Relating to the FIGURE of the EARTH. 23 



27. It may be fhewn, too, nearly in the fame manner, that 

 if a degree of the perpendicular to the meridian were meafured 

 in Siberia, as far north as the latitude of 70 °, fuppofing that to 

 be poilible, and compared with a degree in latitude 45*, or even 

 confiderably farther fouth, it would not give a refult fo exact as 

 the degree of the meridian and perpendicular meafured in the 

 fouth of England. This mews, that the method of afcertain- 

 ing the figure of the earth, propofed by the authors of the Tri- 

 gonometrical Survey , (Phil. Iran/, ibid. p. 529.), as a fubject of 

 future inquiry, is lqfs exact than that which is founded on their 

 own obfervations. 



28. We may alfo afcertain, by the fame means, the relative 

 accuracy of the method of finding the figure of the earth, from 

 the comparifon of a degree of the meridian with a degree of the 

 perpendicular in the fame latitude, and of the method of refol- 

 ving the fame problem by the comparifon of two degrees of the 

 meridian in different latitudes. 



If, then, D be a degree of the meridian, and D' of the per- 

 pendicular, in latitude <p, and if A be a degree of the meridian in 

 a different latitude <p\ it is required to find whether the moft ac- 

 curate value of °- a will be found, by comparing D and D', or T> 



and A. 



Since we have, by what has been already ftated, § 4. 

 mT> — a — ic -f- 3c fin 2 «p, and 

 fflA — a — ic -f- y fin 2 <p', we have alfo 



£ = 1 -f* ~ (nn 2 <p — fin y ) and therefore, 



c 



D— -A 



a — 3A (fin 2 ? — fin V'T 



Now, it has been already ihewn, that, by comparing D and 

 D' we have - zz 2D< ~ f 2 . Suppofing, therefore, equal errors 



