The mathematical equivalence of Brownian motion and classical potential theory has great impulsed the s tudy of potentials of M a r k e r processes. The properties of potentials of Marker chains with discrete times were discussed in detail in [1]. In this paper, we first s tudy the relat ion between the potential operator of a b i r th and death process and the one of its embedded Marke r chains. So that we can study the propert ies of potentials of a b i r th and death process by s tudying the potentials o f its embedded Markov chain. Making use of the potent ial of the process we discuss ~he d is t r ibut ion of the last exit time of a b i r th and death process and its approximate proper ty . At last, we calculate the equi l ibr ium measure and the capacity of a transient set E, and point out the probabilistic approach to the equi l ibr ium measure, which is s t ronger than the wel l -known one in general case pointed out in [5]. The author is thankful to Professor W a n g Zikun and Vice-professor Li Zhizhan fo r their directions. Suppose that X ( t ) = { x ( ~ , ~) , t ~ 0 } is a b i r th and death process defined on some complete probabi l i ty space (/3, ~ B) and valued in the state space ~ = {0, 1, 9, ...}. ~ is the minimum state space. X ( t ) has a s tandard t ransi t ion mat r ix B( t ) (/~,l(t)), ~, ] E S . Its density matr ix is Q. And