from their own particular point of view and to underestimate the requirements of the
other man.
Nevertheless, the writer would not join those pessimists who doubt the possibility of
a solution which will be satisfactory to all. He is, on the contrary, convinced that the
biggest difficulties will disappear of their own accord once the above deseribed differen-
tiation between mathematical, physical, and technical concepts is recognized and a spirit
of tolerance is adopted, conceding that all three descriptions of image formation are
justified, and that the three concept groups derived from them complement each other
and satisfy different requirements. It does not follow from such an understanding that
it is necessary to agree on each and every detail, and that, seen from the viewpoint of
standardization, all three concept groups must be considered equally mature and suitable
for a general fixing.
That the mathematical definitions must not be missing from any standardization
cannot be doubted. Theirs is not only a historical significance, but — exactly because of
the simplification of the real conditions — they are indispensable for many purposes of
theory and instruction.
The physical definitions have had a hard time to assert themselves by the side of
the mathematical, and still today some experts believe that they could be abandoned with-
out disadvantage. While it is not to be denied that there are, within the framework of
photogrammetry, fields of work where it is possible to get along with the mathematical
definitions only, it is just as sure that these definitions fail in other and important
tasks [3]. For many purposes of instrument construction and instrumentology, the phy-
sical definitions cannot be done without. After all, these definitions were not created for
their own sake or for any arbitrary purpose, but are built on a foundation of measuring
and adjusting processes, ideas, and concepts which arose from the needs of practical
work. Instrument design and construction will continue to forge ahead and will use
whatever concepts they need. For this reason, the opportunity offered for international
standardization should not be missed as long as it is still possible to direct this develop-
ment into uniform channels.
The latest arrival are the technical definitions. Investigations relating, for instance,
to the symmetry properties of the principal point are without question necessary and of
merit. It is, however, a totally different question whether they should be made the subject
of standardization proposals. The writer, at any rate, believes that it will be best to
avoid standardizing the technical definition of fundamental concepts, for three distinct
reasons:
In the first place, — regarding for the present only the factual side of the problems
— it cannot be maintained that there is today a condition of maturity for standardi-
zation. As valuable and to the point as individual contributions may appear, the different
proposals diverge so far that it would be very risky to fix one of them as internationally
obligatory by a majority vote. As it is, it will be difficult enough to carry through a
standardization of fundamental concepts which will satisfy all demands, and it would be
impractical to burden this undertaking by additional problems which are still awaiting
clarification.
Moreover, according to the principle of fixing as little as possible, it should be
waited to see whether there is any widespread need for standardizing these technical
definitions. While the writer has no desire to deny that it should be considered whether
the manufacturing errors of an instrument are noticeable and of practical importance,
it must not be forgotten that it is not a general normal case which is here concerned,
but rather exceptions which are to be eliminated as quickly as possible 2). It is still an
2) It will be noted that the case here differs, for instance, from that of the resolving
power, which even under optimal conditions may be considered as a measurable quality
characteristic of a lens.
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