open ocean under the action of the moon. No ordinary-sized sea like the
North Sea, or even the Mediterranean, is big enough for more than a just
appreciable tide to be generated in it. The Pacific, the Atlantic, and
the Southern Oceans are the great tidal reservoirs, and in them the
tides of the earth are generated as low flat humps of gigantic area,
though only a few feet high, oscillating up and down in the period of
approximately twelve hours. The tides we, and other coast-possessing
nations, experience are the overflow or back-wash of these oceanic
humps, and I will now show you in what manner the great Atlantic
tide-wave reaches the British Isles twice a day.
[Illustration: FIG. 109.--Co-tidal lines.]
Fig. 109 shows the contour lines of the great wave as it rolls in east
from the Atlantic, getting split by the Land's End and by Ireland into
three portions; one of which rushes up the English Channel and through
the Straits of Dover. Another rolls up the Irish Sea, with a minor
offshoot up the Bristol Channel, and, curling round Anglesey, flows
along the North Wales coast and fills Liverpool Bay and the Mersey. The
third branch streams round the north coast of Ireland, past the Mull of
Cantyre and Rathlin Island; part fills up the Firth of Clyde, while the
rest flows south, and, swirling round the west side of the Isle of Man,
helps the southern current to fill the Bay of Liverpool. The rest of the
great wave impinges on the coast of Scotland, and, curling round it,
fills up the North Sea right away to the Norway coast, and then flows
down below Denmark, joining the southern and earlier arriving stream.
The diagram I show you is a rough chart of cotidal lines, which I made
out of the information contained in _Whitaker's Almanac_.
A place may thus be fed with tide by two distinct channels, and many
curious phenomena occur in certain places from this cause. Thus it may
happen that one channel is six hours longer than the other, in which
case a flow will arrive by one at the same time as an ebb arrives by the
other; and the result will be that the place will have hardly any tide
at all, one tide interfering with and neutralizing the other. This is
more markedly observed at other parts of the world than in the British
Isles. Whenever a place is reached by two channels of different length,
its tides are sure to be peculiar, and probably small.
Another cause of small tide is the way the wave surges to and fro in a
channel. The tidal wave surging up the English Channel, for instance,
gets largely reflected by the constriction at Dover, and so a crest
surges back again, as we may see waves reflected in a long trough or
tilted bath. The result is that Southampton has two high tides rapidly
succeeding one another, and for three hours the high-water level varies
but slightly--a fact of evident convenience to the port.
Places on a nodal line, so to speak, about the middle of the length of
the channel, have a minimum of rise and fall, though the water rushes
past them first violently up towards Dover, where the rise is
considerable, and then back again towards the ocean. At Portland, for
instance, the total rise and fall is very small: it is practically on a
node. Yarmouth, again, is near a less marked node in the North Sea,
where stationary waves likewise surge to and fro, and accordingly the
tidal rise and fall at Yarmouth is only about five feet (varying from
four and a half to six), whereas at London it is twenty or thirty feet,
and at Flamborough Head or Leith it is from twelve to sixteen feet.
It is generally supposed that water never flows up-hill, but in these
cases of oscillation it flows up-hill for three hours together. The
water is rushing up the English Channel towards Dover long after it is
highest at the Dover end; it goes on piling itself up, until its
momentum is checked by the pressure, and then it surges back. It
behaves, in fact, very like the bob of a pendulum, which rises against
gravity at every quarter swing.
To get a very large tide, the place ought to be directly accessible by a
long sweep of a channel to the open ocean, and if it is situate on a
gradually converging opening, the ebb and flow may be enormous. The
Severn is the best example of this on the British Isles; but the largest
tides in the world are found, I believe, in the Bay of Fundy, on the
coast of North America, where they sometimes rise one hundred and twenty
feet. Excessive or extra tides may be produced occasionally in any place
by the propelling force of a high wind driving the water towards the
shore; also by a low barometer, _i.e._ by a local decrease in the
pressure of the air.
Well, now, leaving these topographical details concerning tides, which
we see to be due to great oceanic humps (great in area that is, though
small in height), let us proceed to ask what causes these humps; and if
it be the moon that does it, how does it do it?
The statement that the moon causes the tides sounds at first rather an
absurdity, and a mere popular superstition. Galileo chaffed Kepler for
believing it. Who it was that discovered the connection between moon and
tides we know not--probably it is a thing which has been several times
rediscovered by observant sailors or coast-dwellers--and it is certainly
a very ancient piece of information.
Probably the first connection observed was that about full moon and
about new moon the tides are extra high, being called spring tides,
whereas about half-moon the tides are much less, and are called neap
tides. The word spring in this connection has no reference to the season
of the year; except that both words probably represent the same idea of
energetic uprising or upspringing, while the word neap comes from nip,
and means pinched, scanty, nipped tide.
The next connection likely to be observed would be that the interval
between two day tides was not exactly a solar day of twenty-four hours,
but a lunar day of fifty minutes longer. For by reason of the moon's
monthly motion it lags behind the sun about fifty minutes a day, and the
tides do the same, and so perpetually occur later and later, about fifty
minutes a day later, or 12 hours and 25 minutes on the average between
tide and tide.
A third and still more striking connection was also discovered by some
of the ancient great navigators and philosophers--viz. that the time of
high water at a given place at full moon is always the same, or very
nearly so. In other words, the highest or spring tides always occur
nearly at the same time of day at a given place. For instance, at
Liverpool this time is noon and midnight. London is about two hours and
a half later. Each port has its own time for receiving a given tide, and
the time is called the "establishment" of the port. Look out a day when
the moon is full, and you will find the Liverpool high tide occurs at
half-past eleven, or close upon it. The same happens when the moon is
new. A day after full or new moon the spring tides rise to their
highest, and these extra high tides always occur in Liverpool at noon
and at midnight, whatever the season of the year. About the equinoxes
they are liable to be extraordinarily high. The extra low tides here are
therefore at 6 a.m. and 6 p.m., and the 6 p.m. low tide is a nuisance to
the river steamers. The spring tides at London are highest about
half-past two.
* * * * *
It is, therefore, quite clear that the moon has to do with the tides. It
and the sun together are, in fact, the whole cause of them; and the mode
in which these bodies act by gravitative attraction was first made out
and explained in remarkably full detail by Sir Isaac Newton. You will
find his account of the tides in the second and third books of the
_Principia_; and though the theory does not occupy more than a few pages
of that immortal work, he succeeds not only in explaining the local
tidal peculiarities, much as I have done to-night, but also in
calculating the approximate height of mid-ocean solar tide; and from the
observed lunar tide he shows how to determine the then quite unknown
mass of the moon. This was a quite extraordinary achievement, the
difficulty of which it is not easy for a person unused to similar
discussions fully to appreciate. It is, indeed, but a small part of what
Newton accomplished, but by itself it is sufficient to confer
immortality upon any ordinary philosopher, and to place him in a front
rank.
[Illustration: FIG. 110.--Whirling earth model.]
To make intelligible Newton's theory of the tides, I must not attempt to
go into too great detail. I will consider only the salient points.
First, you know that every mass of matter attracts every other piece of
matter; second, that the moon revolves round the earth, or rather that
the earth and moon revolve round their common centre of gravity once a
month; third, that the earth spins on its own axis once a day; fourth,
that when a thing is whirled round, it tends to fly out from the centre
and requires a force to hold it in. These are the principles involved.
You can whirl a bucket full of water vertically round without spilling
it. Make an elastic globe rotate, and it bulges out into an oblate or
orange shape; as illustrated by the model shown in Fig. 110. This is
exactly what the earth does, and Newton calculated the bulging of it as
fourteen miles all round the equator. Make an elastic globe revolve
round a fixed centre outside itself, and it gets pulled into a prolate
or lemon shape; the simplest illustrative experiment is to attach a
string to an elastic bag or football full of water, and whirl it round
and round. Its prolateness is readily visible.
Now consider the earth and moon revolving round each other like a man
whirling a child round. The child travels furthest, but the man cannot
merely rotate, he leans back and thus also describes a small circle: so
does the earth; it revolves round the common centre of gravity of earth
and moon (_cf._ p. 212). This is a vital point in the comprehension of
the tides: the earth's centre is not at rest, but is being whirled round
by the moon, in a circle about 1/80 as big as the circle which the moon
describes, because the earth weighs eighty times as much as the moon.
The effect of the revolution is to make both bodies slightly protrude in
the direction of the line joining them; they become slightly "prolate"
as it is called--that is, lemon-shaped. Illustrating still by the man
and child, the child's legs fly outwards so that he is elongated in the
direction of a radius; the man's coat-tails fly out too, so that he too
is similarly though less elongated. These elongations or protuberances
constitute the tides.
[Illustration: FIG. 111.--Earth and moon model, illustrating the
production of statical or "equilibrium" tides when the whole is whirled
about the point G.]
Fig. 111 shows a model to illustrate the mechanism. A couple of
cardboard disks (to represent globes of course), one four times the
diameter of the other, and each loaded so as to have about the correct
earth-moon ratio of weights, are fixed at either end of a long stick,
and they balance about a certain point, which is their common centre of
gravity. For convenience this point is taken a trifle too far out from
the centre of the earth--that is, just beyond its surface. Through the
balancing point G a bradawl is stuck, and on that as pivot the whole
readily revolves. Now, behind the circular disks, you see, are four
pieces of card of appropriate shape, which are able to slide out under
proper forces. They are shown dotted in the figure, and are lettered A,
B, C, D. The inner pair, B and C, are attached to each other by a bit of
string, which has to typify the attraction of gravitation; the outer
pair, A and D, are not attached to anything, but have a certain amount
of play against friction in slots parallel to the length of the stick.
The moon-disk is also slotted, so a small amount of motion is possible
to it along the stick or bar. These things being so arranged, and the
protuberant pieces of card being all pushed home, so that they are
hidden behind their respective disks, the whole is spun rapidly round
the centre of gravity, G. The result of a brief spin is to make A and D
fly out by centrifugal force and show, as in the figure; while the moon,
flying out too in its slot, tightens up the string, which causes B and C
to be pulled out too. Thus all four high tides are produced, two on the
earth and two on the moon, A and D being caused by centrifugal force, B
and C by the attraction of gravitation. Each disk has become prolate in
the same sort of fashion as yielding globes do. Of course the fluid
ocean takes this shape more easily and more completely than the solid
earth can, and so here are the very oceanic humps we have been talking
about, and about three feet high (Fig. 112). If there were a sea on the
_moon_, its humps would be a good deal bigger; but there probably is no
sea there, and if there were, the earth's tides are more interesting to
us, at any rate to begin with.
[Illustration: FIG. 112.--Earth and moon (earth's rotation neglected).]
The humps as so far treated are always protruding in the earth-moon
line, and are stationary. But now we have to remember that the earth is
spinning inside them. It is not easy to see what precise effect this
spin will have upon the humps, even if the world were covered with a
uniform ocean; but we can see at any rate that however much they may get
displaced, and they do get displaced a good deal, they cannot possibly
be carried round and round. The whole explanation we have given of their
causes shows that they must maintain some steady aspect with respect to
the moon--in other words, they must remain stationary as the earth spins
round. Not that the same identical water remains stationary, for in that
case it would have to be dragged over the earth's equator at the rate of
1,000 miles an hour, but the hump or wave-crest remains stationary. It
is a true wave, or form only, and consists of continuously changing
individual particles. The same is true of all waves, except breaking
ones.
Given, then, these stationary humps and the earth spinning on its axis,
we see that a given place on the earth will be carried round and round,
now past a hump, and six hours later past a depression: another six
hours and it will be at the antipodal hump, and so on. Thus every six
hours we shall travel from the region in space where the water is high
to the region where it is low; and ignoring our own motion we shall say
that the sea first rises and then falls; and so, with respect to the
place, it does. Thus the succession of high and low water, and the two
high tides every twenty-four hours, are easily understood in their
easiest and most elementary aspect. A more complete account of the
matter it will be wisest not to attempt: suffice it to say that the
difficulties soon become formidable when the inertia of the water, its
natural time of oscillation, the varying obliquity of the moon to the
ecliptic, its varying distance, and the disturbing action of the sun are
taken into consideration. When all these things are included, the
problem becomes to ordinary minds overwhelming. A great many of these
difficulties were successfully attacked by Laplace. Others remained for
modern philosophers, among whom are Sir George Airy, Sir William
Thomson, and Professor George Darwin.
I may just mention that the main and simplest effect of including
the inertia or momentum of the water is to dislocate the obvious
and simple connexion between high water and high moon; inertia
always tends to make an effect differ in phase by a quarter period
from the cause producing it, as may be illustrated by a swinging
pendulum. Hence high water is not to be expected when the
tide-raising force is a maximum, but six hours later; so that,
considering inertia and neglecting friction, there would be low
water under the moon. Including friction, something nearer the
equilibrium state of things occurs. With _sufficient_ friction the
motion becomes dead-beat again, _i.e._ follows closely the force
that causes it.
Returning to the elementary discussion, we see that the rotation of the
earth with respect to the humps will not be performed in exactly
twenty-four hours, because the humps are travelling slowly after the
moon, and will complete a revolution in a month in the same direction as
the earth is rotating. Hence a place on the earth has to catch them up,
and so each high tide arrives later and later each day--roughly
speaking, an hour later for each day tide; not by any means a constant
interval, because of superposed disturbances not here mentioned, but on
the average about fifty minutes.
We see, then, that as a result of all this we get a pair of humps
travelling all over the surface of the earth, about once a day. If the
earth were all ocean (and in the southern hemisphere it is nearly all
ocean), then they would go travelling across the earth, tidal waves
three feet high, and constituting the mid-ocean tides. But in the
northern hemisphere they can only thus journey a little way without
striking land. As the moon rises at a place on the east shores of the
Atlantic, for instance, the waters begin to flow in towards this place,
or the tide begins to rise. This goes on till the moon is overhead and
for some time afterwards, when the tide is at its highest. The hump then
follows the moon in its apparent journey across to America, and there
precipitates itself upon the coast, rushing up all the channels, and
constituting the land tide. At the same time, the water is dragged away
from the east shores, and so _our_ tide is at its lowest. The same thing
repeats itself in a little more than twelve hours again, when the other
hump passes over the Atlantic, as the moon journeys beneath the earth,
and so on every day.
In the free Southern Ocean, where land obstruction is comparatively
absent, the water gets up a considerable swing by reason of its
accumulated momentum, and this modifies and increases the open
ocean tides there. Also for some reason, I suppose because of the
natural time of swing of the water, one of the humps is there
usually much larger than the other; and so places in the Indian and
other offshoots of the Southern Ocean get their really high tide
only once every twenty-four hours. These southern tides are in fact
much more complicated than those the British Isles receive. Ours
are singularly simple. No doubt some trace of the influence of the
Southern Ocean is felt in the North Atlantic, but any ocean
extending over 90 deg. of longitude is big enough to have its own
tides generated; and I imagine that the main tides we feel are thus
produced on the spot, and that they are simple because the
damping-out being vigorous, and accumulated effects small, we feel
the tide-producing forces more directly. But for authoritative
statements on tides, other books must be read. I have thought, and
still think, it best in an elementary exposition to begin by a
consideration of the tide-generating forces as if they acted on a
non-rotating earth. It is the tide generating forces, and not the
tides themselves, that are really represented in Figs. 112 and 114.
The rotation of the earth then comes in as a disturbing cause. A
more complete exposition would begin with the rotating earth, and
would superpose the attraction of the moon as a disturbing cause,
treating it as a problem in planetary perturbation, the ocean being
a sort of satellite of the earth. This treatment, introducing
inertia but ignoring friction and land obstruction, gives low water
in the line of pull, and high water at right angles, or where the
pull is zero; in the same sort of way as a pendulum bob is highest
where most force is pulling it down, and lowest where no force is
acting on it. For a clear treatment of the tides as due to the
perturbing forces of sun and moon, see a little book by Mr. T.K.
Abbott of Trinity College, Dublin. (Longman.)
[Illustration: FIG. 113.--Maps showing how comparatively free from land
obstruction the ocean in the Southern Hemisphere is.]
If the moon were the only body that swung the earth round, this is all
that need be said in an elementary treatment; but it is not the only
one. The moon swings the earth round once a month, the sun swings it
round once a year. The circle of swing is bigger, but the speed is so
much slower that the protuberance produced is only one-third of that
caused by the monthly whirl; _i.e._ the simple solar tide in the open
sea, without taking momentum into account, is but a little more than a
foot high, while the simple lunar tide is about three feet. When the two
agree, we get a spring tide of four feet; when they oppose each other,
we get a neap tide of only two feet. They assist each other at full moon
and at new moon. At half-moon they oppose each other. So we have spring
tides regularly once a fortnight, with neap tides in between.
[Illustration: FIG. 114.--Spring and neap tides.]
Fig. 114 gives the customary diagrams to illustrate these simple things.
You see that when the moon and sun act at right angles (_i.e._ at every
half-moon), the high tides of one coincide with the low tides of the
other; and so, as a place is carried round by the earth's rotation, it
always finds either solar or else lunar high water, and only experiences
the difference of their two effects. Whereas, when the sun and moon act
in the same line (as they do at new and full moon), their high and low
tides coincide, and a place feels their effects added together. The tide
then rises extra high and falls extra low.
[Illustration: FIG. 115.--Tidal clock. The position of the disk B shows
the height of the tide. The tide represented is a nearly high tide eight
feet above mean level.]
Utilizing these principles, a very elementary form of tidal-clock, or
tide-predicter, can be made, and for an open coast station it really
would not give the tides so very badly. It consists of a sort of clock
face with two hands, one nearly three times as long as the other. The
short hand, CA, should revolve round C once in twelve hours, and the
vertical height of its end A represents the height of the solar tide on
the scale of horizontal lines ruled across the face of the clock. The
long hand, AB, should revolve round A once in twelve hours and
twenty-five minutes, and the height of its end B (if A were fixed on the
zero line) would represent the lunar tide. The two revolutions are made
to occur together, either by means of a link-work parallelogram, or,
what is better in practice, by a string and pulleys, as shown; and the
height of the end point, B, of the third side or resultant, CB, read off
on a scale of horizontal parallel lines behind, represents the
combination or actual tide at the place. Every fortnight the two will
agree, and you will get spring tides of maximum height CA + AB; every
other fortnight the two will oppose, and you will get neap tides of
maximum height CA-AB.
Such a clock, if set properly and driven in the ordinary way, would then
roughly indicate the state of the tide whenever you chose to look at it
and read the height of its indicating point. It would not indeed be very
accurate, especially for such an inclosed station as Liverpool is, and
that is probably why they are not made. A great number of disturbances,
some astronomical, some terrestrial, have to be taken into account in
the complete theory. It is not an easy matter to do this, but it can be,
and has been, done; and a tide-predicter has not only been constructed,
but two of them are in regular work, predicting the tides for years
hence--one, the property of the Indian Government, for coast stations of
India; the other for various British and foreign stations, wherever the
necessary preliminary observations have been made. These machines are
the invention of Sir William Thomson. The tide-tables for Indian ports
are now always made by means of them.
[Illustration: FIG. 116.--Sir William Thomson (Lord Kelvin).]
[Illustration: FIG. 117.--Tide-gauge for recording local tides, a
pencil moved up and down by a float writes on a drum driven by
clockwork.]