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 may be considered to have disappeared or practically so. The decrease in mental vigour in one group will be practically the same as that in another. The positive and negative fluctuations of attention which under like conditions occur during a quarter or half hour are approximately the same from day to day. All that is necessary to ask, then, is: Do the times necessary for learning equal groups of series exhibit the desired distribution?

I can answer this question in the affirmative with sufficient certainty. The two longest series, obtained under conditions similar to each other, which I possess, are, to be sure, not large in the above-mentioned theoretical sense; they suffer, moreover, from the disadvantage that they originated at times separated by comparatively long intervals during which there were necessarily many changes in the conditions. In spite of this, their grouping comes as near as could be expected to the one demanded by the theory.

The first test series taken during the years 1879-80 comprises 92 tests. Each test consisted in memorising eight series of 13 syllables each, which process of learning was continued until two reproductions of each series were possible. The time required for all eight series taken together including the time for the two reproductions (but of course not for the pauses, see ) amounted to an average of 1,112 seconds with a probable error of observation of &plusmn;76. The fluctuations of the results were, therefore, very significant: only half of the numbers obtained fell between the limits 1,036 and 1,188, the other half was distributed above and below these limits. In detail the grouping of the numbers is as follows: