[en] The radiation transfer of the vector electromagnetic field was first formulated by Chandrasekhar while deriving the polarization characteristics of a sunlit sky. There are two subtle problems underlying this treatment. The first concerns the crucial identification of a Stokes parameter with the specific intensity of radiation. While both depend on position in 3-D space, the latter has, intrinsic to it, an additional angular dependence defining the flow of the radiation field. How can this inadequacy be remedied without damaging the results obtained heretofore from Chandrasekhar's formalism. The second problem arises from the fact that the radiative transfer equation describes the transport of an incoherent radiation field through space. This, however, seems to contradict the results of the Van Cittert-Zernike-Wolf theorem which implies that an incoherent field develops coherence as it passes through free space implying, of course, that the radiative transfer equation must involve not incoherent but partially coherent fields. The vector transfer equation of the direct beam (Beer's law) is derived from first principles. The analysis of this equation provides a satisfactory resolution of these two problems. The result also shows that the Beer's law will have to be modified to a matrix law to accommodate systems that are not spherically symmetric. 13 references