46 On Practical Geodesy. 



in which the + sign only should precede the radical portion. 

 This is evident. For since the general expression for sin o> 

 holds when A^ = 90°, in which case N = ; and that sin 

 o) must be positive ; therefore it is the + sign that must in 

 such case, and in all cases, precede the radical. 

 We may also find w in the following manner — 

 Find the arc JJ' by means of formula (79), and the angle 

 D^^ from — 



. cos Z, sin A^ 



sm D,, = ' — YTf — 



" sm JL ' 



and tlien to find w we have — 



cos ^ CLi" — Z') 



*^° ^ " = cob|(L" + ■ ""^ * <^' + ^"> 



To find the azimuth A,, we then have — 



tan J (A, + A J = cos i {I — I) . ^.^^ i ^ 

 ^ ^ ' ^ "^ sin i (I, + I) ' 



And to find s, we have — 



sin L'^ sin w 



sm z, = 



sin A, 

 5 = 2, • E, • sin 1" 



The other entities can be easUy found as indicated by 

 formula. 



1^" If l,„ l„ A,, were given instead of l„ l,„ A, ; then 

 instead of L", D,„ fee, in the preceding formulae, we should 

 have L', D,, &c. 



Otherwise. 



To find the azimuth A,,, we have — 



. . R • cos Z, . . , 



sm A,, = ^ -' • sm A, nearly. 



ii,, • cos l,^ 



And then to find w, we have — ■ 



And when instead of A„ the azimuth A,, is given, the first 

 of these must be replaced by 



A R,, • cos I,, . A 



sm A, = —^ ^ • sm A,, 



K, • cos I, 



&c., &c. 



