Chapter X: Section II: showed that the shorter filled distances are (6)

We have now reviewed all the phenomena so far enumerated of the illusion-bands, and for every case we have identified these bands with the bands which must be generated on the retina by the mere concealment of the rotating sectors by the moving rod. It has been more feasible thus far to treat these deduction-bands as if possibly they were other than the bands of the illusion; for although the former must certainly appear on the retina, yet it was not clear that the illusion-bands did not involve additional and complicated retinal or central processes. The showing that the two sets of bands have in every case identical properties, shows that they are themselves identical. The illusion-bands are thus explained to be due merely to the successive concealment of the sectors of the disc as each passes in turn behind the moving pendulum. The only physiological phenomena involved in this explanation have been the persistence as after-images of retinal stimulations, and the summation of these persisting images into characteristic effects--both familiar phenomena.

From this point on it is permissible to simplify the point of view by accounting the deduction-bands and the bands of the illusion fully identified, and by referring to them under either name indifferently. Figs. 1 to 9, then, are diagrams of the bands which we actually observe on the rotating disc. We have next briefly to consider a few special complications produced by a greater breadth or slower movement of the rod, or by both together. These conditions are called 'complicating' not arbitrarily, but because in fact they yield the bands in confusing form. If the rod is broad, the bands appear to overlap; and if the rod moves back and forth, at first rapidly but with decreasing speed, periods of mere confusion occur which defy description; but the bands of the minor color may be broader or _may be narrower_ than those of the other color.

VII. FURTHER COMPLICATIONS OF THE ILLUSION.

9. If the rod is broad and moves slowly, the narrower bands are like colored, not with the broader, as before, but with the narrower sector.

The conditions are shown in Fig. 9. From 1 to 2 the deduction is increasingly green, and yet the remainder of the characteristic effect is also mostly green at 1, decreasingly so to the right, and at 2 is preponderantly red; and so on to 8; while a like consideration necessitates bands from _x_ to 16. All the bands are in a sense transition-bands, but 1-2 will be mostly green, 2-3 mostly red, and so forth. Clearly the widths of the bands will be here proportional to the widths of the like-colored sectors, and not as before to the oppositely colored.

It may reasonably be objected that there should be here no bands at all, since the same considerations would give an increasingly red band from _B'_ to _A'_, whereas by hypothesis the disc rotates so fast as to give an entirely uniform color. It is true that when the characteristic effect is _A' A_ entire, the fusion-color is so well established as to assimilate a fresh stimulus of either of the component colors, without itself being modified. But on the area from 1 to 16 the case is different, for here the fusion-color is less well established, a part of the essential colored units having been replaced by black, the color of the rod; and black is no stimulation. So that the same increment of component color, before ineffective, is now able to modify the enfeebled fusion-color.

Observation confirms this interpretation, in that band _y-1_ is not red, but merely the fusion-color slightly darkened by an increment of black. Furthermore, if the rod is broad and slow in motion, but white instead of black, no bands can be seen overlying the rod. For here the small successive increments which would otherwise produce the bands 1-2, 2-3, etc., have no effect on the remainder of the fusion-color plus the relatively intense increment of white.

It may be said here that the bands 1-2, 2-3, etc., are less intense than the bands _x_-9, 9-10, etc., because there the recent or weighted unit-effects are black, while here they are the respective colors. Also the bands grow dimmer from _x_-9 to 15-16, that is, as they become older, for the small increment of one color which would give band 15-16 is almost wholly overridden by the larger and fresher mass of stimulation which makes for mere fusion. This last is true of the bands always, whatever the rate or width of the rod.

10. In general, equal sectors give equal bands, but if one sector is considerably more intense than the other, the bands of the brighter color will, for a broad and swiftly-moving rod, be the broader. The brighter sector, though equal in width to the other, contributes more toward determining the fusion-color; and this fact is represented by an intrusion of the stronger color into the transition-bands, at the expense of the weaker. For in these, even the decreased amount of the stronger color, on the side next a strong-color band, is yet more potent than the increased amount of the feebler color. In order to observe this fact one must have the rod broad, so as to give a broad transition-band on which the encroachment of the stronger color may be evident. The process is the same with a narrow rod and narrow transition-bands, but, being more limited in extent, it is less easily observed. The rod must also move rapidly, for otherwise the bands overlap and become obscure, as will be seen in the next paragraph.

11. If the disc consists of a broad and narrow sector, and if the rod is broad and moves at first rapidly but more slowly with each new stroke, there are seen at first broad, faint bands of the minority-color, and narrow bands of the majority-color. The former grow continuously more intense as the rod moves more slowly, and grow narrower in width down to zero; whereupon the other bands seem to overlap, the overlapped part being doubly deep in color, while the non-overlapped part has come to be more nearly the color of the minor sector. The overlapped portion grows in width. As the rate of the rod now further decreases, a confused state ensues which cannot be described. When, finally, the rod is moving very slowly, the phenomena described above in paragraph 9 occur.

The successive changes in appearance as the rod moves more and more slowly, are due to the factors previously mentioned, and to one other which follows necessarily from the given conditions but has not yet been considered. This is the last new principle in the illusion which we shall have to take up. Just as the transition-bands are regions where two pure-color bands overlap, so, when the rod is broad and moves slowly, other overlappings occur to produce more complicated arrangements.

These can be more compactly shown by diagram than by words. Fig. 10, _a_, _b_ and _c_ (Plate VI.), show successively slower speeds of the rod, while all the other factors are the same. In practice the tendency is to perceive the transition-bands as parts of the broad faint band of the minor color, which lies between them. It can be seen, then, how the narrow major-color bands grow only slightly wider (Fig. 10, _a_, _b_) until they overlap (_c_); how the broad minor-color bands grow very narrow and more intense in color, there being always more of the major color deducted (in _b_ they are reduced exactly to zero, _z_, _z_, _z_). In _c_ the major-color bands overlap (_o_, _o_, _o_) to give a narrow but doubly intense major-color band since, although with one major, two minor locus-bands are deducted. The other bands also overlap to give complicated combinations between the _o_-bands. These mixed bands will be, in part at least, minor-color bands (_q_, _q_, _q_), since, although a minor locus-band is here deducted, yet nearly two major locus-bands are also taken, leaving the minor color to predominate. This corresponds with the observation above, that, '... the non-overlapped part has come to be more nearly the color of the minor sector.'

A slightly slower speed of the rod would give an irreducible confusion of bands, since the order in which they overlap becomes very complicated. Finally, when the rod comes to move very slowly, as in Fig. 9, the appearance suffers no further change, except for a gradual narrowing of all the bands, up to the moment when the rod comes to rest.

It is clear that this last principle adduced, of the multiple overlapping of bands when the rod is broad and moves slowly, can give for varying speeds of the rod the greatest variety of combinations of the bands. Among these is to be included that of no bands at all, as will be understood from Fig. 11 (Plate VII). And in fact, a little practice will enable the observer so to adjust the rate of the (broad) rod to that of the disc that no bands are observable. But care must be taken here that the eye is rigidly fixated and not attracted into movement by the rod, since of course if the eye moves with the rod, no bands can be seen, whatever the rate of movement may be.

Thus, all the phenomena of these illusion-bands have been explained as the result solely of the hiding by the rod of successive sectors of the disc. The only physiological principles involved are those (1) of the duration of after-images, and (2) of their summation into a characteristic effect. It may have seemed to the reader tedious and unnecessary so minutely to study the bands, especially the details last mentioned; yet it was necessary to show how _all_ the possible observable phenomena arise from the purely geometrical fact that sectors are successively hidden. Otherwise the assertions of previous students of the illusion, that more intricate physiological processes are involved, could not have been refuted. The present writer does not assert that no processes like contrast, induction, etc., come into play to modify somewhat the saturation, etc., of the colors in the bands. It must be here as in every other case of vision. But it is now demonstrated that these remoter physiological processes contribute nothing _essential_ to the illusion. For these could be dispensed with and the illusion would still remain.

If any reader still suspects that more is involved than the persistence of after-images, and their summation into a characteristic effect, he will find it interesting to study the illusion with a camera. The 'physiological' functions referred to belong as well to the dry-plate as to the retina, while the former exhibits, presumably, neither contrast nor induction. The illusion-bands can be easily photographed in a strong light, if white and black sectors are used in place of colored ones. It is best to arrange the other variable factors so as to make the transition-bands as narrow as possible (p. 174, No. 4). The writer has two negatives which show the bands very well, although so delicately that it is not feasible to try to reproduce them.

VIII. SOME CONVENIENT DEVICES FOR EXHIBITING THE ILLUSION.

The influence of the width of sector is prettily shown by a special disc like that shown in Fig. 12 (Plate VII.), where the colors are dark-red and light-green, the shaded being the darker sector. A narrow rod passed before such a disc by hand at a moderate rate will give over the outer ring equally wide green and red bands; but on the inner rings the red bands grow narrower, the green broader.

The fact that the bands are not 'images of the rod' can be shown by another disc (Fig. 13, Plate VII.). In all three rings the lighter (green) sector is 60° wide, but disposed on the disc as shown. The bands are broken into zigzags. The parts over the outer ring lag behind those over the middle, and these behind those over the inner ring--'behind,' that is, farther behind the rod.

Another effective variation is to use rods alike in color with one or the other of the sectors. Here it is clear that when the rod hides the oppositely-colored sector, the deduction of that color is replaced (not by black, as happens if the rod is black) but by the very color which is already characteristic of that band. But when the rod hides the sector of its own color, the deduction is replaced by the very same color. Thus, bands like colored with the rod gain in depth of tone, while the other pure-color bands present simply the fusion-color.

IX. A STROBOSCOPE WHICH DEPENDS ON THE SAME PRINCIPLE.

If one produce the illusion by using for rod, not the pendulum of a metronome, but a black cardboard sector on a second color-mixer placed in front of the first and rotating concentrically with it, that is, with the color-disc, one will observe with the higher speeds of the rod which are now obtainable several further phenomena, all of which follow simply from the geometrical relations of disc and rod (now a rotating sector), as discussed above. The color-mixer in front, which bears the sector (let it still be called a 'rod'), should rotate by hand and independently of the disc behind, whose two sectors are to give the bands. The sectors of the disc should now be equal, and the rod needs to be broader than before, say 50° or 60°, since it is to revolve very rapidly.

First, let the rod and disc rotate in the same direction, the disc at its former rate, while the rod begins slowly and moves faster and faster. At first there is a confused appearance of vague, radial shadows shuffling to and fro. This is because the rod is broad and moves slowly (cf. p. 196, paragraph II).

As the velocity of the rod increases, a moment will come when the confusing shadows will resolve themselves into four (sometimes five) radial bands of one color with four of the other color and the appropriate transition-bands between them. The bands of either color are symmetrically disposed over the disc, that is, they lie at right angles to one another (if there are five bands they lie at angles of 72°, etc.). But this entire system of bands, instead of lying motionless over the disc as did the systems hitherto described, itself rotates rapidly in the opposite direction from disc to rod. As the rod rotates forward yet faster, no change is seen except that the system of bands moves backward more and more slowly. Thus, if one rotate the rod with one's own hand, one has the feeling that the backward movement of the bands is an inverse function of the increase in velocity of the rod. And, indeed, as this velocity still increases, the bands gradually come to rest, although both the disc and the rod are rotating rapidly.

But the system of bands is at rest for only a particular rate of the rod. As the latter rotates yet faster, the system of bands now commences to rotate slowly forward (with the disc and rod), then more and more rapidly (the velocity of the rod still increasing), until it finally disintegrates and the bands vanish into the confused flicker of shadows with which the phenomenon commenced.

This cycle now plays itself off in the reverse order if the speed of the rod is allowed gradually to decrease. The bands appear first moving forward, then more slowly till they come to rest, then moving backward until finally they relapse into confusion.

But let the rate of the rod be not decreased but always steadily increased. The bands will reappear, this time three of each color with six transition-bands. As before, the system at first rotates backward, then lies still, and then moves forward until it is dissolved. As the rod moves still faster, another system appears, two bands of each color forming a diameter and the two diameters lying at right angles. This system goes through the same cycle of movements. When the increased velocity of the rod destroys this system, another appears having one band of each color, the two lying on opposite sides of the center. The system goes through the same phases and is likewise dissolved. Now, at this point the rod will be found to be rotating at the same speed as the disc itself.

The explanation of the phenomenon is simple. The bands are not produced by a single interruption of the vision of a sector by a rod, but each band is made up of successive superpositions on the retina of many such single-interruption bands. The overlapping of bands has been already described (cf. Fig. 10 and pp. 196-198); superposition depends of course on the same principle.

At the moment when a system of four bands of either color is seen at rest, the rod is moving just one fifth as rapidly as the disc; so that, while the rod goes once around, either sector, say the green one, will have passed behind it exactly four times, and at points which lie 90° apart. Thus, four red bands are produced which lie at right angles to one another. But the disc is revolving at least 24 times in a second, the rod therefore at least 4.8 times, so that within the interval of time during which successive stimuli still contribute to the characteristic effect the rod will have revolved several times, and with each revolution four red bands at right angles to one another will have been formed. And if the rod is moving _exactly_ one fifth as fast as the disc, each new band will be generated at exactly that position on the disc where was the corresponding band of the preceding four. The system of bands thus appear motionless on the disc.

The movement of the system arises when the rate of the rod is slightly less or more than one fifth that of the disc. If slightly less, the bands formed at each rotation of the rod do not lie precisely over those of the previous rotation, but a little to the rear of them. The new set still lies mostly superposed on the previous sets, and so fuses into a regular appearance of bands, but, since each new increment lags a bit behind, the entire system appears to rotate backward. The apparatus is actually a cinematograph, but one which gives so many pictures in the second that they entirely fuse and the strobic movement has no trace of discontinuity.

If the rod moves a trifle more than one fifth as fast as the disc, it is clear that the system of bands will rotate forward, since each new set of bands will lie slightly ahead of the old ones with which it fuses. The farther the ratio between the rates of rod and disc departs from exactly 1:5, whether less or greater, the more rapid will the strobic movement, backward or forward, be; until finally the divergence is too great, the newly forming bands lie too far ahead or behind those already formed to fuse with them and so be apperceived as one system, and so the bands are lost in confusion. Thus the cycle of movement as observed on the disc is explained. As the rate of the rod comes up to and passes one fifth that of the disc, the system of four bands of each color forms in rapid backward rotation. Its movement grows slower and slower, it comes to rest, then begins to whirl forward, faster and faster, till it breaks up again.

The same thing happens as the rate of the rod reaches and exceeds just one fourth that of the disc. The system contains three bands of each color. The system of two bands of each color corresponds to the ratio 1:3 between the rates, while one band of each color (the two lying opposite) corresponds to the ratio 1:2.

If the rod and the disc rotate in opposite directions, the phenomena are changed only in so far as the changed geometrical relations require. For the ratio 1:3 between the two rates, the strobic system has four bands of each color; for 1:2, three bands of each color; while when the two rates are equal, there are two bands of each color, forming a diameter. As would be expected from the geometrical conditions, a system of one band of each color cannot be generated when rod and disc have opposite motions. For of course the rod cannot now hide two or more times in succession a sector at any given point, without hiding the same sector just as often at the opposite point, 180° away. Here, too, the cycle of strobic movements is different. It is reversed. Let the disc be said to rotate forward, then if the rate of the rod is slightly less than one fourth, etc., that of the disc, the system will rotate forward; if greater, it will rotate backward. So that as the rate of the rod increases, any system on its appearance will move forward, then stand still, and lastly rotate backward. The reason for this will be seen from an instant's consideration of where the rod will hide a given sector.

It is clear that if, instead of using as 'rod' a single radial sector, one were to rotate two or more such sectors disposed at equal angular intervals about the axis, one would have the same strobic phenomena, although they would be more complicated. Indeed, a large number of rather narrow sectors can be used or, what is the same thing, a second disc with a row of holes at equal intervals about the circumference. The disc used by the writer had a radius of 11 inches, and a concentric ring of 64 holes, each 3/8 of an inch in diameter, lying 10 inches from the center. The observer looks through these holes at the color-disc behind. The two discs need not be placed concentrically.

When produced in this way, the strobic illusion is exceedingly pretty. Instead of straight, radial bands, one sees a number of brightly colored balls lying within a curving band of the other color and whirling backward or forward, or sometimes standing still. Then these break up and another set forms, perhaps with the two colors changed about, and this then oscillates one way or the other. A rainbow disc substituted for the disc of two sectors gives an indescribably complicated and brilliant effect; but the front disc must rotate more slowly. This disc should in any case be geared for high speeds and should be turned by hand for the sake of variations in rate, and consequently in the strobic movement.

It has been seen that this stroboscope is not different in principle from the illusion of the resolution-bands which this paper has aimed to explain. The resolution-bands depend wholly on the purely geometrical relations between the rod and the disc, whereby as both move the rod hides one sector after the other. The only physiological principles involved are the familiar processes by which stimulations produce after-images, and by which the after-images of rapidly succeeding stimulations are summed, a certain number at a time, into a characteristic effect.

* * * * *

STUDIES IN MEMORY.

* * * * *

RECALL OF WORDS, OBJECTS AND MOVEMENTS.

BY HARVEY A. PETERSON.

Kirkpatrick,[1] in experimenting with 379 school children and college students, found that 3-1/3 times as many objects were recalled as visual words after an interval of three days. The experiment consisted in showing successively 10 written names of common objects in the one case and 10 objects in the other at the rate of one every two seconds. Three days later the persons were asked to recall as many of each series as possible, putting all of one series together. The averages thus obtained were 1.89 words, 6.29 objects. The children were not more dependent on the objects than the college students.

[1] Kirkpatrick, E.A.: PSYCHOLOGICAL, REVIEW, 1894, Vol. I., p.
602.

Since the experiment just described was performed without laboratory facilities, Calkins[2] repeated it with 50 college women, substituting lantern pictures for objects. She obtained in recall, after two days, the averages 4.82 words, 7.45 pictures. The figures, however, are the number of objects or words remembered out of ten, not necessarily correctly placed. Kirkpatrick's corresponding figures for college women were 3.22 words, 5.44 objects. The two experiments substantially agree, Calkins' higher averages being probably due to the shortening of the interval to two days.

[2] Calkins, M.W.: PSYCHOLOGICAL, REVIEW, 1898, Vol. V., p.
451.

Assuming, thus, that objects are better remembered than names in deferred recall, the question arises whether this holds true when the objects and names are coupled with strange and arbitrary symbols--a question which is clearly of great practical interest from the educational point of view, as it is involved in the pedagogical problem whether a person seeking to acquire the vocabulary of a foreign language ought to connect the foreign words with the familiar words or with the objects themselves. And the further question arises: what are the facts in the case of movements instead of objects, and correspondingly in that of verbs instead of nouns. Both questions are the problems of the following investigation.

As foreign symbols, either the two-figure numbers were used or nonsense-words of regularly varying length. As familiar material, nouns, objects, verbs and movements were used. The words were always concrete, not abstract, by which it is meant that their meaning was capable of demonstration to the senses. With the exception of a few later specified series they were monosyllabic words. The nouns might denote objects of any size perceptible to the eye; the objects, however, were all of such a size that they could be shown through a 14×12 cm. aperture and still leave a margin. Their size was therefore limited.

Concerning the verbs and movements it is evident that, while still being concrete, they might be simple or complicated activities consuming little or much time, and further, might be movements of parts of the body merely, or movements employing other objects as well. In this experiment complicated activities were avoided even in the verb series. Simple activities which could be easily and quickly imaged or made were better for the purpose in view.

THE _A_ SET.

The _A_ set contained sixteen series, _A_^{1}, _A_^{2}, _A_^{3}, etc., to _A_^{16}. They were divided as follows:

Numbers and nouns: _A_^{1}, _A_^{5}, _A_^{9}, _A_^{13}.
Numbers and objects: _A_^{2}, _A_^{6}, _A_^{10}, _A_^{14}.
Numbers and verbs: _A_^{3}, _A_^{7}, _A_^{11}, _A_^{15}.
Numbers and movements: _A_^{4}, _A_^{8}, _A_^{12}, _A_^{16}.

The first week _A_^{1-4} were given, the second week _A_^{5-8}, etc., so that each week one series of each of the four types was given the subject.

In place of foreign symbols the numbers from 1 to 99 were used, except in _A_^{13-15}, in which three-figure numbers were used.

Each series contained seven couplets, except _A_^{13-16}, which, on account of the greater difficulty of three-figure numbers, contained five. Each couplet was composed of a number and a noun, object, verb, or movement.

Certain rules were observed in the composition of the series. Since the test was for permanence, to avoid confusion no number was used in more than one couplet. No two numbers of a given series were chosen from the same decade or contained identical final figures. No word was used in more than one couplet. Their vowels, and initial and final consonants were so varied within a single series as to eliminate phonetic aids, viz., alliteration, rhyme, and assonance. The kind of assonance avoided was identity of final sounded consonants in successive words, _e.g._, lane, vine.

The series were composed in the following manner: After the twenty-eight numbers for four series had been chosen, the words which entered a given series were selected one from each of a number of lists of words. These lists were words of like-sounded vowels. After one word had been chosen from each list, another was taken from the first list, etc. As a consequence of observing the rules by which alliteration, rhyme, and assonance were eliminated, the words of a series usually represented unlike categories of thought, but where two words naturally tended to suggest each other one of them was rejected and the next eligible word in the same column was chosen. The following is a typical series from the _A_ set.

_A_^{1}. Numbers and Nouns.

19 42 87 74 11 63 38
desk girl pond muff lane hoop vine

The apparatus used in the _A_ set and also in all the later sets may be described as follows: Across the length of a table ran a large, black cardboard screen in the center of which was an oblong aperture 14 cm. high and 12 cm. wide. The center of the aperture was on a level with the eyes of the subject, who sat at the table. The aperture was opened and closed by a pneumatic shutter fastened to the back of the screen. This shutter consisted of two doors of black cardboard sliding to either side. By means of a large bulb the length of exposure could be regulated by the operator, who stood behind the table.

The series--consisting of cards 4×2½ cm., each containing a printed couplet--was carried on a car which moved on a track behind and slightly below the aperture. The car was a horizontal board 150 cm. long and 15 cm. wide, fixed on two four-wheeled trucks. It was divided by vertical partitions of black cardboard into ten compartments, each slightly wider than the aperture to correspond with the visual angle. A curtain fastened to the back of the car afforded a black background to the compartments. The couplets were supported by being inserted into a groove running the length of the car, 3 cm. from the front. A shutter 2 cm. high also running the length of the car in front of the groove, fastened by hinges whose free arms were extensible, concealed either the upper or the lower halves of the cards at the will of the operator; _i.e._, either the foreign symbols or the words, respectively. A screen 15 cm. high and the same length as the car, sliding in vertical grooves just behind the cards and in front of the vertical partitions, shut off the objects when desired, leaving only the cards in view. Thus the apparatus could be used for all four types of series.

The method of presentation and the time conditions of the _A_ set were as follows:--A metronome beating seconds was used. It was kept in a sound-proof box and its loudness was therefore under control. It was just clearly audible to both operator and subject. In learning, each couplet was exposed 3 secs., during about 2 secs. of which the shutter was fully open and motionless. During this time the subject read the couplet inaudibly as often as he wished, but usually in time with the metronome. His object was to associate the terms of the couplet. There was an interval of 2 secs. after the exposure of each couplet, and this was required to be filled with repetition of only the _immediately preceding couplet_. After the series had been presented once there was an interval of 2 secs. additional, then a second presentation of it commenced and after that a third. At the completion of the third presentation there was an interval of 6 secs. additional instead of the 2, at the expiration of which the test commenced.

_A_^{13-16} had five presentations instead of three. The test consisted in showing the subject either the numbers or the words in altered order and requiring him to write as many of the absent terms as he could. In the object and movement series the objects were also shown and the movements repeated by the subject if words were the given terms. The time conditions in the test were,

Exposure of a term 3 secs.
Post-term interval in A^{1-12} 4 secs.
Post-term interval in A^{13-16} 6 secs.

This allowed the subject 7 secs. for recalling and writing each term in A^{1-12} and 9 sec. in A^{13-16}. If a word was recalled after that time it was inserted, but no further insertions were made after the test of a series had been completed. An interval of 3 min. elapsed between the end of the test of one series and the beginning of the next series, during which the subject recorded the English word of any couplet in which an indirect association had occurred, and also his success in obtaining visual images if the series was a noun or a verb series.

As already indicated, four series--a noun, an object, a verb, and a movement series--given within a half hour, constituted a day's work throughout the year. Thus variations due to changes in the physiological condition of the subject had to affect all four types of series.

Two days later these series were tested for permanence, and in the same way as the tests for immediate recall, with this exception:

Post-term interval in A^{13-16} 8 secs.

Thus 11 secs. were allowed for the deferred recall of each term in A^{13-16}.

In the movement series of this set, to avoid hesitation and confusion, the operator demonstrated to the subject immediately before the series began, once for each word, how the movements were to be made.

The _A_ set was given to three subjects. The results of each subject are arranged separately in the following table. In the tests the words were required in A^{1-4}, in A^{5-16} the numbers. The figures show the number of terms correctly recalled out of seven couplets in A^{1-12} and out of five couplets in A^{13-16}, _exclusive_ of indirect association couplets. The figures in brackets indicate the number of correctly recalled couplets per series in which indirect associations occurred. The total number correctly recalled in any series is their sum. The figures in the per cent. row give the percentage of correctly recalled couplets left after discarding both from the number recalled and from the total number of couplets given those in which indirect associations occurred. This simply diminished the subject's number of chances. A discussion of the propriety of this elimination will be found later. In _A_^{1-12} the absent terms had to be recalled exactly in order, to be correct, but in _A_^{13-16}, on account of the greater difficulty of the three-place numbers, any were considered correct when two of the three figures were recalled, or when all three figures were correct but two were reversed in position, _e.g._, 532 instead of 523. _N_ means noun series, _O_ object, _V_ verb, and _M_ movement series. Series _A_^{1}, _A_^{5}, _A_^{9}, _A_^{13} are to be found in the first and third columns, _A_^{2}, _A_^{6}, _A_^{10}, _A_^{14} in the second and fourth, _A_^{3}, _A_^{7}, _A_^{11}, _A_^{15}, in the fifth and seventh, and _A_^{4}, _A_^{8}, _A_^{12}, _A_^{16} in the sixth and eighth columns.

TABLE I.

SHOWING IMMEDIATE RECALL AND RECALL AFTER TWO DAYS.

_M_.
Series. Im. Rec. Two Days. Im. Rec. Two Days.
N. O. N. O. V. M. V. M.
A^{1-4} 6 7 3 1 6 7 2 1
A^{5-8} 5(1) 6 3(1) 6 6(1) 7 5(1) 6
A^{9-12} 7 7 4 6 7 6(1) 7 6(1)
A^{13-16} 4 5 2 2 5 3 2 2
Total. 22(1) 25 12(1) 15 24(1) 23(1) 16(1) 15(1)
Per cent. 88 96 48 58 96 92 64 66

_S_.
Series. Im. Rec. Two Days. Im. Rec. Two Days.
N. O. N. O. V. M. V. M.
A^{1-4} 6(1) 6 0 0 7 7 0 0
A^{5-8} 6 7 1 3 6 7 0 3
A^{9-12} 7 6 2 2 5 7 0 0
A^{13-16} 5 5 0 0 5 5 3 0
Total. 24(1) 24 3 5 23 26 3 3
Per cent. 96 92 12 19 88 100 12 12

_Hu_.
Series. Im. Rec. Two Days. Im. Rec. Two Days.
N. O. N. O. V. M. V. M.
A^{1-4} 6 7 0 1 5 6(1) 0 2
A^{5-8} 5(2) 7 1(2) 1 7 7 1 0
A^{9-12} 6(1) 7 2 2 6 7 0 5
A^{13-16} 4(1) 4(1) 0 2 5 5 0 1
Total. 21(4) 25(1) 3(2) 6 23 25(1) 1 8
Per cent. 95 100 14 24 88 100 4 32

These results will be included in the discussion of the results of the _B_ set.

THE _B_ SET.

A new material was needed for foreign symbols. After considerable experimentation nonsense words were found to be the best adapted for our purpose. The reasons for this are their regularly varying length and their comparative freedom from indirect associations. An objection to using nonsense syllables in any work dealing with the permanence of memory is their sameness. On this account they are not remembered long. To secure a longer retention of the material, nonsense words were devised in substantially the same manner as that in which Müller and Schumann made nonsense syllables, except that these varied regularly in length from four to six letters. Thus the number of letters, not the number of syllables was the criterion of variation, though of course irregular variation in the number of syllables was a necessary consequence.

When the nonsense words were used it was found that far fewer indirect associations occurred than with nonsense syllables. By indirect association I mean the association of a foreign symbol and its word by means of a third term suggested to the subject by either of the others and connected at least in _his_ experience with both. Usually this third term is a word phonetically similar to the foreign symbol and ideationally suggestive of the word to be associated. It is a very common form of mnemonic in language material. The following are examples:

cax, stone (Caxton);
teg, bib (get bib);
laj, girl (large girl);
xug, pond (noise heard from a pond);
gan, mud (gander mud).

For both of these reasons nonsense words were the material used as foreign symbols in the _B_ set.

The nonsense words were composed in the following manner. From a box containing four of each of the vowels and two of each of the consonants the letters were chosen by chance for a four-letter, a five-letter, and a six-letter word in turn. The letters were then returned to the box, mixed, and three more words were composed. At the completion of a set of twelve any which were not readily pronounceable or were words or noticeably suggested words were rejected and others composed in their places.

The series of the _B_ set were four couplets long. Each series contained one three-letter, one four-letter, one five-letter, and one six-letter nonsense word. The position in the series occupied by each kind was constantly varied. In all other respects the same principles were followed in constructing the _B_ set as were observed in the _A_ set with the following substitutions:

No two foreign symbols of a series and no two terms of a couplet contained the same sounded vowel in accented syllables.

The rule for the avoidance of alliteration, rhyme, and assonance was extended to the foreign symbols, and to the two terms of a couplet.

The English pronounciation was used in the nonsense words. The subjects were not informed what the nonsense words were. They were called foreign words.

Free body movements were used in the movement series as in the _A_ set. Rarely an object was involved, _e.g._, the table on which the subject wrote. The movements were demonstrated to the subject in advance of learning, as in the _A_ set.

The following are typical _B_ series:

B2. Nonsense words and objects.

quaro rudv xem lihkez
lid cent starch thorn

B3. Nonsense words and verbs.

dalbva fomso bloi kyvi
poke limp hug eat

B4. Nonsense words and movements.

ohv wecolu uxpa haymj
gnash cross frown twist

The time conditions for presenting a series remained practically the same. In learning, the series was shown three times as before. The interval between learning and testing was shortened to 4 seconds, and in the test the post-term interval of _A^{13-16}_ retained (6 secs.). This allowed the subject 9 secs. for recalling and writing each term. The only important change was an extension of the number of tests from two to four. The third test was one week after the second, and the fourth one week after the third. In these tests the familiar word was always the term required, as in _A^{1-4}_, on account of the difficulty of dealing statistically with the nonsense words. The intervals for testing permanence in the _B_ set may be most easily understood by giving the time record of one subject.

TIME RECORD OF _Hu_.

Series. Im. Rec. Two Days. Nine Days. Sixteen Days.
B^{1-4} Feb. 12 Feb. 14 Feb. 21 Feb. 28
B^{5-8} Feb. 19 Feb. 21 Feb. 28 Mch. 7
B^{9-12} Feb. 26 Feb. 28 Mch. 7 Mch. 14
B^{13-16} Mch. 5 Mch. 7 Mch. 14 Mch. 21

The two half-hours in a week during which all the work of one subject was done fell on approximately the same part of the day. When a number of groups of 4 series each were to be tested on a given day they were taken in the order of their recency of learning. Thus on March 7 the order for _Hu_ was B^{13-16}, B^{9-12}, B^{5-8}.

Henceforth there was also rotation within a given four series. As there were always sixteen series in a set, the effects of practice and fatigue within a given half-hour were thus eliminated.

In the following table the results of the _B_ set are given. Its arrangement is the same as in Table 1., except that the figures indicate the number of absent terms correctly recalled out of four couplets instead of seven or five. Where blanks occur, the series was discontinued on account of lack of recall. As in Table 1., the tables in the first, third and fifth columns show successive stages of the same series. Immediate recall is omitted because with rare exceptions it was perfect, the test being given merely as an aid in learning.

TABLE II.

SHOWING RECALL AFTER TWO, NINE, AND SIXTEEN DAYS.

Days. Two. Nine. Sixteen. Two. Nine. Sixteen.
N. O. N. O. N. O. V. M. V. M. V. M.
Series. _M._
B^{1-4} 2(1) 4 1(1) 2 1(1) 2 4 4 4 2 4 2
B^{5-8} 3 1 2 1 1 1 2 2 2 1 1 1
B^{9-12} 2 3 0 3 0 2 3 2 2 0 2 2
B^{13-16} 2(1) 3 2(1) 0 2(1) 0 1 2 1 0 1 0
Total 9(2) 11 5(2) 6 4(2) 5 10 10 9 3 8 5
Per cent. 64 69 36 38 29 31 63 63 56 19 50 31

_S._
B^{1-4}¹ 0 2 0 0 0 1 0 1
B^{5-8} 0 0 0 0
B^{9-12}¹ 0 1 0 0 0 1 0 0
B^{13-16}² 0(2) 1 0(2) 1 0(2) 1 0 0(1) 0 0(1) 0 0(1)
Total 0(2) 4 0(2) 1 0(2) 1 0 2(1) 0 1(1) 0 0(1)
Per cent. 0 25 0 6 0 6 0 13 0 7 0 0

_Hu._
B^{1-4} 1(1) 4 0(1) 1 0(1) 2 1 3 0 2 0 0
B^{5-8} 0 1(1) 0 0(1) 0 0(1) 0 1 0 1 0 1
B^{9-12} 0 1 0 0 0 1 0 0 0 1 0 0
B^{13-16} 0(1) 0 0(1) 0 0(1) 0 0 4 0 0 0 0
Total 1(2) 6(1) 0(2) 1(1) 0(2) 3(1) 1 8 0 4 0 1
Per cent. 7 40 0 7 0 20 6 50 0 25 0 6

_B._
B^{1-4} 1 1(1) 0 0 0 0(1) 0 0
B^{6-8} 1 2 1 2 1 1 1 0 1 0 1 0
B^{9-12} 0 2(1) 0 0(1) 0 0(1) 0(1) 2 0 2 0 1
B^{13-16} 1 3 1 1 1 1 1 2 0 1 0 1
Total 3 8(2) 2 3(1) 2 2(1) 2(1) 4(1) 1 3 1 2
Per cent. 19 57 13 21 13 13 13 27 7 20 7 13

_Ho._
B^{1-4}¹ 3 2(1) 2 2(1) 1 0(1) 1(2) 1(2) 1(2) 0(2) 0(2) 0(2)
B^{6-8} 1 1(1) 1 0(1) 1 0 0 1(1) 1 1 0 1
B^{9-12} 0(1) 1 0(1) 1 0(1) 0 1 1 1 1 0 0
B^{13-16}³ 0 0 0 0 0 0 0(1) 4 0(1) 2 0(1) 0
Total 4(1) 4(2) 3(1) 3(2) 2(1) 0(1) 2(3) 7(3) 3(3) 4(2) 0(3) 1(2)
Percent. 33 30 25 23 17 0 17 58 25 33 0 8

_Mo._
B^{1-4} 3 3 3 1 4 1 0 2 0 2 0 2
B^{5-8} 1 4 1 1 1 2 1 2(2) 1 1(2) 1 1(2)
B^{9-12} 2 4 2 4 1 4 0(1) 3(1) 1(1) 3(1) 1(1) 2
B^{13-16} 2(2) 4 2(2) 4 2(2) 2 1 4 1 4 1 4
Total 8(2) 15 8(2) 10 8(2) 9 2(1) 11(3) 3(1) 10(3) 3(1) 9(2)
Percent. 57 94 57 63 57 56 13 85 20 79 20 69

¹Four presentations in learning.
²Five presentations in learning.
³Five days' interval instead of two.

In the following summary the recall after two days is combined from Tables I. and II. for the three subjects _M_, _S_ and _Hu_, there being no important difference in the conditions of experimentation. For the three other subjects this summary is merely a résumé of Table II. The recall after nine and sixteen days in Table II. is omitted, and will be taken up later. The figures are in all cases based on the remainders left after those couplets in which indirect associations occurred were eliminated both from the total number of couplets learned and from the total number correctly recalled. _E.g._, in the case of nouns, _M_ learned, in all, 42 couplets in the _A_ and _B_ sets, but since in 3 of them indirect associations occurred, only 39 couplets are left, of which 21 were correctly recalled. This gives 54 per cent.

SUMMARY OF RECALL AFTER TWO DAYS.--FROM TABLES I. AND II.

N. O. V. M.
M. 54 per cent. 62 per cent. 63 per cent. 61 per cent.
S. 8 " 21 " 7 " 12 "
Hu. 11 " 30 " 5 " 59 "
B. 19 " 57 " 13 " 27 "
Ho. 33 " 30 " 17 " 58 "
Mo. 57 " 94 " 13 " 85 "
Av. 30 per cent. 49 per cent. 20 per cent. 50 per cent.

Av. gain in object couplets, 19 per cent.
" " " movement couplets, 30 per cent.

The first question which occurs in examining the foregoing tables is concerning the method of treating the indirect associations, _i.e._, obtaining the per cents. The number of couplets correctly recalled may be divided into two classes: those in which indirect associations did not occur, and those in which they did occur. Those in which they did not occur furnish us exactly what we want, for they are results which are entirely free from indirect associations. In them, therefore, a comparison can be made between series using objects and activities and others using images. On the other hand, those correctly recalled couplets in which indirect associations _did_ occur are not for our purposes pure material, for they contain not only the object-image factor but the indirect association factor also. The solution is to eliminate these latter couplets, _i.e._, subtract them both from the number correctly recalled and from the total number of couplets in the set for a given subject. By so doing and by dividing the first remainder by the second the per cents, in the tables were obtained. There is one exception to this treatment. The few couplets in which indirect associations occurred but which were nevertheless _incorrectly_ recalled are subtracted only from the total number of couplets in the set.

The method by which the occurrence of indirect associations was recorded has been already described. It is considered entirely trustworthy. There is usually little doubt in the mind of a subject who comprehends what is meant by an indirect association whether or not such were present in the particular series which has just been learned. If none occurred in it the subjects always recorded the fact. That an indirect association should occasionally be present on one day and absent on a subsequent one is not strange. That a second term should effect a union between a first and third and thereafter disappear from consciousness is not an uncommon phenomenon of association. There were thirteen such cases out of sixty-eight indirect associations in the _A_, _B_ and _C_ sets. In the tables they are given as present because their effects are present. When the reverse was the case, namely, when an indirect association occurred on the second, ninth or sixteenth day for the first time, it aided in later recall and was counted thereafter. There were eight such cases among the sixty-eight indirect associations.

Is it possible that the occurrence of indirect associations in, _e.g._, two of the four couplets of a series renders the retention of the other two easier? This could only be so when the intervals between two couplets in learning were used for review, but such was never the case. The subjects were required to fill such intervals with repetitions of the preceding couplet only.

The elimination of the indirect association couplets and the acceptance of the remainders as fair portrayals of the influence of objects and movements on recall is therefore a much nearer approach to truth than would be the retention of the indirectly associated couplets.

The following conclusions deal with recall after two days only. The recall after longer intervals will be discussed after Table III.

The summary from Tables I. and II. shows that when objects and nouns are coupled each with a foreign symbol, four of the six subjects recall real objects better than images of objects, while two, _M_ and _Ho_, show little or no preference. The summary also shows that when body movements and verbs are coupled each with a foreign symbol, five of the six subjects recall actual movements better than images of movements, while one subject, _M_, shows no preference. The same subject also showed no preference for objects. With the subjects _S_ and _B_ the preference for actual movements is not marked, and has importance only in the light of later experiments to be reported.

The great difference in the retentive power of different subjects is, as we should expect, very evident. Roughly, they may be divided into two groups. _M_ and _Mo_ recall much more than the other four. The small percentage of recall in the case of these four suggested the next change in the conditions of experimentation, namely, to shorten with them the intervals between the tests for permanence. This was accordingly done in the _C_ set. But before giving an account of the next set we may supplement these results by results obtained from other subjects.

It was impossible to repeat this set with the same subjects, and inconvenient, on account of the scarcity of suitable words, to devise another set just like it. Accordingly, the _B_ set was repeated with six new subjects. We may interpolate the results here, and then resume our experiments with the other subjects. The conditions remained the same as for the other subjects in all respects except the following. The tests after nine and sixteen days were omitted, and the remaining test for deferred recall was given after one day instead of after two. In learning the series, each series was shown four times instead of three. The results are summarized in the following table. The figures in the left half show the number of words out of sixteen which were correctly recalled. The figures in parentheses separate, as before, the correctly recalled indirect-association couplets. In the right half of the table the same results, omitting indirect-association couplets, are given in per cents, to facilitate comparison with the summary from Tables I. and II.

TABLE III.

SHOWING RECALL AFTER ONE DAY.

N. O. V. M. N. O. V. M.
Bur. 6 10(1) 7(1) 5(4) 38 67 44 31
W. 5(3) 12(1) 6 9 31 75 38 56
Du. 1 11(1) 8 9 6 69 50 56
H. 9(1) 14 8 12 56 88 50 75
Da. 1(3) 7(4) 3(1) 9(3) 7 44 20 56
R. 7(2) 3(3) 5 5(1) 44 19 31 31
Total, 29(9) 57(10) 37(2) 49(8) Av., 30 60 39 51

Av. gain in object couplets, 30 per cent.
" " " movement couplets, 12 per cent.

The table shows that five subjects recall objects better than images of objects, while one subject recalls images of objects better. Similarly, three subjects recall actual movements of the body better than images of the same, while with three neither type has any advantage.

THE _C_ SET.

In the _C_ set certain conditions were different from the conditions of the _A_ and _B_ sets. These changes will be described under three heads: changes in the material; changes in the time conditions; and changes in the method of presentation.

For lack of monosyllabic English words the verbs and movements were dissyllabic words. The nouns and objects were monosyllabic, as before. All were still concrete, and the movements, whether made or imaged, were still simple. But the movements employed objects, instead of being merely movements of the body.