  A general solution of the Jeans equations for oblate scale-free logarithmic
potentials is given. This provides all possible second velocity moments that
can hold up a stellar population of flattened scale-free density against the
gravity field. A two-parameter subset of second moments for the self-consistent
density of Binney's model is examined in detail. These solutions have the
desirable property that the observable dispersions in the radial and proper
motions can be given explicitly. In the spherical limit, the potential of these
models reduces to that of the singular isothermal sphere. The Jeans solutions
for scale-free densities of arbitrary flattening that can correspond to
physical three-integral distribution functions are identified. The problem of
finding distribution functions associated with the Jeans solutions in flattened
scale-free logarithmic potentials is then investigated for Binney's model. An
approximate solution of the collisionless Boltzmann equation is found which
provides a third (partial) integral of good accuracy for thin and near-thin
tube orbits. It is a modification of the total angular momentum. This enables
the construction of many simple three-integral distribution functions. The
kinematic properties of these approximate DFs are shown to agree with a subset
of the Jeans solutions --- which are thereby confirmed as good approximations
to physical solutions.
