2o6 THE GRAMMAR OF SCIENCE 



Of the three types of motion just introduced to the 

 notice of the reader, the first, or point-motion, is that 

 which for our present purposes is most important. The 

 remainder of the present chapter will therefore be devoted 

 to its discussion. The reader will, I trust, pardon its 

 somewhat technical character, for without this investigation 

 of point-motion it would be impossible to analyse the 

 fundamental notions of Matter and Force, or to rightly 

 interpret the Laws of Motion. 



^ 7. — Point- Motion. Relative Character of Position 



and Motion 



Motion has been looked upon as change of position, 

 but if we try to represent the position of a point we must 

 do so with regard to something else. If space be a mode 

 of distinguishing things, we must have at least two things 

 to distinguish before we can talk about position in space. 

 Position of a point is therefore relative, relative to some- 

 thing else, which for the moment we will suppose to be a 

 second point. Absolute position in space, just as absolute 

 space itself (p. 156), is meaningless. Let the letter P 

 (Fig. 8) represent a point, and the letter O a point termed 

 the " origin of reference," from which we are to measure 

 P's relative position. Now the distance from O to P 

 would indicate for us the position of P relative to O, but 

 in our conceptual space we have in general a variety of 

 other points or geometrical bodies besides O which we 



universe. The universe has been with much confusion spoken of as the 

 conception of an infinite mind. But the conceptual basis of the planetary 

 theory lies in geometrical notions, no ultimate evidence of which can be 

 discovered in the perceptual world. Thus, while the planetary theory answers 

 our purposes of description, it could never have been the conception upon 

 which the universe was "designed," for the conception is nowhere found 

 perceptually realised. Starting with his material endowed with all its 

 peculiar properties, the carpenter makes for us a box according to our 

 geometrical description, but in reality not ultimately geometrical. Starting 

 with nothijig but the absolute power of realising conception in perception, 

 he would have produced from our geometrical plan a geometrical box. 

 Geometrical notions could flow as limits from the material universe, but the 

 latter could not flow from the former. Material sensations must certainly have 

 antedated geometrical conceptions, or, at any rate, planetary theory was not 

 the conception upon which the universe was created out of nothing. 



