XXXVl EXPLANATION OF THE PLATER.' 



Academicians themfelves. Confequently, if you Avcrë to 

 apply the whole arch of the Meridian, which crowns the 

 polar Circle, and which contains 47 degrees, to an arch of 

 .47 degrees of the fame Meridian, near the Equator, it 

 would produce a confiderable protuberance, it's degrees 

 being greater. This polar arch of the Meridian could net 

 extend, in length, over the equinoélial arch of the fame 

 Meridian, becaufe it contains the fame number of degrees, 

 and, confequently, a chord of the fame extent. If it ex- 

 tended in length, exceeding the fécond at the rate of 674. 

 fathoms for each degree, it is evident that it would, at the 

 extremity of it's 47 degrees, get out of the circumference of 

 the Earth ; that it would no longer pertain to the circle on 

 \vhich it was traced, and that it would form, on applying 

 it to one of the Poles, a fpecies of flattened mufhroom, 

 which would proj eft round and round, it's brim touching 

 the Earth in no one point. 



In order to render the thing ftill more apparent, let us 

 always fuppofe that the profile of the Earth at the Poles, is 

 an arch of a circle, and that it contains 47 degrees, is it not 

 evident, if you trace a curve on the infide of this arch, as 

 the Academicians do, who flatten the Earth at the Poles, 

 that it mufl be fmaller than this arch within which it is de- 

 fcribed, as being contained in it ; and that the more this 

 curve is flattened, the fmaller it becomes, as it will ap- 

 proach more and more to the chord of the arch, that is to 

 a ftraight line? Of confequence, the 47 degrees, or divi- 

 fions, of this interior curve, will be, each in particular, as 

 they are when taken together, fmaller than the 47 degrees 

 of the arch of the containing circle. But, as the degrees of 

 the polar curve are, on the contrary, greater than thofe of 

 an arch of a circle, it muft follow, that the whole curve 



fliould 



