XXXVIU Ï-XPLANATÏON OF THE PLATES. 



the Tropics. Thefe two arches are, it is well knovva, 

 cacli of 47 degrees. But though they both are fubtendcd by 

 equal angles, A G C and DGF, they are by no means of 

 equal expanfion : for, according to our Aftronomers, a de- 

 gree of the Meridian at the polar Circle is greater, by 674 

 fathoms, than a degree of the fame Meridian near th© 

 Equator. It follows, therefore, that the unknown polar 

 arch X of 47 degrees, exceeds, in extent, the equinodlial 

 archDEF, which likewife contains 47 degrees, by 47 

 times 674 fathoms, which amount 1031,678 fathoms, or 

 twelve leagues and two thirds. The queilion now to be 

 determined, then, is, whether this unknown polar arch x is, 

 contained within the circle, in the curve A ^ C, or coincides 

 with it, as A B C, or falls vvithout it's circumference, in 

 the direilion A / C, 



The unknown polar arch x cannot be contained within 

 the Globe, as A /■ C, as is pretended by our Aftronomcrs, 

 who will have \X. to be flattened there : for if it were con- 

 tained, it would be evidently fmaller than the fpherical 

 arch A B C, which furrounds it, conformably to this axiom, 

 that the thing contained is fmaller than what contains it ; 

 and the more this curve A h C fhall be flattened, the lefs 

 will be it's extent, as it will approach nearer and nearer tqi 

 it's chord, that is, the ftraight line A K C. 



On the other hand, this polar arch x cannot coincide witl^ 

 the fpherical arch ABC, for it exceeds it by twelve leagues 

 and two thirds. It muft belong, therefore, to a curve 

 which falls without the circumference of the Globe, as in, 

 the diredion A/C. The Globe of the Earth, then, is 

 lengthened at the Poles, as degrees of the Meridian are 

 greater there than at the Equator. Aftronomers have con- 



fequcntly 



