They also found a similar relation between the altitude and the apparent size of constellations. Fig. 80 is a reproduction of a diagram which Smith submitted as illustrating the cause of the illusion of apparent enlargement of heavenly bodies near the horizon. If the sky seems to be a flattened vault, the reason for the apparent decrease in the size of the sun, the moon, or the constellations, as they approach the zenith, is suggested by the diagram. It has also been suggested that such illusions as those shown in Figs. 10 and 19 are associated with that of apparent enlargement of heavenly bodies near the horizon. It will be left to the reader to decide whether or not there is any similarity or relation. Zoth appears to have proved, to his own satisfaction at least, that the chief factors are not aerial perspective, the apparent curvature or form of the sky, and the comparison of the sun or moon with objects of known size. He maintained that the illusion of apparent decrease in size as these bodies increase in altitude is due to the necessary elevation of the eye. No available experimental evidence seems to refute his statement. In fact, Guttman's experiments seem to confirm it to some extent. The latter found that there was an apparent diminution in the size of objects of several per cent, in objects slightly more than a foot distant from the eyes, as they were raised so that the line of vision changed from horizontal to an angle of forty degrees. The magnitude of this diminution is not sufficient to promote the acceptance of elevation of the eyes as a primary cause of the illusion in respect to the heavenly bodies. Notwithstanding arguments to the contrary, it is difficult to eliminate aerial perspective and the apparent form of the sky as important factors. That no explanation of this illusion has been generally accepted indicates the complexity of the causes. Certainly the reddish coloration of the sun and moon near the horizon and the contrast with the misty atmosphere combined with the general vague aspect of the atmosphere contribute something if no more than a deepening of the mystery. Variations in the transparency and brightness of the air must play some part. In discussing the great illusions of nature, it appears appropriate to introduce the mirage. This is not due to an error of sense of judgment. The eye sees what is presented but the inversions and other peculiar effects are due to variations in the refractive index of the atmosphere. These variations account for the appearance of "lakes" in arid deserts, of the inverted images of ships and icebergs on the sea and of "pools of water" on pavements. The refractive index of the atmosphere is continually changing, but the changes are chiefly of two types: (1) those due to irregular heating and (2) those due to normal variation with altitude. The former type are particularly responsible for mirages. [Illustration: Fig. 81.--Explanation of a common mirage.]