RELATING TO THE FIGURE OP THE EARTH. 107 



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



ma — I 

 c ~ , 



n . 



7. The arch of the meridian, which wa"; meafured in Peru, Application of 

 compared with that meafured In France, will afford an example [J^ arc mcl^-urfd 

 of the application of thefe formulas. in Peru and that 



The amplitude of the arch meafured in Peru was 3** 7' W *" ^""*'** 

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

 fea, above which it was elevated 1226 toifes, 66 toifes muft be 

 fubtrad^ed, and again 12 toifes added to adapt it to the mean 

 temperature of the atmofphere. Thus correfled it is 176886 

 'toifes. The arch meafured begun 36'^ north of the equator, 

 .and extended to the parallel of 3<' 6' 25" fouth ; we fhall fup- 

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

 to the parallel of 3** 7' \'\ a fuppofition which can produce no 

 fenlible error, and will fomewhat firaplify the calculatio;V 

 Thus ^, in the preceding formula, is an arch of 3** 1' V ex- 

 preffed in decimals of the radius 1, and fo we^ have m^^IZ 

 .0544009, n— .1086408, and ZZZ 176886. 



Again, the amplitude of the whole arch meafured in France 

 from Dunkirk to Perpignan is 8° 20' 2''f and its length 

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

 tude 5ie2M^ and the fouthern in 42**4l'58"f. Hence 

 V' ~ .8907045, and ^' zr .7452459, and therefore w' n 

 ,1454586, n'zz .0585735, / — 475496. ^ 



n'l — nl' 



' Therefore, a zr — ; r ~ 3273325 toifes; 



mn — mn 



'^ - m'l-mV .^ ^ 



— 10917 toifes. 



mn ~ mn 



and —ZZL --— • nearly. 

 a 300 ^ 



Wherefore alfo the longer axis of the meridian is to its conju- 

 gate, or a is to Z» as 300 to 299. 



This proportion agrees well with that which was already 

 pointed out as the moft probable refult, from the comparifon of 

 iingle degrees, and from obfervations of the pendulum. As 

 thefe conclufions are obtained by different methods, they tend 

 greatly to confirm one another. 



8. From this too it feems highly probable, that the uncer- Probability that 

 tainty which yet remains with refped to the true figure of the '^*jj6".^[=°^'^* 



earth weU dctwmined 



