Relating to the FIGURE of the EARTH. 21 

 f m y _ f m y =s fin (<p' + ^) X fin (<p' — <p'), and 



* — fin (?' + ?") x lin (?' — ?"/ 



23. In the fame manner, becaufe otD' = * + <? fin *<p\ by 

 fubftituting for c, we have 



. . m(T>' — Dp fin V , 



mD =a+ fin^ + ^xfinC^ — *")' 

 ^(D' — D")fin> 

 tf = «2D — fin O' + 9") x fin (?' — ?")* 



24. Lastly, fince niD' zz a -\- c tin *<?, 



and mjy = a + * iin V, 

 dividing the firft of thefe equations by the fecond, and reject- 

 ing the higher powers of c, we have 



~£L — ! -f £ (fin *<p' — fin V), and therefore, 



51. 



- == ^-§7 — r-TT77. Hence alfo 



a — finY — finV 

 D' 



D" 



— 1 



, rpr r or more conveniently for calcu- 



* D' — D" 



lation by logarithms, - — D " !in(/ W) x fin<y — yy 



25. We may compare this value of - with that obtained in 



§ 1 8. from other data, in order to determine which of the two 



methods of finding c - is to be preferred, under given circum- 



ftances. Suppofe, for inftance, a degree of the curve perpendi- 

 cular to the meridian, in the latitude <p' to be D', and a degree 

 of the meridian itfelf in the fame latitude to be A' ; it is requi- 

 red to find in what other latitude <p'\ a degree D', perpendicular 

 to the meridian, mull: be meafured, in order that the compari- 



fon of D' and D*, and of D' and A, may give values of -, in 



which the probable error is the fame. 



HERJfc 



