  This is the second installment of a two-part paper on developments in quantum
dispersion theory leading up to Heisenberg's "Umdeutung" paper. In telling this
story, we have taken a paper by John H. Van Vleck as our main guide. In this
second part we present the detailed derivations on which our narrative in the
first part rests. The central result that we shall derive is the Kramers
dispersion formula, which played a key role in the thinking that led to
Heisenberg's "Umdeutung" paper. Closely following Van Vleck's pre-Umdeutung
approach, we derive classical and construct quantum formulae for the
dispersion, emission, and absorption of radiation both for the special case of
a charged harmonic oscillator (sec. 5) and for arbitrary non-degenerate
multiply-periodic systems (sec. 6). In sec. 7, we rederive the same results
using modern quantum mechanics. In sec. 8 we bring together the main
conclusions of our study.
