  In this paper we perform a detailed investigation of the Dirichlet
eight-brane of the Type IIA string theory, when the effects of gravity are
included. In particular, consider what happens when one allows the ten-form
field strength $F_{10}$ to vary discontinuously across the worldvolume of the
brane. Since the ten-form is constant on each side of the brane ($d*F_{10} =
0$), a variation in the bulk term $\int F_{10}*F_{10}$ gives rise to a net
pressure acting on the surface of the brane. This means that the infinite
`planar' eight-brane is no longer a static configuration with these boundary
conditions. Instead, a static configuration is found only when the brane
`compactifies' to the topology of an eight-sphere, $S^8$. These spherical
eight-branes are thus bubbles which form boundaries between different phases of
the massive Type IIA supergravity theory. While these bubbles are generically
unstable and will want to expand (or contract), we show that in certain cases
there is a critical radius, $r_c$, at which the (inward) tension of the brane
is exactly counterbalanced by the (outward) force exerted by the pressure
terms. Intuitively, these `compactified' branes are just spherical bubbles
where the effective cosmological constant jumps by a discrete amount as you
cross a brane worldsheet. We argue that these branes will be unstable to
various semi-classical decay processes. We discuss the implications of such
processes for the open strings which have endpoints on the eight-brane.
