a aloe ed RR Ut RE 
is this so in the presence of distortion [5]. For this reason it suffices, as has been done 
in the Table, to employ the autocollimation process exclusively for physically defining 
the principal point and to dispense with using the point of symmetry defined by resec- 
tion in space. It goes without saying that what has been said in no wise minimizes the 
marked practical importance attaching to the method of resection in space for checking 
symmetry. This method is indispensable both in adjusting and in checking cameras, and 
will also form the basis, if and when it should be decided to set up a technical definition 
for deviations from symmetry due to manufacturing errors. For a physical definition, 
however, it is out of the question. Also in other fields (such as length measurement) no 
one would think of using every important practical measuring process for defining a 
fundamental concept. 
The result accordingly is that standardization can be limited to the definition of 
four points: The fiducial center, the optical center, the mathematical principal point, 
and the collimated principal point. 
It has been proposed to designate the mathematically defined principal point as 
hitherto simply by the term principal point, but the physically defined principal point 
by a new name, like principal point of autocollimation or central point [7, 8]. Such a 
mode of designation would, however, contravene the principles evolved above. The phy- 
sical definition of the principal point is nothing else than an expansion of the concept 
scope of the mathematical definition. Terminological usage long ago carried out this 
expansion of its own accord in that the term principal point, which originally belonged 
only to mathematical central projection, is applied to instruments and to images with 
marked distortion, i.e. in the sense of a physical definition. It would be an unnecessary 
coercion if an attempt were made to block this usage and prescribe a new word. More- 
over, it would lead to not only a superfluous but also a troublesome double designation, 
for in all cases where there is no need to differentiate between mathematical and phy- 
sical definitions, it would be necessary to ponder whether one must speak of the principal 
point or of the principal point of autocollimation. — There are, of course, exceptional 
cases where such a differentiation may be desirable or necessary. Tt might be considered 
whether the employment of the terms principal point of autocollimation, or central 
point should be limited to such cases. Weighty reasons, however, speak against both 
designations. The expression principal point of autocollimation implies a preference of 
the autocoliimation method as against resection in space. While this corresponds to the 
procedure in the selection of the definition, it does not correspond to the results of the 
two measuring processes Which, as has been pointed out above, both supply the same 
point. The designation principal point of autocollimation would cause the wrong impres- 
sion that the point determined by autocollimation must be differentiated from the point 
of symmetry found by resection in space. It would accordingly seem necessary to use a 
neutral designation. This condition is, indeed, satisfied by the term central point, which 
however has the disadvantage of reminding of central projection, which in most cases 
does not prevail when the mathematical and physical definitions must be differentiated. 
But above all, the term centrai point clashes with the above formulated demand that the 
terni should be derived from the higher-order concept principal point with the aid of a 
qualifying addendum which may be omitted wben not needed. It will be recalled that 
the differentiation between the mathematical and the physieally defined principal point 
should clearly be optional and nonobligatory. For this reason, the writer would propose 
to :mploy — as in all other concept designations — the neutral qualifying terms 
“mathematical” and "physical", in the few exceptional cases where it is at all necessary 
to distinguish between a mathematieal and a physieal principal point, and otherwise to 
sp2ak simply of the principal point, 
Camera function and image function are two newly introduced concepts. They 
describe analytically the relation between the object-side principal ray bundle and the 
points of the image plane, This relation is of decisive importance in photogrammetry, 
12 
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