A detailed study of the arrival directions of primary particles of mean energy 2 × 1017 eV recorded by the Haverah Park Stage 1 (500-m) EAS array is reported. After rejecting time intervals randomly to equalize the sidereal running time of the array, upwards of 30 000 showers were available for analysis. In two energy intervals with mean energies about 1017 eV and 5 × 1017 eV significantly lower upper limits have been set on primary particle anistropy, and for all showers the amplitude of the first harmonic in right ascension is 0.6 ± 1.1% with a maximum at about 210°.An azimuthal asymmetry in detected showers (mainly arising from a 2° tilt of the array plane) limits the precision with which variations in declinations could be detected, and no analysis in galactic coordinates has been attempted. However, a plot in squares 10° RA by 10° declination reveals no deviations from isotropy within declination bands, and the overall distribution of intensity fluctuations is consistent with statistical expectation.Some general remarks are made on isotropy measurements.