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stratum of maximum density, and be directed towards an object also situated in that stratum, he will see it in two ways, directly through the uniformly dense air, and indirectly by rays reflected upwards through the lower strata. There will thus be two images seen, one erect by the unrefracted rays, the other inverted by the reflected ones. If the object be detached against the sky, this will also be represented round the inverted image, precisely as if the reflexion took place at the surface of water. See Fig. 203.
Such is the cause of a very curious phænomenon, which the French army observed very frequently in Egypt. The whole of lower Egypt is a vast horizontal plain, broken only by a few eminences, on which the villages are built, to be out of the reach of the inundations of the Nile. In the morning and evening the appearance of the country is such as the real disposition of the objects naturally presents, but in the middle of the day when the ground is heated by an unclouded Sun, the prospect seems bounded on all sides by a general flood; the villages appear like islands in the midst of an immense lake, and under each is seen its image inverted just as it would be given by water. As you approach one of them, the bounds of this apparent inundation retire, the lake which surrounded the village seems to sink away from it, and at length goes to play round some more distant basis. "Thus," says Monge, from whom this description was originally borrowed, "all circumstances concur to complete an illusion, which is sometimes cruel, especially in the desert, where it vainly presents the semblance of water, just at the time when it is most wanted." M. Biot says, that he has observed many phænomena of this kind on the sands at Dunkirk, and he has given the mathematical theory of them in the Memoirs of the Institute for 1809. He has shewn that the successive trajectories which go from the eye of the observer, intersect on their second branches, so as to form a caustic, underneath which, no object is visible. In Fig. 204, LT represents this caustic, and DMS is the limiting trajectory, touching the surface of the Earth.
All objects situated above MS, send but one image to the eye; those in the space SLT send two, one erect, the other inverted; those under the caustic MLT cannot transmit any rays at all to D, and are therefore invisible. In this manner a moving object, a man
