THE EARTH.
The Earth is a great Globe--How the Size of the Earth is
Measured--The Base Line--The Latitude found by the Elevation of the
Pole--A Degree of the Meridian--The Earth not a Sphere--The
Pendulum Experiment--Is the Motion of the Earth slow or
fast?--Coincidence of the Axis of Rotation and the Axis of
Figure--The Existence of Heat in the Earth--The Earth once in a
Soft Condition--Effects of Centrifugal Force--Comparison with the
Sun and Jupiter--The Protuberance of the Equator--The Weighing of
the Earth--Comparison between the Weight of the Earth and an equal
Globe of Water--Comparison of the Earth with a Leaden Globe--The
Pendulum--Use of the Pendulum in Measuring the Intensity of
Gravitation--The Principle of Isochronism--Shape of the Earth
measured by the Pendulum.
That the earth must be a round body is a truth immediately suggested by
simple astronomical considerations. The sun is round, the moon is round,
and telescopes show that the planets are round. No doubt comets are not
round, but then a comet seems to be in no sense a solid body. We can see
right through one of these frail objects, and its weight is too small
for our methods of measurement to appreciate. If, then, all the solid
bodies we can see are round globes, is it not likely that the earth is a
globe also? But we have far more direct information than mere surmise.
There is no better way of actually seeing that the surface of the ocean
is curved than by watching a distant ship on the open sea. When the ship
is a long way off and is still receding, its hull will gradually
disappear, while the masts will remain visible. On a fine summer's day
we can often see the top of the funnel of a steamer appearing above the
sea, while the body of the steamer is below. To see this best the eye
should be brought as close as possible to the surface of the sea. If the
sea were perfectly flat, there would be nothing to obscure the body of
the vessel, and it would therefore be visible so long as the funnel
remains visible. If the sea be really curved, the protuberant part
intercepts the view of the hull, while the funnel is still to be seen.
We thus learn how the sea is curved at every part, and therefore it is
natural to suppose that the earth is a sphere. When we make more careful
measurements we find that the globe is not perfectly round. It is
flattened to some extent at each of the poles. This may be easily
illustrated by an indiarubber ball, which can be compressed on two
opposite sides so as to bulge out at the centre. The earth is similarly
flattened at the poles, and bulged out at the equator. The divergence of
the earth from the truly globular form is, however, not very great, and
would not be noticed without very careful measurements.
The determination of the size of the earth involves operations of no
little delicacy. Very much skill and very much labour have been devoted
to the work, and the dimensions of the earth are known with a high
degree of accuracy, though perhaps not with all the precision that we
may ultimately hope to attain. The scientific importance of an accurate
measurement of the earth can hardly be over-estimated. The radius of the
earth is itself the unit in which many other astronomical magnitudes are
expressed. For example, when observations are made with the view of
finding the distance of the moon, the observations, when discussed and
reduced, tell us that the distance of the moon is equal to fifty-nine
times the equatorial radius of the earth. If we want to find the
distance of the moon in miles, we require to know the number of miles in
the earth's radius.
A level part of the earth's surface having been chosen, a line a few
miles long is measured. This is called the base, and as all the
subsequent measures depend ultimately on the base, it is necessary that
this measurement shall be made with scrupulous accuracy. To measure a
line four or five miles long with such precision as to exclude any
errors greater than a few inches demands the most minute precautions. We
do not now enter upon a description of the operations that are
necessary. It is a most laborious piece of work, and many ponderous
volumes have been devoted to the discussion of the results. But when a
few base lines have been obtained in different places on the earth's
surface, the measuring rods are to be laid aside, and the subsequent
task of the survey of the earth is to be conducted by the measurement of
angles from one station to another and trigonometrical calculations
based thereon. Starting from a base line a few miles long, distances of
greater length are calculated, until at length stretches 100 miles long,
or even more, can be accomplished. It is thus possible to find the
length of a long line running due north and south.
So far the work has been merely that of the terrestrial surveyor. The
distance thus ascertained is handed over to the astronomer to deduce
from it the dimensions of the earth. The astronomer fixes his
observatory at the northern end of the long line, and proceeds to
determine his latitude by observation. There are various ways by which
this can be accomplished. They will be found fully described in works on
practical astronomy. We shall here only indicate in a very brief manner
the principle on which such observations are to be made.
Everyone ought to be familiar with the Pole Star, which, though by no
means the most brilliant, is probably the most important star in the
whole heavens. In these latitudes we are accustomed to find the Pole
Star at a considerable elevation, and there we can invariably find it,
always in the same place in the northern sky. But suppose we start on a
voyage to the southern hemisphere: as we approach the equator we find,
night after night, the Pole Star coming closer to the horizon. At the
equator it is on the horizon; while if we cross the line, we find on
entering the southern hemisphere that this useful celestial body has
become invisible. This is in itself sufficient to show us that the earth
cannot be the flat surface that untutored experience seems to indicate.
On the other hand, a traveller leaving England for Norway observes that
the Pole Star is every night higher in the heavens than he has been
accustomed to see it. If he extend his journey farther north, the same
object will gradually rise higher and higher, until at length, when
approaching the pole of the earth, the Pole Star is high up over his
head. We are thus led to perceive that the higher our latitude, the
higher, in general, is the elevation of the Pole Star. But we cannot use
precise language until we replace the twinkling point by the pole of the
heavens itself. The pole of the heavens is near the Pole Star, which
itself revolves around the pole of the heavens, as all the other stars
do, once every day. The circle described by the Pole Star is, however,
so small that, unless we give it special attention, the motion will not
be perceived. The true pole is not a visible point, but it is capable of
being accurately defined, and it enables us to state with the utmost
precision the relation between the pole and the latitude. The statement
is, that the elevation of the pole above the horizon is equal to the
latitude of the place.
The astronomer stationed at one end of the long line measures the
elevation of the pole above the horizon. This is an operation of some
delicacy. In the first place, as the pole is invisible, he has to obtain
its position indirectly. He measures the altitude of the Pole Star when
that altitude is greatest, and repeats the operation twelve hours later,
when the altitude of the Pole Star is least; the mean between the two,
when corrected in various ways which it is not necessary for us now to
discuss, gives the true altitude of the pole. Suffice it to say that by
such operations the latitude of one end of the line is determined. The
astronomer then, with all his equipment of instruments, moves to the
other end of the line. He there repeats the process, and he finds that
the pole has now a different elevation, corresponding to the different
latitude. The difference of the two elevations thus gives him an
accurate measure of the number of degrees and fractional parts of a
degree between the latitudes of the two stations. This can be compared
with the actual distance in miles between the two stations, which has
been ascertained by the trigonometrical survey. A simple calculation
will then show the number of miles and fractional parts of a mile
corresponding to one degree of latitude--or, as it is more usually
expressed, the length of a degree of the meridian.
This operation has to be repeated in different parts of the earth--in
the northern hemisphere and in the southern, in high latitudes and in
low. If the sea-level over the entire earth were a perfect sphere, an
important consequence would follow--the length of a degree of the
meridian would be everywhere the same. It would be the same in Peru as
in Sweden, the same in India as in England. But the lengths of the
degrees are not all the same, and hence we learn that our earth is not
really a sphere. The measured lengths of the degrees enable us to see to
what extent the shape of the earth departs from a perfect sphere. Near
the pole the length of a degree is longer than near the equator. This
shows that the earth is flattened at the poles and protuberant at the
equator, and it provides the means by which we may calculate the actual
lengths of the polar and the equatorial axes. In this way the equatorial
diameter has been found equal to 7,927 miles, while the polar diameter
is 27 miles shorter.
The polar axis of the earth may be defined as the diameter about which
the earth rotates. This axis intersects the surface at the north and
south poles. The time which the earth occupies in making a complete
rotation around this axis is called a sidereal day. The sidereal day is
a little shorter than the ordinary day, being only 23 hours, 56 minutes,
and 4 seconds. The rotation is performed just as if a rigid axis passed
through the centre of the earth; or, to use the old and homely
illustration, the earth rotates just as a ball of worsted may be made to
rotate around a knitting-needle thrust through its centre.
It is a noteworthy circumstance that the axis about which the earth
rotates occupies a position identical with that of the shortest diameter
of the earth as found by actual surveying. This is a coincidence which
would be utterly inconceivable if the shape of the earth was not in some
way physically connected with the fact that the earth is rotating. What
connection can then be traced? Let us enquire into the subject, and we
shall find that the shape of the earth is a consequence of its rotation.
The earth at the present time is subject, at various localities, to
occasional volcanic outbreaks. The phenomena of such eruptions, the
allied occurrence of earthquakes, the well-known fact that the heat
increases the deeper we descend into the earth, the existence of hot
springs, the geysers found in Iceland and elsewhere, all testify to the
fact that heat exists in the interior of the earth. Whether that heat
be, as some suppose, universal in the interior of the earth, or whether
it be merely local at the several places where its manifestations are
felt, is a matter which need not now concern us. All that is necessary
for our present purpose is the admission that heat is present to some
extent.
This internal heat, be it much or little, has obviously a different
origin from the heat which we know on the surface. The heat we enjoy is
derived from the sun. The internal heat cannot have been derived from
the sun; its intensity is far too great, and there are other insuperable
difficulties attending the supposition that it has come from the sun.
Where, then, has this heat come from? This is a question which at
present we can hardly answer--nor, indeed, does it much concern our
argument that we should answer it. The fact being admitted that the heat
is there, all that we require is to apply one or two of the well-known
thermal laws to the interpretation of the facts. We have first to
consider the general principle by which heat tends to diffuse itself and
spread away from its original source. The heat, deep-seated in the
interior of the earth, is transmitted through the superincumbent rocks,
and slowly reaches the surface. It is true that the rocks and materials
with which our earth is covered are not good conductors of heat; most of
them are, indeed, extremely inefficient in this way; but, good or bad,
they are in some shape conductors, and through them the heat must creep
to the surface.
It cannot be urged against this conclusion that we do not feel this
heat. A few feet of brickwork will so confine the heat of a mighty blast
furnace that but little will escape through the bricks; but _some_ heat
does escape, and the bricks have never been made, and never could be
made, which would absolutely intercept all the heat. If a few feet of
brickwork can thus nearly mask the heat of a furnace, cannot some scores
of miles of rock nearly mask the heat in the depths of the earth, even
though that heat were seven times hotter than the mightiest furnace that
ever existed? The heat would escape slowly, and perhaps imperceptibly,
but, unless all our knowledge of nature is a delusion, no rocks, however
thick, can prevent, in the course of time, the leakage of the heat to
the surface. When this heat arrives at the surface of the earth it must,
in virtue of another thermal law, gradually radiate away and be lost to
the earth.
It would lead us too far to discuss fully the objections which may
perhaps be raised against what we have here stated. It is often said
that the heat in the interior of the earth is being produced by chemical
combination or by mechanical process, and thus that the heat may be
constantly renewed as fast or even faster than it escapes. This,
however, is more a difference in form than in substance. If heat be
produced in the way just supposed (and there can be no doubt that there
may be such an origin for some of the heat in the interior of the globe)
there must be a certain expenditure of chemical or mechanical energies
that produces a certain exhaustion. For every unit of heat which escapes
there will either be a loss of an unit of heat from the globe, or, what
comes nearly to the same thing, a loss of an unit of heat-making power
from the chemical or the mechanical energies. The substantial result is
the same; the heat, actual or potential, of the earth must be
decreasing. It should, of course, be observed that a great part of the
thermal losses experienced by the earth is of an obvious character, and
not dependent upon the slow processes of conduction. Each outburst of a
volcano discharges a stupendous quantity of heat, which disappears very
speedily from the earth; while in the hot springs found in so many
places there is a perennial discharge of the same kind, which in the
course of years attains enormous proportions.
The earth is thus losing heat, while it never acquires any fresh
supplies of the same kind to replace the losses. The consequence is
obvious; the interior of the earth must be growing colder. No doubt this
is an extremely slow process; the life of an individual, the life of a
nation, perhaps the life of the human race itself, has not been long
enough to witness any pronounced change in the store of terrestrial
heat. But the law is inevitable, and though the decline in heat may be
slow, yet it is continuous, and in the lapse of ages must necessarily
produce great and important results.
It is not our present purpose to offer any forecast as to the changes
which must necessarily arise from this process. We wish at present
rather to look back into past time and see what consequences we may
legitimately infer. Such intervals of time as we are familiar with in
ordinary life, or even in ordinary history, are for our present purpose
quite inappreciable. As our earth is daily losing internal heat, or the
equivalent of heat, it must have contained more heat yesterday than it
does to-day, more last year than this year, more twenty years ago than
ten years ago. The effect has not been appreciable in historic time; but
when we rise from hundreds of years to thousands of years, from
thousands of years to hundreds of thousands of years, and from hundreds
of thousands of years to millions of years, the effect is not only
appreciable, but even of startling magnitude.
There must have been a time when the earth contained much more heat than
at present. There must have been a time when the surface of the earth
was sensibly hot from this source. We cannot pretend to say how many
thousands or millions of years ago this epoch must have been; but we may
be sure that earlier still the earth was even hotter, until at length we
seem to see the temperature increase to a red heat, from a red heat we
look back to a still earlier age when the earth was white hot, back
further till we find the surface of our now solid globe was actually
molten. We need not push the retrospect any further at present, still
less is it necessary for us to attempt to assign the probable origin of
that heat. This, it will be observed, is not required in our argument.
We find heat now, and we know that heat is being lost every day. From
this the conclusion that we have already drawn seems inevitable, and
thus we are conducted back to some remote epoch in the abyss of time
past when our solid earth was a globe molten and soft throughout.
A dewdrop on the petal of a flower is nearly globular; but it is not
quite a globe, because the gravitation presses it against the flower and
somewhat distorts the shape. A falling drop of rain is a globe; a drop
of oil suspended in a liquid with which it does not mix forms a globe.
Passing from small things to great things, let us endeavour to conceive
a stupendous globe of molten matter. Let that globe be as large as the
earth, and let its materials be so soft as to obey the forces of
attraction exerted by each part of the globe on all the other parts.
There can be no doubt as to the effect of these attractions; they would
tend to smooth down any irregularities on the surface just in the same
way as the surface of the ocean is smooth when freed from the disturbing
influences of the wind. We might, therefore, expect that our molten
globe, isolated from all external interference, would assume the form of
a sphere.
But now suppose that this great sphere, which we have hitherto assumed
to be at rest, is made to rotate round an axis passing through its
centre. We need not suppose that this axis is a material object, nor are
we concerned with any supposition as to how the velocity of rotation was
caused. We can, however, easily see what the consequence of the rotation
would be. The sphere would become deformed, the centrifugal force would
make the molten body bulge out at the equator and flatten down at the
poles. The greater the velocity of rotation the greater would be the
bulging. To each velocity of rotation a certain degree of bulging would
be appropriate. The molten earth thus bulged out to an extent which was
dependent upon the fact that it turned round once a day. Now suppose
that the earth, while still rotating, commences to pass from the liquid
to the solid state. The form which the earth would assume on
consolidation would, no doubt, be very irregular on the surface; it
would be irregular in consequence of the upheavals and the outbursts
incident to the transformation of so mighty a mass of matter; but
irregular though it be, we can be sure that, on the whole, the form of
the earth's surface would coincide with the shape which it had assumed
by the movement of rotation. Hence we can explain the protuberant form
of the equator of the earth, and we can appeal to that form in
corroboration of the view that this globe was once in a soft or molten
condition.
The argument may be supported and illustrated by comparing the shape of
our earth with the shapes of some of the other celestial bodies. The
sun, for instance, seems to be almost a perfect globe. No measures that
we can make show that the polar diameter of the sun is shorter than the
equatorial diameter. But this is what we might have expected. No doubt
the sun is rotating on its axis, and, as it is the rotation that causes
the protuberance, why should not the rotation have deformed the sun like
the earth? The probability is that a difference really does exist
between the two diameters of the sun, but that the difference is too
small for us to measure. It is impossible not to connect this with the
_slowness_ of the sun's rotation. The sun takes twenty-five days to
complete a rotation, and the protuberance appropriate to so low a
velocity is not appreciable.
On the other hand, when we look at one of the quickly-rotating planets,
we obtain a very different result. Let us take the very striking
instance which is presented in the great planet Jupiter. Viewed in the
telescope, Jupiter is at once seen not to be a globe. The difference is
so conspicuous that accurate measures are not necessary to show that the
polar diameter of Jupiter is shorter than the equatorial diameter. The
departure of Jupiter from the truly spherical shape is indeed much
greater than the departure of the earth. It is impossible not to connect
this with the much more rapid rotation of Jupiter. We shall presently
have to devote a chapter to the consideration of this splendid orb. We
may, however, so far anticipate what we shall then say as to state that
the time of Jupiter's rotation is under ten hours, and this
notwithstanding the fact that Jupiter is more than one thousand times
greater than the earth. His enormously rapid rotation has caused him to
bulge out at the equator to a remarkable extent.
The survey of our earth and the measurement of its dimensions having
been accomplished, the next operation for the astronomer is the
determination of its weight. Here, indeed, is a problem which taxes the
resources of science to the very uttermost. Of the interior of the earth
we know little--I might almost say we know nothing. No doubt we sink
deep mines into the earth. These mines enable us to penetrate half a
mile, or even a whole mile, into the depths of the interior. But this
is, after all, only a most insignificant attempt to explore the interior
of the earth. What is an advance of one mile in comparison with the
distance to the centre of the earth? It is only about one
four-thousandth part of the whole. Our knowledge of the earth merely
reaches to an utterly insignificant depth below the surface, and we have
not a conception of what may be the nature of our globe only a few miles
below where we are standing. Seeing, then, our almost complete ignorance
of the solid contents of the earth, does it not seem a hopeless task to
attempt to weigh the entire globe? Yet that problem has been solved, and
the result is known--not, indeed, with the accuracy attained in other
astronomical researches, but still with tolerable approximation.
It is needless to enunciate the weight of the earth in our ordinary
units. The enumeration of billions of tons does not convey any distinct
impression. It is a far more natural course to compare the mass of the
earth with that of an equal globe of water. We should be prepared to
find that our earth was heavier than a like volume of water. The rocks
which form its surface are heavier, bulk for bulk, than the oceans which
repose on those rocks. The abundance of metals in the earth, the gradual
increase in the density of the earth, which must arise from the enormous
pressure at great depths--all these considerations will prepare us to
learn that the earth is very much heavier than a globe of water of equal
size.
Newton supposed that the earth was between five and six times as heavy
as an equal bulk of water. Nor is it hard to see that such a suggestion
is plausible. The rocks and materials on the surface are usually about
two or three times as heavy as water, but the density of the interior
must be much greater. There is good reason to believe that down in the
remote depths of the earth there is a very large proportion of iron. An
iron earth would weigh about seven times as much as an equal globe of
water. We are thus led to see that the earth's weight must be probably
more than three, and probably less than seven, times an equal globe of
water; and hence, in fixing the density between five and six, Newton
adopted a result plausible at the moment, and since shown to be probably
correct. Several methods have been proposed by which this important
question can be solved with accuracy. Of all these methods we shall here
only describe one, because it illustrates, in a very remarkable manner,
the law of universal gravitation.
In the chapter on Gravitation it was pointed out that the intensity of
this force between two masses of moderate dimensions was extremely
minute, and the difficulty in weighing the earth arises from this cause.
The practical application of the process is encumbered by multitudinous
details, which it will be unnecessary for us to consider at present. The
principle of the process is simple enough. To give definiteness to our
description, let us conceive a large globe about two feet in diameter;
and as it is desirable for this globe to be as heavy as possible, let us
suppose it to be made of lead. A small globe brought near the large one
is attracted by the force of gravitation. The amount of this attraction
is extremely small, but, nevertheless, it can be measured by a refined
process which renders extremely small forces sensible. The intensity of
the attraction depends both on the masses of the globes and on their
distance apart, as well as on the force of gravitation. We can also
readily measure the attraction of the earth upon the small globe. This
is, in fact, nothing more nor less than the weight of the small globe in
the ordinary acceptation of the word. We can thus compare the
attraction exerted by the leaden globe with the attraction exerted by
the earth.
If the centre of the earth and the centre of the leaden globe were at
the same distance from the attracted body, then the intensity of their
attractions would give at once the ratio of their masses by simple
proportion. In this case, however, matters are not so simple: the leaden
ball is only distant by a few inches from the attracted ball, while the
centre of the earth's attraction is nearly 4,000 miles away at the
centre of the earth. Allowance has to be made for this difference, and
the attraction of the leaden sphere has to be reduced to what it would
be were it removed to a distance of 4,000 miles. This can fortunately be
effected by a simple calculation depending upon the general law that the
intensity of gravitation varies inversely as the square of the distance.
We can thus, partly by calculation and partly by experiment, compare the
intensity of the attraction of the leaden sphere with the attraction of
the earth. It is known that the attractions are proportional to the
masses, so that the comparative masses of the earth and of the leaden
sphere have been measured; and it has been ascertained that the earth is
about half as heavy as a globe of lead of equal size would be. We may
thus state finally that the mass of the earth is about five and a half
times as great as the mass of a globe of water equal to it in bulk.
In the chapter on Gravitation we have mentioned the fact that a body let
fall near the surface of the earth drops through sixteen feet in the
first second. This distance varies slightly at different parts of the
earth. If the earth were a perfect sphere, then the attraction would be
the same at every part, and the body would fall through the same
distance everywhere. The earth is not round, so the distance which the
body falls in one second differs slightly at different places. At the
pole the radius of the earth is shorter than at the equator, and
accordingly the attraction of the earth at the pole is greater than at
the equator. Had we accurate measurements showing the distance a body
would fall in one second both at the pole and at the equator, we should
have the means of ascertaining the shape of the earth.
It is, however, difficult to measure correctly the distance a body will
fall in one second. We have, therefore, been obliged to resort to other
means for determining the force of attraction of the earth at the
equator and other accessible parts of its surface. The methods adopted
are founded on the pendulum, which is, perhaps, the simplest and
certainly one of the most useful of philosophical instruments. The ideal
pendulum is a small and heavy weight suspended from a fixed point by a
fine and flexible wire. If we draw the pendulum aside from its vertical
position and then release it, the weight will swing to and fro.
For its journey to and fro the pendulum requires a small period of time.
It is very remarkable that this period does not depend appreciably on
the length of the circular arc through which the pendulum swings. To
verify this law we suspend another pendulum beside the first, both being
of the same length. If we draw both pendulums aside and then release
them, they swing together and return together. This might have been
expected. But if we draw one pendulum a great deal to one side, and the
other only a little, the two pendulums still swing sympathetically.
This, perhaps, would not have been expected. Try it again, with even a
still greater difference in the arc of vibration, and still we see the
two weights occupy the same time for the swing.
We can vary the experiment in another way. Let us change the weights on
the pendulums, so that they are of unequal size, though both of iron.
Shall we find any difference in the periods of vibration? We try again:
the period is the same as before; swing them through different arcs,
large or small, the period is still the same. But it may be said that
this is due to the fact that both weights are of the same material. Try
it again, using a leaden weight instead of one of the iron weights; the
result is identical. Even with a ball of wood the period of oscillation
is the same as that of the ball of iron, and this is true no matter what
be the arc through which the vibration takes place.
If, however, we change the _length_ of the wire by which the weight is
supported, then the period will not remain unchanged. This can be very
easily illustrated. Take a short pendulum with a wire only one-fourth of
the length of that of the long one; suspend the two close together, and
compare the periods of vibration of the short pendulum with that of the
long one, and we find that the former has a period only half that of the
latter. We may state the result generally, and say that the time of
vibration of a pendulum is proportional to the square root of its
length. If we quadruple the length of the suspending cord we double the
time of its vibration; if we increase the length of the pendulum
ninefold, we increase its period of vibration threefold.
It is the gravitation of the earth which makes the pendulum swing. The
greater the attraction, the more rapidly will the pendulum oscillate.
This may be easily accounted for. If the earth pulls the weight down
very vigorously, the time will be short; if the power of the earth's
attraction be lessened, then it cannot pull the weight down so quickly,
and the period will be lengthened.
The time of vibration of the pendulum can be determined with great
accuracy. Let it swing for 10,000 oscillations, and measure the time
that these oscillations have consumed. The arc through which the
pendulum swings may not have remained quite constant, but this does not
appreciably affect the _time_ of its oscillation. Suppose that an error
of a second is made in the determination of the time of 10,000
oscillations; this will only entail an error of the ten-thousandth part
of the second in the time of a single oscillation, and will afford a
correspondingly accurate determination of the force of gravity at the
place where the experiment was made.
Take a pendulum to the equator. Let it perform 10,000 oscillations, and
determine carefully the _time_ that these oscillations have required.
Bring the same pendulum to another part of the earth, and repeat the
experiment. We have thus a means of comparing the gravitation at the two
places. There are, no doubt, a multitude of precautions to be observed
which need not here concern us. It is not necessary to enter into
details as to the manner in which the motion of the pendulum is to be
sustained, nor as to the effect of changes of temperature in the
alteration of its length. It will suffice for us to see how the time of
the pendulum's swing can be measured accurately, and how from that
measurement the intensity of gravitation can be calculated.
The pendulum thus enables us to make a gravitational survey of the
surface of the earth with the highest degree of accuracy. We cannot,
however, infer that gravity alone affects the oscillations of the
pendulum. We have seen how the earth rotates on its axis, and we have
attributed the bulging of the earth at the equator to this influence.
But the centrifugal force arising from the rotation has the effect of
decreasing the apparent weight of bodies, and the change is greatest at
the equator, and lessens gradually as we approach the poles. From this
cause alone the attraction of the pendulum at the equator is less than
elsewhere, and therefore the oscillations of the pendulum will take a
longer time there than at other localities. A part of the apparent
change in gravitation is accordingly due to the centrifugal force; but
there is, in addition, a real alteration.
In a work on astronomy it does not come within our scope to enter into
further detail on the subject of our planet. The surface of the earth,
its contour and its oceans, its mountain chains and its rivers, are for
the physical geographer; while its rocks and their contents, its
volcanoes and its earthquakes, are to be studied by the geologists and
the physicists.