THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 273 



such cumulative scattering effects, we note first that it can be shown from 

 Maxwell's equations that: 



a=— '-, (29) 



477T 



where n and Wq are the refractive indices of the particles and of the medium, 



and V is the number of particles per unit volume. 



Since the value of v is rarely known, it is more convenient to express it in 



terms of weight concentration, molecular weight, and Avogadro's number 



Nc 

 V = — . Then, for unpolarized incident radiation: 



i2, = — (^ — — ^ j — (1 + cos^ 6), where (30) 



c = weight concentration of the scattering particles 

 M = mass of each particle in grams per mole 

 N = Avogadro's number 



The above expression gives Rq for a gas — a collection of scattering particles 

 in a vacuum. For this case. Equations 29 and 30 can be simplified, since 

 Wo = 1. The wavelength, A, of the radiation can be written as Ao, the wave- 

 length in vacuo. 



b. Small-Particle Scattering in Solutions. When light scattering occurs in a 

 solution, the equation just derived can no longer be conveniently applied. 

 To be sure, in an ideal solution the solute molecules are sufficiently widely 

 dispersed to allow Equation 30 to be applied to scattering from these par- 

 ticles alone. Thus, for an ideal solution the increment in scattering due to 

 the solute particles is directly calculable. But if the scattering from the 

 solvent or from the whole solution is considered, it is no longer correct to 

 make a scaler summation of the scattering effects of the individual mole- 

 cules. The scattering centers are now so close together that interference 

 effects become important, i.e., the wavelets scattered from one center may 

 destructively or constructively interfere with those from another. Actually, 

 destructive interference is overwhelmingly the more effective at measurable 

 angles of scattering, and a straightforward application of Equation 30 to 

 liquids would predict a scattering intensity many-fold greater than is 

 observed. It is possible to develop a theory of scattering for solutions from 

 detailed consideration of interference effects, but the calculations are 

 laborious. A more useful approach, due initially to Einstein (1910), is to 

 treat the scattering as a result of statistical fluctuations in the density of the 

 solvent, and in the concentration of the solute molecules, leading to local 

 fluctuations in the dielectric constant and hence in the refractive index 

 (Partington, 1953). Since we are here interested in the scattering due only to 



