1819.] of the Elliptic Arcs of an oblate Spheroid. 121 



•d a i a i /'" i /60459-2 



By Art. 4, compression e = 1 - ^J - = 1 - ^/-^^ = 



1 - -9968 = -0032 = ^, instead of ~ Q . This is in a sup- 

 position that the length of a degree perpendicular to the meri- 

 dian at the equator is 60848 fathoms. 



Example 5. — Given the length of a meridional degree at the 



equator 60-459 • 2 fathoms and the compression — , to find the 

 equatorial diameter and polar axis. 



r> a * n n vr vm 310 x 57 " 29 &c - x 60459-2 . .. ±r 



By Art. 9, C K = j— = — = half the 



polar axis. 



Log. 310 = 2-4913617 



Log, 57-29, 8cc = 1-7581226 



Log. 60459-2 = 4-7814624 



Log. 309 ar. com = 3-5100415 



Log. 3475267 = 6-5409882 



Therefore the polar axis is 6950534 fathoms, differing from Col. 

 Lambton's measure by 358 fathoms. 



By Art. 9, C H = ^-^ = _ x -. 



Log. —-, as above = 6-5409882 



Log. 310 6 = 2-4913617 



Log. 309 ar. com = 3-5100415 



Log. 3486514 = 6-5423914 



Therefore the equatorial diameter is 6973028 fathoms, differing 

 from Col. Lambton by 360 fathoms. 



u , CH-CK 11247 J „ 



Hence we have c t] = ^^ = ^^^, according to 



, _ a - C 22492 1 ,. _ , _ , 



example 5. — . ^^ = ^^ according to Col. Lamb- 

 ton. 



Example 6.— Given the equatorial diameter 6973028 fathoms, 

 to find the circumference of its corresponding circle. 



Log. 2 = 0-3010300 



Log. 3486514 = 6-5423914 



Log. 3-141, Sec = 0-4971499 



Log. 21906414 = 7-3405713 



The required circumference differing from Col. Lambton's by 

 1134 fathoms. 



Example 7.— Given the lengths of a meridional and perpendi- 

 cular degree at the equator 60459*2 and 60848 fathoms, to find 

 the length of a degree at the poles. 



