FIGURE OF THE EARTrf. 



97 



for the purpose, would be singularly qualified for a 

 similar undertaking in Africa, and would furnish us with a 

 measurement in the other hemisphere, as much to be relied 

 upon as the former. He would have the glory of deciding 

 two important questions lay his own observations -, first, the 

 similarity and magnitude of the two hemispheres : and, se- 

 condly, the degree of reliance to be placed on the elliptic 

 hypothesis. 



It might be still further desirable, if other measurements and > n New 

 could also be undertaken, either in New Holland, or in Brazil j ° an ' 

 for though neither of these countries differs much in latitude 

 from the Cape of Good Hope, they are so remote in longitude, 

 that a correspondence of measures so taken would nearly esta- 

 blish the similarity of all meridians. 



Note. 



I shall now explain the formulae employed in deducing the Formulae em- 

 results to which I have come in the foregoing Memoir. The P'°yed in the 

 demonstration of them is to be found in the work of M. De- computation, 

 lambre, on the Meridian. 



In the first place, let a be the radius of the equator, e the ec- 

 centricity, >]• the latitude of one extremity of a side, or arc, iri 

 any series of triangles, and the azimuth of that side. The 

 radius of curvature of this arc will be expressed by 



(1 -| • cos. ty . cos. 2 } 

 1 — e» J 



1— «* J , 1 (1— e"-. sin. *^)i 



= and — = . 



Rl R R a 



Hence we see that R is the radius of the arc at right angles 

 to the meridian. One may in general neglect the azimuth, 

 and take the last radius for the radius Rl. Now, in compu- 

 ting the arc between Clifton and Dunnose, I have supposed 



the oblateness to be — ore 2 = — 2 > and log. a = 0,5147200 



expressed in toises. 



The latitude of the southern extremity of the base is the 

 same as that of Clifton, and its azimuth, if we choose to attend 

 to it, is nearly 335° 23'. This base, considered as an arc of a 



K. i» 

 circle, is reduced to its sine by the formula 8 = log. « — 6R » ' 



Vol.XXXIV.—No. 157. H (K 



