Part 4

“What a hopeless task to try to remember all that!”

“At any rate, if you cannot remember these things my conscience will be clear, for I am simply doing my duty in telling you of them. If you forget, go to the books on astronomy and refresh your memory. But do not persuade yourself that the preliminaries are now finished. You are going to think that my story of the moon resembles Walter Scott’s novels in the length of its introduction; but if, in the end, I can interest you half as much as he finally interests his readers I shall thank the stars for my good fortune.

“The next thing that I must try to explain,” I continued, “is the cause of the moon’s phases, or her continual changes of form. You know that the New Moon is shaped like a thin crescent, and always appears in the west immediately after sundown, with the convex side facing the setting sun. The moon at First Quarter is a half circle and is visible in the southern part of the sky just after sunset. The Full Moon, which we have at present, is a complete round disk, and is always seen directly opposite to the place of the sun, so that she rises when the sun sets. The moon at last quarter is again a half circle, and appears on the meridian in the south at sunrise. The waning moon is like the new moon, crescent-shaped, but the convexity of the bow faces the rising sun, and she is visible only in the morning sky just as dawn begins. To explain the reasons for these changes of shape, which the moon regularly undergoes every month, I must ask you to go indoors and examine a little diagram which I have made.”

“Oh!” said my companion, “it is too bad to abandon this charming spectacle, illuminated by rays so fascinating, for the sake of looking at mathematical lines drawn on paper! But I suppose that this is one of the sacrifices demanded by your inexorable science, and must be made.”

“Yes,” I said, “but if science sometimes demands sacrifices, at least she always rewards them most generously.”

When we had returned to the house I placed upon the drawing-room table this diagram.

Phases and Rotation of the Moon. ]

As I spread it out, my companion, after a regretful glance through the open door at the silvery lawn, on which the moon, having cleared the obstructing branches of the bordering trees, was now pouring down the full splendor of her rays, put her elbows on the table to follow my explanation.

“The globe, half bright and half black, in the center,” I said, “represents the earth. The large circle surrounding the earth we will call the moon’s orbit, which she traverses once every month. The smaller globe, also half white and half black, shown in four successive positions in the orbit, is the moon. Suppose the sun to be away off here on the left. It illuminates the earth and the moon only on the side turned toward it. The opposite side of both is buried in night. Now, let us begin with the moon at the point A. She is then between the earth and the sun, the bright side being necessarily toward the sun and the dark side toward the earth. In that position we do not see the moon at all from the earth, unless she happens to come so exactly in a line with the sun as to cover the latter, in which event we have an eclipse of the sun. Now, suppose the moon to move in her orbit toward B. In a little more than seven days she will arrive at B. In the meantime, while moving away from the position of the sun, she begins to present a part of her illuminated hemisphere toward the earth. This part appears in the form of a sickle, or crescent, which grows gradually broader, until, at B, it has grown to a half circle. In other words, when the moon is in the position B we on the earth see one half of her illuminated surface. This phase is called First Quarter. The narrow crescent, which appears as soon as the moon begins to move from A toward B, is the New Moon. As the moon continues on from B toward C, more and more of her illuminated half is visible from the earth, and when she arrives at C, just opposite to the position of the sun, she becomes a Full Moon. We then see, as occurs to-night, the whole of that face of the moon which is presented sunward. The upper half of the diagram shows how the moon moves from the position of Full Moon back again to New Moon, or conjunction with the sun. During this latter part of her course the moon rises later and later every night, until, when she assumes the form of a waning crescent, she is visible only in the morning sky just before sunrise.

“Now, there is another interesting thing shown by this diagram,” I continued—but my companion, who had followed my explanations thus far with flattering attention, here suddenly ran to the door exclaiming:

“For mercy’s sake, what is happening to the moon?”

Footnote 1:

The Moon’s Path with Respect to the Sun and the Earth. ]

It may be well to add to what is said in the text about the orbit of the moon, that, while the moon does perform a revolution around the earth once a month, yet her orbit is drawn out, by the common motion of both earth and moon around the sun, into a long curve, whose radius is continually changing, but which is always concave toward the sun. This is illustrated in the accompanying diagram. Suppose we start with the earth at A. The moon is then between the sun and the earth, or in the phase of New Moon. The earth’s orbit at this point is more curved than the moon’s, and the earth is moving relatively faster than the moon. At B (First Quarter) the earth is directly ahead of the moon. But now the moon’s orbit becomes more curved than the earth’s and it begins to overtake the earth. At C (Full Moon) the moon has come up even with the earth, but on the opposite side from the sun. From that point to D (Last Quarter) the moon gains upon the earth until she is directly ahead of it. Then, from D to E (New Moon, once more) the earth gains until the two bodies are in the same relative positions which they occupied at A. Throughout the entire lunation, however, notwithstanding the changes which the shape of the moon’s orbit undergoes, the latter is constantly concave toward the sun. This shows that the sun’s attraction is really the governing force, and that the attraction of the earth simply serves to vary the form of the moon’s path, and cause it to move in a virtual ellipse with the earth for its focus.

I glanced over her shoulder, and saw a smudgy scallop in the moon’s edge.

“Really,” I said, “I am ashamed of myself. There is an eclipse of the moon to-night, and I had positively forgotten it! What you see is the shadow of the earth, which has the form of a long cone stretching away more than eight hundred thousand miles into space, and whenever our satellite at the time of Full Moon gets nearly in a direct line with the earth and the sun, it passes through that shadow and undergoes an eclipse. That is what is happening at the present moment.”

“And the shadow has a round form because the earth is round, I suppose.”

“Certainly; the shadow of a globe must have a circular outline. But the shadow of the earth, although it finally diminishes to a point, is, at the moon’s distance, still about 5,700 miles in diameter, or more than two and a half times the diameter of the moon. In consequence of the motion of the earth in its orbit around the sun, its shadow constantly moves eastward, like a great pencil of darkness sweeping straight across the heavens, but invisible to us except when the moon, traveling eastward faster than the shadow, overtakes and passes through it. This does not by any means happen at every full moon, because, for a reason which I shall explain presently, the moon usually passes either above or below the shadow of the earth, and thus escapes an eclipse. When an eclipse does occur it lasts a long time because the shadow is moving in the same direction as the moon. The moon must pass entirely through it before the eclipse ends. On this occasion the moon will be in the shadow more than three hours, and during an hour and a half she will be totally immersed. We shall have plenty of time, then, to observe the phenomenon, and after you have satisfied your curiosity a little by watching the slow advance of the shadow movement across the moon, we can return to our diagram and finish its explanation before the eclipse becomes total.”

Accordingly, after having watched the progress of the eclipse for half an hour, during which time the shadow began perceptibly to diminish the moonlight in the park, we returned to the lamplight and the diagram on the table.

“I was saying,” I resumed, “that another interesting thing in addition to the cause of the moon’s changing phases is represented here. You observe that a little cross stands on each of the four circles representing the moon, and that, in every case, the cross is in the center of that side of the moon which faces the earth. In fact the position of the cross upon the moon is fixed and invariable, and it always points toward the earth because the moon makes exactly one rotation on her axis in the course of one revolution around her orbit, or, as it is often called, one lunation. We know that this is so because we always see the same features of the lunar surface, no matter where the moon may be situated. This is true although, in consequence of the phases, we cannot see the whole face of the moon except when she is full. But whether it is the New Moon, or First Quarter, or Full Moon, or Last Quarter, or Old Moon, that we look at, the mountains and plains visible are identically the same. If the moon did not turn once on her axis in going once around the earth we would see all of her sides in succession, although only at Full Moon could we see an entire hemisphere illuminated by the sun. At Old and New Moon the side presented to the earth would be just the opposite to that presented at Full Moon. At Last Quarter the side facing the earth would be the opposite to that facing the earth at First Quarter.”

“But, tell me,” said my friend, “how did the moon ever come to so humiliating a pass that she must be forever turning on her heel to face the earth?”

“That,” I replied, “is a result of the same forces which originally separated her from the earth and gradually pushed her off to her present distance. In a word it is due to ‘tidal friction.’ Before the moon had solidified, the attraction of the earth raised huge tides in her molten mass. These tides acted on the rotating moon like brakes on a wheel, and at length they slowed down her rotation until its period became identical with that of her revolution around the earth. For the mathematical calculations on which all this is based you must go to Professor Darwin’s book on ‘The Tides,’ or some similar technical treatise; but I imagine you will never do that.”

“Not just at present, I assure you. I do not know what unexpected ambition for the acquirement of scientific knowledge may arise after I have seen those wonders that you have promised to show me in the moon, but, for the moment, I am content to accept your statement of the simple fact.”

“Good!” I replied. “And now, perhaps, you will have the patience to listen to an explanation of a very important relation which exists between the moon and the earth. We are led to it by what I have just said concerning tides. You know, of course that the tides in the oceans are due principally to the attraction of the moon. The sun also raises tides in the seas, but the moon, being so much nearer than the sun, is the chief agent in producing them. Sometimes the moon and the sun act together; at other times they pull in different directions. At Full Moon and at New Moon they pull together, because then they are either on opposite sides of the earth, or both on the same side. At such times we have the highest tides in all our seaports. That occurs about once every fortnight. But when the moon is at either First or Last Quarter, as you will perceive by looking at the diagram, her position, as seen from the earth, is at a right angle with a line drawn to the sun. Then the sun raises tides in one direction and the moon in another direction. The result is that at such periods the tides are lowest. An exact knowledge of these things is very important for mariners because there are harbors whose channels can be navigated by large ships only when the tides are high. Tables predicting the times and heights of the tides have been prepared for all the principal seaports of the world. In truth, the moon renders important services to the inhabitants of the earth, not merely in supplying them with a certain amount of light in the absence of the sun, but also in enabling them to navigate waters which are too shallow for ships except when deepened by the tide. The tides also, in many cases, serve to scour out channels and keep them open.”

“Really, I am quite interested, and the more so because I find the moon, like a dutiful daughter, trying to be of some use to her mother. But have I not heard that the tides occur on both sides of the earth at once, and not simply on the side where the moon happens to be at the time? Please tell me how that can be so?”

“A complete reply to your question would carry us into the realm of mathematical physics, but perhaps I can throw a little light upon the matter with the aid of this second diagram.

The Moon and the Tides. ]

“The eclipse is not yet total,” I continued, glancing out of the door, “and we can finish our explanation before it becomes so. Have the kindness, then, to look at the diagram. Suppose E to be the center of the earth, and M the center of the moon. The protuberant portions of the earth C A D and D B C represent the waters of the ocean pulled away from the surface of the earth, if I may so describe it, by the moon’s attraction. You are probably aware that the attraction of gravitation varies with the distance of the attracting body. The distance from the center of the earth to the center of the moon is about 239,000 miles. But the earth being nearly 8,000 miles in diameter, the surface of the ocean at A is about 4,000 miles nearer to the moon than is the center of the earth E. It follows that the force of the moon’s attraction is greater at A than at E. If the water of the ocean were a fixed, solid part of the earth there would be no perceptible effect resulting from this difference in the amount of the moon’s attraction. But since the water is free to move, to a certain extent, it yields to the attraction, and is drawn up a little toward the moon. At the same time it is, in effect, drawn away from C and D. The consequence is the production of a tide on the side facing the moon.