Let $j:J\rightarrow{\bf P}^{1}$ be an elliptically fibred K3 surface with section and 24 singular fibres over $\Delta=\{p_{1},\ldots,p_{24}\}$ as above. Then there exists open sets $U_{1}^{i}\subseteq U_{2}^{i}\subseteq{\bf P}^{1}$, $i=1,\ldots,24$, each diffeomorphic to a disc, $U^{i}_{j}\cap\Delta=\{p_{i}\}$, positive constants $D_{1},D_{2},D_{3},D_{4},D_{5}$ and $\epsilon_{0}$ such that, for all $\epsilon<\epsilon_{0}$, for any elliptic fibration $f:X\rightarrow{\bf P}^{1}$ with Jacobian $j:J\rightarrow{\bf P}^{1}$ with holomorphic 2-form $\Omega$ with $[\mathop{\rm Re}\Omega]^{2}=[\mathop{\rm Re}\Omega_{J}]^{2}$, and for any Kähler class $[\omega_{\epsilon}]$ on $X$ with $[\omega_{\epsilon}].X_{b}=\epsilon$ and $[\omega_{\epsilon}]^{2}=[\mathop{\rm Re}\Omega]^{2}=[\mathop{\rm Im}\Omega]^{2}$, there exists a Kähler metric $\omega_{\epsilon}$ representing $[\omega_{\epsilon}]$ on $X$ with the following properties: