Zetetic astronomy: Earth not a globe! / An experimental inquiry into the true figure of the earth etc.

by Parallax

It is commonly believed that surveyors when laying out railways and canals, are obliged to allow 8 inches per mile for the Earth’s curvature; and that if this were not done in the latter case the water would not be stationary, but would flow on until at the end of one mile in each direction, although the canal should have the same depth throughout, the surface would stand 8 inches higher in the middle than at the ends. In other words, that the bottom of a canal in which the allowance of 8 inches per mile had not been made, would be a chord to the surface of the contained water, which would be an arc of a circle. To this it is replied, that both in regard to railways and canals, wherever an allowance has been attempted the work has not been satisfactory; and so irregular were the results in the earlier days of railway, canal, and other surveying, that, the most eminent engineers abandoned the practice of the old “forward levelling” and allowing for convexity; and adopted what is now called the “double sight” or “back-and-fore sight” method. 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 existed, one “sight” would compensate for the other; and if the surface were horizontal, the same mode of levelling would apply. So important did the ordnance department of the Government consider this matter, that it was deemed necessary to make the abandonment of all ideas of rotundity compulsory, and in a standing order (No. 6) of the House of Lords as to the preparation of sections for railways, &c., the following language is used, “That the section be drawn to the same horizontal scale as the plan; and to a vertical scale of not less than one inch to every one hundred feet; and shall show the surface of the ground marked on the plan, the intended level of the proposed work, the height of every embankment, and the depth of every cutting; and a datum HORIZONTAL LINE, which shall be the same throughout the whole length of the work, or any branch thereof respectively; and shall be referred to some fixed point stated in writing on the section, near some portion of such work; and in the case of a canal, cut, navigation, turnpike, or other carriage road, or railway, near either of the termini.” No. 44 of the standing orders of the House of Commons is similar to the above order (No. 6) of the House of Lords.

Thus it is evident that the doctrine of the Earth’s rotundity cannot be mixed up with the practical operations of civil engineers and surveyors, and to prevent the waste of time and the destruction of property which necessarily followed the doings of some who were determined to involve the convexity of the Earth’s surface in their calculations, the very Government of the country has been obliged to interfere! Every survey of this and other countries, whether ordnance or otherwise, is now carried out in connection with a horizontal datum, and therefore, as no other method proves satisfactory, it is virtually an admission by all the most practical scientific men of the day that the Earth cannot be other than a plane!

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.

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.