GEODESY, in modern English usage is the science of survey ing tracts of country so large that the curvature of the earth must be allowed for; also the determination of the figure of the Earth, including the various geophysical problems most intimately con nected therewith. Sometimes in modern languages other than English the word cognate to geodesy may mean hardly more than the original Greek (Gr. yew aeaia, the art or science of men suration, from yid, Earth, and boleti", to divide), that is, it may mean merely accurate land surveying, and some epithet, such as higher, must be added to make the phrase coextensive with the English word geodesy.
The earliest geodesy (in the English sense) was concerned almost exclusively with determining the figure of the Earth, a problem then chiefly of speculative interest, for the need of ac curate maps, in which the figure of the Earth must be taken into account, was hardly felt until the time of Columbus.' The naive view of primitive man, still held by the backward and uneducated, was that the Earth is a flat plane, or a circular disk, diversified by seas, rivers and mountains. It might seem as if some notion of the approximate sphericity, or at least of the curvature, of the Earth might have originated with those earlier peoples, such as the Babylonians, who cultivated the science of astronomy, and who must have noticed that when an observer travelled south the aspect of the heavens changed, as stars hitherto never seen came into view over the southern horizon and the number of northern circumpolar stars always on view became smaller, the phe nomena being reversed as the observer journeyed northward. But no record of any explanation of all this based on the curvature of the Earth has come down to us from any pre-Hellenic source. Or it might seem as if any seafaring people, observing a vessel go "hull down, down and under," as the observer's distance from it increased, might have conceived the idea of a spherical or at least of a rotund Earth. But again we have no record of any such doc trine emanating from any of the earlier maritime peoples.
The earliest enunciation of the doctrine of a spherical Earth comes from Pythagoras or from his school of philosophy, and even then the doctrine may have been based quite as much on metaphysical as on physical considerations. By the time of Aristotle, however, the doctrine of a spherical Earth had at least a respectable amount of support among the more learned of his contemporary Greeks. Aristotle devotes a part of his book De 'This does not mean that until about this time there were no maps in which places were located by their latitude and longitude ; there had been such at least as early as the time of the Greco-Egyptian astronomer, Claudius Ptolemy, although they were extremely in accurate. Nor does it mean that fairly accurate charts did not exist before the time of Columbus, for the mediaeval seamen's charts, or portolani, had then long been known, but these made little or no use of latitude and longitude.
Caelo to a defence of the doctrine. He even gives an estimate of the size of the Earth, saying : "Moreover those mathematicians who try to compute the cir cumference of the Earth say that it is 400,000 stadia, which indi cates not only that the earth's mass is spherical in shape but also that it is of no great size as compared with the heavenly bodies." (De Caelo, Book II., Chap. 14.) This passage follows a long argument in favour of the sphericity of the earth. Some of the arguments sound modern enough; others seem strange to our present ways of thinking. This seems to represent the first scientific attempt now on record to determine the size of the Earth. Even the unit has been supplied by the com mentators, the word stadia not occurring in the best texts. How this figure of 400,000 stadia was attained we do not know. It may have been by a process such as that used by Eratosthenes, who will next be mentioned, or it may have been by crude measures of the depression of objects at sea. If we take Aristotle's stadion to be the Attic stadion of 185 meters (607 ft.), then this figure represents a considerable over-estimate, but is of the right order of magnitude, as a mathematician would say.
Eratosthenes of Alexandria (c. 276–c. 195 B.c.) is the first known writer to describe and apply a method for determining the size of the Earth. He assumed that Syene (the modern As suan on the Nile) lay on the Tropic of Cancer so that the sun at the summer solstice was exactly overhead. Eratosthenes ob serving at Alexandria at the solstice found the sun to be 1/5o of a circumference away from the zenith, that is, the difference of latitude between the two places he took to be 1/5o of 36o° = 7° 12'. He assumed that Alexandria and Syene lie on the same meridian, which is not exactly true, and that the distance between them is 5,000 stadia.
On the principle of the exact correspondence between angular distances in the heavens and distances measured on the terrestrial globe it follows that 1/5o of the circumference represents 5,000 stadia, or that the whole circumference is 250,000 stadia. With any plausible modern equivalent of that stadion this is much nearer the truth than Aristotle's figure.
We have reports of two other Greek attempts to determine the circumference of the Earth, but there is no reason to suppose the results to be any better than that found by Eratosthenes. Ptol emy in his Geography gives the length of a degree as 5oo stadia, which makes the circumference i8o,000 stadia. These results are all clouded by the uncertainty as to the modern equivalent of the stadion, and it may well be that the stadion used by differ ent writers was different. The same uncertainty affects a deter mination on principles similar to those of Eratosthenes made on the plains of Shinar in Mesopotamia under the orders of the Caliph Abdullah al Mamun (A.D. 786-833), although the dis tances were actually measured instead of being estimated.
No refinement of theory over Eratosthenes was made until the oblateness of the Earth came into question during the late 17th and the first half of the 18th centuries. For determining dis tances on the Earth, Willebrord Snell (1591-1626) substituted a chain of triangles in Holland for direct measurement.
In 1669 Picard (q.v.) first used the telescope both in the de termination of latitude and in the measurement of angles of tri angulation, a device whereby the accuracy of both operations was increased. Picard's results for the length of a degree were used by Newton in his calculations to prove that the attraction of the Earth is the principal force governing the motion of the Moon in its orbit.
With Newton and his contemporary Huyghens a new era in geodesy begins. The physical proofs of the sphericity of the Earth had so far been proofs of its general rotundity. In the Ptolemaic astronomy it had seemed natural to assume—for reasons usually of a metaphysical sort—the earth to be an exact sphere ; but with the growing conviction that the Copernican system is true and that the earth rotates about its axis, and with the advance in mechanical knowledge due chiefly to Newton and Huyghens, it seemed natural to conceive the earth as an oblate spheroid flat tened at the poles. There was also the experimental evidence of the astronomer Jean Richer, who found that his clock, regulated to keep time at Paris, lost two and a half minutes a day at Cayenne in South America, where he had been sent to make observations.
But the arguments from theory and the evidence of Richer's clock, confirmed by the experience of other observers, seemed to be contradicted by the work of the Cassinis in France. If the Earth is an oblate spheroid, the length of a degree of latitude must increase from the equator to the pole', but the Cassinis, continu ing Picard's work, found a small difference in the opposite direc tion; the length of a degree seemed to decrease as the pole was approached, as if the Earth were a prolate ellipsoid instead of an oblate one.
The difference was small because the range of latitude available in France was comparatively small, and might conceivably be due to observational error ; nevertheless many accepted it as real and there ensued a lively controversy between the Earth-flatteners and the Earth-elongators. To settle the matter the Paris Academy of Sciences sent two expeditions to places whose difference of lati tude was as great as was reasonably possible, one to "Peru" and the other to Lapland. The northern party measured an arc ex tending from Tornea at the upper end of the Gulf of Bothnia to Kittis, not quite a degree to the northward, and finished its work before the Peruvian expedition did. This latter expedition left France in 1735 and did not return till The result of a comparison of the Peruvian with the Lapland arc was a vindication of the theory of an earth flattened at the poles, but it was realized that the inevitable errors made the exact amount of the flattening uncertain. By taking the two measure ments as exact the flattening found was 213; the modern value is Q97• During the century that followed there were numerous measure ments of arc that in this brief sketch cannot even be mentioned by name. The trigonometrical survey of England was begun in 1783, in the first place to establish a geodetic connection between Greenwich and Paris; and Mechain and Delambre undertook operations in France to determine the length of the Gradually of course methods and instruments improved and standards of precision became more exacting. Gauss devised the method of least squares, a method that diminished the arbitrary element that had hitherto entered into the adjustment of con flicting observations. This method was used extensively by the German astronomer Bessel in the Prussian arc of 183o-35. In geodesy, as in astronomy, Bessel was a leader in the introduction of refined methods of observation and higher standards of accuracy.