206 SCIENCE PROGRESS 



tudes as indefinable terms which are capable of entering into the 

 relations of " greater than " and " less than." Every magnitude 

 bears a peculiar relation to some particular concept such that 

 we say it is the magnitude of that concept ; magnitudes are 

 said to be of the same kind when they bear this relation to 

 the same concept. Only magnitudes of the same kind can enter 

 into the relations of greater and less. Thus we can speak of 

 magnitudes of volume and magnitudes of temperature, and we 

 can say that one magnitude of the concept volume is greater 

 or less than another magnitude of volume, but cannot relate 

 it in this way to a magnitude of the concept temperature. 



Quantity is a magnitude which has been particularised by 

 the specification of spatial or temporal conditions, so that, for 

 instance, the statement of the temperature in a given beaker 

 at a given time is a quantity. One quantity is greater than 

 another quantity, when the magnitude of the former is greater 

 than the magnitude of the latter. To speak of equal magni- 

 tudes would be meaningless ; but we can speak of equal quanti- 

 ties — they are quantities having the same magnitude. 



No reasonable ambiguity arises if we place the different 

 kinds of quantities used by physicists in two general classes 

 — those having extensive magnitude and those having intensive 

 magnitude. The first class contains those quantities which 

 have a certain additive nature so that a given quantity can be 

 regarded as being the sum of a number of smaller quantities 

 of the same kind ; the second class contains those which have 

 no such additive nature. Thus volume is typical of quantities 

 of the first class ; likewise mass, energy, entropy. We can 

 decide that such quantities have extensive magnitude by the 

 consideration that the simultaneous presence of two systems, 

 each having a definite quantity of the kind in question, gives 

 a larger system with twice the quantity. On the other hand, 

 density, temperature, permeability, inductivity, are quantities 

 having intensive magnitude. For instance, the consideration 

 of two pieces of platinum at ioo° C. gives a larger piece of 

 platinum at ioo° C, not 200 C. This classification may turn 

 out to be ambiguous ; it is, however, simple and would still 

 have great value even if there should happen to be borderline 

 quantities of such a nature that it was hard to apply the 

 criterion. 



In measuring quantities of the first class we may for this 



