Light scattered by Spherical Meted Particles. 463 



those obtained by putting in the appropriate values of the 

 optical constants of silver, except in the case when the 

 spheres are very small compared with the wave-length. In 

 this case, as is well known, the perfectly conducting particles 

 should give rise to plane-polarized light in a direction 

 making 120° with the incident beam, while the fall theory, 

 taking account of the particular optical properties of the 

 metal composing the particles, shows that there should be 

 plane-polarized light in a direction making 00° with the 

 incident beam, a result which is confirmed by experiment. 

 In fact, the polarization of the light scattered by small 

 imperfectly conducting particles is the same as if the par- 

 ticles were non-conducting. Indeed, it would be impossible 

 to tell by observation on the polarization of the scattered 

 light alone whether we were dealing with particles of a 

 heavily absorbing metallic substance like silver, or of an 

 almost transparent substance like sulphur. The intensity of 

 the scattered light is, however, very different, the metal 

 exhibiting " optical resonance," a phenomenon which has 

 been fully discussed by Mie. 



When suitable alterations in the notation have been made, 

 the expressions given by Sir Joseph Thomson for the electric 

 forces in the scattered wave correspond exactly with those 

 given by Professor Love, the sole difference being in the 

 quantities written in place of M„ and N„. We find that the 

 equivalents of M„ and N„ in Thomson's calculation for the 

 perfect conductor are : 



M - 1 S "^ fK\ 



In this, as before, k= y , and a is the radius of the sphere. 



AISO « f v n(\\l\ l ?A\\r) 



\V di] 1 rj v y 



and v s (Id \' € -"J 



It is convenient to have M n and N„ expressed in terms of 

 the functions i/r n and E», equations (3) and (4), so that the 



