ANALYTICAL AERIAL TRIANGULATION, THOMPSON 5 
orientation gives us the shape of the model and there is obviously much to be said for 
regarding models so obtained as the building blocks with which we construct the whole 
triangulation without deforming them. The obvious success of Jerie's method as applied 
to planimetric coordinates is a very strong argument in support of this. The procedure 
has three very clear practical advantages. In the first place the volume of arithmetic is 
less than in any method that regards the elements of relative orientation as still unknown 
at this stage. Secondly, we can reduce the arithmetic by regarding the adjustment of 
plan coordinates and heights as separate problems. Thirdly we can, if we so desire, regard 
the building blocks as made up of two or more models, thus reducing the arithmetic of 
adjustment still further. (In fact Jerie takes a two-model section as his standard unit.) 
There are, of course, well-established precedents in geodesy for dividing the un- 
knowns into groups that are independently treated. It is, for example, not uncommon to 
divide a large triangulation into figures that are independently adjusted; and it is also 
common to carry out the internal (or “figural” adjustment) as a first step before the 
introduction of scale, azimuth and fixed-point conditions. It is also universal to adjust 
the angles at a station as a separate step from the adjustment of the network. The rea- 
sons for adopting these procedures is economy and one cannot help feeling that the loss 
of accuracy is, at worst, marginal. 
In any event even if we regard a model as having a shape that can be deformed, I 
must agree with Schut that any deformations must be carried out when we are consid- 
ering the strip or block as a whole and not from model to model in a strip. He has given 
one good reason in paragraph 3 but there is another no less important in practice. Any 
gross errors in the data will be apparent at the stage of relative orientation. By treating 
models independently before connecting them together we have much greater flexibility 
in the organisation of the work. A badly observed model can be rejected and reobserved 
and recomputed without disorganising the computation of a strip or block. The block 
computation need begin only when the relative orientations have been proved satisfactory. 
I should suggest that the second procedure described by Schut (computation by 
strips), whether modified in the way he suggests or not has the defect that it pays too 
much attention at the start to the strip in comparison with the block. If only one strip is 
being treated no problem arises, but how are we to adjust the block except by breaking 
the strip into sections and proceeding as Jerie does, or by bringing in the redundancies 
from neighbouring strips and ending up by carrying out the full rigorous procedure that 
Schut calls the third procedure? In either case there seems little point in complicating a 
strip computation. Jerie’s work has surely shown conclusively that strips must not have 
precedence over blocks if a satisfactory final solution is to be obtained. 
As I mentioned above, Jerie builds his standard section from two models. There might 
be some advantage, with little more complication, in employing the second procedure to 
build up this section, but whether the result would be any better than connecting two 
independent models without deformation would have to be decided by trial. 
4. Condition equations. 
Schut is of the opinion that the most practical form of condition is the equation that 
must be satisfied if two corresponding rays are to be coplanar, without particular atten- 
tion being paid to measures or discrepancies at or near the model surface. I have always 
been of this opinion and have consistently adopted it in a series of papers on the subject 
(1944, 1950, 1956, 1959 b). 
For a number of years the Ordnance Survey, as is pointed out by Schut, has used a 
condition equation that expresses the vanishing of the Y-parallax in the model. Recently 
a change has been made and an equation expressing coplanarity in its simplest form has 
been adopted (Arthur 1959, Thompson 1956). But there still remain certain variations