Light scattered hy Spherical Metal Particles. 461 



27T 



In these equations k= — , X being the wave-length of the 



A. 



incident light, //,= cos#, and P n , or P»(/a), is a zonal 

 harmonic o£ degree n, whose axis is the axis of z. The 

 quantities M. n and N„ depend on the boundary conditions to 

 be satisfied at the surface of the sphere. Expressions similar 

 to (1) and (2) have been used by Gr. Mie* to calculate the 

 intensity and polarization of the light scattered by small 

 gold particles. It may be noted that Mie's solution of the 

 problem of the scattering of light by a sphere is identical 

 with Love's, though obtained independently and expressed 

 somewhat differently. 

 The quantities 



(4 ! ^/* P «'-( 2 "+ 1 ) P ») and t 1 ** Pn' 



are functions of n and /j, only, and depend on the direction 

 of observation. Their logarithmic values for various values 

 of fi have been tabulated by Rayleighj. M» and N„ are 

 functions of the size (relatively to the wave-length) and 

 optical properties of the spherical obstacle. Mod Y and 



ry -W7- 



Mod- ^- give the amplitudes of the two components, 



and their squares give the intensities. The complete ex- 

 pression for N n is \ : 



K is the dielectric constant of the material composing the 

 sphere, that of the surrounding medium being supposed 

 equal to unity. The expression for M„ is obtained by writing 

 /a, the magnetic permeability, instead of K. In optical 

 problems we may take pas 1, when M„ becomes 



- E »- l( " )+, fe?y ,E ^ 



* Annalen der Phi/sik, 4 Folge, Bd. xxv. p. 427 (1908). 

 t Proc. Roy. Soc. A. vol. lxxxiv. p. 41 (1910). 



t See equation (28) of Love, Proc. Math. Soc. Lond. vol. xxx. p. 314 

 (1899) ; and Rayleigh, Proc. Roy. Soc, A, vol. lxxxiv. p. 31 (1910). 



