8 
the coefficient of expansion of the tape as a second unknown. Our two measures 
will then be just sufficient to determine the length and the coefficient of expansion 
and both residuals will be zero. Would anyone maintain in such a case that the 
second result is necessarily better than the first? It all depends, of course, on 
how well the coefficient of expansion was known from previous laboratory work. 
If badly determined it is better to regard it as unknown: if not then the a priori 
value should be used. There are two unknowns, length and the coefficient of 
expansion, and the problem is to estimate their values in the best way at our 
disposal not to arrange matters so that the residuals are as small as possible. 
This is all so very obvious that it would not be worth mentioning were it not for 
the fact that the principles are often ignored in writings on aerial triangulation 
adjustment. There are many unknowns to be found and there is a choice of the 
ways of finding them. All can, in principle, be found from the final block 
adjustment. Internal, relative, absolute orientation elements have all to be found 
as well as the coordinates of the points in which we are interested; and the more 
of these unknowns that are allowed to appear in the final adjustment, the smaller 
will be the residuals. There are very good reasons to suppose that the very best 
way to find the internal orientation elements is in a laboratory; and that the best 
way to find the relative orientation elements is by relative orientation measures; 
and that Airborne Profile Recorder measures may be the best way to determine 
the scale and so on. If we ignore all these methods of finding the unknowns and 
simply rely upon the block adjustment we may certainly arrive at a «better 
adjusted» block with smaller discrepancies; but not necessarily at a better answer. 
Before a more elaborate method of adjustment is proposed, and increase of the 
number of unknowns is to be found simultaneously means increased work, it 
should be the responsibility of the proposer to show that his method gives a better 
result for it will certainly not always do so, as we have seen. 
One final point might be raised on the computation of aerial triangulations: what 
should we do about Earth Curvature? One thing at least we should do is to stop 
describing it as an error. Photogrammetric processes are pure geometric processes 
bearing no relation whatever to the gravitational field; and, strictly speaking, 
surveying itself is concerned solely with depicting the topographical features of 
the earth which is a geometrical (is not this what the word means?) and not a 
dynamical problem. It is a matter simply of convenience to the users of maps 
that contour lines are taken to be intersection of equipotential surfaces with the 
topographical surface. The user wants to know whether he is going up or down 
because water will not flow up and it will flow down and it is harder to walk up 
than down. But all this has nothing to do with the shape of the ground, its 
geometry, it is merely one way of presenting this shape to the public. The valuable 
characteristic of photogrammetric methods is that they do give us this shape 
diiectly without any reference to the direction of the vertical; and it is surely 
wrong to modify correct photogrammetric measures to give a distorted result. 
It would seem logical to treat aerial triangulation as if it were purely a geometrical 
problem. This entails simply leaving the photogrammetric measures alone but 
expressing the positions of all control points in terms of rectangular coordinates in 
space and not, as at present, in a mixture of rectangular coordinates and polar