  We develop a theory to account for the cosmic ray spectrum between 1 GeV and
10^4 GeV following the earlier papers of this series. We use the basic concept
that the cosmic ray particles are accelerated in a supernova shock that travels
through the interstellar medium. Physically important ingredients besides the
presence of a strong shock are diffusion, drifts, convection, adiabatic
cooling, the injection history, and the topology of the magnetic field, here
assumed for simplicity to be homogeneous in the interstellar medium. The result
is a spectrum, which for strong shocks in a gas with adiabatic index 5/3 yields
a spectrum of E^-2.42. Interstellar turbulence with a Kolmogorov spectrum then
leads by leakage from the galactic disk to a spectrum which is E^-2.75, as
observed. We argue that the ratio of cosmic ray electrons to protons is
determined by the amount of expansion which takes place from the cessation of
electron injection to the break-up of the shell by cooling instabilities. Since
the highest particle energy reached derives from geometrical arguments, it
depends on the charge of the nucleus and so higher Z elements are predicted to
reach higher energies.
