A young girl, with short garments terminating ten or twelve inches above the feet, will, in walking forward, appear to sink towards the Earth, the space between which and the bottom of the clothes will appear to gradually diminish, and in the distance of half-a-mile the limbs, which were first seen for ten or twelve inches, will be invisible—the bottom of the garment will seem to touch the ground.
A small dog running along will appear to gradually shorten by the legs, which, in less than half a mile, will be invisible, and the body appear to glide upon the earth.
Horses and cattle moving away from a given point will seem to have lost their hoofs, and to be walking upon the outer bones of the limbs.
Carriages similarly receding will seem to lose that portion of the rim of the wheels which touches the Earth; the axles will seem to get lower; and at the distance of a few miles, the body will appear to drag along in contact with the ground. This is very remarkable in the case of a railway carriage when moving away upon a straight and level portion of line several miles in length. These instances, which are but a few of what might be quoted, will be sufficient to prove, beyond the power of doubt or the necessity for controversy, that upon a plane or horizontal surface, the lowest part of bodies receding from a given point of observation will disappear before the higher. This is precisely what is observed in the case of a ship at sea, when outward bound—the lowest part—the hull, disappearing before the higher parts—the sails and mast head. Abstractedly, when the lowest part of a receding object thus disappears by entering the “vanishing point,” it could be seen again to any and every extent by a telescope, if the power were sufficient to magnify at the distance observed. This is to a great extent practicable upon smooth horizontal surfaces, as upon frozen lakes or canals; and upon long straight lines of railway. But the power of restoring such objects is greatly modified and diminished where the surface is undulating or otherwise moveable, as in large and level meadows, and pasture lands generally; in the vast prairies and grassy plains of America; and especially so upon the ocean, where the surface is always more or less in an undulating condition. In Holland and other level countries, persons have been seen in winter, skating upon the ice, at distances varying from ten to twenty miles. On some of the straight and “level” lines of railway which cross the prairies of America, the trains have been observed for more than twenty miles; but upon the sea the conditions are altered, and the hull of a receding vessel can only be seen for a few miles, and this will depend very greatly—the altitude of the observer being the same, upon the state of the water. When the surface is calm, the hull may be seen much farther than when it is rough and stormy; but under ordinary circumstances, when to the naked eye the hull has just become invisible, or is doubtfully visible, it may be seen again distinctly by the aid of a powerful telescope. Although abstractedly or mathematically there should be no limit to this power of restoring by a telescope a lost object upon a smooth horizontal surface, upon the sea this limit is soon observed; the water being variable in its degree of agitation, the limit of sight over its surface is equally variable, as shown by the following experiments:—In May, 1864, on several occasions when the water was unusually calm, from the landing stairs of the Victoria pier at Portsmouth, and from an elevation of 2 ft. 8 in. above the water, the greater part of the hull of the Nab Light-ship was, through a good telescope, distinctly visible; but on other experiments being made, when the water was less calm, no portion of it could be seen from the same elevation, notwithstanding that the most powerful telescopes were employed. At other times half the hull, and sometimes only the upper part of the bulwarks, were visible. If the hull had been invisible from the rotundity of the Earth, the following calculation will show that it should at all times have been 24 feet below the horizon:—The distance of the light-ship from the pier is 8 statute miles. The elevation of the observer being 32 inches above the water, would require 2 miles to be deducted as the distance of the supposed convex horizon; for the square of 2 multiplied by 8 inches (the fall in the first mile of the Earth’s curvation) equals 32 inches. This deducted from the 8 miles, will leave 6 miles as the distance from the horizon to the light ship. Hence 6² × 8 in. = 288 inches, or 24 feet. The top of the bulwarks, it was said, rose about 10 ft. above the water line; hence, deducting 10 from 24 feet, under all circumstances, even had the water been perfectly smooth and stationary, the top of the hull should have been 14 feet below the summit of the arc of water, or beneath the line of sight! This one fact is entirely fatal to the doctrine of the Earth’s rotundity. But such facts have been observed in various other places—the north-west light-ship in Liverpool Bay, and the light vessels of many other channels near the southern, eastern, and western shores of Great Britain. From the beach of Southsea Common, near Portsmouth, the observer lying down near the water, above the surface of which the eye was 2¹⁄₂ feet, and with a telescope looking across Spithead to the quarantine ship lying in the “Roads,” between Ryde and Cowes, in the Isle of Wight, a distance of 7 miles, the copper sheathing of that vessel was distinctly seen, the depth of which was about 2 feet. Making the usual calculation in accordance with the doctrine of the Earth’s convexity, it will be seen that an arc of water ought to have existed between the two points, the summit of which arc should have been 16 feet above the copper sheathing of the vessel!
From an elevation of 2¹⁄₂ feet above the water opposite the Royal Yacht Club House, in West Cowes, Isle of Wight, the pile work and promenade of the pier at Stake’s Bay, near Gosport, and nearly opposite Osborne House, were easily distinguished through various telescopes: the distance is 7 miles, the altitude of the promenade 10 feet, and the usual calculation will show that this pier ought to have been many feet below the horizon!
It is a well-known fact that the light of the Eddystone lighthouse is often plainly visible from the beach in Plymouth Sound; and sometimes, when the sea is very calm, persons can see it distinctly when sitting in ordinary rowing boats in that part of the Sound which will allow the line of sight to pass between Drake’s Island and the western end of the Breakwater. The distance is 14 statute miles. In a list of lighthouses in a work called “The Lighthouses of the World,” by A. G. Findlay, F.R.G.S., published in 1862, by Richard H. Lawrie, 53, Fleet Street, London, it is said, at page 28:—“In the Tables the height of the flame above the highest tide high water level is given, so that it is the minimum range of the light; to this elevation 10 feet is added for the height of the deck of the ship above the sea. Besides the increased distance to which low water will cause the light to be seen, the effect of refraction will also sometimes increase their range.” In the “Tables” above referred to, at page 36 the Eddystone light is said to be visible 13 miles. But these 13 miles are nautical measure; and as 3 nautical miles equal 3¹⁄₂ statute miles, the distance at which the Eddystone light is visible is over 15 statute miles. Notwithstanding that the Eddystone light is actually visible at a distance of 15 statute miles, and admitted to be so both by the Admiralty authorities and by calculation according to the doctrine of rotundity, very often at the same distance, the lantern is not visible at an elevation of 4 feet from the water; showing that the law of perspective, previously referred to, is greatly influenced by the state of the surface of the water over which the line of sight is directed. A remarkable illustration of this influence is given in the Western Daily Mercury, published in Plymouth, of October 25, 1864. Several discussions had previously taken place at the Plymouth Athenæum and the Devonport Mechanics’ Institute, on the true figure of the Earth; subsequent to which a committee was formed for the purpose of making experiments bearing on the question at issue. The names of the gentlemen as given in the above-named journal were “Parallax” (the author of this work), “Theta” (Mr. Henry, a teacher in Her Majesty’s Dock-yard, Devonport), and Messrs. Osborne, Richards, Rickard, Mogg, Evers, and Pearce, all of Plymouth. From the report published as above stated, the following quotation is made:—Observation 6th: “On the beach, at 5 feet from the water level, the Eddystone was entirely out of sight.”
The matter may be summarized as follows:—At any time when the sea is calm and the weather clear, the Light of the Eddystone, which is 89 feet above the foundation on the rock, may be distinctly seen from an elevation of 5 feet above the water level; according to the Admiralty directions, it “may be seen 13 nautical (or 15 statute) miles,”[41] or one mile still farther away than the position of the observers on the above-named occasion; and yet on that occasion, and at a distance of only 14 statute miles, notwithstanding that it was a very fine autumn day, and a clear back ground existed, not only was the lantern, which is 89 feet high, not visible, but the top of the vane, which is 100 feet above the foundation was, as stated in the report, “entirely out of sight.”
[41] “Lighthouses of the World,” p. 36.
FIG. 32.