Cosine double angle

It is noticed that the correction for the solvent birefringence (A n0) occurs only in eq. (3.44b) and not in eq. (3.44a). As was already pointed out in Chapter 2, the extinction angle of a low molecular weight liquid is, practically under all conditions, equal to 45 degrees. From this it is clear that the cosine of the doubled extinction angle of the solvent vanishes, whereas its sine becomes equal to unity. This corresponds to the fact that the solvent yields no contribution to the normal stress effect [cf. eq. (1.6)]. 

The simplest example in which the singular solutions of (4) form a continuous spectrum, but can be easily overlooked, concerns one of the simplest problems of transport theory the diffusion of monoenergetic neutrons in plane geometry. In this case, t, as well as y, z, cease to be variables because the flux is assumed to be independent of them. Furthermore, since the flux is zero except for a single value of E, this is not a significant variable either. Finally, the double variable 2 can be replaced by the direction cosine /jl = 0.x of the velocity with respect to the x axis because the flux does not depend on the azimuthal angle either. If the further simplification is made that the scattering is spherically symmetric and if the total cross section is measured in appropriate units, the transport equation assumes the form... 

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