reaches us in a feeble and exhausted stream, because the force is dispersed in the reflexion.’
XVII. Here Sylla broke in: ‘All these things no doubt |F| have their probabilities; but the strongest point on the other side was either explained away or it escaped our comrade’s attention; which was it?’
‘What do you mean?’ said Lucius. ‘The problem of the half-moon, I suppose?’
‘Precisely,’ said Sylla, ‘for as all reflexion takes place at equal angles, there is some reason in saying that when the moon is in mid-heaven at half-moon, the light is not carried from her on to the earth, but glances off beyond it; for the sun, being |930| on the horizon, touches the moon with his rays, which will therefore, being reflected at equal angles, fall on the further side and beyond us, and will not send the light here; or else there will be a great distortion and variation in the angle, which is impossible.’
‘I assure you’, said Lucius, ‘that point was mentioned also;’ and here he glanced at Menelaus the mathematician, as he went on: ‘I am ashamed, dear Menelaus,’ he said, ‘in your presence to upset a mathematical assumption which is laid down as fundamental in all the Optics of Mirrors. But I feel obliged to say’, he continued, ‘that the law which requires reflexion in all cases to be at equal angles is neither self-evident |B| nor admitted. It is impugned in the instance of convex mirrors, when magnified images are reflected to the one point of sight. It is impugned also in that of double mirrors, when they are inclined towards one another so that there is an angle between them, and each surface returns a double image from one face, four images in all, two on the right, two on the left, two from the outer parts of the surfaces, two dimmer ones deep within the mirrors.[[333]] Plato[[334]] gives the cause why this takes place. He has told |C| us that if the mirrors be raised on either side, there is a gradual shifting of the visual reflexion as it passes from one side to the other. If then some images proceed directly to us, while others glance to the opposite side of the mirrors, and are returned thence to us, it is impossible that reflexion in all cases takes place at equal angles. They observe[[335]] that these images meet in one point, and further claim that the law of equal angles is disproved by the streams of light which actually proceed from the moon to the earth, holding the fact to be |D| far more convincing than the law. However, if we are so far to indulge the beloved geometry as to make her a present of this law, in the first place it may be expected to hold of mirrors which have been made accurately smooth. But the moon has many irregularities and rough parts, so that the rays proceeding from a large body, when they fall on considerable eminences, are exposed to counter-illuminations and reciprocal dispersion; the cross-light is reflected, involved, and accumulated as though it reached us from a number of mirrors. In the next place, even if we allow that the reflexions are produced at equal |E| angles upon the actual surface of the moon, yet, when the distance is so great, it is not impossible that the rays may be broken in their passage, or glance around, so that the light reaches us in one composite stream. Some go further, and show by a figure that many lights discharge their rays along a line inclined to the hypothenuse; but it was not possible to construct the diagram while speaking, especially before a large audience.[[336]]
XVIII. ‘Upon the whole question,’ he went on, ‘I am at a loss to see how they bring up the half-moon against us; the point fails equally upon her gibbous and crescent phases. For if the moon were a mass of air or fire which the sun illuminated, |F| he would not have left half her sphere always in shadow and darkness as seen by us; but even if he touched her in his circuit only in a small point, the proper consequence would follow, she would be affected all through, and her entire substance changed by the light penetrating everywhere with ease. When wine touches water on its extreme surface, or a drop of blood falls into liquid, the whole is discoloured at once, and turned to crimson. But the air itself, we are told, is not filled with sunshine by emanations or beams actually mingling with it, but by a change and alteration caused by something like a prick or touch. Now, how can they suppose that when star touches star or light light, it does not mingle with or alter the substance throughout, but only illuminates |931| those points which it touches superficially? The circular orbit of the sun as he passes about the moon, which sometimes coincides with the line dividing her visible and invisible parts, and at other times rises to right angles with that line so as to cut those parts in two, and in turn be cut by her, produces her gibbous and crescent phases by the varying inclination and position of the bright part relatively to that in shadow. This proves beyond all question that the illumination is contact not commixture, not accumulation of light but its circumfusion. But the fact that she is not only illuminated herself but also sends |B| on the image of her brightness to us, allows us to insist the more confidently on our theory of her substance. For reflexions do not take place on a rarefied body, or one formed of subtle particles, nor is it easy to conceive light rebounding from light, or fire from fire; the body which is to produce recoil and reflexion must be heavy and dense, that there may be impact upon it and resilience from it. To the sun himself the air certainly allows a passage, offering no obstructions or resistance; whereas if timber, stones, or woven stuffs be placed to meet his light many cross rays are caused, and there is illumination all |C| round them. We see the same thing in the way his light reaches the earth. The earth does not pass his ray into a depth as water does, nor yet throughout her whole substance as air does. Just as his orbit passes round the moon, gradually cutting off a certain portion of her, so a similar orbit passes round the earth, illuminating a similar part of it and leaving another unilluminated, for the part of either body which receives light appears to be a little larger than a hemisphere. Allow me to speak geometrically in terms of proportion. Here are three bodies approached by the sun’s light, earth, moon, air; we see that the moon is illuminated like the earth, not like the air; but bodies naturally affected in the same way by the same must be themselves similar.’
XIX. When all had applauded Lucius, ‘Bravo!’ said I, |D| ‘a beautiful proportion fitted to a beautiful theory; for you must not be defrauded of your own.’ ‘In that case,’ he said, with a smile, ‘I must employ proportion a second time, in order that we may prove the moon like the earth, not only as being affected in the same way by the same body, but also as producing the same effect on the same. Grant me that no one of the phenomena relating to the sun is so like another as an eclipse to a sunset, remembering that recent concurrence[[337]] of sun and moon, which, beginning just after noon, showed us |E| plainly many stars in all parts of the heavens, and produced a chill in the temperature like that of twilight. If you have forgotten it, Theon here will bring up Mimnermus and Cydias, and Archilochus, and Stesichorus and Pindar[[338]] besides, all bewailing at eclipse time “the brightest star stolen from the sky” |F| and “night with us at midday”, speaking of the ray of the sun as “a track of darkness” and, besides all these, Homer[[339]] saying that the faces of men are “bound in night and gloom” and “the sun is perished out of the heaven”, i.e. around the moon, and how this occurs according to Nature, “when one moon perishes and one is born”. The remaining points have been reduced, I think, by the accuracy of mathematical methods to the one[[340]] certain principle that night is the shadow of earth, whereas an eclipse of the sun is the shadow of the moon when it falls within our vision. When the sun sets he is blocked from our sight by the earth; when he is eclipsed, by the moon. |932| In both cases there is overshadowing; in his setting it is caused by the earth, in his eclipses by the moon, her shadow intercepting our vision. From all this it is easy to draw out a theory as to what happens. If the effect is similar, the agents are similar; for the same effects upon the same body must be due to the same agents. If the darkness of eclipses is not so profound, and does not affect the atmosphere so forcibly, let us not be surprised; the bodies which cause respectively night and eclipse are similar in nature, but unequal in size. The Egyptians, I believe, say that the moon’s bulk is one two-and-seventieth part of the earth’s, Anaxagoras made her as large as Peloponnesus; but |B| Aristarchus[[341]] proves that the diameter of the earth bears to that of the moon a ratio which is less than sixty to nineteen, and greater than a hundred and eight to forty-three. Hence the earth because of its size removes the sun entirely from our sight, the obstruction is great and lasts all night; whereas if the moon sometimes hides the sun entirely, yet the eclipse does not last long and has no breadth; but a certain brightness is apparent around the rim, which does not allow the shadow to be deep and absolute. Aristotle,[[342]] I mean the ancient philosopher, after giving other reasons why the moon is more |C| often visibly eclipsed than the sun, adds this further one, that the sun is eclipsed by the interposition of the moon,[[343]] [the moon by that of the earth and of other bodies also.] But Posidonius gives this definition of what occurs: an eclipse of the sun is a concurrence of the shadow of the moon with our vision[[344]] ... for there is no eclipse, except to those whose view of the sun can be intercepted by the shadow of the moon. In allowing that the shadow of the moon reaches to us, I do not know what he has left himself to say. There can be no shadow of a star; shadow means absence of light, and it is the nature of light to remove shadow, not to cause it.
XX. ‘But tell me’, he went on, ‘what proof was mentioned |D| next?’ ‘That the moon was eclipsed in the same way’, I said. ‘Thank you for reminding me’, he said. ‘But now am I to turn at once to the argument, assuming that you are satisfied, and allow that the moon is eclipsed when she is caught in the shadow, or do you wish me to set out a studied proof, with all the steps in order?’ ‘By all means,’ said Theon, ‘let us have the proof in full. For my own part, I still somehow need to be convinced; |E| I have only heard it put thus, that when the three bodies, earth, sun, and moon, come into one straight line eclipses occur, the earth removing the sun from the moon, or the moon the sun from the earth; that is, the sun is eclipsed when the moon, the moon when the earth, is in the middle of the three, the first case happening at her conjunction, the second at the half-month.’
Lucius replied: ‘These are perhaps the most important points mentioned; but first, if you will, take the additional argument drawn from the shape of the shadow. This is a cone, such as is caused by a large spherical body of fire or light overlapping a smaller body also spherical. Hence in eclipses the lines which mark off the dark portions of the moon from the bright give circular sections. For when one round body approaches |F| another, the lines of mutual intersection are invariably circular like the bodies themselves. In the second place, I think you are aware that the first parts of the moon to be eclipsed are those towards the East, of the sun those towards the West, |933| and the shadow of the earth moves from East to West, that of[[345]] the moon on the contrary to the East. This is made clear to the senses by the phenomena, which may be explained quite shortly. They go to confirm our view of the cause of the eclipse. For since the sun is eclipsed by being overtaken, the moon by meeting the body which causes the eclipse,[[346]] it is likely, or rather it is necessary, that the sun should be overtaken from behind, the moon from the front, the obstruction beginning from the first point of contact with the obstructing body. The moon comes up with the sun from the West as she races against him, the earth from the East because it is moving from the opposite direction. As a third point, I will ask you to |B| notice the duration and the magnitude of her eclipses. If she is eclipsed when high up and far from the earth, she is hidden for a short time; if near the earth and low down when the same thing happens to her, she is firmly held and emerges slowly out of the shadow; and yet when she is low her speed is greatest, when high it is least. The cause of the difference lies in the shadow; for being broadest about the base, like all cones, and tapering gradually, it ends in a sharp, fine head. Hence, if the moon be low when she meets the shadow, she is caught in the largest circles of the cone, and crosses its most profound and darkest part; if high, she dips as into a shallow pond, because the shadow is thin, and quickly makes her way out. |C| I omit the points of detail mentioned as to bases and permeations, which can also be rationally explained as far as the subject-matter allows. I go back to the theory put before us founded on our senses. We see that fire shines through more visibly and more brightly out of a place in shadow, whether because of the density of the darkened air, which does not allow it to stream off and be dispersed, but holds its substance compressed where it is, or whether this is an affection of our senses; as hot things are hotter when contrasted with cold, and pleasures are more intense by contrast with pains, so bright things stand out more clearly by the side of dark, setting the imagination on the alert by the contrast. The former cause appears the more |D| probable, for in the light of the sun everything in the nature of fire not only loses its brightness, but is outmatched and becomes inactive and blunted, since the sun’s heat scatters and dissipates its power. If then the moon possess a faint, feeble fire, being a star of somewhat turbid substance, as the Stoics themselves say, none of the effects which she now exhibits ought to follow, but the opposite in all respects; she ought to appear when she is now hidden, and be hidden when she now appears; be hidden, that is, all the time while she is dimmed by the surrounding |E| atmosphere, but shine brightly out at intervals of six months, or occasionally at intervals of five, when she passes under the shadow of the earth. (For of the 465 full moons at eclipse intervals, 404 give periods of six months, the remainder periods of five.) At such intervals then the moon ought to appear shining brightly in the shadow. But, as a fact, she is eclipsed and loses her light in the shadow, and recovers it when she has cleared the shadow; also she is often seen by day, which shows that she is anything but a fiery or starlike body.’
|F| XXI. When Lucius had said this, Pharnaces and Apollonides sprang forward together to oppose. Apollonides made way to Pharnaces, who observed that this is a very strong proof that the moon is a star or fire; for she does not disappear entirely in eclipses, but shows through with a grim ashy hue peculiar to herself. Apollonides objected to the word ‘shadow’, a term always applied by mathematicians to a region which is not |934| lighted, whereas the heavens admit of no shadow. ‘This objection’, I said, ‘is contentious, and addressed to the name, not to the thing in any physical or mathematical sense. If any one should prefer to call the region blocked by the earth not “shadow”, but “an unlighted place”, it is still necessarily true that the moon when it reaches that region is darkened. It is merely childish’, I went on, ‘not to allow that the shadow of the earth reaches it, since we know that the shadow of the moon, falling upon the sight and reaching to the earth, causes an |B| eclipse of the sun. I will now turn to you, Pharnaces. That ashy charred colour in the moon, which you say is peculiar to her, belongs to a body which has density and depth. For no remnant or trace of flame will remain in rarefied bodies, nor can burning matter come into existence, without a substantial body, deep enough to allow of ignition and to maintain it, as Homer[[347]] has somewhere said: