IN a previous communication1, an asymptotic theory was outlined for the probabilistic behaviour of a finite dam or reservoir subject to random input and output. A further problem raised by Herman Rubin—that of the amount of water lost by overflow—may be solved by similar methods. In the case of normal diffusion which is treated here, the distribution of the overflow may be found by evaluating its moment generating function. There is an alternative and more general method, which is useful when only the expected overflow is required. The alternative, suggested by R. Morton, is discussed in the succeeding communication.