Principles of Dynamics. 171 



never three possible values for the volume — usually there is 

 only one, sometimes there are two. Accordingly, " v" can have 

 values which the volume cannot have, and it cannot be held 

 that " v " and the volume are the same concept. 



The pressure and the quantity " p 3 ' are, then, perfectly dis- 

 tinct concepts ; but there is a relation between them, into 

 the exact nature of which it is unnecessary for our present 

 purpose to inquire further. For the sake of brevity in what 

 follows I shall call this relation " relation A," and I shall 

 denote the mathematical quantity which bears relation A to 

 a physical measurement by the name of the measurement 

 written with a capital letter. Thus " p *' will be called the 

 Pressure, " T " the Temperature, and " v " the Volume. 



Now let us consider for a moment the quantities a, b, R. 

 It is clear that these are quantities of the same nature as the 

 Pressure, Volume, and Temperature, and are not similar to 

 the pressure, volume, and temperature ; but they differ from 

 those quantities in the fact that they do not bear the relation 

 A to any physical measurements. But, it may be said, b is 

 (or is proportional to) the volume of the molecules of the 

 gas. This is just the fallacy I wish to expose: b may be the 

 Volume of the molecules, but it is not a volume at all. I do 

 not deny that it is very useful to call b the Volume of the 

 molecules; the expression suggests a relation between b and 

 quantities occurring in other equations, but we must not let 

 the name conceal the fact that the term "volume of the 

 molecules'" is meaningless, and that there is no physical 

 measurement which is correlated with b as the volume of the 

 gas is correlated with r. " b " cannot be defined without re- 

 ference to Van der Waals's equation, but u v n can be defined 

 without such reference by means of the relation A which it 

 bears to the volume. 



§ 6, Now, after this preliminary discussion, let us turn to 

 dynamics. 



Dynamics is the study of motion, or the change of distance 

 with time. The only physical measurements which are con- 

 cerned in the study are those of distance and time*. Our 

 object in stating the fundamental principles of theoretical 

 dynamics is to formulate equations such that, when for 

 certain quantities are substituted values depending en dis- 

 tances and times and the equations solved, some of the roots 

 should have values which depend in the same way on other 

 distances and times. 



* It is not relevant to our purpose to inquire. Low distance and time 

 are measured ; it is sufficient to note that there are certain conventional 

 methods which are familiar to all. 



