to rank above others, the widest-scope concept in normal use shall receive the shortest 
possible designation while the subordinate concepts are characterized by specializing 
addenda which can be dropped when necessary. The other way around: short names 
for special concepts, obliges to emphasize that which is special and different also when 
it is desired to express what is general and in common. The English and French langu- 
ages are better suited to this kind of composite designations than the German, for which 
reason deviations from this requirement in German are sometimes hard to avoid. 
The application of these points of view to the mathematical and physical definitions 
gives the following aspect: 
The terminology for mathematical concepts is essentially fixed. Their designations 
have been current for decades, and no changes should therefore be made in them, unless 
by way of exception when a compelling necessity demands such changes in view of the 
other two requirements. The definitions of the physical concepts were formulated much 
later. The concepts themselves, however, have for long been used — more or less 
subconsciously — under the names of mathematical concepts, by applying these without 
much hesitation also in the case of distortion as well as in respect to instruments, or 
therefore, in the physical sense. In this way, a fixed terminology for the physical 
concepts also has formed and demands consideration. 
This likeness of designations can be justified with regard to the objective facts. 
Mistakes or ambiguities need not be feared; for where the mathematical concepts are 
defined at all, viz. in the special case of central projection, the more general physical 
definitions merge into the mathematical definitions, which means that the result of 
the physical measurement exactly corresponds to that of the mathematical construction. 
The physical definitions therefore mean, as against the mathematical ones, an ex- 
pansion of the scope of the concept, with the simultaneous transformation from a geo- 
metrical figure to reality. Such cases of expansion of a concept scope without change 
in designation are not anything unusual in other fields (for instance, the word 
“number” — originally confined to the positive integers — nowadays includes the 
imaginary numbers too). 
The simple designations accordingly no longer permit of determining whether the 
mathematical or the physical definition is meant; they have become names for the 
higher ranking concepts. This is very appropriate, for in many cases no importance 
attaches to a differentiation between mathematical and physical definitions. The plain 
and familiar designations of the concepts then are the proper means of understanding. 
There is no reason for changing anything in this factually and logically justified 
development of terminological usage, and all that is necessary is to consider them in 
every individual case. The new requirement is merely to provide special designations 
for those cases where a distinction must be made between the mathematical and the 
physical definition. It is proposed to this end — in consonance with the above stated 
third requirement — to add the term “mathematical” and “physical” to the concept 
designations, and the indices “math” and “phys” or “m” and "p" to the letters. 
It will be well to consider these principles in the selection of designations. If, 
in individual cases, it is impossible to fulfill all requirements simultaneously, or when 
matters are complicated by special viewpoints, it will be advisable to follow the line of 
the least drawback. 
2. CONCLUSIONS. 
a) A review of the most important mathematical and physical definitions. 
In the accompanying Table, some mathematical and physical definitions are 
compared. This Table is confined to a selection of the most important concepts. 
Nevertheless it should suffice to explain, on the one hand the differences, and on the 
other the analogy between corresponding definitions. 
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