CONTEMPORARY ADVANCES IN PHYSICS 311 



passage I called the "influence" or the "wavelet" which spreads out 

 from the element-of-wave-front in all directions. 



Examining it factor by factor, one sees: 



{a) that the amplitude of the wavelet varies inversely as the distance 

 r from the starting-point, which seems natural; 



{h) that the wavelet is not isotropic, its amplitude diminishing ac- 

 cording to the law (1 + cos d) from a maximum value in the forward 

 to zero in the rearward direction. This is commonly stated as the 

 reason why waves can be propagated in one direction only, not neces- 

 sarily both forward and backward at the same time ; 



(c) that for waves of the same amplitude and different wave-lengths 

 the amplitudes of the wavelets stand in the inverse ratio of the wave- 

 lengths — the shorter the waves, the more powerfully they are dif- 

 fracted ; 



{d) that the wavelet from any point is constantly one quarter of a 

 cycle in advance of the primary wave, varying as — sin nt whereas the 

 wave varies as cos nt. 



The advance-in-phase and the factor m in the amplitude enter, it is 

 clear, because the "wavelet" represents the second term in (75) — 

 the term which involves the slope dsjdx of the wave-function, not the 

 wave-function itself. One might say that the cyclic variation of 

 dsjdx Stirs up a relatively far-reaching commotion in the medium, while 

 the disturbance which the cyclic variation of s excites is rapidly attenu- 

 ated and mostly negligible. Formerly the factor m and the advance- 

 in-phase seemed unnatural and very strange; for they antedated the 

 theorem of Kirchhoff by sixty years, having been forced upon Fresnel 

 before 1820 — and this invites an allusion to history. 



Though it is in connection with Huyghens' principle that one 

 commonly hears of wavelets, that principle itself amounts to a denial 

 of nearly every quality which we associate with the ideas of wavelet 

 or wave. Not only are the "wavelets" of Huyghens' construction 

 quite devoid of anything undulatory or periodic; the construction 

 itself is based on the assumption that there is only one point on each 

 where the amplitude is appreciable — the point on the prolongation of 

 the normal from the primary wave-front (corresponding in my notation 

 to 6 = 0). But to say that a disturbance is transmitted by wavelets 

 such as these is to say that it is transmitted in concentrated form along 

 lines or rays — which is the same thing as saying that it travels like 

 corpuscles. Huyghens' principle in fact leads straight to the doctrine 

 of the rectilinear propagation of light, and fails either to predict or to 

 explain the phenomena which require a wave-theory.* The accredited 



* I am not prepared to say that this is true of the appUcations to crystal optics. 



