470 Mr. E. Talbot Paris on the Polarization of 



at # = 85°. Between the neutral point and = the polari- 

 zation is " reversed/'' that is, the horizontal component I 2 is 

 greater than the vertical component I la When 77 = 1*75 the 

 neutral point is at about 110°, and the reversal has become 

 more pronounced. 



The curve for tj = 2 shows a remarkable change in the 

 character of the polarization. There are now two maxima, 

 two neutral points, and a strong reversal. 



If the dimensions of the sphere were large compared with 

 the wave-length ordinary reflexion would occur, and the 

 examination of the " scattered " light would consist in 

 examining light which had been reflected from the equatorial 

 region of the sphere. Since light could not be polarized 

 by reflexion from a perfectly conducting surface, we should 

 have when r)->oo , P = for all values of 0, provided the 

 incident beam is unpolarized. 



3. Numerical Results for Silver (A = 550 //,//,). 



In order to calculate the polarization of the light scattered 

 by silver it is necessary to make use of the general expres- 

 sions for M n and N n already quoted, giving rj' its appropriate 

 value. In the experiments that have been carried out the 

 silver particles were suspended in water and the observations 

 were made with nearly monochromatic light of wave-length 

 550 fjbfi. For the purposes of this calculation the value of 

 the complex refractive index of silver for A, = 550 fjufju given 

 by R. S. Minor* has been used, viz. m = 0'176-tx 3'305. 

 This must be divided by the refractive index of water, taken 

 to be §, giving v / = m' v ^(0-ld2 — cx2'4,79) v . 



The first step towards obtaining M„ and N TO is to calculate 

 the values of ^ n (V) from the series 



*"(V) = 1- f£rz + 2.4.2n + 3.2» + 5 " " < 15 > 



The convergence of this series is best when n is large, and 

 we could, as explained by Rayleigh, use (15) to obtain the 

 values of ty n (v') for moderate values of n, and then use the 

 sequence-equation 



^s^+*i(V)-(*+ 1 ){+w-i(V) -•+*£»')}, (16) 



to obtain the values of ^jr n (v') °£ lower order. The work 

 * Annalen der Physik, 4 Folge, Bd. x. p. 617 (1903). 



