90 Lord Rayleigh on the 



from (40), as the special forms of (35), (37), (38) applicable 

 to this case, 



/i= g^-„-)[ K AK-^~^-^], . . (41) 



9v 



^^ Mnt.—Ter\ TT A TT-1 "7 



e i(nt-kr) 



[KAK-5], (42) 



X 2 7 



l h = g^-*)[_KAK-'^ti +^-*i\. (43) 



If A/u, = 0, as we shall henceforward suppose, f:g = a:fi, 

 showing that the electrical displacement is in the plane con- 

 taining the secondary ray and the direction of primary elec- 

 trical displacement (z), and 



so that the intensity is proportional to the square of the sine 

 of the angle between the secondary ray and the direction of 

 the primary electrical displacement. The blue colour of the 

 light scattered from small particles is explained by the occur- 

 rence of \ 2 in the denominators of the expressions for f ly g 1} h^ 

 but for further particulars on this subject the reader must be 

 referred to my previous papers. 



Equations (35), (36), &c. are rigorously applicable, however 

 large the region of disturbance, if the square of AK may 

 really be neglected. From them we see that, under the cir- 

 cumstances in question, each element of a homogeneous 

 obstacle acts independently as a centre of disturbance, and 

 that the aggregate effect in any direction depends upon the 

 phases of the elementary secondary disturbances as affected by 

 the situation of the element along the paths of the primary 

 and of the secondary light. In fact, 



P = AK-y w * J ^ e ik *e- ikr dx dy dz. 



If 6, (j> be the angles defining (in the usual notation) the direc- 

 tion of the secondary ray, and r correspond to the origin of 

 coordinates, we have 



p __ ^ |£- l e i(nt-Jcr ) £££ e ik(x+,v sin 6 cos $+y sin 6 sin $ +z cos 8) ^ ^ y ^ .- (^£\ 



and the question now before us for consideration is the value 

 of the integral in (44) as dependent upon the size of the 

 obstacle and the direction of the secondary ray. It is evident 

 that the formulas are applicable only when the whole retarda- 

 tion of the primary light in traversing the obstacle can be 

 neglected in comparison with the wave-length ; but if this 



