1819.] of the Elliptic Arcs of an oblate Spheroid. 119 



degrees perpendicular to the meridian, then will JVT = 3 (P x — P) 

 + M and P' = — ^ H P very near. 



Let S\ S denote the corresponding latitudes, m the length of 

 a meridional degree, p the length of a perpendicular degree at 

 the equator, and e the compression ; then (Art. 5) M v — M = 

 Sem (S'« - S«) and F - P = p e (S v * - S«), therefore W 

 — M : F — P :: 3 m : p :: 3 : 1 nearly, or V M - M = 3 (F-P), 



hence we have M v = 3 (F - P) + M, and V = HLzi* + p 



very near. 



17. The preceding equations are nearly the same as given by 

 Col. Lambton, in Part II. of the Philosophical Transactions for 

 the year 1818, from whence most of the following examples are 

 taken. 



Example 1. — Given 60473-53 fathoms for the length of a meri- 

 dional degree in latitude 9° N. and 60484*5 fathoms for the 

 length of a meridional degree in latitude 12° N. to find the com- 

 pression. 



n . 60484-5 - 6047353 = 10-97 



Compress-on = 3 (60473 . 53 siD ,, lgo _ 60484 . 5sin ,, 9O) (Art. 7), 



Log. 60473-53 = 4-7815653 



Log. sin.* 12° = 2-6357578 



Log. 2614-1 = 3-4173231 



Log. 60484-5 = 4 7816441 



Log. sin.* 9° = 2-3886648 



Log. 1480-16 = 3-1703089 



3 (2614-1 - 1480-16) = 3 x 1133-94 = 3401-82 andthecom- 



10-97 1 



pression = ^^ = — . 



Example 2. — Given 60484-5 fathoms for the length of a meri- 

 dional degree, and 60856*5 fathoms the length of a degree 

 perpendicular to the meridian in latitude 12° N. to find the. 

 compression. 



■r, . a . 60856-5 - 60484-5 = 372 



By Art. 8, compression = 2 x 60484 . 5 x cos ,, IgB - 



Log. cos.« 12° = 1-9808088 



Log. 120969 = 5-0826741 



Log. 115739-8 = 5-0634829 



372 1 



Therefore U ^ 39 . H = -g-jy-y for the compression. 



Example 3.— Given in lat. 13° 34' 44" N. The length of a 

 meridional degree 604-91-46 fathoms, and the compression 



9. 



