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:

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.

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:

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.