French Xatlonal Institute. 27* 



In opcratiofis where it is required to dctoraiine more ex-- 

 actlv ihedilrciv-iicc between" the terrestrial globe and a ptrtecl' 

 sphere, attention inii5t be carried still farther. Trianglc.'J 

 formed on the surface of tlie earit> were corxsidered as vciy 

 small portions of a bphere, which in the exient of each in- 

 angle differs imperceptibly from the spheroid. 



Does thif supposition, less inaccurate than the preceding, 

 promise all the precision wliich we wi<h for ; and since it is- 

 a spheroid which it is required to measure, wjiy have not llio 

 triangles been calculated as spheroidal ? The quesiion is so 

 natural, that it ought to present itself at first siahi to the 

 astronomers who are occupied with the operation, and to 

 each of the scientific men in Europe, who have united in 

 order to examine and judge the work lately executed. In 

 one of the first meetings of the commission, a learned fo- 

 reigner, M. Tralles, remarked that tlie basesof IVie'un and 

 Perpifrnan ought not to be simply considered as arcs entirely 

 in the same plane, but as curves with a double curvature, 

 'litis remark had before been made by Clairaut more than 

 fifty years ago; but it was always ihouaht that the eO'ect of 

 tlij double curvature could not become in the least sensible, 

 except upon intervals much greater than ihoae whicii a;e 

 given us to measure directly; and it was concluded that the 

 consideration of the spheroid would onlv uselessly conipli- 

 crAC calculations which were already become too compli- 

 cited. In fact, the spheroid difl'crs iar less from the sphere 

 than the sphere itself dificrs from a plane, liui the spheri- 

 city of the triangles only introduces into the calculations 

 terms of the second order for the angles, and of the thud 

 order for the sides. It was therefore natural lu ilnnk tluu 

 the terms depending on the spheroid were of an order still 

 higher, and still more in?ensible by their e.\iri.ine minute- 

 ness. But although no person had as yet wiitien upon this 

 sul>jecl, we ought not to conclude from tins that we should 

 remain contented with vague considerations and simple pro- 

 bability. 'I'his point is discussed under the article CukuUJun 

 of Triangles \n the second vokunc of ' ' Tht Dttfnninaliov of lft.i> 

 Meridian," now in the press : it is expected to dtmonitrate, 

 by very simple and entirely elementary cousivltr^uioni,. \\\^\ 

 S 3 the 



