From
Chapter 14, Section 9 of Earth Not a Globe by Dr. Samuel Birley Rowbotham:
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ARCS OF THE MERIDIANThe 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."
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 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?'"
1The 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 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:
| Latitude of Middle Point. Fathoms. |
| Arbury Hill and Clifton 52° 50´ 29.8″ 60.766 |
| Blenheim and Clifton 52 38 56.1 60.769 |
| Greenwich and Clifton 52 28 5.7 60.794 |
| Dunnose and Clifton 52 2 19.8 60.820 |
| Arbury Hill and Greenwich 51 51 4.1 60.849 |
| Dunnose and Arbury Hill 51 35 18.2 60.864 |
| Blenheim and Dunnose 51 13 18.2 60.890 |
| Dunnose and Greenwich 51 2 54.2 160.884 |
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 north to south, they appear to decrease, as if the earth were an oblong instead of an oblate spheroid."
1The 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.
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Chapter Section is continued
here.
Also see
Chapter 14, Section 11 entitled
Degrees of Longitude.