RELATING TO THE FIGUHE OF THE EARTH. 1^9 



25. We may compare this value of^- with that obtained In To determine 



*^ the figure of the 



5 18. from other data, in order to determine which of the two ^^^^^ fjommea- 



fures o/ the per>r 



methods of Undiner ^ is to be preferred, under given circum- pe"'^"^"'''^ '" 



^ a different htU 



fiances. Suppofe, for inftance, a degree of the curve perpen- '*^'^"* 



dicular to the meridian, in the latitude cp' to be D'', and a de* 



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



required to find in what other latitude (p'\ a degree D'^ per-. 



pendicular to the meridian, muft be meafured, in order that the 



comparifon of D' and D^', and of D' and A, may give values 



c 

 of — , In which the probable error is the fame. 



Here, agreeably to an obfervation already made, we may. In 



c 

 Older toeftimate the error produced in ^, in confequence of 



an error in the determination of D', and D'^, and A, fuppofe 



the error to afFe6t D'— D", or D'— D'' only, without paying 



any regard to the variation of D'' in the denominator. There- 



c D'— A 



fore, fjnce by ^ 18 we have - = —t~ ^r-— ,, and again by § 24, 



•^ ^ a 2iy cof *?> o J ^ 



c D'— D^** » ^ 



termining D'— A, and D'— D", and alfo that thefe are the only 

 errors, their effeft will be the fame, in both cafes, if 2 cof <p'* 

 = fin (*<?>^— fin '^<P"). Now, if we fuppofe <?>'' the quantity 

 fought, and add cof ^'* to both fides of the preceding equation, 

 then 3 cof *?>' = fin *(?)' + cof *(f)' - fin ^^'' = 1 - fin ^^p" = 

 cof *<?". The latitude <?>'' therefore muft be fuch, that cof (p" 

 ~ ^ 3 X cof <p^ If, therefore, <p' be fuch that cof ?>' — 



, — , the cofine of (p'^ will be ~ 1, and ^' therefore zz 0. Now, 



^40 44' is the arch of which the cofine zz — rmearly, therefore 



if a degree of the meridian, and of the perpendicular to it, be 

 meafured in latitude 54° 44-', the comparifon of thefe with one 

 another will give a refult as accurate as if the degree of the 

 perpendicular, in that latitude, were compared with the de-r 

 gree at the equator, and more accurate of confequence, th^n if 

 pny other degree of the perpendicular to the meridian, were to 

 ^e CQinpared with D'« 



$6, Henc^ 



