Specific Intensity Equation of Radiative Transfer

The coelficients of are momenls of the size distribution function known as cumulants. In practice, only the first two cumuJants can be accurately determined from the experimental data  

Here the averaging is weighted by d as in (5.38). For a free molecule aerosol we have 

D — df (Chapter 2), so D is proportional to the fourth moment of the particle size distribution. This heavily weights the upper end of the distribution function. If the form of the distribution function is known, the cumulants can be used to evaluate the parameters of the distribution, For example, if the size distribution is self-preserving (Chapter 7), any moment can be used to estimate the complete distribution. 

Let JF be the total quantity of energy passing in time dr through the area da inside cone dQ in the wavelength interval X to X + dX. For small do and da), the energy passing through do inside dQ will be proportional to do du . 

specific intensity of radiation or simply the intensity, /x, is defined by the relation 

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