OF TIDES. 339 



he has judged proper to erect a new one; and a fair exposition of 

 this system will enable us to determine, by comparison, to which 

 we shall give our suffrage. 



It is well known that Sir Isaac Newton and Cassini differed in 

 their opinion respecting the figure of the earth : the former con. 

 ceiving it to be an oblate spheroid, flattened at the poles ; the latter 

 contending it must be oblong, or elongated at the poles. To ascer- 

 tain this point, some of the most celebrated mathematicians of 

 Europe were appointed to determine, by actual measurement, the 

 length of a degree both at the equator and at the pole. They 

 found that the polar degrees exceeded the equatorial, and con- 

 cluded they must consequently be parts of a larger circle, and, of 

 course, that the earth was flattened at the poles. This was univer- 

 sally considered as decisive of the question, till the genius of M. 

 St. Pierre detected a gross and palpable error in the calculation, 

 which had escaped their accurate knowledge and penetration : but^ 

 as the elongation of the poles constitutes a leading feature in the 

 new theory, I shall give it a more detailed examination. 



This polar elongation, as he conceives, is supported by four 

 direct and positive proofs : the first geometrical, upon which he 

 lays the greatest stress, and upon which he has staked his reputa- 

 tion; the second, atmospherical; the third, nautical; the fourth, 

 astronomical : of all which in order. 



The first, or geometrical proof, is what he calls a demonstration, 

 founded on the measurement of the earth, and admitting the polar 

 degrees to exceed the equatorial ; here follows the demonstration : 

 If you place a degree of the meridian at the polar circle on a de- 

 gree of the same meridian at the equator, the first degree, which 

 measures 57>42'2 fathoms, will exceed the second, which is 56,748 

 fathoms, by 674; consequently, if you apply the arc of the meri- 

 dian contained within the polar circle, being 47* to an arc of 47 

 of the same meridian at the equator, it would produce a consider- 

 able protuberance, its degrees being greater. 



To render this more apparent, let us always suppose that the 

 profile of the earth, at the poles, is an arc of a circle containing 47; 

 is it not evident, if you trace a curve on the inside of this arc, as 

 the academicians do when they flatten the earth at the poles, that 

 it must be smaller than the arc within which it is described, being 

 contained in it ? Ami the more this curve is flattened the smaller 



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