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Among the other arguments it must be mentioned that a rainbow never is seen greater than a semicircle: the higher the sun is, too, the smaller is the bow. As our countryman Virgil says:
And deep drinks
The mighty bow,
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when rain is brewing. But the threat the bow conveys is not the same whatever the quarter it has shown itself in. If it rises toward the south, it will bring a heavy fall. The rain in that quarter, such is its force, cannot be mastered by the strongest midday sun. If it shine toward the west, there will be only a dew or a light rain. If it rise in the east or thereabouts, it prognosticates fine weather. If, however, the bow is the sun’s reflection, why does it appear of far larger size than the sun himself? Just because there is a kind of mirror that exhibits objects on a far larger scale than that on which they are presented to it, increasing their form to a portentous magnitude: and in turn there is another kind that reduces the size. And tell me this again, why does an image assume the form of a circle if it does not answer to a circle? You may, perhaps, tell me why the colour of the bow is varied: why its shape is what it is, you will not be able to tell me except by citing some model after which it is formed. Now, other model there is none save that of the sun; when you admit that the rainbow receives its colour from him, it follows that it receives its shape also from him. In short, you and I are agreed that those colours by which its quarter of the heaven is adorned proceed from the sun. But on one point we are not agreed: you say that the colour is real; I maintain that it is only apparent. Whichever it is, real or apparent, it comes from the sun. On your assumption its sudden cessation cannot be explained, seeing that all other bright lights in the sky are dispelled gradually. Its sudden appearance and, at the same time, its sudden extinction make for my contention. For it is a peculiarity of a mirror that the reflection in it is not built up piecemeal, but all at once comes fully into being. Every image in it is destroyed, too, with as great rapidity as it was formed. For to the construction or removal of the images nothing is required but the presentation and withdrawal of the objects.
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In the rainbow-cloud whose nature is in question, there is no proper substance or material: there is only a sham and a likeness without reality. Will you be convinced that this is so? The proof is, the rainbow will cease if you conceal the sun. Place another cloud, I repeat, in front of the sun, and all the bright hues of the bow are gone. But what is to be said, you may ask, in explanation of the size of the bow which is considerably greater than that of the sun? I have already said that there are certain mirrors that multiply every object they reflect. I may now add that every object much exceeds its natural size when seen through water. Letters, however small and dim, are comparatively large and distinct when seen through a glass globe filled with water. Apples floating in a glass vessel seem more beautiful than they are in reality. The stars appear bigger if seen through a cloud, because our vision is blurred in the moisture, and cannot accurately grasp its object. This will become plain to demonstration if you fill a cup with water and throw a ring into it. While the ring lies right at the bottom its appearance is visible on the surface of the water. Anything, in fact, that is: seen through moisture appears far larger than. in reality it is. What wonder that the image of the sun, being seen in a moist cloud, should be reproduced on a scale larger than the original, and that for the two reasons indicated? The cloud contains the two elements, one like glass, which can transmit light, and one also of the character of water; at any rate, if it does not just yet contain the actual water, it is now forming it, its nature is already such as can easily be changed into water.