Abstract
An analysis is presented of any Galilean-invariant classical Hamiltonian theory in which the particles do not interact directly with each other, but interact directly with a number of other dynamical variables. These other dynamical variables are collectively called "the medium." It is shown that only 12 of the variables which describe the medium are crucial for the Galilean invariance of the theory. The generators of Galilean transformations are constructed in their most general form. An example is given. Galilean-invariant approximations to Galilean-invariant theories are discussed.
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