Edgar Poe - The Balloon-Hoax

Mr. ainsworth has not attempted to account for this phenomenon, which however, is quite susceptible of explanation. A line dropped from an elevation of 25,000 feet , perpendicularly to the surface of the earth (or sea), would form the perpendicular of a right-angled triangle, of which the base would extend from the right angle to the horizon, and the hypothenuse from the horizon to the balloon. But the 25,000 feet of altitude is little or nothing, in comparison with the extent of the prospect. In other words, the base and hypothenuse of the supposed triangle would be so long, when compared with the perpendicular, that the two former may be regarded as nearly parallel. In this manner the horizon of the aeronaut would appear to be on a level with the car. But, as the point immediately beneath him seems, and is, at a great distance below him, it seems, of course, also, at a great distance below the horizon. Hence the impression of concavity; and this impression must remain, until the elevation shall bear so great a proportion to the extent of prospect, that the apparent parallelism of the base and hypothenuse disappears—when the earth's real convexity must appear.