then, by no means conspicuous, they are often hardly discernible. But
when we confine our attention to the tides at a single port, the
problem becomes at once a very intelligible one. Indeed, the
investigation of the tides is an easy subject, if we are contented
with a reasonably approximate solution; should, however, it be
necessary to discuss fully the tides at any port, the theory of the
method necessary for doing so is available, and a most interesting and
beautiful theory it certainly is.
Let us then speak for a few moments about the methods by which we can
study the tides at a particular port. The principle on which it is
based is a very simple one.
It is the month of August, the 18th, we shall suppose, and we are
going to enjoy a delicious swim in the sea. We desire, of course, to
secure a high tide for the purpose of doing so, and we call an almanac
to help us. I refer to the Thom's Dublin Directory, where I find the
tide to be high at 10h. 14m. on the morning of the 18th of August.
That will then be the time to go down to the baths at Howth or
Kingstown.
But what I am now going to discourse to you about is not the delights
of sea-bathing, it is rather a different inquiry. I want to ask, How
did the people who prepared that almanac know years beforehand, that
on that particular day the tide would be high at that particular hour?
How do they predict for every day the hour of high water? and how
comes it to pass that these predictions are invariably correct?
We first refer to that wonderful book, the _Nautical Almanac_. In that
volume the movements of the moon are set forth with full detail; and
among other particulars we can learn on page iv of every month the
mean time of the moon's meridian passage. It appears that on the day
in question the moon crossed the meridian at 11h. 23m. Thus we see
there was high water at Dublin at 10h. 14m., and 1h. 9m. later, that
is, at 11h. 23m., the moon crossed the meridian.
Let us take another instance. There is a high tide at 3.40 P.M. on the
25th August, and again the infallible _Nautical Almanac_ tells us that
the moon crossed the meridian at 5h. 44m., that is, at 2h. 4m. after
the high water.
In the first case the moon followed the tide in about an hour, and in
the second case the moon followed in about two hours. Now if we are to
be satisfied with a very rough tide rule for Dublin, we may say
generally that there is always a high tide an hour and a half before
the moon crosses the meridian. This would not be a very accurate
rule, but I can assure you of this, that if you go by it you will
never fail of finding a good tide to enable you to enjoy your swim. I
do not say this rule would enable you to construct a respectable
tide-table. A ship-owner who has to creep up the river, and to whom
often the inches of water are material, will require far more accurate
tables than this simple rule could give. But we enter into rather
complicated matters when we attempt to give any really accurate
methods of computation. On these we shall say a few words presently.
What I first want to do, is to impress upon you in a simple way the
fact of the relation between the tide and the moon.
To give another illustration, let us see how the tides at London
Bridge are related to the moon. On Jan. 1st, 1887, it appeared that
the tide was high at 6h. 26m. P.M., and that the moon had crossed the
meridian 56m. previously; on the 8th Jan. the tide was high at 0h.
43m. P.M., and the moon had crossed the meridian 2h. 1m. previously.
Therefore we would have at London Bridge high water following the
moon's transit in somewhere about an hour and a half.
I choose a day at random, for example--the 12th April. The moon
crosses the upper meridian at 3h. 39m. A.M., and the lower meridian at
4h 6m. P.M. Adding an hour and a half to each would give the high
tides at 5h 9m. A.M. and 5h. 36m. P.M.; as a matter of fact, they are
4h. 58m. A.M. and 5h. 20m. P.M.
But these illustrations are sufficient. We find that at London, in a
general way, high water appears at London Bridge about an hour and a
half after the moon has passed the meridian of London. It so happens
that the interval at Dublin is about the same, _i.e._ an hour and a
half; only that in the latter case the high water precedes the moon by
that interval instead of following it. We may employ the same simple
process at other places. Choose two days about a week distant; find on
each occasion the interval between the transit of the moon and the
time of high water, then the mean of these two differences will always
give some notion of the interval between high water and the moon's
transit. If then we take from the _Nautical Almanac_ the time of the
moon's transit, and apply to it the correction proper for the port,
we shall always have a sufficiently good tide-table to guide us in
choosing a suitable time for taking our swim or our walk by the
sea-side; though if you be the captain of a vessel, you will not be so
imprudent as to enter port without taking counsel of the accurate
tide-tables, for which we are indebted to the Admiralty.
Every one who visits the sea-side, or who lives at a sea-port, should
know this constant for the tides, which affect him and his movements
so materially. If he will discover it from his own experience, so much
the better.
The first point to be ascertained is the time of high water. Do not
take this from any local table; you ought to observe it for yourself.
You will go to the pier head, or, better still, to some place where
the rise and fall of the mere waves of the sea will not embarrass you
in your work. You must note by your watch the time when the tide is
highest. An accurate way of doing this will be to have a scale on
which you can measure the height at intervals of five minutes about
the time of high water. You will then be able to conclude the time at
which the tide was actually at its highest point; but even if no
great accuracy be obtainable, you can still get much interesting
information, for you will without much difficulty be right within ten
minutes or a quarter of an hour.
The correction for the port is properly called the "establishment,"
this being the average time of high water on the days of full and
change of the moon at the particular port in question.
We can considerably amend the elementary notion of the tides which the
former method has given us, if we adopt the plan described by Dr.
Whewell in the first four editions of the _Admiralty Manual of
Scientific Inquiry_. We speak of the interval between the transit of
the moon and the time of high water as the luni-tidal interval. Of
course at full and change this is the same thing as the establishment,
but for other phases of the moon the establishment must receive a
correction before being used as the luni-tidal interval. The
correction is given by the following table--
Hour of Moon's transit after Sun:
0| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11
-+----+----+----+----+----+----+----+----+----+----+----
0|-20m|-30m|-50m|-60m|-60m|-60m|-40m|-10m|+10m|+20m|+10m
Correction of establishment to find luni-tidal interval:
Thus at a port where the establishment was 3h. 25m., let us suppose
that the transit of the moon took place at 6 P.M.; then we correct the
establishment by -60m., and find the luni-tidal interval to be 2h.
25m., and accordingly the high water takes place at 8h. 25m. P.M.
But even this method is only an approximation. The study of the tides
is based on accurate observation of their rise and fall on different
places round the earth. To show how these observations are to be made,
and how they are to be discussed and reduced when they have been made,
I may refer to the last edition of the _Admiralty Manual of Scientific
Inquiry_, 1886. For a complete study of the tides at any port a
self-registering tide-gauge should be erected, on which not alone the
heights and times of high and low water should be depicted, but also
the continuous curve which shows at any time the height of the water.
In fact, the whole subject of the practical observation and discussion
and prediction of tides is full of valuable instruction, and may be
cited as one of the most complete examples of the modern scientific
methods.
In the first place, the tide-gauge itself is a delicate instrument;
it is actuated by a float which rises and falls with the water, due
provision being made that the mere influence of waves shall not make
it to oscillate inconveniently. The motion of the float when suitably
reduced by mechanism serves to guide a pencil, which, acting on the
paper round a revolving drum, gives a faithful and unintermitting
record of the height of the water.
Thus what the tide-gauge does is to present to us a long curved line
of which the summits correspond to the heights of high water, while
the depressions are the corresponding points of low water. The long
undulations of this curve are, however, very irregular. At spring
tides, when the sun and the moon conspire, the elevations rise much
higher and the depressions sink much lower than they do at neap tides,
when the high water raised by the moon is reduced by the action of the
sun. There are also many minor irregularities which show the tides to
be not nearly such simple phenomena as might be at first supposed. But
what we might hastily think of as irregularities are, in truth, the
most interesting parts of the whole phenomena. Just as in the
observations of the planets the study of the perturbations has led us
to results of the widest interest and instruction, so it is these
minor phenomena of the tides which seem most pregnant with scientific
interest.
The tide-gauge gives us an elaborate curve. How are we to interpret
that curve? Here indeed a most beautiful mathematical theorem comes to
our aid. Just as ordinary sounds consist of a number of undulations
blended together, so the tidal wave consists of a number of distinct
undulations superposed. Of these the ordinary lunar tide and the
ordinary solar tide are the two principal; but there are also minor
undulations, harmonics, so to speak, some originating from the moon,
some originating from the sun, and some from both bodies acting in
concert.
In the study of sound we can employ an acoustic apparatus for the
purpose of decomposing any proposed note, and finding not only the
main undulation itself, but the several superposed harmonics which
give to the note its timbre. So also we can analyze the undulation of
the tide, and show the component parts. The decomposition is effected
by the process known as harmonic analysis. The principle of the
method may be very simply described. Let us fix our attention on any
particular "tide," for so the various elements are denoted. We can
always determine beforehand, with as much accuracy as we may require,
what the period of that tide will be. For instance, the period of the
lunar semi-diurnal tide will of course be half the average time
occupied by the moon to travel round from the meridian of any place
until it regains the same meridian; the period of the lunar diurnal
tide will be double as great; and there are fortnightly tides, and
others of periods still greater. The essential point to notice is,
that the periods of these tides are given by purely astronomical
considerations from the periods of the motions theory, and do not
depend upon the actual observations.
We measure off on the curve the height of the tide at intervals of an
hour. The larger the number of such measures that are available the
better; but even if there be only three hundred and sixty or seven
hundred and twenty consecutive hours, then, as shown by Professor G.
H. Darwin in the _Admiralty Manual_ already referred to, it will
still be possible to obtain a very competent knowledge of the tides in
the particular port where the gauge has been placed.
The art (for such indeed it may be described) of harmonic analysis
consists in deducing from the hourly observations the facts with
regard to each of the constituent tides. This art has been carried to
such perfection, that it has been reduced to a very simple series of
arithmetical operations. Indeed it has now been found possible to call
in the aid of ingenious mechanism, by which the labours of computation
are entirely superseded. The pointer of the harmonic analyzer has
merely to be traced over the curve which the tide-gauge has drawn, and
it is the function of the machine to decompose the composite
undulation into its parts, and to exhibit the several constituent
tides whose confluence gives the total result.
As if nothing should be left to complete the perfection of a process
which, both from its theoretical and its practical sides, is of such
importance, a machine for predicting tides has been designed,
constructed, and is now in ordinary use. When by the aid of the
harmonic analysis the effectiveness of the several constituent tides
affecting a port have become fully determined, it is of course
possible to predict the tides for that port. Each "tide" is a simple
periodic rise and fall, and we can compute for any future time the
height of each were it acting alone. These heights can all be added
together, and thus the height of the water is obtained. In this way a
tide-table is formed, and such a table when complete will express not
alone the hours and heights of high water on every day, but the height
of the water at any intervening hour.
The computations necessary for this purpose are no doubt simple, so
far as their principle is concerned; but they are exceedingly tedious,
and any process must be welcomed which affords mitigation of a task so
laborious. The entire theory of the tides owes much to Sir William
Thomson in the methods of observation and in the methods of reduction.
He has now completed the practical parts of the subject by inventing
and constructing the famous tide-predicting engine.
The principle of this engine is comparatively simple. There is a chain
which at one end is fixed, and at the other end carries the pencil
which is pressed against the revolving drum on which the prediction is
to be inscribed. Between its two ends the chain passes up and down
over pulleys. Each pulley corresponds to one of the "tides," and there
are about a dozen altogether, some of which exercise but little
effect. Of course if the centres of the pulleys were all fixed the pen
could not move, but the centre of each pulley describes a circle with
a radius proportional to the amplitude of the corresponding tide, and
in a time proportional to the period of that tide. When these pulleys
are all set so as to start at the proper phases, the motion is
produced by turning round a handle which makes the drum rotate, and
sets all the pulleys in motion. The tide curve is thus rapidly drawn
out; and so expeditious is the machine, that the tides of a port for
an entire year can be completely worked out in a couple of hours.
While the student or the philosopher who seeks to render any account
of the tide on dynamical grounds is greatly embarrassed by the
difficulties introduced by friction, we, for our present purpose in
the study of the great romance of modern science opened up to us by
the theory of the tides, have to welcome friction as the agent which
gives to the tides their significance from our point of view.
There is the greatest difference between the height of the rise and
fall of the tide at different localities. Out in mid-ocean, for
instance, an island like St. Helena is washed by a tide only about
three feet in range; an enclosed sea like the Caspian is subject to no
appreciable tides whatever, while the Mediterranean, notwithstanding
its connection with the Atlantic, is still only subject to very
inconsiderable tides, varying from one foot to a few feet. The
statement that water always finds its own level must be received, like
many another proposition in nature, with a considerable degree of
qualification. Long ere one tide could have found its way through the
Straits of Gibraltar in sufficient volume to have appreciably affected
the level of the great inland sea, its effects would have been
obliterated by succeeding tides. On the other hand, there are certain
localities which expose a funnel-shape opening to the sea; into these
the great tidal wave rushes, and as it passes onwards towards the
narrow part, the waters become piled up so as to produce tidal
phenomena of abnormal proportions. Thus, in our own islands, we have
in the Bristol Channel a wide mouth into which a great tide enters,
and as it hurries up the Severn it produces the extraordinary
phenomenon of the Bore. The Bristol Channel also concentrates the
great wave which gives Chepstow and Cardiff a tidal range of
thirty-seven or thirty-eight feet at springs, and forces the sea up
the river Avon so as to give Bristol a wonderful tide. There is hardly
any more interesting spot in our islands for the observation of tides
than is found on Clifton Suspension Bridge. From that beautiful
structure you look down on a poor and not very attractive stream,
which two hours later becomes transformed into a river of ample
volume, down which great ships are navigated. But of all places in the
world, the most colossal tidal phenomena are those in the Bay of
Fundy. Here the Atlantic passes into a long channel whose sides
gradually converge. When the great pulse of the tide rushes up this
channel, it is gradually accumulated into a mighty volume at the
upper end, the ebb and flow of which at spring tides extends through
the astonishing range of not less than fifty feet.
These discrepancies between the tides at different places are chiefly
due to the local formations of the coasts and the sea-beds. Indeed, it
seems that if the whole earth were covered with an uniform and deep
ocean of water, the tides would be excessively feeble. On no other
supposition can we reasonably account for the fact that our barometric
records fail to afford us any very distinct evidence as to the
existence of tides in the atmosphere. For you will, of course,
remember that our atmosphere may be regarded as a deep and vast ocean
of air, which embraces the whole earth, extending far above the
loftiest summits of the mountains.
It is one of the profoundest of nature's laws that wherever friction
takes place, energy has to be consumed. Perhaps I ought rather to say
transformed, for of course it is now well known that consumption of
energy in the sense of absolute loss is impossible. Thus, when energy
is expended in moving a body in opposition to the force of friction,
or in agitating a liquid, the energy which disappears in its
mechanical form reappears in the form of heat. The agitation of water
by paddles moving through it warms the water, and the accession of
heat thus acquired measures the energy which has been expended in
making the paddles rotate. The motion of a liquid of which the
particles move among each other with friction, can only be sustained
by the incessant degradation of energy from the mechanical form into
the lower form of diffused heat. Thus the very fact that the tides are
ebbing and flowing, and that there is consequently incessant friction
going on among all the particles of water in the ocean, shows us that
there must be some great store of energy constantly available to
supply the incessant draughts made upon it by the daily oscillation of
the tides. In addition to the mere friction between the particles of
water, there are also many other ways in which the tides proclaim to
us that there is some great hoard of energy which is continually
accessible to their wants. Stand on the bank of an estuary or river up
and down which a great tidal current ebbs and flows; you will see the
water copiously charged with sediment which the tide is bearing along.
Engineers are well aware of the potency of the tide as a vehicle for
transporting stupendous quantities of sand or mud. A sand-bank impedes
the navigation of a river; the removal of that sand-bank would be a
task, perhaps, conceivably possible by the use of steam dredges and
other appliances, whereby vast quantities of sand could be raised and
transported to another locality where they would be innocuous. It is
sometimes possible to effect the desired end by applying the power of
the tide. A sea-wall judiciously thrown out will sometimes concentrate
the tide into a much narrower channel. Its daily oscillations will be
accomplished with greater vehemence, and as the tide rushes furiously
backwards and forwards over the obstacle, the incessant action will
gradually remove it, and the impediment to navigation may be cleared
away. Here we actually see the tides performing a piece of definite
and very laborious work, to accomplish which by the more ordinary
agents would be a stupendous task.
In some places the tides are actually harnessed so as to accomplish
useful work. I have read that underneath old London Bridge there used
formerly to be great water-wheels, which were turned by the tide as it
rushed up the river, and turned again, though in the opposite way, by
the ebbing tide. These wheels were, I believe, employed to pump up
water, though it does not seem obvious for what purposes the water
would have been suitable. Indeed in the ebb and flow all round our
coasts there is a potential source of energy which has hitherto been
allowed to run to waste. The tide could be utilized in various ways.
Many of you will remember the floating mills on the Rhine. They are
vessels like paddle steamers anchored in the rapid current. The flow
of the river makes the paddles rotate, and thus the machinery in the
interior is worked. Such craft moored in a rapid tide-way could also
be made to convey the power of the tides into the mechanism of the
mill. Or there is still another method which has been employed, and
which will perhaps have a future before it in those approaching times
when the coal-cellars of England shall be exhausted. Imagine on the
sea-coast a large flat extent which is inundated twice every day by
the tide. Let us build a stout wall round this area, and provide it
with a sluice-gate. Open the gate as the tide rises, and the great
pond will be filled; then at the moment of high water close the
sluice, and the pond-full will be impounded. If at low tide the sluice
be opened the water will rush tumultuously out. Now suppose that a
water-wheel be provided, so that the rapid rush of water from the exit
shall fall upon its blades; then a source of power is obviously the
result.
At present, however, such a contrivance would naturally find no
advocates, for of course the commercial aspect of the question is that
which will decide whether the scheme is practicable and economical.
The issue indeed can be very simply stated. Suppose that a given
quantity of power be required--let us say that of one hundred horse.
Then we have to consider the conditions under which a contrivance of
the kind we have sketched shall yield a power of this amount. Sir
William Thomson, in a very interesting address to the British
Association at York in 1881, discussed this question, and I shall here
make use of the facts he brought forward on that occasion. He showed
that to obtain as much power as could be produced by a steam-engine
of one hundred horse power, a very large reservoir would be required.
It is doubtful indeed whether there would be many localities on the
earth which would be suitable for the purpose. Suppose, however, an
estuary could be found which had an area of forty acres; then if a
wall were thrown across the mouth so that the tide could be impounded,
the total amount of power that could be yielded by a water-wheel
worked by the incessant influx and efflux of the tide would be equal
to that yielded by the one hundred horse engine, running continuously
from one end of the year to the other.
There are many drawbacks to a tide-mill of this description. In the
first place, its situation would naturally be far removed from other
conveniences necessary for manufacturing purposes. Then too there is
the great irregularity in the way in which the power is rendered
available. At certain periods during the twenty-four hours the mill
would stop running, and the hours when this happened would be
constantly changing. The inconvenience from the manufacturer's point
of view of a deficiency of power during neap tides might not be
compensated by the fact that he had an excessive supply of power at
spring-tides. Before tide-mills could be suitable for manufacturing
purposes, some means must be found for storing away the energy when it
is redundant, and applying it when its presence is required. We should
want in fact for great sources of energy some contrivance which shall
fulfil the same purpose as the accumulators do in an electrical
installation.
Even then, however, the financial consideration remains, as to whether
the cost of building the dam and maintaining the tide-mill in good
order will not on the whole exceed the original price and the charges
for the maintenance of a hundred horse power steam-engine. There
cannot be a doubt that in this epoch of the earth's history, so long
as the price of coal is only a few shillings a ton, the tide-mill,
even though we seem to get its power without current expense, is
vastly more expensive than a steam-engine. Indeed, Sir William Thomson
remarks, that wherever a suitable tidal basin could be found, it would
be nearly as easy to reclaim the land altogether from the sea. And if
this were in any locality where manufactures were possible, the
commercial value of forty acres of reclaimed land would greatly exceed
all the expenses attending the steam-engine. But when the time comes,
as come it apparently will, that the price of coal shall have risen to
several pounds a ton, the economical aspect of steam as compared with
other prime movers will be greatly altered; it will then no doubt be
found advantageous to utilize great sources of energy, such as Niagara
and the tides, which it is now more prudent to let run to waste.
For my argument, however, it matters little that the tides are not
constrained to do much useful work. They are always doing work of some
kind, whether that be merely heating the particles of water by
friction, or vaguely transporting sand from one part of the ocean to
the other. Useful work or useless work are alike for the purpose of my
argument. We know that work can never be done unless by the
consumption or transformation of energy. For each unit of work that is
done--whether by any machine or contrivance, by the muscles of man or
any other animal, by the winds, the waves, or the tides, or in any
other way whatever--a certain equivalent quantity of energy must have
been expended. When, therefore, we see any work being performed, we
may always look for the source of energy to which the machine owes its
efficiency. In fact, it is the old story illustrated, that perpetual
motion is impossible. A mechanical device, however ingenious may be
the construction, or however accurate the workmanship, can never
possess what is called perpetual motion. It is needless to enter into
details of any proposed contrivance of wheels, of pumps, of pulleys;
it is sufficient to say that nothing in the shape of mechanism can
work without friction, that friction produces heat, that heat is a
form of energy, and that to replace the energy consumed in producing
the heat there must be some source from which the machine is
replenished if its motion is to be continued indefinitely.
Hence, as the tides may be regarded as a machine doing work, we have
to ascertain the origin of that energy which they are continually
expending. It is at this point that we first begin to feel the
difficulties inherent in the theory of tidal evolution. I do not mean
difficulties in the sense of doubts, for up to the present I have
mentioned no doubtful point. When I come to such I shall give due
warning. By difficulties I now mean points which it is not easy to
understand without a little dynamical theory; but we must face these
difficulties, and endeavour to elucidate them as well as we can.
Let us first see what the sources of energy can possibly be on which
the tides are permitted to draw. Our course is simplified by the fact
that the energy of which we have to speak is of a mechanical
description, that is to say, not involving heat or other more obscure
forms of energy. A simple type of energy is that possessed by a
clock-weight after the clock has been wound. A store of power is thus
laid up which is gradually doled out during the week in small
quantities, second by second, to sustain the motion of the pendulum.
The energy in this case is due to the fact that the weight is
attracted by the earth, and is yielded according as the weight sinks
downwards. In the separation between two mutually attracting bodies, a
store of energy is thus implied. What we learn from an ordinary clock
may be extended to the great bodies of the universe. The moon is a
gigantic globe separated from our earth by a distance of 240,000
miles. The attraction between these two bodies always tends to bring
them together. No doubt the moon is not falling towards the earth as
the descending clock-weight is doing. We may, in fact, consider the
moon, so far as our present object is concerned, to be revolving
almost in a circle, of which the earth is the centre. If the moon,
however, were to be stopped, it would at once commence to rush down
towards the earth, whither it would arrive with an awful crash in the
course of four or five days. It is fortunately true that the moon does
not behave thus; but it has the ability of doing so, and thus the mere
separation between the earth and the moon involves the existence of a
stupendous quantity of energy, capable under certain conditions of
undergoing transformation.
There is also another source of mechanical energy besides that we have
just referred to. A rapidly moving body possesses, in virtue of its
motion, a store of readily available energy, and it is easy to show
that energy of this type is capable of transformation into other
types. Think of a cannon-ball rushing through the air at a speed of a
thousand feet per second; it is capable of wreaking disaster on
anything which it meets, simply because its rapid motion is the
vehicle by which the energy of the gunpowder is transferred from the
gun to where the blow is to be struck. Had the cannon been directed
vertically upwards, then the projectile, leaving the muzzle with the
same initial velocity as before, would soar up and up, with gradually
abating speed, until at last it reached a turning-point, the elevation
of which would depend upon the initial velocity. Poised for a moment
at the summit, the cannon-ball may then be likened to the
clock-weight, for the entire energy which it possessed by its motion
has been transformed into the statical energy of a raised weight. Thus
we see these two forms of energy are mutually interchangeable. The
raised weight if allowed to fall will acquire velocity, or the rapidly
moving weight if directed upwards will acquire altitude.
The quantity of energy which can be conveyed by a rapidly moving body
increases greatly with its speed. For instance, if the speed of the
body be doubled, the energy will be increased fourfold, or, in
general, the energy which a moving body possesses may be said to be
proportional to the square of its speed. Here then we have another
source of the energy present in our earth-moon system; for the moon is
hurrying along in its path with a speed of two-thirds of a mile per
second, or about twice or three times the speed of a cannon-shot.
Hence the fact that the moon is continuously revolving in a circle
shows us that it possesses a store of energy which is nine times as
great as that which a cannon-ball as massive as the moon, and fired
with the ordinary velocity, would receive from the powder which
discharged it.
Thus we see that the moon is endowed with two sources of energy, one
of which is due to its separation from the earth, and the other to the
speed of its motion. Though these are distinct, they are connected
together by a link which it is important for us to comprehend. The
speed with which the moon revolves around the earth is connected with
the moon's distance from the earth. The moon might, for instance,
revolve in a larger circle than that which it actually pursues; but
if it did so, the speed of its motion would have to be appropriately
lessened. The orbit of the moon might have a much smaller radius than
it has at present, provided that the speed was sufficiently increased
to compensate for the increased attraction which the earth would
exercise at the lessened distance. Indeed, I am here only stating what
every one is familiar with under the form of Kepler's Law, that the
square of the periodic time is in proportion to the cube of the mean
distance. To each distance of the moon therefore belongs an
appropriate speed. The energy due to the moon's position and the
energy due to its motion are therefore connected together. One of
these quantities cannot be altered without the other undergoing
change. If the moon's orbit were increased there would be a gain of
energy due to the enlarged distance, and a loss of energy due to the
diminished speed. These would not, however, exactly compensate. On the
whole, we may represent the total energy of the moon as a single
quantity, which increases when the distance of the moon from the earth
increases, and lessens when the distance from the earth to the moon
lessens. For simplicity we may speak of this as moon-energy.
But the most important constituent of the store of energy in the
earth-moon system is that contributed by the earth itself. I do not
now speak of the energy due to the velocity of the earth in its orbit
round the sun. The moon indeed participates in this equally with the
earth, but it does not affect those mutual actions between the earth
and moon with which we are at present concerned. We are, in fact,
discussing the action of that piece of machinery the earth-moon
system; and its action is not affected by the circumstance that the
entire machine is being bodily transported around the sun in a great
annual voyage. This has little more to do with the action of our
present argument than has the fact that a man is walking about to do
with the motions of the works of the watch in his pocket. We shall,
however, have to allude to this subject further on.
The energy of the earth which is significant in the earth-moon theory
is due to the earth's rotation upon its axis. We may here again use as
an illustration the action of machinery; and the special contrivance
that I now refer to is the punching-engine that is used in our
ship-building works. In preparing a plate of iron to be riveted to the
side of a ship, a number of holes have to be made all round the margin
of the plate. These holes must be half an inch or more in diameter,
and the plate is sometimes as much as, or more than, half an inch in
thickness. The holes are produced in the metal by forcing a steel
punch through it; and this is accomplished without even heating the
plate so as to soften the iron. It is needless to say that an intense
force must be applied to the punch. On the other hand, the distance
through which the punch has to be moved is comparatively small. The
punch is attached to the end of a powerful lever, the other end of the
lever is raised by a cam, so as to depress the punch to do its work.
An essential part of the machine is a small but heavy fly-wheel
connected by gearing with the cam.
This fly-wheel when rapidly revolving contains within it, in virtue of
its motion, a large store of energy which has gradually accumulated
during the time that the punch is not actually in action. The energy
is no doubt originally supplied from a steam-engine. What we are
especially concerned with is the action of the rapidly rotating wheel
as a reservoir in which a large store of energy can be conveniently
maintained until such time as it is wanted. In the action of punching,
when the steel die comes down upon the surface of the plate, a large
quantity of energy is suddenly demanded to force the punch against the
intense resistance it experiences; the energy for this purpose is
drawn from the store in the fly-wheel, which experiences no doubt a
check in its velocity, to be regained again from the energy of the
engine during the interval which elapses before the punch is called on
to make the next hole.
Another illustration of the fly-wheel on a splendid scale is seen in
our mighty steel works, where ponderous rails are being manufactured.
A white-hot ingot of steel is presented to a pair of powerful rollers,
which grip the steel, and send it through at the other side both
compressed and elongated. Tremendous power is required to meet the
sudden demand on the machine at the critical moment. To obtain this
power an engine of stupendous proportions is sometimes attached
directly to the rollers, but more frequently an engine of rather less
horse-power will be used, the might of this engine being applied to
giving rapid rotation to an immense fly-wheel, which may thus be
regarded as a reservoir full of energy. The rolling mills then obtain
from this store in the fly-wheel whatever energy is necessary for
their gigantic task.
These illustrations will suffice to show how a rapidly rotating body
may contain energy in virtue of its rotation, just as a cannon-ball
contains energy in virtue of its speed of translation, or as a
clock-weight has energy in virtue of the fact that it has some
distance to fall before it reaches the earth. The rotating body need
not necessarily have the shape of a wheel--it may be globular in form;
nor need the axes of rotation be fixed in bearings, like those of the
fly-wheel; nor of course is there any limit to the dimensions which
the rotating body may assume. Our earth is, in fact, a vast rotating
body 8000 miles in diameter, and turning round upon its axis once
every twenty-three hours and fifty-six minutes. Viewed in this way,
the earth is to be regarded as a gigantic fly-wheel containing a
quantity of energy great in correspondence with the earth's mass. The
amount of energy which can be stored by rotation also depends upon the
square of the velocity with which the body turns round; thus if our
earth turned round in half the time which it does at present, that is,
if the day was twelve hours instead of twenty-four hours, the energy
contained in virtue of that rotation would be four times its present
amount.
Reverting now to the earth-moon system, the energy which that system
contains consists essentially of two parts--the moon-energy, whose
composite character I have already explained, and the earth-energy,
which has its origin solely in the rotation of the earth on its axis.
It is necessary to observe that these are essentially distinct--there
is no necessary relation between the speed of the earth's rotation and
the distance of the moon, such as there is between the distance of the
moon and the speed with which it revolves in its orbit.
For completeness, it ought to be added that there is also some energy
due to the moon's rotation on its axis, but this is very small for
two reasons: first, because the moon is small compared with the
earth, and second, because the angular velocity of the moon is also
very small compared with that of the earth. We may therefore dismiss
as insignificant the contributions from this source of energy to the
sum total.
I have frequently used illustrations derived from machinery, but I
want now to emphasize the profound distinction that exists between the
rotation of the earth and the rotation of a fly-wheel in a machine
shop. They are both, no doubt, energy-holders, but it must be borne in
mind, that as the fly-wheel doles out its energy to supply the wants
of the machines with which it is connected, a restitution of its store
is continually going on by the action of the engine, so that on the
whole the speed of the fly-wheel does not slacken. The earth, however,
must be likened to a fly-wheel which has been disconnected with the
engine. If, therefore, the earth have to supply certain demands on its
accumulation of energy, it can only do so by a diminution of its
hoard, and this involves a sacrifice of some of its speed.
In the earth-moon system there is no engine at hand to restore the
losses of energy which are inevitable when work has to be done. But we
have seen that work is done; we have shown, in fact, that the tides
are at present doing work, and have been doing work for as long a
period in the past as our imagination can extend to. The energy which
this work has necessitated can only have been drawn from the existing
store in the system; that energy consists of two parts--the
moon-energy and the earth's rotation energy. The problem therefore for
us to consider is, which of these two banks the tides have drawn on to
meet their constant expenditure. This is not a question that can be
decided offhand; in fact, if we attempt to decide it in an offhand
manner we shall certainly go wrong. It seems so very plausible to say
that as the moon causes the tides, therefore the energy which these
tides expend should be contributed by the moon. But this is not the
case. It actually happens that though the moon does cause the tides,
yet when those tides consume energy they draw it not from the distant
moon, but from the vast supply which they find ready to their hand,
stored up in the rotation of the earth.
The demonstration of this is not a very simple matter; in fact, it is
so far from being simple that many philosophers, including some
eminent ones too, while admitting that of course the tides must have
drawn their energy from one or other or both of these two sources, yet
found themselves unable to assign how the demand was distributed
between the two conceivable sources of supply.
We are indebted to Professor Purser of Belfast for having indicated
the true dynamical principle on which the problem depends. It involves
reasoning based simply on the laws of motion and on elementary
mathematics, but not in the least involving questions of astronomical
observation. It would be impossible for me in a lecture like this to
give any explanation of the mathematical principles referred to. I
shall, however, endeavour by some illustrations to set before you what
this profound principle really is. Were I to give it the old name I
should call it the law of the conservation of areas; the more modern
writers, however, speak of it as the conservation of moment of
momentum, an expression which exhibits the nature of the principle in
a more definite manner.