In an investigation of the influence of the relative positions of Venus and the Earth upon sun-spots, ten successive series of 584 days each were used and the mean spottedness of the Sun for each day of one synodic revolution of Venus was determined. It was then noticed that there were frequent recurrences of maximum and minimum sun-spot activity at periods approximating to one synodic solar rotation period in the sunspot zone. Since the days which were combined to form each of the mean days were separated from one another by periods of 584 days, these sun-spot maxima and minima could not be due to the persistence of individual sun-spots. These facts suggested that if a sufficiently long series of daily sun-spot numbers were arranged in proper solar rotation periods their average should give a maximum and a minimum sun-spot activity for one solar rotation. To test this inference 182 successive periods of 27.3 days each, beginning April 25, 1917, and ending December 1, 1930 (making 4969 successive days), were added and their average taken. The result of the average sun-spottedness for 27 days of one synodic solar rotation is shown by the continuous line of the lower curve in Figure 1. The mean sun-spot relative numbers are shown by the ordinates and the rotation days by the abscissas. A rotation period of 27.3 days was taken because it is given by both Carrington and Spoerer as the mean rotation period of the sun-spot zone of the Sun. It was noticed that in the later rotation periods the maximum sun-spot frequency occurred on an earlier rotation day than in the beginning periods. This suggested that the rotation period adopted was too long and that the true period must be nearer 27 . 25 than 27 . 3 days. Accordingly, two series of 80 solar rotations of 27.25 days each, separated by an interval of 872 days, this being 32 periods