1. SeeR. Carnap:Philosophical Foundations of Physics (New York and London, 1966), Chap. 5.
2. A more general equation to describe a nonstatic gravitational field appears to be the equation ▿2 φ − (1/c 2)(∂2 φ/∂t 2) = 4πGϱ. If we admit that φ is a scalar function in a Lorentz transformation and ρ the density of mass at rest, this equation is invariant in a Lorentz transformation.
3. SeeA. Einstein:On the influence of gravitation on the propagation of light, inThe Principle of Relativity (New York, N. Y., 1952).
4. See, for example,L. I. Schiff:Am. J. Phys.,28, 340 (1960). The deduction of the angle of deflection previously shown is similar to the one shown bySchiff; however, that paper has several debatable aspects; for example, there appear magnitudes likeΓ N (except for a change in nomenclature) of dubious meaning, since dΓ N represents a local measurement.
5. It is possible, although it is not necessary for our purpose, to postulate an exact expression forF N . An example is the expression $$F_N = - \nabla _N \varphi m_0^2 /m_N - m_N V_N (V_N \cdot \nabla _N \varphi )/C^2 $$ , it is consistent with eq. (49), it is invariant in a Lorentz’s transformation (φ is a static potential measured by the Galilean observer) and it has Newton’s force as a first approximation.