[Illustration: FIG. 6.] [Illustration: FIG. 7.] The ship coming into view from the east would have to ascend an inclined plane for 20 miles until it arrived at the centre of the arc A B, whence it would have to descend for the same distance. The square of 20 miles multiplied by 8 inches gives 266 feet as the amount the vessel would be below the line C D at the beginning and at the end of the 40 miles. If we stand upon the deck of a ship, or mount to the mast head; or go to the top of a mountain, or ascend above the Earth in a balloon, and look over the sea, the surface appears as a vast inclined plane rising up until in the distance it intercepts the line of sight. If a good mirror be held in the opposite direction, the horizon will be reflected as a well-defined mark or line across the centre, as represented in diagram, Figure 7. Ascending or descending, the distant horizon does the same. It rises and falls with the observer, and is always on a level with his eye. If he takes a position where the water surrounds him--as at the mast-head of a ship out of sight of land, or on the summit of a small island far from the mainland, the surface of the sea appears to rise up on all sides equally and to surround him like the walls of an immense amphitheatre. He seems to be in the centre of a large concavity, the edges of which expand or contract as he takes a higher or lower position. This appearance is so well known to sea-going travellers that nothing more need be said in its support. But the appearance from a balloon is familiar only to a small number of observers, and therefore it will be useful to quote from those who have written upon the subject. “_The Apparent Concavity of the Earth as seen from a Balloon._--A perfectly-formed circle encompassed the visible planisphere beneath, or rather the concavo-sphere it might now be called, for I had attained a height from which the surface of the Earth assumed a regularly hollowed or concave appearance--an optical illusion which increases as you recede from it. At the greatest elevation I attained, which was about a mile-and-a-half, the appearance of the World around me assumed a shape or form like that which is made by placing two watch-glasses together by their edges, the balloon apparently in the central cavity all the time of its flight at that elevation.”--_Wise’s Aeronautics._ “Another curious effect of the aerial ascent was, that the Earth, when we were at our greatest altitude, positively appeared _concave_, looking like a huge dark bowl, rather than the convex sphere such as we naturally expect to see it. * * * The horizon always appears to be on a level with our eye, and seems to rise as we rise, until at length the elevation of the circular boundary line of the sight becomes so marked that the Earth assumes the anomalous appearance as we have said of a _concave_ rather than a _convex_ body.”--_Mayhew’s Great World of London._