THE LAWS OF MOTION 313 



same body, and suppose we find these portions, however 

 we test them, present to us the same groupings of physical 

 and chemical sense-impressions, then we shall term these 

 portions of the same substance. Further, if portions of a 

 body, taken from any part of it whatever, always appear 

 of the same substance, so that, if we could postulate 

 exactly the same perceptions of shape, any one portion 

 might be mistaken for any other, then we shall say that 

 the body is homogeneous. Now although we cannot realise 

 a particle in perception, still we conceive that if particles 

 were to be formed by taking smaller and smaller elements 

 from every part of such a homogeneous substance, all 

 these particles would be of equal mass} We thus come 

 to look upon our conceptual symbol for a homogeneous 

 body as a uniform distribution of particles of equal mass 

 throughout a geometrical surface. Applying our laws as 

 to the motion of particles to such a uniform distribution 

 of particles, we construct a motion for the geometrical 

 form which closely describes our routine of sense-im- 

 pressions in the case of those perceptual bodies which 

 approximate to the conceptual ideal of homogeneity. 

 We then define the sum of the masses of the particles 

 contained in any portion of our geometrical form as the 

 mass of this portion. From this it follows at once that : 

 The masses of any two portions of the same homogeneous 

 S7ibstance are proportional to their volumes. 



This result is not a truism ; ' it flows only from the 

 uniform distribution of particles which we postulate for a 

 homogeneous substance, and this distribution is a con- 

 ception only justified, like the law of gravitation, by the 

 results which it describes being in accordance with our 

 perceptual experience. If we take two small and equal 

 volumes of a homogeneous substance, then the smaller 

 they are the more nearly we can describe our perceptual 

 experience of them by the conceptual symbols, " particles 

 of equal mass." If we take two small and equal volumes 

 of two different homogeneous substances, then, the smaller 



^ /.£. of like individuality seep. 299. 

 - It might well be described as the sixth fundamental law of motion. 



