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Changes in the direction of the Earth's magnetic field at a given site are produced in part by wobble of the main geomagnetic dipole, in part by fluctuations in the intensity and direction of the non-dipole field, and in part by changes in the intensity of the main dipole field. These three processes combine to produce an angular variance that is strongly latitude dependent. A method is presented for isolating the contribution due to variation with latitude of the average intensity of the non-dipole field.

Variations in the lengths of geomagnetic polarity, intervals are analyzed by means of a probability model based on the theory of Bernouli trials. Polarity reversals are assumed to occur as the result of the interaction between steady oscillations of the geomagnetic dipole and secular variations of the nondipole field. The particular cycle on which a polarity inversion occurs is determined by the magnitude of the nondipole field, which is assumed to vary randomly and independently of dipole variations. The reversal properties of the geomagnetic dynamo are characterized by the single parameter p, the probability that a polarity inversion will occur during one cycle of change in the geomagnetic dipole moment. From an analysis of polarity changes during the past 10 m.y., the value of p is estimated to be 0.05. During the Permian period, it was at least two orders of magnitude smaller. The analysis suggests that within the past 10 m.y. there have occurred hitherto undiscovered short geomagnetic polarity events with durations shorter than 0.05 m.y.

Confidence limits are calculated for the precision parameter K used in the analysis of palaeomagnetic data and for the angular standard deviation 0. A set of tables for 95 per cent and 99 per cent confidence limits is presented.