obtained directly from the physical process, shows that the functions rt and d are nonnegative for x,y > 0. It follows from standard arguments that as A 0 these functions approach the solutions of (2). 4. Solution of Oriqinal Problem.-The solution of the problem posed in (2.1) can be carried out in two ways, once the functions r(y,x) and t(y,x) have been determined. In the first place, since u(x) = r(y,x), a determination of r(y,x) reduces the problem in (2.1) to an initial value process. Secondly, as indicated in reference 1, the internal fluxes, u(z) and v(z) can be expressed in terms of the reflection and transmission functions. Computational results will be presented subsequently.