(7.2) 
using 
lae of 
mulae 
or all 
using 
0 the 
com- 
justed 
time 
stem. 
addi- 
tment 
ld be 
requi- 
ended 
n 
ment 
— 
  
RADIAL TRIANGULATION, DISCUSSION 85 
d. Result of the adjustment method of section 
corrections to 
final coordinates 
preliminary coordinates errors 
de, — —0.16 m Co = 1421.91 m 0.00 m 
dyg = —0.04 m Jo ^ 121885 m +0.01 m 
da, — —0.13 m $57 —1097.07 m 10.05 m 
dy; — 40.03 m Ynp 1718.19 m +0.07 m 
(dxz = 0.00 m) Xp = 39.85 m +001 m 
(dyg — 0.00 m) Ug 2627.60 m +0.02 m 
e. Result of the adjustment method of section 6: 
corrections to : : 
preliminary coordinates final coordinates BIO 
de, = —0.16 m X = 1421.91 m 0.00 m 
dy, = —0.03 m Yo = 1218.86 m 0.00 m 
dæ, = —0.18 m Xp —1097.12 m 0.00 m 
dy, = +0.08 m 757 1718.24 m +0.02 m 
dey = +0.01 m Xp = 39.86 m 0.00 m 
dyy= 0.00 m Yp = 2627.60 m 10.02 m 
SUMMARY. 
Simplified computing methods for the adjustment of single rhomboids are derived 
rm . * s "2 n ; % . » : * . * } 
The solutions represent different approximations to the rigorous least squares adjust- 
ment and do not require the use of logarithmic tables. 
RESUME. 
Des méthodes de calculs simplifiées pour la compensation de rhombes individuels 
sont dérivées. Les solutions représentent différentes approximations à la méthode des 
moindres carrées et elles n'exigent pas l'application de tables logarithmiques. 
ZUSAMMENFASSUNG. 
Für die Ausgleichung einzelner Rauten werden vereinfachte Berechnungsmethoden 
abgeleitet, die abgestufte Näherungslôsungen im Vergleich zur strengen Ausgleichung 
darstellen und ohne die Verwendung logarithmischer Grössen auskommen. 
Mr F. ACKERMANN: As you know, the 
rhomboid is the basic unit of radial triangula- 
tion, and it has to be computed from the ob- 
served directions. As there is always one 
redundant observation present, the computation 
of a rhomboid involves an adjustment problem. 
Up to now the practice has been to do a least 
square adjustment of the observed radial direc- 
tions and to compute the co-ordinates of the 
corner points of the rhomboid. 
I tried in my paper, which you will find in 
1959/60 Photogrammetria, Congress-number A, 
page 81 to make the adjustment of the rhom- 
boid easier and a little more handy by reversing 
the procedure of computation. If you start 
computing the coordinates by the corner points 
of the rhomboid with the direct observations 
you get at the right hand principal point a linear 
closing error, and the problem was only to find 
rules of how to distribute the closing error. 
A similar problem you find in the adjustment 
of the traverse for instance, so the adjustment 
should be shifted to the direction of the prelim- 
Archives 5 
inary co-ordinate. The solution turned out to be 
extremely simple. You have to give a quarter 
and a sixteenth of the closing error to the pre- 
liminary co-ordinates of the wing points of the 
rhomboid. This solution is still in accordance 
with the least squares solution, the reliability 
depends only on the shape of the rhomboid. 
For square-shaped rhomboids it is a rigorous 
solution. If the rhomboid deviates from the ideal 
square shape it is an approximate adjustment. 
Further development of the formula showed 
what additional corrections would be necessary 
if the rhomboid had an odd shape. It was found 
that there was hardly any need to apply addi- 
tional corrections. 
The solution is very practica! as it can easily 
be adapted to the requirements of precision and 
to the available computational means. The 
statement holds also for electronic computation. 
We have in Delft set up a programme for the 
Stantec Zebra computor and computed a block 
of about fifty rhomboids with very satisfactory 
results. A special difficulty in this case was that