70 THE ANATOMY OF SCIENCE 



remained the same, with the same lines, and the 

 same intervals between events, and the same 

 slope between the lines AA' and BB' which 

 shows the relative velocity of the two beads. In 

 other words, the intrinsic properties of the fig- 

 ure are independent of a parallel shift of the 

 axes of reference. 



We see, therefore, that we are very close to 

 having a geometry. Let us see whether the pos- 

 tulates also imply any operation analogous to 

 rotation. Once more looking at the left side of 

 Figure 14, we see the string with knots O and P 

 represented as stationary, as is also the bead A, 

 while the beads B and C are moving. But by the 

 postulate of the relativity of motion we might 

 take the bead B as at rest and the string and 

 other beads as in motion, so that the right-hand 

 diagram of Figure 14* would equally well repre- 

 sent the facts. But this suggests at once the 

 non-Euclidean geometry which we discussed in 

 the last lecture and which is characterized by 

 shear rotation. 



Indeed, as we pursue the inquiry we find com- 

 plete identity, detail by detail, between the 

 kinematics of Ne\vton and this peculiar geome- 

 try in which now any distance along the parallel 

 lines OP, O'P', represents a measurement with 



