$4-58$ A bronze ${}_B=16\mathrm{.}9\frac{{10}^{-6}}{}C$ sleeve with an inside diameter of $99\mathrm{.}8$ mm is to be placed over a solid steel ${}_s=11\mathrm{.}9\frac{{10}^{-6}}{}C$ cylinder, which has an outside diameter of $100$ mm $.$ If the temperatures of the cylinder and sleeve remain equal, how much must the temperature be increased in order for the bronze sleeve to slip over the steel cylinder?