I now propose giving you a description of the moon, and I doubt not it will afford you some degree of pleasure.

Pupil. Indeed it will, as I know little more than that she is a secondary planet or satellite, revolving round the earth, and with it round the sun.

Tutor. You know her mean distance from the earth.

Pupil. I did not recollect that: 240 thousand miles.

Tutor. Right. Her diameter is about 2161 miles, and her bulk about a fiftieth part of the earth’s. Her axis is almost perpendicular to the plane of the ecliptic, consequently she can have no diversity of seasons.

Pupil. What is her period?

Tutor. The time she takes to revolve from one point of the heavens to the same again is called her siderial or periodical revolution, and is performed in 27 days, 7 hours, 43 minutes; but synodical revolution, or the time taken up to revolve from the sun to the same apparent situation with respect to the sun again, or from change to change, is 29 days, 12 hours, and 44 minutes.

Pupil. I do not clearly comprehend it.

Tutor. If the earth had no annual motion, the period of the moon would be uniformly 27 days, 7 hours, 43 minutes; but you are to consider that whilst the moon is revolving round the earth, the earth is advancing in its orbit, and of course she must be so much longer in completing her synodical revolution as the difference of time between that and her siderial revolution. This I will make clear to you in a few minutes.—What is the situation of the hour-hand and minute-hand of a watch at twelve o’clock?

Pupil. They will be in conjunction.

Tutor. And will they be in conjunction at one?

Pupil. No, Sir.

Tutor. Yet the minute-hand has made a complete revolution: but before they can be in conjunction again the minute-hand must move forward till it overtakes the hour-hand.

Pupil. I now understand it, and must beg you to explain to me the different phases of the moon.

Tutor. Take this ivory ball, and suspend it by the string with your hand between your eye and the candle. Let the candle represent the sun, the ball the moon, and your head the earth. In this situation, as the candle enlightens only one half of the ball, the part turned from you will be enlightened, and the part turned to you will be dark. This will be a representation of the moon at change, and as no part of her enlightened hemisphere is turned to the earth, she can reflect no light upon it, and consequently is invisible to us. She now rises and sets nearly with the sun.—Turn yourself a little to the left, and you will observe a streak of light like what is called the new moon.

Pupil. I see it clearly.

Tutor. Move round one quarter.

Pupil. One half of the side next me is now enlightened.

Tutor. You may conceive it to be the moon at first quarter.—Go on, and you will see the light increase till the ball is opposite to the candle, when the side next you will be wholly illumined, and will give you a just idea of the moon at full, which now rises about the time of sun-setting, being opposite to the sun: and, the farther she advances in her orbit the later she rises.

Pupil. It is plain it must be so. She rises with the sun at change, being then in conjunction: and as she revolves in her orbit the same way as the earth does on its axis, the earth will have farther to revolve each day before it can see the moon. At the full she is in opposition, and of course rises when the sun sets: and so continues to rise later and later, till the change again.

Tutor. You imagine that the moon rises exactly with the sun when she is at change; and when he sets, at full. I will presently convince you of your mistake; and would have you now proceed with your ball. Place it again opposite to the candle, and as you turn round you will find the light gradually decrease as it before increased, that the side that was before enlightened is now dark, and the dark side light. When you have gone three quarters round, one half of the side next you will be enlightened, and will resemble the moon at last quarter. As you go on the darkened part will increase, till you arrive at the place you set off from, where the light is quite obscured.

Pupil. I have now completed the circuit, and am much delighted with it, as by this simple contrivance I can perceive the various changes of the moon, and that the western side is enlightened from the change to the full, and the eastern side from the full to the change.

Tutor. I find then it has fully answered the purpose intended.

Pupil. Indeed it has. But if you will give me leave I will use the ball again.

Tutor. By all means.

Pupil. I perceive, as I move round, that the same side of the ball is turned towards me whilst every part is turned to the candle. Is it so with the moon?

Tutor. It is: and as every part of the moon is turned to the sun, she makes one revolution on her axis whilst she makes one in her orbit.

Pupil. This is very singular. If the same side of the moon be always turned to the earth, the opposite side of course can never see it.

Tutor. And they must likewise be deprived of the earth as a moon.

Pupil. True. But how is it known that the same side of the moon is always opposed to the earth?

Tutor. The moon, like our earth, consists of mountains and valleys, which, when seen through a good telescope, are very beautiful. The mountainous parts appear as lucid spots and bright streaks of light: and as the same spots, &c. are constantly turned to the earth, she must keep the same side to the earth.

Pupil. It is very clear. Are there no seas?

Tutor. It was formerly imagined that the dark parts were seas, but later observations prove that they are hollow places or caverns, which do not reflect the light of the sun. Besides, if there were seas there would consequently be exhalations, and if exhalations, clouds and vapours, and an atmosphere to support them. That there are no clouds is evident, because when our atmosphere is clear, and the moon above our horizon in the night-time, all her parts appear constantly with the same clear, serene, and calm aspect.

Pupil. Has the moon then no atmosphere?

Tutor. If she has it is imperceptible to us: for, when she approaches any star, we cannot discover with our best telescopes any change of colour or diminution of lustre in the star till the instant it is lost behind her: whence it is clear, that she can have no such gross medium as our atmosphere to surround her.

Pupil. May we not then doubt whether she be inhabited or not, as without air we cannot breathe?

Tutor. The same Almighty Being who created us and gave us air to breathe, may have provided a different way for their existence. It does not hold good that, because we could not live there, she is not inhabited. Fish will live a considerable time in water under an exhausted receiver: and, I have heard of a toad being found in a block of marble. Your doubt therefore, I think, ought not to be admitted.

Pupil. I am satisfied. And must now beg to be informed how I may observe the moon’s motion.

Tutor. Her real motion round the earth, may be easily known by remarking when she is near any particular star. Thus, suppose you see her west, that is to the right of it, she will be approaching, then in conjunction with, and afterwards pass it towards the east. Her apparent motion is that of rising and setting, which is occasioned by the rotation of the earth on its axis.

Pupil. I remember not long since, when you shewed me Jupiter, that the moon was west of him: the next evening I saw her almost appear to touch him, and soon after at a great distance from him easterly. I now see that her real motion is from west by south to east, and her apparent motion from east by south to west.

Tutor. If you have no objection, I will now explain the cause of eclipses.

Pupil. So far from it, that it will give me the greatest pleasure.

Tutor. Take your ivory ball, suspend it as before, in a right line between your eye and the candle.—Can you see the candle?

Pupil. No, Sir.

Tutor. For what reason.

Pupil. Because the ball prevents the light coming to me.

Tutor. This then represents an eclipse of the sun, which can never happen but when the moon is between the sun and the earth, which must be at the change: for, as light passes in a right line, the sun is hidden to that part of the earth which is under the moon, and therefore he must be eclipsed. If the whole of the sun be obscured by the body of the moon, the eclipse is total: if only a part be darkened, it is a partial eclipse; and so many twelfth parts of the sun’s diameter, as the moon covers, so many digits are said to be eclipsed.

Pupil. May not the word digit be applied to the moon as well as the sun?

Tutor. It may: for it means a twelfth part of the diameter of either the sun, or the moon.

Pupil. As you have now shewn me the cause of an eclipse of the sun, I am anxious to have that of the moon explained.

Tutor. We must again have recourse to your little ball.—Turn yourself round till it is opposite to the candle in a line with your head, and you will see that no light can be thrown on it from the candle, because your head is between them. In like manner the rays of the sun are prevented falling on the moon, by the interposition of the earth: she must therefore be eclipsed.

Pupil. I see it clearly. And as an eclipse of the sun happens when the moon is at change, that of the moon must be when she is at full; for, it is then only the earth’s shadow can fall on the moon, the earth being at no other time between the sun and her.

Tutor. The diameter of the shadow is about three times that of the moon, and consequently the moon must be totally eclipsed whilst she continues in it. On the contrary, the shadow of the moon at an eclipse of the sun, covers so small a part of the earth’s surface, that the sun is totally or centrally eclipsed to but a small part of it; and its duration is very short. But a faint or partial shadow surrounds this darkened shade, in which the sun is more or less eclipsed, as the place is nearer to or farther from its center; this partial shadow is called the penumbra. I have prepared for you a little drawing, representing an eclipse both of the sun and moon, which I think will enable you better to understand what I have been explaining. (Plate IV. Fig. 1 and 2.) In the former, p. p. is the penumbra.

Pupil. In what does a central differ from a total eclipse?

Tutor. An eclipse of the sun may be central, and not total; for, those who are under the point of the dark shadow, will see the edge of the sun like a fine luminous ring, all around the dark body of the moon when the sun is eclipsed at the moon’s greatest distance from the earth; but when she is nearest the earth at an eclipse of the sun, the eclipse is total. When the penumbra first touches the earth, the general eclipse begins; when it leaves the earth, the general eclipse ends. An eclipse of the moon always begins on the moon’s eastern side, and goes off on her western side; but an eclipse of the sun begins on the sun’s western side, and goes off on his eastern side. When the moon is eclipsed in either of her nodes, the eclipse is both central and total.

Pupil. Pray, what is the reason we have not an eclipse at every full and change of the moon?

Tutor. For the same reason that Mercury and Venus are not seen to pass over she sun’s disc at every inferior conjunction.

Pupil. Is the orbit of the moon then inclined to the plane of the ecliptic?

Tutor. It is: and no eclipse of the sun can happen but when the moon is within 17 degrees of either of her nodes: neither can there be one of the moon, unless she be within 12 degrees. At all other new moons she passeth either above or below the sun, as seen from the earth: and at all other full moons above or below the earth’s shadow, according as she is north or south of the ecliptic. You now see that the moon must sometimes rise before and sometimes after the sun at change, and before or after he sets at full.

Pupil. I do, Sir, and am much obliged to you for this pleasing account of the moon, and of eclipses: and if you have any thing farther to observe, it will afford me additional pleasure.

Tutor. You may, at some time or other, have an opportunity of seeing a total eclipse of the moon; it will therefore be necessary to prepare you for a phÆnomenon which otherwise you might be much surprized at, and that is, that after the moon is immersed in the earth’s shadow, she is still visible.

Pupil. This is a phÆnomenon that I am not able to account for; for, the moon being an opaque body, she cannot shine by her own light^[16], and the rays of the sun are prevented falling on her by the interposition of the earth, she cannot therefore shine by reflection.

Tutor. It is by reflection that we see her; for the rays of the sun which fall upon our atmosphere are refracted or bent into the earth’s shadow, and so falling upon the moon are reflected back to us. If we had no atmosphere, she would be totally dark, and of course invisible to us.

Pupil. What is her appearance?

Tutor. It is that of a dusky colour, somewhat like tarnished copper.—I have one thing more to remark before we quit this subject, which is, that the moon’s nodes have a retrograde or backward motion, in a direction contrary to the earth’s annual motion, and go through all the signs and degrees of the ecliptic in little less than nineteen years, when there will be a regular period of eclipses, or return of the same eclipses for many ages.

Pupil. Pray, Sir, what do you propose for our next subject?

Tutor. The ebbing and flowing of the sea, or cause of the tides.