CONTEMPORARY ADVANCES IN PHYSICS 285 



meets a wall with a very narrow opening. Does a narrow segment of 

 the ripple go clean through the opening and continue onward as a 

 sharply-ended crescent? Not so; a new circular or semicircular 

 ripple spreads out from the aperture as a new centre. 



This is called, in the science of light, a phenomenon of diffraction. 

 Actually, it is a phenomenon which reveals the law of wave-propaga- 

 tion — a law, which in the deceptively simple cases of spherical, 

 circular, or infinite plane waves is artfully concealed. When one sees 

 a circular ripple broadening over the surface of a lagoon, it seems as if 

 each arc of the circular crest were advancing independently and of its 

 own momentum; as if each segment of the circle at a given moment 

 were due entirely to the corresponding segment of the smaller circle 

 which existed a fraction of a second earlier. Nothing could be further 

 from the truth. At a given moment, a given segment of the circle 

 is due to the collaboration of all the segments of the earlier smaller 

 circle; and it will collaborate with all the segments of its own circle 

 to build the future yet larger one ; and if isolated from the rest of the 

 circumference, it would build a new family of circular ripples all by 

 itself. Somewhat as the primitive animals which can regenerate their 

 amputated parts, a wave-system seems to possess in each of its elements 

 something of the power to build itself anew. 



Such is the nature of ripples on water and sound-waves in air. 

 As for a general definition of wave-motion, perhaps there is no better 

 way of making one than to accept this manner of propagation as the 

 distinctive mark. It may seem strange, however, that there should 

 be any question about definition. Does not everyone know what a 

 wave is? and is not the difference between a wave-theory and a 

 corpuscle-theory made instantly clear by their names? 



Well ! it would not be hard to compile a series of paradoxical state- 

 ments, by which to show that our immediate off-hand notion of a 

 "wave" is not by any means sufificiently precise to serve as basis for 

 an elaborate physical theory. Even in the ancient and familiar 

 instance of circular ripples on water, even for students acquainted 

 with the concepts of wave-length and wave-speed, there are possi- 

 bilities of confusion. It is not expedient to define the wave-length as 

 the distance from one crest to the next, for this is inconstant. It is 

 not expedient to define the wave-speed as the speed with which a 

 crest advances, for this may depend upon the form of the wave. 

 It is injudicious to think exclusively about the profile of the water- 

 surface as a sequence of visible elevations and depressions gliding 

 steadily onward without change of shape; for any part of the profile 

 may alter itself incessantly as it advances, departing more and more 



