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# Figure and Magnitude of Tee Eartit

## distance, measured, arch, alexandria, accurate, circumference and till

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FIGURE AND MAGNITUDE OF TEE EARTIT.

The progress made during the seventeenth century, in ascertaining the magnitude and figure of the earth, is particularly connected with the establishments which ive have just been considering. Concerning the figure of the earth, no accurate information was lived from antiquity, if we except that of the mathematical principle on which it was to be determined. The measurement of an arch of the merididn was attempted by Era, tosthenes of Alexandria, in perfect conformity with that principle, but by means very in adequate to the importance and difficulty of the problem. By measuring the BUD'S dis tance from the zenith of Alexandria, on the solstitial day, and by knowing, as he thought he did, that, on the same day, the sun was exactly in the zenith of Syene, he found the distance in the heavens between the parallels of those places to be 7° 12', or a 50th part of the circumference of a great circle. Supposing, then, that Alexandria and Syene were in the same meridian, nothing more was required than to find the distance between them, which, when multiplied by 50, would give the circumference of the globe. The manner in which this was attempted by Eratosthenes is quite characteris tic of the infant state of the arts of experiment and observation. He took no trouble to ascertain whether Alexandria and Syene were due north and south of one another : the truth is, that the latter is considerably east of the former, so that, though their hori zontal distance had been accurately known, a considerable reduction would have been ne cessary, on account of the distance of the one from the meridian of the other. It does not appear, however, that Eratosthenes was at any more pains to ascertain the distance than the bearing of the two places. He assumed the former just as it was commonly esti mated ; and, indeed, it appears that the distance was not measured till long when it was done by the command of Nero. • It was in this way that the ancients made observations and experiments ; the mathe matical principles might be perfectly understood, but the method of obtaining accurate data for the application of those principles was not a subject of attention. The power of resolving the problem was the main object ; and the actual solution was a matter of very inferior importance. The slowness with which the art of making accurate experiments

and observations has matured, and the great distance it has kept behind theory, is a remarkable fact in the history of the physical sciences. It has been remarked, that ma thematicians had found out the area of the circle, and calculated its circumference to more than a hundred places of decimals, before artists had divided an arch into minutes of a de gree ; and that many excellent treatises had been written on the properties of curves, be fore a straight line had been drawn of any considerable length, or measured with any to, lerable exactness, on the surface of the globe.

## The next measurement on record is that of the astronomers of

Almamon, in the plains of Mesopotamia, and the manner of conducting the operation appears have been far more accurate than that of the Greek philosophers ; but, from a want of knowledge of the measures employed, it his conveyed no information-to posterity.

The first arch of the meridian measured in modern times with an accuracy any way. corresponding to the difficulty of the problem, was by Snellius, a Dutch who has given an account of it in a volume which he calls Bratosthenes Batavu.s, publish ed in 1617. The arch was between Bergen-op-zoom and Alkmaar ; its amplitude wag 1° 11' 30", and the distance was determined by a series of triangles, depending MI a base line carefully measured. The length of the degree that resulted was 65,021 toises, which, as was afterwards found, is considerably too .small. Certain errors were discovered, and when they were corrected, the degree came out 57,033 toises, which is not far from the truth. The corrections were made by Snellius himself, who measured his base over again, and also the angles of the triangles. He died, however, before he could publish the result. Muschenbroek, who calculated the whole anew from his papers, came to the conclusion just mentioned, which, of course, was not known till long after the time when the measure was executed. No advantage, accordingly, was derived to the world from this measurement till its value was lost in that of other measurements still more accurately conducted.

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