176 THE GRAMMAR OF SCIENCE 



molecular theory of bodies postulates essentially their 

 discontinuity. Take, for example, a spherical drop of 

 water — to follow Lord Kelvin — suppose it to be as big 

 as a football, then if we could magnify the whole drop up 

 to the size of the earth, the structure, he tells us, would be 

 more coarse-grained than a heap of small shot, but prob- 

 ably less coarse-grained than a heap of footballs.^ 



Now I propose later to return to the atomic hypothesis. 

 At present I will only ask the reader to look upon atom 

 and molecule as conceptions which very greatly reduce the 

 complexity of our description of phenomena. But what 

 it is necessary to notice at this stage is : that the con- 

 ception atom, when applied to our perceptions, is opposed 

 to the conception of surface as the continuous boundary 

 of a body. We have here an important example of 

 what is not an uncommon occurrence in science, namely, 

 two conceptions which cannot both correspond to realities 

 in the perceptual world. Either perceptual bodies have 

 continuous boundaries, and the atomic theory has no 

 perceptual validity ; or, conversely, bodies have an atomic 

 structure, and geometrical surfaces are perceptually im- 

 possible. At first sight this result might appear to the 

 reader to involve a contradiction between geometry and 

 physics ; it might seem that either physical or geometrical 

 conceptions must be false. But the whole difficulty really 

 lies in the habit we have formed of considering bodies as 

 objective realities unconditioned by our perceptive faculty. 

 We cannot too often recall the fact that bodies are for us 

 more or less permanent, more or less clearly defined 

 groups of sense-impressions, and that the correlations and 

 sequences among the sense-impressions are largely con- 

 ditioned by the perceptive faculty. At the present time 

 we have no sense-impressions corresponding to geometrical 

 surface or to atom ; we may legitimately doubt whether 

 our perceptive faculty is of such a nature that it could 

 present impressions in any way corresponding to these 

 conceptions. It is impossible, therefore, to say that one 

 of these conceptions must be real and the other unreal, 

 1 Popular Lectures and Addresses, vol. i., "The Size of Atoms," p. 217. 



