Part 11

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.

_Mrs. B._ The motion of a pendulum is opposed by the resistance of the air in which it vibrates, and by the friction of the part by which it is suspended: were it possible to remove these obstacles, the motion of a pendulum would be perpetual, and its vibrations perfectly regular; each being of equal distance, and performed in equal times.

_Emily._ That is the natural result of the uniformity of the power which produces these vibrations, for the force of gravity being always the same, the velocity of the pendulum must consequently be uniform.

_Caroline._ No, Emily, you are mistaken; the force is not every where the same, and therefore the effect will not be so either. I have discovered it, Mrs. B.; since the force of gravity is less at the equator than at the poles, the vibrations of the pendulum will be slower at the former place than at the latter.

_Mrs. B._ You are perfectly right, Caroline; it was by this means that the difference of gravity was discovered, and the true figure of the earth ascertained.

_Emily._ But how do they contrive to regulate their time in the equatorial and polar regions? for, since in our part of the earth the pendulum of a clock vibrates exactly once in a second, if it vibrates faster at the poles, and slower at the equator, the inhabitants must regulate their clocks in a manner different from us.

_Mrs. B._ The only alteration required is to lengthen the pendulum in one case, and to shorten it in the other; for the velocity of the vibrations of a pendulum depends on its length; and when it is said that a pendulum vibrates quicker at the pole than at the equator, it is supposed to be of the same length. A pendulum which vibrates seconds in this latitude is about 39-1/7 inches long. In order to vibrate at the equator in the same space of time, it must be somewhat shorter; and at the poles, it must be proportionally lengthened.

The vibrations of a pendulum, resemble the descent of a body on an inclined plane, and are produced by the same cause; now you must recollect, that the greater the perpendicular height of such a plane, in proportion to its length, the more rapid will be the descent of the body; a short pendulum ascends to a greater height than a larger one, in vibrating a given distance, and of course its descent must be more rapid.

I shall now, I think, be able to explain to you the cause of the variation of the seasons, and the difference in the length of the days and nights in those seasons; both effects resulting from the same cause.

In moving round the sun, the axis of the earth is not perpendicular to the plane of its orbit. Supposing this round table to represent the plane of the earth's orbit, and this little globe, the earth; through this I have passed a wire, representing its axis and poles. In moving round the table, I do not hold the wire perpendicular to it, but obliquely.

_Emily._ Yes, I understand, the earth does not go round the sun in an upright position, its axis is slanting or oblique; and, it of course, forms an angle with a line drawn perpendicular to the plane of the earth's orbit.

_Mrs. B._ All the lines, which you learnt in your last lesson, are delineated on this little globe; you must consider the ecliptic as representing the plane of the earth's orbit; and the equator, which crosses the ecliptic in two places, then shows the degree of obliquity of the axis of the earth; which amounts to 23-1/2 degrees, very nearly. The points in which the ecliptic intersects the equator, are called the equinoctial points.

But I believe I shall render the effects of the obliquity of the earth's axis clearer to you, by the revolution of the little globe round a candle, which shall represent the sun. (Plate IX. fig. 2.)

As I now hold it, at A, you see it in the situation in which it is in the midst of summer, or what is called the summer solstice, which is on the 21st of June.

_Emily._ You hold the wire awry, I suppose, in order to show that the axis of the earth is not upright?

_Mrs. B._ Yes; in summer, the north pole is inclined towards the sun. In this season, therefore, the northern hemisphere enjoys much more of his rays than the southern. The sun, you see, now shines over the whole of the north frigid zone, and notwithstanding the earth's diurnal revolution, which I imitate by twirling the ball on the wire, it will continue to shine upon it as long as it remains in this situation, whilst the south frigid zone is at the same time completely in darkness.

_Caroline._ That is very strange; I never before heard that there was constant day or night in any part of the world! How much happier the inhabitants of the north frigid zone must be than those of the southern; the first enjoy uninterrupted day, while the last are involved in perpetual darkness.

_Mrs. B._ You judge with too much precipitation; examine a little further, and you will find, that the two frigid zones share an equal fate.

We shall now make the earth set off from its position in the summer solstice, and carry it round the sun; observe that the pole is always inclined in the same direction, and points to the same spot in the heavens. There is a fixed star situated near that spot, which is hence called the north polar star. Now let us stop the earth at B, and examine it in its present situation; it has gone through one quarter of its orbit, and is arrived at that point at which the ecliptic cuts, or crosses, the equator, and which is called the autumnal equinox.

_Emily._ The sun now shines from one pole to the other, just as it would constantly do, if the axis of the earth were perpendicular to its orbit.

_Mrs. B._ Because the inclination of the axis is now neither towards the sun, nor in the contrary direction; at this period of the year, the days and nights are equal in every part of the earth. But the next step she takes in her orbit, you see, involves the north pole in darkness, whilst it illumines that of the south; this change was gradually preparing as I moved the earth from summer to autumn; the arctic circle, which was at first entirely illumined, began to have short nights, which increased as the earth approached the autumnal equinox; and the instant it passed that point, the long night of the north pole commences, and the south pole begins to enjoy the light of the sun. We shall now make the earth proceed in its orbit, and you may observe that as it advances, the days shorten and the nights lengthen, throughout the northern hemisphere, until it arrives at the winter solstice, on the 21st of December, when the north frigid zone is entirely in darkness, and the southern has uninterrupted daylight.

_Caroline._ Then, after all, the sun which I thought so partial, confers his favours equally on all.

_Mrs. B._ Not so either: the inhabitants of the torrid zone have much more heat than we have, as the sun's rays fall perpendicularly twice in the course of a year, on every place within the tropics, while they shine more or less obliquely on the rest of the world, and almost horizontally at the poles; for during their long day of six months, the sun moves round their horizon without either rising or setting; the only observable difference, is that it is more elevated by a few degrees at mid-day, than at midnight.

_Emily._ To a person placed in the temperate zone, in the situation in which we are in England, the sun will shine neither so obliquely as it does on the poles, nor vertically as at the equator; but its rays will fall upon him more obliquely in autumn, and winter, than in summer.

_Caroline._ And therefore, the inhabitants of the temperate zones, will not have merely one day, and one night, in the year, as happens at the poles, nor will they have equal days, and equal nights, as at the equator; but their days and nights will vary in length, at different times of the year, according as their respective poles incline towards, or from the sun, and the difference will be greater in proportion to their distance from the equator.

_Mrs. B._ We shall now follow the earth through the other half of her orbit, and you will observe, that now exactly the same changes take place in the southern hemisphere, as those we have just remarked in the northern. Day commences at the south pole, when night sets in at the north pole; and in every other part of the southern hemisphere the days are longer than the nights, while, on the contrary, our nights are longer than our days. When the earth arrives at the vernal equinox, D, where the ecliptic again cuts the equator, on the 21st of March, she is situated, with respect to the sun, exactly in the same position, as in the autumnal equinox; and the only difference with respect to the earth, is, that it is now autumn in the southern hemisphere, whilst it is spring with us.

_Caroline._ Then the days and nights are again every where equal.

_Mrs. B._ Yes, for the half of the globe which is enlightened, extends exactly from one pole to the other, the sun has just risen to the north pole, and is just setting to the south pole; but in every other part of the globe, the day and night is of twelve hours length; hence the word equinox, which is derived from the Latin, meaning equal night.

As our summer advances, the days lengthen in the northern hemisphere, and shorten in the southern, till the earth reaches the summer solstice, when the north frigid zone is entirely illumined, and the southern is in complete darkness; and we have now brought the earth again to the spot from whence we first accompanied her.

_Emily._ This is indeed a most satisfactory explanation of the cause of the different lengths of our days and nights, and of the variation of the seasons; and the more I learn, the more I admire the simplicity of means by which such wonderful effects are produced.

_Mrs. B._ I know not which is most worthy of our admiration, the causes, or the effects of the earth's revolution round the sun. The mind can find no object of contemplation more sublime, than the course of this magnificent globe, impelled by the combined powers of projection and attraction, to roll in one invariable course, around the source of light and heat: and what can be more delightful than the beneficent effects of this vivifying power on its attendant planet. It is at once the grand principle which animates and fecundates nature.

_Emily._ There is one circumstance in which this little ivory globe appears to me to differ from the earth; it is not quite dark on that side of it which is turned from the candle, as is the case with the earth when neither moon nor stars are visible.

_Mrs. B._ This is owing to the light of the candle, being reflected by the walls of the room, on every part of the globe, consequently that side of the globe, on which the candle does not directly shine, is not in total darkness. Now the skies have no walls to reflect the sun's light on that side of our earth which is in darkness.

_Caroline._ I beg your pardon, Mrs. B., I think that the moon, and stars, answer the purpose of walls in reflecting the sun's light to us in the night.

_Mrs. B._ Very well, Caroline; that is to say, the moon and planets; for the fixed stars, you know, shine by their own light.

_Emily._ You say, that the superior heat of the equatorial parts of the earth, arises from the rays falling perpendicularly on those regions, whilst they fall obliquely on these more northern regions; now I do not understand why perpendicular rays should afford more heat than oblique rays.

_Caroline._ You need only hold your hand perpendicularly over the candle, and then hold it sideways obliquely, to be sensible of the difference.

_Emily._ I do not doubt the fact, but I wish to have it explained.

_Mrs. B._ You are quite right; if Caroline had not been satisfied with ascertaining the fact, without understanding it, she would not have brought forward the candle as an illustration; the reason why you feel so much more heat if you hold your hand perpendicularly over the candle, than if you hold it sideways, is because a stream of heated vapour constantly ascends from the candle, or any other burning body, which being lighter than the air of the room, does not spread laterally but rises perpendicularly, and this led you to suppose that the rays were hotter in the latter direction. Had you reflected, you would have discovered that rays issuing from the candle sideways, are no less perpendicular to your hand when held opposite to them, than the rays which ascend when your hand is held over them.

The reason why the sun's rays afford less heat when in an oblique direction, than when perpendicular, is because fewer of them fall upon an equal portion of the earth; this will be understood better by referring to plate 10. fig. 1, which represents two equal portions of the sun's rays, shining upon different parts of the earth. Here it is evident, that the same quantity of rays fall on the space A B, as fall on the space B C; and as A B is less than B C, the heat and light will be much stronger in the former than in the latter; A B, you see, represents the equatorial regions, where the sun shines perpendicularly; and B C, the temperate and frozen climates, where his rays fall more obliquely.

_Emily._ This accounts not only for the greater heat of the equatorial regions, but for the greater heat of our summers, as the sun shines less obliquely in summer than in winter.