386 MR. J. C. MAXWELL GARNETT ON 



PART I. 



2. Consider the incidence of light of wave-length X on a sphere ot metal of 

 radius a. Suppose the constants of the metal relative to the surrounding medium, 

 which we may first suppose to be aether, are n, the coefficient of refraction, and K, 

 the coefficient of absorption. Let us write 



N = w(l IK) .......... (1), 



where, as usual, t denotes v 1. 



We shall use the following notation to denote the electric vector : 



Incident light ....... E {X = exp {ip (t z/c)} , Y = 0, Z = 0}. 



Transmitted -f reflected light . . Ej {X 1; Y 1; Z,}. 



Here p = 'iTrc/X, c being the velocity of light in vacuo. 



HERTZ (' Ausbreitung der electrischeii Kraft,' Leipzig, 1892, p. 150) has shown that 

 the electric and magnetic forces at any point (x, y, z) due to an oscillating electric 

 doublet of moment Ae' 3 " along the axis of x are given by 



' E = v - (v-n, o, o) ........ (2), 



-, -, 35 



c\ ozct oy tit] 



where 



II = A/r.exp [<-p(t r/c)}, 



for these expressions satisfy MAXWELL'S equations 



,/p 7TT 



f = c curl H, . - = - c curl E and div E = div H = 0, 



dt dt 



and when r is very small compared with the wave-length (X = 2-irc/p) of the emitted 

 waves the expression for E reduces to 



E = V (3n/3x), 



which is at any time the electric force which would be electrostatically due to the 

 doublet if its moment remained constant and equal to its value at that time. 



Lord RAYLEIGH ('Phil. Mag.,' XLIV., pp. 28-52, 1897, and 'Collected Papers,' 

 vol. 4, p. 321) has extended this theorem to the case of a very small sphere. In the 

 region for which the distance, r, from the centre of a small sphere of radius a excited 



