  Crofton's formula of integral geometry evaluates the total motion invariant
measure of the set of $k$-dimensional planes having nonempty intersection with
a given convex body. This note deals with motion invariant measures on sets of
pairs of hyperplanes or lines meeting a convex body. Particularly simple
results are obtained if, and only if, the given body is of constant width in
the first case, and of constant brightness in the second case.
