SPACE 



45 



we have to do is to get quite clear as to which places in space 

 are filled with resistance and which are not. 



The resistances in space are all resistances of bodies, i.e. 

 they are three-dimensional. They all, without exception, 

 have a body, quite independently of the qualities they possess. 

 Therefore they may all be described as collections of material 

 points or atoms. How the atoms are referable to local signs 

 has already been discussed. 



Matter is always in motion, and since substances cannot 

 all be at the same time in the same place — i.e. cannot possess 

 the same local signs — they get in one another's way, and, in 

 their movements, mutually influence one another. 



We are able to resolve movements into series of direction- 

 signs ; and so, if we regard only their spatial character and 

 neglect their other qualities, it is possible to refer all sub- 

 stances to local signs and direction-signs. The great advan- 

 tage of this is that all reciprocal actions of substances in space 

 can be measured and reckoned, and can be brought under 

 mathematical formulae. 



Physics has striven towards this goal, with admirable 

 results. It has succeeded in subjecting to its mathematical 

 formulae the reciprocal action of all the qualities of matter, in 

 so far as these are of a spatial nature. 



Physics succeeded first with sounds, because matter 

 was present in the form of air, the movements of which 

 carried the waves of sound from place to place, and made it 

 possible to convert the theory of- sound into a theory of air- 

 vibrations. Indeed, Helmholtz went so far as to explain 

 dissonances as perturbations of the sine-waves. In so doing, 

 he transgressed the limits set him by the spatial factors. The 

 effects of sound-qualities on the subject have their own par- 

 ticular laws, which have absolutely nothing to do with the y 

 laws of space ; and it is these, and these only, that can be 

 formulated mathematically. 



