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2. THE CALCULATION OF ANALYTICAL AERIAL TRIANGULATION 
At the risk of repetition, there are a number of points that can be made on the 
subject of the computation of analytical aerial triangulation and which should 
stimulate some discussion. There is perhaps an insufficient realisation of the fact, 
whell known to geodesists, that the calculation of a triangulation must inevitably 
be divided into two distinct parts: a preliminary computation and a, so called, 
adjustment. This division is forced on us simply because the formulae used in a 
preliminary computation are non-linear, whereas the adjustment, if it is to be done 
by the method of least squares, would be quite intractable unless the equations 
to be solved to obtain the final values for the unknown are linear. Of course, 
when put in this way, there is no one who would say the statement was not 
obvious, but are its implications fully realised? One would think not, to judge 
by discussions on the methods of setting about a calculation. The main impli 
cation is that the method for the preliminary computation should be chosen for 
reasons which have no' necessary connection with those that decide the method of 
adjustment subsequently selected. The condition that must be satisfied for the 
preliminary computation is simply that, assuming, of course, sufficiently accurate 
data, it should give results that can be modified to give final values by the use of 
linear equations only. Apart from this the choice is entirely in the hands of the 
computer and should be made so the method is as easy and efficient as possible. 
What do we mean by efficient in this context? Simply, it might be suggested, a 
form of computation that draws attention to any mistakes in the data early and 
in such a way as to allow re-observation with the minimum of disorganisation and 
recomputation. This means in effect the division of the calculation into a number 
of steps that each provide some form of check. A suitable series of such steps 
are: (i) relative orientation and computation of model coordinates (residual pa 
rallaxes); (ii) attachment of adjacent models (agreement of pass points); (iii) linear 
transformation of strip coordinates to a common block system (agreement of tie 
points). The checks available are in parenthesis. Once the computer is satisfied 
with these results he continues to block adjustment which may be done in any way 
he wishes and the method or choice of unknowns used need bear no relation 
whatever to the preliminary computation. For example, there is no reason why 
the elements of relative orientation need be held fixed simply because relative 
orientations formed one of the preliminary steps. The method to be adopted for 
the block adjustment should depend upon statistical considerations allied to 
economy: the method of preliminary computation is chosen to give any reasonable 
answer and as many intermediate checks as possible. Analytical aerial triangu 
lation is not becoming popular, particularly in the smaller organisations, as rapidly 
as it might, and this is in some measure due to the difficulty of avoiding gross 
errors in the data. Those of us who are convinced that digital methods are the 
way to reduce the errors of triangulation should pay attention to this if we expect 
to see their general acceptance by photo grammetrists. 
Strictly speaking we should perhaps exclude problems of block adjustment from 
discussions of analytical triangulation for they have to be carried out no matter 
how the basic data is obtained. However, digital methods, by presenting us with 
the data in their most elementary form, do allow a very great freedom in the