(5) 
(6) 
nined 
of the 
1, can 
in the 
Is, for 
inates 
  
  
The ideal co-ordinates in the projection plane are found by multiplying 
h 
the co-ordinates of Table 1 by —. 
C 
If normal equations are formed for observations at twenty-five points the 
solution gives the following expression for the [vv]: 
[w] = [dxdx] + [dydy] — 5 ([dx]* + [dy]®) — & (Nasi? + Nags?) 
[ 2 vi b 
— 5 a tm 2[dx]) + (Noss 2 [dy ]) } (7) 
In this formula the following notation is used: 
dx — the measured x minus the ideal x 
dy — the measured y minus the ideal y 
15 55 25 
New = —[dy] +[dy] — idv] + id] 
11 51 21 
51 
1 
ICM 
45 
41 
55 52 54 
+ [dx] — idx] + [dx] 
15 12 14 
51 55 52 54 15 
Noa = — [dy] + [dy] — [dv] + 3[dy] ...-+ [dx] 
11 15 12 14 11 
55 25 45 
— [dx] -Fi[dx] — 4[dx] 
51 21 41 
Nass = 4dyy — 1dysı + 2dyı2 — 2dys, — 2dy,, + 2dysa — 4dyıs + 4dyss 
+ 2dyzı — 2dyay d- dysg — dyas — dyg, + dy,4 — 2dyss + 2dyss 
51 55 52 54 
+4[dx] + 4[dx] + [dx] + [dx] 
11 15 12 14 
Nosy = Ádxyy — 4dxg, + 24x19 — 24x59 — 24x44 + 2dX54 — 4dx15 + 4dxs5 
T 2dxgy — 2dx, + dX29 — AX49 — dX94 + dX44 — 2dX25 + 2dX45 
15 55 25 45 
+4[dy]_ +4[dy] + [dy]. + [dy] 
11 51 21 41 
51 
The notation [dx] , for instance, means dx, + dxg1 + dxg, + dXa + dxs, 
11 
1 
and [dx] j means dx,, + dx,2 + dx13 + dx, + dxig. 
1 
From [vv] the standard error of one observation is found as 
i id = JE 
, 50-6 44 
Also the correction to the elements of orientation, their weight and 
correlation numbers can be determined from the solution of the normal equa- 
tions in a general shape. For investigations of the error propagation this is 
of great interest. 
  
  
  
  
  
  
  
  
  
  
  
  
ANE dst. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
      
    
  
   
    
    
   
  
    
   
   
    
   
     
E tt t ERA iem ed ERE ee = SE E : 
GNESNENSIS PF REVUE ANE UN HORE ONTAE NEN Em 
TD mee