In order to convey a general idea of the causes of these phenomena, let ABCD, Fig. 35, be a glass trough filled with water, and let a small ship be placed at S. An eye situated about E, will see the top-mast of the ship S, directly through the plate of glass BD. Fix a convex lens _a_ of short focus upon the plate of glass BD, and a little above a straight line SE joining the ship and the eye; and immediately above the convex lens a place _a_ concave one _b_. The eye will now see, through the convex lens _a_, an _inverted_ image of the ship at S´, and through the concave lens _b_, an erect image of the ship at S´´, representing in a general way the phenomena shown in Fig. 33. But it will be asked, where are the lenses in nature to produce these effects? This question is easily answered. If we take a tin tube with glass plates at each end, and fill it with water, and if we cool it on the outside with ice, it will act like a _concave_ lens when the cooling effect has reached the axis; and, on the other hand, if we heat the same tube filled with water, on the outside, it will act as a _convex_ glass. In the first case the density of the water diminishes towards the centre, and in the second it increases towards the centre. The very same effects are produced in the air, only a greater tract of air is necessary for showing the effect produced, by heating and cooling it unequally. If we now remove the lenses _a_, _b_, and hold a heated iron horizontally above the water in the trough ABC, the heat will gradually descend, expanding or rendering rarer the upper portions of the fluid. If, when the heat has reached within a little of the bottom, we look through the trough at the ship S in the direction ES´, we shall see an inverted image at S´, and an erect one at S´´; and if we hide from the eye at E all the ship S, excepting the top-mast, we shall have an exact representation of the phenomenon in Fig. 33. The experiment will succeed better with oil in place of water; and the same result may be obtained without heat, by pouring clear syrup into the glass trough till it is nearly one-third full, and then filling it up with water. The water will gradually incorporate with the syrup, and produce, as Dr. Wollaston has shown, a regular gradation of density, diminishing from that of the pure syrup to that of the pure water. Similar effects may be obtained by using masses of transparent solids, such as glass, rock-salt, &c.