10.7 The explanation of the similarities and differences between spaces and times derived from different consentient sets of the Newtonian group, and of the fact of there being a Newtonian group at all, will be derived in Parts II and III of this enquiry from a consideration of the general characteristics of our perceptive knowledge of nature, which is our whole knowledge of nature. In seeking such an explanation one principle may be laid down. Time and space are among the fundamental physical facts yielded by our knowledge of the external world. We cannot rest content with any theory of them which simply takes mathematical equations involving four variables () and interprets () as space coordinates and as a measure of time, merely on the ground that some physical law is thereby expressed. This is not an interpretation of what we mean by space and time. What we mean are physical facts expressible in terms of immediate perceptions; and it is incumbent on us to produce the perceptions of those facts as the meanings of our terms. Einstein has interpreted the Lorentzian formulae in terms of what we will term the 'message' theory, discussed in the next chapter. APPENDIX TO CHAPTER III Let and be two consentient sets of the Newtonian group. Let () be the rectangular axis system in the space of , and be the rectangular axis system in the space of . First consider the traditional theory of relativity. Then the time-system is independent of the consentient set of reference. Fig. 3. At the time let the event-particle which instantaneously happens at the point in the space of a happen at in the space of , and let the event-particle which happens at in the space of happen at in the space of . Let the axis be in the direction of the motion of in the -space, and the axis be in the direction reversed of the motion of in the -space. Also let be so chosen that lies on . Then the event-particles at the instant which happen on are the event-particles which happen at the instant on . Also we choose and so that the event-particles which happen at time on and respectively happen on straight lines in the -space which are parallel to and . Let be the velocity of in -space and be the velocity of a in -space. Then (with a suitable origin of time) These are the 'Newtonian' formulae for relative motion.