  The gravitational Lagrangian based on special relativity and the assumption
of a fourth rank tensor interaction, derived by Kennedy (1972), is used to
check Mach's principle in a homogeneous isotropic expanding universe. The
Lagrangian is found to be consistent with Mach's principle when the density is
the critical density and inertial mass is suitably renormalized. The Kennedy
approach only gives the Lagrangian to first order in the gravitational coupling
constant. By invoking the equivalence principle higher order corrections are
found which renormalize the gravitational masses to the same values as the
inertial masses. It is not the same as the correction derived from general
relativity by Einstein-Infeld-Hoffmann, but otherwise the Lagrangians agree.
