122 Approximate Values of the Radii of Curvature, fyc. [Aug. 



By Art. 10, M=p \/~> hence we have 



Log. 60848 = 4-7842463 



Log. 60459-2 = 4-7814624 



Difference = 0-0027839 



i difference = 0013919 



Log. 60848 = 4-7842463 



Log. 61043-3 = 4-7856382 



If p had been taken 60851*1, as found by the latter part of 

 example 4, instead of 60848, a degree at the poles would be 

 61048 fathoms. 



Example 8. — Given the length of a meridional degree at the 



equator 60459-2 fathoms and the compression g — , to find the 



length of a meridional degree in latitude 59°. 

 By Art. 5, we have M — m = 3 e m s 2 . 



Log. 3 =■ 0-4771213 



Log. — = 3-5086383 



Log. 60459-2 = 4-7814624 



Constant log = 2-7672220 



Log. sin.* 59° = f-8661312 



Log. 429-88 Z 2-6333532 



m = 60459-2 



M = 60889-08 fathoms the required length. 



In this manner were the lengths of the meridional degrees, as 

 given in the table, obtained, which agrees with Col. Lambton's 

 table, calculated to every third degree. 



Example 9. — Given the length of a degree perpendicular to the" 

 meridian at the equator 60848 fathoms, and the compression 



— , to find the length of a perpendicular degree in lat. 75°. 



By Art. 5, we have P — p = p e s a . 



Log. 60848 = 4-7842463 



Log. ~- = 3~5086383 



Constant log - 2-2928846 



Log. sin.* 75° = 1-9698876 



Log. 183-13 = 2-2627722 



p = 60848-0 



P = 61031-13 fathoms the required length. 



