48. (Pg. 66) To what is the wedge compared? (fig. 8.)
49. (Pg. 66) How does its power increase?
50. (Pg. 67) Why is it rather a compound than a simple power?
51. (Pg. 67) What common instruments act upon the principle of the
inclined plane, or the wedge?
52. (Pg. 67) Why does a knife cut best when drawn across?
53. (Pg. 67) The screw has two essential parts; what are they?
54. (Pg. 67) What other instrument is used to turn the screw?
55. (Pg. 67) How can you compare the screw with an inclined plane? Fig.
10.
56. (Pg. 68) By what two means may the power of the screw be increased?
57. (Pg. 68) How do we estimate the power gained by the screw?
58. (Pg. 68) Is the lever always attached to the nut, as in the figure?
59. (Pg. 68) What is said respecting the composition of all machines,
and for what must allowance always be made in estimating their power?
60. (Pg. 69) What is meant by friction, and what causes it?
61. (Pg. 69) How may friction be diminished?
62. (Pg. 69) Friction is of two kinds, what are they?
63. (Pg. 69) For what purpose are wheels often used?
64. (Pg. 69) When is the friction of a carriage wheel changed from the
rolling to the rubbing friction?
65. (Pg. 70) What is a medium, and in what proportion does it diminish
motion?
66. (Pg. 70) Under what circumstances must a body be placed, in order to
move without impediment?
CONVERSATION VI.
CAUSES OF THE MOTION OF THE HEAVENLY BODIES.
OF THE EARTH'S ANNUAL MOTION. OF THE PLANETS AND THEIR MOTION. OF THE
DIURNAL MOTION OF THE EARTH AND PLANETS.
CAROLINE.
I am come to you to-day quite elated with the spirit of opposition, Mrs.
B.; for I have discovered such a powerful objection to your theory of
attraction, that I doubt whether even your conjuror Newton, with his
magic wand of gravitation, will be able to dispel it.
_Mrs. B._ Well, my dear, pray what is this weighty objection?
[Illustration: PLATE VI.]
_Caroline._ You say that the earth revolves in its orbit round the sun
once in a year, and that bodies attract in proportion to the quantity of
matter they contain; now we all know the sun to be much larger than the
earth: why, therefore does it not draw the earth into itself; you will
not, I suppose, pretend to say that we are falling towards the sun?
_Emily._ However plausible your objection appears, Caroline, I think you
place too much reliance upon it: when any one has given such convincing
proofs of sagacity and wisdom as Sir Isaac Newton, when we find that his
opinions are universally received and adopted, is it to be expected that
any objection we can advance should overturn them?
_Caroline._ Yet I confess that I am not inclined to yield implicit faith
even to opinions of the great Newton: for what purpose are we endowed
with reason, if we are denied the privilege of making use of it, by
judging for ourselves.
_Mrs. B._ It is reason itself which teaches us, that when we, novices in
science, start objections to theories established by men of knowledge
and wisdom, we should be diffident rather of our own than of their
opinion. I am far from wishing to lay the least restraint on your
questions; you cannot be better convinced of the truth of a system, than
by finding that it resists all your attacks, but I would advise you not
to advance your objections with so much confidence, in order that the
discovery of their fallacy may be attended with less mortification. In
answer to that you have just proposed, I can only say, that the earth
really is attracted by the sun.
_Caroline._ Take care, at least, that we are not consumed by him, Mrs.
B.
_Mrs. B._ We are in no danger; but Newton, our magician, as you are
pleased to call him, cannot extricate himself from this difficulty
without the aid of some cabalistical figures, which I must draw for him.
Let us suppose the earth, at its creation, to have been projected
forwards into universal space: we know that if no obstacle impeded its
course it would proceed in the same direction, and with a uniform
velocity for ever. In fig. 1. plate 6, A represents the earth, and S the
sun. We shall suppose the earth to be arrived at the point in which it
is represented in the figure, having a velocity which would carry it on
to B in the space of one month; whilst the sun's attraction would bring
it to C in the same space of time. Observe that the two forces of
projection and attraction do not act in opposition, but perpendicularly,
or at a right angle to each other. Can you tell me now, how the earth
will move?
_Emily._ I recollect your teaching us that a body acted upon by two
forces perpendicular to each other, would move in the diagonal of a
parallelogram; if, therefore, I complete the parallelogram, by drawing
the lines C D, B D, the earth will move in the diagonal A D.
_Mrs. B._ A ball struck by two forces acting perpendicularly to each
other, it is true, moves in the diagonal of a parallelogram; but you
must observe that the force of attraction is continually acting upon our
terrestrial ball, and producing an incessant deviation from its course
in a right line, which converts it into that of a curve-line; every
point of which may be considered as constituting the diagonal of an
infinitely small parallelogram.
Let us retain the earth a moment at the point D, and consider how it
will be affected by the combined action of the two forces in its new
situation. It still retains its tendency to fly off in a straight line;
but a straight line would now carry it away to F, whilst the sun would
attract it in the direction D S; how then will it proceed?
_Emily._ It will go on in a curve-line, in a direction between that of
the two forces.
_Mrs. B._ In order to know exactly what course the earth will follow,
draw another parallelogram similar to the first, in which the line D F
describes the force of projection, and the line D S that of attraction;
and you will find that the earth will proceed in the curve-line D G.
_Caroline._ You must now allow me to draw a parallelogram, Mrs. B. Let
me consider in what direction will the force of projection now impel the
earth.
_Mrs. B._ First draw a line from the earth to the sun representing the
force of attraction; then describe the force of projection at a right
angle to it.
_Caroline._ The earth will then move in the curve G I, of the
parallelogram G H I K.
_Mrs. B._ You recollect that a body acted upon by two forces, moves
through a diagonal, in the same time that it would have moved through
one of the sides of the parallelogram, were it acted upon by one force
only. The earth has passed through the diagonals of these three
parallelograms, in the space of three months, and has performed one
quarter of a circle; and on the same principle it will go on till it has
completed the whole of the circle. It will then recommence a course,
which it has pursued ever since it first issued from the hand of its
Creator, and which there is every reason to suppose it will continue to
follow, as long as it remains in existence.
_Emily._ What a grand and beautiful effect resulting from so simple a
cause!
_Caroline._ It affords an example, on a magnificent scale, of the
curvilinear motion, which you taught us in mechanics. The attraction of
the sun is the centripetal force, which confines the earth to a centre;
and the impulse of projection, the centrifugal force, which impels the
earth to quit the sun, and fly off in a tangent.
_Mrs. B._ Exactly so. A simple mode of illustrating the effect of these
combined forces on the earth, is to cut a slip of card in the form of a
carpenter's square, as A, B, C; (fig. 2. plate 6.) the point B will be a
right angle, the sides of the square being perpendicular to each other;
after having done this you are to describe a small circle at the angular
point B, representing the earth, and to fasten the extremity of one of
the legs of the square to a fixed point A, which we shall consider as
the sun. Thus situated, the two sides of the square will represent both
the centrifugal and centripetal forces; A B, representing the
centripetal, and B C, the centrifugal force; if you now draw it round
the fixed point, you will see how the direction of the centrifugal force
varies, constantly forming a tangent to the circle in which the earth
moves, as it is constantly at a right angle with the centripetal force.
_Emily._ The earth then, gravitates towards the sun, without the
slightest danger either of approaching nearer, or receding further from
it. How admirably this is contrived! If the two forces which produce
this curved motion, had not been so accurately adjusted, one would
ultimately have prevailed over the other, and we should either have
approached so near the sun as to have been burnt, or have receded so far
from it as to have been frozen.
_Mrs. B._ What will you say, my dear, when I tell you, that these two
forces are not, in fact, so proportioned as to produce circular motion
in the earth? We actually revolve round the sun in an elliptical or oval
orbit, the sun being situated in one of the foci or centres of the oval,
so that the sun is at some periods much nearer to the earth, than at
others.
_Caroline._ You must explain to us, at least, in what manner we avoid
the threatened destruction.
_Mrs. B._ Let us suppose that when the earth is at A, (fig. 3.) its
projectile force should not have given it a velocity sufficient to
counterbalance that of gravity, so as to enable these powers conjointly
to carry it round the sun in a circle; the earth, instead of describing
the line A C, as in the former figure, will approach nearer the sun in
the line A B.
_Caroline._ Under these circumstances, I see not what is to prevent our
approaching nearer and nearer the sun, till we fall into it: for its
attraction increases as we advance towards it, and produces an
accelerated velocity in the earth, which increases the danger.
_Mrs. B._ There is another seeming danger, of which you are not aware.
Observe, that as the earth approaches the sun, the direction of its
projectile force is no longer perpendicular to that of its attraction,
but inclines more nearly to it. When the earth reaches that part of its
orbit at B, the force of projection would carry it to D, which brings it
nearer the sun instead of bearing it away from it.
_Emily._ If, then, we are driven by one power, and drawn by the other to
this centre of destruction, how is it possible for us to escape?
_Mrs. B._ A little patience, and you will find that we are not without
resource. The earth continues approaching the sun with a uniformly
increasing accelerated motion, till it reaches the point E; in what
direction will the projectile force now impel it?
_Emily._ In the direction E F. Here then the two forces act
perpendicularly to each other, the lines representing them forming a
right angle, and the earth is situated just as it was in the preceding
figure; therefore, from this point, it should revolve round the sun in a
circle.
_Mrs. B._ No, all the circumstances do not agree. In motion round a
centre, you recollect that the centrifugal force increases with the
velocity of the body, or in other words, the quicker it moves the
stronger is its tendency to fly off in a right line. When the earth,
therefore, arrives at E, its accelerated motion will have so far
increased its velocity, and consequently its centrifugal force, that the
latter will prevail over the force of attraction, and force the earth
away from the sun till it reaches G.
_Caroline._ It is thus then that we escape from the dangerous vicinity
of the sun; and in proportion as we recede from it, the force of its
attraction, and, consequently, the velocity of the earth's motion, are
diminished.
_Mrs. B._ Yes. From G the direction of projection is towards H, that of
attraction towards S, and the earth proceeds between them with a
uniformly retarded motion, till it has completed its revolution. Thus
you see that the earth travels round the sun, not in a circle, but an
ellipsis, of which the sun occupies one of the _foci_; and that in its
course, the earth alternately approaches and recedes from it, without
any danger of being either swallowed up, or being entirely carried away
from it.
_Caroline._ And I observe, that what I apprehended to be a dangerous
irregularity, is the means by which the most perfect order and harmony
are produced.
_Emily._ The earth travels then at a very unequal rate, its velocity
being accelerated as it approaches the sun, and retarded as it recedes
from it.
_Mrs. B._ It is mathematically demonstrable, that, in moving round a
point towards which it is attracted, a body passes over equal areas, in
equal times. The whole of the space contained within the earth's orbit,
is in fig. 4, divided into a number of areas or surfaces; 1, 2, 3, 4,
&c. all of which are of equal dimensions, though of very different
forms; some of them, you see, are long and narrow, others broad and
short: but they each of them contain an equal quantity of space. An
imaginary line drawn from the centre of the earth to that of the sun,
and keeping pace with the earth in its revolution, passes over equal
areas in equal times; that is to say, if it is a month going from A to
B, it will be a month going from B to C, and another from C to E, and so
on; and the areas A B S, B C S, C E S, will be equal to each other,
although the lines A B, B C, C E, are unequal.
_Caroline._ What long journeys the earth has to perform in the course of
a month, in one part of her orbit, and how short they are in the other
part!
_Mrs. B._ The inequality is not so considerable as appears in this
figure; for the earth's orbit is not so eccentric as it is there
described; and in reality, differs but little from a circle: that part
of the earth's orbit nearest the sun is called its _perihelion_, that
part most distant from the sun, its _aphelion_; and the earth is above
three millions of miles nearer the sun at its perihelion than at its
aphelion.
_Emily._ I think I can trace a consequence from these different
situations of the earth; are not they the cause of summer and winter?
_Mrs. B._ On the contrary, during the height of summer, the earth is in
that part of its orbit which is most distant from the sun, and it is
during the severity of winter, that it approaches nearest to it.
_Emily._ That is very extraordinary; and how then do you account for the
heat being greatest, when we are most distant from the sun?
_Mrs. B._ The difference of the earth's distance from the sun in summer
and winter, when compared with its total distance from the sun, is but
inconsiderable. The earth, it is true, is above three millions of miles
nearer the sun in winter than in summer; but that distance, however
great it at first appears, sinks into insignificance in comparison with
95 millions of miles, which is our mean distance from the sun. The
change of temperature, arising from this difference, would scarcely be
sensible, even were it not completely overpowered by other causes which
produce the variations of the seasons; but these I shall defer
explaining, till we have made some further observations on the heavenly
bodies.
_Caroline._ And should not the sun appear smaller in summer, when it is
so much further from us?
_Mrs. B._ It actually does, when accurately measured; but the apparent
difference in size, is, I believe, not perceptible to the naked eye.
_Emily._ Then, since the earth moves with the greatest velocity in that
part of its orbit in which it is nearest the sun, it must have completed
its journey through that half of its orbit, in a shorter time than
through the other?
_Mrs. B._ Yes, it is about seven days longer performing the summer-half
of its orbit, than the winter-half; and the summers are consequently
seven days longer in the northern, than they are in the southern
hemisphere.
The revolution of all the planets round the sun, is the result of the
same causes, and is performed in the same manner, as that of the earth.
_Caroline._ Pray what are the planets?
_Mrs. B._ They are those celestial bodies, which revolve like our earth,
about the sun; they are supposed to resemble the earth also in many
other respects; and we are led by analogy, to suppose them to be
inhabited worlds.
_Caroline._ I have heard so, but do you not think such an opinion too
great a stretch of the imagination?
_Mrs. B._ Some of the planets are proved to be larger than the earth; it
is only their immense distance from us, which renders their apparent
dimensions so small. Now, if we consider them as enormous globes,
instead of small twinkling spots, we shall be led to suppose that the
Almighty would not have created them merely for the purpose of giving us
a little light in the night, as it was formerly imagined; and we should
find it more consistent with our ideas of the Divine wisdom and
beneficence, to suppose that these celestial bodies should be created
for the habitation of beings, who are, like us, blessed by his
providence. Both in a moral, as well as a physical point of view, it
appears to me more rational to consider the planets as worlds revolving
round the sun; and the fixed stars as other suns, each of them attended
by their respective system of planets, to which they impart their
influence. We have brought our telescopes to such a degree of
perfection, that from the appearances which the moon exhibits when seen
through them, we have very good reason to conclude that it is a
habitable globe: for though it is true that we cannot discern its towns
and people, we can plainly perceive its mountains and valleys: and some
astronomers have gone so far as to imagine that they discovered
volcanos.
_Emily._ If the fixed stars are suns, with planets revolving round them,
why should we not see those planets as well as their suns?
_Mrs. B._ In the first place, we conclude that the planets of other
systems (like those of our own) are much smaller than the suns which
give them light; therefore at a distance so great as to make the suns
appear like fixed stars, the planets would be quite invisible. Secondly,
the light of the planets being only reflected light, is much more feeble
than that of the fixed stars. There is exactly the same difference as
between the light of the sun and that of the moon; the first being a
fixed star, the second a planet.
_Emily._ But the planets appear to us as bright as the fixed stars, and
these you tell us are suns like our own; why then do we not see them by
daylight, when they must be just as luminous as they are in the night?
_Mrs. B._ Both are invisible from the same cause: their light is so
faint, compared to that of the sun, that it is entirely effaced by it:
the light emitted by the fixed stars may probably be as great as that of
our sun, at an equal distance; but they being so much more remote, it
is diffused over a greater space, and is in consequence proportionally
lessened.
_Caroline._ True; I can see much better by the light of a candle that is
near me, than by that of one at a great distance. But I do not
understand what makes the planets shine?
_Mrs. B._ What is that which makes the gilt buttons on your brothers
coat shine?
_Caroline._ The sun. But if it was the sun which made the planets shine,
we should see them in the day-time, when the sun shone upon them; or if
the faintness of their light prevented our seeing them in the day, we
should not see them at all, for the sun cannot shine upon them in the
night.
_Mrs. B._ There you are in error. But in order to explain this to you, I
must first make you acquainted with the various motions of the planets.
You know, that according to the laws of attraction, the planets
belonging to our system all gravitate towards the sun; and that this
force, combined with that of projection, will occasion their revolution
round the sun, in orbits more or less elliptical, according to the
proportion which these two forces bear to each other.
But the planets have also another motion: they revolve upon their axis.
The axis of a planet is an imaginary line which passes through its
centre, and on which it turns; and it is this motion which produces day
and night. It is day on that side of the planet which faces the sun; and
on the opposite side, which remains in darkness, it is night. Our earth,
which we consider as a planet, is 24 hours in performing one revolution
on its axis; in that period of time, therefore, we have a day and a
night; hence this revolution is called the earth's diurnal or daily
motion; and it is this revolution of the earth from west to east which
produces an apparent motion of the sun, moon and stars, in a contrary
direction.
Let us now suppose ourselves to be beings independent of any planet,
travelling in the skies, and looking upon the earth from a point as
distant from it as from other planets.
_Caroline._ It would not be flattering to us, its inhabitants, to see it
make so insignificant an appearance.
_Mrs. B._ To those accustomed to contemplate it in this light, it could
never appear more glorious. We are taught by science to distrust
appearances; and instead of considering the fixed stars and planets as
little points, we look upon them either as brilliant suns, or habitable
worlds; and we consider the whole together as forming one vast and
magnificent system, worthy of the Divine hand by which it was created.
_Emily._ I can scarcely conceive the idea of this immensity of creation;
it seems too sublime for our imagination;--and to think that the
goodness of Providence extends over millions of worlds throughout a
boundless universe--Ah! Mrs. B., it is we only who become trifling and
insignificant beings in so magnificent a creation!
_Mrs. B._ This idea should teach us humility, but without producing
despondency. The same Almighty hand which guides these countless worlds
in their undeviating course, conducts with equal perfection, the blood
as it circulates through the veins of a fly, and opens the eye of the
insect to behold His wonders. Notwithstanding this immense scale of
creation, therefore, we need not fear that we shall be disregarded or
forgotten.
But to return to our station in the skies. We were, if you recollect,
viewing the earth at a great distance, in appearance a little star, one
side illumined by the sun, the other in obscurity. But would you believe
it, Caroline, many of the inhabitants of this little star imagine that
when that part which they inhabit is turned from the sun, darkness
prevails throughout the universe, merely because it is night with them;
whilst, in reality, the sun never ceases to shine upon every planet.
When, therefore, these little ignorant beings look around them during
their night, and behold all the stars shining, they cannot imagine why
the planets, which are dark bodies, should shine; concluding, that since
the sun does not illumine themselves, the whole universe must be in
darkness.
_Caroline._ I confess that I was one of these ignorant people; but I am
now very sensible of the absurdity of such an idea. To the inhabitants
of the other planets, then, we must appear as a little star?
_Mrs. B._ Yes, to those which revolve round our sun; for since those
which may belong to other systems, (and whose existence is only
hypothetical) are invisible to us, it is probable that we also are
invisible to them.
_Emily._ But they may see our sun as we do theirs, in appearance a fixed
star?
_Mrs. B._ No doubt; if the beings who inhabit those planets are endowed
with senses similar to ours. By the same rule we must appear as a moon
to the inhabitants of our moon; but on a larger scale, as the surface of
the earth is about thirteen times as large as that of the moon.
_Emily._ The moon, Mrs. B., appears to move in a different direction,
and in a different manner from the stars?
_Mrs. B._ I shall defer the explanation of the motion of the moon till
our next interview, as it would prolong our present lesson too much.
Questions
1. (Pg. 71) What revolution does the earth perform in a year?
2. (Pg. 71) Had the earth received a projectile force only, at the time
of its creation, how would it have moved?
3. (Pg. 72) What do the lines A B, and A C, represent in fig. 1. plate
6?
4. (Pg. 72) What have you been taught respecting a body acted upon by
two forces at right angles with each other?
5. (Pg. 72) How does the force of gravity change the diagonal into a
curved line?
6. (Pg. 72) Describe the operation of the forces of projection and of
gravity as illustrated by the parallelograms in the figure?