6 



BIOLOGICAL EFFECTS OF RADIATION 



So long as the corpuscle is too far from the boundary surface to 

 feel any force from the water, it moves in a straight line with unchanging 

 momentum; for the forces exerted on it by the air, being equally applied 

 in all directions, balance one another out. In the region near the 

 boundary this remains the truth for the components of force parallel 



to the surface; but the components along the normal, 

 applied respectively from the direction toward the 

 air and the direction toward the water, need not be 

 perfectly equal. After the corpuscle has gone through 

 the transition region and reached the depths of the 

 water, it continues in a straight line with a 

 momentum of which the component parallel to the 

 boundary is still the same as it was in the air, while 

 the normal component is changed. Denote by pt 

 and pn these two components of the original 

 momentiun of the particle through the air; by p the 

 magnitude of their resultant which is the magnitude 

 of the original momentum; by p[, p'„, and p' the 

 corresponding quantities for the final flight of the 

 corpuscle through the water. From Fig. 2 we see: 



sin d' = 



V' 



U) 



Putting this side by side with equation (5), we notice that the two equa- 

 tions may be rendered compatible with one another, that the two pictures 

 may be interchanged at will, provided that we assume that the momentum 

 of the corpuscles varies inversely as the speed of the wave fronts. 



Nothing has yet been said about wave-length in the course of this 

 argument, and for a very good reason: in Huygens' construction from 

 which equation (5) was derived, there is no allusion whatever to periodic 

 vibration or undulatory motion or any sort of rhythm. Indeed when 

 Huygens drew the diagram of which Fig. 1 is essentially a remote copy, 

 he meant the line corresponding to A A' to represent what we should now 

 call a single "pulse," and while he said that one should suppose many 

 such pulses emerging one after another from a candle flame, he empha- 

 sized that one should not ( !) suppose them following one another at equal 

 intervals. In using the word "wave front" I have been implying a train 

 of regular waves, of which the line A A' — or rather, the plane of which it 

 is the trace — is a locus of constant phase. This implication was foreign 



