independent of Space Measurement. 



389 



" standtians" (as I proposed some time ago to call the 

 projective steps). 



Notice in passing that the world-lines of two particles p^ p 2 

 having i^uaZ constant velocities intersect on the ft-line (fig. 3), 

 and vice versa, every two right world-lines crossing on II 

 represent uniform motion with equal projective velocities *. 



Fie. 3. 



Such particles p ± , p 2 are always the same number of 

 staudtians apart. This singularity of the 12-line in the 

 graphical representation must be well kept in mind : two 

 particles meet actually when and only when their repre- 

 sentative lines cross outside the ft-line, but not on the ft-line 

 (unless the particles are permanently united). A sub-case 

 of this is a pair of constant-place lines, i.e. crossing in ft,; 

 the corresponding two particles, fixed for ever in two distinct 

 places, obviously do not meet. 



It may be well to describe the four-particles experiment of 

 Section 4 with the aid of equation (1) and thus to verify 

 analytically the determinateness of its result. Let, for the 



* The proof of this statement follows at once from the fundamental 

 properties of such a pair of lines with respect to the reference system. 

 Cf. ' Projective Vector Algebra,' more especialh r the paragraphs dealing- 

 with equal vectors. 



