RE ue 
GV-16 PHOTOGRAMMETRIC ENGINEERING 
10, + V14y + COS A, = COS a5, SEC "yi 
X205 + V20y + COS a; = COS a, SEC y» 
X3@z + Y3@y + COS a, = COS ag, SEC 7¥3 
x1b; + vib, + cos 8. = cos B,, sec y1 
X2b 7 + V2by + cos 8, = cos B;, sec v2 
X3b, 4- ysb, 4- cos 8, — cos Bs, sec y; 
X16: + 416y l- COS y, 7 COS y,, SeC 'y1i 
X265 d- yacy + COS y, = COS y,, SEC "yo 
abs | yc, + COS Y, = COS Y,, SEC y; 
The unknowns are a., a,, and cos «, in the first group; b,, b,, and cos 6, in the 
second group; and c,, c,, and cos y; in the third group. Only the quantities 
COS a, cos B, and cos y, are needed and these quantities are in error as a 
function of the error in the assumed f in the formation of the sec y values. 
(az (Ay COS a; COS ay, 
41104 + y145, + 14c0s B, — sec y14c0s f,, 
| | | 
(Cz Cy (COS 'y; (COS 'y;, 
(az ‘ay (COS a; (COS As, 
| | | | 4 = 
X310; + v24b, + 1{c0s B, = sec y:{Cos Be, 
Les Cy (COS y; [COS vs, 
- p. 
[a z (Ay (cos a; COS ag, 
| | 
X31 b. + ya1by + 14cos B. — sec 'y31 C05 Bs; 
Les ley (COS y (COS vs, 
If the assumed f value were correct, the corresponding values of cos «a, cos Ba, 
and cos y, would be equally correct. In which case, the following equation would 
be satisfied: 
cos 2a, + cos? 8, 4- cos? y, — 1. 
As a consequence of errors in f, 
/ 9 1 
cos? a, + cos?! 6, + cos y, = — 
m? 
and er A 
1 
m= —— RR UNES 
(cos? a, + cos? 8, 4- cos? y,)!^? 
The direction cosines of z may be improved by the factor m. 
COS aA, = M COS à; 
cos O,/ z m cos D, 
cos y,” = m cos y, 
à. ^