Part 4

TUTOR. It does so; and the inhabitants of London by this motion are carried at the rate of 560 miles an hour[13].

[Footnote 13: The hourly motion under the equator is 900 miles.]

PUPIL. What an astonishing rapidity!

TUTOR. Now, the sun with the rest of the heavenly bodies must move round the earth, or the earth must revolve on its axis in 24 hours, to cause that appearance.

PUPIL. That is plain.

TUTOR. Well then, great as you may suppose the velocity of the earth on its axis to be, if the sun move round the earth his hourly motion will be nearly 25 millions of miles; and beyond conception would be that of the fixed stars. Which now do you think is most probable, that the sun and stars should move round the earth, or that they, by the simple motion of the earth, should appear to be in motion?

PUPIL. The latter, to be sure, Sir.—I have one difficulty remaining, which is this; if a lark rise from a field near London and remain in the air a quarter of an hour, if the earth move at the rate of 560 miles an hour, it will go 140 miles whilst the lark is suspended, and yet it continues over the field,—how can this be?

TUTOR. This objection to the motion of the earth has been made by those who were older and who thought themselves wiser too than yourself. They either did not know or did not consider, that the atmosphere which surrounds the earth is a part of itself, and gravitates towards it, and therefore partakes of the earth’s motion and carries the lark along with it. Besides, as the Sun, Venus, Mars, and Jupiter are known to revolve on their axes, we have reason to suppose that the other planets, together with the earth, must have the same motion[14].

[Footnote 14: Dr. Herschell says that several of the fixed stars revolve on their axes.]

PUPIL. How is it known that they do revolve on their axes; and in what time do they perform their revolutions?

TUTOR. By the assistance of telescopes dark spots have been seen on the disc of the sun, by the motion of which it is found that he revolves on his axis in 25-1/4 days; Venus performs her diurnal revolution in about 23 ho. 21 min.; Mars goes round his axis in 24 ho. 39 min.; and Jupiter in 9 ho. 56 min.; as to the rest, no spot or any fixed point has been discovered to ascertain the length of their day; Mercury being too near the sun, and Saturn and the Georgium Sidus too remote for our observations.

PUPIL. I can no longer doubt of the earth’s motion: and, if it will not be improper, a description of the atmosphere will give me pleasure.

TUTOR. That I can have no objection to. The atmosphere is a thin, invisible fluid, most dense or heavy near the earth, but grows gradually rarer or lighter the higher we ascend, so much so, that at the tops of some high mountains it is difficult to breathe. It serves not only to suspend the clouds, furnish us with wind and rain, and answer the common purposes of breathing, but is also the cause of the morning and evening twilight, and of all the glory and brightness of the firmament.

PUPIL. How, pray?

TUTOR. If there were no atmosphere, the sun would yield no light but when our eyes were directed towards him; and the heavens would appear dark and as full of stars as on a dark winter’s night; but the atmosphere being strongly illuminated by the sun, reflects the light back upon us, and makes the whole heavens to shine so strongly, that the faint light of the stars is obscured, and they are rendered invisible.

PUPIL. I find then the atmosphere is of more use than I imagined. But how is it the cause of the twilight?

TUTOR. The atmosphere is about 45 miles above the surface of the earth, therefore the sun’s rays falling upon the higher parts of it before rising, by reflection causes a faint light, which increases till he appears above the horizon; and in the evening it decreases after he sets, till he is 18 degrees below the horizon, where the morning twilight begins, and the evening twilight ends.

PUPIL. By the horizon, I think you mean that distant boundary of our sight where the heavens and the earth seem to join all around us, as it appears from an eminence.

TUTOR. The very same. ’Tis that imaginary circle which intercepts from our view the sun, moon, and stars each night; and when, by the rotation of the earth, they appear to descend below it, we say they are set; as on the contrary, each morning, when they appear above it, we say they rise.

“To find the spacious line, cast round thine eyes, “And where the earth’s high surface joins the skies, “Where stars first set, and first begin to shine, “There draw the fancy’d image of this line.”

PUPIL. A very pleasing description, indeed.

TUTOR. You will remember that this is called the _rational horizon_; but that which respects land and water is called the _sensible horizon_. The former divides the heavens into two equal parts, and is 90 degrees distant from a point directly over our heads, called the _zenith_, and the opposite point of the heavens directly under our feet, called the _nadir_.—But I must resume the subject of the atmosphere.

PUPIL. Had I not thought you had finished your description of the atmosphere, I should not have presumed to interrupt you.

TUTOR. What I have told you respecting the horizon is necessary for you to be acquainted with; therefore, the suspension is immaterial.—You must, I make no doubt, have observed the sun and moon at rising and setting to appear larger than when higher above the horizon.

PUPIL. I have, frequently, Sir.

TUTOR. And cannot you tell the reason of it?

PUPIL. No, Sir.

TUTOR. The reason is this: In viewing them, when near the horizon, you see them through a thicker medium than when they are higher, that is, you see them through a greater quantity of the atmosphere; and you not only see them larger, but really above the horizon whilst they are actually below it.

PUPIL. How do you account for this, Sir?

TUTOR. Light, like material bodies, if it meet with no obstruction, will move in right lines; now, the rays of the sun in coming to the earth must pass through a great quantity of the atmosphere, which being a fluid, refracts or bends the rays of light, by which refraction it is that we are favoured with the sight of the sun 3-1/4 minutes every morning before he rises above the horizon, and every evening after he sinks below it, which in one year amounts to more than 40 hours. This refraction is greatest near the horizon, and ends in the zenith.

PUPIL. Pray, Sir, can you make this clearer by an experiment?

TUTOR. I have just thought of one. Take a bason filled with water, and a strait stick or piece of wire; put it perpendicularly into the water, that is, that it lean neither way, and there will be no refraction; incline it a little towards the edge of the bason and it will appear a little bent at the surface of the water; incline it still more, and the refraction will be greater.

PUPIL. I have often seen this appearance when I have put my stick into water, but did not before know the cause.

TUTOR. You may try one more experiment. Pour the water out of the bason, and set the bason on the floor; put a guinea into it, and let it represent the sun.—Why do you smile?

PUPIL. Because I have not the sun’s representative to try the experiment with.

TUTOR. Well, well, put a shilling into the bason and call it the moon, and it will answer the same purpose:—Walk backward till you just lose sight of it, then the right line from your eye continued over the edge of the bason must pass beyond the money at the bottom of it.

PUPIL. That is evident.

TUTOR. Keep your position, and desire some friend to pour the water gently into the bason so as not to remove the money, and you will clearly distinguish it. Now, if you call the edge of the bason the horizon, the water the atmosphere, and the shilling the moon, is it not clear that you will see it above the horizon, when it is really below it?

PUPIL. I think so, Sir.

TUTOR. Well, try the experiment, and let me know the result when I next see you.

DIALOGUE IX.

TUTOR.

I presume, Sir, you have made the experiment I recommended to you.

PUPIL. I have, Sir; and am so well convinced of what you told me, that nothing farther need be said on the subject.

TUTOR. As that is the case, I shall proceed.—I dare say you do not forget what the plane of the ecliptic is.

PUPIL. I do not, Sir; but have a perfect recollection of it.

TUTOR. Now, remember, that the axis of the earth is not upright or perpendicular to the plane of the ecliptic, but inclines to, or leans towards it, 23-1/2 degrees, and makes an angle with it of 66-1/2 degrees.

PUPIL. An angle signifies a corner; but that cannot be the meaning here.

TUTOR. That is what is generally understood by an angle: but, in geometry, it means the meeting of any two lines which incline to one another, in a certain point. Now, if you conceive the axis of the earth to be one line, and the plane of the ecliptic the other, the point where they meet or cross each other will form an angle.

PUPIL. I think I understand it; but how can it contain 23-1/2 or 66-1/2 degrees?

TUTOR. You know what a degree is.

PUPIL. If I remember right it is the 360th part of a circle.

TUTOR. It is so: and the measure of an angle is an arc or part of the circumference of a circle, whose angular point is the center: and so many 360th parts as any arc contains, so many degrees the measure of the angle is said to be; thus, Z C P (Plate III. fig. 1.) makes an angle of 23-1/2 degrees, because the arc Z P contains 23-1/2 360th parts of the whole circle. Then if A B represent the plane of the ecliptic, and N C S the axis of the earth, as D N contains the same number of degrees as Z P, will not its inclination from a perpendicular be 23-1/2 degrees?

PUPIL. Nothing can be plainer.

TUTOR. For the same reason, as P B contains 66-1/2 parts of the whole circle, the axis of the earth makes an angle of 66-1/2 degrees with the plane of the ecliptic. And, if you add 23-1/2 to 66-1/2 the sum will be 90, which is the measure Z B, or the fourth part of the circle, and makes what is called a right angle, at the point or center C.

PUPIL. It is very clear:—but what do the other letters refer to?

TUTOR. The extremities of the earth’s axis are called the poles, N the north, and S the south pole, and P the north-pole star, to which, and to the opposite part of the heavens, the axis always points. These extremities in the heavens appear motionless, whilst all other parts seem in a continual state of revolution: the circle of motion appears to increase with the distance from the apparently motionless points to that circle in the heavens which is at an equal distance between them, called the equinoctial, represented by the letters Æ Q; and is the same I promised some time ago to explain to you.

PUPIL. I recollect it: and as the line A B represents the plane of the ecliptic, I suppose the line Æ Q is the plane of the equinoctial, which I see crosses it as you then told me.

TUTOR. You are right: and it makes an angle with it of 23-1/2 degrees. It is called the equinoctial, because when the sun appears there, that is, in Aries or Libra, the days and nights are equal in all parts of the world, which I shall shew you in due time; and shall now explain to you what I have just mentioned, that the axis of the earth always points to the same parts of the heavens. I am apprehensive you will think it strange that this should be the case, and the axis keep parallel to itself.

PUPIL. What am I to understand by the axis being parallel to itself?

TUTOR. Two lines are said to be parallel when they do not incline to but keep at equal distances from each other; so that if they were infinitely continued, they would never meet. Now, if you can conceive a line drawn parallel to the earth’s axis in any part of its orbit, it will be parallel to it in every other part of it. A little drawing I have by me, (Plate III. fig 2.) where the earth is represented in four different parts of its orbit, I think will make this plain to you.

PUPIL. I comprehend your meaning clearly. But, as the orbit of the earth is 190 millions of miles in diameter, I have not the least conception how it can incline to the same points. Had you not told me to the contrary, I should have thought it must move round them in every revolution of the earth about the sun.

TUTOR. That such a motion would be perceptible is evident, if the fixed stars were near the earth; but, compared with their distance, 190 millions of miles is but a mere point: therefore, the axis always inclines to the same points of the heavens.

PUPIL. This is a greater proof of the inconceivable distance of the stars than what you mentioned before, and I thought that very astonishing:

Wonders on wonders constantly arise, Whene’er we view the earth, or sea, or skies.

TUTOR. It is very true. And the more we search, the more we have cause to admire the works of the Almighty.

PUPIL. Pray, Sir, what is the next thing you propose?

TUTOR. To make you acquainted with the other circles you see in the figure (Plate III. fig. 1.) as it is very necessary you should know them.

PUPIL. Will you be kind enough to tell me their names, Sir, and I will endeavour to remember them?

TUTOR. That line which divides the globe into two equal parts, called the northern and southern hemispheres, which answers to the equinoctial in the heavens, and is equally distant from the two poles, is called the _equator_; the other which crosses it, as I before told you, is the _ecliptic_; the smaller circle, north of the equator, is the _tropic of Cancer_; that south of it, the _tropic of Capricorn_; the circles next the poles are called the _polar circles_; or that next the north pole, the _arctic circle_, and that next the south pole, the _antarctic circle_; each of which is 23-1/2 degrees distant from its respective pole, as are the tropics from the equator.

PUPIL. You have not mentioned the lines which cross the other circles, and terminate in the poles; what are they called?

TUTOR. They are called _meridians_, because when any of them, as the earth revolves on its axis, is opposite to the sun, it is mid-day or noon along that line. Twenty-four of these lines are usually drawn on the globe to correspond with the twenty-four hours of the day; but you are not to suppose there are no more than twenty-four; for every place that lies ever so little east or west of another place has a different meridian.—To make this clearer to you, we will suppose the upper 12 (Plate III. fig. 1.) to be opposite the sun, it will of course be noon along that line; the next meridian marked 1, being 15 degrees east, will have passed the meridian 1 hour, consequently it will there be one in the afternoon, and so on, according to the order of the figures, till you come to the lower 12, which being the part of the earth turned directly from the sun, it will be midnight on that meridian; on the next meridian, as you proceed round, it will be one in the morning, the next two, and so on till you arrive at the upper twelve, where you set off. So you see there must be a continual succession of day and night. This difference of time between places lying under different meridians is what is called longitude.

PUPIL. I think I have heard of a Mr. Harrison, who made a time-keeper for determining the longitude. Shall I trespass at all if I beg a little farther information on this subject?

TUTOR. It is my wish at all times to satisfy your curiosity, when I can do it with propriety. I shall therefore comply with your request.—Mr. Harrison’s time-keeper, and those made since by other artists, are so constructed, that the heat and cold of different climates will not affect them; for, all metals are more or less expanded by heat, and contracted by cold; for which reason it is, that a clock or watch made in the usual way will not keep equal time. Now, all that is required of these time-keepers to ascertain the longitude is this: Suppose a captain of a vessel sailing from London to the West Indies, we will say Kingston, in Jamaica. On his passage thither he makes an observation, and finds the sun on the meridian, or that it is twelve o’clock in that situation, when by his time-keeper it is two in the afternoon in London, whence he concludes he is 30 degrees west of London.

PUPIL. I must beg you to explain this to me, as I do not understand why two hours of time should be equal to 30 degrees of longitude.

TUTOR. You must consider, that as the earth makes a complete revolution on its axis in 24 hours, it must pass over 360 degrees in that time: now, if you divide 360 by 24, the quotient 15, will be the number of degrees passed over in one hour; 30 degrees will be equal to two hours, &c. The difference of time between London and his situation is two hours, consequently the difference of longitude must be 30 degrees: and, it must be west, because the sun had passed the meridian of London; for, as the earth revolves from west by south to east, one place which lies east of another must come first to the meridian or opposite to the sun. Therefore, when longitude is reckoned from London, if the place lie east of that meridian the time will be before; if west, after London.

PUPIL. I see it clearly; and as 60 minutes make an hour, if I divide it by 15, the quotient 4 will be the minutes answering to one degree.

TUTOR. You are right: and for the same reason, 4 seconds of time are equal to one minute of longitude, which you know is the 60th part of a degree.—Our captain when arrived at Kingston, finds the difference of time between it and London 5 ho. 6 min. 32 sec. Can you tell me the longitude of Kingston?

PUPIL. If I bring the hours and minutes to minutes, and divide by 4, the quotient I think will be degrees, will it not?

TUTOR. It will: and the seconds of time divided by 4, will be minutes of longitude. Now try if you can do it.

PUPIL. Five hours 6 minutes, multiplied by 60 will be 306 minutes, this divided by 4, will give 76 degrees and 2 over, which 2 is half a degree, or 30 minutes: and 32 seconds of time divided by 4, will be 8 minutes of longitude, the sum of which is 76 degrees 38 minutes for the longitude of Kingston.

TUTOR. Very well.—I have just now thought of another method of reducing time to longitude, and longitude to time, which you may probably find easier. However, when you are in possession of both, you may use which you please.

PUPIL. That which is easiest must, I think, be best.

TUTOR. I will give it you, and let me have your opinion of it.

To reduce time to longitude.

Multiply the hours, minutes, and seconds of time by 15, or rather by the factors as they are called, namely 3 and 5, carrying one for every 60 in the minutes and seconds, and setting down the remainder, thus:

ho. min. sec. 5 6 32 difference of 3 time. ──────────────── 15 19 36 5 ──────────────── Degrees 76 38 0 longitude. ════════════════

Divide the degrees and minutes of longitude by 5 and 3 and the quotient will be the difference of time.

PUPIL. I give this the preference.

TUTOR. As longitude is seldom mentioned without being accompanied with latitude, that you may not be ignorant of its meaning when you meet with it, I shall just tell you that it is the distance of any place from the equator, reckoned in degrees and minutes on the meridian, and is either north or south as the place lies north or south of the equator. The latitude of any place is equal to the elevation of the pole above the horizon. The latitude of the heavenly bodies is reckoned from the ecliptic, and terminates in the arctic and antarctic circles: and their longitude begins at the point Aries.

PUPIL. What is the measure of a degree?

TUTOR. A degree of latitude is 60 geographical, or 69-1/2 English miles: and a degree of longitude on the equator is equal to it, because the equator as well as the meridians divides the globe into two equal parts. But a degree of longitude decreases as you approach the poles: for at the poles the meridians meet in a point, consequently a degree there can have no dimension. To-morrow I will shew you the cause of the seasons.

DIALOGUE X.

PUPIL.

I think, Sir, when you left me last night you told me our next business would be to explain the nature of the seasons?

TUTOR. I did so, and am persuaded you will find no great difficulty in comprehending it.—Cast your eye on the little drawing I gave you, (Plate III. fig. 2.) where the earth is represented as situated at the four quarters of the year, namely, Spring, Summer, Autumn, and Winter.—But before we proceed to an explanation it will be necessary to remark, that, in the little scheme the eye is supposed to be elevated above the plane of the earth’s orbit, and that we see it very obliquely. The orbit by this means appears very elliptical; and, the enlightened hemisphere, or that half of the earth which is turned to the sun in the spring, and the darkened hemisphere, or that turned from him in the autumn, are there represented.

PUPIL. This I understand.

TUTOR. Well then, we will begin with the spring.—In this situation of the earth the equator is exactly opposed to the sun: and, as he always enlightens a hemisphere, or half of its surface, his rays will reach to both the poles: whence, from the diurnal revolution of the earth, the day and night are equal all over the globe.

PUPIL. This I remember you told me happened when the sun was in Aries and Libra. The sun is now entering Aries: and, as we are in the rays of the sun one half of the diurnal revolution, and in the shadow of the earth, or dark, the other half, the day and night must be equal.

TUTOR. Certainly. And as the sun enters Aries in the equinoctial, it is then called the _Vernal_, that is, _Spring Equinox_. When the sun enters the opposite sign Libra, the same effects are produced, and it is then called the _Autumnal Equinox_.

PUPIL. You have passed on from Spring to Autumn.

TUTOR. I have so.—We will now return, and trace the earth in its orbit from spring to summer.—You have already seen that the north and south poles are both enlightened, and that the day and night are equal at the equinoxes. If the axis of the earth were perpendicular to the plane of the earth’s orbit, this would constantly be the case, and we should have no diversity of seasons: for, the sun being over the equator, the poles must be perpetually enlightened, and of course we should have equal day and night at all times of the year.

PUPIL. That is plain. I suppose then that it is to the inclination of the earth’s axis we are indebted for the increase and decrease of days.

TUTOR. It is occasioned by the inclination of the earth’s axis and its preserving its parallelism, which I explained to you last evening.—As the sun is now in the first point of Aries, the earth you know must be in the beginning of Libra, it being the opposite sign.—Now fix your attention on the scheme, and imagine the earth to be advancing in its orbit through Libra, Scorpio, and Sagittarius: and at the first degree of Capricorn give me your opinion of the earth’s position.

PUPIL. The north pole is turned to the sun, the south pole from him, and the tropic of Cancer is opposite to him.

TUTOR. How many degrees are the tropics from the equator, or, in other words, what is the inclination of the earth’s axis?

PUPIL. Twenty-three degrees and a half.