CONTEMPORARY ADVANCES IN PHYSICS 287 



fascinating details of the landscape are distorted when seen from 

 above, and finally they are lost in the haze of distance. It grows 

 more difficult to lead others to the heights, and sometimes even the 

 explorer cannot retrace his path and return to the firm ground of 

 experience whence he departed. Yet repeatedly in the evolution of 

 physics it happens that a theory, already grown so abstract that it 

 seems almost completely severed from reality, suddenly makes new 

 contact with the world of phenomena by a prediction so novel and 

 daring that except for the far preliminary excursion it would probably 

 never have been conceived; as for instance the existence of quanta, 

 the "Einstein shift" of the lines in the spectrum of the sun, the 

 diffraction of electrons by crystals. Remembrance of such episodes 

 as these is an encouragement, when the path seems devious and 

 steep. 



Propagation of Waves 



The laws of the propagation of waves — the so-called "laws of diffrac- 

 tion" — are the most important topic with which we have to deal; 

 for they involve the very nature and definition of wave-motion, and in 

 the end the distinction between a corpuscular and an undulatory 

 theory of matter may rest upon these. Let us attend first of all to the 

 making of this distinction. 



Imagine, then, a multitude of particles — bullets, or atoms, or sand- 

 grains — all rushing along through space in the same direction with the 

 same speed, say northward with the speed c. Suppose that the loca- 

 tion of each is stated for a certain moment of time, say /q. The question 

 to be asked is a very simple one, of the yes-or-no variety. At an 

 arbitrarily-chosen point P, at an arbitrarily-chosen moment /, will 

 there be a grain of sand or will there not? 



It is easy to see what determines the answer. If at the point P at 

 the moment / there is a grain of sand, it must have spent the time- 

 interval extending from to to t in travelling northward along the straight 

 south-to-north path which ends at P, and therefore commences at a 

 point Po due south of P and distant from it by c(t — to) units of length. 

 If therefore at the moment to there is a grain of sand at Po, the answer 

 to the question is yes. Otherwise it is no. No other knowledge is 

 required, or even relevant. It is not necessary to know the location 

 of any of the particles which are not upon the north-south line travers- 

 ing P. It is not even necessary to know the location of any particle 

 which is upon that line, provided that at the instant to it is surely 

 somewhere else than at Pq. The state of affairs in P at ^ is controlled 

 by the state of affairs in Po at to, and by nothing else whatever. 



