FIG. 71.
IT has already been proved that the astronomers of the Copernican school merely assumed the rotundity of the earth as a doctrine which enabled them to explain certain well-known phenomena. "What other explanation can be imagined except the sphericity of the earth?" is the language of Professor de Morgan, and it expresses the state of mind of all who hold that the earth is a globe. There is on their part an almost amusing innocence of the fact, than in seeking to explain phenomena by the assumption of rotundity, another assumption is necessarily involved, viz., that nothing else will explain the phenomena in question but the foregone and gratuitous conclusion to which they have committed themselves. To argue, for instance, that because the lower part of an outward-bound vessel disappears before the mast-head, the water must be round, is to assume that a round surface only can produce such an effect. But if it can be shown that a simple law of perspective in connection with a plane surface necessarily produces this appearance, the assumption of rotundity is not required, and all the misleading fallacies and confusion involved in or mixed up with it may be avoided.
Before explaining the influence of perspective in causing-the hull of a ship to disappear first when outward bound, it is necessary to remove an error in its application, which artists and teachers have generally committed, and which if persisted in will not only prevent their giving, as it has hitherto done, absolutely correct representations of natural things, but also deprive them of the power to understand the cause of the lower part of any receding object disappearing to the eye before any higher portion--even though the surface on which it moves is admittedly and provably horizontal.
In the first place it is easily demonstrable that, as shown in the following diagrams, fig. 71, lines which are equi-distant
"The range of the eye, or diameter of the field of vision, is
[paragraph continues] 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 sixtieth 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." 1
The above may be called the law of perspective. It may be given in more formal language, as the following:. when any object or any part thereof is so far removed that its greatest diameter subtends at the eye of the observer, an angle of one minute or less of a degree, it is no longer visible.
From the above it follows:--
1.--That the larger the object the further will it require to go from the observer before it becomes invisible.
2.--The further any two bodies, or any two parts of the same body, are asunder, the further must they recede before they appear to converge to the same point.
3.--Any distinctive part of a receding body will be-come invisible before the whole or any larger part of the same body.
The first and second of the above propositions are self-evident. The third may be illustrated by the following diagram, fig. 73.
Let A represent a disc of wood or card-board, say one foot in diameter, and painted black, except one inch diameter in the centre. On taking this disc to about a hundred feet away from an observer at A, the white centre will appear considerably diminished--as shown at B--and on removing it still further the central white will become invisible, the disc will appear as at C, entirely black. Again, if a similar disc is coloured black, except a segment of say one inch in depth at the lower edge, on moving it forward the lower segment will gradually disappear, as shown at A, B, and C, in diagram fig. 74. If the
disc is allowed to rest on a board D, the effect is still more striking. The disc at C will appear perfectly round--the white segment having disappeared.
The erroneous application of perspective already referred to is the following:--It is well known that on looking along a row of buildings of considerable length, every object below the eye appears to ascend towards the eye-line; and every thing above the eye appears to descend towards the same eye-line; and an artist, wishing to represent such a view on paper, generally adopts the following rule:--draw a line across the paper or canvas at the altitude of the eye. To this line, as a vanishing point, draw all other lines above and below it, irrespective of their distance, as in the diagram 75.
Let A, B, and C, D, represent two lines parallel but not equi-distant from the eye-line E, H. To an observer at E, the vanishing point of C, D, would be at H, because the lines C, D, and E, H, would come together at H, at an angle of one minute of a degree. But it is evident from a single glance at the diagram that H cannot be the vanishing point of A, B, because the distance E, A, being greater than E, C, the angle A, H, E, is also greater than C, H, E--is, in fact, considerably more than one minute of a degree. Therefore the line A, B, cannot possibly have its vanishing point on the line E, H, unless it is carried forward towards W. Hence the line A, W, is the true perspective line of A, B, forming an angle of one minute at W, which is the true vanishing point of A, B, as H is the vanishing point of C, D, and G, H, because these two lines are equidistant from the eye-line.
The error in perspective, which is almost universally committed, consists in causing lines dissimilarly distant from the eye-line to converge to one and the same vanishing point. Whereas it is demonstrable that lines most distant from an eye-line must of necessity converge less rapidly, and must be carried further over the eye-line before they meet it at the angle one minute, which constitutes the vanishing point.
A very good illustration of the difference is given in fig. 76. False or prevailing perspective would bring the lines A, B, and C, D, to the same point H; but the true or natural perspective
brings the line A, B, to the point W, because there and there only does A, W, E, become the same angle as C, H, E. It must be the same angle or it is not the vanishing point.
The law represented in the above diagram 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 in nature. In the pictures which abound in our public and private collections, however, it may too often be witnessed, giving a degree of distortion to paintings and drawings--otherwise beautifully executed, which
strikes the observer as very unnatural, but, as he supposes, artistically or theoretically correct.
The theory which affirms that all parallel lines converge to one and the same point on the eye-line, is an error. It is true only of lines equi-distant from the eye-line; lines more or less apart meet the eye-line at different distances, and the point at which they meet is that only where each forms the angle of one minute of a degree, or such other angular measure as may be decided upon as the vanishing point. This is the true law of perspective as shown by nature herself; any idea to the contrary is fallacious, and will deceive whoever may hold and apply it to practice.
In accordance with the above law of natural perspective, the following illustrations are important as representing actually observed phenomena. In a long row of lamps, standing on horizontal ground, the pedestals, if short, gradually diminish until at a distance of a few hundred yards they seem to disappear, and the upper and thinner parts of the lamp posts appear to touch the ground, as shown in the following diagram, fig. 77.
The lines A, B, and C, D, represent the actual depth or length of the whole series of lamps, as from C to A. An observer placing his eye a little to the right or left of the point E, and
looking along the row will see that each succeeding pedestal appears shorter than the preceding, and at a certain distance the line C, D, will appear to meet the eye-line at H--the pedestals at that point being no longer visible, the upper portion of each succeeding lamp just appears to stand without pedestal. At the point H where the pedestals disappear the upper portions of the lamps seem to have shortened considerably, as shown by the line A, W, but long after the pedestals have entered the vanishing point, the tops will appear above the line of sight E, H, or until the line A, W, meets the line E, H, at an angle of one minute of a degree. A row of lamps such as that above described may be seen in York Road, which for over 600 yards runs across the south end of Regent's Park, London.
On the same road the following case may at any time be seen.
Send a young girl, with short garments, from C on towards D; on advancing a hundred yards or more (according to the depth of the limbs exposed) the bottom of the frock or longest garment will seem to touch the ground; and on arriving at H, the vanishing point of the lines C, D, and E, H, the limbs will have disappeared, and the upper part of the body would continue visible, but gradually shortening until the line A, B, came in contact with E, H, at the angle of one minute.
If a receding train be observed on a long, straight, and horizontal portion of railway, the bottom of the last carriage will seem to gradually get nearer to the rails, until at about the
distance of two miles the line of rail and the bottom of the carriage will seem to come together, as shown in fig. 79.
The south bank of the Duke of Bridgewater's canal (which passes between Manchester and Runcorn) in the neighbourhood of Sale and Timperley, in Cheshire, runs parallel to the surface of the water, at an elevation of about eighteen inches, and at this point the canal is a straight line for more than a statute mile. On this bank eight flags, each 6 ft. high, were placed at intervals of 300 yards, and on looking from the towing path on the opposite side, the bank seemed in the distance to gradually diminish in depth, until the grass and the surface of the water converged to a point, and the last flag appeared to stand not on the bank but in the water of the canal, as shown in the diagram fig. 80.
The flags and the bank had throughout the whole length the altitude and the depth represented by the lines respectively A, B, and C, D.
Shooting out into Dublin Bay there is a long wall about three statute miles in length, and at the end next to the sea stands the Poolbeg Lighthouse. On one occasion the author sitting in a boat opposite "Irish Town," and three miles from the sea end
of the wall, noticed that the lighthouse seemed to spring from the water, as shown in the diagram fig. 81.
The top of the wall seemed gradually to decline towards the sea level, as from B to A; but on rowing rapidly towards A the lighthouse was found to be standing on the end of the wall, which was at least four feet vertical depth above the water. as seen in the following diagram, fig. 82.
From the several cases now advanced, which are selected from a great number of instances involving the same law, the third proposition (on page 203) that "any distinctive part of a body will become invisible before the whole or any larger part of the same body," is sufficiently demonstrated. It will therefore be readily seen that the hull of a receding ship obeying the same law must disappear on a plane surface, before the mast head. If it is put in the form of a syllogism the conclusion is inevitable:--
Any distinctive part of a receding object becomes invisible before the whole or any larger part of the same object.
The hull is a distinctive part of a ship.
Ergo, the hull of a receding or outward bound ship must disappear before the whole, inclusive of the mast head.
To give the argument a more practical and nautical character it may be stated as follows:
That part of any receding body which is nearest to the surface upon which it moves, contracts, and becomes in-visible before the parts which are further away from such surface--as shown in figs. 63, 64, 65, 66, 67, 68, 69, and 70.
The hull of a ship is nearer to the water--the surface on which it moves--than the mast head.
Ergo, the hull of an outward bound ship must be the first to disappear.
This will be seen mathematically in the following diagram, fig. 83.
The line A, B, represents the altitude of the mast head; E, H, of the observer, and C, D, of the horizontal surface of the sea. By the law of perspective the surface of the water appears to ascend towards the eye-line, meeting it at the point H, which is the horizon. The ship appears to ascend the inclined plane C, H, the hull gradually becoming less until on arriving at the horizon H it is apparently so small that its vertical depth subtends an angle, at the eye of the observer, of less than one minute of a degree, and it is therefore invisible; whilst the
angle subtended by the space between the mast-head and the surface of the water is considerably more than one minute, and therefore although the hull has disappeared in the horizon as the vanishing point, the mast-head is still visible above the horizon. But the vessel continuing to sail, the mast-head gradually descends in the direction of the line A, W, until at length it forms the same angle of one minute at the eye of the observer, and then becomes invisible.
Those who believe that the earth is a globe have often sought to prove it to be so by quoting the fact that when the ship's hull has disappeared, if an observer ascends to a higher position the hull again becomes visible. But this, is logically premature; such a result arises simply from the fact that on raising his position the eye-line recedes further over the water before it forms the angle of one minute of a degree, and this includes and brings back the hull within the vanishing point, as shown in fig. 84.
The altitude of the eye-line E, H, being greater, the horizon or vanishing point is formed at fig. 2 instead of at fig. 1, as in the previous illustration.
Hence the phenomenon of the hull of an outward bound vessel being the first to disappear, which has been so universally quoted and relied upon as proving the rotundity of the earth, is fairly, both logically and mathematically, a proof of the very contrary, that the earth is a plane. It
has been misunderstood and misapplied in consequence of an erroneous view of the laws of perspective, and the unconquered desire to support a theory. That it is valueless for such a purpose is now completely demonstrated.
203:1 "Wonders of Science," by Mayhew, p. 357.
