The quest continues for cases of interest where the differential
equations for the Polya process are amenable to an asymptotic solution.
We introduce a tenable class of urns that generalize the classical Ehrenfest model, 
and analyze the Ehrenfest process obtained by embedding the discrete evolution in real time.
We show that lurking under the Ehrenfest process is a limiting binomial distribution, 
whose number of trials is an integer invariant property of the process.