  The bulk of solar coronal radiative loss consists of soft X-ray emission from
quasi-static loops at the cores of Active Regions. In order to develop
diagnostics for determining the heating mechanism of these loops from
observations by coronal imaging instruments, I have developed analytical
solutions for the temperature structure and scaling laws of loop strands for a
wide range of heating functions, including footpoint heating, uniform heating,
and heating concentrated at the loop apex. Key results are that the temperature
profile depends only weakly on the heating distribution -- not sufficiently to
be of significant diagnostic value -- and that the scaling laws survive for
this wide range of heating distributions, but with the constant of
proportionality in the RTV scaling law ($P_{0}L \thicksim T_{max}^3$) depending
on the specific heating function. Furthermore, quasi-static analytical
solutions do not exist for an excessive concentration of heating near the loop
footpoints, a result in agreement with recent numerical simulations. It is
demonstrated that a generalization of the solutions to the case of a strand
with a variable diameter leads to only relatively small correction factors in
the scaling laws and temperature profiles for constant diameter loop strands. A
quintet of leading theoretical coronal heating mechanisms is shown to be
captured by the formalism of this paper, and the differences in thermal
structure between them may be verified through observations. Preliminary
results from full numerical simulations demonstrate that, despite the
simplifying assumptions, the analytical solutions from this paper are stable
and accurate.
