On Practical Geodesy. 65 



To find L' we can also use the formula — 



tan A (l" — L') = ^"^ 1 /W T x \ ' tan h z„ 

 2 ^ >' sin 1 (D, + A,) 2 '> 



To find 8,, we have — 



log j-^ = 3-83451 



sin L' = 1-89655 .-. 8, = 0° ,, 00', 15"-3098 



sin i (^ + L') = r-89946 .-. l'=L' — 8, = 51°, 59',59"-9999 



log {I" — L') = 3-55445 



.-. log 8. = 1-18497 .-. L = 38°.. 00'.. 00" 0001 



To find A^, we have- 



sin T), tan ^ z, 



sin D, = 1-85149 

 tan ^z, = 2-08865 .\ D, — A, = 0°, 00', 00"-1334 

 log 8, = 1-18497 But D, = 134, 44, 02 -8573 



... log(D,— A,) = 1-12511 .-. A, = 134°, 44', 02"-7239 



l^° In the "Account of the Principal Triangulation of 

 Great Britain and Ireland " the formula from which to find 

 Z^is— 



s sin I (D, — A ,) 



^^~^" - p- sin 1" ' sin 1 (D, + A,) 



• |l +'^-cos2i(A,-A,)sinM"| 



and the resulting value of I, — I, = l\^ 00', 00" -0059 



.-. l^ = 38°, 00', 00"-0059 which 

 is too great by 0''"006, while by the method in this paper the 

 error is only O^'-OOOl. 



In the treatise on " Geodesy " in Spon's Dictionary of 

 Engineering, the unknown latitudes in the first and second 

 cases of the problem are determined by means of the 

 formulae — 



r 5 • cos A, s^ - sin^ A, tan I,} ,^ , ., , , 



' " ( R, sm 1" ' 2 • K", • sm 1" j ^ ''' 



f , sjcosA, g' • sin ^ A, tan Z, ] 



