Where the first impression falls on one sense, and the second on another, the perception of the intervening time tends to be less certain and delicate, and it makes a difference which impression comes first. Thus, Exner found[526] the smallest perceptible interval to be, in seconds:

From sight to touch0.071
From touch to sight0.053
From sight to hearing0.16
From hearing to sight0.06
From one ear to another 0.064

To be conscious of a time interval at all is one thing; to tell whether it be shorter or longer than another interval is a different thing. A number of experimental data are on hand which give us a measure of the delicacy of this latter perception. The problem is that of the smallest difference between two times which we can perceive.

The difference is at its minimum when the times themselves are very short. Exner,[527] reacting as rapidly as possible with his foot, upon a signal seen by the eye (spark), noted all the reactions which seemed to him either slow or fast in the making. He thought thus that deviations of about 1/100 of a second either way from the average were correctly noticed by him at the time. The average was here 0.1840''. Hall and Jastrow listened to the intervals between the clicks of their apparatus. Between two such equal intervals of 4.27'' each, a middle interval was included, which might be made either shorter or longer than the extremes. "After the series had been heard two or even three times, no impression of the relative length of the middle interval would often exist, and only after hearing the fourth and last [repetition of the series] would the judgment incline to the plus or minus side. Inserting the variable between two invariable and like intervals greatly facilitated judgment, which between two unlike terms is far less accurate."[528] Three observers in these experiments made no error when the middle interval varied 1/60 from the extremes. When it varied 1/120, errors occurred, but were few. This would make the minimum absolute difference perceived as large as 0.355''.

This minimum absolute difference, of course, increases as the times compared grow long. Attempts have been made to ascertain what ratio it bears to the times themselves. According to Fechner's 'Psychophysic Law' it ought always to bear the same ratio. Various observers, however, have found this not to be the case.[529] On the contrary, very interesting oscillations in the accuracy of judgment and in the direction of the error—oscillations dependent upon the absolute amount of the times compared—have been noticed by all who have experimented with the question. Of these a brief account may be given.

In the first place, in every list of intervals experimented with there will be found what Vierordt calls an 'indifference-point;' that is to say, an interval which we judge with maximum accuracy, a time which we tend to estimate as neither longer or shorter than it really is, and away from which, in both directions, errors increase their size.[530] This time varies from one observer to another, but its average is remarkably constant, as the following table shows.[531]

The times, noted by the ear, and the average indifference-points (given in seconds) were, for—

Wundt[532]0.72
Kollert[533] 0.75
Estel (probably)0.75
Mehner 0.71
Stevens[534] 0.71
Mach[535] 0.35
Buccola (about)[536] 0.40

The odd thing about these figures is the recurrence they show in so many men of about three fourths of a second, as the interval of time most easy to catch and reproduce, Odder still, both Estel and Mehner found that multiples of this time were more accurately reproduced than the time-intervals of intermediary length;[537] and Glass found a certain periodicity, with the constant increment of 1.25 sec., in his observations. There would seem thus to exist something like a periodic or rhythmic sharpening of our time-sense, of which the period differs somewhat from one observer to the next.