(5) 
of each term in the Taylor expansion, showing that in the case of 1°tip 
and 1°tilt (i.e. 1.° 4 inclination from the vertical) the scale error is nowhere 
greater than 1/10,000. The error remains less than 1/6000 for 3° inclination 
in the ease of 6" wide angle photography. It was also shown that this 
goodness of the representation can be kept in mountainous regions by. rep- 
lacing the photo coordinates by their values divided by the measured parallax. 
This high intrinsic precision leaves little to be desired. It should 
also be noted that the pattern of the residuals is determinable and can be 
corrected knowing the approximate values of the orientation elements. 
4. Representation of Model Deformations by the Equation 
of the Hyperbolic Paraboloid 
  
  
It was also interesting to study the expected precision of representing 
the model deformations directly by the equation of the hyperbolic paraboloid, 
which amounts to the lumping of the effects of relative orientation together 
with those of the absolute orientation. The resulting loss of precision may 
be appreciated from considerations of the height error whose expression 
contains two terms which do not have opposite numbers in the corresponding 
expansion of X, namely. 
> (% COS Boy) (-xy 9 cosy ) and 2; (% COS Ay) (x'^Ssiny). 
P P 
The influence of these terms would partly be eliminated by the auto-adjust- 
ment of the coefficients of x' and y in the linear expressions. The residual 
errors, however, increase with the absolute tilt, but they remain below 
68 H 
1000,000 
degrees in the first case, and the product of the absolute tilt and the 
relative tip in the second. When each angle is two degrees the maximum 
value of the residual is about H/4,000. 
times the product of the absolute and relative tilts measured in 
s. Limitations of the Available photogrammetric Instruments 
Based on the Polynomial Representation of the Mode! Deformations. 
In recent years a number of instruments have been produced on 
the principle of the representation of model deformation by some simple 
function of the photographic coordinates. Popular types are the Zeiss 
Stereotop, the Galileo Cartographic Stereomicrometer and the Drobyschew 
precision Stereometer.