With the use of Wiener-Hopf method in collaboration with the initial value theorem for Laplace transformation, which is alternative way to the Buckleys first evaluation. it can be proved rigorously that the initial value problem for the radiant interchange in the semi-infinite cylindrical blackbody cavity, that is to say, the effective emissivity at its mouth is valued to be square root of the wall emissivity. Finally, a conjugate final value proWern is a little commented on.