168 GEODESIC INYESTIGATIONS. . 



f^^ If the given data were I". , A", "2, , s : then it is evident that formula 

 (a) should be written as follows ; 



c<.tt(t„-ft,)=:-gi;f±fl].coti-^" 



otherwise : — 



To find the arc S, D,, or z, ,— 



s. sin 2 



sm. z. 



I (5, 2)2 — 4. s. sin- i 2 (i?, 2 — *) I ^ 



The triangle P S^ D„ gives — 



tan i (A, + CO) = cosUZ^-O ^^^ ^ ^, 



cos i (f/ -}" */) 



tan i (D,, - 0,) =^ !|^LfA^. cot i ^' 

 from which to find D„ and a' . 



m 1 • ^'/ cos \ (z, — i 2) sin D,, 



ihen we have, sin A = ^-^^-^ ~ — '- '-i 



cos 4 2 



from which to find A". 



cos 1 {A' + ^" 4- co) 



tan i" f,, = — 1 , ., — i — 777 ; • cot i / , 



" cos ^ (^ "T -^ — '^J 



from which to find I". 



The various other entities \ 2', ^ 2", &c., can now be found as in Problem 1. 



I^^ In the determination of the difierence of longitude co, as in Chambers's 

 " Practical Mathematics," and in the treatise on " Geodesy" in " Bohn's 

 Dictionary of Engineering," the formula employed is erroneous in principle, 

 and must lead to resiilts more or less incompatible. 



The formula is — 



s. sin A' 



R, cos I" . sin 1" 



It would be better to find /", and i?^^ approximately {I" is there found 

 before finding u), and put — 



s. sin A' . sin 2 



sin ce = 



R"cosl" . 2 



-c, sin A' R,, cos I" ■ , ■ •,, ,^ 



i?or ; = —^ IS at variance with the expressions — 



sin A M, cos I 



s Fin A' s . sin A" 



Rj cos I" . sin 1" i2„ cos I' . sin \" 



' This problem and problem 1 are the only two contained in this paper 

 which have been solved elsewhere. They have received special attention in 

 the elaborate work published by the Ordnance Department in 1858, entitled — 

 " Account of the Principal Triangulation of Q-reat Britain and Ireland." 



