Relating to the FIGURE of the E A RT H. 27 



32. Again, if <p' and <p" are the latitudes of the extremities of 

 an arch of the meridian, the length of which has been meafu- 

 red, and found = l\ then, according to § 5. we have 



If, therefore, m be the coefficient of tf, in the former equation, 

 and n the coefficient of c ; and if m' be the coefficient of a, in 

 the latter equation, and n' of c , we have, as in § 6. 



n'l — nl' J m'l — ml' r 



a — — 7- r-t an d c — —-, -, or lmce m z±> 12 



mn' — m'n' mn — mn* ' 



n'l—nf j m'l— I' 1r c m'l — I 1 



a — - v " , ■ . and c ~ tr ; alio - zz -n 7/ . 



— ,1 — mri* n — m'n' a n'l — nl' 



33. In this way of determining a and c, the parallel of lati- 

 tude may either interfect the arch of the meridian meafured or 

 not. If it interfect that arch, this method may have the fame 

 advantage that was taken notice of in another folution, viz. that 

 the whole of the data may be furnifhed from the fame fyftem 

 of trigonometrical operations. Thus, in the furvey of Great Bri- 

 tain, an arch of 5 or 6 degrees of a parallel to the equator might 

 be meafured, and compared with the whole length of the meri- 

 dian, comprehended between the northern and fouthern extre- 

 mities of the Ifland, amounting nearly to 9 degrees. 



It is plain, from what has already been faid, that the refuk 

 deduced from this comparifon would pofTefs every advantage, 

 and would be entitled to more credit, than any determination 

 of the figure of the earth that is yet known. 



34. On the fuppofition that, in a furvey of a country, the 

 measurement is made along a feries of triangular planes, all gi- 

 ven in pofition and magnitude, there is yet another method of 

 determining the figure of the earth, more general than any of 

 the former. On the fuppofition juft mentioned, it is evident, 

 that the length of a ftraight; line, or chord, drawn from a given 



D 2 angle 



- 



