Page:Memory (1913).djvu/94

 Nevertheless the course of the numbers cannot be described by a simple formula.

Rather is this the case if one takes into consideration, not the gradually decreasing necessity for work, but the just as gradually decreasing saving of work.

Of these numerical sequences two—namely, the second and fourth rows—form with great approximation a decreasing geometrical progression with the exponent 0.5. Very slight changes in the numbers would be sufficient fully to bring out this conformity. By slight changes, the first row might also be transformed into a geometrical progression with the exponent 0.6. On the contrary, a large error in the results of investigation would need to be assumed in order to get out of Row 3 any such geometric progression (whose exponent would then be about one third).

If not for all, yet for most, of the results found, the relation can be formulated as follows: If series of nonsense syllables or verses of a poem are on several successive days each time learned by heart to the point of the first possible reproduction, the successive differences in the repetitions necessary for this form approximately a decreasing geometrical progression. In the case of syllable-series of different lengths, the exponents of these progressions were smaller for the longer series and larger for the shorter ones.

Although the tests just described were individually not more protracted than the others, yet relatively they required many days, and the average values were consequently derived from a rather small number of observations. So here, even more than elsewhere, I am unable to affirm that the simple conformity to law approximately realised in the results so far obtained would