iiifS Examination of Si. PimSs Hjpol-hrjis 



than the arc of a circle : now to be of greater extent it mirfl 

 be more protuberant : the polar curve, of conference, forma 

 a lengthened ellipfis. Q. E. D.* 



It mult be acknowledged that this demonftratlon is very 

 perfpicuous and convincing. How the molt celebrated aca- 

 demicians and mathematicians, for nearly half a century, 

 could have overlooked a proportion fo plain and fimplc, can 

 only be afcribed, in the opinion of St. Pierre, to their ob- 

 ftinate and inveterate prejudices. He purfues his victory in a 

 ft rain of vain and indecent exultation, which would difhonour 

 a more refpc&able caufe; but, perhaps, a little attention will 

 induce us to doubt at leaft whether the charge of grofs igno- 

 rance may not, with jultiee, be retorted on their accufer. 



It would have been indeed extraordinary, if men of fci- 

 ence had been abfurd enough to imagine that a larger arc 

 might be included in a lei's ; but they might fuppofe, with 

 propriety and juftice, that the fmaller arc of a larger circle 

 can be included in the larger arc of a fmaller circle, which, 

 Jjp the prefent inftunce, appears to be the cafe. In meafuring 

 a degree on the meridian, a certain fpot is fixed upon, where 

 the elevation of the polar Itar is taken bv'a quadrant ; from 

 this fpot they proceed in a direct line north, till the quadrant 

 indicates an additional elevation of one degree. In propor- 

 tion as this degree conititutes a part of a larger or fmaller 



* Let x, Fig. 3. Plate V. be the unknown ?tc of the meridian, 

 comprehended above the ar&lc circle A B C ; and let DEF be the arc 

 i,t the fame meridian, comprehended between the tropics; chefe two arcs 

 are each 47 . According to our aftionomers, a degree at the polar circle 

 fa greater 1 v 674 fathom* than a degree of the fame meridian near the 

 equator; the arc x therefore exceeds, in cxte- . the arc DEF by 

 674X47, or 31,678 fathoms = iz* leagu .. The qucftion to be deter- 

 mined is, whether this unknown polar arc .v ; om i ,^d within the 

 circle in the curve AbC, or coincides wit' .,, ^3 A BC, or falls without 

 its circumference, as A :-. C. The arc x cannot We contained within 

 the circle, as A AC, for it < ould -hen be evidently (mailer than the arc 

 ABC i md i!e more this curcc AbC ii flattened;, the lefs will be' 

 its exui it, is '1 will approach nearer and nearer to the ftraight line A C j 

 neither can it coincide with the arc AB C, for it exceeds it ii? leagues. 

 Jt mufl helong, therefore, to a curve falling without the circle, as A x C. 

 The ... the earth, therefore, is lengthened at ihe poles, fincc 



flegrcwi, of the meridian there than at the equator. 



circle, 



