  Observed violations of the $c$-axis optical sum rule can give important
information on deviations from in-plane Fermi liquid behavior and on the nature
of interlayer coupling between adjacent copper oxide planes. Application of a
magnetic field perpendicular to these planes is another way to probe in-plane
dynamics. We find that the optical sum rule is considerably modified in the
presence of the $c$-axis magnetic field. Interlayer correlation of pancake
vortices is involved in the sum rule modification; however, details of the
vortex distribution in the plane are less important.
