  We discuss aspects of gravitational modifications of Schrodinger dynamics
proposed by Diosi and Penrose. We consider first the Diosi-Penrose criterion
for gravitationally induced state vector reduction, and compute the reduction
time expected for a superposition of a uniform density cubical solid in two
positions displaced by a small fraction of the cube side. We show that the
predicted effect is much smaller than would be observable in the proposed
Marshall et al. mirror experiment. We then consider the ``Schrodinger -Newton''
equation for an N-particle system. We show that in the independent particle
approximation, it differs from the usual Hartree approximation applied to the
Newtonian potential by self-interaction terms, which do not have a consistent
Born rule interpretation. This raises doubts about the use of the
Schrodinger-Newton equation to calculate gravitational effects on molecular
interference experiments. When the effects of Newtonian gravitation on
molecular diffraction are calculated using the standard many-body Schrodinger
equation, no washing out of the interference pattern is predicted.
