Ratio of Beat-interval Value in Seconds of Average Interval, to Group-interval. 5/12 3/12 2/12 1.000: 1.400 3.5 5.3 9.0 1.000: 1.000 4.0 5.4 9.6 1.000: 0.714 5.2 8.4 10.8 The quantitative relations presented by these figures are consistent throughout. For every rate of speed the average rhythmic group is smallest when the interval separating the successive groups is at its maximum; it is largest when this interval is at its minimum; while in each case a median value is presented by the relation of uniformity among the intervals. In the second as well as the first of the ratios included in the foregoing table the interval which separates adjacent groups is felt to be distinctly longer than that internal to the group; in the third the relative durations of the two intervals are those which support psychological uniformity. In the latter case, in consequence of the freer passage from group to group, the continuity of the rhythmical series is more perfectly preserved than in the former, and the integration of its elements into higher syntheses more extended. The extension of the numerical limits of the rhythm group in subjective rhythm which appear in consequence of progressive acceleration in the rate of succession is given for a series of six different values of the separating intervals in the following table, the figures of which represent the average for six observers: TABLE V. HIGHEST UNITS WHICH APPEAR. Value of interval in secs.: 12/12 7/12 5/12 3/12 2/12 1/12 No. of el's in rhythm group: 2.5 3.0 4.0 7.0 9.0 11.0 Average duration of group: 2.500 1.750 1.666 1.750 1.500 0.917 SIMPLE UNITS. No. of els. in simplest group: 2.5 2.3 2.9 3.7 4.7 5.0 Duration of simplest group: 2.50 1.34 1.21 0.92 0.78 0.41 The rate of increase here presented in the number of elements is not sufficiently rapid to counterbalance the acceleration of speed and maintain a constancy in the duration of the group. The greatest value of this period is coördinated with the slowest rate of succession, the lowest with the most rapid. As the speed increases, the duration of the rhythmic unit is shortened. Its average duration for all rates here included is 1.680 sec., or, without the first of the series (one-second intervals, at which only two of the observers received the impression of rhythm), 1.516 sec. These values are not for the simplest combinations, but for the highest synthetical unit which was immediately apprehended in the series of stimulations. This compounding becomes more pronounced as the rate of succession is accelerated, but even at intervals of 5/12 and 7/12 sec. it is the characteristic mode of apprehension.