188 RECENT DEVELOPMENT OF APPROXIMATE INSTRUMENTS, DISCUSSION 
approximate solutions gave really a good result; 
and in the hope of finding out better approaches 
to the design of plotting instruments which could 
combine precision with low cost. 
In general, the theory of approximation of 
the machines which existed at the time was very 
inadequate. Tô my mind, the simplest and most 
logical design of the class of instruments should 
be based on the generation of what we call the 
scale parameter, because as soon as this para- 
meter is correctly evaluated as a function of the 
photographic coordinate, the determination of 
the ground position and height becomes simply 
linear transformations. 
I have further shown that the scale parameter 
is very well represented by the equation of the 
hyperbolic paraboloid in the photo coordinates 
re-scaled according to the parallax. There would 
be no need to split the models because the error 
will never exceed 1 : 10,000 for 11° of inclina- 
tion of the camera axis. For 3° this error is 
about 1 : 6,000. 
There will also be no need to stratify the 
model for the equation hold in mountainous 
regions.