354 



Lord Rayleigh on Light dispersed from 



unpolarized light be incident, the scattered light is polarized in 

 the plane perpendicular to the length o£ the cylinder, and the 

 polarization is complete if the cylinder be small enough. 



It is now proposed to make application of these solutions 

 to meet the problem in two dimensions of the incidence of 

 plane waves upon a perfectly reflecting plane surface from 

 which rises an excrescence, also composed of perfectly reflect- 

 ing material, and having the form of a semi-cylinder whose 

 axis lies in the plane. We shall show that it is legitimate 

 to substitute the complete cylinder, provided that we suppose 

 incident upon it two sets of plane waves adjusted to one 

 another in a special manner. 



In the figure A B E D represents the actual reflector, 

 upon which are incident waves advancing along PO, a direction 



POD=P'OD = * ; QOD = 0. 



making an angle a with the surface OD. The secondary 

 disturbance is required (at a great distance (V) along OQ 

 inclined to OD at an angle <£. But for the present we 

 suppose the cylinder to be complete and the plane parts of the 

 reflector AB, CD to be abolished ; and in addition to the 

 waves advancing along PO we consider others of the same 

 quality advancing along a line P'O equally inclined to the 

 surface upon the other side. The angle 6 of previous for- 

 mulas is represented now by POQ, P'OQ whose values are 

 tf> — a and <£-f a. Thus we may write 



so that 



VLI ~[- LA,* X11UQ »* KJ 111U V (UlUVJ 



COS = COS (<£—#), cos #' = cos ((£ + «), 



cos + cos 6' = 2 cos a cos (j), 

 cos 6 — cos 6 r =2 sin a sin $. 



