ADJUSTMENT OF RHOMBOIDS, ACKERMANN 
Hence the corrections to the observed directions are 
  
    
          
  
  
  
  
  
  
  
    
   
  
  
  
  
   
  
    
    
    
    
   
    
   
    
         
    
    
  
  
    
   
   
  
  
Vi Zu K Vg = us K vg = UK V. — u.K V) = uy K 
vy = UK pc uK vg = ugk vg = ugk V0 = %;0K (7.2) 
To achieve this solution the machine has first to compute the discrepancy t using 
the equation (4.4), the programming of which, according to the ordinary formulae of 
coordinate geometry, does not present any difficulties. Instead of deriving formulae 
from (7.2) which would yield the final coordinates directly, as it is desirable for all Ë 
methods adapted to desk machines, the program can be simplified in this case by using | 
the first part of it again. The corrections (7.2) can be added by the computer to the 
original observations and, with these corrected observations, the program for the com- 
putation of the preliminary coordinates is repeated, giving as a result the final adjusted 
i il coordinates. This method is a rigorous adjustment method and has at the same time 
E the advantage that the computations can be done in an arbitrary coordinate system. 
Moreover the connection of adjacent rhomboids is achieved directly without any addi- 
tional transformation. 
With this example the considerations about different possibilities for the adjustment | 
a Mi of single rhomboids, based on least squares solutions, may be concluded. It should be | 
N clear that the solutions could be modified still more according to other specific requi- 
rements, and other developments can take place. In this sense the paper was intended 
to show some possibilities and has been able, perhaps, to give some stimulus. 
  
  
  
   
  
8. Numerical example. 
  
a. Given coordinates and observed directions: 
x, = 0.00 m r, — 47.9388 rg = 102.0408 
Xp = 0.00 m T, = 102.8268 T7 181.1428 
y, = 0.00 m T3 = 138.9998 rs 245.8458 
yp — 1307.22 m ry, = 303.9618 To 300.9788 
(b = 1307.22 m) rs = 0.0128 rio = 352.2888 | 
b. Computation of the linear discrepancy Ae and of preliminary coordinates: 
  
€; = 142481 m e, = 1321.27 m le = +0.58 m 
do =1171.38 m ep = 1320.69 m (t = —0.44.10—3) 
*, = 1422.07 m *, =—1096.94 m x, 39.86 m x, = 39.84 m | 
0 0 ‘Cc D | 
Yo 1218.89 m 7p = 171816 m Vy 2627.89 m V n 2627.31 m 
0 0 “0 D 
  
c. Result of the rigorous least squares adjustment (see section 3 or 7): 
corrections to 
AM ; final coordinates 
preliminary coordinates 
de, = —0.16 m Zo = 1421.91 m 
dy, = —0.03 m Yo = 1218.86 m | 
dz —0.18 m xp = —1097.12 m 
dy, = +0.10 m Yo 1718.26 m 
de, = +0.01 m Xp = 39.86 m | 
M | 
dy, = +0.02 m yg ^ 2627.62 m | 
M 
These corrections dz, ...dy, would be the remaining errors if no adjustment 
M 
would be applied.