  We construct spherical, hydrostatic models of dense molecular cores and Bok
globules consisting of two distinct, spatially separate gas components: a
central, isothermal region surrounded by a negative-index, polytropic envelope.
The clouds are supported against their own self-gravity by a combination of
thermal, mean magnetic, and turbulent wave pressure. The latter two are
included by allowing for locally adiabatic, non-isentropic pressure components.
Such models are meant to represent, in a schematic manner, the velocity and
density structure of cores and globules, as inferred from molecular line and
dust continuum observations. We show by explicit construction that it is
possible to have dense cores comparable to the Jeans mass embedded in stable
clouds of much larger mass. In a subsequent paper, we show that composite
polytropes on the verge of gravitational instability can reproduce the observed
velocity and density structure of cores and globules under a variety of
physical conditions.
