  The new scale-covariant formulation of the Dirac's Large Number Hypothesis
(LNH) is proposed. The basic equations of LNH are formulated in the
scale-covariant and "G-invariant" (invariant on the transformation law for G)
form. On the basis of the Scale Covariant Theory of Gravitation and Dirac's LNH
the cosmological model is constructed that gives as result the closed static
Einstein's Universe in the gravitational system of units (g.s.u.) and the
closed expanding Universe in the atomic system of units (a.s.u.). The simple
dynamical model of atomic clock is proposed that leads to the same connection
between the a.s.u. and the g.s.u. as the LNH and allows to specify the
parameters of the model. The question about the equivalence of inertial and
gravitational masses in the arbitrary system of units is ivestigated. It is
deduced that the equivalence of inertial and gravitational masses in the
arbitrary system of units takes place only for the unique transformation law
for G even if the equivalence of two kinds of mass in the g.s.u. is assumed. It
is shown that the model predicts the conservation of the black-body spectrum of
the microvave background radiation independently of choice of the
transformation law for G. It is argued that the some paradoxes of the standard
cosmology can be overcomed in the given model without the supposition about the
existence in the past of a phase of inflationary expansion.
