288 BELL SYSTEM TECHNICAL JOURNAL 



Let the same question be put in another way. Be it supposed that 

 we are required to predict whether or not there will be a particle in the 

 place P at the moment t; and that we are offered our choice of data 

 concerning the places of the particles at any prior moment. Let us 

 choose at random some point P' due south of P, distant from it by r' 

 units of length. Then there is only one piece of information for which 

 we have to ask: is there a sandgrain passing through P' at the moment 

 (/ — r' jc), earlier than / by r'jc units of time? Any other information 

 would be not only superfluous, but useless. Had we chosen some point 

 lying south of P at a distance r" , the condition prevailing there at the 

 moment (/ — r' jc) would have had no bearing upon the problem ; but 

 the condition there at the moment (/ — r"lc) would have been all- 

 powerful. Had we chosen some point not lying south of P, nothing 

 happening there at any time would have had any bearing upon the 

 question to be answered. 



In fine: at any moment t' there is a corresponding point P' lying 

 south of P, which holds the destiny of the point P at the moment t. 

 That which is predestined to befall in P at ^ is at every prior instant 

 concentrated, so to speak, at a particular point of space. As time 

 draws on towards t, this point moves on toward P, travelling always 

 along the north-south line — travelling always, let us say, along a certain 

 ray which at the proper moment carries it right into P. 



All these remarks may seem too evident and trivial to be worth the 

 making; yet they deserve attention, for it is here that the contrast 

 lies between motion of particles and motion of waves, between un- 

 dulatory theories and corpuscular. If the region around the point P 

 is traversed not by corpuscles but by waves, it is not correct to say that 

 the condition at the point P at the moment t is determined by the con- 

 dition in some other point ait some prior moment. Even if the waves 

 appear to be travelling northward with the constant speed c, it is not 

 right to say that the state of affairs prevailing in P at / is controlled 

 entirely by the state of affairs prevailing at the moment (/ — r/c) at 

 the point r units southward from P. The destiny of P at / is not 

 travelling towards it concentrated into a point moving along a ray. 

 Under some circumstances it appears to be right to say so ; but this is 

 only a semblance, as experiments in other conditions will clearly prove. 



Suppose for instance that one is confronted with the task of sheltering 

 the point P, first against corpuscles and then against waves, which 

 are advancing from the south. It seems natural to put some obstacle 

 athwart that particular north-south line which traverses P; for ex- 

 ample, to place a solid disc so that its axis lies upon that line. If the 

 disc can arrest all the particles which fly towards it, and cannot deflect 



