The aërial troopers seen at Souterfell were produced by the very same process as the spectre of Dover Castle, having been brought by unequal refraction from one side of the hill to the other. It is not our business to discover how a troop of soldiers came to be performing their evolutions on the other side of Souterfell; but if there was then no road along which they could be marching, it is highly probable that they were troops exercising among the hills in secret, previously to the breaking out of the rebellion in 1745. The image of the Genevese barque which was seen sailing at a distance from the real one, arose from the same cause as the images of ships in the air; with this difference only, that in this case the strata of equal density were vertical or perpendicular to the water, whereas, in the former cases they were horizontal or parallel to the water. The state of the air which produced the lateral image may be produced by a headland or island, or even rocks, near the surface, and covered with water. These headlands, islands, or sunken rocks being powerfully heated by the sun in the daytime, will heat the air immediately above them, while the adjacent air over the sea will retain its former coolness and density. Hence there will necessarily arise a gradation of density varying in the same horizontal direction, or where the lines of equal density are vertical. If we suppose the very same state of the air to exist in a horizontal plane which exists in a vertical plane, in Fig. 36, then the same images would be seen in a horizontal line, viz., an inverted one at _s p_, and an erect one at _s´p´_. In the case of the Genevese barque, the rays had not crossed before they reached the eye, and therefore the image was an erect one. Had the real Genevese barque been concealed by some promontory or other cause from the observation of Messrs. Jurine and Soret, they might have attached a supernatural character to the spectral image, especially if they had seen it gradually decay, and finally disappear on the still and unbroken surface of the lake. No similar fact had been previously observed, and there were no circumstances in the case to have excited the suspicion that it was the spectre of a real vessel produced by unequal refraction.