Let the periodic spectrum of the Hill’s operator ${{ - d^2 } / {dx^2 + p(x)}}$ have n nonzero gaps. We give explicit formulas for the isospectral manifold of operators ${{ - d^2 } / {dx^2 + q(x)}}$ having the same spectrum. This allows us to realize the isospectral manifold explicitly as a torus. What makes this possible is an explicit solution of the flow \[ \left. {\frac{d}{{dt}}q = \frac{d}{{dx}}\frac{\partial }{{\partial q(x)}}\Delta (\lambda ,q)} \right|_{\lambda = \mu _n (q)} \] introduced by McKean and Trubowitz, where $\Delta $ is the discriminant and $\mu _n (q)$ is the nth Dirichlet eigenvalue. The general case (in which there are an infinite number of nonzero gaps) is handled by a limiting process.