Memory: A Contribution to Experimental Psychology/Chapter 7

by Hermann Ebbinghaus

Layout 2

CHAPTER VII

RETENTION AND OBLIVISCENCE AS A FUNCTION OF THE TIME

Section 26. Explanations of Retention and Obliviscence

All sorts of ideas, if left to themselves, are gradually forgotten. This fact is generally known. Groups or series of ideas which at first we could easily recollect or which recurred frequently of their own accord and in lively colors, gradually return more rarely and in paler colors, and can be reproduced by voluntary effort only with difficulty and in part. After a longer period even this fails, except, to be sure, in rare instances. Names, faces, bits of knowledge and experience that had seemed lost for years suddenly appear before the mind, especially in dreams, with every detail present and in great vividness; and it is hard to see whence they came and how they managed to keep hidden so well in the meantime. Psychologists—each in accordance with his general standpoint—interpret these facts from different points of view, which do not exclude each other entirely but still do not quite harmonise. One set, it seems, lays most importance on the remarkable recurrence of vivid images even after long periods. They suppose that of the perceptions caused by external impressions there remain pale images, “traces,” which, although in every respect weaker and more flighty than the original perceptions, continue to exist unchanged in the intensity possessed at present. These mental images can not compete with the much more intense and compact perceptions of real life; but where the latter are missing entirely or partly, the former domineer all the more unrestrainedly. It is also true that the earlier images are more and more overlaid, so to speak, and covered by the later ones. Therefore, in the case of the earlier images, the possibility of recurrence offers itself more rarely and with greater difficulty. But if, by an accidental and favorable grouping of circumstances, the accumulated layers are pushed to one side, then, of course, that which was hidden beneath must appear, after whatever lapse of time, in its original and still existent vividness.^[1]

For others^[2] the ideas, the persisting images, suffer changes more and more affect their nature; the concept of obscuration comes in here. Older ideas are repressed and forced to sink down, so to speak, by the more recent ones. As time passes one of these general qualities, inner clearness and intensity of consciousness, suffers damage. Connections of ideas and series of ideas are subject to the same process of progressive weakening; it is furthered by a resolution of the ideas into their components, as a result of which the now but loosely connected members are eventually united in new combinations. The complete disappearance of the more and more repressed ideas occurs only after a long time. But one should not imagine the repressed ideas in their time of obscuration to be pale images, but rather to be tendencies, “dispositions,” to recreate the image contents forced to sink down. If these dispositions are somehow supported and strengthened, it may happen at any one moment that the repressing and hindering ideas become depressed themselves, and that the apparently forgotten idea arises again in perfect clearness.

A third view holds that, at least in the case of complex ideas, obliviscence consists in the crumbling into parts and the loss of separate components instead of in general obscuration. The idea of resolution into component parts recently spoken of supplies here the only explanation. “The image of a complex object is dim in our memory not because as a whole with all its parts present and in order it is illuminated by a feebler light of consciousness, but it is because it has become incomplete. Some parts of it are entirely lacking. Above all the precise connection of those still extant is, in general, missing and is supplied only by the thought that some sort of union once existed between them; the largeness of the sphere in which, without being able to make a final decision, we think this or that connection equally probable, determines the degree of dimness which we are to ascribe to the idea in question.”^[3]

Each of these opinions receives a certain, but not exclusive, support from the actual inner experiences, or experiences supposed to be actual, which we at times have. And what is the reason? It is that these fortuitous and easily obtained inner experiences are much too vague, superficial and capable of various interpretations to admit in their entirety of only a single interpretation, or even to let it appear as of preponderating probability. Who could, with even tolerable exactness, describe in its gradual course the supposed overlaying or sinking or crumbling of ideas? Who can say anything satisfactory about the inhibitions caused by series of ideas of different extent, or about the disintegration that a firm complex of any kind suffers by the use of its components in new connections? Everybody has his private “explanation” of these processes, but the actual conditions which are to be explained are, after all, equally unknown to all of us.

If one considers the limitation to direct, unaided observation and to the chance occurrence of useful experiences, there seems but little prospect of improvement in conditions. How will one for example determine the degree of obscuration reached at a certain point, or the number of fragments remaining? Or how can the probable course of inner processes be traced if the almost entirely forgotten ideas return no more to consciousness?

Section 27. Methods of Investigation of Actual Conditions

By the help of our method we have a possibility of indirectly approaching the problem just stated in a small and definitely limited sphere, and, by means of keeping aloof for a while from any theory, perhaps of constructing one.

After a definite time, the hidden but yet existent dispositions laid down by the learning of a syllable-series may be strengthened by a further memorisation of the series, and thereby the remaining fragments may be united again to a whole. The work necessary for this compared with that necessary when such dispositions and fragments are absent gives a measure for what has been lost as well as for what remains. The inhibitions which idea-groups of different sorts or extents may occasion in relation to others must, as a result of the interposition of well defined complexes of ideas between learning and relearning, betray itself in the more or less increased work of relearning. The loosening of a bond of connection by some other use of its components can be investigated in a similar manner as follows: after a certain series has been studied, new combinations of the same series are memorised and the change in the amount of work necessary for relearning the original combination is then ascertained.

First, I investigated the first mentioned of these relations and put the question: If syllable series of a definite kind are learned by heart and then left to themselves, how will the process of forgetting go on when left merely to the influence of time or the daily events of life which fill it? The determination of the losses suffered was made in the way described: after certain intervals of time, the series memorised were relearned, and the times necessary in both cases were compared.

The investigations in question fell in the year 1879-80 and comprised 163 double tests. Each double test consisted in learning eight series of 13 syllables each (with the exception of 38 double tests taken from 11-12 a.m. which contained only six series each) and then in relearning them after a definite time. The learning was continued until two errorless recitations of the series in question were possible. The relearning was carried to the same point; it occurred at one of the following seven times,—namely, after about one third of an hour, after 1 hour, after 9 hours, one day, two days, six days, or 31 days.

The times were measured from the completion of the first set of first learnings, as a consequence of which no great accuracy was required in case of the longer intervals. The influence of the last four intervals was tested at three different times of day (p.33). Some preliminary remarks are necessary before the results obtained can be communicated.

Similar experimental conditions may be taken for granted in the case of the series relearned after a number of whole days. At any rate there is no way of meeting the actual fluctuations even when external conditions are as far as possible similar, other than by a multiplication of the tests. Where the inner dissimilarity was presumably the greatest, namely after the interval of an entire month, I approximately doubled the number of tests.

In the case of an interval of nine hours and an interval of one hour between learning and relearning, there existed, however, a noticeably constant difference in the experimental conditions. In the later hours of the day mental vigor and receptivity are less. The series learned in the morning and then relearned at a later hour, aside from other influences, require more work for relearning than they would if the relearning were done at a time of mental vigor equal to that of the original learning. Therefore, in order to become comparable, the numerical values found for relearning must suffer a diminution which, at least in the case of the 8 hour interval, is so considerable that it cannot be neglected. It must be ascertained how much longer it takes to learn at the time of day, B, series which were learned in "a" seconds at the time of day, A. The actual determination of this quantity presupposes more tests than I, up to the present, possess. If a necessary but inexact correction is applied to the numbers found for 1 and for 8 hours, these become even more unreliable than if left to themselves.

In the ease of the smallest interval, one third of an hour, the same drawback reappears, though to a less degree; but it is probably compensated for by another circumstance. The interval as a whole is so short that the relearning of the first series of a test followed almost immediately or after an interval of one or two minutes upon the learning of the last series of the same test. For this reason the whole formed so to speak, one continuous test in which the relearning of the series took place under increasingly unfavorable conditions as regards mental freshness. But on the other hand the relearning after such a short interval was done rather quickly. It took hardly half of the time required for the learning. By this means the interval between the learning and relearning of a certain series became gradually smaller. The later series therefore had more favorable conditions with regard to the time interval. In view of the difficulty of more accurate determinations, I have taken it for granted that these two supposed counteracting influences approximately compensated each other.

Section 28. Results

In the following table I denote by:

L the time of first learning of the series in seconds, just as they were found, therefore including the time for the two recitations.

WL the time for relearning the series also including the recitations.

WLk the time of relearning reduced where necessary by a correction.

Δ the difference L—WL or L—WLk, as the case may be—that is, the saving of work in the case of relearning.

Q the relation of this saving of work to the time necessary for the first learning, given as a per cent. In the calculation of this quotient I considered only the actual learning time, the time for recitation having been subtracted.^[4]

The latter was estimated as being 85 seconds for two recitations of 8 series of 13 syllables each; that would correspond to a duration of 0.41 seconds for each syllable (p. 31).

⁠Thus $\scriptstyle {\rm {Q}}={\tfrac {100\ \Delta }{\rm {L-85}}}$

Finally A, B, C mean the previously mentioned times of day, 10-11 a.m., 11-12 a.m., 6-8 p.m.

I. 19 minutes.⁠12 tests.⁠Learning and relearning at the time A.

L	WL	Δ	Q
1156	467	689	64.3
1089	528	561	55.9
1022	492	530	56.6
1146	483	663	62.5
1115	490	625	60.7
1066	447	619	63.1
985	453	532	59.1
1066	517	549	56.0
1364	540	824	64.4
975	577	398	44.7
1039	528	511	53.6
952	452	500	57.7
m=1081	498	583	58.2 P.E.m=1

II. 63 minutes.⁠16 tests.⁠The learning at the time A, the relearning at the time B. For ascertaining the influence of this difference in the time of day I have the following data. Six series of 13 syllables each were learned at the time B (not including the time of recitation) in 807 seconds (P.E._m=10) as an average of 39 tests. Just as many series of the same kind were learned at the time A in 763 seconds (P.E._m=7) as an average of 92 tests. Thus the values found in the later period are about 5 per cent. of their own amount too large as compared with those obtained in the earlier period. Therefore the times found for relearning at the time B must be decreased by about 5 per cent. to make them comparable with those of learning.

L	WL	WLk	Δ	Q
1095	625	594	501	49.6
1195	821	780	415	37.4
1133	669	636	497	47.4
1153	687	653	500	46.8
1134	626	595	539	51.4
1075	620	589	486	49.1
1138	704	669	469	44.5
1078	565	537	541	54.5
1205	770	731	474	42.3
1104	723	687	417	40.9
886	644	612	274	34.2
958	591	562	396	45.4
1046	739	702	344	35.8
1122	790	750	372	35.9
1100	609	579	521	51.3
1269	709	674	595	50.0
m⁠1106	681	647	459	44.2 P.E.m=1

III. 525 minutes.⁠12 tests.⁠The learning at the time A, the relearning at the time C. The different influence of the two times of day is calculated as follows: eight series of 13 syllables each required, with 38 tests at time C, 1173 seconds (P.E._m=10); similar series with 92 tests at time A required 1027 seconds (P.E._m=8). The first number is approximately 12 per cent. of its own value larger than the second; therefore I have subtracted that much from the numerical values found for the time C.

L	WL	WLk	Δ	Q
1219	921	811	408	36.0
975	815	717	258	29.0
1015	858	755	260	28.0
954	784	690	264	30.4
1340	955	840	500	39.8
1061	811	714	347	35.6
1252	784	690	562	48.2
1067	860	757	310	31.6
1343	1019	897	446	35.5
1181	842	741	440	40.1
1080	799	703	377	37.9
1091	806	709	382	38.0
m⁠1132	855	752	380	35.8 P.E.m=1

IV. One day.⁠26 tests, of which 10 were at time A, 8 at time B (here as everywhere consisting of only 6 series each), 8 at time C.

A
L	WL	Δ	Q
1072	811	261	26.4
1369	861	508	39.6
1227	823	404	35.4
1263	793	470	39.4
1113	754	359	34.9
1000	644	356	38.9
1103	628	475	46.7
888	754	134	16.7
1030	829	201	21.3
1021	660	361	38.6
m⁠1109	756	353	33.8 P.E.m=2

B

L	WL	Δ	Q
889	650	239	29.0
824	537	287	37.8
897	593	304	36.5
825	599	226	29.7
854	562	292	37.0
863	761	122	14.9
742	433	309	45.6
907	653	254	30.1
m⁠853	599	254	32.6 P.E.m=2.2

C

L	WL	Δ	Q
1212	935	277	24.6
1215	797	418	37.0
1096	647	449	44.4
1191	684	507	45.8
1256	898	358	30.6
1295	781	514	42.5
1146	936	210	19.8
1064	750	314	32.1
m⁠1184	803	381	34.6 P.E.m=2.3

The average differences between times of learning and relearning at the different times of day vary somewhat with regard to their absolute values. (Of course in the case of B the number 254 must first be multiplied by 4/3, because it is derived from only 6 series.) But the relations of these differences to the times of first learning (the Q's) harmonize sufficiently well. If, therefore, all the Q's are combined in a general average, Q=33.7 (P.E._m=1.2).

V. Two days.⁠26 tests; 11 of these at the time A, 7 at B, 8 at C.

A
L	WL	Δ	Q
1066	895	171	17.4
1314	912	402	32.7
963	855	108	12.3
964	710	254	28.9
1242	888	354	30.6
1243	710	533	46.0
1144	895	249	23.5
1143	874	269	25.4
1149	953	196	18.4
1090	855	235	23.4
1376	847	529	41.0
m⁠1154	854	300	27.2 P.E.m=2.3

B

L	WL	Δ	Q
752	549	203	29.5
1087	740	347	33.9
1073	620	453	44.9
826	693	133	17.5
905	548	357	42.4
811	763	48	6.4
782	618	164	22.8
m⁠891	647	244	28.2 P.E.m=3.5

C

L	WL	Δ	Q
1246	889	357	31.6
1231	885	346	30.2
1273	1039	234	19.7
1319	925	394	31.9
1125	971	154	14.8
1275	891	384	32.3
1322	857	465	37.6
1170	880	290	26.7
m⁠1245	917	328	28.1
			P.E.m=1.8

The combination of the three average values of Q, which are stated in per cents and lie close to each other, for the 26 tests gives Q=27.8 (P.E._m=1.4)

VI. Six days⁠26 tests, 10 at the time A, 8 at B, 8 at C.

A
L	WL	Δ	Q
1076	868	208	21.0
992	710	282	31.1
1082	756	326	32.7
1260	973	287	24.4
1032	864	168	17.7
1010	955	55	5.9
1197	818	379	34.1
1199	828	371	33.3
943	697	246	28.7
1105	868	237	23.2
m⁠1090	834	260	25.2
			P.E.m=1.9

B

L	WL	Δ	Q
902	564	338	40.3
793	517	276	37.9
848	639	209	26.5
871	709	162	20.1
1034	649	385	39.7
745	728	17	2.5
975	645	330	36.2
805	766	39	5.3
m⁠872	652	220	26.1
			P.E.m=4

C

L	WL	Δ	Q
1246	922	324	27.9
1334	1097	237	19.0
1293	393	354	21.0
1401	988	413	31.4
1214	992	222	19.7
1299	1045	254	20.9
1358	1047	311	24.4
1305	881	424	34.8
m⁠1306	989	317	24.9
			P.E.m=1.6

The average of the total 26 savings of work, stated in per cents, is 25.4 (P.E._m=1.3).

VIII. 31 days.⁠45 tests; 20 at the time A, 15 at B, 10 at C.

A
L	WL	Δ	Q
1069	813	256	26.0
1109	785	324	31.6
1268	858	410	34.7
1280	902	378	31.6
1180	848	332	30.3
1095	888	207	20.5
1089	988	101	10.1
1113	1043	70	6.8
1090	1025	65	6.5
997	876	121	13.3
1116	934	182	17.7
1060	893	167	17.1
930	796	134	15.9
1030	769	261	27.6
980	862	118	13.2
1079	805	274	27.6
1254	978	276	23.6
1164	938	226	20.9
1127	869	258	24.8
1268	972	296	25.0
m⁠1115	892	223	21.2
			P.E.m=1.3

B

L	WL	Δ	Q
831	638	193	25.2
867	516	351	43.7
960	748	212	23.7
828	675	153	20.0
859	705	154	19.4
838	661	177	22.9
946	887	59	6.7
833	780	53	6.9
696	532	164	25.9
757	626	131	18.9
906	733	173	20.5
1024	915	109	11.4
930	780	150	17.3
899	756	143	17.1
1018	705	313	32.8
m⁠879	710	169	20.8
			P.E.m=1.4

C

L	WL	Δ	Q
1424	1004	420	31.4
1307	1102	205	16.4
1351	893	458	36.2
1245	1090	155	13.4
1258	895	363	31.0
1155	1070	85	7.9
1219	800	419	36.9
1278	1110	168	14.1
1120	1051	69	6.7
1250	1055	195	16.7
m⁠1261	1007	254	21.1
			P.E.m=2.7
The average of 45 savings of work expressed in per cents=21.1 (P.E.m=0.8).

A hasty glance at the figures above reveals the fact that for each interval of time the savings in work which become evident when the series is relearned have very fluctuating values. (This saving in work is each time the measure for the amount remembered at the end of the interval.) This is especially the case with their absolute values (Δ), but is also the case with the relative values (Q). The results are taken from the earlier period and suffer from several disturbing influences to which my attention was first drawn by the tests themselves.

In spite of all irregularities in detail, however, they group themselves as a whole with satisfactory certainty into an harmonious picture. As a proof of this the absolute amount of the saving in work is of less value. The latter evidently depends upon the time of day—i.e., upon the changes in the time of the first learning dependent upon it. When this change is greatest (time C), Δ also is greatest; for the time B, they are in ¾ of the cases larger than for the time A (after multiplying by 4/3). On the other hand, the values (Q) found for the relation of each saving of work to the time originally spent, are apparently almost independent of this ratio. Their averages are close together for all three times of day, and do not show any character of increase or decrease in the later hours. Accordingly I here tabulate the latter.

	I		II	III		IV
No.	After X hours		So much of the series learned was retained that in relearning a saving of Q% of the time of original learning was made	P.E.m		The amount forgotten was thus equivalent to v% of the original in terms of time of learning
	X=		Q=			v=
1	0	.33	58.2	1		41.8
2	1	.	44.2	1		55.8
3	8	.8	35.8	1		64.2
4	24	.	33.7	1	.2	66.3
5	48	.	27.8	1	.4	72.2
6	6×24		25.4	1	.3	74.6
7	31×24		21.1	0	.8	78.9

Section 29. Discussion of Results

1. It will probably be claimed that the fact that forgetting would be very rapid at the beginning of the process and very slow at the end should have been foreseen. However, it would be just as reasonable to be surprised at this initial rapidity and later slowness as they come to light here under the definite conditions of our experiment for a certain individual, and for a series of 13 syllables. One hour after the end of the learning, the forgetting had already progressed so far that one half the amount of the original work had to be expended before the series could be reproduced again; after 8 hours the work to be made up amounted to two thirds of the first effort. Gradually, however, the process became slower so that even for rather long periods the additional loss could be ascertained only with difficulty. After 24 hours about one third was always remembered; after 6 days about one fourth, and after a whole month fully one fifth of the first work persisted in effect. The decrease of this after-effect in the latter intervals of time is evidently so slow that it is easy to predict that a complete vanishing of the effect of the first memorisation of these series would, if they had been left to themselves, have occurred only after an indefinitely long period of time.

2. Least satisfactory in the results is the difference between the third and fourth values, especially when taken in connection with the greater difference between the fourth and fifth numbers. In the period 9-24 hours the decrease of the after-effect would accordingly have been 2½ per cent. In the period 24 to 48 hours it would have been 6.1 per cent; in the later 24 hours, then, about three times as much as in the earlier 15. Such a condition is not credible, since in the case of all the other numbers the decrease in the after-effect is greatly retarded by an increase in time. It does not become credible even under the plausible assumption that night and sleep, which form a greater part of the 15 hours but a smaller part of the 24, retard considerably the decrease in the after-effect.

Therefore it must be assumed that one of these three values is greatly affected by accidental influences. It would fit in well with the other observations to consider the number 33.7 per cent for the relearning after 24 hours as somewhat too large and to suppose that with a more accurate repetition of the tests it would be 1 to 2 units smaller. However, it is upheld by observations to be stated presently, so that I am in doubt about it.

3. Considering the special, individual, and uncertain character of our numerical results no one will desire at once to know what “law” is revealed in them. However, it is noteworthy that all the seven values which cover intervals of one third of an hour in length to 31 days in length (thus from singlefold to 2,000fold) may with tolerable approximation be put into a rather simple mathematical formula. I call:

t the time in minutes counting from one minute before the end of the learning,

b the saving of work evident in relearning, the equivalent of the amount remembered from the first learning expressed in percentage of the time necessary for this first learning,

c and k two constants to be defined presently

Then the following formula may be written:

$\scriptstyle b={\tfrac {100\ k}{(\log t)^{c}+k}}$

By using common logarithms and with merely approximate estimates, not involving exact calculation by the method of least squares,

k=1.84

c=1.25

Then the results are as follows:

t	b Observed	b Calculated	δ
20	58.2	57.0	+1.2
64	44.2	46.7	-2.5
526	35.8	34.5	+1.3
1440	33.7	30.4	+3.3
2×1440	27.8	28.1	-0.3
6×1440	25.4	24.9	+0.5
31×1440	21.1	21.2	-0.1

The deviations of the calculated values from the observed values surpass the probable limits of error only at the second and fourth values. With regard to the latter I have already expressed the conjecture that the test might have given here too large a value; the second suffers from an uncertainty concerning the correction made. By the determination made for t, the formula has the advantage that it is valid for the moment in which the learning ceases and that it gives correctly b=100. In the moment when the series can just be recited, the relearning, of course, requires no time, so that the saving is equal to the work expended.

Solving the formula for k we have

⁠$\scriptstyle k={\tfrac {b\ (\log t)^{c}}{100-b}}$

This expression, 100—b the complement of the work saved, is nothing other than the work required for relearning, the equivalent of the amount forgotten from the first learning. Calling this, v, the following simple relation results:

⁠$\scriptstyle {\tfrac {b}{v}}={\tfrac {k}{(\log t)^{c}}}$

To express it in words: when nonsense series of 13 syllables each were memorised and relearned after different intervals, the quotients of the work saved and the work required were about inversely proportional to a small power of the logarithm of those intervals of time. To express it more briefly and less accurately: the quotients of the amounts retained and the amounts forgotten were inversely as the logarithms of the times.

Of course this statement and the formula upon which it rests have here no other value than that of a shorthand statement of the above results which have been found but once and under the circumstances described. Whether they possess a more general significance so that, under other circumstances or with other individuals, they might find expression in other constants I cannot at the present time say.

Section 30. Control Tests

At any rate, even though only for my own case, I can to a certain extent give support to two of the values mentioned by tests which were made at other periods.

From a period even further back than that of the investigations above mentioned I possess several tests with series of ten syllables, fifteen series composing one test. The series were first memorised and then, at an average of 18 minutes after the first learning, each series was relearned. Six tests had the following results:—

L	LW	δ	Q[* 1]
848	436	412	57.5
963	535	428	50.9
921	454	467	58.5
879	444	435	57.5
912	443	469	59.4
821	461	360	51.6
m=891	462	429	56.0 P.E.m=1
The time subtracted from the L when calculating the Q for two reproductions of 15 series is 123 seconds.

When relearning series of ten syllables each, 18 minutes after the first memorisation, 56 per cent of the work originally expended was therefore saved. The number agrees satisfactorily with the one found above (p. 68) for the relearning of series of syllables of 13 syllables each after 19 minutes, 58 per cent. Also the fact that the latter, notwithstanding the longer interval, is still a little greater, harmonises completely, as will be seen, with the results of the next chapter. According to them, shorter series, when memorised, are forgotten a little more quickly than longer ones.

From the period of 1883-84, I have seven tests, consisting of nine series of 12 syllables each that were relearned 24 hours after the first memorisation. The following results were obtained:

L	LW	δ	Q
791	508	283	37.9
750	522	228	32.3
911	533	378	43.6
725	494	231	33.9
783	593	190	27.1
879	585	294	35.2
689	535	154	23.9
m⁠790	539	251	33.4 P.E.m=1.7

The after-effect of the first memorisation still noticeable after 24 hours, was here equivalent to a saving of work of 33.4 per cent of the first expenditure. This number also agrees satisfactorily with the one communicated above for the relearning of series of 13 syllables each after 24 hours (33.7 per cent), although these two were obtained at far separated time-periods and in the course of widely different investigations.

   

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Footnotes

1. This is the opinion of Aristotle and is still authoritative for many people. Lately, for instance, Delboeuf has taken it up again, and has used it as a complement to his “théorie générale de la sensibilité.” In his article, Le sommeil et les rêves (Rev. Philos. IX, p. 153 f.), he says: “Nous voyons maintenant que tout acte de sentiment, de pensée ou de volition en vertu d’une loi universelle imprime en nous une trace plus ou moins profonde, mais indélébile, généralement gravée sur une infinité de traits antérieurs, surchargée plus tard d’une autre infinité de linéaments de toute nature, mais dont l’écriture est néanmoins indéfiniment susceptible de reparaître vive et nette au jour.” (We see now that by a general law every act of feeling, thought or will leaves a more or less deep but indelible impress upon our mind, that such a tracing is usually graven upon an infinite number of previous traces and later is itself overlaid with innumerable others but nevertheless is still capable of vivid and clear reappearance.) It is true that he proceeds: “néanmoins…il y a quelque vérité dans l’opinion qui veut que la mémoire non seulement se fatigue mais s’oblitère” (nevertheless…there is some truth in the opinion that memory not only becomes fatigued but that it disappears”), but he explains this by the theory that one memory might hinder another from appearing. “Si un souvenir ne chasse pas l’autre, on peut du moins prétendre qu’un souvenir empeche l’autre et qu’ainsi pour la substance cérébrale, chez l’individu, il y a un maximum de saturation.” (If one recollection does not actually drive out another, it may at least be maintained that one recollection hinders the other and that thus the brain of each individual is saturated.)

   The curious theory of Bain and others that each idea is lodged in a separate ganglion cell, an hypothesis impossible both psychologically and physiologically, is also rooted to a certain extent in Aristotle’s view.

2. Herbart and his adherents. See, for instance, Waitz, Lehrbuch der Psychologie Sect. 16.
3. Lotze, Metaphysik (1879), p. 521; also Mikrokosmos (3) I, p. 231 ff.
4. A theoretically correct determination of the Probable Errors of the differences and quotients found would be very difficult and troublesome. The directly observed values L and WL would have to be made the basis of it. But the ordinary rules of the theory of errors cannot he applied to these values, because these rules are valid only for observations gained independently of one another, whereas L and WL are inwardly connected because they were obtained from the same series. The source of error, “difficulty of the series,” does not vary by chance, but in the same way for each pair of values. Therefore I took here the learning and relearning of the series as a single test and the resulting Δ or Q, as the case may be, as its numerical representative. From the independently calculated Δ and Q, the probable errors were then calculated just as from directly observed values. That is sufficient for an approximate estimate of the reliability of the numbers.