  The Casimir force on a $D$-dimensional sphere due to the confinement of a
massless scalar field is computed as a function of $D$, where $D$ is a
continuous variable that ranges from $-\infty$ to $\infty$. The dependence of
the force on the dimension is obtained using a simple and straightforward
Green's function technique. We find that the Casimir force vanishes as $D\to
+\infty$ ($D$ non-even integer) and also vanishes when $D$ is a negative even
integer. The force has simple poles at positive even integer values of $D$.
