24 On Prdctical Geodesy. 



equal ; but we know, in any such case, that the angles D^^, 

 A^^, D^, A^, are equal. 



2°. From the first of the equations we should infer that A^^ 

 is less than D^^ when A^ is acute ; but we know that A^^ must 

 be always greater than D^^, when l^ is greater than l^^, or 

 when A^ is greater than A^^. 



3°. In the example 1 worked out in this paper, we have, 

 by using correct formulae — 



A,, — D,, = 0^' • 1334; D, — A, = 0" • 1334. 

 But if we were to use the above erroneous formulae, we 

 would find the values — 



A,, — D,, = 0" • 1315 ; D, — A, = 0" • 1352. 



^p° On page 676 the formula 96 is misprinted : - — ^77 



being there used instead of sin V. 



27. From (4*6) and (47) it is easy to deduce the following 

 expression — 



. 1 _ J cos ^ (A, + A,, + x) cos 1 (A, + A,, — x) 



aLlX 7) V :;; ;— 7 ; r 



^ COS i (A, + A,J 



in which the angle x is found from — 



sin J a; = sin J {I, + l^) • sin | w. 



28. The perpendicular from Z^^ to the line B^JZ^ is equal 

 Z^Z^^ • sin L"; and .*. it is evident that the perpendicular 

 from Z^^ on the normal-chordal plane S^S^^Z^ is equal to 

 Z^Zoo • sin L" • sin D^^. But the perpendicular from Z^^ on 

 the chord SoSSoo is evidently equal to R^^ • cos a^^: Hence, 

 obviously — 



Z Z,, • sin L" • sin D,, 



sin A - ° °° ^' 



K,^ ' cos a„ 



But, 



Z<,Zgj, = e^ (R^ sin l^ — R.^^ sin l^) ; sin L" sin D,^ = cos l^ sin A^ ; 



and 



R, cos I, sin CD 



cos a„ = —L -1 _ 



k ' sm A^^ 



Hence we have — 



2 7 sin A, sin A,, /sin I, sin l.\ , . 



sin A ^ e-k' L '1 • i_^ ^\ (93) 



sin o) ^ R// R, / 



7 R^ — R^/ sin A, sin A,, /-o • ?/ , -n • 7 \ — 1 



sm A = « -^ rr— ^ T ' (xv . sin I + K,, sin I,) 



K, • K,, sm o) . 



sin A =-pr — ^ — '-, -^ ''{ — — • (cos^ I,, sin^ A,, — cos^ I. sin^ A J 



R, sin t,+R,, sm I,, 



