me a little time to familiarise to myself, an idea so different from
that which I have been accustomed to entertain. And pray, at what rate
do we move?
_Mrs. B._ The motion produced by the revolution of the earth on its
axis, is about seventeen miles a minute, to an inhabitant on the
equator.
_Emily._ But does not every part of the earth move with the same
velocity?
_Mrs. B._ A moment's reflection would convince you of the contrary: a
person at the equator must move quicker than one situated near the
poles, since they both perform a revolution in 24 hours.
_Emily._ True, the equator is farthest from the axis of motion. But in
the earth's revolution round the sun, every part must move with equal
velocity?
_Mrs. B._ Yes, about a thousand miles a minute.
_Caroline._ How astonishing!--and that it should be possible for us to
be insensible of such a rapid motion. You would not tell me this sooner,
Mrs. B., for fear of increasing my incredulity.
Before the time of Newton, was not the earth supposed to be in the
centre of the system, and the sun, moon, and stars to revolve round it?
_Mrs. B._ This was the system of Ptolemy, in ancient times; but as long
ago as the beginning of the sixteenth century it was generally
discarded, and the solar system, such as I have shown you, was
established by the celebrated astronomer Copernicus, and is hence called
the Copernican system. But the theory of gravitation, the source from
which this beautiful and harmonious arrangement flows, we owe to the
powerful genius of Newton, who lived at a much later period, and who
demonstrated its truth.
_Emily._ It appears, indeed, far less difficult to trace by observation
the motion of the planets, than to divine by what power they are
impelled and guided. I wonder how the idea of gravitation could first
have occurred to sir Isaac Newton?
_Mrs. B._ It is said to have been occasioned by a circumstance from
which one should little have expected so grand a theory to have arisen.
During the prevalence of the plague in the year 1665, Newton retired
into the country to avoid the contagion: when sitting one day in an
orchard, he observed an apple fall from a tree, and was led to consider
what could be the cause which brought it to the ground.
_Caroline._ If I dared to confess it, Mrs. B., I should say that such an
inquiry indicated rather a deficiency than a superiority of intellect. I
do not understand how any one can wonder at what is so natural and so
common.
_Mrs. B._ It is the mark of superior genius to find matter for wonder,
observation, and research, in circumstances which, to the ordinary mind,
appear trivial, because they are common; and with which they are
satisfied, because they are natural; without reflecting that nature is
our grand field of observation, that within it, is contained our whole
store of knowledge; in a word, that to study the works of nature, is to
learn to appreciate and admire the wisdom of God. Thus, it was the
simple circumstance of the fall of an apple, which led to the discovery
of the laws upon which the Copernican system is founded; and whatever
credit this system had obtained before, it now rests upon a basis from
which it cannot be shaken.
_Emily._ This was a most fortunate apple, and more worthy to be
commemorated than all those that have been sung by the poets. The apple
of discord for which the goddesses contended; the golden apples by which
Atalanta won the race; nay, even the apple which William Tell shot from
the head of his son, cannot be compared to this!
Questions
1. (Pg. 80) Into what two classes are the planets divided, and how are
they distinguished?
2. (Pg. 80) By what reasoning do you prove that the sun contains a
greater quantity of matter than any other body in the system?
3. (Pg. 81) What two circumstances govern the force with which bodies
attract each other?
4. (Pg. 81) Were a planet removed to double its former distance from the
sun, what would be the effect upon its attractive force?
5. (Pg. 81) Why would it be reduced to one-fourth?
6. (Pg. 81) What is meant by the square of a number, and what examples
can you give?
7. (Pg. 81) What then would be the effect of removing it to three, or
four times its former distance?
8. (Pg. 81) How is the rule upon this subject expressed?
9. (Pg. 81) Does this apply to any power excepting gravitation?
10. (Pg. 81) How is it that a secondary planet revolves round its
primary, and is not drawn off by the sun?
11. (Pg. 82) What is said respecting the revolution of the moon, and of
the earth, round a common centre of gravity?
12. (Pg. 82) By what law in mechanics is this explained?
13. (Pg. 82) What motions then has the earth, and are these remarks
confined to it alone?
14. (Pg. 82) What effect have the planets upon the sun, and what is said
of the common centre of gravity of the system?
15. (Pg. 83) What other motion has the sun, and how is it proved?
16. (Pg. 83) How may you observe the motion of a planet, by means of a
fixed star?
17. (Pg. 83) What is represented by fig. 1. plate 7?
18. (Pg. 83) Why are the orbits represented as circular?
19. (Pg. 83) In what order do the planets increase in size as
represented, fig. 2. plate 7?
20. (Pg. 83) What are we told respecting Mercury?
21. (Pg. 84) What respecting Venus?
22. (Pg. 84) When does Venus become a morning, and when an evening star?
23. (Pg. 84) What is said of the Earth?
24. (Pg. 84) What of Mars?
25. (Pg. 84) What four small planets follow next?
26. (Pg. 85) What is said of Jupiter?
27. (Pg. 85) What of Saturn?
28. (Pg. 85) What of Herschel?
29. (Pg. 85) Why do we conclude that the moons of Saturn afford less
light than ours?
30. (Pg. 85) In what proportion will the light and heat at Saturn be
diminished, and why?
31. (Pg. 86) What do the comets resemble, and what is remarkable in
their orbits?
32. (Pg. 86) What is said of the number of comets?
33. (Pg. 86) What is a constellation?
34. (Pg. 86) How are the twelve constellations, or signs, called the
zodiac, situated?
35. (Pg. 86) Name them.
36. (Pg. 86) What is meant by the sun being in a sign?
37. (Pg. 86) What causes the apparent change of the sun's place?
38. (Pg. 87) The stars appear of different magnitudes, by what may this
be caused?
39. (Pg. 87) We are not sensible of the motion of the earth; what fact
is mentioned to illustrate this point?
40. (Pg. 87) What does this teach us?
41. (Pg. 88) Would the slowness, or the rapidity of the motion, if
steady, produce any sensible difference?
42. (Pg. 88) If we do not feel the motion of the earth, how may we be
convinced of its reality?
43. (Pg. 89) Were we to deny the motion of the earth upon its axis, what
must we admit respecting the heavenly bodies?
44. (Pg. 89) What distance is an inhabitant on the equator carried in a
minute by the diurnal motion of the earth?
45. (Pg. 89) Why is not the velocity every where equally great?
46. (Pg. 89) What distance does the earth travel in a minute, in its
revolution round the sun?
47. (Pg. 89) What was formerly supposed respecting the motion of all the
heavenly bodies?
48. (Pg. 89) What do we mean by the Copernican system, and what is said
respecting Copernicus and Newton?
49. (Pg. 90) What circumstance is said to have given rise to the
speculations of Newton, on the subject of gravitation?
CONVERSATION VIII.
ON THE EARTH.
OF THE TERRESTRIAL GLOBE. OF THE FIGURE OF THE EARTH. OF THE PENDULUM.
OF THE VARIATION OF THE SEASONS, AND OF THE LENGTH OF DAYS AND NIGHTS.
OF THE CAUSES OF THE HEAT OF SUMMER. OF SOLAR, SIDERIAL, AND EQUAL OR
MEAN TIME.
MRS. B.
As the earth is the planet in which we are the most particularly
interested, it is my intention this morning, to explain to you the
effects resulting from its annual, and diurnal motions; but for this
purpose, it will be necessary to make you acquainted with the
terrestrial globe: you have not either of you, I conclude, learnt the
use of the globes?
_Caroline._ No; I once indeed, learnt by heart, the names of the lines
marked on the globe, but as I was informed they were only imaginary
divisions, they did not appear to me worthy of much attention, and were
soon forgotten.
_Mrs. B._ You supposed, then, that astronomers had been at the trouble
of inventing a number of lines, to little purpose. It will be impossible
for me to explain to you the particular effects of the earth's motion,
without your having acquired a knowledge of these lines: in plate 8.
fig. 2. you will find them all delineated: and you must learn them
perfectly, if you wish to make any proficiency in astronomy.
_Caroline._ I was taught them at so early an age, that I could not
understand their meaning; and I have often heard you say, that the only
use of words, was to convey ideas.
_Mrs. B._ A knowledge of these lines, would have conveyed some idea of
the manner in which they were designed to divide the globe into parts;
although the use of these divisions, might at that time, have been too
difficult for you to understand. Childhood is the season, when
impressions on the memory are most strongly and most easily made: it is
the period at which a large stock of terms should be treasured up, the
precise application of which we may learn when the understanding is more
developed. It is, I think, a very mistaken notion, that children should
be taught such things only, as they can perfectly understand. Had you
been early made acquainted with the terms which relate to figure and
motion, how much it would have facilitated your progress in natural
philosophy. I have been obliged to confine myself to the most common and
familiar expressions, in explaining the laws of nature; although I am
convinced that appropriate and scientific terms, might have conveyed
more precise and accurate ideas, had you been prepared to understand
them.
_Emily._ You may depend upon our carefully learning the names of these
lines, Mrs. B.; but before we commit them to memory, will you have the
goodness to explain them to us?
_Mrs. B._ Most willingly. This figure of a globe, or sphere, represents
the earth; the line which passes through its centre, and on which it
turns, is called its axis, and the two extremities of the axis A and B,
are the poles, distinguished by the names of the north and the south
pole. The circle C D, which divides the globe into two equal parts
between the poles, and equally distant from them, is called the equator,
or equinoctial line; that part of the globe to the north of the equator,
is the northern hemisphere; that part to the south of the equator, the
southern hemisphere. The small circle E F, which surrounds the north
pole, is called the arctic circle; that G H, which surrounds the south
pole, the antarctic circle; these are also called polar circles. There
are two circles, intermediate between the polar circles and the equator;
that to the north I K, called the tropic of Cancer; that to the south, L
M, called the tropic of Capricorn. Lastly, this circle, L K, which
divides the globe into two equal parts, crossing the equator and
extending northward as far as the tropic of Cancer, and southward as far
as the tropic of Capricorn, is called the ecliptic. The delineation of
the ecliptic on the terrestrial globe is not without danger of conveying
false ideas; for the ecliptic (as I have before said) is an imaginary
circle in the heavens, passing through the middle of the zodiac, and
situated in the plane of the earth's orbit.
_Caroline._ I do not understand the meaning of the plane of the earth's
orbit.
_Mrs. B._ A plane, is an even flat surface. Were you to bend a piece of
wire, so as to form a hoop, you might then stretch a piece of cloth, or
paper over it, like the head of a drum; this would form a flat surface,
which might be called the plane of the hoop. Now the orbit of the earth,
is an imaginary circle, surrounding the sun, and you can readily imagine
a plane extending from one side of this circle to the other, filling
up its whole area: such a plane would pass through the centre of the
sun, dividing it into hemispheres. You may then imagine this plane
extended beyond the limits of the earth's orbit, on every side, until it
reached those fixed stars which form the signs of the zodiac; passing
through the middle of these signs, it would give you the place of that
imaginary circle in the heavens, call the ecliptic; which is the sun's
apparent path. Let fig. 1. plate 9, represent such a plane, S the sun, E
the earth with its orbit, and A B C D the ecliptic passing through the
middle of the zodiac.
[Illustration: PLATE IX.]
_Emily._ If the ecliptic relates only to the heavens, why is it
described upon the terrestrial globe?
_Mrs. B._ It is convenient for the demonstration of a variety of
problems in the use of the globes; and besides, the obliquity of this
circle to the equator is rendered more conspicuous by its being
described on the same globe; and the obliquity of the ecliptic shows how
much the earth's axis is inclined to the plane of its orbit. But to
return to fig. 2. plate 8.
The spaces between the several parallel circles on the terrestrial globe
are called zones: that which is comprehended between the tropics is
distinguished by the name of the torrid zone; the spaces which extend
from the tropics to the polar circles, the north and south temperate
zones; and the spaces contained within the polar circles, the frigid
zones. By the term zone is meant a belt, or girdle, the frigid zones,
however, are not belts, but circles, extending 23-1/2 degrees from their
centres, the poles.
The several lines which, you observe to be drawn from one pole to the
other, cutting the equator at right angles, are called meridians; the
number of these is unlimited, as a line passing through any place,
directly to the poles, is called the meridian of that place. When any
one of these meridians is exactly opposite to the sun, it is mid-day, or
twelve o'clock in the day, at all the places situated any where on that
meridian; and, at the places situated on the opposite meridian, it is
consequently midnight.
_Emily._ To places situated equally distant from these two meridians, it
must then be six o'clock.
_Mrs. B._ Yes; if they are to the east of the sun's meridian it is six
o'clock in the afternoon, because they will have previously passed the
sun; if to the west, it is six o'clock in the morning, and that meridian
will be proceeding towards the sun.
Those circles which divide the globe into two equal parts, such as the
equator and the ecliptic, are called greater circles; to distinguish
them from those which divide it into two unequal parts, as the tropics,
and polar circles, which are called lesser circles. All circles, you
know, are imagined to be divided into 360 equal parts, called degrees,
and degrees are again divided into 60 equal parts, called minutes. The
diameter of a circle is a right line drawn across it, and passing
through its centre; were you, for instance, to measure across this round
table, that would give you its diameter; but were you to measure all
round the edge of it, you would then obtain its circumference.
Now Emily, you may tell me exactly how many degrees are contained in a
meridian?
_Emily._ A meridian, reaching from one pole to the other, is half a
circle, and must therefore contain 180 degrees.
_Mrs. B._ Very well; and what number of degrees are there from the
equator to one of the poles?
_Caroline._ The equator being equally distant from either pole, that
distance must be half of a meridian, or a quarter of the circumference
of a circle, and contain 90 degrees.
_Mrs. B._ Besides the usual division of circles into degrees, the
ecliptic is divided into twelve equal parts, called signs, which bear
the name of the constellations through which this circle passes in the
heavens. The degrees measured on the meridians from the equator, either
towards the north, or towards the south, are called degrees of latitude,
of which there may be 90; those measured from east to west, either on
the equator, or any of the lesser circles, are called degrees of
longitude, of which there may be 180; these lesser circles are also
called parallels of latitude. Of these parallels there may be any
number; a circle drawn from east to west, at any distance from the
equator, will always be parallel to it, and is therefore called a
parallel of latitude.
_Emily._ The degrees of longitude must then vary in length, according
to the dimensions of the circle on which they are reckoned; those, for
instance, at the polar circles, will be considerably smaller than those
at the equator?
_Mrs. B._ Certainly; since the degrees of circles of different
dimensions do not vary in number, they must necessarily vary in length.
The degrees of latitude, you may observe, never vary in length; for the
meridians on which they are reckoned are all of the same dimensions.
_Emily._ And of what length is a degree of latitude?
_Mrs. B._ Sixty geographical miles, which is equal to 69-1/2 English
statute miles; or about one-sixth more than a common mile.
_Emily._ The degrees of longitude at the equator, must then be of the
same dimensions, with a degree of latitude.
_Mrs. B._ They would, were the earth a perfect sphere; but it is not
exactly such, being somewhat protuberant about the equator, and
flattened towards the poles. This form proceeds from the superior action
of the centrifugal power at the equator, and as this enlarges the
circle, it must, in the same proportion, increase the length of the
degrees of longitude measured on it.
_Caroline._ I thought I had understood the centrifugal force perfectly,
but I do not comprehend its effects in this instance.
_Mrs. B._ You know that the revolution of the earth on its axis, must
give to every particle a tendency to fly off from the centre, that this
tendency is stronger, or weaker, in proportion to the velocity with
which the particle moves; now a particle situated near to one of the
poles, makes one rotation in the same space of time as a particle at the
equator; the latter, therefore, having a much larger circle to describe,
travels proportionally faster, consequently the centrifugal force is
much stronger at the equator than in the polar regions: it gradually
decreases as you leave the equator and approach the poles, at which
points the centrifugal force, entirely ceases. Supposing, therefore, the
earth to have been originally in a fluid state, the particles in the
torrid zone would recede much farther from the centre than those in the
frigid zones; thus the polar regions would become flattened, and those
about the equator elevated.
As a large portion of the earth is covered with water, the Creator gave
to it the form, denominated an _oblate spheroid_, otherwise the polar
regions would have been without water, and those about the equator,
would have been buried several miles below the surface of the ocean.
_Caroline._ I did not consider that the particles in the neighbourhood
of the equator, move with greater velocity than those about the poles;
this was the reason I could not understand you.
_Mrs. B._ You must be careful to remember, that those parts of a body
which are farthest from the centre of motion, must move with the
greatest velocity: the axis of the earth is the centre of its diurnal
motion, and the equatorial regions the parts most distant from the axis.
_Caroline._ My head then moves faster than my feet; and upon the summit
of a mountain, we are carried round quicker than in a valley?
_Mrs. B._ Certainly; your head is more distant from the centre of motion
than your feet; the mountain-top than the valley; and the more distant
any part of a body is from the centre of motion, the larger is the
circle it will describe, and the greater therefore must be its velocity.
_Emily._ I have been reflecting, that if the earth is not a perfect
circle----
_Mrs. B._ A sphere you mean, my dear: a circle is a round line, every
part of which is equally distant from the centre; a sphere or globe is a
round body, the surface of which is every where equally distant from the
centre.
_Emily._ If, then, the earth is not a perfect sphere, but prominent at
the equator, and depressed at the poles, would not a body weigh heavier
at the equator than at the poles? For the earth being thicker at the
equator, the attraction of gravity perpendicularly downwards must be
stronger.
_Mrs. B._ Your reasoning has some plausibility, but I am sorry to be
obliged to add, that it is quite erroneous; for the nearer any part of
the surface of a body is to the centre of attraction, the more strongly
it is attracted; because it is then nearest to the whole mass of
attracting matter. In regard to its effects, you might consider the
whole power of gravity, as placed at the centre of attraction.
_Emily._ But were you to penetrate deep into the earth, would gravity
increase as you approached the centre?
_Mrs. B._ Certainly not; I am referring only to any situation on the
surface of the earth. Were you to penetrate into the interior, the
attraction of the parts above you, would counteract that of the parts
beneath you, and consequently diminish the power of gravity in
proportion as you approach the centre; and if you reached that point,
being equally attracted by the parts all around you, the effects of
gravity would cease, and you would be without weight.
_Emily._ Bodies, then, should weigh less at the equator than at the
poles, since they are more distant from the centre of gravity in the
former than in the latter situation?
_Mrs. B._ And this is really the case; but the difference of weight
would be scarcely sensible, were it not augmented by another
circumstance.
_Caroline._ And what is this singular circumstance, which seems to
disturb the laws of nature?
_Mrs. B._ One that you are well acquainted with, as conducing more to
the preservation than the destruction of order,--the centrifugal force.
This we have just observed to be strongest at the equator; and as it
tends to drive bodies from the centre, it is necessarily opposed to, and
must lessen the power of gravity, which attracts them towards the
centre. We accordingly find that bodies weigh lightest at the equator,
where the centrifugal force is greatest; and heaviest at the poles,
where this power is least: the weight being diminished at the equator,
by both the causes mentioned.
_Caroline._ Has the experiment been made in these different situations?
_Mrs. B._ Louis XIV. of France, sent philosophers both to the equator,
and to Lapland, for this purpose: the severity of the climate, and
obstruction from the ice, have hitherto rendered every attempt to reach
the pole abortive; but the difference of gravity at the equator, and in
Lapland is very perceptible.
_Caroline._ Yet I do not comprehend how the difference of weight could
be ascertained, for if the body under trial decreased in weight, the
weight which was opposed to it in the opposite scale must have
diminished in the same proportion. For instance, if a pound of sugar did
not weigh so heavy at the equator as at the poles, the leaden pound
which served to weigh it, would not be so heavy either; therefore they
would still balance each other, and the different force of gravity could
not be ascertained by this means.
_Mrs. B._ Your observation is perfectly just: the difference of gravity
in bodies situated at the poles, and at the equator, cannot be
ascertained by weighing them; a pendulum was therefore used for that
purpose.
_Caroline._ What, the pendulum of a clock? how could that answer the
purpose?
_Mrs. B._ A pendulum consists of a line, or rod, to one end of which a
weight is attached, and by the other end it is suspended to a fixed
point, about which it is made to vibrate. When not in motion, a
pendulum, obeying the general law of attraction, hangs like a plumb
line, perpendicular to the surface of the earth, but if you raise the
pendulum, gravity will bring it back to its perpendicular position. It
will, however, not remain stationary there, for the momentum it has
acquired during its descent, will impel it onwards, and if unobstructed,
it will rise on the opposite side to an equal height; from thence it is
brought back by gravity, and is again forced upwards, by the impulse of
its momentum.
_Caroline._ If so, the motion of a pendulum would be perpetual, and I
thought you said, that there was no perpetual motion on the earth.