n the 
n, are 
dition 
ected. 
(6.1) 
(6.2) 
(6.3) 
(6.4) 
the 
gain 
6.5) 
ions 
ions 
  
ADJUSTMENT OF RHOMBOIDS, ACKERMANN 83 
neglected in section 5 which are due to the deviations of 
shape. A rough estimation indicates that the additional influence of the shape of the 
rhomboid amounts approximately to 10% of the linear discrepancy Ae when the devia- 
tions Ar are in the order of 10s. Hence the additional terms make it immediately possible 
to decide whether the simpler solution can be applied. 
Instead of expressing the shape of the rhomboid in term 
deviations Ar, which are interrelated, the 
the rhomboid from the ideal 
s of the ten directional 
six independent deviations in coordinates from 
the ideal position of the points C, D, and E can be used. Introducing the terms Ax — 
=x —®y AY = y—1y, for which approximate values are sufficient, the results (6.5) 
can be presented in the practically equivalent form: 
c de 1 
Yo = 0, me m $14 165 (3 d=, + 21 Ayo +83 Axp + 5 Ayp —Azg t 3 Ayg) ] 
e 4e "d 
Ye = Yo, "os 1 1 1b (24265 T 1T, 19 : t Ayp — Avg . ) § 
d Ae 4 x 
x, = Sa, US 114 165 (—3 4254-5 lyg —3 dap +21 4yp + Ax, + 3 Ag) | 
d Ae 1 6n 
pm D, * e 16 [11 4b GU F 4yo —2 Av, - 17 Ay, *- Aer YE 
le 
xp = it, +a p.) 39p Ve t Ap t Ayg) 
: 2 
le 
UE f(y, t 2 ) 32b (3 Av, t 3 Ax —11 Aog) 
C ) = 
7. Rhomboid adjustment by means of electronic computer. 
At the beginning it was mentioned that the ideas presented here were evolved in 
connection with the preparation of a block of radial triangulation which was carried out 
at the Technical University of Delft. In this case an electronic computer — the Stantec 
Zebra — was available for the computations. So finally, without going into details, some 
considerations are given, along which the available solutions can be made suitable for 
automatic computation. But it is emphasized that many other solutions could be applied. 
For an electronic computer, working at medium or high speed, it is desirable to 
choose a very general program, which would cover all rhomboids which could be expected. 
In the case which is referred to here, this was particularly important and even extended 
to multiple rhomboids, because, due to the requirements of block adjustment, in every 
second rhomboid the usual single wing-points were replaced by respectively three closely 
grouped points, Depending on the connection with the adjacent strips this resulted in 
different types of rhomboids with a varying number of wing-points. Hence a program 
as general as possible was desirable which would yield directly the final coordinates of 
all points involved. 
As an example, a suitable solution is mentioned here, which could be derived from 
the formulae given in section 3. 
If the coefficients of the linearized condition equation are designed by Wpn Ugg 
then the solution of the normal equation, without introducing any approximation, except 
for the simplified weight assumptions, is 
K = 
(7.1)