sound, therefore, is to cause a decrease in the apparent
duration of the interval which follows it, and an
increase in that of the interval which precedes it.
The illusion is more pronounced and invariable in the
case of the interval following the louder sound than
of that preceding it, the proportion of such characteristic
misinterpretations to the whole number of judgments
in the two cases being, for A, 77 per cent.; for B,
54 per cent. The effect on interval A is very
strong. In the second group, where the ratio
of this interval to the others of the series is 3:2,
it is still judged to be equal to these others in 50
per cent. of the cases, and less in 35 per cent.
Further, these figures do not give exhaustive expression
to the whole number of errors which may be represented
in the judgments recorded, since no account is taken
of greater and less but only of change of sign; and
an interval might be underestimated and still be reported
greater than the remaining intervals of the series
in a group of experiments in which the relation of
the interval in question to these remaining intervals
ranged from the neighborhood of equivalent values to
that in which one was double the other. If in
a rough way a quantitative valuation of errors be
introduced by making a transference from any one sign
to that adjacent to it (e.g.
, — to =,
or = to +) equal to one
, and that from one
extreme sign to the other equal to two
difference in the influence exerted on the two intervals
will become still more evident, since the errors will
then have the total (quantitative) values of A 46,
and B 19, or ratio of 1.000:0.413.
Next, the position of the louder sound in the series
of six was changed, all other conditions being maintained
uniform throughout the set of experiments. The
series of intervals bore the following relative values:
A, 0.900; B, 1.100; all other intervals, 1.000.
The louder sound was produced by a fall of 0.875 inch;
all others by a fall of 0.250 inch. The louder
sound occurred successively in the first, second,
third, fourth and fifth positions of the series.
In the first of these forms it must of course be remembered
that no interval B exists. The results of the
experiment are shown in the following table:
Position Apparent Values.
Errors. % of Errors Ditto in
B A B A T in tot. judg.
quant. Series + = — + =
— B A B A 1
2 6 6 0 12 12
85.7 85.7 2 2 8 2 1 7
4 10 11 21 83.3 91.6 73.3 91.6 3
1 9 3 1 8 3 10 11 21 76.9 91.6
71.9 91.6 4 1 8 4 2 6 5
9 11 20 69.2 84.6 52.8 84.6 5 0
12 0 0 4 8 12 12 24 100.0 100.0 60.0
100.0 Totals, 4 37 9 6 31 26 41 57
98 82.3 90.7 64.5 90.7
Total judgments, 113; Errors (B = 31),
A = 57.