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 on the third day if no repetitions had occurred on the second, and we should then have in the difference, x — 75, the separate effect of the 109 repetitions actually given. Since the forgetting increased somewhat from the second to the third day, x would be somewhat greater than 109. In the same way, for the determination of the effect of the 75 repetitions of the third day, we should need to learn in some way or other with how many repetitions (y), the series would have been learned by heart on the fourth day which, on the first day, required 158; and on the second, 109. The difference, y — 56, would then give the measure of that effect; and so on. For the ascertainment of x, the results of Chapter VII give a certain basis. There the result was that, in the case of 13-syllable series, the amount forgotten at the end of 24 hours was to that forgotten at the end of 2x24 hours as 66 to 72. But the employment of this relation, itself insecure, would be justifiable only in case of the 12-syllable series, and would accordingly not help in the determination of y, etc. One could at the best suppose that the resulting quotients would approximate yet more closely to unity.

Accordingly I renounce these uncertain assumptions, and content myself with presenting the relations of the successive repetitions to the successive savings by showing that the presupposed pure effect of the separate repetitions would be represented by somewhat greater and presumably less divergent numbers.

Although the course of these figures, which are, as has been said, inexact as to their absolute values, is tolerably regular in the case of the 24-syllable series only, its general character agrees very well with what would be expected from the results of Chapter IV. The effect of the repetitions is at first