Figure of the Earth, 145 



three times that of water, has inferred a mean density of 4.746. 

 It will therefore be evident that the ellipticity ought to be less 

 than tj-^ ; but the mere application of the calculus does not fur- 

 nish the measure of its true amount, for we are ignorant of the 

 nature of the substances under investigation, and the circum- 

 stances under which they were first united in one mass. Had the 

 earth been originally a fluid, with a compressibility equal to that 

 found to exist in water by the experiments of Canton, the ellip- 

 ticity would have been 3-^ ; but this hypothesis is probably wide 

 of the truth, and the inferred ellipticity consequently incorrect. 



In order to ascertain the real figure of the earth, it is absolutely 

 necessary to have recourse to experiment and observation. The me- 

 thod that would at first appear most obvious, is that of actually 

 measuring a portion of one of its meridians : should its degrees be 

 found all equal, a truly spherical figure might be inferred ; should 

 they decrease from the Equator to the Pole, an elongation would be 

 proved ; but should the degrees nearest to the Pole be found the 

 •longest, no doubt need be entertained that the earth is flattened 

 in the direction of its axis of revolution. With these views a 

 portion of a meridian, extending from Dunkirk to the southern 

 frontier of France, was measured by Picard and Cassini. The 

 apparent result of this operation led to conclusions totally differ- 

 ent from those deduced from the theory of gravitation, and the 

 laws of central forces. The southernmost degrees of this arc ap- 

 peared to be the longest ; and thus ground was afforded for the 

 belief that the earth was an oblong instead of an oblate spheroid*. 



The measure of Picard and Cassini being at variance with the 

 received hypothesis, but the instruments and methods of the age 

 being insufficient to discover the error, it was proposed, by way 

 of ascertaining the truth in the most unexceptionable manner, to 

 measure a degree under the Equator, and another as near to the 

 Pole as was practicable. With this view, Maupertuis was sent to 

 Lapland, and Condamine to Peru. Their measures confirmed the 

 general theory of Newton, in manifesting the oblateness of the 

 earth. The degree of Maupertuis, compared with those measured 

 in France, gave for the fraction expressing the degree of oblate- 

 ness, y\^ ; but by a recent measure of the same degree by Soan- 

 berg, an error of more than 200 toises, in excess, has been 

 detected, and the determination of this astronomer, compared with 

 degrees measured in France, reduces the flattening to j^ f . The 

 French arc has subsequently been extended into Spain, and as 

 far south as the island of Formentera. In England an arc of 



* The same arc has since been more correctly measured by Mechain and 

 Delambre, towards the end of the last century, by which a different result was 

 obtained, giving the fraction 2 *j for the flattening at the Poles. 



Vol. XX. L 



