1. The quantitative dependence of transmitter release on external calcium concentration has been studied at the frog neuromuscular junction, using intracellular recording and taking the amplitude of the end-plate potential (e.p.p.) as an index of the number of packets released.2. The relation between [Ca] and the e.p.p. is highly non-linear. The initial part of this relation on double logarithmic co-ordinates gives a straight line with a slope of nearly four (mean 3.78 +/- 0.2 S.D. in 28 experiments). Addition of a constant amount of Mg reduces the e.p.p. without altering the slope of the log e.p.p./log Ca relation.3. The slope of this logarithmic relation diminishes as [Ca] is raised towards the normal level.4. The results are explained quantitatively on the hypothesis that Ca ions combine with a specific site X on the nerve terminal forming CaX, and that the number of packets of acetylcholine released is proportional to the fourth power of [CaX].5. The analysis suggests that a co-operative action of about four calcium ions is necessary for the release of each quantal packet of transmitter by the nerve impulse.