*Project Gutenberg*. Public domain.

____________ +-D \/ log k/y_{1} x_{1} = --------------------------------- ____________ ____________ \/ log k/y_{1} +- \/ log k/y_{2}

where D = x_{1} +- x_{2}, and k = value of y when x = 0.

x_{1} and x_{2} must, however, not be great, since
the condition that the curve with which we are dealing
shall approximate the form denoted by the equation
is more nearly fulfilled by those portions of the
curve lying nearest to the *Y* axis.

Now since for any ordinates, y_{1} and y_{2} which
we may select from the table, we know the value of
x_{1} +- x_{2}, we can compute the value of x_{1},
which conversely gives us the amount to be added to
or subtracted from a given term in the series of *CT*’s
to produce the value of the average *ET*.
This latter value, we find, by computing by the formula
given above, using the four terms whose values lie
nearest to the *Y* axis, is 5.25 secs.

In Table II are given similar computations for each of the nine subjects employed, and from this it will be seen that in every case the standard is overestimated.

## TABLE II. *ST*= 5.0 SECS.

Subject. Average ET. No. of Series.A. 5.75 50B. 5.13 40Hs. 5.26 100P. 5.77 38Mn. 6.19 50Mr. 5.25 60R. 5.63 24Sh. 5.34 100Sn. 5.57 50

This overestimation of the 5.0 sec. standard agrees with the results of some of the experimenters on auditory time and apparently conflicts with the results of others. Mach[4] found no constant error. Hoering[5] found that intervals over 0.5 sec. were overestimated. Vierordt,[6] Kollert,[7] Estel[8] and Glass,[9] found small intervals overestimated and long ones underestimated, the indifference point being placed at about 3.0 by Vierordt, 0.7 by Kollert and Estel and 0.8 by Glass. Mehner[10] found underestimation from 0.7 to 5.0 and overestimation above 5.0. Schumann[11] found in one set of experiments overestimation from 0.64 to 2.75 and from 3.5 to 5.0, and underestimation from 2.75 to 3.5. Stevens[12] found underestimation of small intervals and overestimation of longer ones, placing the indifference point between 0.53 and 0.87.

[4] Mach, E.: ‘Untersuchungen
ueber den Zeitsinn des Ohres,’

*Sitzungsber. d. Wiener Akad.*,
Math.-Nat. Kl., Bd. 51, Abth.

2.

[5] Hoering: ’Versuche
ueber das Unterscheidungsvermoegen des

Hoersinnes fuer Zeitgroessen,’
Tuebingen, 1864.

[6] Vierordt: *op. cit.*

[7] Kollert, J.: ‘Untersuchungen
ueber den Zeitsinn,’ *Phil.
Studien*, I., S. 79.

[8] Estel, V.: ‘Neue
Versuche ueber den Zeitsinn,’ *Phil.
Studien*, II., S. 39.