﻿Regular Reflexion of Light by Gas Molecules. 627 



immediate object of inquiry ; what has to be determined is 

 the relation between the energy o£ the plane waves pro- 

 pagated in the direction (say) of x decreasing and the energy 

 diffusely scattered. To find the plane-wave energy, imagine 

 a sufficiently large (acoustical) lens of focal length / placed 

 in front of the square b X b ; an " image " will be formed at 

 the principal focus, and will take the form of a diffraction 

 pattern whose scale is determined by fX/b ; X being the 

 wave-length concerned, and equal to 2ttJv . It will be con- 

 venient to suppose / so large that the lens, having degenerated 

 into a sensibly flat plate, may be removed, and so need 

 trouble us no further. 



5. No matter how sparsely the vibrators are spread in the 

 2/z-plane, we can postpone the discussion of more delicate 

 points by taking the square b x b so large that it can be 

 divided up into numerous elements, each containing many 

 vibrators ; / will then, perhaps, be enormous, but that does 

 not matter : we can apply the methods familiar in physical 

 optics to determine the distribution of disturbance in the 

 diffraction pattern. In any case it conduces to simplicity 

 that b : X should be large. In the plane x= — /', taking y ! , z' 

 as current coordinates, ?/ — 0, z' = Q is the position of the 

 geometrical "image," and at that point the amplitude * due 

 to air vibrators, all acting in complete agreement of phase, is 

 ab 2 a ; where a is the amplitude due to a single vibrator 

 at distance /. The distribution of amplitude (g) over the 

 diffraction pattern is thus known to be 



, 9 sin a sin 8 



where a — nrbx'IXf\ /3-~7rby'/Xf. 



6. As an arbitrary measure of the energy of the "image " 

 we may take the surface-integral of g 2 over the diffraction 

 pattern ; that is, in effect (since dx' =~Xfdct/7rb, dy' ' —\fd/3/7rl>) , 



a 2 b 2 a 2 X*f r f" sin 2 asin 2 /3^ JO 



a 2 b 2 a 2 \ 2 f C C sin « sin 



/100 / "OO 



l/ _ 00 */ — 00 



= a 2 b 2 a 2 X 2 / 2 . 



d*d/3 



7. The energy diffusely scattered has 'next to be con- 

 sidered. With the origin as centre let a sphere of radius/' 



* Amplitude of pressure-variation for example. 



2S2 



