ANALYTICAL AERIAL TRIANGULATION, AUTHOR’S PRESENTATION 19 
en- In the second place a correctly triangulated strip has the same scale throughout 
vill while the horizontal scale of the map changes continuously. This does not affect single 
nd models or short strips but introduces scale and azimuth errors in longer strips. 
Ay The correction for earth curvature can be performed by giving appropriate correc- 
ase tions to the photograph coordinates. In the case of approximately vertical photographs 
and not too mountainous terrain a symmetrical radial correction gives very satisfactory 
lec- results. This correction can be added to the lens correction and does not then increase 
the the computations. 
the The variation of horziontal scale in a map projection is automatically taken into 
account by a second or third degree conformal transformation of plane coordinates, pro- 
Tee vided that three or four sufficiently separated horizontal control points occur in the 
. of strip. If only two horizontal control points occur, the coefficients of such transformations 
one can be computed very simply and with a very satisfactory accuracy from the scale factor 
)0S- in the map projection, expressed as an analytical function of the map coordinates. 
the A paper on these two corrections and their effect on single models and on strips of 
und up to 500 miles long will be published shortly. 
ese 
)ro- References. 
tive [1] Schut, G. H., An Analysis of Methods and Results in Analytical Aerial Trian- 
gulation, Photogrammetria, 1957-58, No. 1. See also the references in this paper. 
lels. [2] Schut, G. H., Construction of Orthogonal Matrices and their Application in Ana- 
this lytical Photogrammetry, Photogrammetria, 1958-59, No. 4. To the references in this 
1 in paper the following should now be added: 
the Thompson, E. H., A Method for the Construction of Orthogonal Matrices, The 
Photogrammetric Record, April, 1959. 
Thompson, E. H., An Exact Linear Solution of the Problem of Absolute Orien- 
| an tation, Photogrammetria, 1958-59, No. 4. 
[3] Schut, G. H.,, Bemerkungen zu der Abhandlung ‘Zur analytischen Behandlung 
photogrammetrischer Aufgaben' von Dr. Ing. habil, K. Rinner, Bildmessung und 
axes Luftbildwesen, 1958, No. 2. 
[4] Schut, G. H, A Program for Analytical Aerial Triangulation by the N.R.C. 
"hts. Method on the IBM-650, Publication AP-PR 16 of the Division of Applied Physies 
e of of the National Research Council of Canada, September 1959. 
med [5] Sehmid, H. H., An Analytical Treatment of the Problem of Triangulation by 
ngi- Stereophotogrammetry, Photogrammetria, 1956-57, Nos. 2 and 3. 
con- [6] Arthur, D. W. G., A Stereocomparator Technique for Aerial Triangulation. Ord- 
nance Survey Professional Papers New Series, No. 20, 1955. 
have [7] Herget, P. The Reduction of Aerial Photographs on Electronic Computers, 
for Photogrammetric Engineering, 1954, No. 5. 
labo- 
ften 
jints Author's Presentation of the Paper 
: the 
ntrol So many papers have been written already error in thinking has been committed. 
on the subject of analytical aerial triangulation, 
A number of methods have been constructed 
, the that on being approached to write a paper for in this way and many more are possible. Some 
Sys: this Congress at first I hesitated, but I then of the published methods contain undesirable 
decided to increase the number by one. features such as needlessly complicated deriva- 
| ne Upon study of the existing literature it be- tions and computations which have no effect 
ation came clear that there was still a need for a upon the triangulation results, and even deriva- 
systematic review of the theory of analytical 
aerial triangulation as opposed to its practice. 
In practice a method can be constructed by 
selecting a triangulation procedure from 
amongst several, deriving a set of condition 
equations which your observations must satisfy 
and devising a way of solving those equations 
from the unknowns. Such a method can then be 
adorned with the name of the organisation or the 
name of the person who constructed it, and thus 
we have a method which will work if no serious 
tions which are not based upon sound math- 
ematical reasoning. 
From the point of view of the theory of 
analytical aerial triangulation, all this is really 
unsatisfactory. It is not possible to construct a 
sound theory by merely lifting the published 
method and retaining all the characteristics; 
rather each method must be investigated, un- 
desirable features rejected and a sound theory 
built up from what is left over. This is a job 
which cannot be accomplished by one person