as parts of this duration-block that the relation of succession of one end to the other is perceived. We do not first feel one end and then feel the other after it, and from the perception of the succession infer an interval of time between, but we seem to feel the interval of time as a whole, with its two ends embedded in it. The experience is from the outset a synthetic datum, not a simple one; and to sensible perception its elements are inseparable, although attention looking back may easily decompose the experience, and distinguish its beginning from its end.

When we come to study the perception of Space, we shall find it quite analogous to time in this regard. Date in time corresponds to position in space; and although we now mentally construct large spaces by mentally imagining remoter and remoter positions, just as we now construct great durations by mentally prolonging a series of successive dates, yet the original experience of both space and time is always of something already given as a unit, inside of which attention afterward discriminates parts in relation to each other. Without the parts already given as in a time and in a space, subsequent discrimination of them could hardly do more than perceive them as different from each other; it would have no motive for calling the difference temporal order in this instance and spatial position in that.

And just as in certain experiences we may be conscious of an extensive space full of objects, without locating each of them distinctly therein; [so, when many impressions follow in excessively rapid succession in time, although we

of immedia" may be distinctly aware that they occupy some duration,

working

Temory to

covellence A

asks

and are not simultaneous, we may be quite at a loss to tell which comes first and which last; or we may even invert their real order in our judgment. In complicated reactiontime experiments, where signals and motions, and clicks of the apparatus come in exceedingly rapid order, one is at first much perplexed in deciding what the order is, yet of the fact of its occupancy of time we are never in doubt.

"la durée dans la succession; on ne l'y trouvera jamais; la durée a précédé la succession; la notion de la durée a précédé la notion de la succession. Elle en est donc tout-à-fait indépendante, dira-t-on? Oui, elle en est tout. à-fait indépendante.”

STM

ACCURACY OF OUR ESTIMATE OF SHORT DURATIONS.

We must now proceed to an account of the facts of timeperception in detail as preliminary to our speculative conclusion. Many of the facts are matters of patient experimentation, others of common experience.

First of all, we note a marked difference between the elementary sensations of duration and those of space. The former have a much narrower range; the time-sense may be called

Capaci

mi

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a myopic organ, in comparison with the eye, for example.compac The eye sees rods, acres, even miles, at a single glance, and that' these totals it can afterward subdivide into an almost infinite number of distinctly identified parts. The units of duration, on the other hand, which the time-sense is able to take in at a single stroke, are groups of a few seconds, is pirty and within these units very few subdivisions-perhaps forty at most, as we shall presently see-can be clearly discerned. The durations we have practically most to deal with-minutes, hours, and days-have to be symbolically conceived, and constructed by mental addition, after the fashion of those extents of hundreds of miles and upward, which in the field of space are beyond the range of most men's practical interests altogether. To 'realize' a quarter of a mile we need only look out of the window and feel its length by an act which, though it may in part result from organized associations, yet seems immediately performed. To realize an hour, we must count 'now!-now! -now!-now!' indefinitely. Each 'now' is the feeling of a separate bit of time, and the exact sum of the bits never makes a very clear impression on our mind.

concept of

How many bits can we clearly apprehend at once? chunk? Very few if they are long bits, more if they are extremely short, most if they come to us in compound groups, each including smaller bits of its own.

Hearing is the sense by which the subdivision of durations is most sharply made. Almost all the experimental work on the time-sense has been done by means of strokes of sound. How long a series of sounds, then, can we group in the mind so as not to confound it with a longer or a shorter series?

dry Indust the capacity

memory

Our spontaneous tendency is to break up any monoto nously given series of sounds into some sort of a rhythm. We involuntarily accentuate every second, or third, or fourth beat, or we break the series in still more intricate ways. Whenever we thus grasp the impressions in rhythmic form, we can identify a longer string of them without confusion.

Each variety of verse, for example, has its 'law'; and the recurrent stresses and sinkings make us feel with peculiar readiness the lack of a syllable or the presence of one too much. Divers verses may again be bound together in the form of a stanza, and we may then say of another stanza, "Its second verse differs by so much from that of the first stanza," when but for the felt stanza-form the two differing verses would have come to us too separately to be compared at all. But these superposed systems of rhythm soon reach their limit. In music, as Wundt* says, "while the measure may easily contain 12 changes of intensity of sound (as in 12 time), the rhythmical group may embrace 6 measures, and the period consist of 4, exceptionally of 5 [8?] groups."

Wundt and his pupil Dietze have both tried to determine experimentally the maximal extent of our immediate distinct consciousness for successive impressions.]

Wundt found + that twelve impressions could be distinguished clearly as a united cluster, provided they were caught in a certain rhythm by the mind, and succeeded each other at intervals not smaller than 0.3 and not larger than 0.5 of a second. This makes the total time distinctly apprehended to be equal to from 3.6 to 6 seconds.

.

evidence for

STM

Dietze gives larger figures. The most favorable intervals for clearly catching the strokes were when they came at from 0.3 second to 0.18 second apart. Forty strokes might then be remembered as a whole, and identified without error when repeated, provided the mind grasped them in five subgroups of eight, or in eight sub-groups of five strokes each. When no grouping of the strokes beyond making couples of Physiol. Psych.," II. 54, 55. † Ibid. II. 213.

*

Philosophische Studien, II. 362.

them by the attention was allowed-and practically it was found impossible not to group them in at least this simplest of all ways—16 was the largest number that could be clearly apprehended as a whole.* This would make 40 times 0.3 second, or 12 seconds, to be the maximum filled duration of which we can be both distinctly and immediately aware.

The maximum unfilled, or vacant duration, seems to lie within the same objective range. Estel and Mehner, also working in Wundt's laboratory, found it to vary from 5 or 6 to 12 seconds, and perhaps more. The differences seemed due to practice rather than to idiosyncrasy.t

These figures may be roughly taken to stand for the most important part of what, with Mr. Clay, we called, a few pages back, the specious present. The specious present has, in addition, a vaguely vanishing backward and forward fringe; but its nucleus is probably the dozen seconds or less that have just elapsed.

If these are the maximum, what, then, is the minimum amount of duration which we can distinctly feel?

The smallest figure experimentally ascertained was by Exner, who distinctly heard the doubleness of two successive clicks of a Savart's wheel, and of two successive snaps

* Counting was of course not permitted. It would have given a symbolic concept and no intuitive or immediate perception of the totality of the series. With counting we may of course compare together series of any length-series whose beginnings have faded from our mind, and of whose totality we retain no sensible impression at all. To count a series of clicks is an altogether different thing from merely perceiving them as discontinuous. In the latter case we need only be conscious of the bits of empty duration between them; in the former we must perform rapid acts of association between them and as many names of numbers.

Estel in Wundt's Philosophische Studien, II. 50. Mehner, ibid. II. 571. In Dietze's experiments even numbers of strokes were better caught than odd ones, by the ear. The rapidity of their sequence had a great influence on the result. At more than 4 seconds apart it was impossible to perceive series of them as units in all (cf. Wundt, Physiol. Psych., II. 214). They were simply counted as so many individual strokes. Below 0.21 to 0.11 second, according to the observer, judgment again became confused. It was found that the rate of succession most favorable for grasping long series was when the strokes were sounded at intervals of from 0.3" to 0.18′′ apart. Series of 4, 6, 8, 16 were more easily identified than series of 10, 12, 14, 18. The latter could hardly be clearly grasped at all. Among odd numbers, 3, 5, 7 were the series easiest caught; next, 9, 15; hardest of all, 11 and 13; and 17 was impossible to apprehend

of an electric spark, when their interval was made as small as about of a second.*

With the eye, perception is less delicate. Two sparks, made to fall beside each other in rapid succession on the centre of the retina, ceased to be recognized as successive by Exner when their interval fell below 0.044".†

Where, as here, the succeeding impressions are only two in number, we can easiest perceive the interval between them. President Hall, who experimented with a modified Savart's wheel, which gave clicks in varying number and at varying intervals, says: ‡

"In order that their discontinuity may be clearly perceived, four or even three clicks or beats must be farther apart than two need to be. When two are easily distinguished, three or four separated by the same interval . . . are often confidently pronounced to be two or three respectively. It would be well if observations were so directed as to ascertain, at least up to ten or twenty, the increase [of interval] required by each additional click in a series for the sense of discontinuity to remain constant throughout.” §

* The exact interval of the sparks was 0.00205'. The doubleness of their snap was usually replaced by a single-seeming sound when it fell to 0.00198", the sound becoming louder when the sparks seemed simultaneous. The difference between these two intervals is only Too of a second; and, as Exner remarks, our ear and brain must be wonderfully efficient organs to get distinct feelings from so slight an objective difference as this. See Pflüger's Archiv, Bd. xI.

Ibid. p. 407. When the sparks fell so close together that their irradi ation-circles overlapped, they appeared like one spark moving from the posi tion of the first to that of the second; and they might then follow each other as close as 0.015" without the direction of the movement ceasing to be clear. When one spark fell on the centre, the other on the margin, of the retina, the time-interval for successive apprehension had to be raised to 0.076",

Hall and Jastrow: Studies of Rhythm, Mind, x1. 58.

§ Nevertheless, multitudinous impressions may be felt as discontinuous, though separated by excessively minute intervals of time. Grünhagen says (Pflüger's Archiv, vi. 175) that 10,000 electric shocks a second are felt as interrupted, by the tongue (). Von Wittich (ibid. II. 329), that between 1000 and 2000 strokes & second are felt as discrete by the finger. W. Preyer, on the other hand (Die Grenzen des Empfindungsvermögens, etc., 1868, p. 15), makes contacts appear continuous to the finger when 36.8 of them foilow in a second. Similarly, Mach (Wiener Sitzgsb., LI. 2, 142) gives about 36. Lalanne (Comptes Rendus, LXXXII. p. 1314) found summation of finger contacts after 22 repetitions in a second. Such discrepan, figures are of doubtful worth. On the retina 20 to 30 impressions a second