Electromagnetic Theory of Light, 93 



being that included between the secondary ray and the axis 

 of x, may be expressed by 



sin % =v/(/3 2 + 7 2 )^ (50) 



Our theory, as hitherto developed, shows that, whatever the 

 shape and size of the particles, there is no scattered light in 

 a direction parallel to the primary electric displacements, 

 except such as may depend upon squares and higher powers 

 of the difference of optical properties. In order to render an 

 account of the " residual blue " observed by Tyndall when 

 particles in their growth have reached a certain magnitude, it 

 is necessary to pursue the approximation. By (28), with Ap 

 neglected, we have 



Wt+ 



^ +K (£ + £'M AK -) 



and two similar equations in g 2 an( i h- On the supposition 

 that/ 1? g l} h x are known throughout the region of disturbance, 

 these equations may be solved in the same way as (29), (30), 

 and (31). For the sake of brevity we may confine ourselves 

 to the particular direction for which the terms of the first order 

 vanish. Thus at a sufficient distance / along the axis of z y 



A=-^^/A^e-^dacWd 7 , . . (52) 



92^-^^9A^- ] e-^d.cWd 7) . . (53) 



h 2 = (54) 



We have now to find the values of J\ and g x within the 

 region of disturbance, to which of course (35) &c. are not ap- 

 plicable. In the general solution (32), h is a function of x 

 only ; so that the elements of the integral vanish in the interior 

 of a homogeneous obstacle, and we have only to deal with the 

 surface. Integrating by parts across this surface, we find 



r being a function of a and * only through («— .?•). In like 



