A stochastic model for the temporal evolution of the contribution to cloud cover by fair weather cumuli is presented. A differential equation is obtained for a probability generating function. The general solution of the differential equation is obtained and this is used to obtain the probability generating function for the number of clouds at time t given the number at time O. It is noted that the real interest is in the joint probability generating function for the numbers of clouds at times t sub 1,...,t sub n given that at time O there are no clouds. The methods of obtaining this joint probability generating function is exemplified by the solution for the case n2. A Mathematical Appendix at the end of this report carries out certain of the derivations in greater detail. The definition and some properties of probability generating functions are also included there.