rectiof and configuration of any object space whatsoever. To determine other 
than direction and configuration of object space involves additional data derived 
independently of the image-recording camera. This object space includes geo- 
graphic surfaces. 
To this end, general equations are derived for total orientation in which the 
given data are object and image space coordinates referred to an arbitrary origin. 
The unknowns are the focal length and the location of the principal point re- 
ferred to the image space coordinate system, the space coordinates of the lens 
referred to the object space coordinate system, and the elements of angular orien- 
tation--tilt, swing, and azimuth--referred to the object space coordinate system. 
It may be shown that any exterior orientation equation is a simplification 
of the general equation arising out of the interior orientation being predetermined. 
For example, if the explicit general orientation equations are subjected to the 
calculus of iteration, and further if it is agreed that the elements of interior orien- 
tation are known, we obtain an equation with three differential unknowns which is 
identical to the equations published by Professor Earl Church, of Syracuse Uni- 
versity, for determining the position of a camera in space. Thus his solution, 
like all others, is a special case of the general equations subjected to the cal- 
culus of iteration. 
In a similar manner it may be shown that any interior orientation equation is 
a simplification of the general equation arising out of the exterior orientation 
being observed directly. It may be further shown that all plane camera calibra- 
tion equations, commonly employed, are additional simplifications of the general 
interior orientation equations, which are themselves simplifications of the total 
orientation equations. In this respect it is readily shown that the plane cali- 
bration equations published by Dr. Roelofs, the plane calibration equations pub- 
lished by Dr. Washer, the plane calibration equations published by General Hotine, 
the plane calibration equations published by Mr. Sewell, and those published by 
myself are identical, differing only in notation and degree of simplification. In 
establishing these general relations we discover that the controversy over princi- 
pal point, point of symmetry, central point, plate perpendicular, and center cross 
is due entirely to inadequate definition and restricted concepts. 
Undoubtedly the greatest development of photogrammetry is due to its utility 
in the delineation of geographic object space; yet that which is responsible for 
its rapid development in a topographic sense has imposed a restriction on a gen- 
eralized photogrammetric concept applicable in a non-topographic sense. An 
example of this that all photogrammetrists are familiar with may be found in the 
popular notion of vanishing points. It is generally known that any system of lines 
in object space vanish at a point on the image plane where a line passing through 
the lens parallel to the system pierces the image plane. Yet enslavement to the 
cartographic field leads students of photogrammetry to the false notion that lines 
vanish only on the image of the geodetic horizon and the image of a normal to the 
geodetic horizon, whereas these particular vanishing points are nothing more than 
cartographic applications of the general laws of perspective. 
In closing, I would like to say that faith in both a real and academic require- 
ment of a generalized mathematical treatment of photogrammetry is the principal 
motivation for writing a book entitled Analytical Photogrammetry. 
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