J4CF Or TIDES-. 



it becomes. Of consequence, the 47 of this entire curve will be- 

 individually smaller than the 47 of the containing arc. But as* 

 the degrees of the polar curve exceed those of the arc of a circle, 

 it must follow that the whole curve is of greater exient than the 

 arc of a circle: now to be of greater extent it must be more pro- 

 tuberant: the polar curve, of consequence, forms a lengthened 

 ellipsis. Q. E. D. 



It must be acknowledged that this demonstration is very perspi. 

 euous and convincing. How the most celebrated academicians and 

 mathematicians, for nearly half a century, could have overlooked a 

 proposition so plain and simple, can only be ascribed, in the opinion 

 of St. Pierre, to their obstinate and inveterate prejudices. He 

 pursues his victory in a strain of vain and indecent exultation, whicb 

 would dishonour a more respectable cause; but, perhaps, a little 

 attention will induce us to doubt at least whether the charge of 

 gross ignorance may not, with justice, be retorted on their accuser. 



It would have been indeed extraordinary, if men of science had 

 been absurd enough to imagine that a larger arc might be included 

 in a less; but they might suppose, with propriety and justice, that 

 the smaller arc of a larger circle can be included in the larger arc 

 of a smaller circle, which, in the present instance, appears to be the 

 case. In measuring a degree on the meridian, a certain spot is 

 fixed upon, where the elevation of the polar star is taken by a 

 quadrant; from this spot they proceed in a direct line north, till 

 the quadrant indicates an additional elevation of one degree. In 

 proportion as this degree constitutes a part of a larger or smaller 

 circle, a greater or less portion of ground will be passed over be- 

 fore the desired elevation is observed ; and the measurement of this 

 ground unequivocally decides whether this degree is part of a larger 

 or smaller circle. In this case the measurement is admitted, but 

 the conclusion denied. St. Pierre seems to have supposed, that the 

 academicians divided the polar arc into 47 parts, and then measured 

 one of these parts: a thing impracticable and ridiculous. The fact 

 is, that the polar arc, which, if the earth were a perfect sphere, 

 would contain 47> does not actually contain so many, but perhaps 

 about 46 of a larger circle ; and if the polar degrees are parts of 

 a larger circle, as they certainly are, it is demonstrable evident that 

 the real arc must be contained within the spherical arc, and, con-? 

 sequently, that the earth is flattened at the poles. 



I now proceed to state the three remaining proofs adduced by 



