____________
+-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           50
B.            5.13           40
Hs.           5.26          100
P.            5.77           38
Mn.           6.19           50
Mr.           5.25           60
R.            5.63           24
Sh.           5.34          100
Sn.           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.