Reprinted from 
PHOTOGRAMMETRIC ENGINEERING 
March 
1960 
  
Reduction of the Effect of the Deflection 
of the Vertical on Photogrammetric Work | 
  
in Geodetically Unexplored Regions | 
(The Cross Bases Method)* f 
  
B 
H. M. KARARA, E 
Asst. Prof. of Civil Engineering, i 
Univ. of Illinois, Urbana, Ill. ÿ 
ABSTRACT: In regions having no geodetic control, the effect of the deviation of Br 
the vertical could be of considerable effect on photogrammetric work. Even 
though astronomical fixations could be made available, the unknown magnitude 
of the station error may introduce considerable weakness in astronomic control. 
Upon the other hand, the deflection of the vertical will have relatively little effect 
upon the astronomical azimuths of base lines. A method that makes use of 
measured base lines instead of position coordinates of ground control points 
would certainly have particular advantage in geodetically unexplored regions. 
ETS 
k 
  
Instead. of requiring the position coordinates of numerous selected ground con- i 
trol points, the Cross Bases Method, outlined in this paper, requires the use of ki 
measured baselines at the beginning and end of the flight strip. For each of | 
these bases, which are approximately transverse to the strip axis, the length and E 
azimuth are determined. Also, it is necessary to measure the difference in eleva- 
tion of the ends of each base, and determine a representative elevation at the d 
beginning, middle and end of the flight strip. Then the aerotriangulation pro- 
ceeds in the plotter in the same manner as the classical method. The adjustment 
of a strip controlled by such a method is also given and discussed in this paper. 
Various investigations conducted by the author and described here indicate that 
  
  
the same accuracy is secured as in the classical methods of ground control. 
n 
NE of the most important tasks of pho- deflection of the vertical has relatively little bi 
O togrammetry nowadays is the precise effect upon astronomically determined azi- li 
small-scale mapping of unmapped areas. In muths. Such a case can be compared to meas- n 
many of these areas, no geodetic control uring horizontal angles by means of a transit 3 
whatever exists. The ground-control points whose vertical axis is not really vertical but fl 
needed for mapping are usually obtained by inclined by an angle a to the vertical. Unless i 
astronomical determination of longitudes and the direction of the line of sight is very steep, i 
latitudes. One must be clear that such a meth- the effect will not be more than a few seconds. fit 
od of determining the ground control is very The Cross Bases Method is based upon the A 
dangerous. The unknown magnitude of sta- 
tion error due to eventual deviation in the 
vertical, caused by irregular masses of topog- 
raphy, could introduce considerable weakness 
in astronomic control and thence to the pho- 
togrammetric map. The deflection of the 
vertical is relatively small (some seconds of 
arc) in flat countries, larger in accidented re- 
gions; in extreme cases (e.g. Colombia, South 
America) it may amount to nearly one minute 
of arc. Under such unfavorable conditions, 
the coordinate error could be as large as one 
mile or even more. Upon the other hand, the 
above mentioned facts and requires a mini- 
mum of ground-control. Instead of requiring 
the position of numerous ground-control 
points, the Cross Bases Method requires the 
use of measured independent base lines at the 
beginning and end of the flight-strip (Figure 
1). For each of these bases which are approxi- 
mately transverse to the photographic strip, 
the length and azimuth are determined. Also, 
it is necessary to measure the difference in 
elevation of the ends of each base, and to de- 
termine a representative elevation at the be- 
ginning, middle and end of the flight-strip. 
* This paper is an "invited" contribution to Commission III of the International Society of Pho- 
togrammetry, and is to be presented to the 1960 International Congress, Sept. 1930, London, England.