110 INVESTIGATION OP CERTAIN THEOREM* 



arch meafured in Peru, will afford a variety of data for deter- 

 mining the true figure of the earth. 

 Obfervations of But furveys of the kind now referred to, afford likewife 

 tTSL^meridian ^^^®'* "^^^er'a's ^roi" which the folution of this great geogra* 

 and of parallels phical problem may be deduced. Thefe are chiefly of two 

 of latitude. fo^ts^ viz. the magnitude of arches, either of the curves per- 

 pendicular to the meridian, or of the circles parallel to the 

 equator. Examples of the firft of thele have been given by 

 General Roy and Mr. Dalby ; the obfervations which follow 

 are directed toward both. 

 Large perpcndi- 13. With refped to the meafurement of arches perpendicu- 

 veilj'difficuk ^^^ ^^ ^^® meridian, it may be obferved, that the direaions of 

 meafurement J gravity at different points of fuch arches do not interfedt one 

 another at all, unlefs the diftances of thofe points from the faid 

 meridian be very fmall. On this account the meafurement of 

 a large arch perpendicular to the meridian would involve in it 

 confiderable difliculty ; to avoid which it is neceffary that the 

 arch meafured be but fmall, or one that does not greatly ex- 

 and fmall ones ceed a fingle degree. Such meafurements are of courfe ob- 



erroneous from noxious to all the errors that arife from the deflexion of the 



partial gravjta- , , , . r • i r ^ 



tion. plumb-lme, and cannot therefore furnilh data for determining 



the figure of the earth, equally valuable with thofe which may 

 be derived from large arches of the meridian. The method 

 of determining the figure of the earth, from degrees of the 

 perpendicular to the meridian, is not however without its ad- 

 vantages, and in certain circumftances is preferable to any 

 other that proceeds by the meafurement of arches equally 

 fmall. This method is twofold ; as a degree of the meridian 

 may be compared with a degree of the perpendicular to it in 

 the fame latitude ; or two degrees perpendicular to the meri- 

 dian, in different latitudes, may be compared with one an- 

 other. The advantages peculiar to each will appear from the 

 following inveftigalion. 

 To find the axes ^^' Let It be required to find the axes of an elliptical fphe- 

 of a fphcroid roid, from comparing a degree of the meridian in any latitude 

 a2cg."rth"°^ ^'^^ ^ degree of the curve perpendicular to the meridian in 

 merid. with one the fame latitude. 



of the perpend. Let theellipfis ADBE (Fig. on page 105) reprefent a meri- 

 dian, of which a degree is meafured at F. Let the perpen- 

 dicular 



