(3) 
(4) 
jector 
(5) 
(6) 
(7) 
(8) 
(9) 
e the 
f the 
ding 
ulas: 
(10) 
(11) 
(12) 
(13) 
(14) 
(15) 
   
   
109 
From these formulas the errors of the approximate orientation of the projector, dy,» 
  
  
  
  
  
  
  
  
  
  
... ete., can be found. If we want to determine these errors such that [vv] = mini- 
dz» - 
g mum we form normal equations in accordance with the 
51 52 53 54 ss method of least squares. 
Five points. 
" 42 43 44 45 
The grid is shown in Fig. 2. We use for instance, 
the points 11, 15, 33, 51, and 55. The dimensions of the 
31 32 33 34 33 grid = 2a X 2a. If we want to determine the correc- 
tions of the elements of orientation we rewrite for- 
, 2 23 24 25 mulas (14) and (15) as follows: 
y x'h x’ , 
n 12 13 14 15 Vy m dus f dz, — 7 dx — FE hdg 
ig. 2. jected grid. y? 
Fig.2. The projected gri = 14 v) kde e du (16) 
, y x2 xy’ 
omen dtm dz, + Uu" dx —|1- E hdg, — io —dy (17) 
The coordinates of the five points 11, 15, 33, 51, and 55 are shown in Table 1 together 
with the corresponding coefficients of (16) and (17). If no systematic errors are assumed 
to be present, all 25 points can be used simultaneously for the adjustment. This has been 
demonstrated in [1] and can be applied to instruments with mechanical projection. Par- 
ticularly the square sum [vv] can serve as an indication upon the quality of the instru- 
ment since this quantity expresses the square sum of the coordinate errors that cannot 
be corrected by the elements of orientation. The standard error of the observations can 
be determined from [vv] with the wellknown formula u = 
[vv] 
n—u 
  
In accordance with the usual procedure we form the normal equations: 
5dx, 
5dy, 
8a2 
4a2 
5+ T da, 
402 
5+ "E 
dz 
  
dy, 
8a2 
+ 
hdx 
  
4a2 
4a2 
+15 + do + [dy] =0 
+ aNg; =0 
+ aN;2 = 0 
(18) 
8a4 8a2 a2 
+ Fach um hdg tog wid) 
8a4 8a? a2 
+ = = +5 Ma uo Ns t [dv =0