Electromagnetic Theory of Light. 

 or if ; as before, T be the volume of the sphere, 



/•= 



ttT 



x 2 P { 



k 2 p 2 

 ^-*p)(KAK"0 2 -^ 



95 



(60) 



92=0. 



Comparing (60) and (41), we see that the amplitude of the 

 light scattered along z is not only of higher order in AK,but is 

 also of the order k 2 c 2 in comparison with that scattered in other 

 directions. The incident light being white, the intensity of 

 the component colours scattered along z varies as the inverse 

 8th power of the wave-length, so that the resultant light is a 

 rich blue. 



There is another point of importance to be noticed. Although 

 when the terms of the second order are included the scattered 

 light does not vanish along the axis of z, the peculiarity is not 

 lost, but merely transferred to another direction. Putting 

 together the terms of the first and second orders, we see that 

 the scattered light will vanish in a direction in the plane of xz y 

 inclined to z (towards a) at a small angle 6, such that 



6'=-KAK- 1 S- 2 = ^S 2 . . . . (61) 



15 



K 15* 



In the usual case of particles optically denser than the sur- 

 rounding medium, AK is positive, from which we gather that 

 the direction in which the scattered light vanishes to the second 

 order of approximation is 

 inclined backwards, so that 

 the angle through which 

 the light may be supposed 

 to be bent by the action 

 of the particle is obtuse. 



The fact that, when the 

 primary light is polarized, 

 there is in one perpendi- 

 cular direction no light 

 scattered by very small 

 particles, was stated by 

 Stokes*; but it is, I believe, to Tyndall that we owe the obser- 

 vation that with somewhat larger particles the direction of 

 minimum illumination becomes oblique. I do not find, how- 

 ever, any record of the direction of the obliquity (that is, of 

 the sign of the small angle 6), and have therefore made a few 

 observations for my own satisfaction. 



In a darkened room a beam of sunlight was concentrated 



* Phil. Trans. 1852, § 183. 



