4 Commission III Inviled paper 
Some Observations 
on 
Analytical Aerial Triangulation 
by E. H. THOMPSON, 
University College London. 
1. In order that this paper, together with that of G. H. Schut, should provide material 
for discussion, I have to some extent based my comments upon Mr. Schut’s paper which 
I had the opportunity of seeing before putting these notes together. 
2. I would like, first, to draw attention to a point which appears sufficiently obvious 
but which is certainly overlooked in published literature. It is simply that if the elements 
of relative orientation and scale are known approximately, (to within errors of observa- 
tion) any subsequent procedures, however they may be elaborated by the inclusion of 
redundant observations, weighting of observations, treating the block as a whole, etc. 
are simply problems in the solution of linear equations. That these solutions may be 
arithmetically tedious is not denied, we know of formidable problems in the adjustment 
of geodetic triangulations, but they do not present the difficulties that arise from the 
solution of a set of non-linear equations. 
In my own approaches to the problem I have clearly made the distinction between 
the prior determination of the elements of relative orientation to an accuracy of the order 
of the errors and the subsequent procedures which comprise the introduction of redun- 
dant observations and block adjustment. The determination of the relative orientation 
elements is a non-linear problem involving, whatever method we may adopt, a consider- 
able amount of arithmetic, but we have no need to complicate it by unnecessary elabora- 
tion. To be more specific, no useful purpose is served by including observations on more 
than the minimum number of points (five) until rotations have been obtained that satisfy 
these five points. Once this has been done any number of redundant points may be in- 
troduced and small corrections to the rotations obtained by the solution of a set of (linear) 
normal equations following the conventional least-square procedure. If it is argued that 
the subsequent corrections are so large that the linear assumption is not justified then it 
follows that the observation errors are so large that the basic assumption of the least- 
square theory is invalid and one would doubt whether the observations were worth using 
at all. 
I would not suggest that the initial solution and subsequent inclusion of redundant 
points should necessarily be two distinct steps requiring two approaches to the computer. 
A single programme could divide the work in this way: all the data might be supplied to 
the computer in the first place but the internal procedure would be subdivided so that 
the non-linear work was done on five points only. (I would concede that the inclusion of 
a sixth point at this stage would provide a control on gross error which might justify the 
extra work. But the decision should depend upon the frequency of gross errors.) 1) 
The above arguments apply a fortiori to the introduction of external data such as 
information from adjacent models as in Schmidt’s method. If aerial triangulation is to 
be of any value, such information can only result in first order changes in the elements 
of orientation and need only be introduced after the really intractable problem of ob- 
taining approximate values has first been solved. 
3. I should like to deal next with a point raised by Schut in his paragraph 3. Relative 
1) The Ordnance Survey now organises the computation in this way.