  The evaluation of the determinant of the Laplacian defined on two dimensional
regions of various shapes is an essential ingredient in calculating the
scattering amplitudes of strings. In lightcone parameterization the regions are
rectangular in shape with several slits of different length and location cut
parallel to the $\tau$ axis of the rectangle. This paper offers a compendium of
applications of the methods of Kac and McKean and Singer to the calculation of
such worldsheet determinants. Particular attention is paid to the effect of
corners on the determinants. The effect of corners joining edges with like
boundary conditions is implicit in Kac's results. We discuss the generalization
to a corner joining a Dirichlet edge to a Neumann edge, and apply it to a
scattering amplitude involving D-branes.
