(4) 
(5) 
(6) 
equation, one 
) 0.5V (7) 
Xi, OY,, AND 
one gets the 
te directions 
sec’ a, Va) 
(8) 
(9) 
t a» Va» 
| (cosec y, 
Va) ] 
[-0.5 (2, -V) 
e^ yi 
pd Vy, 
(10) 
$ (8), (9) and 
52 a2) 0% (11) 
(12) 
(2: - 0.5V) cosec? a, 
  
9727. s [0:5 Z. cot qi * ]? cu [+0.5(Z, -V) 
(cot à; - cot 02) 
2 
(2; - 0.5V)cosec^ a» 2 sec! Y1 
2 x2 
con TR T OS Yc? + 10.25-Z: 
  
tan? Yı 
4 
+0,25 Zon VI Sec. Y2]o*y (13) 
tan? Y2 
Substituting the values of trigonemetric functions aj, 02, Y; and yo? of 
equations 11, 12 and 13 by their values of Cartesian coordinates Xj, Yj and 
Zi, one gets 
  
  
  
  
Dial 2 
Y. (C-B)^ (X91 )- Xx "Ic -By e v7] 
GR I A a^a (14) 
i Y^ à y? 
1l 1 
You. (2 +72) J[(x - B)^s Y?] 
c?Y, - B^ CT 1 i bri i -]c?o (15) 
T y* Y* 
1 1 
i Y; (X; * YD 2 2 
2 TL. he - 1l: + 
072, [-0.5 2,57 N 9 Y I? c?a [0.5 (Z; 
(X 38) Y X. B)? y 
- V) y C299 S nocs3 ]? 02a 
i. Y, 
(x2 4.24727 Q4 y) 
+ [0.2527 1 1 1 t : * 0-252, ir v2 
(x2 « y2)2 77 
1 1 i 
Lex, = B} + Y * 21 Lex, =1B) 4 12] 
  
2 
2 ne 2 212 = 2 ] g Y (16) 
LOG B)^« vil (2, - V) 
where Oy is the standard deviation of the measured horizontal ‘directions. 
Oy is the standard deviation of the measured vertical directions. 
zi 
tan Yı = Ta 
(X: + Yt) 
Zs 
tan Yo. = + 
  
((Xi - BJ* + y^ 
The above equations can be simplified to these forms. 
  
2 
GX > .. [2X8 - ORYOÓ « (7R7. Ay?) X* - (8Y?B « 4B/] X? « (Y 
a B?y? 1 1 X l 1 1 1 
i 
* D'« AB^y7) x? - 2BY* x. + B^y*] (17) 
1 1 x 1 1