  Taking a hint from Dirac's large number hypothesis, we note the existence of
cosmologically combined conservation laws that work to cosmologically long
time. We thus modify Einstein's theory of general relativity with fixed
gravitation constant $G$ to a theory for varying $G$, with a tensor term
arising naturally from the derivatives of $G$ in place of the cosmological
constant term usually introduced \textit{ad hoc}. The modified theory, when
applied to cosmology, is consistent with Dirac's large number hypothesis, and
gives a theoretical Hubble's relation not contradicting the observational data.
For phenomena of duration and distance short compared with that of the
universe, our theory reduces to Einstein's theory with $G$ being constant
outside the gravitating matter, and thus also passes the crucial tests of
Einstein's theory.
