Part 4

An argument for the Earth’s convexity is thought by many to be found in the following facts:--“Fluid or semi-fluid substances in a state of motion invariably assume the globular form, as rain, hail, dew, mercury, and melted lead, which, poured from a great height becomes divided into spherical masses, as in the manufacture of small shot, &c.” “There is abundant evidence from geology that the Earth has been a fluid or semi-fluid mass, and it could not, therefore, continue in a state of motion through space without becoming spherical.” Without denying that the Earth has been, at some former period, in a pulpy or semi-fluid state, it is requisite to prove beyond all doubt that it has a motion upon axes and through space, or the conclusion that it is therefore spherical is premature and illogical. It will be shown in a subsequent part of this work, that such axial and orbital motion does not exist, and therefore any argument founded upon and including it as a fact is necessarily fallacious. In addition to this, it may be remarked that the tendency in falling fluids to become globular is owing to what has been called “attraction of cohesion” (not “attraction of gravitation”), which is very limited in its operation. It is confined to small quantities of matter. If, in the manufacture of small shot, the melted metal is allowed to fall in masses of several ounces or pounds, instead of being divided into particles weighing only a few grains, it will never take a spherical form, and shot of an inch in diameter could not be made by this process. Bullets of even half-an-inch diameter can only be made by casting the metal into spherical moulds. In tropical countries, the rain instead of falling in drops or small globules, often comes down in large irregular masses, which have no approximation whatever to sphericity. So that it is manifestly unjust to affirm of large masses of matter like the Earth that which only belongs to minute portions or a few grains in weight. The whole matter taken together entirely fails as an argument for the Earth’s rotundity.

Those who hold that the Earth is a globe will often affirm, with visible enthusiasm, that in an eclipse of the Moon there is proof positive of rotundity. That the shadow of the Earth upon the Moon is always round; and that nothing but a globe could, in all positions, cast a circular shadow. Here again the essential requirements of an argument are wanting. It is _not proved_ that the Moon is eclipsed _by a shadow_. It is _not proved_ that the _Earth moves_ in an orbit, and therefore takes _different positions_. It is _not proved_ that the Moon receives her light from the Sun, and that therefore her surface is darkened by the Earth intercepting the Sun’s light. It will be shown in the proper place that the Earth has no motion in space or on axes; that it is not a shadow which eclipses the Moon; that the Moon is not a reflector of the Sun’s light, but is _self-luminous_; and therefore could not possibly be obscured by _a shadow_ from any object whatever. The subject is only introduced here because it forms one of the category of supposed evidences of the Earth’s rotundity. But to call that an argument where every necessary proposition is assumed, is to stultify both the judgment and the reasoning powers!

Many place great reliance upon what is called the “spherical excess” observed in levelling, as a proof of the Earth’s rotundity. In Castle’s Treatise on Levelling it is stated that “the angles taken between any three points on the surface of the Earth by the theodolite, are, strictly speaking, spherical angles, and their sum must exceed 180 degrees; and the lines bounding them are not the chords as they should be, but the tangents to the Earth. This excess is inappreciable in common cases, but in the larger triangles it becomes necessary to allow for it, and to diminish each of the angles of the observed triangle by one-third of the spherical excess. To calculate this excess, divide the area of the triangle in feet by the radius of the Earth in seconds and the quotient is the excess.”

The following observation as made by surveyors, also bears upon the subject:--If a spirit-level or theodolite be “levelled,” and a given point be read upon a graduated staff at the distance of about or more than 100 chains, this point will have an altitude slightly in excess of the altitude of the cross-hair of the theodolite; and if the theodolite be removed to the position of the graduated staff and again levelled, and a backward sight taken to the distance of 100 chains, another excess of altitude will be observed; and this excess will go on increasing as often as the experiment or backward and forward observation is repeated. From this it is argued that the line of sight from the spirit-level or theodolite is a tangent, and that the surface of the Earth is therefore spherical.

Of a similar character is the following observation:--If a theodolite or spirit-level be placed upon the sea-shore, and “levelled,” and directed towards the sea, the line of the horizon will be observed to be a given amount below the cross-hair of the instrument, to which a certain dip, or inclination from the level will have to be given to bring the cross-hair and the sea horizon together. It is concluded that as the sea horizon is always observed to be below the cross-hair of the “levelled” theodolite, the line of sight is a tangent, the surface of the water convex, and therefore the Earth is a globe.

[Illustration: FIG. 21.]

The conclusion derived from the last three observations is exceedingly plausible, and would completely satisfy the minds of scientific men as to the Earth’s sphericity if a perfect explanation could not be given. The whole matter has been specially and carefully examined; and one very simple experiment will show that the effects observed do not arise from rotundity in the Earth’s surface, but from a certain peculiarity in the instruments employed. Take a convex lens or a magnifying glass and hold it over a straight line drawn across a sheet of paper. If the glass be so held that a part of the straight line can be seen _through_ it, and another part seen _outside_ it, a difference in the _direction_ of the line will be observed, as shown in the diagram Figure 21. Let A B C represent a straight line. If a lens is now held an inch, or more, according to its focal length, over the part of the line A B, and the slightest amount out of its centre, that part of the line A B which passes under the lens will be seen in the direction of the figures 1.2; but if the lens be now moved a little out of its central position in the opposite direction, the line B C will be observed at 3.4, or below B C. A lens is a magnifying glass because it _dilates_ or spreads out from its centre the objects observed through it Therefore whatever is magnified by it is seen a little out of its axis or centre. This is again necessitated by the fact that the axis or actual centre is always occupied by the cross-hair. Thus the line-of-sight in the theodolite or spirit-level not being axial or absolutely central, reads upon a graduated staff a position which is necessarily slightly divergent from the axis of vision; and this is the source of that “spherical excess” which has so long been considered by surveyors as an important proof of the Earth’s rotundity. In this instance, as, indeed, in all the others given as evidence that the Earth is a globe, the premises do not fully warrant the conclusion--which is premature,--drawn before the whole subject is fairly examined; and when other causes are amply sufficient to explain the effects observed.

SECTION 2.

THE EARTH NO AXIAL OR ORBITAL MOTION.

If a ball be allowed to drop from the mast-head of a ship _at rest_, it will strike the deck at the foot of the mast. If the same experiment be tried with a ship _in motion_, the same result will be observed. Because, in the latter case, the ball is acted upon simultaneously by two forces at right angles to each other--one, the momentum given to it by the moving ship in the direction of its own motion, and the other the force of gravity, the direction of which is square to that of the momentum. The ball being acted upon by the two forces together will not go in the direction of either, but will take a diagonal course, as shown in the following diagram, Figure 22.

[Illustration: FIG. 22.]

[Illustration: FIG. 23.]

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. So far, there need be no discussion--the explanation is granted. But now let the experiment be modified in the following way:--Let the ball be thrown _upwards from_ the mast-head of a moving vessel; it will partake as before of two motions, the upward and the horizontal, and will take a diagonal course upwards and with the vessel until the two forces expend themselves, when it will begin to fall by the force of gravity only, and drop into the water far behind the ship, which is still moving horizontally. Diagram Figure 23 will illustrate this effect. The ball being thrown upwards in the direction A C, and the vessel moving from A to B, will cause it to pass in the direction A D, arriving at D when the vessel reaches B; the two forces having expended themselves when the ball arrives at D, it will begin to descend by the force of gravity in the direction D B H, but during its fall the vessel will have reached the position S, so that the ball will drop far behind it at the point H. To bring the ball from D to S _two forces_ would be required, as D H and D W; but as D W does not exist, the force of gravity operates _alone_, and the ball necessarily falls behind the vessel at a distance proportionate to the altitude attained at D, and the time occupied in falling from D to H.

The same result will be observed on throwing a ball directly upwards from a railway carriage when in rapid motion, as shown in the following Figure 24. While the carriage or tender passes from A to B, the ball thrown from A to C will reach the position D, but while the ball then comes down by the force of gravity, _operating alone_, to the point H, the carriage will have advanced to W, so that the ball will always drop more or less behind the carriage, according to the force first given to it in the direction A C and the time occupied in ascending to D, and thence descending to H. It is therefore demanded that if the Earth had a motion upon axes from west to east, and a ball, instead of being dropped down a mine or allowed to fall from the mast head of a ship, be _shot upwards_ into the air; from the moment of its beginning to descend the surface of the Earth would turn from under its direction, and it would fall behind or to the west of its line of descent. On making the experiment _no such effect is observed_, and therefore the conclusion is unavoidable, that the Earth DOES NOT MOVE UPON AXES!

[Illustration: FIG. 24.]

[Illustration: FIG. 25.]

The following experiment has been tried, with the object of obtaining definite results. If the Earth is a globe, having a circumference of 25,000 miles at the equator, the circumference at the latitude of London (51°) will be about 16,000 statute miles; so that the motion of the Earth’s surface, if 25,000 miles in 24 hours at the equator, in England would be more than 700 feet per second. An air-gun was firmly fixed to a strong post, as shown at A in Figure 25, and carefully adjusted by a plumb-line, so that it was perfectly vertical. On discharging the gun, the ball ascended in the direction A C, and invariably (during several trials) descended within a few inches of the gun at A; twice it fell back upon the very mouth of the barrel. The average time that the ball was in the atmosphere was 16 seconds; and, as half the time would be required for the ascent and half for the descent, it is evident that if the Earth had a motion once round its axis in 24 hours, the ball would have passed in 8 seconds to the point D, while the air-gun would have reached the position B H. The ball then commencing its descent, requiring also 8 seconds, would in that time have fallen to the point H, while the Earth and the gun would have advanced as far as W. The time occupied being 8 seconds, and the Earth’s velocity being 700 feet per second, the progress of the Earth and the air-gun to W, in advance of the ball at H, would be 5,600 feet! In other words, in these experiments, the ball, which always fell back to the place of its detachment, should have fallen 5,600 feet, or considerably more than one statute mile to the west of the air-gun! Proving beyond all doubt that the supposed axial motion of the Earth DOES NOT EXIST!

The same experiment ought to suffice as evidence against the assumed motion of the Earth in an orbit; for it is difficult, if not impossible, to understand how the behaviour of the ball thrown from a vertical air-gun should be other in relation to the Earth’s forward motion in space than it is in regard to its motion upon axes. Besides, if it is proved _not_ to move upon axes, the assumption that it moves in an orbit round the Sun is useless for theoretical purposes, and there is no necessity for either denying or in any way giving it farther consideration. But that no point may be taken without direct evidence, let the following experiment be tried:--Take two carefully-bored iron tubes, about two yards in length, and place them, one yard asunder, on the opposite sides of a wooden frame, or a solid block of wood or masonry; so adjust them that their axes of vision shall be perfectly parallel to each other, and direct them to the plane of some notable fixed star, a few seconds previous to its meridian time. Let an observer be stationed at each tube; and the moment the star appears in the first tube, let a knock or other signal be given, to be repeated by the observer at the second tube when he first sees the star. A distinct period of time will elapse between the signals given, showing that the same star is not visible at the same moment by two lines of sight parallel to each other and only one yard asunder. A slight inclination of the second tube towards the first would be required for the star to be seen at the same moment. If now the tubes be left in their position for six months, the same star will be visible at the same meridian time, without the slightest alteration being required in the direction of the tubes. 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 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! It will be useless to say in explanation that the stars are so infinitely distant that a difference in the angle of inclination of the tube in six months could not be expected, as it will be proved in a subsequent section that _all_ the stars are within a few thousand miles from the Earth’s surface!

SECTION 3.

THE TRUE DISTANCE OF THE SUN AND STARS.

As it is now demonstrated that the Earth is a plane, the distance of the Sun and Stars may readily be measured by plane trigonometry. The base line in any operation being horizontal and always a carefully measured one, the process becomes exceedingly simple. Let the altitude of the Sun be taken on a given day at 12 o’clock at the high-water mark on the sea shore at Brighton, in Sussex; and at the same hour at the high-water mark of the River Thames, near London Bridge; the difference in the Sun’s altitude taken simultaneously from two stations upon the same meridian, and the distance between the stations, or the length of the base line ascertained, are all the elements required for calculating the exact distance of the Sun from London or Brighton; but as this distance is the hypothenuse of a triangle, whose base is the Earth’s surface, and vertical side the zenith distance of the Sun, it follows that the distance of the Sun from that part of Earth to which it is vertical is less than the distance from London. In the Diagram, Figure 26, let L B represent the base line from London to Brighton, a distance of 51 statute miles. The altitude at L and at B taken at the same moment of time will give the distance L S or B S. The angle of altitude at L or B, with the length of L S or B S, will then give the vertical distance of the Sun S from E, or the place which is immediately underneath it. This distance will be thus found to be considerably less than 4,000 miles.

[Illustration: FIG. 26.]

The following are the particulars of an observation made, a few years ago, by the officers engaged in the Ordnance survey. Altitude of the Sun at London 55° 13′; altitude taken at the same time, on the grounds of a public school, at Ackworth, in Yorkshire, 53° 2′; the distance between the two places in a direct line, as measured by triangulation, is 151 statute miles. From these elements the true distance of the Sun may be readily computed; and proved to be under 4,000 miles!

Since the above was written, an officer of the Royal Engineers, in the head-quarters of the Ordnance Survey, at Southampton, has furnished the following elements of observations recently made:--

Southern Station, Sun’s altitude, 45° Northern ditto, „ „ 38° Distance between the two stations, 800 statute miles.

The calculation made from these elements gives the same result, viz., that the actual distance of the Sun from the Earth is less than 4,000 miles.

The same method of measuring distances applies equally to the Stars; and it is easy to demonstrate, beyond the possibility of doubt, so long as assumed premises are excluded, that all the visible objects in the firmament are contained within the distance of 6,000 miles!

From these demonstrable distances it follows unavoidably that the _magnitude_ of the Sun, Moon, Stars, &c., is very small--much smaller than the Earth from which they are measured; and to which therefore they cannot possibly be other than secondary, and subservient.

SECTION 4.

THE SUN MOVES IN A CIRCLE OVER THE EARTH, CONCENTRIC WITH THE NORTH POLE.

As the Earth has been shown to be fixed, the motion of the Sun is a visible reality; and if it be observed from any northern latitude, and for any period before and after the time of southing, or passing the meridian, it will be seen to describe an arc of a circle; an object moving in an arc cannot return to the centre of such arc without having completed a circle. This the Sun does visibly and daily. To place the matter beyond doubt, the observation of the Arctic navigators may be referred to. Captain Parry, and several of his officers, on ascending high land in the vicinity of the north pole, repeatedly saw, for 24 hours together, the sun describing a circle upon the southern horizon.

SECTION 5.

THE DIAMETER OF THE SUN’S PATH IS CONSTANTLY CHANGING--DIMINISHING FROM DECEMBER 21ST TO JUNE 15TH, AND ENLARGING FROM JUNE TO DECEMBER.

This is a matter of absolute certainty, proved by what is called, in technical language, the northern and southern declination, which is simply saying that the Sun’s path is nearest the north pole in summer, and farthest away from it in winter. This difference in position gives rise to the difference of altitude, as observed at various periods of the year, and which is shewn in the following table, given in “The Illustrated London Almanack,” for 1848, by Mr. Glaisher, of the Royal Observatory, Greenwich.

“Sun’s altitude at the time of Southing, or being on the meridian:--

Sun’s Time of Southing. altitude. M. S. (Common clock, or London mean time.) June 15 62° 0 4 before noon. „ 30 61²⁄₃° 3 18 afternoon. July 15 59²⁄₃° 5 38 „ „ 31 56¹⁄₂° 6 4 „ Aug. 15 52¹⁄₂° 0 11 „ „ 31 47° 0 5 „ Sep. 15 38²⁄₃° 4 58 before noon. „ 30 35¹⁄₂° 10 6 „ Oct. 31 24° 16 14 „ Nov. 30 17° 10 58 „ Dec. 21 12° 0 27 „ „ 31 15° 3 29 afternoon. Jan. 1 15¹⁄₂° 3 36 „ „ 15 17° 9 33 „ „ 31 21° 13 41 „ Feb. 15 25° 14 28 „ „ 29 30¹⁄₂° 12 43 „ March 15 {On the Equator} 36° 9 2 „ { at 6 a.m. } 38¹⁄₂° 0 0 „ „ 21 42¹⁄₂° 4 10 before noon. April 15 48° 0 8 „ „ 30 53° 2 58 „ May 15 57° 3 54 „ „ 31 60° 2 37 „

In the following diagram (Fig. 27) A A A represent the Sun’s daily path on December 21st, and B B B the same on June 15th. N the North Pole, S the Sun, E Great Britain. The figures 1 2 3 the Arctic Circle, and 4 5 6 the extent of sunlight. The arrows show the direction of the Sun’s motion.

[Illustration: FIG. 27.]

SECTION 6.

CAUSE OF DAY AND NIGHT, SEASONS, &c.