Relating to the FIGURE of the EARTH. 21 

 fin ^?>' — fin '<p" = fin {<p' + ?>'0 X fin ((p' — f), and 



23. In the fame manner, becaufe mD' zz a -\- c Cm '(p', by 

 fubftituting for c, we have 



T^r I mCD' — D")tm^P ^„ , 



, ct(D' — D'Qfin"^ 



« = mD — fin (?' + ?") x&n {(?' — <?")' 



24. Lastly, fince wD' =z a + c fin '?>', 



and mD* = a + c fin '(p'', 

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

 ing the higher powers of c, we have 



21 — , -j_ f (fin "(p' — fin Y)y and therefore, 



51_ 

 51-1 



' or more conveniently for calcu- 



a~ fill ; .' + If-' ) X lin (.^— *") ' 



lation by logarithms, ^ = d" fin (/ + /') x fin (?>'_ 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 ^ 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, muft 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. 



Herk. 



