Thus

as comparable with a 'repetition.' The 'arithmetical prodigy,' Diamandi, could write down a number of ten digits after learning them for 15", whereas a number of 20 digits occupied him for 2′ 15′′, one of 100 digits, 25′ and one of 200 1 hr. 15'. it is obvious-obvious indeed without any experimentationthat beyond a certain finite and not very great number of elements there is an end to all such memorising. Unhappily the details of Ebbinghaus's experiment conflict with this a priori certainty and must be wrong somewhere'. Substituting poetry for gibberish of equal amount, Ebbinghaus found that one-tenth the number of repetitions sufficed; the enormous saving thus effected shewing how numerous and intimate are the ready-made associations that 'rhyme and reason' involve. But at one and the same time to memorise five verses even of sense requires more than five times as many repetitions as the memorising of Two or three lines of inquiry here present themselves, e.g. (1) as to the immediate effects of a series of repetitions; (2) as to retention after an interval, (a) as a function of the number of repetitions previously made, and (b) as a function of the time; (3) as to the respective effects of more or less cumulating, or more or less distributing, the repetitions, on the number of these required. Let us glance at each in turn.

one.

I. It is at once obvious that beyond a certain point exhaustion of attention renders further repetition for a time futile; thus Ebbinghaus found 64 repetitions at one sitting of six 16-syllable nonsense verses, a task lasting some three-quarters of an hour, was apt to bring on asthenia, a sort of epileptic aura, and the like!" But keeping well within this heroic limit, a certain 'law of diminishing return,' to use an economic analogy discloses itself; though sometimes it may be overlaid by

1 Thus, while 12 syllables required 16·6 repetitions, and the addition of a second 12, 44 repetitions, i.e. 274 more, the addition of a third 12 required only 55, i.e. only 11 more. At this rate the process should, as the number of syllables increased, become comparatively easier—which seems plainly absurd. This was pointed out by one of Ebbinghaus's early critics (A. Elsas, Phil. Monatshefte, 1887, p. 88) and repeated by another (A. Höfler, Vierteljahrschr. f. wissenschaftliche Phil. 1887, p. 346). But it was ignored by everybody including Ebbinghaus, Wundt and—I must add-myself!

2 Thus taking a line of 10 syllables, the number of syllables reproduced correctly and in their proper order, after 1, 3, 6, 9 and 12 'repetitions,' were 2.2, 2.5, 28, 34, 3'9 respectively, as the averages of a series of experiments with each of eight persons. "The first repetition is undoubtedly the best," assuming, of course, that the subjects

counteracting tendencies. Thus the speedy cessation of early distractions due to difficulties in pronunciation or in adaptation to strange experimental conditions, &c., often leads to a slight improvement consequent on the removal of these hindrances to undivided attention.

But in a given repetition it is noteworthy that all the syllables of a line do not fare alike. The first reading is the best and usually suffices for the reproduction of the second and the last syllable in addition to the first: the intermediate syllables, on the other hand, invariably require many repetitions, as already said, before the whole line is correctly 'learnt.' And yet all these syllables can-for a while-be distinctly recognised long before they can be directly recalled. So they are said to remain 'below the threshold of reproduction,' to which, however, every fresh repetition brings them nearer, till at length they are above it. But while still subliminal they prove to be more or less associated, for the mention of one of these syllables will often ensure not merely its own recognition but also the reproduction of the next. How is it that uniform attention on the subject side leads to so much objective diversity? In dealing with the middle syllables attention-though its 'amount' be uniform is distributed differently from what it is in the case of the two end syllables. With these there is only one thing to do either to receive the new or to retain the old; in the middle of the line both these things have to be done, and neither is done so effectually. Thus the initial syllables-which receive more undivided attention—are more deeply 'impressed,' while the final-the attention to which, is not so immediately disturbed1are 'impressed' for longer, than the middle syllables.

2. (a) On relearning a line after an interval of twenty-four hours Ebbinghaus found in the case of the same experiments start with their attention fully concentrated. Some persons naturally do this, many do not; the experimenter has therefore to take special precautions to secure as much uniformity as he can in this respect. Cf. W. G. Smith, "The Place of Repetition in Memory," Psychological Rev. iii. (1896), pp. 20 ff. The figures given are unquestionably low, partly, as the writer points out, in consequence of the method employed, but partly, as his detailed tables shew, in consequence of the lax attention of three out of his eight subjects. Cf. too Lipmann, Zeitschr. f. Psych. xxxv. (1904), p. 213; Witasek, ibid. xliv. (1907), p. 247; Reuther, Psych. Studien, i. (1906), Plates 1 and 2.

1 The pause between two lines being of much greater length than the interval between two syllables.

W. P.

15

that there was an average saving of one repetition for every three made the day before. A line of 16 syllables, for example, required some 30 repetitions, and could then be said off correctly. If only 8 repetitions were taken at first, the line being 'underlearnt,' it probably appeared quite strange the next day, yet the proportional saving was no less. On the other hand, if an additional 30 repetitions followed immediately on the first, the line being 'doubly learnt,' in spite of the familiarity next day apparent, the proportional saving was no greater. We are so far led to infer that the stronger associations effected by many repetitions at one time fall off more rapidly than the weaker associations effected by fewer repetitions at one time. Herbart in his 'psychical dynamics'-influenced probably by physical analogies-conjectured that the 'sinking' or 'inhibition' of presentations generally was proportional to their intensity; the less there was to sink, the slower the sinking became. Recent experiments certainly point in this direction. (b) As to retention as a function of the time-we all know that memories fade with time, but not at what precise rate. Ebbinghaus, by a series of prolonged experiments, ascertained the rate to be proportional to the logarithm of the time-a result already implied in that connecting retention and intensity, as Herbart assumed; albeit in inquiries of this kind independent confirmation is always of value.

3. Had the proportional saving just described held good indefinitely, some 100 repetitions of the 16 syllables at one time should have dispensed with any further repetition twenty-four hours afterwards; whereas, in fact, this result seemed never attainable. Beyond a certain degree of accumulation, an everdiminishing return was manifest, and that apparently short of the stage at which exhaustion of attention began to be felt. But, contrariwise, when the repetitions were distributed over several days, an ever-increasing efficiency was then the result. Thus, for Ebbinghaus, 38 repetitions spread over three days were as effective as 68 taken together. The results of careful experiments by Jost with two different subjects, using G. E. Müller's 'method of scoring' (to be described later on), are still more conclusive1. Comparing 8 repetitions on three successive days

A. Jost, "Die Assoziationsfestigkeit in ihrer Abhängigkeit von der Verteilung der Wiederholungen," Zeitschr. f. Psych. xiv. (1897), pp. 436 ff.

with 4 repetitions on six, and 2 on twelve, the efficiencies, tested twenty-four hours later, were respectively as 115, 35, and 54; and probably, as Jost surmises, the effect of the maximum distribution-single 'repetition' on twenty-four successive days -would have been more advantageous still, securing in fact the superiority of a first impression (cf. 1, above) on every occasion. This result again, is in part explained by the law of sinking already found. For if the sinking were simply proportional to the time, or were independent of the intensity, there would sa far be no reason why one mode of distributing a given number of repetitions should be more economical than another. There is, however, another reason for this superiority, less clearly implied, to which we shall come presently1.

Rhythmizing.

§ 2. Invariably, and almost of necessity, a more or less complex rhythmical articulation becomes apparent as the syllables are repeated, even when-as in the improved methods of G. E. Müller and his collaborateurs-they are presented singly and at regular intervals. A series of twelve syllables, for example, would be connected into six trochees, with a caesura in the middle of the verse; while in each half of it the first, and -somewhat more-the last, of the accented syllables would be specially emphasized; thus:

bám fís | lúp tŏl | gén kĕr || dúb năf | mís pon | sáv niz In trying to suppress this tendency and to repeat the syllables in a monotonous, staccato fashion, just as they were presented, the tempo, though really unchanged, seemed to be distinctly quickened, a consequence, doubtless, of the greater effort involved. Moreover, the attempt, which was seldom successful, about doubled the number of repetitions required for learning off, thereby shewing how much is gained by this psychical organization of disconnected material. But the gain thus ensured was manifest in other ways. Each foot, whether dissyllabic or trisyllabic, became a new complex unit, the elements to be connected by successive association being thereby reduced to a half or a third, and the whole line seemingly shortened. The

1 Cf. § 6 below, p. 240.

varied intonation, again, helped to fix the place of each foot in the verse, thus further facilitating the mind's survey of the whole. Such a transformation can hardly be accounted for so long as retention and association are regarded as merely mechanical and passive processes.

Psychical rhythm, upon which we here touch, has also been experimentally investigated at great length, alike in its physiological, psychological and aesthetical aspects. The topic is far too intricate and unsettled for discussion here, yet two or three points may be noted in passing. We are not specially concerned with objective rhythms, recurring series of impressions, that is to say, in which there are actually periodic variations of intensity, interval and the like. What is remarkable is that even a perfectly regular succession of sounds (or touches), qualitatively and quantitatively all alike, a series therefore devoid of all objective rhythm, is nevertheless apprehended by most people as rhythmically grouped-provided the rate lies between the limits of about o'8" and o14". The slower of these rates leads to simple groups of two, replaced by groups of four or eight as the rate increases; groups of three and six also occur, though less frequently. The average duration of the groups, whether these are large or small, is comparatively constant, ranging between a length of about 16" for 2-groups and about 116" for 8-groups. With slower rates there was no grouping at all and with faster rates 'simply a periodic intensive change in the series'.' A close connexion of rhythm with the normal tempo of attention seems thus clearly indicated.

The subject usually keeps time by taps, nods or other accompanying movements. The pulse and respiration are also implicated. These organic rhythms have even been regarded as the prime source of all psychical rhythm and of its manifold aesthetic effects. Some connexion there is unquestionably. As the decimal system corresponds to our possession of ten fingers, and our movements to the structure of our limbs, so here we may assume that physiological processes fix the limits within which psychical rhythm is possible, but yet may be as little an adequate cause of it or its developments as fingers are of arithmetic, or legs of an Irish jig. In motor rhythms, such as the last, the initiative is obviously psychical, and the respiratory and other periodic 1 Cf. Bolton's paper (cited on the next page), pp. 214 f.