THE LAWS OF MOTION 315 



of the standard substances, it is a quantity which varies 

 from point to point of the heterogeneous body. 



Clearly the notion of density thus discussed affords 

 a key to the manner in which we are to conceive the 

 symbols for physical bodies constructed from aggregates 

 of particles. By means of density we individualise sub- 

 stances and kinetically classify the particles which are 

 the conceptual elements of bodies. Density forms the 

 kinetic scale we have been in search of (p. 300) ; it is the 

 fundamental means by which we measure the relative 

 magnitude of the accelerations which we conceive the 

 ideal elements of bodies to experience in each other's 

 presence. It throws life into the geometrical forms 

 by means of which we conceptualise the phenomenal 

 universe. 



The reader must, however, be careful to note that the 



whole of this discussion of density abounds in purely ideal 



notions. I have defined homogeneity ; but homogeneity 



thus defined is a limit drawn purely in conception to a 



process of comparison which can be begun but not 



completed perceptually. No perceptual substance is 



accurately homogeneous. Further, I have spoken about 



taking "equal volumes," a process which is a geometrical 



conception, and never exactly realisable in perception, 



where continuous boundaries cannot be postulated (p. 



171). Then; again, I have spoken of taking a "volume 



at a point," and of the " density of a heterogeneous body 



at a point," conceptual limits again having no exact 



perceptual equivalents. Lastly, I have spoken of density 



as equal to the ratio of the masses of " certain volumes," 



and of aggregates of particles as filling " geometrical 



forms." These indications will be sufficient to show the 



reader that density, like mass, is a conceptual notion, an 



ideal means of classifying the symbols of our conceptual 



model of the universe. We do, indeed, choose these 



densities so that our model shall describe as accurately 



as possible our perceptual experience, but the density 



itself belongs to the conceptual sphere, and is defined 



with regard to the geometrical forms by which we 



