  We give elementary proofs of two `folklore' assertions about near-symplectic
forms on four-manifolds: that any such form can be modified, by an evolutionary
process taking place within a finite set of balls, so as to have a prescribed
positive number of zero-circles; and that, on a closed manifold, the number of
zero-circles for which the splitting of the normal bundle is trivial has the
same parity as 1+b_1+b_2^+.
