The idea of mass being equivalent to [L³/t²] comes straight from Maxwell; Miles just takes it and runs with it as mechanics. Maxwell's derivation is as follows:

                "For the acceleration due to the attraction of a mass m at a distance r is by the Newtonian Law m/r². Suppose this attraction to act for a very small time t on a body originally at rest, and to cause it to describe a space s, then by the formula of Galileo, s = (1/2)ft² = (1/2)(m/r²)t²; whence m = 2(r²s/t²). Since r and s are both lengths, and t is a time, this equation cannot be true unless the dimensions of m are [L³T^-2]. The same can be shewn [sic] form any astronomical equation in which the mass of the body appears in some but not all of the terms."