Let $j:J\rightarrow B$ be an elliptically fibred K3 surface with a section and singular fibres all of type $I_{1}$, and let $f_{i}:X_{i}\rightarrow B$ be a sequence of elliptically fibred K3 surfaces with jacobian $j$. Let $\omega_{i}$ correspond to a Ricci-flat Kähler metric on $X_{i}$ with $\omega_{i}^{2}$ independent of $\,i$, and with $\int_{f_{i}^{-1}(b)}\omega_{i}=\epsilon_{i}\rightarrow 0$ as $i\rightarrow\infty$. Then the sequence of Riemannian manifolds $(X_{i},\epsilon_{i}\omega_{i})$ converges in the Gromov–Hausdorff sense to $B$, the metric on $B$ being induced from the (singular) Riemannian metric given, in local coordinates, by $W_{0}^{-1}dy\otimes d\bar{y}$, with $W_{0}$ as defined in §4.