436 Prof. Rowland on Spherical Waves of Light 



produces the same effect at all points of space as the original 

 wave. Should the wave be spherical and of short radius, the 

 normal component will enter and complicate the result, though 

 the solution can be obtained, but would evidently be compli- 

 cated. But if the wave have a radius of an inch or even less, 

 the displacement is practically perpendicular to the radius, 

 and the solution here given will apply. 



Let I, m, n be the direction-cosines of the normal to such a 

 wave, and l f , m', and n f the direction-cosines of the electric 

 displacement which is represented by 



J € -I&(R-V*x 



Then the values of the arbitrary displacement and magnetic 

 induction to substitute in the general equations of p. 426 to 

 produce such a wave will evidently be 



where V\ ml 1 ', n u are the direction-cosines of the magnetic 

 induction. We also have 



IV + mm! + nn f = 0, 



IV +mm /f +nri l = 0, 



Z'Z" + mW + n'w"=q, 



Returning again to the equations of p. 433, we see that the 

 polarized light is diffracted equally in all directions from a 

 very small orifice and independent of its plane of polarization. 

 Furthermore, the plane of polarization at any point is found 

 by drawing a sphere through that point with its centre at the 

 orifice, and then drawing a plane through the given point and 

 the point where the incident light first cuts the sphere, and 

 cutting the plane of polarization of the incident light in a line 

 perpendicular to the incident ray. The intersection of the 

 plane and sphere then give the direction of the polarization. 



It is seen that in both these particulars my solution differs 

 from that of Prof. Stokes, and the construction is the same 

 whether one takes the electric or magnetic quantities as the 

 direction of polarization. 



The system of planes for the electric and magnetic quan- 

 tities form a system of orthogonal circles on the sphere. 



