RECENT ADVANCES IN SCIENCE 207 



purpose distinguish two groups. In the first group will appear 

 those quantities which can be regarded as composed of a finite 

 number of distinct and identical parts, one of these parts being 

 naturally chosen as a unit of measurement, which will then 

 consist in a process of counting. Quantities of this kind are 

 often used in the natural sciences, as in the statement of a 

 number of petals in a given species of flower, in the correlation 

 of the pressure of a gas with the number of molecules it con- 

 tains ; they are associated with a discrete series of magnitudes 

 which can be put into a one-to-one correspondence with the 

 ordinal numbers. The second group of quantities having 

 extensive magnitude contains those which cannot be regarded 

 as the sum of a finite number of parts ; in this case the magni- 

 tudes of a given kind form a continuous series and can only be 

 put into a one-to-one relation with the whole series of real 

 numbers. Volume is an example, as it does not accord with 

 our present ideas of space to consider a volume as composed of 

 a finite number of parts which could not be further subdivided. 



The measurement of quantities of the second class, viz. 

 those having intensive magnitude, must be effected by some 

 device in which the magnitudes to be measured are put into a 

 one-to-one correspondence with a series of quantities having 

 extensive magnitude. Thus, in the case of temperature, we 

 correlate magnitudes of temperature with lengths of a mercury 

 thread, volumes of a gas, etc. 



Nearly all the quantities of different kinds used by the 

 physicist are capable of being defined in terms of the few 

 remaining ones, with the aid of certain other indefinables which 

 consist in the operations " multiplied by," " divided by," etc. 

 Thus a quantity of velocity is regarded as a quantity of length 

 divided by a quantity of time ; a quantity of area is a quantity 

 of length multiplied by a quantity of length ; and we have 

 the well-known dimensional symbols to represent this relation 

 of derived to fundamental quantities in as succinct a manner 

 as possible. 



In choosing a set of fundamental kinds of quantity it is 

 desirable to keep in mind the following considerations : the 

 number of kinds shall be sufficient and not redundant ; all the 

 kinds chosen shall have extensive magnitude and further the 

 requirements of simplicity. 



It appears, as was pointed out by Riicker thirty years ago, 



