Manclicster Memoirs, Vol. liv. (1910), .V('. 14- 7 



For instance, if two observers /^,., A, pass an observer B 

 at different times, their distance apart as measured by B 

 is zero, while measured from ^^'s point of view it is not. 



The relation between the two sets of measurements 

 may be obtained by taking into account the fact that the 

 analytical conditions that an observer P should be able at 

 time /"i to observe an event which happened at another 

 point Q at time /.,, ought to be of the same form in the 

 two S3'stems of coordinates. 



If (.I'j, jj'i, ,c'i), (.ro,jJ'.,, r:^ are the coordinates of /^ and 

 Q, we have, in the first place, the necesssary conditions 



(A- - x^- + O'l -y^' + {z, - cj- = r(/, - fj^ />/,. 

 These conditions, combined with the kinematical 

 character of the motion of the B's relative to the A's, are 



establish a correspondence between the spheres connected with tlie diflerent 

 positions of B and ,-/ l^y associating together two spheres which toucli 

 internally, then since the two series of spheres are such that any sphere of a 

 series surrounds all the smaller ones of the series, it is clear that as the radius 

 of a. B sphere increases the radius of the corresponding A sphere also 

 increases. Fig. 4. This shows that B observes the events happening to .-1 in the 



Fig. 4. 



correct order. This is not necessarily the case if one or both of the observers 

 are moving with a velocity greater than that of light ; in fact under certain 

 conditions it would be possible for one observer to witness the other's 

 experiences in the reverse order. For instance in figure 3 if the four crosses 

 denote successive positions of B, it appears that the first and last positions 

 are seen by A at one instant and the two intermediate positions at another 

 instant. The two earlier positions of B are thus seen in the reverse order, 

 and the two later positions in the correct order. 



