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No. XXII. 



Obfervat'ions on the Figure of the Earth. By Joseph 

 Clay, M. A. P. S. 



T 



'HE fubjedl of this paper was fuggefted to 

 me by a perufal of the " Studies of Nature," 

 by Bernardin de St. Pierre. The pofitive manner in 

 which tliat author aflerts that the earth is a prolate fphe- 

 roid, the arrogance with which he challenges refutation, 

 and above all the erroneous theories which he has built on 

 this aflertion, feem to require all doubts to be removed 

 by a mathematical demonftration. It is known that de- 

 grees of latitude increafe in length as we approach to the 

 poles. Upon this ground, St. Pierre places his principal 

 argument which in fubftance is that if two lines diverg- 

 ing from the centre of an ellipfis, intercept a part of the 

 curve, the further that part is from the centre, the longer 

 will it be ; and converfely, as the arch of one degree is 

 longer near the pole than an arch of one degree near the 

 equator, the axis muft be longer than the equatorial dia- 

 meter. His error arifes from fuppofing, that degrees of 

 latitude are meafurcd by the angles of femi-diameters of 

 the meridian. This is not the cafe. The only mode of 

 determining the latitude is by obferving the altitude of the 

 heavenly bodies, cither by the mural quadrant or fedlor 

 or by Hadley's odlant. Suppohng the fun to be the body 

 altitude of which is taken, and fuppofing it to be in the 

 equator and on the meridian, the complement of its al- 

 titude is equal to the latitude of the place of obfervation. 

 The parallax of the fun is fo fmall, that rays of light 

 coming from it may without fenfible error be confider- 

 ed as coming in parallel lines ; this being premifed, let 



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