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(9183) R. W. G. says: I am sincerely interested in knowing the shape and motions of the earth. Please answer the following questions in Notes and Queries:
1. Have any surveys ever been made to determine whether the known curvature of the earth’s surface is convex or concave?
A. All surveys of any extended portion of the surface of the earth demonstrate that the surface of the earth is convex. No line a mile long run for a canal in which water is to flow can be run without taking into the measurement the convexity of the earth, which is almost exactly 8 inches in one mile. For two miles it is very nearly 32 inches. See any book upon leveling or geodetic surveying for the mathematics of this. The fact that the surface of still water is a convex surface shows that the surface of the earth is convex, since water covers about three-quarters of the earth’s surface. It is said that an Englishman a few years ago wagered that no one could prove that the surface of the earth was convex, and put the money in the hands of the editor of a sporting paper. A surveyor took up the wager and set stakes of the same height in a lake a mile apart, and proved that the middle of the three stakes was eight inches above the two on either side of it. The editor decided that this was proof and paid over the money.
2. If so, who made the survey, and when?
A. Every survey which runs a level for any number of miles demonstrates the convexity of the earth’s surface. The survey to establish the length of the meter in France about 1780 is such a survey. All the work of the United States Coast and Geodetic Survey is such work. The laying out of great irrigation canals in the West and the surveying of public lands of the United States are also examples. The pendulum method is also complete as a demonstration of the shape of the earth.
3. Are there any demonstrable proofs of the earth’s rotation upon its axis?
A. The terrestrial proofs of the earth’s rotation upon its axis are equally conclusive. The principal ones are the eastward deviation of bodies dropped from a great height, the Foucault experiment with a long pendulum, and the gyroscope. Besides these may be mentioned the deviation of projectiles to the height in the northern hemisphere, the trade winds, and the rotation of cyclones. All of these are discussed at considerable length in the work of Young referred to above. If our correspondent is not convinced by these demonstrations he would hardly be convinced ‘‘though one rose from the dead.’’
4. Are there any demonstrable proofs that the earth moves around the sun? All the proofs given in Young’s, Newcomb’s, or Proctor’s works are astronomical that must depend for their truth on something that is assumed, and as a proof founded on an assumption is no proof until the assumption is proven, I want a demonstrable proof that is not founded on an assumption, if there be such an one.
A. From the nature of the case, there can be no terrestrial proofs of the earth’s revolution around the sun. This is an astronomical fact. The aberration of light and the parallax of the stars are explicable only by the earth’s revolution around the sun. These have satisfied astronomers for nearly a century and will still be deemed satisfactory. They may be ‘founded on an assumption,’’ but an assumption is entirely legitimate, and proof for the assumption will establish its truth as certainly as proof of fact from which a law may be deduced, will establish that law.—Notes and Queries Department, Scientific American, Sept. 26, 1903.
In the above we have a collection of the most important so called proofs of the popular system of astronomy; and inasmuch as the Scientific American is one of the oldest and most widely circulated scientific publications in America, if not in the world, we may consider that the statements contain the best possible arguments in support of the usual conclusions concerning the earth’s form and motion. We therefore devote the Court of Inquiry Department of this issue to consideration of these so called proofs—notwithstanding the fact that all of the points have been covered, one by one, many times in the past in the columns of this publication. The correspondent of the Scientific American asks four pertinent questions relative to geodesy and astronomy—particularly concerning (a) whether surveys have been made to determine definitely the contour of the earth; (b) and if so, when and where; (c) concerning proofs of the theory of the earth’s diurnal rotation; and (d) proofs of the earth’s motion about the sun.
The strength of these proofs is indicated in the remark, “‘If our correspondent is not convinced by these demonstrations, he would hardly be convinced ‘though one rose from the dead,’’’—which means, in this case, that if one is not satisfied with the proofs as given above there are no more forceful arguments to use, no further proofs to present, no further facts to cite. As an example of how thoroughly the editor of the Notes and Queries department of the Scientific American may be mistaken in general, we refer particularly to his statements concerning the Englishman and surveyor. We note that ‘‘the surveyor set stakes of the same height in a lake a mile apart, and proved that the middle of the three stakes was eight inches above the two on either side of it. The editor decided that this was proof, and paid over the money.”’
Would the writer of the above be surprised that the ‘‘surveyor’’ was none other than Professor A. Russell Wallace; that the site of the experiment was on the Old Bedford Canal northeast of London; that the distance viewed through the telescope was six miles, instead of two; that but one stake was used—and that one midway between two bridges six miles apart; that the stake in each of several observations was below the cross-hair of the leveled telescope; and that notwithstanding the fact that the money was paid to Professor Wallace, the Englishman finally recovered his wager? We are familiar with all the facts of the famous Wallace-Hampden wager, having in our possession the literature published subsequent to the experiment—the reports of the referees, diagrams, and arguments used by both sides.
So likewise are such statements as the following inaccurate and untrue: ‘All surveys of any extended portion of the earth demonstrate that the earth is convex. No line a mile long run for a canal in which water is to flow, can be run without taking into the measurement the convexity of the earth, which is almost exactly eight inches to the mile. The fact that the surface of still water is a convex surface shows that the surface of the earth is convex, since water covers about three-fourths of the earth’s surface.” We not only most emphatically deny that the surface of still water is convex, but we authoritatively declare from the basis of known facts of actual demonstration, that the waters of all rivers, canals, lakes, bays, seas, and oceans the world over, are concave.
Not only are canals laid out and constructed without taking the earth’s curvature into consideration, but there is absolutely no necessity for making any allowance for convexity. In laying out canals so that the surface of the water flowing through the same may be parallel to the datum line all the way across, processes of leveling are employed. We have quoted authorities on this subject many times before. On page 74 of Johnson’s ‘Theory and Practice of Surveying,”’ these processes are described; they involve the back and foresight method, concerning which Professor Johnson says that ‘‘the effect of the earth’s curvature is eliminated by so doing, however long the sights may be.”’ By this method a canal could be surveyed across a continent without making a single measurement with reference to any tangent of the earth’s supposed arc of convexity, and without a single calculation relative to the ratio of the earth’s curvature. The reason for this is that in this leveling the operators level their instruments at each setting, and therefore follow the curvature of the earth, no matter what may be the ratio, and no matter whether that curvature be convex or concave.
However, there are kinds of surveys employed in which doubtless surveyors believe they are making allowance for convexity—but certainly they do not claim to do so in canal surveying. Canals were surveyed and accurately constructed centuries before the idea was conceived that allowance for convexity is virtually made in certain surveys. In geodetic works, tables of the earth’s curvature are given “corrected for refraction.’’ Why do these tables appear? To enable the surveyors to build elevated stations so that they may be seen from other stations at low altitudes and at given distances; they are also used in connection with formulas for observations at one station only. To explain: Suppose at the beginning of a short canal one observation only should be made through a levelled transit. A target placed one mile away would be 5 or 6 inches higher than the transit, and so on according to the square of the distance; so that it becomes necessary where such a method is employed to get the datum line by deducting the amount of divergence of the visual line and the earth’s surface; but this divergence is not due to convexity, but to optical factors operative in conjunction with the upward curvation of the visual line.
In certain kinds of surveying these tables become necessary because there is an appearance of convexity—a deceptive appearance due entirely to incurvation of the lines of vision, and to vertical perspective and geolinear foreshortening. The whole system of modern astronomy rests upon this optical illusion, which deceives the astronomer as well as the surveyor. There is no more evidence that the earth is convex because it appears to be so, than there is evidence that the two metallic lines of a railway track actually approach each other because they appear to do so.
The famous survey about 1780 for the purpose of determining the length of the meter, which is one ten-millionth part of the earth’s arc from the pole to the equator, demonstrates the curvature of the earth north and south, but it contained not a single element to show that that arc is convex. Geodetic surveys prove that the earth is a sphere; and all the extended surveys—coast surveys and surveys of public lands—show conclusively that the earth is not flat, but spherical; but the modern scientific mind is wholly unwarranted in concluding that because it is not flat it must be convex; or that because it is demonstrated that the earth curves about 8 inches to the mile, it must curve convexly. Not one of these proofs of the earth’s sphericity determines the direction of the earth’s curvature.
But to refer to the first question, “Have any surveys been made to determine whether the known curvature of the earth’s surface is convex or concave?’ Is the editor of the Scientific American not aware that such a survey was instituted and successfully conducted in 1897, on the Gulf coast of Florida? If he is not aware of it, it might be an addition to his stock of scientific knowledge if he were apprised of the fact that the earth’s demonstrated concavity enters as a most important factor in the subject of astronomy—even as an essentially new element in the explanation of all cosmic phenomena. The facts of this survey are in no way in conflict with the facts of other surveys; but its methods are more direct in that they serve as a definite test of the earth’s surface.
Having determined by means of this survey that the surface upon which we live is actually concave, we insist that all astronomical phenomena not only may be, but must be explained from the basis of the entirely new conception of universal relations. There are no facts which may be suggested as in conflict with our definite conclusions because, first, Nature presents no conflicting evidences concerning the character of the universe; second, we accept all facts of astronomical, geodetic, geographical, and geological research. Neither are there any phenomena that can be used as a basis of argument against the conclusion that the earth is concave, because from the known basis of the earth’s concavity we fully explain and interpret all phenomena.
The hypothesis of the earth’s motion is contingent upon the idea that the earth is a convex body. If the earth is not convex, there is no possible chance of the earth’s supposed diurnal and annual motions; and in the discussion of the subject, we may pivot the whole question upon the actual shape of the earth. If we possessed no proof whatever that the earth is a concavity, we should have as much right to assume that it is so as the other side has to assume that it is convex; and if from the basis of assumed concavity we should explain all the various phenomena of the heavens, as well as the so called proofs of the earth’s motion; and if in addition to explaining all the usual astronomical phenomena, we should solve all the unsolved problems which confront the scientific world, we should have the decided advantage of the other side. But the Koreshan premise is demonstrated; consequently there is no possible chance of the Copernican hypothesis being true.
The prevailing astronomical hypotheses or assumptions were put forth in the effort of the mind to reach a conception of universal relations from the basis of deceptive appearances; the hypotheses have served to explain in a way, the most common phenomena of the heavens—for the hypotheses were framed in accordance with appearances. But now if proofs of these hypotheses are asked for, the facts that the hypotheses are intended to explain, are offered as proofs that the hypotheses are true. At one point it is said that such and such phenomena can be explained upon no other basis; and at another point the same phenomena are said to prove the hypotheses! A consistent fallacy may devise an apparent fitness of fact and conclusion; but if the premise is wrong its conclusions cannot be true, even though they present an apparent harmony.
It is obvious that if there were no other way of explaining the action of Foucault’s pendulum and gyroscope, the deviation of projectiles, trade-winds, and the rotation of cyclones, than that put forth in modern astronomy, we might consider the earth’s rotation a probability, and likewise, if there were no other possible explanation of the aberration of light and the parallax of the stars, the retrograde motion of the planets at certain points of their orbits, than upon the hypothesis of the earth’s annual motion about the sun, we might concede the possibility of such motion.
There can be no rational consideration of astronomical facts apart from the form of the earth; therefore, there are no astronomical phenomena which, independently of the primary assumption that the earth is a convex body, are at all suggestive of the earth’s motion through space—and it is frankly admitted in the above that there can be no terrestrial proofs of the earth’s mobility. Neither can there be any proofs of the earth’s diurnal rotation; and it is a fact that there are no positive proofs or demonstrations of the theory of the earth’s convexity.
The battle-ground between the old astronomy and the new Cosmogony is the earth’s surface. The premise is the main thing; the known contour of the earth, the direction of its curvature, must constitute the foundation—without which deceptive fallacies must result. The astronomical world will not long remain satisfied with the present conclusion concerning the relation of the earth and sun. The fact of the earth’s concavity will create a far greater revolution in astronomy than the newly discovered properties of radium have produced in modern physics and chemistry, which are now undergoing radical changes.
Editorial transcription checked against the cited scans; the historical claims remain those of The Flaming Sword.
The Flaming Sword · Vol. 17, No. 47 · Oct 9, 1903 · PDF pp. 10-12