416

Tidal Evolution

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UNIVERSITY OF CALIFORNIA
LOS ANGELES

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LOS ANGELES

CONTENTS:

Evolution * *

A Concise Statement of the effect of Tidal Friction on the Diurnal
Motion of the Earth.

B. R. BAUMGARDT,

SECRETHRT SOUTHERN, CKLIFORNIH SCIENCE ASSOCIHTION.

LOS ANGELES:
PRINTED FOR THE ASSOCIATION.

1895.

PUBLICATIONS

(California £Jcience

LOS ANGELES

TIDAL EVOLUTION

BY B. R. BAUHQARDT.

All phenomena may be grouped into two classes — those
that are rythmic or periodic in their nature, and those that
are constant and unchanging, that is, do not increase and then
decrease with a regular rythmic periodicity.

To the first class, which is by far the largest, belong all
the more obvious phenomena connected with the various man-
ifestations of force in nature, such as light, heat, electricity,
sound, motion, etc., as well as those more mysterious ones
which we comprehend under the general term of life.

The swaying motion of a reed in a stream, the rustling
of the leaves in a tree, the pulsation of the blood in the
arteries and veins of the human body, the rise and fall every
twelve hours of the tides on our seashores, the periodic
maxima and minima every eleven years of spots on our pri-
mary, the sun, the accelerating and retarding motions of the
planets in their celestial orbits, the inequalities of our satellite,
the precession of the equinoxes— that wonderful wabbling
motion of our earth's axis around the celestial pole in a
majestic orbit requiring 25,000 years for its accomplishment —
the occillating change of position of the major axis of the
earth's elliptical orbit — the great cycle of the solar system,
when, according to L,a Grange, all the planetary perturbations
shall have compensated each other and a new cycle commenced,
the wonderful periodic increase and decrease of light in
many of the variable stars and many other astronomical phe-
nomena are all, I think, typical illustrations of the first class,
or those that are decidedly rythmic in their nature.

447065

6 TIDAL EVOLUTION.

But all phenomena are not of this kind. There are some
astronomical phenomena which, at least in their broadest and
most philosophical sense, differ entirely from this class. They
do not increase and then decrease in regular rythmic varia-
bility, and for this reason differ entirely from the more obvious
ones such as I have enumerated. To one of these I am about
to invite your attention for a while this evening, and I hope
to be able to show you that in the subject we are to consider
we are really dealing with one of the most important factors
in the evolution of our earth-moon system.

All intelligent people who have lived by the seashore are
familiar with the rise and fall of the sea which takes place
twice in every diurnal rotation of the earth on its axis. Long
ages ago these tides ceased to be a mystery to man, and in
fact before their theoretical explanation was mathematically
explained man was perfectly acquainted with their action,
their intensity, their maxima and minima, known as spring
and neap, and most important of all, with the wonder-
ful fact that in some mysterious way these tides were con-
nected with the position of the moon in relation to the sun.
Both Pliney and Aristotle refer to the alliance between the
times of high water and the stage of the moon.

Not however, until Sir Isaac Newton in 1687 presented
to the Royal Society his immortal Principia, was it possible
for men to understand the abstract principle of the cause of
the tides. In this celebrated work Newton, in a manner which
makes it seem as if he was divinely inspired, unfolded to the
astonished world, the mechanical theory of nniversal, grav-
itation, showing that every particle of matter in the universe
attracts every other particle with a force which is ever pro-
portionate to the co-attracting masses, and inversely propor-
tionate to the square of the distances separating them.

The moon, therefore, attracts every particle of matter on
our earth, both solid and liquid. The solids, however, are
not enabled to yield in such a marked way as the liquids are;
for the latter are forced by the moon's attraction to rise bodily
toward her to a certain extent, and in this way cause the
phenomenon of high tide. It must not be forgotten that the

TIDAL EVOLUTION. 7

solid crust is also to a certain degree attracted to the moon,
away from the waters on the distant side from the satellite, thus
leaving the waters in a high wave behind. This is the explana-
tion of the neap tides. The intervening positions between the
two high tides, that is, the positions which are as it were, in
quadrature with the moon, form the ebbs.

Thus, with a little reflection, we find that the earth is
forced through the attraction of the moon to depart from the
spherical form and made as it were to bulge out into an oblate
ellipsoid, the major axis of which keeps forever following the
direction of the moon in her ceaseless journey around her
primary.

But some of you may think that these tides certainly are of
a rhythmic character. Do they not rise and fall? Are they not
a very pulsation of the ocean, now strong, now weak, but
ever changing in a regular periodic succession ? And have I
not myself just given the rise and fall of the tides as an illus-
tration of rhythmic phenomena?

In answer to this I will simply propose that we
change our point of view. No doubt, from a terres-
trial and therefore limited standpoint the tides do appear
to be of a rythmic character. But let us rise from the
terrestrial to the general, to the truly philosophical point
of view, rising high enough to view the whole globe at
a glance; or let us, perhaps, rather view the axial rotation of
our earth from the standpoint of the moon. What now has
become of the rise and fall of the tides and their rythmic char-
acteristics? Where now will we detect their periodic spring and
neap, their flood and ebb? All have disappeared, being only
relative phenomena, caused by our terrestrial surroundings and
confined limited point of view. In their place we behold only
one single gigantic tidal wave, extending from pole to pole
parallel to the earth's axis, forever following in the wake of
the moon's course.

What a worthy subject it would be for us this evening to
consider some of the extraordinary physical phenomena con-
nected so closely with the action of the tides, such as their
surprising smallness in midocean, in the Mediterranean sea,

8 TIDAL EVOLUTION.

the Caspian, the Baltic aad other confined areas; their enor-
mous heights, on the other hand, in such places as the English
channel and the Bay of Fundy. The high tides of both of the
latter places are especiallyinteresting to me, having witnessed
them personally from the end of the three-mile pier at Havre
on the Channel, and from the wharfs at St. John, N. B., on
the Bay of Fundy. Time, however, will not permit of this,
and I pass on at once to the consideration of the dynamical
question of the friction which the tides are causing on the
earth and its effect upon the diurnal motion of the planet.

No truth rests on more firm foundation than the axiom
that work cannot be accomplished without the consumption
ot energy in some of its forms. This is based upon the immu-
table law of correlation of forces.

Now the tides are performing a wronderful amount of work,
rebuilding our continents, hollowing out bays and aiding in
the formation of bars, besides raising bodily at the present
time, all the waters of the earth on an average three feet every
24 hours. In past ages the force displayed was much greater,
depending of course upon the proximity of the moon. Thus,
as we shall see a little later, when the moon was only 40,000,
instead of as at present 240,000, miles from the earth, the
tides, in place of averaging three feet, did indeed average 648
feet in height. Such tides as these would sweep almost every
city from the face of the earth. Just reflect upon what an
enormous amount of wrork tides like these must have been able to
accomplish, and what important factors they must have been
in the evolution of the early stages of the earths' crust.

But from what source is the energy derived at the expense
of which all this work was and is today performed?

As the moon is the direct cause of the tides, it would, at
a superficial glance appear that we might be justified in at-
tributing the source of energy to our satellite. But is this
true? Will it hold good? No doubt it seems plausable, but
it is, nevertheless, a fallacy. To illustrate this, permit me to
quote an illustration from Sir Robert Ball. He says that it
is one of those cases by no means infrequent in dynamics,
where the truth is widely different from what seems to be the

TIDAL EVOLUTION. 9

case, and illustrates it with the example of a rifle which is fired
by the pulling of a trigger by the rifleman's finger. No one
would assert that the energy by which the rifle ball was fired
off was supplied by the rifleman. Certainly not. The energy
was of course due to the gunpowder, and all the rifleman did
was to provide the means by which the energy stored up in
the gunpowder became liberated.

In almost the same way the tides raised by the moon are
simply the originating cause whereby a certain amount of
energy stored up in the earth itself is liberated and applied
to perform such work as the tides are competent to perform.

The store house of energy upon which the tides through
the agency of the moon are making such large and continuous
drafts is to be found in the momentum stored up in the axial
revolution of the planet. No doubt this is an enormous store
house of energy. No doubt it seems to us all but inexhausti-
ble. But as the power drawn from it by the tides is not
replaced, the irresistible consequence is that the momentum
of rotation is being dissipated, and that this rotation is slowly
but surely decreasing. As a result the day which is now 24
hours is becoming longer.

If I am not mistaken, it was Immanuel Kant, who, more
than a century ago first called attention to the fact that the
tides in rolling from east to west were reducing the earth's
diurnal motion. He showed that countless aeons of time may
elapse before the momentum can be completely exhausted,
but it is nevertheless true that the energy is decreasing and
the relation of the earth-moon system tending toward equilli-
brium. At present the axial revolution of the earth is not
measurably longer than it was 100 years ago. Even in 1000
years the change in the length of the day may perhaps be
only a fraction of a second. But the importance attached to
this dissipation of momentum lies in the fact that this phe-
nomenon, though acting majestically slow, is not of a rythmic
nature but continues right on ceaselessly and eternally in the
same direction.

L,a Place's celebrated theory that opposite currents are as
to their effect upon the rotation of the earth as plus and minus

w TIDAL EVOLUTION.

naught, and that there are no forces at work in nature which
do not always find their compensating opposites, I believe
does not hold good in the case of tidal friction. Silently and
slowly though it be, the tides are nevertheless uninterruptedly
acting as a brake upon the rotation of the earth, and in mil-
lions of years the accumulated effect will not only become
appreciable but even of a startling magnitude. Many attempts
have been made to compute this increase in the length of the
day, but of course the results must be taken with a good deal
of reserve. Dr. J. B. Mayer, after an elaborate analysis of
the subject, arrives at a value of 1-16 of a second for every
2500 years.

Perhaps the best authority on the matter is Sir William
Thomson, who in a careful calculation of the age of the
earth's crust shows that it cannot be less than 10,000,000
years, because the figure of our globe differs so little from
equilibrium in planetoid compression — that is, the polar com-
pression is nearly the same as that which the present diurnal
motion would produce in a molten world. Nearly the same,
but not quite. What may be the value of this trifling dif-
ference? The product of this discrepancy will furnish us with
an approximation of the relative amount of the lengthening
of the day. The same high authority has arrived at a valua-
tion of i per cent for 20,000,000 years. Out of curiosity I
have myself calculated what this i per cent means in fractions
of diurnal motion, and have found it to roughly correspond to
864 seconds, or 14^2 minutes. Therefore, if any assurance
can be placed on the figures which Sir William Thomson sub-
mits, it would appear that the earth today does require 14^
minutes more to perform one revolution on its axis than it did
20,000,000 years ago. It only needs to be added that this is
not presented as an accurate result, but rather as an inter-
esting speculation.

But in accordance with Galileo's third law of motion,
that to every action there must always be an equal and oppo-
site reaction, it may be asked in what way this reaction
exhibits itself in the tidal action of the earth-moon system.
The moon, as we have seen, acts upon the earth by retarding

TIDAL EVOLUTION. n

her axial rotation; the earth conversely reacts upon the moon
by pushing her further and further away. In this manner the
reaction exhibits itself. At first thought there does not seem
to be much importance attached to this phenomenon, but a little
reasoning will soon show that in this reaction we are
dealing with a problem which for far-reaching conclusions is
perhaps unparalled in the whole solar system.

At present the distance separating the two bodies is about
240,000 miles, and the length of the day is about 24 hours.
If the theory of tidal friction be true, then both the distance
of the moon and the position of the earth must have been
shorter yesterday than today, shorter the day before yesterday
than yesterday, and so on. Looking backward a million years,
the revolution was perhaps only some minutes shorter than it
is today, and the radius of the moon 's orbit — which of course
is the distance of the satellite from the earth — was correspond-
ingly shorter.

Before arriving at the critical result of this analysis, there
are two other dynamical elements which must be taken into
consideration and thoroughly understood. First, that in
accordance with Keppler's second law, that the radius vector
always describes equal areas in equal times, it follows that the
moon in past ages must have completed her lunation in shorter
periodic time than at present. Second, that the quicker the
earth turns on her axis the more centrifugal force becomes dis-
played and that if the rotation becomes too quick the centrif-
ugal force will become so pronounced that it will overcome
the cohesion of the particles of the earth and the gravitation
which attracts them toward the center. The result wTould be
that the globe would fly to pieces, or, which is still more
likely, would leave a ring behind from off its outward bulged
equatorial zone.

Thus then by retracing our steps backward in time in
accordance with tidal evolution we arrive at a critical
time, when the moon must have been grazing the surface of
the earth, and when one revolution of the earth on its axis
must have corresponded to one lunation of the moon. It
would appear that the time required was about three hours.

12 TIDAL EVOLUTION.

Prof. G. H. Darwin of Oxford has calculated that this
state of affairs of the earth-moon system could not have
existed less than 50,000,000 years ago.

Studying the theory of tidal evolution of the past, we
therefore find that it insensibly leads us to a belief that the
moon was once a part of this earth, and that from a prepon-
derance of the centrifugal force it became in some way or
other fractured off and left behind* This, of course, must
have taken place when the matter of the system was still in a
plastic or molten, or perhaps even in a gaseous state.

But plainly this is onlyan illustration of L,a Place's cel-
ebrated nebular hypothesis — that all the ponderable material
now constituting the various bodies of the solar system once
have existed as a rarefied mass of gaseous matter — a nebula —
and that as this nebula cooled by radiating its heat into space, it
contracted and was gradually shaped into its present form.

In the future the moon will continue to retard the earth
in her diurnal motion and to increase and separate herselt
more and more from her primary. In the same way that the
earth has caused our satellite to complete one revolution on
her axis in the same time as is required for her lunation
(thereby forcing her to always exhibit the same face toward
the earth) , in exactly the same way the moon will compel our
earth to slow down the time of the diurnal motion until it
corresponds exactly to the moon's periodic time. It has been
computed that the length of the month as well as the length
of the day at that important epoch will be about 54 of our
days or about 1400 hours.

We will then have what is known as a stable dynamical
equilibrium, with the earth and the moon always presenting
the same faces toward each other, and this state of affairs
would last forever, providing that no extraneous forces were
brought to bear on the system.

But as every particle of matter attracts every other par-
ticle in the universe, it follows that the sun also, must,
in the same way as the moon, raise tides on the earth. So
the sun does, too, but as the tide generating power of attraction,
as far as distance goes, acts on the inverse square, we have so

TJDAL EVOLUTION. 13

far not found it necessary to even mention the solar tides.
But when the earth-moon system has attained equilibrium the
sun-raised tides will continue right on in their action. To be
sure, they are very small compared to those raised by the
moon, but it is well to remember that it is just these small
forces acting day in and day out, silently, quietly, persistently,
uninterruptedly in the same direction, which in the end
accomplish stupendous results. When the earth and moon
shall have come to a mutual rest, the solar tides will continue
to retard the earth in her diurnal motion until at last the day
will become longer than the month.

This may seem to many to be an impossible state of af-
fairs— that the month which is now 27 times longer than the
day should actually become shorter. But why not? If these
conditions existed today they would be just as natural to us as
our present. In fact, we are able with a great deal of satis-
faction to corroborate our reasoning with a remarkable example
in our solar system. The planet Mars is but little more than
half the size of our earth. We are therefore justified in
believing that this brother sphere has passed through his
evolution quicker and is further along the road of his destiny
than is the case with our earth. With this in mind it is
interesting to find that in the case of this planet and his satel-
lite Phobes, the Martian day is actually three times longer
than the periodic time of the satellite — a signal prophesy ot
the future of our own earth-moon system.

For the same reason that we expected Mars to be in
advance of our earth in his evolution, we would anticipate
Jupiter on the other hand to befar behind. On this giant planet,
which is so much larger and so much farther distant from our sun
— its center of heat and attraction, we may confidently expect
to find conditions prevailing which existed on our earth many
millions of years ago. And, indeed, in this we shall not
find ourselves to have judged wrong. It does not take very
many observations with a powerful telescope to tell that this
planet is not solid, but is rather in a plastic, if not even in,, a
molten condition. But most significant of all, his axial revo-
lution is accomplished in about 10 hours — a phenomenon which

447O65

14 TIDAL EVOLUTION.

indeed corresponds to the letter with what tidal evolution tells
us was the past conditions of our own earth.

Then again observe the comprehensive fact that both
Mercury and Venus, the two planets nearest to the sun,
always, according to the most reliable observations, turn the
same face toward the sun. Tidal friction has, as it were,
arrested the axial revolutions of both of these planets, and
forced them to forever pay obeisance to their primary.

Leaving the so'ar system and passing outward to the
siderial we soon find further corroboration of our theory.
We have seen this evening that one of the effects of tidal
friction is that the two attracting bodies keep pushing further
and further away from each other. In the case of the earth-
moon system the pushing is pretty well one-sided on account
of the great difference in size of the two bodies. But suppose
that both bodies were of about the same mass. What would
be the result? This is what the consequence would be. The
earth would, push the moon and the moon the earth about an
equal amount, and this would in its turn give rise to exceed-
ingly elongated elliptical orbits. Now one of the most
remarkable facts connected with nearly all the binary systems
of double stars far away in the bosom of unmeasurable space
is their exceedingly eccentric elliptical orbits, caused undoubt-
edly by mutual tidal action of the components of the systems.
My authority for this statement is Herr T. J. J. Lee of Berlin.

There is another collateral consequence which must follow
from a combination of tidal action and gravitation on a primi-
tive plastic planet. During the course of evolution the earth's
mass must have suffered a screwing motion so that the polar
regions have traveled a little from west to east, relative to the
equator. Prof. G. A. Darwin of Oxford thinks that this fur-
nishes a possible explanation of the north and south trend of
our great continents.

Tidal evolution has indeed furnished explanations for
many important questions about the remote past and dim,
distant future of the bodies of our solar system. It has per-
haps helped us along one more step in our painstaking search
for truth and groping for exact knowledge. This is, however,

TIDAL EVOLUTION. 15

all that it has done. The mystery of the great whole and the
origin of the universe it leaves as great as ever. Sometimes
we feel hopeful that eventually the genius of man will unfold
it all. And indeed we have good cause and a perfect right to
be proud of what the human intellect has been able to accom-
plish. But it seems to me that every step ahead only tends
to show the greater extent of the unknowable. As Carlyle
has so finely said in his Sartor Resartus: *' System of Nature!
To the wisest man, wide as is his vision, nature remains of
quite infinite depth, of quite infinite expansion; and all exper-
ience thereof limits itself to some few computed centuries and
measured square miles. The course of nature's phases on this,
our little fraction of a planet, is partially known to us; but
who knows what deeper courses these depend on; what
infinitely larger cycles of courses our little epicycle revolves
upon. To the little tadpole or minnow every cranny and
pebble, and quality and accident of its little native creek may
have become familiar, but does the minnow understand the
ocean tides and periodic currents, the trade winds or mon-
soons or the moon's eclipses, by all of which the conditions of
its little creek is regulated, and may (immiraculously enough)
be quite overset and reversed ? Just such a little minnow is
man, his creek, this planet; his ocean, the immeasurable all;
his monsoons and periodic currents, the mysterious course of
nature through aeons and aeons."

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