THE RELATIVITY OF SPACE. iii 



no reason for arranging these points in one order 

 rather than another, nor, consequently, for attributing 

 three dimensions to space. 



But this is not the case. May I be permitted for 

 a moment to use the language of those who know 

 geometry already ? It is necessary that I should do 

 so, since it is the language best understood by those 

 to whom I wish to make myself clear. When I wish 

 to parry the blow, I try to reach the point whence 

 the blow comes, but it is enough if I come fairly near 

 it. Then the parry Bi may answer to Ai, and to 

 A2 if the point which corresponds with Bi is sufficiently 

 close both to that which corresponds with Ai and to 

 that which corresponds with A2. But it may happen 

 that the point which corresponds with another parry 

 B2 is near enough to the point corresponding with 

 A I, and not near enough to the point corresponding 

 with A2. And so the parry B2 may answer to Ai 

 and not be able to answer to A2. 



For those who do not yet know geometry, this may 

 be translated simply by a modification of the law 

 enunciated above. Then what happens is as follows. 

 Two parries, Bi and B2, are associated with one alarm 

 A I, and with a very great number of alarms that we 

 will place in the same category as Al, and make to 

 correspond with the same point in space. ]3ut we 

 may find alarms A2 which are associated with B2 and 

 not with Bi, but on the other hand are associated with 

 B3, which are not with Ar, and so on in succession, 

 so that we may write the sequence 



Bi, Ai,B2, A 2, B3, A3, B4, A4, 

 in which each term is associated with the succectiing 



