A common type of mirage is illustrated in Fig. 81. This is often visible on deserts where the hot sand causes the adjacent layer of air to expand and therefore, the refractive index to increase. This layer of air then may be considered to operate like an inverted prism. The rays of light close to the earth are bent convex to the earth and the curvature of those higher up may be reversed. The reason that an object may appear double, or as if mirrored by the surface of a nearby pond, is clearly shown in the illustration. Similar atmospheric conditions are found sometimes over pavements and over bodies of water. As one rides along in an automobile ascending an incline, if he closely observes at the moment the line of sight is just on the level of the pavement, he will often be rewarded by the sight of a mirage. An approaching pedestrian may have no feet (they are replaced by a bit of sky) and the distant pavement will appear to contain pools of water on its surface. Sometimes on deserts, over ice fields, or on northern seas, mirages are of the inverted type. A horseman or ship may appear suspended in the air in an inverted position. When the density of the air is great enough so that only the upper rays reach the eye, the object will be seen inverted and far above the surface upon which nothing is seen. Many modifications of these types are possible through variations in the refractive indices of various strata of air. Sometimes the air is stratified horizontally and even vertically, which results in magnification as well as other peculiar effects. As one rides over the desert in a rapidly moving train or automobile these vagaries of nature are sometimes very striking, because the speed of motion will make the effects of the varying refractive indices more marked. A distant foothill may appear to float in the air or to change its shape very rapidly. An island surrounded by quiet air and water may appear like a huge mushroom barely supported by a stem. Arctic mirages are no less wonderful than those of the hot barren deserts. While traveling along over the ice and snow distant white peaks may assume the most fantastic shapes. At first they may appear flattened like a table-land and then suddenly they may stretch upward like spires. They may shrink then spread like huge mushrooms supported by the stalk-like bases and stretching out laterally. Suddenly they may shoot upward into another series of pinnacles as if another range had suddenly arisen. Such antics may go on for hours as one travels along a frozen valley. Even a change of position of the eyes accompanying a change from erect to lying down may cause remarkable contortions of the distant mountains and one is reminded of the psalmist's query, "Why hop ye so, ye hills?"