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 the former advance much faster and the latter noticeably more slowly. It cannot, therefore, be said in any exact sense of the words that the more frequently a series needs to be repeated to-day in order to be learned by heart the more repetitions will be saved in its reproduction after 24 hours. The relation in force seems to be much more complicated and its exact determination would require more extensive investigations.

The relation of repetitions for learning and for repeating English stanzas needs no amplification. These were learned by heart on the first day with less than half of the repetitions necessary for the shortest of the syllable series. They acquired thereby so great stability that for their reproduction on the next day proportionally no more work was needed than for the series of 24 syllables—i.e., about half of the first expenditure.

We will now take into consideration the results for the successive days taken as a whole. On each day the average number of repetitions necessary for the committing of a given series is less than on the preceding day. With the longer series, in whose case the first output of energy is great, the decrease in the amount of work each time necessary to reach the first possible reproduction is proportionally rapid. With the shorter series, where the first output is small, the decrease is proportionally slow. On this account the numbers of repetitions necessary for the different series approach each other more and more. With the series of 24 and 36 syllables this is apparent even from the second day; from the fourth day on, the numbers fall absolutely together. And by the fifth day they have approached very closely to the number of repetitions still necessary, in accordance with the slower decrease, for the learning of the 12-syllable series.

A simple conformity to law cannot be discovered in this successively decreasing necessity for work. The quotients of the necessary repetitions on two successive days approach unity. If the final repetition were not subtracted, as was done in the concluding table of Section 31, but were reckoned in, this approach would be somewhat faster. (In the case of the English stanzas it generally takes place only under these conditions.)