of such facilitation, it dawned upon me that this was the correct and natural thing. After what has been said above (p. 27ff) one might think that in the case of the remaining experiments, this idea has possibly favored a more attentive and therefore quicker learning of the derived series, and so has, at least, decidedly strengthened the resulting saving in work, even if it has not caused it altogether.
For the three largest of the numbers found,—consequently, for the facilitation of the work which took place in the case of the omission of 1, 2, and 3 intervening syllables—this objection is of slight significance. For these are proportionately so large that it would be attributing too much to an involuntary heightening of a state of attention, voluntarily concentrated without this to the utmost, if an actual influence is ascribed to it here. Moreover, the gradation of the numbers, decisively issuing as they do from the distribution of the individual values and running parallel with the number of skipped intermediate terms, is inconceivable on any such hypothesis as this. For the supposed greater concentration of the attention could clearly work only in general. How could it possibly bring about so regular a gradation of numbers in the case of tests which were separated from each other by weeks and months?
The objection presented above could render doubtful only the fourth result, the proportionally slight saving in the learning of series formed from other series by skipping seven intermediate terms.
Clearly in this case the exact determination of the difference is of especial interest because of the significant size of the interval over which an association took place.
In the case of the present investigations there exists the possibility of so arranging them that knowledge concerning the outcome of the gradually accumulating results is excluded and so that consequently the disturbing influence of secret views and desires disappears. I have accordingly instituted a further group of 30 double tests in the following way as a control of the above results, and especially of the least certain of them.
On the front side of a page were written six syllable series selected by chance and on the reverse side of the same sheet six series formed from them by one of the methods of derivation described above (p.97). For each of the five transforma-
