The bank having the altitude 1.3 and 2.4 will, in the distance of two or three miles (according to its depth) disappear to the eye of an observer placed at Figure 1; and the telegraph pole at Figure 2 will seem not to stand upon a bank at all, but upon the actual railway. The line 3.4 will merge into the line 1.2 at the point B, while the line 5.6 will only have descended to the position C.
FIG. 16.
Many other familiar instances could be given to show the true law of perspective; which is, that parallel lines appear in the distance to converge to one and the same datum line, but to reach it at different distances if themselves dissimilarly distant. This law being remembered, it is easy to understand how the hull of an outward-bound ship, although sailing upon a plane surface disappears before the mast-head. In [Figure 16], let A B represent the surface of the water; C H the line of sight; and E D the altitude of the mast-head. Then, as A B and C H are nearer to each other than A B and E D, they will converge and appear to meet at the point H, which is the practical, or, as it would be better to call it, the optical horizon. The hull of the vessel being contained within the lines A B and C H, must gradually diminish as these converge, until at H, or the horizon, it enters the vanishing point and disappears; but the mast-head represented by the line E D is still above the horizon at H, and will require to sail more or less, according to its altitude, beyond the point H before it sinks to the line C H, or, in other words, before the lines A B and E D form the same angle as A B and C H.
It will be evident also that should the elevation of the observer be greater than at C, the horizon or vanishing point would not be formed at H, but at a greater distance; and therefore the hull of the vessel would be longer visible. Or, if, when the hull has disappeared at H, the observer ascends from the elevation at C to a higher position nearer to E, it will again be seen. Thus all these phenomena which have so long been considered as proofs of the Earth’s rotundity are really optical sequences of the contrary doctrine. To argue that because the lower part of an outward-bound ship disappears before the highest the water must be round, is to assume that a round surface only can produce this effect! But it is now shown that a plane surface necessarily produces this effect; and therefore the assumption is not required, and the argument involved is fallacious!
It may here be observed that no help can be given to this doctrine of rotundity by quoting the prevailing theory of perspective. The law represented in the foregoing diagrams is the “law of nature.” It may be seen in every layer of a long wall, in every hedge and bank of the roadside, and indeed in every direction where lines and objects run parallel to each other; but no illustration of the contrary perspective is ever to be seen! except in the distorted pictures, otherwise cleverly and beautifully drawn as they are, which abound in our public and private collections.
The theory which affirms that parallel lines converge only to one and the same point upon the eye-line is an error. It is true only of lines equidistant from the eye-line. It is true that parallel lines converge to one and the same eye-line, but meet it at different distances when more or less apart from each other. This is the true law of perspective as shown by Nature herself; any other idea is fallacious and will deceive whoever may hold and apply it to practice.
As it is of great importance that the difference should be clearly understood, the following diagram is given. Let E L ([Figure 17]) represent the eye-line and C the vanishing point of the lines, 1 C 2 C; then the lines 3.4.5.6, although converging somewhere to the line E L, will not do so to the point C, but 3 and 4 will proceed to D and 5 and 6 to H. It is repeated, that lines equidistant from the datum will converge on the same point and at the same distance; but lines not equidistant will converge on the same datum but at different distances! A very good illustration of the difference is given in [Figure 18]. Theoretic perspective would bring the lines 1, 2, and 3 to the same datum line E L and to the same point A. But the true or natural law would bring the lines 2 and 3 to the point A because equidistant from the eye-line E L; but the line 1 being farther from E L than either 2 or 3, would be taken beyond the point A on towards C, until it formed the same angle upon the line E L as 2 and 3 form at the point A.
FIG. 17.