

1819.] vfthe Elliptic Arcs of an oblate Spheroid. 123 



In this manner might the lengths of the perpendicular degrees, 

 as given in the table, be calculated, but I have preferred the 

 following method : 



By Art. 16, F = -^ — + P, where W - M represent the 



difference between any two contiguous meridional degrees (as 

 shown in the table) and P v , P, the lengths of two corresponding 

 perpendicular degrees ; therefore, by beginning at the equator, 

 or at the poles, the table may be easily formed ; for by example 

 4, the length of a perpendicular degree at the equator is given ; 

 and by example 7, the length of a degree at the poles is known. 



Length of 1°= °-? + 60848-0 = 60848-1 



2 = °-± + 60848-1 = 60848-3 



3 = °_? + 60848-3 = 60848-6 



4 = — + 60848-6 = 60849-0 



3 



5 = !l 6 + 60849-0 = 60849-5 



6 = r + 60849-5 = 60850-2 



and so on. 



The length of a degree corresponding to 3° of latitude by the 

 former part of this example is 60848-54 fathoms, and of 6° of lat. 

 60850-14 fathoms. 



Example 10. — Given the equatorial diameter 6973028 and the 

 polar axis 6950534 fathoms, to find the length of the elliptic 

 quadrant. 



By Mr. Barlow's tables, p. 292, we have c {1 — (-^- + 



3d* 

 i 



)) C X 2 

 j = elliptic meridian, where 1 ^-r^ = 1 — (1 — e) 



= e (2 - e) = — = — = d, and the log. c = 7-3405713 



v ; (310)» 96100 ' & 



(example 6). 



Log. d = 3-8089672 



Log. 2?, ai.com. .... = 1-3979400 



Sum = 3-2069072 Number = -0016103 



Log. 3 = 0-4771213 



Log. d* , = 5-6179344 



Log. 2» x 4* ar. com. = 2-1938200 



Sum = 6-2888757 Number =-0000019448 



•0016122448 



