In order to define the direction of attention on the part of the observer it was made known that the factors to be compared were the durations of the intervals adjacent to the louder sound in relation to the remaining intervals of the series, and that all other temporal and intensive values were maintained unchanged from experiment to experiment.  In no instance, on the other hand, did any subject know the direction or nature of the variation in those quantities concerning which he was to give judgment.  In all, five subjects shared in the investigation, C., E., F., H. and N. Of these C only had musical training.  In the tables and diagrams the interval preceding the louder sound is indicated by the letter B, that following it by the letter A. Totals—­judgment or errors—­are indicated by the letter T, and errors by the letter E. The sign ‘+’ indicates that the interval against which it stands is judged to be greater than the remaining intervals of the series, the sign ‘=’ that it is judged equal, and the sign ‘-’ that it is judged less.

The first series of changes consisted in the introduction of variations in the duration of the interval following the loud sound, in the form of successive increments.  This loud sound was at the third position in the series.  All intensive relations and the duration of the interval preceding the louder sound remained unchanged.  The results of the experiment are presented in the following table.

TABLE XXVIII.

Ratio of A to         B           A          Errors   Total   Per cent. 
Other Intervals.  +   =   —   +   =   —    B   A   T  judgts. of errors

1.000 :  0.625 2 2 2 4 2 0 4 2 6 12 50 1.000 :  0.666 4 2 0 1 3 2 4 5 9 12 75 1.009 :  0.714 5 3 0 2 2 4 5 6 11 16 69 1.000 :  0.770 5 4 0 1 1 7 5 8 13 18 72 1.000 :  0.833 1 5 0 0 0 6 1 6 7 12 50

    Totals, 17 16 2 8 8 19 19 27 46 70

The value of the interval following the louder sound is correctly reported eight times out of thirty; that preceding it is correctly reported sixteen times out of thirty.  The influence which such a change in intensive value introduced at a single point in a series of sounds exerts on the apparent relation of its adjacent intervals to those of the remainder of the series is not equally distributed between that which precedes and that which follows it, but affects the latter more frequently than the former in a ratio (allowing latitude for future correction) of 2:1.  In the case of interval A the error is one of underestimation in twenty-seven cases; in none is it an error of overestimation.  In the case of interval B the error is one of overestimation in seventeen instances, of underestimation in two.  The influence of the introduction of such a louder