RELATING TO THE FIGURE OF THE EARTH. 171 



D'— D, and alfo paying no regard to the inequality of A afid 

 D' in the denominators of thefe fra6lions, as it is notfo great as 

 materially to affed the quantity that is fought for here, we Ihall 



have the errors in - nearly the fame in both formulas, when <? 



a ■' 



and cp' are fuch that 2 cof *cp = 3 fm *4> -- 3 fin *?>', or when 



2 



-• col ?)* = fin *?> — fin *(p', that is, adding cof *9 to both fides, 



- cof *?! n fin *<p -f cof *^ — fin *<?>', and, therefore, - 



5 5 



-cof ^^Jzz 1 - fin *<?>'zz cof *(?)', orcof <?>'zr (coftp) v'-. 



o »> 



29. If, therefore, cofJpzZv/-* cof (p'ZI 1, that is <p'z:0, 



io that A, the fecond of the degrees of the meridian, muft 



3 

 in this cafe be under the equator. But ^- 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 exad 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 exad, 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 =z 50<> 4] 'j then we will have (p^ z=. 35** 7^, fo that D 

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

 35^ 1', in order that the refult may be as good as when D and 

 V>' are compared with one another. 



From this it is evident, that the method of comparing de- The former me- 



grees of the meridian, and perpendicular in the fame latitude, thod h preferable 

 r , 1 •/•/>! /. , unlefs the degs. 



has even an advantage over the companion of degrees of the of the mer. be 



meridian in different latitudes, unlefs thefe lafi are taken at a^arafunder. 

 confiderable difiance from one another. 



In this way may many ufeful conclufions be derived con- 

 cerning the degree of credit due to meafurements already 

 made, as well as with refpe6l to the feleiSlion of the places 

 where they are to be made hereafter. On thefe I (hall enter The /ormermc- 

 no further at prefent, and fiiall only add, that, befides the ad- ^hodalfo fup- 

 vantages or diladvantages which the method of comparmg to- obfervers and 

 gether degrees of the meridian and perpendicular in the fame *^ ^^'"^ inftra* 

 latitude has, and which are fubje6ls of calculation, it has an- 

 ' . other 



