Of the Figwre of the Eartli. 115 



-ciilnference, the curve approximates to a circle, and be- 

 comes one when those hnes coincide. 



The portions of the circumference of any figure, cor- 

 responding to measures of angles at its center, the circle 

 only excepted, are, and ever must remain unknown till 

 its nature and limitations are determined from other 

 principles, e. g. 



In the ellipsis* PEpc, the measure of a degree at P, is 

 not the measure of a degree of a circle, whose center is 

 at O, the center of tlie ellipsis ; but it is the measure of 

 ti degree of the circle of curvature, whose center is 

 some where beyond at C ; and in like manner, the mea- 

 sure of a degree at E, is not the measure of a degree of 

 a circle, whose center is at O, but the measure of a de- 

 gree of the circle of curvature, whose center is some- 

 where at f/, nearer the point E. 



What the lengths of those portions of the periphery 

 may be, which correspond to given angles at the center 

 of the figure, is impossible to determine, in the case of 

 the earth's mensuration, as we cannot go to its center, 

 nor make observations on its surface, which supposing 

 the earth's figure and magnitude unknown, can afford 

 the necessary data for the determination of this point. It 

 is evident, the. jforeu, that it is not as in ordinary calcula- 

 tions, from the measures of angles at the center of the 

 figure, that we can obtain a solution of the problem of 

 the figure of the earth. If this could be obtained by no 

 other methods, it is certain that it would for ever remain 

 a secret. But by the aid of that sublime geometry, 

 which in modern times has been so happily employed 

 in abstruse and difiicult inquiries of this nature, tlie 

 problem vv^ill admit of a complete solution, from very 

 simple data. Nothing more is requisite, than what was 

 supposed above, viz, the measure of a degree at P and 

 E, or at the polar and equatorial diamaters, if the figure 

 be an ellipsis ; for then the diamater of the circle of 

 curvature will be exactly equal to the parameters of the 

 diameters at those points, which being knowii, the ellip- 

 sis itself will be known. 



The same data for any two other points of the meri- 

 1 dian, is also sufiicient, provided tliose two points be not 



* See Fig. 5, plate l. 



