Ice has formed on a shallow pond, and a steady state has been reached, with the air above the ice at $-5.0^{\circ} \mathrm{C}$ and the bottom of the pond at $4.0^{\circ} \mathrm{C}$. If the total depth of ice $+$ water is $1.4 \mathrm{~m}$, how thick is the ice? (Assume that the thermal conductivities of ice and water are $0.40$ and $0.12 \mathrm{cal} / \mathrm{m} \cdot \mathrm{C}^{\circ} \cdot \mathrm{s}$, respectively.)