Relating to the FIGURE of the EARTH. 9 



be the length of any other arch, ?n' the coefficient of <?, and n of 

 f , computed in the fame manner, we have ma — tic = /, 



and m'a — ti'c n: /'. 



■tTri r^l — ft' '"'t — ml' j c vi'l — ml' . 



Whence a =: — -, — ; c z=. — -, — and - =: -r, ;r. It 



mn — m n ' mn — mn a n I — /;/ 



may be ufeful, in the numerical calculation, to obferve alfo that 



ma — / 



~~ n ' 



7. The arch of the meridian, which was meafured in Peru, 

 compared with that meafured in France, will afford an example 

 of the application of thefe formulas. 



The amplitude of the arch meafured in Peru was 3°. 7'. i'\ 

 and its length 176940 toifes. To reduce this to the level of the 

 fea, above which it was elevated 1226 toifes, <d6 toifes muft be 

 fubtradled, and again 1 2 toifes added to adapt it to the inean 

 temperature of the atmofphere. Thus corred;ed it is 176886 

 toifes. The arch meafured begun 't^Q' north of the equator, and 

 extended to the parallel of 3°. 6'. 25" fouth ; we fliall fuppofe it 

 to have begun under the equator, and to have extended to the 

 parallel of 3°. 7'- i", a fuppofition which can produce no fen- 

 fible error, and will fomewhat fimplify the calculation. Thus 

 <p, in the preceding formula, is an arch of 3°. 7', 1" exprefled in 

 decimals of the radius i, and fo we have m ■=. .0544009, n ■=. 

 -1 086408, and / = 176886. 



Again, the amplitude of the whole arch meafured in France 

 from Dunkirk to Perpignan is 8°. 20'. 2"^, and its length 

 475496 toifes. The northern extremity of this arch is in lati- 

 tude 51°. 2'. i", and the fouthern in 42°. 41'. 58"i. Hence 

 (^' ■=. .8907045, and (p' = .7452459, and therefore »/ =. . 1454586, 

 «' = .0585735, / = 475496. 



Therefore,« = |^^£^ = 3273325 toifes ; 



c ■=.' 



mn — m n 

 m'l — ml' 



10917 toifes, 



Part I, B Wherefore 



