The mixed boundary value problem of the potential inside a cylindrical conducting box of radiusaand height 2cin which is mounted coaxially and concentrically a thin flat charged conducting disk of radiusbis solved approximately. A formula for the coefficients in the Bessel function potential series is derived which is valid forc>¼aandb<¾a. The boundary conditions are met rigorously except that the disk is not quite flat. Figures show its deviation for twelve parameter values. A formula for narrow gaps is derived. Upper and lower limits for the capacitance for twelve parameter values are tabulated.