  It has recently been proposed that the Universe might be accelerating as a
consequence of extra dimensions with time varying size. We show that although
these scenarios can lead to acceleration, they run into serious difficulty when
taking into account limits on the time variation of the four dimensional
Newton's constant. On the other hand, models of ``Cardassian'' expansion based
on extra dimensions which have been constructed so far violate the weak energy
condition for the bulk stress energy, for parameters that give an accelerating
universe.
