  We analyse a generalisation of general relativity that incorporates a cosmic
time-variation of the velocity of light in vacuum, $c,$ and the Newtonian
gravitation 'constant', $G,$ proposed by Albrecht and Maguejo. We find exact
solutions for Friedmann universes and determine the rate of variation of $c$
required to solve the flatness and classical cosmological constant problems.
Potential problems with this approach to the resolution of the flatness and
classical cosmological constant problems are highlighted. Reformulations are
suggested which give the theory a more desirable limit as a theory of varying
$G$ in the limit of constant $c$ and its relationship to theories with varying
electron charge and constant $c$ are discussed.
