Relating to the FIGURE of the EARTH. 15 



gravity at different points of fuch arches do not interfecfl 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 difficulty ; to avoid which it is neoeffary that the 

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

 a fingle degree. Such meafurements are of courfe obnoxious 

 to all the errors that arife from the defledlion of the plumb-line, 

 and cannot therefore furniih data for determining the figvire of 

 the earth, eq-ually valuable with thofe which may be derived 

 from large arches of the meridian. The method of determi- 

 ning the figure of the earth,, from degrees of the pei-pendicular 

 to the meridian, is not however without its advantages, 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 perpepdicular to it in the fame latitude ; or two 

 degrees perpendicular to the meridian, in different latitudes, may 

 be compared with one another. The advantages peculiar to 

 each will appear from the following inveftigation. 



14. Let it be required to find the axes of an elliptic iphe- 

 roid, from comparing a degree of the meridian in any lati- 

 tude with a degree of the curve perpendicular to the meridian 

 in the fame latitude. 



Let the ellipfis ADBE (fig. i. PI. I.) reprefent a meridian, of 

 which a degree is meafured at F. Let the perpendicular to the 

 meridian in F meet the lefs axis DE in R. Then R will be the 

 centre of curvature of the circle cutting the meridian at right 

 angles in F ; for at any point in that circle indefinitely near to 

 F, the diredion of the plumb-line, or of gravity, as it always 

 paffes through tJie axis DEj, will cut DE in R ; it will therefore 



alfo 



