18 
This step is concerned with a rough assembly of the constituent 
sub-blocks and therefore a unique solution for equation 4.32 will be 
adequate (i.e. , there is no need for a least squares solution). Since 
equation 4.32 involves 7 unknowns (s, a, 6, y, c x , c y , c z ), a minimum of 
two points of known X and Y, and three points of known Z is required 
for a unique solution. A suitable choice for tie points between sub-blocks 
would be the air stations common to adjacent sub-blocks. Because of the 
particular layout of the current method, at least three exposure stations 
are common to any pair of adjacent sub-blocks. The use of these exposure 
stations strengthens the tie between sub-blocks, gives depth to the 
solution, and expedites the convergence of height solution in the final 
adjustment. 
The execution of this step is simplified further by reducing the 
number of equations from seven to four. This is achieved by eliminating 
the three translations, c x , c y , and c z , through the subtraction of 
equations of the same coordinate for two different points. For example: 
Xij2 = s (a x 1>2 + b yl,2 + c z l,2^ .... 4.33 
where 
Xj ^ “ Xj — X2, etc. 
Four equations of type 4.33 are obtained in terms of the four unknowns, 
s, a, B, and y. Since these equations are non-linear, the same scheme used 
for equation 3.01, including Taylor*s expansion, should be applied. 
At the conclusion of sub-block assembly, all points, including 
exposure stations, pass points and control points, in the entire block will 
have their coordinates referred to one general coordinate system. The 
points used in the preceding transformation will have the same, or very 
nearly the same, coordinates. Nevertheless, all other points may have up to 
four different sets of coordinates depending on the number of sub-blocks in 
which the point appears. The differences between these sets, though, are 
not large and they are minimized in the following and final stage of 
adjustment.