The historical record of earthquakes can be used to estimate the probability that any particular locality will be shaken by earthquakes
 in the future. This approach assumes that the past record is representative of what will happen in the future, an assumption which, while not valid for long-term estimates, can be used to estimate return periods of the order of the length of the historical record or less. Intensity is chosen as the parameter which best describes the totality
 of earthquake shaking. Formulae relating intensity to the magnitude of 
the earthquake, its location and that of the observer are developed.
 The complex structure of New Zealand demands three attenuation patterns, each characteristic of a distinct source region. The historical record
 of earthquake occurrence is then examined, models fitted to the statistical population of intensities likely to have been observed at each of a grid of sites throughout the country, and the parameters of these models expressed in terms of the mean return periods for intensities equalling or exceeding MM VI, VII, VIII and IX.