The relatively meager results set forth in the preceding section are corroborated in the present set of experiments.  That such a variation of intensity introduced into an otherwise undifferentiated auditory series, while it affects the time-values of both preceding and following intervals, has a much greater influence on the latter than on the former, is as apparent here as in the previous test.  The number of errors, irrespective of extent, for the two intervals are:  B, 82.3 per cent, of total judgments; A, 90.7 per cent.  When the mean and extreme sign displacements are estimated on the quantitative basis given above these percentages become B, 64.5; A, 90.7, respectively—­a ratio of 0.711:1.000.

The direction of error, likewise, is the same as in the preceding section.  Since the actual values of the two intervals here are throughout of extreme sign—­one always greater, the other always less—­only errors which lie in a single direction are discriminable.  Illusions lying in this direction will be clearly exhibited, since the differences of interval introduced are in every case above the threshold of discrimination when the disturbing element of variations in intensity has been removed and the series of sounds made intensively uniform.  In case of a tendency to underestimate B or overestimate A, errors would not be shown.  This problem, however, is not to be met here, as the results show; for there is recorded a proportion of 82.3 per cent. of errors in judgment of interval B, and of 90.7 per cent. in judgment of interval A, all the former being errors of overestimation, all of the latter of underestimation.

The influence of position in the series on the effect exerted by such a change of intensity in a single member can be stated only tentatively.  The number of experiments with the louder sound in position five was smaller than in the other cases, and the relation which there appears cannot be absolutely maintained.  It may be also that the number of intervals following that concerning which judgment is to be given, and with which that interval may be compared, has an influence on the accuracy of the judgment made.  If we abstract from this last set of results, the tendency which appears is toward an increase in accuracy of perception of comparative durations from the beginning to the end of the series, a tendency which appears more markedly in the relations of the interval preceding the louder sound than in those of the interval which follows it.  This conclusion is based on the succession of values which the proportion of errors to total judgments presents, as in the annexed table.

TABLE XXX.

  Percentage of Errors for Each Position.