The Physical Significance of Birkhoff's Gravitational Equations

Birkhoff's gravitational equations are put in terms of $\mathrm{dt}$ in place of the local time $\mathrm{ds}$ used by him. The transformed equations show that Lorentzian mass has been used, and to the Newtonian attractive force is added a force normal to the direction of motion, $\frac{v^2}{c^2}$ times the component of the gravitational force normal to the motion.