reflected from some Collodion Films. 127 



The suffixes and 1 refer respectively to the primary and 

 scattered waves. The direction of propagation being 

 supposed parallel to x and that of vibration parallel to z, we 

 have f =g = 0, and 



]i Q = e int e ikx , (1) 



e int k e i n g the time factor for simple progressive waves. For 

 the scattered vibration at the point («, [3, 7) distant r from 

 the element of volume (dv dy dz) of the obstacle, we have 



wher« 



/i.*.*i= £51 {«*£/. -0 2 +£ 2 )}, ■• • (2> 



P=-^jJJv-'^%<fe, • • . (3) 



and the integration is over the volume of the obstacle. If 

 the obstacle is very small in comparison with the wave- 

 length (X) of the vibrations, h e~ ikr may be removed from 

 under the integral sign and 



• P= g , .... (4, 



T denoting the volume of the obstacle. In the direction of 

 primary vibration « = /3 = 0, so that in this direction there is 

 no scattered vibration. It will be understood that our sup- 

 positions correspond to primary light already polarized. 

 If, as usually in experiment, the primary light is unpolarized, 

 the light scattered perpendicularly to the incident rays is 

 plane polarized and can be extinguished with a nicoi. 



The formation of colour depends upon other factors. 

 When the obstacle is very small, P is constant, and the 

 secondary vibration varies as P, so that the intensity is as 

 the inverse fourth power of the wave-length, as in the theory 

 of the blue of the sky. In this case it is immaterial whether 

 the obstacles are of the same size or not, but for larger sizes 

 when the colour depends mainly upon the variation of P, 

 strongly marked effects require an approximate uniformity. 

 If the distribution be at random, the colours due to a large 

 number may then be inferred from the calculation relating 

 to a single obstacle; but if the distribution were in regular 

 patterns, complications would ensue from the necessity for 

 taking phases into account, as in the theory of gratings. 

 For the present purpose it suffices to consider a random 

 distribution, although we may suppose that the centres, or 

 more generally corresponding points, of the obstacles lie in 

 a plane perpendicular to the direction of the primary light. 



