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open question whether it is best to make these exceptional cases the basis of new con-
cepts and above all, of the fundament of a standardization.
Weightiest, however, is the third reason, Even if it is assumed that the clarification
of fundamentals and the necessity of technical definition are in order, it does not follow
that it will be advisable to consider manufacturing errors in the definition of fundament-
al concepts proper. It will be much more natural to base the fundamental concepts upon
the ideal case of the error-free instrument, and to reserve the technical definitions for
the deviations from these physical concepts which are caused by the manufacturing
errors 3). This mode of procedure,indeed, has proved suited in other fields (as, for
instance, optical axis: Physical definition on the assumption of an error-free optical
system; centering error: Technical definition for deviations due to manufacturing
errors). The question of standardizing such correction values lies beyond the scope of
the present investigation, which concerns itself only with fundamental concepts proper.
With these, there would seem no necessity for advancing beyond the physical definitions.
For these reasons, it would not seem advisable to expand the already existing and
unavoidable side-by-side existence of mathematical and physical definitions of analogous
fundamental concepts, by the technical definitions.
c) Problems of designation.
As has been shown, a clean-cut differentiation between mathematical and physical
definitions is the simple means and that which corresponds to the existing facts, for
placing at the disposal of any photogrammetrist the concepts which are suitable for his
field and his mode of view. This separation, however, brings up the question of how
analogous mathematical and physical concepts are interrelated, and especially whether
and when it becomes advisable to differentiate them from each other by designation.
The significance of this question must not be underestimated; for when it is already
unavoidable to have two parallel series of concepts in order to satisfy all requirements,
everything should be done to facilitate the understanding between the “mathematical”
and “physical”’-minded thinkers. To this end, the first need is a clear and adaptable
terminology, whereby that which is common and that which differs in the two modes
of view can be clearly expressed. The designation of a concept should therefore not be
left to a more or less happy inspiration in individual cases, but it should be endeavoured
to establish fundamental clarity on what is essential.
The most important requirements can be reduced to three: The designation of a
concept should be in consonance with existing terminological usage, with the objective
facts, and with the logical interrelation of the concepts. The first condition needs no
comment or argument. Unfortunately, it is sometimes contrary to the two others, and
its fulfillment may be particularly difficult when international agreement is at the
same time attempted. The second condition serves for avoiding factual errors and
confusion; as an instance, it will not do to apply the same name to different concepts.
Compliance with this rule is not as self-evident as would at first blush appear. The
third demand must be satisfied in order to render the designations convenient, easy to
memorize, and adaptable. By way of an example, it demands that when one concept is
3) An example of such a definition is the so-called "tangential distortion" [7]. Nothing
shall here be said about the advisability of this formation of concepts. At any rate, its
designation is not very happy. For, first, it has been customary in opties all along to
designate that direction which is radial in the image as tangential or meridional, and
the direction which is tangential in the image as sagittal. Second, there corresponds to
the “tangential” component a radial component, which is likewise due to manufacturing
errors only. This latter represents the usually asymmetrical correction in that condition
which is still today termed distortion, — and therefore. properly not distortion but altera-
tion of distortion.
