  In this note we consider compactifications of ${\cal M}$-theory on
$Spin(7)$-holonomy manifolds to three-dimensional Minkowski space. In these
compactifications a warp factor is included. The conditions for unbroken N=1
supersymmetry give rise to determining equations for the 4-form field strength
in terms of the warp factor and the self-dual 4-form of the internal manifold.
