318 NEW SYSTEM 



as to absolute motion, nothing can determine it mathe- 

 matically, since all ends [se termine] in relations, with 

 the result that there is always a perfect equivalence of 

 hypotheses as in astronomy 79 ; so that, whatever number 

 of bodies we take, we may arbitrarily assign rest or such 

 and such a degree of velocity to whichever we like, with- 

 out it being possible for us to be refuted by the pheno- 

 mena of motion, whether it be in a straight line, in 

 a circle, or composite. Yet it is reasonable to attribute 

 to bodies real motions, according to the supposition 

 which explains the phenomena in the most intelligible 

 way, for this is in harmony with the notion of activity 

 [action] which we have here maintained 80 . 



from one body to another. Each body, he would say, has a force, 

 which is the cause of its actual motions, and when two bodies 

 collide, there is not a transference of motion from one to the other, 

 but a certain release of the pent-up force in each, and this release 

 shows itself in the elasticity of their rebound. See Introduction, 

 Part iii. pp. 89 sqq. 



79 ' Absolute motion ' would be motion that is not in any degree 

 rest. But motion must always be determined through relation. 

 One body has motion only in reference to another, and, accordingly, 

 if we wish to determine which of the two really (i. e. absolutely) 

 moves, we must refer them both to some third body and so ad 

 infinitum. The ' equivalence of hypotheses in astronomy' probably 

 refers to the fact that the hypothesis of Copernicus (1473-1543), 

 according to which all the planets move round the sun, and the 

 hypothesis of Tycho Brahe (1546-1601), according to which the sun 

 moves round the earth and the other planets move round the sun, 

 equally well explained the phenomena as observed at that time. 

 Cf. G. iv. 369, and Descartes, Principia, Part iii. 15-18. 



80 See Appendix C, p. 204. 



