X 
= f fan (X-X n ) + a 1? (Y-Y n ) + a n 3 (Z-Z n )] 
a.31 (X-X G ) + a^2 (Y-Y 0 ) + (Z-Z Q ) 
y = f fa p1 (x-x„) + a 22 (Y-Y q ) + a 2 , (Z-Z Q )] 
a 31 (X-X Q ) + a 32 (Y-Y 0 ) + a 33 (Z-Z 0 ) 
This pair of formulas constitute the space equations of the 
line on which lie three points, namely, the object on the 
ground, the inner lens node of the camera (perspective center), 
and the image on the focal plane. The elements of angular 
orientation 00, 8, k are embodied in the a’s. One finds 
through successive approximations the values of the parameters 
co, 8, k, X, Y, Z, Xo, Yo, Zo that satisfy all the pairs 
of equations for a redundant number of images so that the 
sum of the squares of the residual discrepancies in the 
observed (and corrected) x and y is minimum. Theoretically 
at least, and in certain practice also, all these equations 
for all the images on all overlapping photographs of a strip 
or block can be dealt with simultaneously. 
The simultaneous solution consists of the, reduction of 
a large set of linear equations where the number of unknown 
parameters is somewhat greater than 15 per photograph. The 
solution is not too serious if a large, fast, cheap computer 
is available. However, the application of such large computers 
to this work is not yet common. (It is my opinion that the 
1968 Congress will report quite differently). Consequently, 
my office proceeded in i960 to use a small computer to derive 
a provisional solution to the problem so that, when the large 
computation is performed, only one single iteration is required. 
To our surprise, the provisional solution is so accurate 
that it is seldom necessary to proceed to the simultaneous * 
adjustment. This is about the stage of development where 
the practical application now standa in the U.S.A., with 
several facilities utilizing the C&GS routine, which itself 
is being improved. But it is the desire of many of us in 
C&GS to apply eventually the simultaneous adjustment in every 
instance, and this perhaps is a trend that others may also 
follow. 
In every application in the U.S.A., computer programs 
are incorporated to compensate the observed image coordinates 
for the lens and film distortions and atmospheric refraction. 
Earth curvature is ideally recognized through the application 
of some type of geocentric coordinates for the ground points, 
although a few applications correct the observed image 
coordinates, which is easier to do. 
Provisional results are obtained through a numerical 
simulation of the stereo plotter, applying the same perspective 
equations shown above, but incorporating relative orientation,