  Newtonian adiabatics is the consistent truncation of the adiabatic
approximation to second order in small velocities. To be complete it must unify
two hitherto disjoint intellectual streams in the study of adiabatic motion.
The newer stream focuses on Berry's induced vector potential, or geometric
magnetism, and Provost and Vallee's induced scalar potential, reflecting
geometry in Hilbert space. The older stream focuses on Inglis' induced inertia,
influencing the geometry of adiabatic-parameter space. Starting with the
Hamiltonian of the newer stream, unification is simple: A naive or primitive
inertia, whose inverse appears in two terms of that Hamiltonian, is replaced by
the convention-independent sum of primitive and induced inertia tensors.
