166 GEODESIC INTESTIGATIONS. 



Then taking the means of the three vahies of each of the angles A , A", 



a 

 as the most reliable, we should compute "T" from the more accurate equation. 



tan^- I' - i^rr I" ('''' ^' " ^^^ ^ ^^ \ ^ 

 « _. Vsm A" . cos i 2 / 



*^ /" siu ^' ■ cos i^' \ ^_]_ 



Vsin A" . cos i 2" / 



By selecting suitable pairs of stations it is evident we should be enabled to 

 approximate closely to the value of ,-• 



Problem 4. 



Given the two latitudes l', I", and the length s and circular measure 3 

 of the geodesic arc joining the stations : to find the azimuths A', A", the 

 difference of longitude w , and all the other entities. 



We can find the arcs S, D^^, S^, D, or z,, z^„ from — 



s. sin 2 



{ (i2, 232 _ 4s . sinH 2 (i2, 2 — 5) p 



sin z^, = s.sin:^ 



{(R„ 2)'^ — 4 s . sinH 2 {E„ 2 — s)}» 



We can find the arcs F D„ P D^„ or L„ L^^, by means of — 



M,{1 — e-) sin I' + R„ e^ sin I" 



cot L, = -^ '— -, '-^ 



if, cos i 



, _ i?,, (1 — e-) sin I" + R, e- sin I' 



cot i,, = — '^ ^ ,„ 



-«„ cos ( 



Tlien from the triangles 5^, P D,„S,, P D^, we can at once obtain the two 

 azimuths A', A", and the difference of longitude to . We have — 



tani^'= (^i"^y---.) sin(y-0|i 

 (. smj3 . sm {p — L,,) ) 



taniA"= pin (g-.Jsin(g-U-)i 

 ( sm 2 . sm (g- — ij j 



tan* co= (^m(^-XJ sin (p - Z,) | j 

 (. sin ^ . sin (^ — z,) ) 



( sin (g- — L^') sin (g — ?,,) "j ^ 

 I sin g . sin {q — z^^) ) 



in which ^ = ^ (l^ + z, + ij, and 2 = i (^,/ + z^, + L^ 



The other entities can be found as in Problem 1. 



