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1. The mean quantal content of the frog end-plate potential was examined under conditions that reduced evoked transmitter release to very low values.

2. When the calcium concentration of the Ringer is reduced below 10^-4 M a deviation occurs from the fourth power dependence of the mean quantal content (m) on the calcium concentration such that more quanta are released than is expected from the behaviour of m at higher calcium concentrations.

3. At 10^-5 M this extra quantal release is more than two orders of magnitude greater than that predicted by the fourth power relationship.

4. The calcium dependence of very low values of m was studied in low calcium Ringer in which the calcium was buffered by either citrate or EDTA. It was found that in the fourth power dependence of m on the external calcium concentration changes rather suddenly to an approximately linear dependence.

5. The inclusion of small concentrations of cobalt in the Ringer was found to reduce m to very low values even in the presence of millimolar concentrations of calcium.

6. The fourth power dependence of m on the external calcium concentration at high values of m was unaffected by the presence of cobalt. At low quantal contents the transition to a linear dependence on external calcium was again seen, but was shifted to calcium concentrations that did not require buffering.

7. The fourth power to linear transition is discussed in terms of its relevance to the relationship between m and the m.e.p.p. frequency.