Page:Memory (1913).djvu/85

 accordingly have been 2&frac12; per cent. In the period 24 to 48 hours it would have been 6.1 per cent; in the later 24 hours, then, about three times as much as in the earlier 15. Such a condition is not credible, since in the case of all the other numbers the decrease in the after-effect is greatly retarded by an increase in time. It does not become credible even under the plausible assumption that night and sleep, which form a greater part of the 15 hours but a smaller part of the 24, retard considerably the decrease in the after-effect.

Therefore it must be assumed that one of these three values is greatly affected by accidental influences. It would fit in well with the other observations to consider the number 33.7 per cent for the relearning after 24 hours as somewhat too large and to suppose that with a more accurate repetition of the tests it would be 1 to 2 units smaller. However, it is upheld by observations to be stated presently, so that I am in doubt about it.

3. Considering the special, individual, and uncertain character of our numerical results no one will desire at once to know what “law” is revealed in them. However, it is noteworthy that all the seven values which cover intervals of one third of an hour in length to 31 days in length (thus from singlefold to 2,000fold) may with tolerable approximation be put into a rather simple mathematical formula. I call:

t the time in minutes counting from one minute before the end of the learning,

b the saving of work evident in relearning, the equivalent of the amount remembered from the first learning expressed in percentage of the time necessary for this first learning,

c and k two constants to be defined presently

Then the following formula may be written:

$$\scriptstyle b=\tfrac{100\ k}{(\log t)^c+k}$$

By using common logarithms and with merely approximate estimates, not involving exact calculation by the method of least squares,

k=1.84

c=1.25