Of the Figure of the Earth. 113 



plitude ; or by the distance of lines perpendicular to the 

 tangents in those points, whose intersection constitutes 

 a small known angle, suppose of one degree. A degree 

 of this circle being known, the circle itself is known ; 

 and if this be known in two or more points of the curve, 

 the dimensions of the figure, viz. the ratios of the axes, 

 ordinates, parameters, &:c. rnay be found. 



With a view to tlie foregoing process, mathematicans, 

 in order to determine the figure of the earth, directed 

 the measurement of a degree to be made in two or more 

 distant parts of die meridian ; where, supposing tlie fig- 

 ure elliptical, the curvature mustnecessai'ily have a per- 

 ceptible difference. If these requisites could be obtain- 

 ed accurately^ the conclusions respecting the form of the 

 eaith were considered as incontrovertible as any prop- 

 ositions of Euclid ; and as ultimately decisive of the dis- 

 pute which had been, for a long time, maintained on this 

 subject. For Cassini and his followers had opposed the 

 deductions of Newton, wholly on the ground that the 

 measure of a degree of the meridian near the pole, would 

 be found less than that of one near the equator ; which 

 opinion he was led into from a comparison of the lengths 

 of the arches, which had been imperfectly measured by 

 Snellius, Picard, Musschenbroek, and others. 



The Newtonians, on the other hand, maintained that 

 these measures were not sufficiently accurate, or prop- 

 erly adapted to the determination of this question ; but 

 if an exact mensuration could be made of the length of 

 ■ a degree of the meridian near the pole, and also at or 

 near the equator, that all physical arguments, which in 

 themselves are merely probable or hypothetical, must 

 yield to the certain and demonstrable conclusions of the 

 mathematics. For, if the measure of a degree at or 

 near the pole, should be found less than one at or near 

 the equator, the axis of the earth must necessarily be 

 longer than a diameter of the equator ; and on tlie con- 

 trary, if the length of a degree at or near the pole should 

 be greater than one at or near the equator, the equatori- 

 al diameter of the earth must necessarily be more ex- 

 tended than its axis. These deductions, though not ob- 



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