The metric space $(Z_{\sigma,\tau}(\lambda^{-1}R),\lambda^{-2}g_{\lambda})$, where $g_{\lambda}$ is the Riemannian (orbifold) metric from the Gibbons-Hawking ansatz, converges in the Gromov-Hausdorff sense to $(R,g^{ij}_{\infty})$, with the limiting metric $g^{ij}_{\infty}=V^{ij}ds_{i}ds_{j}+W^{pq}dt_{p}dt_{q}$.