  The approach to model composite interstellar dust grains, using the exact
solution to the light scattering problem for multi-layered spheres as suggested
by Voshchinnikov & Mathis (1999), is further developed. Heterogeneous scatteres
are represented by particles with very large number of shells, each including a
homogeneous layer per material considered (amorphous carbon, astronomical
silicate and vacuum).
  The applicability of the effective medium theory (EMT) mostly utilized
earlier to approximate inhomogeneous interstellar grains is examined on the
basis of the new model.
  It is shown that the EMT rules generally have an accuracy of several percent
in the whole range of particle sizes provided the porosity does not exceed
about 50%.
  For larger porosity, the EMT rules give wrong results.
  Using the model, we reanalyze various basic features of cosmic dust --
interstellar extinction, scattered radiation, infrared radiation, radiation
pressure, etc. As an example of the potential of the model, it is applied to
reproduce the extinction curves in the directions to $\zeta$ Oph and $\sigma$
Sco using subsolar cosmic abundances. We also conclude that metallic iron even
in negligible amount ($\la 1$ % by the volume fraction) is unlikely to form a
layer on or inside a grain because of peculiar absorption of radiation by such
particles.
