# Figure and Magnitude of Tee Eartit

## found, distance, meridian, toises, measured, degree, force and earth

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A computation which, for the time, deserves considerable prairie, is that of Norwood, in 1635, who measured the distance between London and York, taking the bearings as he proceeded along the road, and reducing all to the direction of the meridian, and to the horizontal plane. The difference of latitude he found, by observation of the solstices, to be r ew, and from that and his measured distance, he concluded the degree to be 807,170 feet English, or 57,800 toises. This has been found to be a near approxima. tion ; yet his method was not capable of great accuracy, nor did he always execute it in the best manner. " Sometimes," says he, " I measured, sometimes I paced, and I be lieve I am within a scantling of the truth." Fernel, a French physician, measured with a wheel from Paris to Amiens, which are nearly in the same meridian, and he determined the degree from thence to be 56,746 French toises ; a result which falls short of the truth, though not very considerably.

These investigations, it is plain, could not but leave considerable uncertainty with re spect to the magnitude of the earth. The Academy of Sciences became interested in the question, and the measurement of an arch in the meridian was undertaken under its au spices, and executed by the Abbe Picard, already known for his skill in the operations of practical geometry. He followed a method similar to that of Snellius, according to which, the distance between Amiens and Malvoisine was found from a series of triangles, and a base of 5663f toises. He determined the difference of latitude by means of a zenith sector of • ten feet radius, and found it to be 55". The whole distance was 78,850 tains, whence the degree came out 57,060 toises. This was the first measurement of a degree • of the meridian, on which perfect reliance could be placed.

Hitherto no doubt had been entertained of the spherical figure of the earth, and, of con , sequence, of the equality of all the degrees of the meridian, so .that if one was known, the whole circumference was determined. Men, with the precipitation which they so of ten manifest, of assuming, evidence, the conclusion which appears most simple, were no sooner satisfied that the earth was round, than they supposed it to be truly spherical. An observation soon occurred, which gave reason to suspect, that much more must be done before its figure or its magnitude were completely ascertained.

, , With a view of observing the sun's altitude in the vicinity of the equator, where the distance from the zenith being inconsiderable, the effects of refraction must 43e of small ac' count, it was agreed, by the same academy, to send an astronomer, M. Richer, to make

observations at the island of Cayenne, in South America.

Richer observed the solstitial altitude of the sun at that place in 1672, and found the distance of the tropics to be 46° 57' 4" ; and, therefore, the obliquity of the ecliptic 281 sr, agreeing almost precisely with the determination of Cassini. • The most remarkable circumstance, however, which occurred in the course of this voy age, was, that the clock, though furnished with a pendulum of the same length which vi brated seconds at Paris, was found, at Cayenne, to lose two minutes and a half a-day near ly. This created great astonishment in France, especially after the accuracy of it was confirmed by the observations of Varin and Deshayes, who, some years afterwards, visited different places on the coast of Africa and America, near the line, and found the necessity - of shortening the pendulum, to make it vibrate seconds in those latitudes. The first ex planation of this remarkable phenomenon was given by Newton, in the third book of his Principia, published in 1687, where it is deduced as a necessary consequence of the earth's rotation on its axis, and of the centrifugal force thence arising. That force changes both the direction and the intensity of gravity, giving to the earth an oblate spheroidal figure, more elevated at the equator than the poles, and making bodies fall, and pendulums vibrate, more slowly in low than in high latitudes.

This solution, however, did not, any more than the book in which it was contained, make its way very readily into France. The first explanation of the retardation of the pendulum, which was received there, was given by Huygens in 1690. Huygens deduced it also from the centrifugal force, arising from the earth's rotation, and the view which he took was simpler, though much less accurate than that of Newton. It had, indeed, the simplicity which often arises from neglecting one of the essential conditions of a problem ; but it was nevertheless ingenious, and involved a very accurate knowledge of the nature of centrifugal force. I am thus brought to touch on a subject which belongs properly to the second part of this Dissertation, for which the fuller discussion of it must of course be reserved.

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