  Let X be a compact oriented Riemannian manifold and let $\phi:X\to S^1$ be a
circle-valued Morse function. Under some mild assumptions on $\phi$, we prove a
formula relating:
  (a) the number of closed orbits of the gradient flow of $\phi$ of any given
degree;
  (b) the torsion of a ``Morse complex'', which counts gradient flow lines
between critical points of $\phi$; and
  (c) a kind of Reidemeister torsion of X determined by the homotopy class of
$\phi$.
  When $\dim(X)=3$ and $b_1(X)>0$, we state a conjecture analogous to Taubes's
``SW=Gromov'' theorem, and we use it to deduce (for closed manifolds, modulo
signs) the Meng-Taubes relation between the Seiberg- Witten invariants and the
``Milnor torsion'' of X.
