8 C. L. SADRON 



oscillators. Each of these, when excited by the incident light, emits energy 

 in all directions. If the dimensions of the particle are sufficiently small 

 relatively to the wavelength X of the incident light — say less than about 

 X/20 — all the oscillators are practically in phase and all of them can be 

 considered as a unit. In that case, the intensity is scattered according to 

 Eq. (10) where P(0) = 1 whatever the value of may be. There is no 

 dissymmetry in the distribution of the scattered intensity of light. 



When the dimensions of the particle are larger than X/20, a detectable 

 difference of phase between the wavelets scattered by each oscillator occurs 

 and interferences take place, hence, a decrease of the intensity of the energy 

 scattered in each direction is taken care of by the function P(0), which 

 can be calculated without any difficulty when the distribution of the oscilla- 

 tors in the space is known. 



It is established in general that P(0) is a function of the product hL 

 where L is a length characteristic of the dimensions of the particle, and where 



4tt . 



/i = T sin 2 



X being the wavelength of the incident light in the solution; (X = X'/n if 

 X' is the wavelength in vacuum). 



Let us recall some expressions of P(0) for different types of particles. 



1. Sphere of radius L 



P(0) = \j^- (sin hL - hL cos hLU (13) 



2. Rigid rod of length 2L 



p(e) = hk Si(2hL) ~ (rw^J ( 14) 



where 



Si(2hL) = — dz 



.'o x 



3. Thin disc of diameter 2L 



w^I'-eH (is) 



where J\ is the first order Bessel function. 



4. Gaussian chain molecule. If we assume that the elementary oscilla- 

 tors succeed each other like the beads of a necklace, the distance between 

 two successive oscillators being able to vary around its mean square value 

 b 2 according to a Gaussian distribution, P(0) is given by 



w-mml?™*™- 1 ] (16) 



