An empirical method of estimating dense rock (D.R.E.) equivalent volumes erupted as airfall tephra, described in a companion paper in this volume, is elaborated, and its accuracy discussed. Estimates obtained from a single eruption can be classified as to whether they show positive, negative, or constant relative dispersion. For positively dispersed tephras (estimated volumes increasing with distance), this procedure improves the accuracy of the method. The technique is applied to selected andesitic tephras erupted from Egmont Volcano, New Zealand, during the last 28 000 years, which are found to range in volume from about 1.5 x 107 m3 up to about 2.4 x 108 m3 D.R.E. With a factor of about 16 between the smallest and largest volumes, this contrasts sharply with the rhyolite volcanoes in New Zealand, where the difference factor is usually of the order of 100. The largest tephra eruptions at Egmont are small compared to the largest debris avalanches, which have exceeded 1010 m3 (10 km3) in volume._x000D_
The magnitude versus frequency relationship, calculated using a maximum likelihood method, establishes the limits of eruption magnitude at Mt Egmont as 107 to 109 m3 D.R.E. For some volcanoes, the magnitude-frequency relationship changes with time, owing to clustering of eruptions, separated by long dormant intervals. Ngauruhoe Volcano, New Zealand, is an example. Within eruptive episodes, the mean interval between eruptions of >_ 105 m3 is about 0.9_x000D_
0.65 years. The mean interval between eruptive episodes in which >_ 106 m3 is erupted, including episodes in which this volume is erupted gradually, is about 25.8_x000D_
6.6 years, and the mean dormant interval between all episodes is about 5.2_x000D_
3.0 years. At present Ngauruhoe is in an unusually prolonged dormant period, 50% longer than any in the historical record, since 1839.