466 Mr. E. Talbot Paris on the Polarization of 



supposed perfectly transparent. Let k be the coefficient of 

 " absorption " of the turbid medium, taking into account the 

 losses of light due to both the above causes ; and let k 1 be 

 the coefficient which represents the loss due to scattering 

 alone. Then (k — k') may be called the coefficient of "pure 

 absorption." Expressions for tc and k' have been found by 

 Gr. Mie*. If there are N particles per cubic centimetre, 

 these expressions, when translated into the present notation, 

 may be written 



*=the real part of ex N^T (2n + l)(M B + N n ), 

 K ' = N |^ T (2n + 1) (mod M n 2 + mod N n 2 ). 



If the particles are perfectly conducting, then since a 

 perfect conductor cannot absorb energy, the coefficient of 

 " pure absorption," K — K', must be zero, andM w and N n must 

 satisfy the equation 



mod M w 2 + modN n 2 = the real part of i(M» + N»). (14) 



And the same relation must be satisfied if the particles are 

 transparent. 



For example, when n=l, we find from Table I., 



mod Mj 2 + mod N x 2 = 0-33728, 

 and real part of i(M 1 + N 1 ) = 0'33728t. 

 The logarithmic values of 



<*, + 1 >y and (( 2n + l) r P„' _ (2B + 1)p | 



have been tabulated by Rayleigh for the values of jm given 



* Annalen der Physih, 4 Fol^e, Bd. xxv. p. 436 (1908). 

 t A quantity a 15 corresponding to N lt has been tabulated by Mie for 



2 3 

 the case of a perfect conductor. a x and N x are connected by N x = -— a lm 



The only point at which the values of a x overlap those of N x , given 

 above, is when 77 (or a in Mie's notation) =1. In this case the value 

 given for a Y is 0-638— tX 0-437, whence ^=0-425 -iX 0*291 instead of 

 0*455 — 1 X 0*292 as in Table I. It can, however, be asserted, without 

 recalculation, that the value of N x given in Table I. is correct, since it 

 satisfies equation (J 4). 



