The representation of the moon in pictures of the ordinary size (some three feet long by two in height) is a case in which the artist habitually—one may almost say invariably—departs greatly from scientific truth, and it is a question as to whether he is justified in what he does. Take first the case of the low-lying moon near the horizon as contrasted with the high moon. Everyone knows that the moon (and the sun[4] also) appears to be much bigger when it is low than when it is high. Everyone who has not looked into the matter closely is prepared to maintain that the luminous disc in the sky—whether of moon or of sun—not merely seems to, but actually does, occupy a bigger space when it is low down near the horizon than when it is high up, more nearly overhead. Of course, no one nowadays imagines that the moon or the sun swells as it sinks or diminishes in volume as it rises. Those who think about it at all, say that the greater length of atmosphere through which one sees the low sun or moon, as compared with the high, magnifies the disc as a lens might do. This, however, is not the case. If we take a photograph of the moon when low and another with the same instrument and the same focus when it is high, we find that the celestial disc produces on the plate (as it does on our eyes) a picture-disc of practically the same size in both positions. In fact, the high moon or sun produces a picture-disc of a little larger size than the low moon or sun. I have here reproduced (Pl. IV) a photograph, published by M. Flammarion, in which the moon has been allowed to print itself on a photographic plate exposed during the time the moon was rising, and it is seen that the track of the moon has not diminished in width as it rose higher and higher. No one will readily believe this, yet it is a demonstrable fact. Astronomers have made accurate measurements which show that there is no diminution of the disc under these circumstances, but a slight increase—since the moon is a very little nearer to us when overhead than when we see it across the horizon.
Plate IV.—The track of the rising moon registered by continuous exposure of a photographic plate. It is given here in order to show that the diameter of the visible disc of the moon does not diminish as it rises. The slight increase in the breadth of the track registered by the moon's disc is probably due to a little distortion caused by the side portion of the lens. After M. Flammarion. The actual width of the moon's disc as printed here is a little over one eighth of an inch, which, if we regard it as "a picture" and not merely as a mechanical record, implies that the observer's eye is only about 14-1/2 inches distant from the picture plane instead of the more usual 18 inches, which corresponds to a diameter of the pictured moon's disc of between 1/6th and 1/7th of an inch (.156 inch).
If we put a piece of glass coated with a thin layer of water-colour paint into a frame, and then make a peep-hole in a board which we fix upright between us and the upright piece of framed glass, we can keep the framed glass steady (let us suppose it to be part of the window of a room), and then we can move the peep-hole board back from it into the room to measured distances. At a distance of one and a half feet from the framed glass, which is that at which an artist usually has his eye from his canvas or paper, we can trace on the smeared or tinted piece of glass the outlines of things seen through it exactly as they fill up the area of the glass—men, houses, trees, the moon. The moon's disc (and the same is true of the sun) is found always to occupy a space on the glass which is 1/115th of the distance of the eye from the framed glass plate. When the eye-to-frame distance is eighteen inches, the diameter of the disc of the moon on the smeared glass will occupy exactly 1/115th of eighteen inches, which is between one-sixth and one-seventh of an inch. Similarly if the peep-hole is at nine and a half feet or 114 inches from the framed glass (which stands for us as the equivalent of an artist's picture) the moon will occupy almost exactly one inch in diameter—the size of a halfpenny. With such a simple apparatus of peep-hole and smeared glass in an upright frame, it is easy to mark off the size covered by the moon (or sun), whether low or high, on the smeared glass, and it is found never to vary whether high or low—so long as the same "eye-to-frame" or "peep-hole" distance is preserved. That seems to be an important fact for painters of sun-sets and moon-rises. But what do they do? They never give the right size (namely one-sixth of an inch) which corresponds to an eye-to-frame distance of eighteen inches. They give to a high moon, if they are very careful, a quarter of an inch for diameter. This means that the observer is about two and a half feet, or thirty inches from the picture—nearly twice what the artist's eye really is as he paints. And then—if painting a moon-rise or sunset—they suddenly pretend to go to a distance of nine and a half feet from the picture and make the moon an inch across because it is low down, or even give the moon two inches in diameter, which would mean that they (and those who look at the picture when hung up for view) are observing at nineteen feet distance from the front plane or frame of the picture. They do not alter the other features in the picture to suit this change of distance of the eye from the frame and there is no warning given. Certainly there is no obvious and necessary reason for treating a picture containing a high moon as though you were three feet from the front plane of the scene presented, and a low moon as though you were twenty feet from that plane! The confusion which may result in the representation of other objects when these changes of eye-to-frame distance are made is shown by the following simple facts. According to the simple laws of perspective, if the eye is at thirty inches from the picture-plane or frame (as declared by a moon drawn of a little more than a quarter of an inch broad), a post or a man six feet high drawn on the canvas as three inches high absolutely and definitely means that that man or post is sixty feet away from the observer inside the picture. The height of the represented object is the same fraction of the real object as the eye-to-frame distance is of the distance of the observer to the real object. If by a two-inch moon the artist has thrown you back from the front plane of the scene to a distance of nineteen feet, then the six-foot post or man drawn as three inches high definitely asserts that it or he is 456 feet distant within the picture. So, too, if the church tower which cuts the moon is really sixty feet high and is drawn of two inches vertical measure in the picture, it is an assertion—when the moon is represented one quarter of an inch broad—that the church tower is 290 yards, or a sixth of a mile distant. If, on the other hand, other things remaining the same, the moon is drawn two inches in diameter, the church tower is now asserted to be eight times as far off, or about a mile and a third. Very generally these facts are not considered by painters. They represent the low moon (or sun) big because the erroneous mental impression is common to all of us that it is big—that is, bigger, much bigger, than the high moon or sun, and they do not follow out the consequences in perspective of the pictorial increase of the moon's apparent diameter.
If we could ascertain why it is that the low moon produces a false impression of being bigger—as a mere disc in the scene—than does the high moon, we might be able to discover how an artist could produce, as Nature does, an impression or belief in its greater size whilst keeping it all the time to its proper size. The explanation of the illusion as to the increased size of the sun's or moon's disc when low, given by M. Flammarion and other astronomers, is that the low sun or moon is unconsciously judged by us as an object at a greater distance than the high moon or sun. This is due to the long vista of arching clouds above and of stretching landscape or sea below when the sun or moon is looked at as it appears on or near the horizon. The illusion is aided by the dulness of the low moon and the brightness (supposed nearness) of the high moon. Being judged of (unconsciously) as further off than the high moon, the low moon is estimated as of larger size although of the same size. This is, I believe, the correct explanation of the illusion. When one gazes upwards to the sky, a small insect slowly flying across the line of sight sometimes is "judged of" as a huge bird—an eagle or a vulture—since we refer it to a distance at which birds fly and not to the shorter distance to which insects approach us. It seems that it would be possible for the painter, by carefully studying actual natural facts and introducing their presentation into his picture, to produce the impression of greater distance, and therefore of size, into a quarter-inch moon placed near the horizon. He is not compelled for want of other means to "cut the difficulty" and paint a falsely inflated moon which shall brutally and by measurement call up the illusion of increased size. I reproduce here (Pl. V) an interesting drawing which shows how such illusions of size can be produced. It is none the worse for my purpose because it is an advertisement by the well-known firm who have kindly lent it to me. The three figures represented in black are all of the same height, yet the furthest one appears to be much taller and bigger altogether than the middle one, and the middle one than the nearest. This result is obtained by suggesting distance as separating the right-hand figure from us, whilst giving it exactly the same height as the others. This seems to me to be a simple case of an illusion of increased size produced by a suggestion of increased distance when all the time there is equality in size—as in the case of the moon on the horizon compared with the moon overhead. It would be interesting to see an attempt on the part of a competent painter to produce in this way (which is, I believe, Nature's way) the illusion of increased size in a low-lying moon without really increasing the visual size of his painted moon as compared with one in another picture (to be painted by him) representing the moon bright, clear and small, overhead.
Plate V.—Drawing of three figures—Lord Lansdowne, Mr. Lloyd George, and Mr. Asquith—showing how an illusion of size may be produced in a picture. The figure of Mr. Asquith is of the same actual vertical measurement as that of Lord Lansdowne, viz. two inches and one eighth. Yet owing to the position in which the three figures are placed and the converging lines—suggesting perspective—the drawing of Mr. Asquith does not merely represent a much taller man than does that of Lord Lansdowne, but actually gives the impression, at first sight, that the little black figure representing Mr. Asquith is longer and bigger altogether than that representing Lord Lansdowne. Yet the figures are of the same dimensions. It is owing to illusion of the same nature that the disc of the low moon appears larger than that of the high moon.
The theatrical scene-painter has another kind of difficulty with the low moon and the setting sun. He can never be right for more than one row of seats—one distance—in the theatre. Here there is no peep-hole, no frame or picture-plane. The observer is in the picture. If the moon is represented by an illuminated disc of one foot in diameter, it will, when looked at at a distance of 115 feet, have the same visual size as the moon itself, but if your seat is nearer the scene it will look too large, if further off it will look too small. There is no getting over this difficulty, as the standard of actual Nature is set up on the stage by the men and women appearing on it at a known distance. It used to be asked in classical times by ingenious puzzle-makers—"What is the size of the moon?" A true answer to that question would be "that of a plate a foot in diameter seen at a distance of a hundred and fifteen feet."