ARCS OF THE MERIDIAN.

The discrepancies and anomalies so often observed in pendulum experiments, have led the followers of Newton to seek the desired evidence in measurements of arcs of the meridian; but here again they are even more unfortunate than in their efforts with the pendulum. It is certain that the question when attempted to be answered by such measurements, is less satisfactory than was expected, and in many respects the results are contradictory.

"The determination of the exact figure of the earth (M. Biot remarks) has, for the last century and a half, been one of the constant aims of the labours of the French Academy of Sciences. From the time of the first measure of a degree by Picard, which enabled Newton to establish the law of universal gravitation, the highest efforts of astronomy and analysis have been directed to the consolidation of all the elements of that great phenomenon; and to the development of all the consequences, which they allow us to draw, not only as to the figure, but also as to the interior condition of the terrestrial spheroid."

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Notwithstanding that every possible phase of human ingenuity has been brought to bear on this operation, which was expected to furnish positive proof of the Newtonian assumptions, the whole has been, geodetically and mathematically, a provoking failure. This will be evident from the following explanation of the process adopted, and quotations of opinions respecting it:--

"If we conceive a great circle in the heavens, the 360 radii of which converge towards and meet in the centre of the earth, this will be the normal circle by which true degrees are, and alone can be, determined on the terrestrial surface, intersected by those radii. Practically the points of intersection are determined by the plumb-line. Supposing now the earth to be a perfect sphere, . . . all plumb-lines or normals prolonged would meet in the earth's centre, and consequently coincide with the radii of the normal circle, determining in a direct manner true degrees on the terrestrial surface; and therefore assuming the figure of the earth to slightly deviate from that of a perfect sphere, it is natural to conclude, without a positive proof or reason to the contrary, that the plumb-lines would continue to be directed to the earth's centre all the same. Astronomy, however, not only without any proof or reason whatever, assumes that they do not; but, moreover, starting on the assumption that the imaginary shape lent to the earth by Sir Isaac Newton's theory, is its real shape, gives to the plumb-lines such imaginary directions as are needed in order to adopt the empirical results of geodetic measurements to the earth's imagined form. . . . That the direction of the plumb-lines or normals to any given point on the earth's surface is perpendicular to a tangent to that point, or to the plane of its horizon is, as I have already shown, and as appears also

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distinctly from Sir John Herschel's own words, a mere assumption, unsupported by even the shadow of a reason; for what possible connection can there be between the positive force or 'law of nature' which determines the directions of the plumb-line, and the imaginary line and plane, which astronomers term 'a tangent' and 'the horizon?'" 1

The actual results. of these repeated efforts will be seen in the following quotations. In the ordnance survey of Great Britain, which was conducted by the Duke of Richmond, Colonel Mudge, General Roy, Mr. Dalby and others, base lines were measured on Hounslow Heath and Salisbury Plain, with glass rods and steel chains; "when these were connected by a chain of triangles and the length computed, the result did not differ more than one inch from the actual measurements--a convincing proof of the accuracy with which all the operations had been conducted. The two stations of Beachy Head in Sussex, and Dunnose in the Isle of Wight, are visible from each other, and more than sixty-four miles asunder, nearly in a direction from east to west, their exact distance was found by the geodetical operations to be 339,397 feet (sixty-four miles and 1477 feet). The azimuth, or bearing of the line between them with respect to the meridian, and also the latitude of Beachy Head, were determined by astronomical observations. From these data the length of a degree perpendicular to the meridian was computed, and this, compared with the length of a meridional degree in the same latitude, gave the proportion of the polar to the equatorial axis. The result thus obtained, however, differed considerably 

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from that obtained by meridional degrees. It has been found impossible to explain the want of agreement in a satisfactory way. . . . By comparing the celestial with the terrestrial arcs, the length of degrees in various parallels was determined as in the following table:

Notwithstanding the "accuracy with which all the operations had been conducted," the skill and ingenuity and perfection of the instruments employed were such that after measuring base lines far apart and triangulating from summit to summit of the hills, between the stations the actually measured and the mathematically calculated results "did not differ more than one inch." Such exactitude was never scarcely contemplated, and certainly could not be surpassed, if at all equalled, by the ordnance officers or practical surveyors of any other country in the world; and yet they failed to corroborate the assumption of polar depression or diminution in the axial radius of the earth. "For instead of the degrees increasing as we proceed from

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north to south, they appear to decrease, as if the earth were an oblong instead of an oblate spheroid." 1

The fallacy involved in all the attempts to prove the oblate spheroidal form of the earth, is, that the earth is first assumed to be a globe, the celestial surface above it to be concave, and the plumb-lines to be radii. If this were the true condition of things, then all the degrees of latitude would be the same in length; and if the earth were really "flattened at the poles," the degrees would certainly shorten in going from the equator towards the north. If, however, the celestial surface is not concave, but horizontal, two plumb-lines suspended north and south of each other would be parallel, and would indicate equal length in all the degrees of latitude, thereby spewing the earth to be parallel with the celestial surface, and therefore a plane. The differences required by a globe are not found in practice, but such as a plane would produce are invariably found. Hence the failure of geodesy becomes evidence against rotundity, but demonstrating that the earth is parallel to the horizontal heavens, and therefore of mathematical and logical necessity A PLANE. It is ever the case, when falsehood is tested in the crucible of experiment, that its value is diminished or destroyed, whilst the contrary is the case with truth, which, like gold, the more intense the fire of criticism the more brilliant it appears.

"When we come to compare the measures of meridional arcs made in various parts of the earth, the results obtained exhibit discordances far greater than what we have shown to be attributable to error of observation, and which render it

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evident that the hypothesis (of flattened rotundity) in strictness of its wording is untenable. The lengths of the degree of the meridian were astronomically determined from actual measurement made with all possible care and precision, by commissioners of various nations, men of the first eminence, supplied by their respective governments with the best instruments, and furnished with every facility which could tend to ensure a successful result." 1

The first recorded measurement of a degree of latitude is that by Eratosthenes, 230 B.C.

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It may be interesting to state here a few of the instances of the great care and accuracy manifested by the English ordnance surveyors; from which we may conclude that their published results may be implicitly relied on.

"A base on Salisbury Plain was measured in 1794 with steel chains, and was found to be 36574.4 feet long, and the length, as obtained by triangulation from the Hounslow Heath base, being 36574.3, exhibited therefore a difference of little more than an inch in a length of nearly seven miles." 1

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"The measurement of this base (on Belhelvie Sands in 1817) occupied from May 5 to June 6, and Ramsden's steel chain was again the instrument used. Its length, when compared with the unit ordnance standard bar O, is found to be 26.516.66 feet, and the length as deduced (in 1827) from the Lough Foyle base, is 26.518.99 feet."

"Salisbury Plain base, measured by steel chains (1794), was 36.575.64 feet. By Colby's compensation bars (1849), it was found to be 36.577.95 feet. Computed from Lough Foyle base (1827), 36.577.34 feet." 1

Thus it will be seen that the least error between actual measurement of base lines, and the results by triangulation and computation from distant bases was 0.1 foot, a shade more than 1 inch, and the greatest error 2.33 feet.

"These measurements are the most correct that, perhaps, have ever been made on the face of the earth. Men of the greatest skill have been employed; instruments of the most perfect construction have been used; every precaution has been adopted to avoid error, and all that science could do has been done." 2

How strange it appears, that one of the most ingenious mathematicians the world ever produced, assumed for certain purposes that the earth was a globe, that it revolved, that its revolutions caused the fluid and plastic matter of

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its substance to determine towards the equator--causing it to "bulge out" to a greater extent than the diameter in the direction of the axis, and therefore the circumference .at the equator must be greater than the circumference at right angles, or in the direction of latitude; or, in other words, that the degrees of latitude must diminish towards the poles, and yet "men of the greatest skill," with "instruments of the most perfect construction," having availed themselves of "all that science can do," have succeeded in making measurements the most exact "ever made on the face of the earth," have found results the very reverse of all that the Newtonian theory deemed essential to its consistency and perfection! Instead of the degrees diminishing towards the pole they were found to increase; as if the earth were egg-shaped or prolonged through its axis, and not, like an orange, flattened at the sides--"as if;" to use more scientific language, "the earth were an oblong instead of an oblate spheroid."

Well may such language as the following be used by practical writers!

"The geodetic operations carried out during the last century and a half for the purpose of determining the figure and the dimensions of the earth have, up to this time, led to no satisfactory results. Having been performed by the most eminent astronomers, with the most perfect instruments, in short with all the resources of modern science, it would seem that they ought to have led to a final solution of this most interesting problem; such, however, is by no means the case. Every new measure of a meridian arc has but added, and adds, to the existing doubts, and want of concordance, nay to the positive

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contradictions which the various operations exhibit, as compared with one another." 1

"The remarkable circumstance to which I would direct attention is, that in the middle of the nineteenth century, and at a time when astronomy and analysis celebrate their most brilliant triumphs, the ground itself on which the truth of all their practical observations and theoretical deductions mainly rests, continues a subject of doubt and perplexity as much as ever it was in the almost forgotten days of Sir Isaac Newton. After 150 years of unceasing efforts astronomy has yet to discover whether the terrestrial equator forms an ellipse or a circle. After a century and a half of unsuccessful calculation, analysis is still seen toiling to invent empirical formulas for the purpose of establishing a tolerable accordance between the geodetic measurements of to-day and those of yesterday." 2

Had it been seen in the days of Newton, or even a century ago, that the surface of standing water was not convex, and therefore that the earth could not be a globe at all, the great expense and labour, and the inconceivable anxiety which astronomers have experienced through the contradictions and inconsistencies developed during their attempts to reconcile the facts of nature with the fancies of speculative mathematicians, would have been avoided, and society saved from the infliction of an education which, in the most confused manner, includes a system of astronomy at variance with every perception of the senses, contrary to every day experience, and demonstrably false both in its. groundwork and in its principal ramifications.

Footnotes

241:1 "Figure of the Earth," by Johannes Von Gumpach; 2nd Edit., pp. 229 to 244. Hardwicke, London, 1862.

243:1 "Von Gumpach," pp. 38-53.

244:1 "Encyclopedia of Geography," by Hugh Murray, and several Professors of the University of Edinburgh.

245:1 "Encyclopædia of Geography," by Hugh Murray, &c.

246:1 "Treatise on Astronomy," by Sir J. F. W. Herschel.

247:1 "Professional Papers of the Corps of Royal Engineers." By Major General Colby; vol. iii., p. 10.

248:1 "Professional Papers of Royal Engineers," new series; vol. iii,, p. 27.

248:2 "The Earth," p. 20, by Captain A. W. Drayson, Royal Artillery.

250:1 "Memoirs of the Imperial Academy of Sciences of St. Petersburg." By General Von Schubert. St. Petersburg, 1859.

250:2 "Figure of the Earth," p. 3, by von Gumpach.