24 INVESTIGATION of certain THEOREMS 



to be committed in the determination of D — A, and of D' D, 



and aHb paying no regard to the inequality of A and D' in the 

 denominators of thefe fractions, as it is not fo great as material- 

 ly to affect the quantity that is fought for here, we fhall have 



the errors in - nearly the fame in both formulas, when <p 



and <p' are fuch that 2 cof *<p = 3 fin 2 <p — 3 fin 2 <p', or when 



I cof <p* = fin 2 <p — fin 2 p', that is, adding cof 2 <p to both fides, 



s - cof % <p =r fin 3 <p -f- c °f i( P — fin 2 <p', and, therefore, 



- cof J <p = 1 — fin 2 <p' ±= cof 3 <p\ or cofp' = (cof <£>)/-. 



29. If, therefore, cof<£> rz y^, cof <p' = 1, that is <p' n o, 



lb that- A, the fecond of the degrees of the meridian, mud 



in this cafe be under the equator. But yf- is the cofine of 



39 . 14, in which latitude therefore if D and D' be meafured, 

 the refult, by comparing them with one another, is as exact as 

 if D were compared with the degree under the equator. Hence, 

 if D and D' are meafured in a lower latitude than the above, 

 the refult will be more exact, than if D were compared with the 

 degree at the equator. 



If we fuppofe D and D', meafured in the fouth of England, 

 fo that <p — 50 . 41' ; then we will have <p' =. 35 . 7', fo that D 

 muft be compared with a degree of the meridian as far fouth as 

 35 . 7', in order that the refult may be as good as when D and 

 D' are compared with one another. 



F^om this it is evident, that the method of comparing de- 

 grees of the meridian, and perpendicular in the fame latitude, 

 has even an advantage over the comparifon of degrees of the 

 meridian in different latitudes, unlefs thefe laft are taken at a 

 considerable diftance from one another. 



In 



