FIG. 18.
The subject of perspective will not be rendered sufficiently clear unless an explanation be given of the cause and character of what is technically called the “vanishing point.” Why do objects, even when raised above the earth, vanish at a given distance? It is known, and can easily be proved by experiment, that “the range of the eye, or diameter of the field of vision is 110°; consequently this is the largest angle under which an object can be seen. The range of vision is from 110° to 1°. * * The smallest angle under which an object can be seen is upon an average for different sights the 60th part of a degree, or one minute in space; so that when an object is removed from the eye 3000 times its own diameter, it will only just be distinguishable; consequently, the greatest distance at which we can behold an object, like a shilling, of an inch in diameter is 3000 inches or 250 feet.”[3] It may, therefore, be very easily understood that a line passing over the hull of a ship, and continuing parallel to the surface of the water, must converge to the vanishing point at the distance of about 3000 times its own elevation; in other words, if the surface of the hull be 10 feet above the water it will vanish at 3,000 times 10 feet; or nearly six statute miles; but if the mast-head be 30 feet above the water, it will be visible for 90,000 feet or over 17 miles; so that it could be seen upon the horizon for a distance of eleven miles after the hull had entered the vanishing point! Hence the phenomenon of a receding ship’s hull being the first to disappear, which has been so universally quoted and relied upon as proving the rotundity of the Earth is fairly and logically a proof of the very contrary! It has been misapplied in consequence of an erroneous view of the law of perspective, and the desire to support a theory. That it is valueless for such a purpose has already been shown; and that, even if there were no question of the Earth’s form involved, it could not arise from the convexity of the water, is proved by the following experiment:—Let an observer stand upon the sea-shore with the eye at an elevation of about six feet above the water, and watch a vessel until it is just “hull down.” If now a good telescope be applied the hull will be distinctly restored to sight! From which it must be concluded that it had disappeared through the influence of perspective, and not from having sunk behind the summit of a convex surface! Had it done so it would follow that the telescope had either carried the line-of-sight through the mass of water, or over its surface and down the other side! But the power of “looking round a corner” or penetrating a dense and extensive medium has never yet been attributed to such an instrument! If the elevation of the observer be much greater than six feet the distance at which the vanishing point is formed will be so great that the telescope may not have power enough to magnify or enlarge the angle constituting it; when the experiment would appear to fail. But the failure would only be apparent, for a telescope of sufficient power to magnify at the horizon or vanishing point would certainly restore the hull at the greater distance.
[3] “Wonders of Science,” by Mayhew, p. 357.
FIG. 19.
An illustration or proof of the Earth’s rotundity is also supposed to be found in the fact that navigators by sailing due east or west return in the opposite direction. Here, again, a supposition is involved, viz., that upon a globe only could this occur. But it is easy to prove that it could take place as perfectly upon a circular plane as upon a sphere. Let it first be clearly understood what is really meant by sailing due east and west. Practically it is sailing at right angles to north and south: this is determined ordinarily by the mariners’ compass, but more accurately by the meridian lines which converge to the northern centre of the Earth. Bearing this in mind, let N in [Figure 19] represent the northern centre; and the lines N. S. the directions north and south. Then let the small arrow, Figure 1, represent a vessel on the meridian of Greenwich, with its head W. at right angles, or due west; and the stern E due east. It is evident that in passing to the position of the arrow, Figure 2, which is still due west or square to the meridian, the arc 1.2 must be described; and in sailing still farther under the same condition, the arcs 2.3, 3.4, and 4.1 will be successively passed over until the meridian of Greenwich, Figure 1, is arrived at, which was the point of departure. Thus a mariner, by keeping the head of his vessel due west, or at right angles to the north and south, practically circumnavigates a plane surface; or, in other words, he describes a circle upon a plane, at a greater or lesser distance from the centre N, and being at all times square to the radii north and south, he is compelled to do so—because the earth is a plane, having a central region, towards which the compass and the meridian lines which guide him, converge. So far, then, from the fact of a vessel sailing due west coming home from the east, and vice versa, being a proof of the earth’s rotundity, it is simply a phenomenon, consistent with and dependent upon its being a plane! The subject may be perfectly illustrated by the following simple experiment:—Take a round table, fix a pin in the centre; to this attach a thread, and extend it to the edge. Call the centre the north and the circumference the south; then, at any distance between the centre and the circumference, a direction at right angles to the thread will be due east and west; and a small object, as a pencil, placed across or square to the thread, to represent a ship, may be carried completely round the table without its right-angled position being altered; or, the right-angled position firmly maintained, the vessel must of necessity describe a circle on being moved from right to left or left to right. Referring again to the diagram, [Figure 19], the vessel may sail from the north towards the south, upon the meridian Figure 1, and there turning due west, may pass Cape Horn, represented by D, and continue its westerly course until it passes the point C, or the Cape of Good Hope, and again reaches the meridian, Figure 1, upon which it may return to the north. Those, then, who hold that the earth is a globe because it can be circumnavigated, have an argument which is logically incomplete and fallacious. This will be seen at once by putting it in the syllogistic form:—
A globe only can be circumnavigated:
The Earth has been circumnavigated:
Therefore the Earth is a globe.