Mach's principle and the rest mass of the graviton

The question of the graviton rest mass is briefly discussed and then it is shown that the Sciama-Dicke formulation of Mach's principle admits, in the linear approximation, the calculation of the graviton rest mass. One finds that the value of the graviton rest mass depends on the cosmological model adopted, the mean matter density in the universe, the speed of light, and the constant of gravitation. The value obtained for an infinite, stationary universe is 7.6 × ${10}^{-67\mathrm{}}$ g. The value for evolutionary cosmological models is found to depend critically on the mass and "radius" of the universe, both null and non-null values occurring only for certain values of these parameters. Problems that arise as a consequence of the linear approximation are pointed out.