  We study the geometrical corrections to the simple Proximity Force
Approximation for the non-retarded Casimir force. We present analytical results
for the force between objects of various shapes and substrates, and between
pairs of objects. We compare the results to those from more exact numerical
calculations. We treat spheres, spheroids, cylinders, cubes, cones, and wings;
the analytical PFA results together with the geometrical correction factors are
summarized in a table.
