1. A study has been made of the effects of changing [Ca]O and [Mg]O on the binomial statistic parameters p and n that control the average quantal content (m) of the excitatory post-synaptic potential (e.p.s.p.) due to acetylcholine release at preganglionic nerve terminals. 2. When [Ca]O was increased in the range from 0-2 to 0-5 mM, p increased as the first power of [Ca]O whereas n increased as the 0-5 power of [Ca]O; when [Mg]O was increased in the range from 5 to 200 mM, p decreased as the first power of [Mg]O whereas n decreased as the 0-5 power of [Mg]O. 3. The increase in quantal release of a test impulse following a conditioning impulse was primarily due to an increase in n; the increase in quantal content of successive e.p.s.p.s in a short train was due to an increase in n and p, and the increase in n was quantitatively described in terms of the accumulation of a Ca-receptor complex in the nerve terminal. 4. The decrease in quantal content of successive e.p.s.p.s during long trains of impulses over several minutes was primarily due to a decrease in n. These results are discussed in terms of an hypothesis concerning the physical basis of n and p in the release process.