2.3 Mathematical Basis 
  
Again utilizing Figure 1 as a reference, measurements 
(x;j>Yij) of target images on the photographs constitute 
the photogrammetric "observations" (similar to observing 
horizontal and vertical angles with a theodolite or transit). 
These observations are related to the exposure station 
location X Yci»Z the orientation of the camera axis 
ci? ci? 
which can be represented by three rotations o;, Bis Kg 
about the photographic coordinate system axes and the 
location of the target itself Aa Ya Zar In functional 
form these relations are expressed as: 
sid] .. 
544] > Az. Stl Oi» $1» Ki1»X35Y1,2, 
The actual equation very simply expresses the fact that the 
exposure station, the target and its image all lie on the 
same straight line. 
At this juncture let us drop our earlier assumption 
that the locations of the exposure stations and the directions 
of the camera axes are known in advance. Hence, for each 
image measured on a photograph, a pair of "observation 
equations" of the functional form given above are generated 
(in the computer program). Each equation pair contains two 
measured values to the left of the equal sign and 9 unknown 
values to the right. But, once all such equations are 
generated there are many more observed values than unknowns 
and the system is, therefore, overdetermined and may be 
solved by the method of "least squares".