  We use a method recently suggested for evaluating the slope of the Isgur-Wise
function, at the zero-recoil point, on the lattice. The computations are
performed in the quenched approximation to lattice QCD, on a $24^3 \times 48$
lattice at $\beta=6.2$, using an $O(a)$-improved action for the fermions. We
have found unexpectedly large finite-volume effects in such a calculation.
These volume corrections turned out to be purely geometrical and independent of
the dynamics of the system. After the study of these effects on a smaller
volume and for different quark masses, we give approximate expressions that
account for them. Using these approximations we find $\xi^\prime(1)=-1.7 \pm
0.2$ and $\xi^\prime(1)=-1.4 +0.2-0.1$ for the slope of the Isgur-Wise
function, for two mesons composed of a heavy quark slightly heavier and
lighter, respectively, than the charm quark, and in both cases, a light
antiquark whose mass is about that of the strange quark.
