Analysis of the Belinfante--Swihart theory of gravity

We show that the Belinfante-Swihart (BS) theory can be reformulated in a representation in which uncharged matter responds to gravity in the same way as in metric theories. The BS gravitationally modified Maxwell equations can also be put into metric form to first order in the deviations of the physical metric from flat space, but not to second order; consequently, the theory is nonmetric except in first order. We also show that the theory violates the high-precision E\"otv\"os-Dicke experiment, but cannot be ruled out by the gravitational precession of gyroscopes.