A topological approach to the determination of macroscopic field vectors

Passage from the microscopic to the macroscopic description of the electromagnetic field is achieved with the use of Maxwell equations in integral form. Certain integrals in these equations depend on the topological relations between the integration domains and the molecule volumes. This dependence gives rise to two methods of field-vector averaging, and leads to the doubling of the number of field vectors for the macrodescription. The physical meanings of the vectors D and H and of the equations into which they enter are elucidated more clearly and more fully in such an exposition.