changes of position, with respect to the horizon, which the sun
undergoes in the course of the year, occasion such a difference in the
amount of heat received from him. Two causes contribute to increase the
heat of Summer and the cold of Winter. The higher the sun ascends above
the horizon, the more directly his rays fall upon the earth; and their
heating power is rapidly augmented, as they approach a perpendicular
direction. When the sun is nearly over head, his rays strike us with far
greater force than when they meet us obliquely; and the earth absorbs a
far greater number of those rays of heat which strike it
perpendicularly, than of those which meet it in a slanting direction.
When the sun is near the horizon, his rays merely glance along the
ground, and many of them, before they reach it, are absorbed and
dispersed in passing through the atmosphere. Those who have felt only
the oblique solar rays, as they fall upon objects in the high latitudes,
have a very inadequate idea of the power of a vertical, noonday sun, as
felt in the region of the equator.
The increased length of the day in Summer is another cause of the heat
of this season of the year. This cause more sensibly affects places far
removed from the equator, because at such places the days are longer and
the nights shorter than in the torrid zone. By the operation of this
cause, the solar heat accumulates there so much, during the longest days
of Summer, that the temperature rises to a higher degree than is often
known in the torrid climates.
But the temperature of a place is influenced very much by several other
causes, as well as by the force and duration of the sun's heat. First,
the _elevation_ of a country above the level of the sea has a great
influence upon its climate. Elevated districts of country, even in the
torrid zone, often enjoy the most agreeable climate in the world. The
cold of the upper regions of the atmosphere modifies and tempers the
solar heat, so as to give a most delightful softness, while the
uniformity of temperature excludes those sudden and excessive changes
which are often experienced in less favored climes. In ascending certain
high mountains situated within the torrid zone, the traveller passes, in
a short time, through every variety of climate, from the most oppressive
and sultry heat, to the soft and balmy air of Spring, which again is
succeeded by the cooler breezes of Autumn, and then by the severest
frosts of Winter. A corresponding difference is seen in the products of
the vegetable kingdom. While Winter reigns on the summit of the
mountain, its central regions may be encircled with the verdure of
Spring, and its base with the flowers and fruits of Summer. Secondly,
the proximity of the _ocean_ also has a great effect to equalize the
temperature of a place. As the ocean changes its temperature during the
year much less than the land, it becomes a source of warmth to
contiguous countries in Winter, and a fountain of cool breezes in
Summer. Thirdly, the relative _humidity_ or _dryness_ of the atmosphere
of a place is of great importance, in regard to its effects on the
animal system. A dry air of ninety degrees is not so insupportable as a
humid air of eighty degrees; and it may be asserted as a general
principle, that a hot and humid atmosphere is unhealthy, although a hot
air, when dry, may be very salubrious. In a warm atmosphere which is
dry, the evaporation of moisture from the surface of the body is rapid,
and its cooling influence affords a most striking relief to an intense
heat without; but when the surrounding atmosphere is already filled with
moisture, no such evaporation takes place from the surface of the skin,
and no such refreshing effects are experienced from this cause. Moisture
collects on the skin; a sultry, oppressive sensation is felt; and chills
and fevers are usually in the train.
LETTER XII.
LAWS OF MOTION.
"What though in solemn silence, all
Move round this dark, terrestrial ball!
In reason's ear they all rejoice,
And utter forth a glorious voice;
For ever singing, as they shine,
'The hand that made us is divine.'"--_Addison._
HOWEVER incredible it may seem, no fact is more certain, than that the
earth is constantly on the wing, flying around the sun with a velocity
so prodigious, that, for every breath we draw, we advance on our way
forty or fifty miles. If, when passing across the waters in a
steam-boat, we can wake, after a night's repose, and find ourselves
conducted on our voyage a hundred miles, we exult in the triumphs of
art, which could have moved so ponderous a body as a steam-ship over
such a space in so short a time, and so quietly, too, as not to disturb
our slumbers; but, with a motion vastly more quiet and uniform, we have,
in the same interval, been carried along with the earth in its orbit
more than half a million of miles. In the case of the steam-ship,
however perfect the machinery may be, we still, in our waking hours at
least, are made sensible of the action of the forces by which the motion
is maintained,--as the roaring of the fire, the beating of the piston,
and the dashing of the paddle-wheels; but in the more perfect machinery
which carries the earth forward on her grander voyage, no sound is
heard, nor the least intimation afforded of the stupendous forces by
which this motion is achieved. To the pious observer of Nature it might
seem sufficient, without any inquiry into second causes, to ascribe the
motions of the spheres to the direct agency of the Supreme Being. If,
however, we can succeed in finding the secret springs and cords, by
which the motions of the heavenly bodies are immediately produced and
controlled, it will detract nothing from our just admiration of the
Great First Cause of all things. We may therefore now enter upon the
inquiry into the nature or laws of the forces by which the earth is made
to revolve on her axis and in her orbit; and having learned what it is,
that causes and maintains the motions of the earth, you will then
acquire, at the same time, a knowledge of all the celestial machinery.
The subject will involve an explanation of the laws of motion, and of
the principles of universal gravitation.
It was once supposed, that we could never reason respecting the laws
that govern the heavenly bodies from what we observe in bodies around
us, but that motion is one thing on the earth and quite another thing in
the skies; and hence, that it is impossible for us, by any inquiries
into the laws of terrestrial Nature, to ascertain how things take place
among the heavenly bodies. Galileo and Newton, however, proceeded on the
contrary supposition, that Nature is uniform in all her works; that the
same Almighty arm rules over all; and that He works by the same fixed
laws through all parts of His boundless realm. The certainty with which
all the predictions of astronomers, made on these suppositions, are
fulfilled, attests the soundness of the hypothesis. Accordingly, those
laws, which all experience, endlessly multiplied and varied, proves to
be the laws of terrestrial motion, are held to be the laws that govern
also the motions of the most distant planets and stars, and to prevail
throughout the universe of matter. Let us, then, briefly review these
great laws of motion, which are three in number. The FIRST LAW is as
follows: _every body perseveres in a state of rest, or of uniform motion
in a straight line, unless compelled by some force to change its state_.
By _force_ is meant any thing which produces motion.
The foregoing law has been fully established by experiment, and is
conformable to all experience. It embraces several particulars. First, a
body, when at rest, remains so, unless some force puts it in motion; and
hence it is inferred, when a body is found in motion, that some force
must have been applied to it sufficient to have caused its motion. Thus,
the fact, that the earth is in motion around the sun and around its own
axis, is to be accounted for by assigning to each of these motions a
force adequate, both in quantity and direction, to produce these
motions, respectively.
Secondly, when a body is once in motion, it will continue to move for
ever, unless something stops it. When a ball is struck on the surface of
the earth, the friction of the earth and the resistance of the air soon
stop its motion; when struck on smooth ice, it will go much further
before it comes to a state of rest, because the ice opposes much less
resistance than the ground; and, were there no impediment to its
motion, it would, when once set in motion, continue to move without
end. The heavenly bodies are actually in this condition: they continue
to move, not because any new forces are applied to them; but, having
been once set in motion, they continue in motion because there is
nothing to stop them. This property in bodies to persevere in the state
they are actually in,--if at rest, to remain at rest, or, if in motion,
to continue in motion,--is called _inertia_. The inertia of a body
(which is measured by the force required to overcome it) is proportioned
to the quantity of matter it contains. A steam-boat manifests its
inertia, on first starting it, by the enormous expenditure of force
required to bring it to a given rate of motion; and it again manifests
its inertia, when in rapid motion, by the great difficulty of stopping
it. The heavenly bodies, having been once put in motion, and meeting
with nothing to stop them, move on by their own inertia. A top affords a
beautiful illustration of inertia, continuing, as it does, to spin after
the moving force is withdrawn.
Thirdly, the motion to which a body naturally tends is _uniform_; that
is, the body moves just as far the second minute as it did the first,
and as far the third as the second; and passes over equal spaces in
equal times. I do not assert that the motion of all moving bodies is _in
fact_ uniform, but that such is their _tendency_. If it is otherwise
than uniform, there is some cause operating to disturb the uniformity to
which it is naturally prone.
Fourthly, a body in motion will move in a _straight line_, unless
diverted out of that line by some external force; and the body will
resume its straight-forward motion, whenever the force that turns it
aside is withdrawn. Every body that is revolving in an orbit, like the
moon around the earth, or the earth around the sun, _tends_ to move in a
straight line which is a tangent[7] to its orbit. Thus, if A B C, Fig.
28, represents the orbit of the moon around the earth, were it not for
the constant action of some force that draws her towards the earth, she
would move off in a straight line. If the force that carries her towards
the earth were suspended at A, she would immediately desert the circular
motion, and proceed in the direction A D. In the same manner, a boy
whirls a stone around his head in a sling, and then letting go one of
the strings, and releasing the force that binds it to the circle, it
flies off in a straight line which is a tangent to that part of the
circle where it was released. This tendency which a body revolving in an
orbit exhibits, to recede from the centre and to fly off in a tangent,
is called the _centrifugal force_. We see it manifested when a pail of
water is whirled. The water rises on the sides of the vessel, leaving a
hollow in the central parts. We see an example of the effects of
centrifugal action, when a horse turns swiftly round a corner, and the
rider is thrown outwards; also, when a wheel passes rapidly through a
small collection of water, and portions of the water are thrown off from
the top of the wheel in straight lines which are tangents to the wheel.
[Illustration Fig. 28.]
The centrifugal force is increased as the velocity is increased. Thus,
the parts of a millstone most remote from the centre sometimes acquire a
centrifugal force so much greater than the central parts, which move
much slower, that the stone is divided, and the exterior portions are
projected with great violence. In like manner, as the equatorial parts
of the earth, in the diurnal revolution, revolve much faster than the
parts towards the poles, so the centrifugal force is felt most at the
equator, and becomes strikingly manifest by the diminished weight of
bodies, since it acts in opposition to the force of gravity.
Although the foregoing law of motion, when first presented to the mind,
appears to convey no new truth, but only to enunciate in a formal manner
what we knew before; yet a just understanding of this law, in all its
bearings, leads us to a clear comprehension of no small share of all the
phenomena of motion. The second and third laws may be explained in fewer
terms.
The SECOND LAW of motion is as follows: _motion is proportioned to the
force impressed, and in the direction of that force_.
The meaning of this law is, that every force that is applied to a body
produces its full effect, proportioned to its intensity, either in
causing or in preventing motion. Let there be ever so many blows applied
at once to a ball, each will produce its own effect in its own
direction, and the ball will move off, not indeed in the zigzag, complex
lines corresponding to the directions of the several forces, but in a
single line expressing the united effect of all. If you place a ball at
the corner of a table, and give it an impulse, at the same instant, with
the thumb and finger of each hand, one impelling it in the direction of
one side of the table, and the other in the direction of the other side,
the ball will move diagonally across the table. If the blows be exactly
proportioned each to the length of the side of the table on which it is
directed, the ball will run exactly from corner to corner, and in the
same time that it would have passed over each side by the blow given in
the direction of that side. This principle is expressed by saying, that
a body impelled by two forces, acting respectively in the directions of
the two sides of a parallelogram, and proportioned in intensity to the
lengths of the sides, will describe the diagonal of the parallelogram in
the same time in which it would have described the sides by the forces
acting separately.
The converse of this proposition is also true, namely, that any single
motion may be considered as the _resultant_ of two others,--the motion
itself being represented by the diagonal, while the two _components_ are
represented by the sides, of a parallelogram. This reduction of a motion
to the individual motions that produce it, is called the _resolution of
motion_, or the _resolution of forces_. Nor can a given motion be
resolved into _two_ components, merely. These, again, may be resolved
into others, varying indefinitely, in direction and intensity, from all
which the given motion may be considered as having resulted. This
composition and resolution of motion or forces is often of great use, in
inquiries into the motions of the heavenly bodies. The composition often
enables us to substitute a single force for a great number of others,
whose individual operations would be too complicated to be followed. By
this means, the investigation is greatly simplified. On the other hand,
it is frequently very convenient to resolve a given motion into two or
more others, some of which may be thrown out of the account, as not
influencing the particular point which we are inquiring about, while
others are far more easily understood and managed than the single force
would have been. It is characteristic of great minds, to simplify these
inquiries. They gain an insight into complicated and difficult subjects,
not so much by any extraordinary faculty of seeing in the dark, as by
the power of removing from the object all incidental causes of
obscurity, until it shines in its own clear and simple light.
If every force, when applied to a body, produces its full and legitimate
effect, how many other forces soever may act upon it, impelling it
different ways, then it must follow, that the smallest force ought to
move the largest body; and such is in fact the case. A snap of a finger
upon a seventy-four under full sail, if applied in the direction of its
motion, would actually increase its speed, although the effect might be
too small to be visible. Still it is something, and may be truly
expressed by a fraction. Thus, suppose a globe, weighing a million of
pounds, were suspended from the ceiling by a string, and we should apply
to it the snap of a finger,--it is granted that the motion would be
quite insensible. Let us then divide the body into a million equal
parts, each weighing one pound; then the same impulse, applied to each
one separately, would produce a sensible effect, moving it, say one
inch. It will be found, on trial, that the same impulse given to a mass
of two pounds will move it half an inch; and hence it is inferred, that,
if applied to a mass weighing a million of pounds, it would move it the
millionth part of an inch.
It is one of the curious results of the second law of motion, that an
unlimited number of motions may exist together in the same body. Thus,
at the same moment, we may be walking around a post in the cabin of a
steam-boat, accompanying the boat in its passage around an island,
revolving with the earth on its axis, flying through space in our annual
circuit around the sun, and possibly wheeling, along with the sun and
his whole retinue of planets, around some centre in common with the
starry worlds.
The THIRD LAW of motion is this: _action and reaction are equal, and in
contrary directions_.
Whenever I give a blow, the body struck exerts an equal force on the
striking body. If I strike the water with an oar, the water communicates
an equal impulse to the oar, which, being communicated to the boat,
drives it forward in the opposite direction. If a magnet attracts a
piece of iron, the iron attracts the magnet just as much, in the
opposite direction; and, in short, every portion of matter in the
universe attracts and is attracted by every other, equally, in an
opposite direction. This brings us to the doctrine of universal
gravitation, which is the very key that unlocks all the secrets of the
skies. This will form the subject of my next Letter.
FOOTNOTE:
[7] A tangent is a straight line touching a circle, as A D, in Fig. 28
LETTER XIII.
TERRESTRIAL GRAVITY.
"To Him no high, no low, no great, no small,
He fills, He bounds, connects, and equals all."--_Pope._
WE discover in Nature a tendency of every portion of matter towards
every other. This tendency is called _gravitation_. In obedience to this
power, a stone falls to the ground, and a planet revolves around the
sun. We may contemplate this subject as it relates either to phenomena
that take place near the surface of the earth, or in the celestial
regions. The former, _gravity_, is exemplified by falling bodies; the
latter, _universal gravitation_, by the motions of the heavenly bodies.
The laws of terrestrial gravity were first investigated by Galileo;
those of universal gravitation, by Sir Isaac Newton. Terrestrial gravity
is only an individual example of universal gravitation; being the
tendency of bodies towards the centre of the earth. We are so much
accustomed, from our earliest years, to see bodies fall to the earth,
that we imagine bodies must of necessity fall "downwards;" but when we
reflect that the earth is round, and that bodies fall towards the centre
on all sides of it, and that of course bodies on opposite sides of the
earth fall in precisely opposite directions, and towards each other, we
perceive that there must be some force acting to produce this effect;
nor is it enough to say, as the ancients did, that bodies "naturally"
fall to the earth. Every motion implies some force which produces it;
and the fact that bodies fall towards the earth, on all sides of it,
leads us to infer that that force, whatever it is, resides in the earth
itself. We therefore call it _attraction_. We do not, however, say what
attraction _is_, but what it _does_. We must bear in mind, also, that,
according to the third law of motion, this attraction is mutual; that
when a stone falls towards the earth, it exerts the same force on the
earth that the earth exerts on the stone; but the motion of the earth
towards the stone is as much less than that of the stone towards the
earth, as its quantity of matter is greater; and therefore its motion is
quite insensible.
But although we are compelled to acknowledge the _existence_ of such a
force as gravity, causing a tendency in all bodies towards each other,
yet we know nothing of its _nature_, nor can we conceive by what medium
bodies at such a distance as the moon and the earth exercise this
influence on each other. Still, we may trace the modes in which this
force acts; that is, its _laws_; for the laws of Nature are nothing else
than the modes in which the powers of Nature act.
We owe chiefly to the great Galileo the first investigation of the laws
of terrestrial gravity, as exemplified in falling bodies; and I will
avail myself of this opportunity to make you better acquainted with one
of the most interesting of men and greatest of philosophers.
Galileo was born at Pisa, in Italy, in the year 1564. He was the son of
a Florentine nobleman, and was destined by his father for the medical
profession, and to this his earlier studies were devoted. But a fondness
and a genius for mechanical inventions had developed itself, at a very
early age, in the construction of his toys, and a love of drawing; and
as he grew older, a passion for mathematics, and for experimental
research, predominated over his zeal for the study of medicine, and he
fortunately abandoned that for the more congenial pursuits of natural
philosophy and astronomy. In the twenty-fifth year of his age, he was
appointed, by the Grand Duke of Tuscany, professor of mathematics in the
University of Pisa. At that period, there prevailed in all the schools a
most extraordinary reverence for the writings of Aristotle, the
preceptor of Alexander the Great,--a philosopher who flourished in
Greece, about three hundred years before the Christian era. Aristotle,
by his great genius and learning, gained a wonderful ascendency over the
minds of men, and became the oracle of the whole reading world for
twenty centuries. It was held, on the one hand, that all truths worth
knowing were contained in the writings of Aristotle; and, on the other,
that an assertion which contradicted any thing in Aristotle could not be
true. But Galileo had a greatness of mind which soared above the
prejudices of the age in which he lived, and dared to interrogate Nature
by the two great and only successful methods of discovering her
secrets,--experiment and observation. Galileo was indeed the first
philosopher that ever fully employed experiments as the means of
learning the laws of Nature, by imitating on a small what she performs
on a great scale, and thus detecting her modes of operation. Archimedes,
the great Sicilian philosopher, had in ancient times introduced
mathematical or geometrical reasoning into natural philosophy; but it
was reserved for Galileo to unite the advantages of both mathematical
and experimental reasonings in the study of Nature,--both sure and the
only sure guides to truth, in this department of knowledge, at least.
Experiment and observation furnish materials upon which geometry builds
her reasonings, and from which she derives many truths that either lie
for ever hidden from the eye of observation, or which it would require
ages to unfold.