Let $j:J\rightarrow{\bf P}^{1}$ be an elliptic K3 surface with a section, and let $f_{l}:X_{l}\rightarrow{\bf P}^{1}$ be a sequence of elliptic K3 surfaces with jacobian $j:J\rightarrow{\bf P}^{1}$. Let $\omega_{l}$ be a Ricci-flat Kähler metric on $X_{l}$ with $Vol(X_{l})$ independent of $l$. Let $\epsilon_{l}=Area_{\omega_{l}}(f_{l}^{-1}(y))$ for any point $y\in{\bf P}^{1}$, and suppose $\epsilon_{l}\rightarrow 0$ as $l\rightarrow\infty$. Describe the behaviour of the metric $\omega_{l}$ as $l\rightarrow\infty$.