This study investigates the quantitative relationship between external calcium concentration and transmitter release at the frog neuromuscular junction. Using intracellular recording, the amplitude of the end-plate potential (e.p.p.) was used as an index of the number of packets released. The relationship between [Ca] and e.p.p. is highly non-linear, with a slope of nearly four on double logarithmic coordinates. Addition of Mg reduces the e.p.p. without altering the slope of the log e.p.p./log Ca relation. The slope of this logarithmic relation diminishes as [Ca] approaches normal levels. The results are explained by the hypothesis that Ca ions combine with a specific site X on the nerve terminal to form CaX, and that the number of acetylcholine packets released is proportional to the fourth power of [CaX]. The analysis suggests that about four calcium ions are involved in the release of each quantal packet. The study tested the hypothesis that a cooperative action of several Ca ions is necessary for transmitter release. The results suggest that the e.p.p. is proportional to the fourth power of [CaX], and that the slope of the log-log plot is approximately four. The parameters K1 and K2 were estimated, with K1 ranging from 0.5 to 2.0 mm and K2 from 1.95 to 4.8 mm. The results support the hypothesis of a cooperative action of four Ca ions in the release of each quantal packet. The study also discusses potential factors that may affect the results, such as changes in post-synaptic sensitivity, sodium-calcium antagonism, and divalent ion antagonism with curare. The findings suggest that the cooperative action of four Ca ions is necessary for the release of a unit of transmitter by the nerve impulse.This study investigates the quantitative relationship between external calcium concentration and transmitter release at the frog neuromuscular junction. Using intracellular recording, the amplitude of the end-plate potential (e.p.p.) was used as an index of the number of packets released. The relationship between [Ca] and e.p.p. is highly non-linear, with a slope of nearly four on double logarithmic coordinates. Addition of Mg reduces the e.p.p. without altering the slope of the log e.p.p./log Ca relation. The slope of this logarithmic relation diminishes as [Ca] approaches normal levels. The results are explained by the hypothesis that Ca ions combine with a specific site X on the nerve terminal to form CaX, and that the number of acetylcholine packets released is proportional to the fourth power of [CaX]. The analysis suggests that about four calcium ions are involved in the release of each quantal packet. The study tested the hypothesis that a cooperative action of several Ca ions is necessary for transmitter release. The results suggest that the e.p.p. is proportional to the fourth power of [CaX], and that the slope of the log-log plot is approximately four. The parameters K1 and K2 were estimated, with K1 ranging from 0.5 to 2.0 mm and K2 from 1.95 to 4.8 mm. The results support the hypothesis of a cooperative action of four Ca ions in the release of each quantal packet. The study also discusses potential factors that may affect the results, such as changes in post-synaptic sensitivity, sodium-calcium antagonism, and divalent ion antagonism with curare. The findings suggest that the cooperative action of four Ca ions is necessary for the release of a unit of transmitter by the nerve impulse.