GRAVITATION.
73. =Attraction Between Masses.=--I have thus far treated of
attraction as existing between the atoms or particles of matter
when they are brought very near together, which is called the
attraction of _cohesion_. But it exists also between any portions
of matter that are separate from each other. Thus if two cork
balls be placed on the surface of water near to each other, their
attraction will soon bring them together. To have the experiment
striking, the balls must be varnished, that they may glide easily
over the water. Bubbles of glass will exhibit the same attraction.
So, also, floating pieces of wood are apt to be found together; and
when a ship is wrecked, as soon as the sea becomes calm the parts
of the wreck are in collections here and there. Now when a stone
falls to the ground, it does so for precisely the same reason that
the two cork balls come together in the water. The idea of all who
have not been informed on such subjects is, that the stone comes
to the ground because the ground is down and the stone is up, and
there is nothing to support the stone in the air. They have no idea
that some power makes the stone come down. There is such a power,
and it is the attraction which the earth and the stone have for
each other. If you hold the stone in your hand, and thus prevent
its falling, you simply resist a power which is pulling it down. If
you could in any way suspend the attraction of the earth and the
stone for each other, you could let go of the stone, and it would
remain just there in the air, and would not come down until the
attraction is restored.
74. =Attraction Mutual.=--The cork balls move toward each other
because their attraction is mutual. So do the earth and stone
really move toward each other for the same reason. As the stone is
drawn toward the earth, so is the earth drawn toward the stone.
But the earth is so large a thing to be drawn that its motion is
exceedingly small--so small that practically it may be considered
as nothing.
75. =Illustration.=--This may be clearly illustrated if we compare
the force of attraction to the force of muscular action. Suppose a
man in a boat pulls on a rope which is made fast to a ship lying
loose at the wharf, and in this way draws his boat toward it. He
does not dream that he moves the ship at all; but he in reality
does, for if instead of one boat a hundred or more pull upon the
ship, they will move it so much as to make the motion apparent. In
the case of the single boat, the ship as really moves as when a
hundred boats are pulling on it, but it is only the one hundredth
part as much. Now let the ship represent the earth, and the little
boat some body, as a stone, attracted by it. The earth and the
stone move toward each other, just as the ship and the boat do. And
if, as we multiplied the number of boats, we should multiply the
bulk of the stone till it is of an immense size, it would have by
its attraction a perceptible influence upon the earth's motion.
Observe in regard to the illustration, that it makes no difference
whether the man be in the boat or in the ship as he pulls. In
either case he exerts an equal force on the ship and the boat,
making them to approach each other. So it is with the attraction
between the earth and the stone. It is a force exerted equally upon
both. Its effect on the earth is not manifest, because it is so
much larger than the stone; just as the effect of the man's pulling
is not manifest upon the ship, because it is so much larger than
the boat.
76. =Proportion of the Mutual Motions of Attraction.=--Let us
pursue the illustration a little farther. If a man stand in a
boat, and pull a rope made fast to another boat of the same size
and weight, both boats, in coming together, will move over the
same space. Just so it is with the attraction between two bodies
having the same quantities of matter or equal weights--they attract
each other equally, and therefore meet each other half way. Let
now one boat be ten times as great and as heavy as the other. The
small boat would move ten times as much as the large one when the
man brings them together by pulling the rope. In like manner, if
a body one-tenth as large as the earth should approach it, they
would attract each other, but in coming together the body would
move ten times as far as the earth would. In the case of falling
bodies, even though they may be of great size, the earth moves so
slightly to meet them that its motion is wholly imperceptible. It
has been calculated that if a ball of earth the tenth part of a
mile in diameter were placed at the distance of a tenth part of a
mile from the earth, as the earth and this body would be moved by
their attraction to meet each other, the motion of the earth would
be only the eighty thousandth of a millionth (1/80,000,000,000) of
an inch.
77. =Attraction Universal.=--The attraction of which I have been
speaking exists between all bodies, however distant they may be
from each other. Sun, earth, moon, and stars attract each other;
and in obedience to this attraction they have a tendency to come
together in one great mass, and would do so if another force acting
in opposition to this did not prevent it. This force will be
treated of in another part of this book.
78. =The Tides.=--One effect of the attraction between the earth
and the moon is quite familiar. I refer to the tides. When the tide
rises it is because the water of the ocean feels the attracting
force of the moon. The moon actually lifts the water toward itself.
The attraction of the sun sometimes increases and sometimes
diminishes the tides, according to its position in relation to the
moon and the earth. If the land were as movable as the water, or,
in other words, if its particles were held together by no stronger
attraction than those of water, there would be the same motion that
there is in the ocean over the surface of the earth, as in its
revolution successive portions of it present themselves toward the
moon.
79. =Meaning of the Word Gravitation.=--The attraction thus
existing between different bodies of matter separated from each
other is called the attraction of gravitation or gravity, in
distinction from the attraction of _cohesion_ treated of in the
previous chapter. This name was given to it because we have such
common examples of its influence in the fall of bodies to the
earth. They are said to _gravitate_ toward the earth. And they are
said to do so by the force or attraction of gravitation or gravity.
The term _terrestrial_ gravitation is sometimes used in speaking
of the earth's attraction, in distinction from the same thing in
operation in other planets.
[Illustration: Fig. 22.]
[Illustration: Fig. 23.]
80. =Attraction Toward the Earth's Centre.=--All bodies are
attracted toward the centre of the earth. This is because the
earth is globular, as may be made clear by Fig. 22. Let the circle
represent the earth, and _a_ a body attracted by it. The lines
drawn from the body to the earth represent the attractive force
exerted by the earth upon the body. It is obvious from these that
there is as much attraction on the one side of the line drawn
from the body to the earth's centre as there is on the other. The
attractive force, then, of the earth as a whole is exerted upon the
body in the direction of this middle line. It tends to draw it,
therefore, toward the centre. If, therefore, a weight be suspended
by a string, the line of the string continued would go to the
centre of the earth. This being so, it is clear that two weights
suspended by two strings do not hang perfectly parallel to each
other. The difference is so slight in an ordinary pair of scales
that it can not in any way be perceived. But if it were possible to
suspend in the heavens a beam so long as to stretch over a large
extent of the earth's circumference, as represented in Fig. 23, the
scales attached to it would be very far from hanging parallel to
each other. Substances suspended in different parts of the globe
are hanging in different directions, and those which are hung up
by our fellow-men on the opposite side of the earth, are hanging
directly toward us.
[Illustration: Fig. 24.]
81. =Up and Down.=--All falling bodies fall toward the centre of
the earth, and the same remarks can be made on this point that I
have made in relation to suspended weights. Up and down are merely
relative terms--_up_ being from the centre of the earth, and _down_
toward it. As the earth moves round on its axis, the same line of
direction which we call upward at one time is downward at another.
This may be illustrated on Fig. 24. Let the circle represent the
circumference of the earth. In the daily revolution we pass over
this whole circle. If we are at D at noon, we are at E at six
o'clock, and at F at midnight. If, therefore, the ball A be dropped
from some height at noon, the line in which it falls will be at
right angles to a line in which it will fall if you drop it from
the same height at six o'clock; for this height will have moved in
this time from A to B. If it be dropped from the same height at
midnight its line of direction will be directly opposite to what
it was twelve hours before; for the height will have moved in that
time to C.
It is not always true that falling bodies tend exactly toward the
centre of the earth. It is nothing in the centre that attracts
them, but it is the substance of the whole earth; and as this is
irregular in its density and form, the attraction will be irregular
also. Thus it is found by accurate experimenting that a plumb line
suspended in the neighborhood of a mountain is so attracted by it
that it will not hang exactly parallel with another suspended at
some distance from the mountain. The difference is not, however,
enough in any case to have any practical bearing.
82. =Weight.=--I have said before (§ 52) that what we call weight
is not a property of matter, but merely the result of a property,
the attraction of gravity. This I will now illustrate. If two
bodies are falling to the earth, and one of them contains ten times
as many particles of matter as the other, ten times as much force
of gravity is required, and is actually exerted, to bring it to the
ground. This will appear plain to you if you bear in mind that a
body does not come to the ground because there is nothing to keep
it there, but because it is drawn down by the force of attraction,
and then compare this force to any other force, as, for example,
that of muscular action. If you draw toward you two weights, one of
which is twenty times as heavy as the other, or, in other words,
has twenty times the quantity of matter that the other has, you
must exert twenty times as much strength on the former as you do on
the latter. Just so it is with the force of attraction. The earth
attracts or draws toward itself a body having twenty times the
quantity of matter that another has with twenty times the amount
of force. And the first body will have twenty times the weight of
the other, for it will make twenty times the pressure upon any
thing that resists the force with which the earth draws it toward
itself. Weight, then, is _the amount of the pressure occasioned by
the attraction existing between the earth and the body weighed_.
If you place a substance in one side of a pair of scales, it goes
down because of the attraction between it and the earth. By placing
weights in the other side until the scales are balanced, you find
how much is needed to counteract the downward pressure caused by
the attraction of the substance and the earth for each other; or,
in other words, you find out how much it weighs. In doing this you
use certain standard weights; that is, certain quantities of matter
which have been agreed upon by mankind, and are called by certain
names, as pounds, ounces, etc. When a spring is used in weighing,
the spring has been tried by these standard weights, and its scale
has been marked accordingly.
83. =Weight not Fixed, but Variable.=--Weight does not depend alone
upon the density of the body weighed, but also upon the density
of the earth. For the attraction causing the pressure which we
call weight is a _mutual_ attraction, and is in proportion to the
quantities of matter in both the body and the earth. If, therefore,
the density of the earth were increased twice, three times, or
four times, the weights of all bodies would be increased in the
same proportion; that is, the force with which the earth would
attract them would be twice, three times, or four times as great
as now. This would not be perceived by any effect on balances,
for the weights and the articles weighed would be alike increased
in weight. But it would be perceived in instruments that indicate
the weights of bodies by their influence on a spring. These would
disagree with scales and steelyards just in proportion to the
increase of the earth's density. It would be perceived also in the
application of muscular and other forces in raising and sustaining
weights. Every stone would require twice, three times, or four
times the muscular effort to raise it that it does now.
84. =Weight Varies with Distance.=--The nearer two bodies are to
each other the greater is their attraction. The nearer a body is
to the earth the greater is the attraction that presses it toward
the earth; in other words, the greater is its weight. The force of
gravity, or weight, is greatest, therefore, just at the surface of
the earth, and it diminishes as we go up from the earth. As we go
from the earth, the force of gravity lessens in such a proportion
that it is always _inversely_ as the square of the distance from
the centre of the earth. I will explain. If the distance from the
centre of the earth to its surface, which is 4000 miles, be called
1, then 4000 miles from the earth would be called 2, or twice as
far from the centre, and 8000 miles from the earth would be 3, and
so on. The squares of these numbers would be 1, 4, 9, 16, etc.
Now as weight lessens so as to be _inversely_ as the square of the
distance, a body weighing a pound on the surface of the earth would
weigh but a quarter of a pound at the distance of 4000 miles, and
but the ninth part of a pound at 8000 miles. A body weighs less on
the summit of a high mountain than it would in the valley below,
because it is farther away from the great bulk of the earth, and
therefore is not so strongly attracted. The difference, however,
is but small. A man weighing two hundred and fifty pounds in the
valley would weigh but half a pound less if on the summit of a
mountain four miles high.
85. =Weight Every Where.=--I have spoken of weight only in relation
to the earth. But there is weight in bodies every where, for there
is attraction wherever there is matter. The weight of substances on
the surface of different heavenly bodies varies according to the
quantities of matter in those bodies. As the moon is much smaller
than the earth, what weighs a pound with us would weigh much less
than a pound in the moon. And as the sun is much larger than the
earth, what is a pound with us would be much more than a pound
there. If we knew the exact densities of the sun and the moon and
the earth, as well as their size, we could estimate exactly the
difference in the weights which any body would have in them; for
the attraction which causes the pressure that we call weight is as
the quantity of matter, and the quantity of matter depends on both
density and size.
86. =Cohesion, Capillary Attraction, and Gravitation the
Same.=--The attraction of cohesion, capillary attraction, and
gravitation are only different modes of action of the same power;
viz., the attraction which matter every where has for matter. At
first thought it would appear that there is something peculiar in
the attraction of particles when they are brought together so as
to adhere. For if we take any substance, a piece of glass, for
example, its particles seem to be held together by an attraction
vastly stronger than that attraction which inclines different
bodies to move toward each other. If you break the glass, however
closely you may press the two pieces together, they will not
unite again. It would seem, at first view, that there must be
some peculiar arrangement of the particles which is destroyed by
breaking the glass. But we can readily account for the facts in
another way. The attraction between bodies of matter is the greater
the nearer we bring them together. The nearer, for example, is the
moon to any portion of the earth, the greater is the attraction
which it exerts, as seen in the tides; and if it were much nearer
to the earth than it is, our tides would prove awfully destructive.
What is true of masses is also true of the particles of which
they are composed. Though their attraction is comparatively
feeble when at a distance from each other, it increases, not in
the arithmetical but the geometrical ratio (§ 84), as they come
nearer together; so that when they are exceedingly near together
the attraction is very powerful. It must be remembered in regard
to the pieces of broken glass that you can not bring the particles
on their surfaces as near as they were before the glass was
broken, for the crack does not disappear. And as the attraction is
inversely as the square of the distance, a little distance must
make a great difference. The particles of some substances you can
bring so near together as to cause adhesion, as you saw in the case
of the two bullets (§ 66). That their adhering together depends
merely upon their particles being brought near to each other
appears from the fact, that the smoother you make the surfaces the
more strongly will they adhere. And the reason that liquids and
semi-liquids adhere so readily to solid substances is, that their
particles, moving freely among each other, have thus the power of
arranging themselves very near to the particles of the solid. Thus,
when a drop of water hangs to glass, all the particles of water
in that part of the drop next to the glass touch, or rather are
exceedingly near to, the particles of the glass.
87. =Variety in the Results of Attraction.=--It is one and the
same force, then, which binds the particles of a pebble together,
and makes it fall to the ground--which "moulds the tear" and "bids
it trickle from its source"--which gives the earth and all the
heavenly bodies their globular shape, and, in connection with
another power hereafter to be noticed, makes them revolve in their
orbits. How sublime the thought that this one simple principle that
gives form to a drop extends its influence through the immensity of
space, and so marshals "the host of heaven" that, without the least
interruption or discord, they all hold on their course from year
to year and from age to age! It is thus that Omnipotence makes the
simplest means to produce the grandest and most multiform results.
88. =Opposition Between the Modes of Attraction.=--Although
cohesion and gravitation are essentially the same thing, we see
them continually acting in opposition to each other. Abundant
illustrations might be given, but, I will cite only a few.
[Illustration: Fig. 25. Fig. 26.]
89. =Why Pitchers have Lips.=--If you pour water out of a tumbler
there is a struggle between the attraction of cohesion and
gravitation for the mastery--the attraction of cohesion tending
to make the water adhere to the tumbler, and run down its side,
as in Fig. 25, and gravitation tending to make it fall straight
down. But when water is poured out of a pitcher, as in Fig. 26,
the lip of the pitcher acts in favor of the attraction of gravity;
for the water would have to turn a very sharp corner to run
down the outside of the pitcher in obedience to the attraction
of cohesion. In pouring water from a tumbler, we can often, by a
quick movement, throw the water, as we may say, into the hands
of gravity before the attraction of cohesion can get a chance to
turn it down the tumbler's side. If you can only make the water
_begin_ to run from the tumbler without going down its side there
will be no difficulty; for there is an attraction of cohesion
between the particles of the water, tending to make them keep
together, which in this case acts against the cohesion between the
water and the glass, and therefore acts in favor of gravitation.
It is cohesion that forms the drop on the lip of a vial as we
drop medicine--cohesion between the particles of the liquid,
and cohesion between these particles and those of the glass. It
is gravitation, on the other hand, that makes the drop fall, it
becoming so large that the force of gravity overcomes the cohesion
between the drop and the vial.
90. =Size Limited by Gravity.=--Were it not for the attraction
of gravity there would be no limit to the size of drops of any
liquid. When the drop reaches a certain size, it falls because it
is so heavy; or, in other words, because with its slight cohesion
the attraction of the earth brings it down. Now if this attraction
could be suspended, and the attraction of cohesion left to act
alone, particles of water might be added to the drop to any extent,
and they would cling there. You can see the struggling between
cohesion and gravitation very prettily illustrated if you watch the
drops of rain on a window-pane. If two drops happen to be quite
near together they unite by attraction, and then, being too large
to allow of its being retained there by cohesion in opposition to
gravitation, the united drop runs down. If it meet with no other
drop it soon stops, because by cohesion some portion of it clings
to the glass all along its track, and so at length lessens it
sufficiently to allow it to remain suspended again. It is from the
influence of the attraction of gravitation that different kinds of
liquids furnish drops of different sizes, the heavier giving small,
and the lighter large ones. Thus you can drop from a vial a larger
drop of alcohol than of water, and a larger one of water than of
nitric acid. You have another illustration of a similar character
in the adhesion of chalk to a black-board or any surface. The chalk
crayon itself can not adhere, for the attraction of the earth does
not permit it. But small quantities of it can adhere for the same
reason that water adheres to surfaces in small quantities. So also
dust clings to sides of furniture, though a lump of dirt would not.
[Illustration: Fig. 27.]
[Illustration: Fig. 28.]
91. =Illustrated in Solid Bodies.=--We can illustrate the
limitation of size in solid masses by Figs. 27 and 28. Suppose
that _a_ and _b_, Fig. 27, are two projections of timber from a
post, _b_ being twice as large as _a_. It is evident that _b_
can not support twice as much weight as _a_, for gravitation is
dragging it downward from its attachment to the upright post with
twice the force that it does _a_. The case is still stronger when,
as represented in Fig. 28 (p. 64), the larger timber is twice as
long as the smaller. Here _d_ has four times the bulk of _c_. But
it can not support four times as much weight at its end, not only
because its own weight presses it downward, but because half of
its weight is at a greater distance from the place of attachment
than the smaller beam is. Gravitation here operates in opposition
to cohesion in such a way that the projecting timber, if carried
to a certain size, will fall by its own weight, either breaking in
two, or tearing away from its attachment. This tendency is very
commonly resisted in buildings and other structures by braces, as
represented in Fig. 29. Here the weight of the horizontal timber
at some distance on each side of _a_, is made to press upon the
upright post instead of directly downward.
[Illustration: Fig. 29.]
92. =Farther Illustrations.=--The size of bodies, both animate and
inanimate, is limited by the Creator in obedience to the principles
above developed. This is seen in the fact that there are no animals
on the land to compare in size with the monsters of the deep. A
whale does very well in the water, because he is buoyed up by that
element; but an animal as large as a whale could not well exist on
land, because gravitation would act so strongly in opposition to
cohesion. At least it would be necessary, in order that he might
walk about, or even hold together, that his great bulk should be
made up of very firm and tenacious materials. Whenever any thing
very large or tall is to be supported, its support is always broad
and composed of very cohesive materials. We see this exemplified
in the massive trunks of full-grown trees, as compared with the
slender trunks of trees of the same kinds in the nursery. We see
it exemplified in the fact that the highest mountains are built of
the hardest rocks, while the soft chalk formations are confined
to those of small size. There is a limit to the height even of
the granite mountains in the influence of gravity. If carried
much higher than they are, the attraction of the earth, in its
opposition to cohesion, would tear them apart in their fissures, or
cause the immense weight to crush their foundations. In the moon,
where gravitation is less than on the earth (§ 85), mountains can
be much higher without these results, and accordingly the telescope
shows them to be so. In Jupiter, on the other hand, which is much
larger than the earth, the mountains, if there be any, can not rise
to any great height, and if there be any living beings as large as
we are in that planet they must be made of vastly firmer materials
to prevent their being crushed by their own weight.
93. =The Above Principles Transgressed by Man.=--Man often
transgresses these principles in his structures. For example,
a building settles because the foundation is not strong enough
to bear the superincumbent weight; in other words, the force of
gravitation is not sufficiently taken into the account. When a very
tall building is erected, the lower portions ought to be made of
very cohesive substances. Firm granite is therefore an appropriate
material for the lower story of tall brick buildings. At least
should the walls of the lower stories of such buildings be made
thicker than they ordinarily are, to resist properly the force
of gravitation in the weight above. Stores intended to bear much
weight on their floors are often built without due regard to the
cohesive force required to sustain the weight. Long timbers are
sometimes supported only at the ends, when their own weight, to say
nothing of what may be brought to press upon them, requires that
they should be supported at other points. While in modern buildings
the timbers are often too small, in some old buildings the upper
timbers are so heavy as to lessen rather than increase the strength
of the structure. Especially is this true of the unsightly beams
which in some ancient houses we see extending along the ceilings
above. Many other examples could be given, but these will suffice.
The practiced eye, in looking at a building, instinctively requires
that every part should be _seen_ to be suitably supported. A
gallery in a church, therefore, if without pillars or braces from
the wall, is displeasing to such an eye, even though there may be
really sufficient support provided in the mode of structure. The
same can be said of galleries supported by slender iron pillars,
especially if they be painted of some light color so as to look as
if they were wood rather than iron. For the same reason porticoes
without pillars are unsightly. So, too, the eye instinctively looks
for a sufficient base to every pillar and pilaster. The concealment
of the base in any way, or the substitution of any thing else for
it, is an unpleasant anomaly, and yet such anomalies are sometimes
seen even in expensive buildings.
94. =Attraction of Natural Philosophy and of Chemistry.=--The
attraction of which I have treated in this and the previous
chapters is that which belongs to Natural Philosophy, in
distinction from that of Chemistry. Its effects are only
mechanical, while the attraction of Chemistry goes beyond this,
and affects the _composition_ of substances. For example, the
attraction between the two gases, oxygen and hydrogen, which makes
them unite to form water, belongs to Chemistry; while that which
makes the particles of water cohere is in the province of Natural
Philosophy.