Parallax

“ Another experiment conducted by Parallax the same morning was creditable to his ingenuity. Nothing better, perhaps, was ever devised to deceive people, apparently by ocular evidence, into the belief that the earth is flat—nor is there any clearer evidence of the largeness of the earth's globe compared with our ordinary measures. On the Hoe, some ninety or a hundred feet above the sea-level, he had a mirror suspended in a vertical position facing the sea, and invited the bystanders to look in that mirror at the sea-horizon. ”

“ The earth-flatteners form a considerable section of the paradoxical family. They experienced a practical rebuff, a few years since, which should to some degree have shaken their faith in the present chief of their order. To do this chief justice, he is probably far less confident about the flatness of the earth than any of his disciples. Under the assumed name of Parallax he visited most of the chief towns of England, propounding what he calls his system of zetetic astronomy. Why he should call himself Parallax it would be hard to say ”

“ These bodies go on nearly in great circles while their motion continues swift; but about the end of their course, when that part of their apparent motion which arises from the parallax bears a greater proportion to their whole apparent motion, they commonly deviate from those circles; and when the earth goes to one side, they deviate to the other; and this deflection, because of its corresponding with the motion of the earth, must arise chiefly from the parallax ”

“ Our nearest neighbor among the stars, so far as known, has a parallax of less than 1′′. A parallax as great as 1′′ would indicate a velocity of something like 1,500 miles per second. Either the Nova is very near us, or else the velocity of the Nebula is almost inconceivably great. Indeed, if the parallax should prove to be too small for measurement, the fact would imply a velocity so great that it might be better explained as a motion of light, rather than of matter. ”

“ Another consideration has made these authors enlarge this distance a little more: for since the moon's diameter is rather more than a quarter of the earth's diameter, if the sun's parallax be supposed 15 seconds, the body of the moon would be larger than that of Mercury, viz. a secondary planet larger than a primary one, which seems repugnant to the regular proportion and symmetry of the mundane system. ”

“ The quantity of the horizontal parallax of any object is in proportion to its distance from the place of observation, being greater or less as the object is nearer to or farther removed from the spectator. ”

“ On land, not bordering on the sea, any mode of attempting to ascertain the horizon amounts almost to absurdity. Another obstacle to ascertaining the horizon is parallax, which, though in itself it is ascertainable, admitting the earth to be a perfect sphere, yet as the observation for parallax is necessarily affected by refraction, it must, inevitably, partake of the uncertainty which is always attendant on refraction: other considerations might easily be adduced, but more would appear unnecessary. ”

“ Actual change of position on our own part is found indeed to be invariably accompanied by an apparent displacement of the objects about us, such apparent displacement as a result of our own change of position being known as "parallax." ”

“ She’s like a soda water bottle with the cork out. You can’t do anything till all the gas has escaped.”
“I’ll just go down and see how the Sports Committee are getting along. Oh, by the way, I’ve booked you and Ethel for our houseboat at Henley.”
“Thanks. I’ll remember.”
On the lawn below Lady Marchendale’s terrace garden Lord Parallax was flirting with a clever and audacious little woman in grey and silver. Ostensibly they were playing croquet, while old Percival Kex, Esq., sat in a French cane chair under the lime tree, and quizzed Parallax when he came within range. ”

“ It would be rash, therefore, even if no other evidence were available, to reject the faith that the earth is a globe because, as seen from a balloon, it looks like a basin. Indeed, to be strictly logical, the followers of Parallax ought on this account to adopt the faith that the earth is not flat, but basin-shaped, which hitherto they have not been ready to do. ”

“ The largest triangles we can measure are such as have the earth’s orbit for base, and the distance of a fixed star for altitude. The angular magnitude resulting from subtracting the sum of the two angles at the base of such a triangle from 180° is called the star’s parallax. ”

“ This connection between nearness and rapidity of proper motions is indeed what we should expect to find, since a given amount of real motion of the star along its orbit will produce a larger angular displacement, proper motion, the nearer the star is to the earth, and this fact has guided astronomers in selecting the stars to be observed for parallax, the proper motion being determined first and the parallax afterward. ”

“ A mean parallax of 8′′.796 is given by Mr. C. G. Abbot, based on a combination of results from a number of different methods, and this corresponds to a distance of 92,930,000 miles. To the astronomer, who seeks extreme exactness, the slightest difference is important. 143It should be noted that the figures 8′′.807 or 8′′.796 represent the parallactic displacement of the sun, as seen not from the opposite ends of the earth's entire diameter, but from opposite ends of its radius, or semi-diameter. Accordingly it is equal to half of the angle at S in Fig. ”

“ As we ascend, the Earth beneath us seems to recede—actually to sink away—while the horizon gradually and gracefully lifts a diversified slope stretching away farther and farther to a line that, at the highest elevation, seems to close with the sky. Thus upon a clear day, the æronaut feels as if suspended at about an equal distance between the vast blue oceanic concave above, and the equally expanded terrestrial basin below. ”

“ If he takes a position where the water surrounds him—as at the mast-head of a ship out of sight of land, or on the summit of a small island far from the mainland, the surface of the sea appears to rise up on all sides equally and to surround him like the walls of an immense amphitheatre. He seems to be in the centre of a large concavity, the edges of which expand or contract as he takes a higher or lower position. ”

“ 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. ”

“ It is geometrically demonstrable [181] that all the visible luminaries in the firmament are within a distance of a few thousand miles, not more than the space which stretches between the North Pole and the Cape of Good Hope; and the principle of measurement—that of plane triangulation—which demonstrates this important fact, is one which no mathematician, demanding to be considered a master in the science, dare for a moment deny. All these luminaries then, and the Sun itself, being so near to us, cannot be other than very small as compared with the Earth we inhabit. ”

“ It was considered that whether the surface were convex or horizontal, or whether the convexity were more or less than the supposed degree, would be of no consequence in practice if the spirit level or theodolite were employed to read both backwards and forwards; for whatever degree of convexity [55] existed, one “sight” would compensate for the other; and if the surface were horizontal, the same mode of levelling would apply. ”

“ If we stand upon the deck of a ship, or mount to the mast head; or go to the top of a mountain, or ascend above the Earth in a balloon, and look over the sea, the surface appears as a vast inclined plane rising up until in the distance it intercepts the line of sight. If a good mirror be held in the opposite direction, the horizon will be reflected as a well-defined mark or line across the centre, as represented in diagram, Figure 7.
Ascending or descending, the distant horizon does the same. It rises and falls with the [17] observer, and is always on a level with his eye. ”

“ 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 ball passing from A to C by the force of gravity, and having at the moment of its liberation received a momentum from the ship in the direction A B, will by the conjoint action of the two forces, take the direction A D, falling at D, just as it would have fallen at C had the vessel remained at rest. In this way, it is contended by those who hold that the Earth is a moving sphere, a ball allowed to fall from the mouth of a deep mine reaches the bottom in an apparently vertical direction, the same as it would if the Earth were motionless. ”

“ While the meridian line m N will in the course of 24 hours range round the whole circle of the heavens, and point successively in the direction n N, o N, p N, r N, s N, t N, and u N, the pendulum’s plane of vibration x y, whether at m, at n, at o, at p, at r, at s, at t, or at u, will always be parallel to itself, pointing invariably to the same star, and were a circular table placed under the pendulum, its plane of vibration, while really stationary, would appear to perform a complete revolution. ”

“ From which result it is concluded that if the Earth had moved a single yard in an orbit through space there would at least be the difference of time indicated by the signals, and the slight inclination of the tube which the difference in position of one yard required. But as no such difference in the direction of the tube is required, the conclusion is unavoidable that in six months a given meridian upon the Earth has not moved a single [71] yard, and that therefore the Earth has not the slightest degree of orbital motion—or motion at right angles to the meridian of a given star! ”

“ The photographic right ascensions gave the values 8-80" + 0.007" ± 0.0027" (Hinks) and 8.80" + 0.0067" + 0.0025" (Perrine) ; the micro metric observations gave the value 8.8o6"+0.004 (Hinks) . [2]
II. The velocity of light (q.v.) has been measured with all the precision necessary for the purpose. The latest result is 299,860 kilometres per second, with a probable error of perhaps 30 kilometres—that is, about the ten-thousandth part of the quantity itself. This degree of precision is far beyond any we can hope to reach in the solar parallax. ”

“ We impress a peculiar motion on the pendulum in setting it a going. The Earth is at the same time carrying the pendulum eastward, but at the pole the one motion will not interfere with the other. The only action of the Earth on the pendulum there is that of attracting it towards its own (the Earth’s) centre. But this attraction is exactly in the plane of vibration and merely tends to continue the oscillatory motion without disturbing it. It is otherwise if the experiment is made at some other point, say 20 degrees distant from the pole. ”