﻿of Light by Metallic Particles. 455 



Note on the preceding Paper by Prof. J. J. Thomson. 



I made, about two years ago, some rough experiments on 

 the polarization of light scattered by small particles of gold, 

 the results of which were in agreement with those of Professor 

 Threlfall. I regarded these experiments as confirming tho 

 results of Maxwell and Wien, that the resistance of metals to 

 the very rapidly alternating currents which constitute light 

 is much greater than to steady currents. 



It is, moreover, difficult to make these experiments so as to 

 be a fair test of the theory, as it is only when the size of the 

 particles is within narrow limits that the theory would be 

 applicable, even supposing the resistance to be as low as for 

 steady currents. To scatter the light the diameters of the 

 particles must be small compared with the wave-length of 

 light, while the theory given in my ' Researches on Electricity 

 and Magnetism ' requires that the depth to which the currents 

 produced by the light penetrate the particle should be a small 

 fraction of the radius of the particle. Now at a depth d below 

 the surface of the sphere the intensity of the induced current 

 varies as e~ kd , where &={27r/z,/?/<r}2, where p is the magnetic 

 permeability, a the specific resistance of the metal, and 2ir/p 

 the time of oscillation of the incident electrical vibration. 

 Thus the currents at a depth 1/k below the surface will only 

 be 1/e of their value at the surface ; we may therefore take 1/k 

 as the measure of the thickness of the film filled by the currents. 

 For gold cr = 2100 for steady currents. p=l, and for the D line 

 p = 2tt x 5-097 x 10 u ; thus l/ib=3'2 x 10" 7 . The wave-length 

 of the D line is 5*89 x 10" 5 , about 170 times 1/k. Thus, for 

 the theory to be applicable, the diameter of the particles must 

 be small compared with X and large compared with 1/k. As 

 X is only 170 times 1/k this makes the range for the dia- 

 meter very small. A more satisfactory test of the theory 

 could be made with longer wave-lengths and larger particles ; 

 for the thickness to which the currents descend varies as the 

 square root of the wave-length, so that the ratio of the wave- 

 length to the thickness of the current-film increases as the 

 wave-length increases. 



