PART II

The purpose of the latter half of this discussion of repetition is to consider a certain number of examples of its use in typical buildings of all the European styles of architecture from Greece down, and to show that the principles laid down in the earlier half have been expressed almost without exception in those of recognized merit. In other words it is to show that the laws of repetition, which have been brought out in the experiments of the first part, and which would of necessity be true if that explanation were correct, have indeed been exemplified in types of architecture universally accepted as beautiful.

The illustrations have all been drawn from architecture beginning with Greece, and not from the older Eastern styles. Egyptian architecture, although it recognized the importance of repetition to some extent, in its colonnades, avenues of sphinxes, and hieroglyphic decoration, never reduced it to any principle, nor adhered to any one scheme throughout a piece of work. Supports of the same kind and diameter have no fixed relation to each other, they may be of the same or different lengths, and may vary in diameter as well. Spaces between columns of one size and design may vary considerably, and the entablatures be of different proportions. The art of Egypt was not rhythmic.

The architecture of Assyria and Chaldea had even less of repeated forms in its style. They made but little use of columns or piers, and had few arches. The bare Assyrian edifice was like a great box, perpendicular to its foundations, and the long walls pierced by hardly an opening in the way of windows or doors.

Persian architecture was noted for extreme nicety of execution, but a monotony in all its forms, and conventionality about its use of the column, which makes it little more fruitful for our study of repetition as an artistic value. In its decorations of bas-relief, the pose and gesture of each figure is so exactly similar that they appear almost machine-made. When a little variety is introduced, it is evidently done with misgivings, and shows none of the spontaneity or first-hand pleasure in either repetition or variation which would make it profitable for illustration.

Such a lack of feeling for repetition is, indeed, according to the peculiar genius of these styles of architecture, what might have been expected. The ruling idea, especially in Egyptian and Assyrian architecture, was ponderous strength. Everything was built with the idea of remaining immoveable through centuries to come. The enormous temples and tombs, the long palaces with their heavy walls without an opening to relieve them, the pyramids themselves like mountains of rock--all these meant strength and immutability, to which the motion and rhythm involved in repetition was totally foreign in spirit. In Persia indeed (as well as India and China, which will not be considered here) there was a change in tone. The column was used, not the massive one of Egypt, but a lighter shaft, which showed a tendency toward other effects than immensity and strength.

With this change of ideal, repetition in some kind of system made its appearance, but its variations were tentative. It had not become used to its new sense, and it was left for Greece to develop the rhythm and movement of repetition, and to combine it with proportion and symmetry into its perfection.

The method of analysis employed has been to go through a certain number of architectural photographs, picking out all the examples of repeated forms of any description, and classifying them according to the principles which they exemplified or seemed to violate. For this purpose a collection of about five thousand photographs from the library of Robinson Hall, Harvard University, was analyzed. The photographs were taken in order of styles: Greek, Roman, Romanesque, Gothic, Italian and French Renaissance, and modern. The examples of the different points in question were taken as they came in the cataloguing of the library stacks, without respect to whether they appeared to bear out the previous conclusions or not.

VARIATION OF ALTERNATING UNITS

The first principle which we shall consider is the variation allowable in the units of an alternating series. It will be remembered that the principle was as follows: (1) In any series of two alternating units, the one on which the most energy is expended is regarded as the principal unit, the less important one as an alternate. Variation of the principal unit is allowable, often desirable and even necessary; variation of the alternate never allowable, unless other circumstances change the situation. If the minor unit is changed, so that in interest it equals the major unit, the rest-phase of the rhythm is destroyed, the effect is of two rival repetitions going along together, and fatigue results. If variation in the alternates exceeded that of the principal units, the balance of the rhythm would change, the alternate become the major unit, and a new series begin.

From the very nature of the case, then, it will be impossible to look for variations in alternates, which make it exceed the principal units in interest. We must investigate alternating series, in order to see if one of the elements remains the same, while the other may or may not vary. If this were true, a rest-phase for the rhythm would be assured in the series, while the principal unit might vary, provided the same amount of attention were required in each case. (2) It will also be remembered that size and limiting shape were the factors that could not vary without doing violence to the rhythm, while content might vary almost without restriction. (3) The position of alternating units as regards each other cannot vary; the two units are so dependent on each other that the position of one must remain halfway between two of the opposite kind. In other words, if the two series of units run between each other, they form one series or rhythm. Two rhythms cannot be kept up alongside; so if one unit, however regularly placed with regard to another of its own kind, recurs at unequal distances from the other units, the feeling of the repetition is lost, the rhythm broken, unless the two units can be grouped into one, and so make a single rhythm again.

We shall, then, look for alternating series, of which the two units are at equal and invariable distances from each other; the variations of content (if such there are) occur only in the major unit; and are of the filling, not of the including shape or size.

It may be readily seen that there are difficulties in finding alternating series which exactly illustrate this particular point, or in reducing them to any system. It was necessary to look through many photographs to find one that presented the required conditions (i. e., two repeated series of units, alternating with each other), and when found, they were of so many different varieties, from windows in an apse to reliefs on a fountain, that each has had to be described by itself, and any rigid classification was impossible. Moreover, it was difficult to find a scale of judgment by which to decide whether a series was really alternating or plain repetition. From one point of view, every repetition is alternating, that is, the repeated unit always alternates with an empty space. Although such repetitions bear out the theory still further, and emphasize yet more strongly the invariability of alternates, and the possibility of variations in the principal units, I have used the term in a stricter sense, and only given illustrations of repeated objects, when one unit actually alternated with another definite unit.

Had the other sense of the term been used, examples might have been multiplied without limit, of slightly varying repeated units, and unvarying alternate blank spaces. But it was felt that such accumulation of illustration was unnecessary, and that what was true in a stricter sense of the term would be recognized as true for the larger number of cases that might be cited with a wider meaning. If the minor units had a definite enclosing outline, they were counted even though they were blank within, but without an enclosing outline, that is, if they were mere spaces, they were not considered, although the fact that there is such universal use of this type of decoration shows only more conclusively how the necessity of the invariability of alternates is taken for granted as an axiom of design.

Another type of alternate repetition was not included in the illustrations, i. e., when two sets of units alternated, without variation in either one. To this class belong all the conventionalized designs used so much in all kinds of decoration, and of which a very full account is given in Owen Jones's Grammar of Ornament.

These, to be sure, illustrate the negative points, viz., that size and shape are unalterable for rhythmic repetition; that distances must be equal and invariable; and that alternate units must not vary. But since the principal units do not vary either, it seemed needless to give them as examples of the point in question. A mention of this class of alternating repetitions, of which there is such a great number, is enough to show that they fall within the theory. But one example is as good as a thousand, and their inclusion among the illustrations for rhythmic alternates will be taken for granted without further mention.

We are left, then, to the consideration of those alternating repetitions alone, where both have a definite outline, and one or both varies to a greater or lesser extent. The effort will be to show that the unit which for some reason is of principal importance in the rhythm, is the one chosen to vary, and if not that the repetition suffers thereby.

125 EXAMPLES

A. Variations in Principal Unit alone: 87.

I. Content alone:

a. Metopes and Tryglyphs in Friezes: 9. b. Arches and Columns: 2. c. Statues in niches alternating with supports: 37. d. Windows alternating with supports or decorations: 12. e. Paintings or mosaics: 7. f. Carved designs in screens or ceilings: 17.

II. Size and Content.

a. Doors, paintings and reliefs on façades. Vary in size to emphasize symmetry: 4. b. Statues or shields over arcades. Vary in size to complicate rhythm: 1.

B. Variations in Principal Unit AND Alternate: 37.

I. Content alone:

a. Windows and decorations on façades. Alternates vary in design to emphasize symmetry: 4. b. Windows and turrets. Vary alternately in design to complicate rhythm: 2. c. Reliefs alternating with tablets; reliefs or statues and pillars: Alternates vary in design to give richer effect: 11. d. Alternate unit is human figure: 9. e. Alternate unit varies in design, but is on a different level: 3. f. Irregular variation in alternates (windows, shields, and railings): 3.

II. Of Size of Alternate Unit.

a. Windows and supports. Vary in size to emphasize symmetry: 1. b. Statues and pillars; windows and pilasters. Alternates vary in size to complicate rhythm: 3. c. Vary in size irregularly. Disorder: 1.

C. Variation of Distance.

Row of windows--Distance between first two is wider: 1.

The 125 illustrations of alternating repetition which were taken at random among 5000 photographs show a decided compliance with the principles already laid down. But there are many divergences as well, which it is necessary to consider, to see whether they are really contrary in principle or fall under its wider application. Eighty-two accord exactly with the principles with which we started. The distances between each set of units are equal and invariable; one unit varies in content but not in size or including shape; the alternating unit is invariable.

There is an interesting modification of this principle in the case of the metopes and triglyphs of the Greek friezes. Here the triglyphs are unquestionably the principal units structurally, and to many observers the principal beat of the rhythm when taken rhythmically. But the triglyphs never vary and the metopes do, which would seem at first to violate the rule that principal units alone, and not alternates, should vary. This difficulty is obviated in two ways. With the spatial type of observer, the triglyph is indeed the principal beat of the rhythm when the series is at such a distance that the difference in the metopes (if there is such) cannot be detected. When, however, the series is nearer at hand, there ceases to be any rhythm, but each carved relief is taken for itself without regard to the others. With the rhythmic type of observer, if the triglyph has been the principal unit before, the principal beat changes on nearer approach to the metope and the whole series shifts its accent. It is impossible for any observer to keep the triglyph as the principal unit of the rhythm, when so near that differences in the metope are easily perceived.

There are still thirty-eight cases which vary from these rules, and many of them vary in more than one respect. These exceptions fall into several classes, quite distinctly marked off from one another, and will be taken up in turn.

In five cases, the size of the principal unit varies as well as the content, but in four cases the variation of size is either at each end, or in the centre unit, to emphasize bilateral symmetry of the series as a whole. The series in this case is taken as a larger unity of which the separate units are parts; and hence they are not only repeated with respect to themselves, but are symmetrical with respect to the whole. In the other case where the size of the principal unit varies, it varies on every other one, thereby complicating but not confusing the rhythm, i. e., a stronger accent comes on every other principal unit.

There are also five cases in which the alternate spaces vary in size. Three vary regularly, thereby enriching the rhythm by introducing alternate heavy beats, and one varies at each end of the series to emphasize bilateral symmetry of the whole, with regard to the central unit. In the other case the alternates vary in both shape and size, with no regularity and from the point of view of repetition alone, disorder is all that results. This is on the Palazzo Pretoria in Pistoia, where carved shields occur at equal distances between windows. These shields are not component parts of the building, but were added with some other kind of significance; hence they express nothing so far as repetition for its own sake is concerned.

The other variations are all in the content of the alternate, minor space. Four vary symmetrically in the designs on each side of the central point, so as to accent the bilateral symmetry of the whole taken as a unity. Two vary rhythmically in design, i. e., there are two sets of designs which alternate with each other in the unaccented spaces. When they vary regularly in design, the rhythm of the whole is enriched not confused, provided there are only two sets, not three or more. The alternate spaces are passed over on the way to the principal unit, but by having an alternating design between them (varying only in detail, but of the same general character) a more complex rhythm is introduced which is good, since in both cases the alternates and principal units are so different they could not possibly be confused with each other, even though both varied. (In one case, turrets and statues vary with windows of the same shape but different decorations; in the other, arched windows and arched spaces alternate with statues.)

Eleven more cases of variation in the minor as well as major spaces fall under another head. These do not vary with regularity, but are different in each case--the detail of the design varying, while the shape, size, and distance remain unchanging. It is interesting to notice that these examples of variations of alternates were almost all taken from examples of Renaissance architecture, where a richness of effect was desired, even at the expense of regular rhythm. This could, indeed, be attained in no other way so well as this. In all these eleven cases, the conditions are alike: both of the repeated units are enclosed by limiting lines of unchanging outline. The principal units are more prominent than the others on account of greater size or interest, but the alternates, instead of retiring entirely into the background, have slight variations in decoration. This variation is always only in detail: the tracery on the pillars of the tomb of Louis XII, of the Loggia dei Novoli, in the Chiesi di Frari, Venice, etc. So unimportant in fact is the variation that it is not observed until one attends closely to it, and yet the rhythm is just enough disturbed by its presence to give a feeling of extra sensation or luxuriance which cannot be attained through variation of the major units alone. It is in the alternate spaces that the feeling of repetition lies. Any material change in them destroys the series, but a slight variation in the lines of decoration, a little rearrangement of the conventional curves in each alternate, gives, even though unattended to, in fact partly because unattended to, a vague feeling of variety, of some superfluous sensation being brought into consciousness, although the regular shape, size, and distance of the objects remains unchanged. It is this feeling of superfluity and slight disturbance which constitutes the peculiar richness of certain styles. These examples, then, far from falling outside of the laws of repetition, owe their opulence of sensations to the very principles of regular rhythm which they violate.

Another set of exceptions will involve more searching analysis. Nine of the examples described have the human form for the alternate unit, and in every case where this happens, the alternate varies. In the majority of cases where statues of the human form alternate with any other object, the statue is taken as the principal unit on account of its superior interest, but this is not always the case. In the Padua Basilica, and in the Church of St. Guistiana, cherubs alternate with conventional decorations, but the latter are so much larger and more elaborate that they would naturally be taken as the principal units. In the other seven cases, statues alternate with bas-reliefs which also have human figures in them; hence, since the bas-reliefs equal the statues in interest and exceed them in size and importance, they are taken as principal units.

It might at first be expected from the previous discussion that, in order not to shatter the repetition, the alternate statues must be alike, must be conventionalized into identity; but this is not the case. Another principle now comes into play. We demand variation in the human form whatever its place in art, even in the unimportant position of alternate in a repetition, and although they are kept as much alike in pose, size, level of head and feet, general character (i. e., cherubs do not alternate with old men, nor draped figures with undraped), yet there is some variation of pose or direction of glance, to keep them from being duplicates. We should expect this variety of repetition to be in danger of becoming fatiguing because of its lack of an unchanging rest-phase, but this difficulty was evidently felt in building them, for in every case some unchanging element has been supplied to the series to bind it together and to keep the constant changes of attention from upsetting the series. The cherubs of the Padua Basilica are in high relief against a uniform rectangular background which does not vary, and which furnishes an alternate just in character with the principal unit, the bas-relief. In the Cantoria of Donatello, although the dancing children move across the whole space, uniform double columns occur at intervals, and supply an unchanging alternate, while the children vary in position behind them. Around the pulpit of Lincoln Cathedral, although both units, reliefs, and statues vary, the pilasters behind the statues are invariable and supply a constant, unchanging factor in the series. In the alternating reliefs and statues of the Milan Cathedral or in the paintings of different sizes in All Souls Church, Oxford, an unchanging element is supplied in the frame, which is of like design in every case, so that in passing from one to the other an unvarying alternate is always present. In the Sienna font, and in the statue to Leonardo da Vinci, which are types of a vast quantity of repeated forms, there is uniformity in the minor pedestals and in the frames of the alternating bas-reliefs, which supplies the unchanging factor.

Moreover, another factor is noticeable in this kind of repeated series,--it is never long. The fatigue which would certainly result from a too long continuance of varied alternates, even with unvarying factors in the way of supports, pillars, and frames, is obviated in various ways. The series is either short and the whole has a definite bilateral symmetry, as in the Padua Basilica, and in the Oxford church; or, as in a great number of cases, the series goes around a fixed central point so that only three units are seen at a time. It is thus especially that this method is used in fonts, pulpits, and monuments, where from the circular arrangement enough can never be brought into the field at once to fatigue the attention.

This consideration of alternates which vary widely, as do human figures, even when they are alike in size, general shape, and character, and, moreover, the discovery that there is almost without exception an invariable element between the other alternating units, i. e., a third alternate; or behind them, as in the case of the pilaster behind the statue, may well bring up two questions:

(1) When the unchanging factor comes between the other two units, is not it in reality the alternate, and the two other units either variations of shape and size of one principal unit or two sets of principal units? In other words, do we not actually apperceive the two principal objects as the units of importance, and take the unvarying factor which comes between, no matter how slight it may be, as the alternate? Do we not demand the unvarying as our alternate, no matter how many variations may be in the other figures?

(2) When the unchanging factor comes behind the alternating statue, in the same plane with the bas-relief, do we not inevitably take it as the alternate in the series, and regard the statues more as episodes or attendants on the series but with real values of their own? Is not the fact that the unvarying factor and principal units are in the same plane an indication that they constitute a real series, while the statues or paintings which are in a plane by themselves make a series, harmonizing with the other, it is true, and in part coinciding with it, but felt in a different way? Therefore the actual repeated series conforms to the given conditions and is made to do so in every case by its unchanging alternate in the same plane; while human figures with values of their own never can be considered quite as alternates, but are really felt to be a series by themselves.

This introduces another question. In two more cases of varying alternates, there was variation in decoration above the level of the rest of the series. In the Borghese Casino, there is variation in the busts placed over the alternate windows. In the Venice rood-screens, there is variation in the carving of the alternating supports, which rise above the rest of the series. Is that part of the series above the level of the principal units really included in its perception? It would seem rather that when the series as a whole is being taken, those variations above the level of the main units (if they are not very marked, and they were not in either of these two cases) are ignored or only felt in a vague way as added richness. When, however, the attention is turned toward them especially, they form a series of their own, in which they become the principal units, and alternate with empty spaces. There is no limit to the changes possible in apperception, according to the level and plane of the alternating units.

There are three cases left; two where alternates vary in content with no system, and one with variation in distance. The first two are differently carved sections of railing on the side of Freiburg Cathedral, and a differently decorated frieze of squares and circles in the S. Lorenzo Cloisters, Rome. The effect is only of disconnected and fragmentary series in both cases, and especially in the latter case it is impossible to feel it as a repetition at all unless the variations are ignored, and the attention fixed on the unvarying factor of size.

The variation of distance is in the Beauvais Palais de Justice, where the first window is at an unequal distance from the others in the series. The effect is only of disorder and accident.

We have, then, surveyed all our examples of alternate repetition, and found that in the exceptions to the general principles laid down some other effect than repetition as such was sought. Either (1) symmetry for the series as a unity was required, which demanded variation of the end or central units. In so far, then, as it fulfilled the requirements of symmetry, those of repetition were disregarded.

(2) Richness of effect was accomplished by those slight variations in decoration of alternates as well as the principal units. These by their vague suggestions of different combinations of similar elements, and minor differences felt but not attended to, gave a superfluity of experience which made up its peculiar richness.

(3) When the human form (or any other form of especial meaning in itself) makes the alternate unit, some variation is demanded as in keeping with its own significance, since in proportion as a thing has meaning in itself, it must not be exactly duplicated. But an invariable alternate is always supplied in the way of a frame, or background, which is felt as the real rest-phase of the rhythm, while the varying alternate forms have a place in a series of their own. Also, since such a complex attitude would be fatiguing, such series are always short, or circular, so that few units are in the field at once.

(4) Regular variations in size or content, in either major or minor which recur at fixed intervals, give a heightened rhythmical effect by making certain beats heavier than the rest. As has been stated before, the major unit holds within it the real significance of the content of the experience; the minor unit holds the secret of the rhythmic effect.

(5) Only 4 examples of the 125 were found to repeat themselves alternately with irregular variation of alternates and violation of the other principles laid down at the start. These can only be regarded as accidents, as faulty examples of art, whose virtue lies in some other part of the work as a whole, and not by any beauty they possess in themselves as repeated series.

SUMMARY

125 Illustrations.

I. Variations in Principal Unit alone, 87

82 Content 5 Size 4 Symmetry 1 Rhythm

II. Variations in Alternate Unit (and Principal Unit) 32 Content 11 Richness 9 Human figure 2 Rhythm 4 Symmetry 3 Different level 3 Disorder 5 Size 1 Symmetry 3 Rhythm 1 Disorder

III. Variation in Distance 1 Disorder

Several questions have been raised in this discussion of variations, but one which seems directly leading from it will be considered next.

When is variation necessary in a repeated series? We have considered the numerous cases where variation is possible, and the different ways in which a series may vary according to the idea to be expressed. Moreover, what appeared to be exceptions to the rule were shown to be guided by a desire for some other effect than repetitions as such.

But when do we demand variation in a series? Is there any case where variation of the unit is not only allowable, but positively necessary to its æsthetic value?

There were no experiments on this question, for it will be seen from what follows that they would have been impracticable. But observation of several thousand photographs has made the following clear: When the series consists of objects having an æsthetic significance of their own, not depending on something else for their value, then variation is demanded. In other words, when a thing is an end in itself, we do not tolerate an exact duplicate. It may have a place in a series of others similar to it, but its own meaning loses force if another is beside it precisely alike. When, however, an object has no great significance by itself, or when however great its value, it be regarded as means to something greater, hence not an end in itself, it may be repeated without variation.

This principle may be stated from another point of view: Any work of art, of the highest significance in itself alone, must not be repeated at all. There must not be even the suggestion of repetition. The highest values are individual, and to have a copy or a series defeats its whole reason for being. Thus, a second Sistine Madonna, or a series of Venuses, would shock our whole æsthetic feeling. Moreover, we do not want a suggestion of repetition; even a series of different Madonnas in similar frames would take away from the significance of each, in so far as they were regarded as a series, and not as a mere collection of detached units.

But grading down from these works of the highest value in art, there comes a point where an object, although possessing considerable value in itself, is not so intensely individual but that it can gain somewhat by a place in a series of others like it in some respects, but differing enough so that each still keeps its own meaning distinct from the rest.

The balance between these two artistic aims, i. e., the significance of the unit, and the rhythm of the series, must be adjusted with great nicety, and certain principles obtain wherever such series are found. It would be useless to cite the numberless cases where such series occur. Many have already been given in the examples of statues of saints, paintings on altar-pieces, and reliefs alternating with statues. One such series is a type of all. The human form represents that which has the most significance in itself, so when it is used in a rhythmic series, its individuality must be toned down and conventionalized; it must have no marked feature in one unit that does not appear in another; the head and feet must be on the same level, or vary with regularity; the general character and spirit of all must be similar, but never identical.

The reducing to a common type is the demand of the rhythmic series; the difference in attitude and arrangement of detail is the demand of the unit.

Thus, the subjects chosen for repetition of this kind are in the majority of cases apostles and saints, whose spirit and general conception are the same; typical representations of abstract qualities, such as Virtue, Courage, etc.; or conventionalized cherubs, and even animals. As has been stated before, a long series of this kind is impossible without fatigue. In proportion as the object is repeated the individual units lose their own meaning, and they must have their individuality definitely toned down and conventionalized to avoid the clash between the two artistic values. Yet their essential peculiarity must always be maintained, for we refuse to admit or allow the total identity of any expression of living values, especially as expressed in the human form.

It may be urged that statues are often arranged at regular intervals around a building, where the effect of repetition is distinct, and yet each statue is distinctly valuable for itself. But a distinction must be insisted upon. The statues form a repeated series as regards uniformity in position, height, pedestal, and color, so that the direct sensuous effect may be called rhythmic. But as the attention fastens on each for itself and takes it for its own meaning, it ceases to be part of a series at all, but becomes a unit in a world of its own.

But what of the cases where the human form is repeated in a series, and does not vary? Examples of this are rare, but they do occur, and are interesting, since they throw light on what has been already said. In the whole collection of photographs only two were found where a series of identical statues of the human form occurred,--The Porch of the Maidens in the Erectheum of Athens, and the Baths of the Forum in Pompeii. In the former case the left knee of the caryatids on the right of the centre, and the right knee of those on the left of it, are raised a little; but aside from this slight variation the six statues are exactly alike. In the latter case a row of titans all around the interior bear the ceiling on their uplifted forearms and are all alike. These two examples are very perfect of their kind, and, far from offending us, are very satisfactory. The reason is obvious. In both cases the statues are not the æsthetic end in themselves, but are there for a purpose, namely, that of a support. They are not ends but means to something else, and as soon as we feel that in regard to any work which would otherwise be of individual significance, it ceases to be individual, or to demand a peculiar expression different from all others, but may be duplicated without offence. Therefore, since the support of the superstructure obviously is dependent on the maidens in the one case and on the giants in the other, and since instead of existing simply for their own value they are there to hold up the roof, their artistic significance changes at once from ends to means, and variation is not required. Moreover, it will be found in the majority of cases that we demand this invariability in actual supports. Although we find but these two cases where caryatids are actually identical, we find also that in most cases the caryatids do not really uphold the weight, but a pillar or pier behind them supplies the real architectural support, and, that although they have a place in front of the pillar and give an apparent assistance in bearing the weight of the roof, yet the eye is not deceived. We see that the work is really done by the pillar behind them, so they that resume their place as artistic ends demanding variation, and not as means to something else. The following examples were found:

Milan. Arca di S. Pietro Martire. Pillars uphold the arch while four statues of women stand just in front. The pillars bear the weight although the statues add strength to the whole. The statues are varied.

Dijon. House of Caryatids. Piers behind the caryatids give real supports to the roof, while the figures added for decoration are all varied.

Dresden. Zwinger. Conventionalized figures ending at the waist are put on the outside of unvarying piers which bear the actual weight of the superstructure. The figures are all varied, but they cannot be conceived as really bearing the strain, since they have no foundation, but are merely added to the pier as a decoration.

Rouen. Tomb of Duc de Brezé. Four caryatids, all different, under four jutting projections of the arch. These projections are built securely into the rest of the structure and do not depend in the slightest on the figures for support. The figures are not integral parts of the whole architecturally, for the arch would stand exactly as well if they walked away, which indeed they are apparently in the act of doing.

Toulouse. Hotel de la Borde. Two caryatids under jutting projections of a window. The projections are securely built into the lintel and no weight rests on the caryatids nor even appears to. They are there solely as decorations and are different.

Paris. Hotel de Ville. Two caryatids under jutting projection of a window, again. Here is a very slight variation of the two female figures. The position of each is reversed to accent the symmetry of the whole. Very little weight is actually borne by them, but more than in the former cases, and we find proportionately less variation in the figures. They approach identity, but there is variation in detail.

These were the main instances found of the point in question, and are a type of the other minor ones found in support of pulpits, choir-stalls, and windows. It will be seen that in no case but the two classic ones given at the beginning are the human figures architecturally necessary to the structures, and in these cases they do not vary. In the other cases they are more or less playful, and the effect of the whole would be very unsteady did the superstructure actually depend upon them for support; but since piers rise invariably behind them and bear the weight, they fall into the sphere of decoration and from that point of view they must and do vary.

We have, then, considered variation of units in a repeated series, where they may vary and where they must, and we find the real value of repetition to appear in inverse proportion to the individual significance of the separate units; the more interesting or expressive the unit is in itself with individual significance, the less do we want it repeated; and so repetition of the human form must be conventionalized to the type (or to the same unvarying features), with enough individual differences still remaining to meet the demands both of the series and the individual. What apparent exceptions we have found to this rule have been shown to be meeting, in reality, another artistic demand.

ENDS OF SERIES AND ARRANGEMENT OF REPETITIONS WITHIN THE UNIT

The next question to consider is the ends necessary for a repeated series. Do they end with a heavier or with a lighter unit than the rest of the series, or with a unit of the same size? It will be remembered in the experiments touching this point that the subjects, without exception, preferred the series ending with heavier units. We should then expect, in examples of repeated groups of posts, pillars, etc., alternating with wider or more prominent ones of the same kinds, that the series would end with the heavier or more prominent one. Examples of railings or balustrades alternating with heavier supports are so common, and the supports come so invariably on the end, that repeated examples seem almost unnecessary. But another question arose in connection with this: Does not the apperception of a group of lines equidistant from each other consist in going back and forth over them from edge to edge, with no rest on one point more than on another; while in a group of lines arranged at equal distances each side of the centre but not from each other, to emphasize bilateral symmetry, does not the attention rest on the centre, and move from the centre of one group to the next?

Moreover, we found that a wider space or embankment of some sort was necessary, to finish off a series of groups in which the separate lines were equidistant from each other, than to finish the groups whose lines were symmetrically arranged. This suggests that the activity which goes back and forth in the former case, being less coördinated and not bound to a middle point, needs more at the end to stop it than is needed in the latter case, when the attention is more upon the centre of each figure. It would seem, then, that the former arrangement would be appropriate for railings and balustrades, where the effect is of continuity either running wholly around the structure and into itself again or where a continuity of parts is desired and a connected series. The other arrangement divides the series into discrete parts. If the attention is stopped at every central point, the effect is less of continuity and more of separate unities bound together externally by their equal distances. We should, then, expect such series of units much less in continuous balustrades, but if they occurred at all, that they would be in connection with separate unities that did not want continuity or place in a series emphasized at the expense of their individuality. All this we might expect from the experiments alone, although whether such a refinement would have got into architecture seems questionable. Moreover, the question whether a symmetrical group of units needs a less heavy end to finish it than a group of the equidistant type is even more difficult to illustrate. Although the two types may be given under some conditions in experiments, in actual architecture they never appear so, for the two types never appear in the same buildings allowing them to be compared. Besides, few photographs are taken exactly in front, and no two at just the same angle. Any accurate measurement of such end piers and any comparison of them is out of the question in the present methods of research.

One other question may be considered here. Does a series ever occur in which three units are repeated regularly, instead of one or two? In experiments we discovered that the subject found it impossible to feel repetitions of three in a series, and the only way that such a series was tolerable was when the three could be grouped somehow into one or two units. Therefore we should not expect to find such repetitions frequently, if at all.

To sum up: Do series always end with a heavier unit? Are units equally distant from each other more adapted to continuous or run-on railings, while units with symmetrical arrangements within themselves are found more often where separateness of objects enclosed is more aimed at than their connection? Is a less heavy end found after symmetrical series than after the other kind? Are repetitions of three units used at all, and if so in what way?

Obviously the only illustrations of these questions will be found in the arrangement of posts and pillars in balustrades of whatever description. In these cases alone do we find repeated series, with repetitions within the unit, as well as of the unit as a whole. The following examples have been taken by looking over about one thousand photographs and by recording every instance that occurred.

100 Examples

A. 73 Continuous Railings: Balustrades across façades; around roofs; up flights of stairs; around towers and baptisteries.

I. 57 Rhythmic Units: a. 31 Even numbers of units in group. Support arches 5. b. 26 Odd number of units in group. 11 Support even number of arches. 6 More than eight units in group. 1 Two sections of railing. Odd number in ends, decoration in centre section to emphasize symmetry. 4 No grouping. Too many to count. 4 Other reasons not assignable.

II. 16 Symmetrical units: Slabs with carved reliefs or plain; Carved scroll or diamond designs alternating with posts; Heraldic designs on shields; Conventional decorations in stone or wrought iron.

B. 27 Detached enclosures: Separate windows and doors. I. 4 Symmetrical units: II. 23 Rhythmic unit-groups. a. 10 Odd number of units in group. b. 11 Even number of units in group. 4 Support odd number of arches. 4 Although before separate windows make a continuous row across the side of the building. 2 Three sections of railing. Odd number in ends, even in centre section to emphasize symmetry. 1 No reason assignable. c. Indefinite number in group. Iron bars in railings, and slender pillars on façade.

C. 8 Do not end on the heaviest unit.

D. No cases of regular repetition of three units.

Having 100 illustrations of repetitions of groups, with units repeated equidistantly between them, and of elements distinctly symmetrical, several new factors came to light. In all the one thousand photographs looked over, not a single instance was found of unit-groups with the units within, arranged at other than equal distances. There were many variations in the number of units in the groups; but the number being given, the units were arranged at equal distances from each other wherever the effect desired was of detached sections or of continued series. There are obvious structural reasons for this. Any repetition of groups for a balustrade or protective railing, which is the almost exclusive use of this variety of repetition, would be weakened by wider apertures on either side of the centre. A reasonably enclosed space is necessary to make the railing of value, therefore the specifically symmetrical unit as opposed to the rhythmic unit was found always in carvings, scrolls, bas-reliefs, etc., alternating with vertical supports. We should expect, then, in general, that in railings where an aspect of continuity of progress along some border or a tendency to go around an enclosure was sought, the units would be rhythmic in character, impelling one to motion and to carrying the eye and general organism out of repose into movement. We should expect, on the contrary, that symmetrical units would be found where repose or partial distinctness of the separate elements enclosed was desired, and where the attention was not to be carried away in so marked a degree. Seventy-three of the one hundred illustrations were of balustrades where the rhythmic factor was presumably aimed at.

The Rathaus at Braunschweig had a symmetrical design alternately occurring, but with four in a section, so that the section as a whole was not symmetrical and the attention was driven on, and in the other cases some other effect than rhythm was obviously aimed at. The genius of the structures was heavy and massive and the balustrade made in keeping with them, since an effect of motion or rhythm would have clashed with the spirit of the whole.

These examples have all been of the balustrades around enclosures, balconies, etc. Since the rhythmic unit has been found more fitting for them, we should expect, conversely, that in front of separate unities, such as windows, doors, etc., the symmetrical unit would be more in evidence. At first sight, the facts do not seem to bear us out in this. Of twenty-seven examples of separate windows, doors, and gates enclosed by railings, only four had distinctly symmetrical designs. (Casa Palladio, Bergamo Chapel, Petit Trianon.) These are wrought-iron designs in the centre with repeated rods on each side, or a row of six pillars with the central two larger and more decorated. Twenty-three, however, remain to be accounted for, and the solution of the difficulty is observed at once in the distinction between odd and even numbers. As was previously suggested there are obvious difficulties in having posts in a balustrade at any but equal distances, since the gaps left by unequal distances from the centre would destroy their reason for being. This difficulty can easily be overcome in wrought iron by extra central decoration, although it is not always done by any means; but in stone balustrades, unless there is carved open-work, or solid reliefs, there is no other choice than repeated posts, either divided into sections or continuous, and no variation is possible except to have an even or odd number of them. We should then expect that there would be an odd number in separate detached enclosures, bringing a post in the centre to emphasize the balance, while in a continuous series each group would have an even number, thus giving no centre to fixate upon, but driving the attention on without repose at any one point more than another. It might seem doubtful that any such refinement should have been actually expressed in architecture, but examination of these examples shows this treatment to be very general. Of the twenty-three examples of separate enclosed details, eleven have an odd number of posts. Of the ten that remain, four are examples of windows along the side of a building, with separate detachments of balustrade in front of each. By having an even number of group-units the continuity of the row is maintained in spite of a separation of the sections. Two of the ten are sections of balustrade over the central doorway of a building. These balustrades are divided into three sections, of which the centre is widest and the ends only half as wide. Thus, although there are six posts in the central section, the balustrade as a whole is distinctly divided into a bilateral symmetrical arrangement. Three of the others have an even number of pillars, but they support an odd number of arches; and the arch, not the pillar, is taken as the unit of the repeated series. (Arches will be discussed later.) The one example unaccounted for represents a number of possible cases, where for some reason, following out a general scheme of building, or what not, the odd number is not insisted upon for separate clusters. But the fact that only one out of twenty-three is thus unexplained shows an unmistakeable tendency in the other direction.

A distinction between odd and even numbers cannot be felt above eight repetitions without actual counting, and often not even then.

The two final exceptions are of a gate and a decoration over a door (Fontainebleau, Piacenza) where there are nine or more units in the group. It is impossible to feel the system of this arrangement, and the result is proportionately confusing. A reservation must be made here concerning iron railings. There is no discrimination between odd and even in the number of iron rods in a section of railing and no tendency to symmetrical designs rather than rhythmic before detached enclosures. This is because from the nature of the case, there is no distinction possible between odd and even in the number of slender iron rods necessary to enclose a space with any security. There must of necessity be so many of them that the difference cannot be perceived, and so slight is the importance of each rod that the effect is more of a variegated surface than of actual beats of a rhythm. As soon as iron is wrought into large enough shapes, each repeated detail is of the same importance as in stone, but the slender rods commonly used in iron railings, although their repetition is rhythmic like all the others, give too slight a motor impulse to carry the attention past the heavy limits of whatever they enclose. They are found in front of many windows, but on account of the lightness of their rhythm compared with the solidity of limiting piers, no confusion results.

Having thus concluded that the odd numbers of units in groups is more adapted for separate enclosures, is the opposite true? In the continuous balustrade, previously discussed, are the units of groups made up of an even number of elements? Of the fifty-seven examples cited of continuous railings, thirty-one have an even number of posts in their groups. These conform to the rule: but what will explain the twenty-six remaining? It will be noticed that six of these have too many in a group for the eye to perceive any difference between odd and even, since they range from nine to thirteen. When so many units are in a group, the effect is always of the run-on type, whether the actual number turns out to be odd or even on subsequent count. One has a balustrade with only two sections on a side, each side of the centre door. Seven are in each section, and since the appearance of a symmetrical whole is the desired effect, an odd number is more in keeping than an even; in fact, this example, Monte Berico, might better come under the other head of separate enclosures, although it partakes of the character of both. Another balustrade with three in a section (Blois Château) is so heavy and massive in all its parts that fixity and solidity is more in keeping with it than rhythm. Eleven of them, that is, the larger proportion of all those with an odd number of pillars in a section, support arches, and the arch is taken as the unit instead of the separate pillar; and we find an even number of arch-units in each section, which is what we should have expected. It is a noticeable fact, which was previously suggested in connection with separate enclosures, that when a row of pillars supports a plain lintel, the pillar is taken as the unit of repetition. (When the row is on the front of a building, temple, etc., the opening may be the unit, if the purpose of the central door or the fact of going through is in the mind: but when the series stands for itself, the pillar is the unit.) When pillars support arches, the arch is the unit, unless it is very narrow as in the Moorish style, when the pillar is often so high and the arch so narrow in comparison that its value is weakened.

Of the thirty-one balustrades with an even number of parts in a section, four sets of pillars bear arches, and make an odd number of them. This would seem to make an exception to the rule were they not so narrow in two cases that the pillar was still the unit, and in the other two the motif of the arch was built around the intervening piers, so that they did not seem divided into sections at all, but continuous.

We have thus surveyed the whole field of repetitions of rhythmic and symmetrical units, and their difference in treatment according to the end they serve, and the results bear out our expectations. The symmetrical unit, as exemplified chiefly by an odd number of units in groups, is more used for detached enclosures; and the rhythmic type, with even numbers, is used more especially for continuous ones. In the former case the motor tendency is toward the central balance, while in the latter it is driven on out of itself through the series. When pillars support arches, the arch is the unit; when they support lintels, the pillars themselves remain the unit. Any number of units over eight loses its value of odd or even, since the difference can no longer be perceived and becomes rhythmic whether odd or even.

It must not be supposed that these rules are inevitably carried out or that the effect is necessarily poor if they are not. It shows a general æsthetic demand, however, which in individual cases may be modified by other demands, or altered in parts to make a more unified whole. When, however, the series is taken for itself, and judged entirely on its own merits, these conclusions will be found generally valid.

We have still to consider whether series always end with a heavy unit. All the series examined do end in this way; in fact we feel the necessity of this so clearly that one illustration would be as good as a hundred. But there is a difference in the use of the end unit, which is noticeable in any two series of symmetrical and rhythmic units. Of the sixteen examples of continuous series whose units were distinctly symmetrical instead of rhythmic, eight of them, although ending on supports, do not end on the principal unit of the series. This can be best shown by one or two examples. The Orvieto Cathedral has on the façade a balustrade of rectangular reliefs alternating with supports. The reliefs are undoubtedly the more interesting and important element of the series, yet the series ends with the less important element, the support or post, and we feel that it must do so. The Palazzo Contarini has a balustrade on its façade in which carved wheel-like designs alternate with supports which come at the ends. Why, in these cases, do we feel it as inevitable that the heavier and more important unit should not come at the end, as with rhythmic units we feel that they should? The answer to this is partly structural and partly æsthetic. We must feel, first of all, that the series is properly supported, that it will not fall away at the ends or down in the middle, and for this reason support of some kind must come at the end to hold it up and give a feeling of solidity and stability. But why are not these supports made the more interesting and important unit so that they might still bear up the superstructure and end the series as well? Here the æsthetic demand appears. As soon as the object is regarded as an æsthetic unity and care put upon it to make it beautiful for its own sake, it must not be thought of as the end of any series. It must be cut off from the rest of the world by supports or framed in some way, and while it still may have a place in a series, provided it is sufficiently conventionalized and not too important in itself, it must not be thought of as either ending or beginning, as depending on a series to give it importance, or lending support to anything else. It simply exists, cut off from the world, even though in the balustrade not an integral part of it, and one ought to be able to remove it without affecting the stability of the structure.

The question whether series of symmetrical units have less heavy ends to finish them than series of rhythmic units cannot be settled by these methods of analysis. While it seems certain that the rhythmic series drives the attention on by its greater motor activity, and hence would need more of an end to stop it, so many other factors enter in of more importance, such exact measurements would be necessary (quite impossible with the photographs of the scale here used), the refinement would be so great, since the stone of which most of the examples are made, by its own weight supplies a check to rhythmic activity, all these considerations make it impossible to illustrate this conclusion and it must remain an experimental result alone.

There remains one question: Is regular repetition of three units ever found? They may be in combination of some kind so that they fall into a rhythm of twos, but are they ever found repeated as three separate and distinct units? The answer to this is without exception. Of the five thousand photographs analyzed, not one instance of this kind of series was found. In many cloisters the pillars are of different design, and often one design is repeated through an otherwise varying series, but their repetition is either without scheme of any kind, or in some combination that falls into a rhythm of twos. No three-rhythm has been used in art, any more than it has been found possible in experiments.

ARCHES

It has been noticed in the preceding discussion that when a series of pillars supports arches, the arch, not the pillar, is taken as the unit. If this is so, it would seem that the arch by binding two pillars together with a curve awakens a more vigorous response than the vertical line of the pillars, and this greater expenditure of activity makes it to be taken as the element of repetition. It suggested that the arch (like the rhythmic unit) tends to drive attention on out of one unit to the next in the series. The outward thrust of the arch arouses an outward-tending activity, and for this reason a row of arches would need, to give a finished, stable effect, a wider and heavier embankment at the end than a series of lintels. The experiments on this point were inconclusive owing to the difficulty of obtaining a series of arches and of lintels which should be comparable in size. For this reason the validity of this suggestion must depend upon the actual treatment of arches in architecture. It would seem that the arch would, like the rhythmic unit, be more appropriate for continuous series than for detached short rows; or if the series were short, the ends should be treated in some way, by reduction in size, change in width of pillar, pier, or decoration, so that the outward-activity might be counteracted by some inward thrust or some accentuation of the centre. Thus the unity or balance of the series as a whole would prevent the arches from seeming to "run away" which they might appear to do without such treatment. We shall, then, look through photographs of buildings where arches are used, to find if their treatment carries out the supposition.

It may be seen at once that such a treatment of arches differs from the arrangement necessary to make plain lintels effective. The pillars on the front of Greek temples were indeed slightly farther apart at the middle entrance, and the centre was moreover further accented by the point of the pediment. But on the sides the rows of from thirteen to sixteen columns had equal interspace and no noticeably heavier columns or embankment of any kind at the ends, for none was necessary. The series appeared ended whenever it stopped, and did not carry the attention over, nor demand some finish to "hold it down," as does the arch. The pillars, to be sure, completely surrounded the temple, and so were, in name, continuous. But on a building with square corners, the other sides do not carry the series on to the eye (with variations in foreshortening of the ends) as in a circular structure, and the effect of continuity is not immediate.

Many examples might be given of buildings with pillars and lintels on the façade, which have no visible modifications of central or end columns to give balance or symmetry to the whole, and yet which are perfectly satisfactory as repeated series and do not demand either such treatment or further continuation, but are complete and finished: London, Trafalgar Square; Rome, Pantheon; Vienna, St. Karl, Barrome Kirche; Berlin, Schillerplatz, etc. These have the centre accented by the superstructure, but there is no discernible modification of the series itself.

Examples might be multiplied, but there are sufficient to illustrate the essential stability of repeated vertical units and to contract them with the outward-tending, run-on effect of arches which need various kinds of treatments to finish a series.

165 Arch Series.

A. 45 Go completely around exteriors: Colosseum, arenas, baptisteries, towers, cloisters, courts, basilicas, tombs.

59 Series that end:

B. I. 30 Central arch largest: triumphal arches, doors and windows on façades of churches. II. 1 Central arch smallest: doors on Peterborough Cathedral. III. 4 End arches larger: windows or decorative arches on the walls of buildings. IV. 6 End arches smaller: windows, decorative arches, or arches halfway around a court. V. 6 Arches go obliquely into higher central point and back: decorative arches running into the pointed roof on Romanesque façades. VI. 6 Central arch accented by decoration: windows and gates. VII. 6 End arches in different planes: doors on façades of buildings or in gates.

C. 20 Arches go around interiors: up naves and across the apse of churches, halls, and loggias.

D. 27 Around the outside of porches, apses, etc.; diminish in size at ends; are carried on in the transepts; motif is carried on, although whole arch is not; end arches are closed, or centres decorated.

7 Good

E. 14 Other arrangements: Roman aqueducts (endless); interlacing arches; filled with statues; finished by gables or turrets; bridges (land on each side a sufficient embankment); arches included in large ones.

7 Poor

Series not sufficiently finished at the ends; only two arches in series; three arches, with first arch different from the others.

Of one hundred and sixty-five examples of such series examined, only seven do not conform to the principles we have considered, and these are proportionately unsatisfactory. Forty-five illustrate buildings where the arches go completely around the outside of a structure, so that the series instead of requiring an end simply runs into itself again. It will be noticed further, that unlike series of columns around rectangular Greek temples, these are around circular structures where the series does not change its direction suddenly but by degrees. With the exception of courts and cloisters where the observer stands within and sees the whole series, these are all around domes, baptisteries, etc., where the end arches in the field at any one point of view are seen in perspective gradually fading off and yet leading attention on around the building. There may indeed be arches which go across square-cornered buildings or even around them, but in these cases some other device is necessary to make each side a finished series in itself. The mere fact of its continuance around a corner where it cannot be seen from the same point of view is not enough. (These various arrangements of arches on a flat façade will be taken up later.) Rows of arches are often used around towers square as well as round, but towers from their very shape and size allow the observer to see different sides from nearly the same point of view, so the series is not broken up into sections on different sides of the tower as it is in a larger building. Twenty more examples are of arches in interiors and are all of arches down a nave, with either a regular arch or an arch motif carried across the apse. It might be supposed that an arrangement of arches in an interior would be more difficult than on an exterior surface, since the genius of an arch is its outward thrust and its tendency to run on. Without careful treatment it would spoil the interior by trying to overstep its bounds; by making certain walls look wider than others; the arched sections utterly discrete in general character from the plain or otherwise decorated section. In point of fact, the use of the arch-series in interiors is quite conventionalized, and all the illustrations are of loggias, or of churches where the arch goes down the nave and in a more or less modified form across the apse. In the Sistine Chapel the arched windows go down the side walls and across the end in a vaulted double-arch. In some cases a series of Roman arches down the nave has a more or less pointed arch across the apse, but in every case the continuity has been kept in some way so that the series is unbroken. Moreover the columns in the cathedral naves are often so high and the arches so proportionally narrow that the pillar instead of the arch is taken as the unit. This is somewhat true in St. Mark, Venice, also in St. Sophia, Constantinople, where the large arches are divided into sections of seven smaller ones, each one of which is so narrow that the pillar is felt as the repeated unit instead of the arch; or if the arch be taken, the narrow span prevents it from too great outward thrust.

Thirty of the arch-series are on façades of buildings or in structures by themselves, as gates and triumphal arches, where the central arch is larger than the other, thereby emphasizing the middle point and drawing attention to it away from the ends. This centralizing a series or balancing it as a whole may be accomplished in various ways. Two examples make the central arch larger instead of smaller. Six make the end arches smaller while four make them larger. It will be readily seen that just which one of these variations is chosen for the series depends on the function of the series. The central arch is wider, with only one exception, when the series is of arched doors and the central door is the main entrance; while the end arches are more apt to be varied when the series is purely decorative and serves no function. The central balance may be further gained by differences of level. In the decorations of many façades, especially the early Romanesque, rows of arches go obliquely into the point of the roof and by this strong pointing toward the centre create an inward tendency. Six of the illustrations have the central arch accented by decoration; seven have heavier piers around the central and end arches; six have the end arches brought out into a nearer plane which effectually finishes the series. All these examples illustrate the necessary disposition of arches on a flat wall or façade where the series in the field of vision must end suddenly, that is, cannot gradually fade away around a corner. The variety and yet invariability of these devices shows the need felt for some finish at the end, some balance of the whole with the central accent, which need, apparently, is not felt for pillars and lintels.

When the arch-series is on a circular structure, such as apses, porches, and the like, even when it does not entirely surround it, as an arena or spire, the regular diminishing of the series on either side, owing to the curve, supplies the finish necessary, and the size and arrangement of the arches need not vary otherwise. Twelve of the examples illustrate such a use of the arch, and although in some cases, Morano Cathedral, Nomantala Church, the arches are continued into the transepts gradually tapering in size, or are modified in size growing narrower from the centre, as in the Bergamo Church, such a treatment is not necessary for finished effect. The difference in proportion resulting from a curved series, or even on arches carried around a square corner (as in porches on Goslar and Braunschweig Rathäuser), where the series is open enough to clearly see its continuity as it runs into the main building, will suffice to make a series finished without modifications of the arch-units.

There are many instances of long rows of very narrow arches on cathedral façades which are too narrow to give outward tendency, or else they have statues within them which really take the attention and form a series of vertical units in place of the arches. There is also the common device of interlacing arches, where a supporting pillar of another arch stands in the centre of every arch, thereby always driving the attention backward and restraining it. Perhaps the natural outward tendency of the arch-series and the necessity for its limitation can be seen by violations of the principle. Seven of the examples do not conform to any application of this rule and the results are not satisfactory so far as the mere series itself is concerned. Over the right and left doors of the Piacenza Cathedral are sections of nine arches which end abruptly and do not even meet each other. The Fredericksborg Schloss at Copenhagen has a row of fifteen arches enclosing a court. These run into wings on each side, to be sure, but all seen at once as they are and without central or end modification they are too sharply cut off and inclined to overstep their limits. The Loggia dei Lanzi at Florence, with its three wide arches and narrow pillars, the William Tell Chapel in Switzerland, with only two arches, illustrate forcibly the tendency of an arch to move outward, to appear too wide for the superstructure and too "active" unless bound down in some way. Four arches on the right and left of the façade of Marmonte Church, but not across the centre, have the same unfinished effect. The roman arch on one side of the St. Lo Cathedral façade with two gothic arches on the other defy every principle of repetition and symmetry as well.

From this survey of one hundred and sixty-five of arch-series we find through a variety of means a uniformity of purpose in their treatment; that all point to a common demand, however differently expressed, according to the function of the series. The series must be prevented from "running away." It must either run completely around a structure into itself, or be balanced as a whole so that the attention which naturally runs off the ends is driven towards the centre. This may be accomplished by enlarging, decreasing, decorating, or pointing toward centre of the arch by means of the obliquity of both halves of the series. It may also be brought by enlarging, decreasing, changing the plane of the end arches or altering the size of the limiting piers. The essential value of the arch may be altered by narrowing it, by filling it with something more important than itself, thereby making it only an attendant series upon its content, by interlacing it, or by any device that transforms or revises its outward tendency.

165 Examples of Arch-Series.

45 Go around outside a circular structure. 32 Go around interior and apses. 30 Central arch largest. 2 Central arch smallest. 4 Ends largest. 6 Ends smallest. 6 Central arch accented by decoration. 6 Central arch accented by upward incline of two halves. 6 Ends in different planes. 7 Different width of piers around centre and ends. 5 Very narrow arches. 9 Other reasons. 7 Unaccounted for.

The question discussed in the experiments, as to whether narrower interspacing was required between units decorated toward the centre, and units blank, or covered entirely with non-centrally accented decoration, could not be taken up in the latter analysis. To settle such a point, illustrations would have to be found of blank and decorated units of the same shape and size, in the same structure, and their relative interspacing compared. But no such examples were found, where the spacing was not regulated by some obvious structural reason other than pure pleasure in the repetition. This must stand, therefore, solely as an experimental result.

The use made of difference in plane or end, to facilitate two series being taken along together, whereas they would be fatiguing if the same in those respects, has been touched upon in the discussion of statues and bas-reliefs, and other series of more complicated units. Where the unit and alternate are both rich and significant, and would tire the observer by following each other at the distances they are obliged to be in a series, a slight difference in plane relieves the situation, and is used largely in monuments, fountains, pulpits, and such structures.

Many other questions have come up in the investigation which might be discussed in the same manner as the preceding, but can only be hinted at in conclusion:

Just what factors make an element and its alternate congruous? What is the exact relation of lines, which makes the scroll decoration in a balustrade alternate satisfactorily with an upright support, while the alternation of the arches in the Colosseum with the Greek pillars between them is incongruous?

In what does the pleasure in repeated series differ, when the observer is not certain just what is the repeated element? May there be a bare rhythmic pleasure, when the series is too far away to distinguish what the elements are, or when they run together, so that no definite demarcation is felt between them? Do such series excite a pleasure of repetition without content as to elements, and does it differ from mere variation and contrast?

The series of unsymmetrical units was found in the experiments to have a peculiarly unstable run-on effect similar to that of rhythmic units and of arches. Are they used in the same kind of cases as the others were, when a particularly active effect is desired?

Must a space be wholly enclosed, to be taken as a unit?

In a series of projections along a wall, the projections are taken as the unit, even when they almost meet at the top of the alternate space. When they actually do meet at the top, the enclosed space becomes the unit instead.

These questions and others similar might be experimented upon, and examples of their treatment analyzed, as in the previous questions discussed.

FOOTNOTES:

THE FEELING-VALUE OF UNMUSICAL TONE-INTERVALS

BY L. E. EMERSON

Modern theories of melody start always with the presupposition that the scale must be composed of tones having the simple mathematical relation to one another of 2, 3, 4, 5, 6 (and by Meyer 7) and their multiples in order to give pleasant combinations of successive tones. But the question arises whether other tone-combinations which given together appear disharmonious may not, by their mere acoustical difference, similarity, and contrast, awake definite feelings of pleasure. And if such feeling-tones exist independently from harmony it is evident that they would enter into every melody in addition to the strictly musical feelings of harmony and that they deserve consideration as a factor of music. It would not even appear impossible that if every successive tone-distance has its particular natural feeling-character, the distances of successive harmonious tones might be only through secondary factors as habit and training preëminent among the various possibilities of combinations. A tone-consciousness, which under the guidance of experiences of harmony has been trained in our musical tone-relations, must give instinctive preference to such successions as our melodies offer. But if we artificially inhibit the conscious relation to our musical system by introducing a continuous tone-series, or at least one of steps much smaller than musical intervals, do we destroy the possibility of pleasure, and if not, do we find the pleasure in the musical interval stronger than that in other instances? That even the musical subject introduced into the realm of smallest tone-steps can easily forget and inhibit his normal standards is well known; the whole acoustical perspective seems changed by the new intervals, and the subject begins at once to build up a new temporary system of relations. The experiments in Wundt's laboratory have shown that in such cases the theoretical judgment of distances is indeed quite different from the standardized one; the octave may appear equal to the higher fifth. I wanted to study in a similar way the feeling-value in such a state of musical disorientation, when all imaginative representations of our musical intervals are inhibited.

The instrument I used was an Appun Tonmesser giving reed-tones from 128 to 512 vibrations in intervals of 4 vibrations between adjacent tones. The intervals with which I experimented varied from 4 to 88 vibrations in steps of 4. The observers were all experimental psychologists, and varied in musical discrimination from a very low to a very high degree of natural ability and skill.

The observer reported his pleasure in the progression given, in the traditional grades of 1 to 7, where 1 represents the greatest degree of pleasure, 2 means very pleasant, 3 pleasant, 4 indifferent, 5 unpleasant, 6 very unpleasant, and 7 most unpleasant of all.

The immediate problem was: What is the relation between the width of interval used and the pleasure got by hearing the motive a-b-a and b-a-b, where a is always the lower tone. The method of procedure was to take a fixed tone (460 vibrations in the first case) and get a series of observations on successive progressions b-a-b where a differed from b by 4, 8, 12 ... 56 vibrations. The greatest difference thus is approximately a musical whole tone. Then a series of observations was taken on a-b-a where a similarly differed from b by 4, 8, 12 ... 52 vibrations. The progressions were given in irregular order, that there might be no chance of the observer getting into a fixed habit of replying. The intimate relation between the pleasure in successive musical tones and the pleasure in musical harmonies suggested naturally the question whether the feeling-value of these unmusical progressions was not somehow dependent upon the affective character of the simultaneous presentation of the same tones. Therefore after a progression had been given once and judgment recorded, the two tones used were given as a "harmony," that is simultaneously, and a judgment taken as to its agreeableness. This was immediately followed by the same progression, thus giving opportunity to observe the relation between the feeling-tone of the interval as it appeared in successive and in simultaneous presentation.

The results of this part of the investigation are graphically represented in the following plates. Tables I and II indicate the feeling-value of a-b-a where a, the lower tone, is 460 vibrations, and b is from 4 to 56 vibrations in addition, and the feeling-value of b-a-b where b, the higher tone, is 460 vibrations and a is from 4 to 56 vibrations less.

The base-lines from which the vertical lines to the curves are drawn represent the feeling-tone 4, the indifference-point. Above comes 3, 2, 1 and below 5, 6, 7; each square represents a unit. The horizontal abscissæ represent the width of the interval; the arrows indicate the musical intervals. The observers are given by initials. The first evident fact for both average curves of Plate V is that the maximum pleasure does not coincide with a musical interval, but comes with an interval four or eight vibrations less than either the half or the full tone of the musical scale. While in both cases the first elevation of the curve comes before the semi-tone, b-a-b shows a decrease of pleasure as the whole step is approached while a-b-a rises again. The order a-b-a is liked better than b-a-b.

Plate VI gives the "harmony" curve for the same tone-combinations, and it is clear at the first glance that the curves for the simultaneous tones do not correspond to those for the successive ones; in many respects they are directly the opposite. The hypothesis that the pleasure in such an amusical "melody" results from the resolution of the corresponding "harmony" is thus untenable; both are highly independent of each other. Yet, here too we notice the insignificance of the musical interval, while the strong pleasure in the tones different by 4 vibrations only refers probably to the complete fusion of the tones; there arises a direct enjoyment from the four waves of sound in every second, given by the beats. The pleasure-curve of these simultaneous tones indicates of course that the inhibition of the musical dispositions and expressions holds over from the successive to the simultaneous series. The pleasure is thus clearly different from that in real harmony.

Plate VII finally gives the "melody" curve for aba and bab with changes from four to four vibrations when the interval started with is larger than a full musical step. In aba the a is 384 vibrations and b varies from 436 to 516, the variations lying thus between the musical Second and the musical Fourth. It is evident that here again no feeling-preference is given to the musical intervals.

The question arises whether such small tone-intervals of amusical character allow the construction of more complex combinations of æsthetic value. Can we have amusical micromelodies with their own completeness and feeling of end? The following experiments represent a first step into this field. We used three tones only, a, b, c in 26 different combinations, and each of the 26 variations with intervals of 4, 8 and 12 vibrations between a-b and b-c. Each of the resulting 78 "melodies" was given repeatedly to six subjects in a time-order which allowed one second for each tone. The subject had to judge on the pleasantness of the whole progression and had further to judge whether it produced a feeling of end or not.

The combinations followed in the experiments in this order: abc, cbabc, abcb, cba, abcba, cbab, bcba, cbabcb, ababc, babc, abcbab, babcba, cbcba, bcbabc, abca, acba, acb, cbac, abcab, cabc, cbacb, acbab, cab, bca, cabcb, bac. The lowest tone was varied between 200 and 444 vibrations; b and c were thus always still less distant than the next musical tone. The chief results may be shortly characterized as follows. There are hardly any judgments of indifference, the combinations are always decidedly pleasing or unpleasing. Of course a certain training in the apperception of such small-interval melodies preceded the real experiments and produced an attitude of adjustment to amusical relation. If we are in the midst of musical tone-relations and go over directly to such miniature intervals, we are seeking for the fulfilment of the habitual expectation and feel dissatisfied, or in the best case the procession is an indifferent chance combination. But as soon as a certain training with small intervals has inhibited the strictly musical expectations, a new setting of judgments with new standards comes in and a new source of pleasantness is opened. Of course even then no extreme feelings are to be expected; while the indifference-judgment 4 is lacking, the strong pleasure and displeasure, the judgments 1 and 7 are completely lacking too; three fourths of the judgments are 3 and 5. The pleasantness is decidedly more frequent than the unpleasantness, and this relation increases with the interval. The differences of four vibrations were especially with the higher tones hardly distinct for some of the subjects. Among 288 judgments in each group there were 150 pleasant and 138 unpleasant when the distances between a-b and b-c were four vibrations, 208 pleasant and 80 unpleasant when the distances were 8 vibrations, and 226 pleasant and 64 unpleasant when the distances were 12 vibrations.

The order of pleasantness expressed by the fraction of judgments of pleasantness and unpleasantness is the following: the largest number of pleasant feelings belonged to the figures cbab and bac, immediately followed by abcb; the further order downwards in affective value was: cab, cbac, babc, abca, cbcba, ababc, abc, cabc, acba, cbabcb, bcba, acb, abcba, cba, cbabc, abcab, babcba, cbacb, acbab, bcbabc, abcbab, and cabcb as least pleasant.

As to the feeling of end or æsthetic completeness the results are similar and yet independent. In a few cases the answer was "doubtful," but in the overwhelming majority a definite reply was given; and while the judgment of completeness was by far more frequent in the pleasant combinations than in the unpleasant ones, yet often the unpleasant processions appeared as complete and the pleasant ones as incomplete. Here again the feeling of completeness grows with the interval, being smallest for the figures with distances of four vibrations. But most characteristic seems the fact that the feeling of end is in no way as in music dependent upon the return to the starting-point. The combinations which involved such return to the "tonica" show in no way a preponderance of judgments of completeness. If we order the results according to the number of this æsthetic factor the figures acba, cbac, and cabc stand very low, giving in the majority of cases the suggestion of not-completeness in spite of their return to the beginning, while the figures of the type abcb, cbab, or cba, or even the complex babcba, suggest in a majority of judgments the feeling of an end. The feeling of an end comes, according to the subjective reports of the observers, with an "internal unity of meaning" of the phrase given. This unity of meaning is here evidently quite independent from any simple mathematical relation.

The music-like quality of the figures was emphasized frequently in the subjective records. "I just enjoyed the progressions as music." "The elements are the same as in music." A melody of 384, 392, 400 was called a "very mournful strain"; 444, 452, 460 "Wagnerian motive; Tristan and Isolde"; and the same tones in another order "Very pleasant; expressed a pathetic resignation," or "Sounds like a little piece of music"; and so in most varied forms.

The basis of these experiments is of course by far too slender to build on them a theory, yet our results suggest at least a greater interest in the æsthetics of those tone-combinations which are excluded from our regular music. This interest is reënforced by the self-observations of all participants. They felt strongly that after all our musical pleasure in melody does not belong intrinsically to the tone-perception, but is learned and acquired like the grammar of our mother tongue. Such grammar too controls completely our internal demands for expression, and yet the learning of a different language can bring a new adjustment and a new set of psychophysical dispositions for linguistic demands. That whole apparently natural demand for the tone-combinations which give fusion and consonance can be inhibited during the listening to amusical combinations as soon as a short training in miniature intervals changes the acoustical perspective.

The development of instrumental music demanded evidently the selection of distinctly separated tones and of intervals which give harmonious combinations. The external conditions of resonant chambers may have reënforced this selective process of historical music. It is certainly different with oriental nations, which produce music not in resounding chambers but in the free air and who are singers and not players, using instruments mostly for producing a mere body of tone as a background against which the melodies move; their intervals appear to our musical ear at first bizarre, and yet there too we are readjusted to the new dispositions for satisfaction with unsuspected quickness. We have no right to identify æsthetic pleasure in successive tones with the pleasure in our conventional music with the simple mathematical relations which alone give the pleasure of fusion; but being accustomed to this system of harmonies and being trained to expect it also in the resolved form of the melody, we need indeed an inhibition of habits and a certain new training till the more modest pleasure in amusical tone progressions comes to its natural right.

ASSOCIATION, APPERCEPTION ATTENTION

CERTAINTY AND ATTENTION

BY FRANCES H. ROUSMANIERE

The results of the experiments on the feeling of certainty which I have conducted fall into two divisions--those on the nature of the feeling itself, and those on the effect of voluntarily attending to certain aspects of a total experience upon certainty in the judgments as to the constitution of that experience. The problems of the first division are: Are there different kinds of certainty? In any one kind of certainty are there degrees, and if so, are these of a limited or an unlimited number? Can certainty be analyzed into elements? The problems of the second division are: Can it be said that in the report of any experience the judgments made with the highest degree of certainty will be confined to an attended-to group, and if not, will there be more there than elsewhere? In such a report will the direction of voluntary attention toward certain aspects materially alter the distribution of the judgments of the highest order of certainty over the various aspects of any given field?

These two divisions are so distinct in problem and result as to make it seem best to describe them as independent experiments. As some interesting results on the relation of error to the different grades of certainty and to the effect of attention developed in connection with this second division of the experiment, those results are given also.

In general the same subjects took part throughout the experiments. One, an instructor in Harvard University, whom I shall call K, was not subject for the second division of the experiment. Two others, E and H, both graduate students in Harvard University, could not serve as subjects in an important part of the first division. Of those remaining, B was a student in Radcliffe College, F an instructor in Harvard University, and A, C, and D graduate students in Harvard University. These last five were my subjects for all parts of the experiment.

I. THE NATURE OF THE FEELING OF CERTAINTY

The general method here was, of course, the method of introspection. Situations were created about which the subject might be expected to make judgments with different sorts or different degrees of certainty, if such should be possible. He was then questioned as to his experience. The method has the fault of all introspective methods, viz., its results can in no case be verified. The results here are none the less suggestive, and, for the second problem, at any rate, definite enough to be convincing.

Most of the experiments were conducted in connection with visual fields. In working at the first problem which we have now to consider, however, the certainty connected with the dermal sensations and that connected with the simple reasoning process of addition were also examined. The apparatus used consisted of three sets of cards. On one set were pasted geometrical shapes cut from colored paper, and black and white letters or figures. Each of these cards was shown to a subject for a second and a half, or two seconds. After the exposure he told what he judged to be on the card, giving all that he could about the nature of his feeling of confidence (or certainty) for each judgment. On the second set of cards square pieces of tin, smooth rubber, rough rubber, cotton, felt, undressed kid, leather, eiderdown, flannel, coarse and fine sandpaper, and pricked paper were stuck, six on each card. The experimenter passed these cards so that these bits of material rubbed against the forefinger of the subject, while a curtain kept the card and the hand hidden from the subject's sight. Here, again, the subject judged of what had been on the card, just as he had done after seeing each of the first set of cards. Small sample cards, each having pasted upon it a piece of one of the substances used, were also behind the curtain, and the subject was allowed to feel of these as much as he wished while giving his report. Such sample cards were required because of the underdevelopment of the association of names of any kind with the dermal sensations. A single card with three groups of figures for addition upon it made up the third part of the apparatus. Here the subject was asked first to add the columns rapidly and to introspect as to his certainty of the correctness of the different results; then to go over the addition again, and yet a third time, and to compare his feelings of certainty in the different cases. The introspection was developed partly through the help of questions put by the experimenter, but in asking these questions great care was taken to prevent their influencing the judgment of the subject. Some observations made by the subjects during the second division of the experiment (also conducted in connection with visual fields) are, also, introduced here. Apart from this, the experiments on the feeling of certainty connected with this sense of sight were greater in number than the other experiments; and it is those that have given us most of the data for answering the second and third problems.

The subjects did not agree in their answers to the first problem. Some found not only that the certainty connected with their belief in the results of their addition seemed to be of a distinct type from that connected immediately with the sense of sight, but also that there were different sorts of certainty connected immediately with the sense of sight itself. Others found but one kind of a feeling of certainty. All agreed, however, that so far as the kind or kinds of certainty associated with them was concerned there was no difference between the sense of sight and the dermal senses, so that it would seem to be true that any distinctions which are to be found within the feeling of certainty will not be distinctions springing from the difference in the sense-organs. Within the sense of sight, however, subjects B, E, and F divided their feelings of certainty into two classes,--an absolute feeling of certainty which they felt could not be shaken, and a feeling of confidence which they would act upon but which they felt might be shaken by questioning, and which seemed different by more than degree from the feeling of certainty proper. Subjects A, C, K and H found no such marked distinction between their feeling of greatest certainty and all lesser feelings of conviction. Subject D at one time felt that the distinction into two such distinct classes, the definitely certain and the more wavering, fitted his experience, and at another time said that it seemed to him that each degree of conviction stood for an unique feeling of certainty and that any two of them were as different from each other as any other two. A second division of the feelings of certainty into two classes is to be found with subjects A, F and H. This developed in connection with the visual experiments again. The distinction here may be called one into psychological and logical certainty. The latter rests on reasoning either from the probable character of the field, or from a feeling as to its general character, to the nature of some detail. We shall notice the characteristics of these two classes later. One subject, A, further distinguished as different the feelings of certainty connected with the two methods of logical certainty just given. The others made no such distinctions. In the experiment with the columns for addition only six subjects, A, B, C, D, F, and K took part. Of these the two who had made the distinction into psychological and logical certainty with the visual experiments (subjects A and F) again made the same distinction. Subject F, however, who had had occasion to do a good deal of important work with statistics, found practically no element of logical certainty in connection with his addition, though it seemed to him that what confidence he felt in his result should be distinguished from the psychological certainty he had had as to the character of the visual fields. Subject B felt no certainty in her results except as she could so hold the process together as to have what seemed to her a simultaneous experience. When she had to judge of the results of a set of successive experiences that could not be so unified, she characterized her state of consciousness not as holding a feeling of certainty or of uncertainty, but as simply lacking any feeling of certainty. The other three subjects found no difference between the feelings of certainty and uncertainty associated with visual experiences and those associated with the process of addition. As a whole, it seems then that we must answer our first problem by saying that the case seems to be different with different individuals. With some the highest grade of certainty associated with a sense-experience is sharply distinct from the other grades, and with some again there appear at least the two general classes of psychological and logical certainty. On the other hand, there seem to be people for whom the feeling of certainty has no such sharp distinctions of kind within it.

The results as to the second problem may be more briefly and more distinctly given. No subject found any evidence that the number of the grades of certainty which he could distinguish would be limited by anything except his keenness in introspection, although in the simple tests given for the experiment, four was the greatest number of grades distinguished at any one time. Two of the subjects (B and F), who set the highest grade of certainty apart from the judgments made with lesser confidence, said that there might be degrees within that higher grade as well as among the "uncertainties." There was no evidence that logical certainty differed from psychological in respect of the grades to be found within it, and some evidence that they were alike in that respect, although logical certainty was less carefully examined. It would seem, then, that our second problem is to be answered thus: There are degrees present in some if not in all kinds of certainty, and there is no evidence that the number of these degrees is limited.

It was not generally found possible to analyze the feeling of certainty into a sum of elements, although certain characteristics seemed to be persistent in it. Here again there is marked individual variation. The general test used for the difference in degrees of confidence was the question "On which judgment would you risk more?" This satisfied every one as a true criterion for such distinctions, but subjects H and C said that for them the feeling of certainty had a much more distinct relation with the past than with the future. Perhaps for that reason, subject H proposed the test "Which judgment could I be converted from most easily and simply?" The distinctness of an image had something to do with the feeling of certainty for subject C. Beyond this, he could not characterize his feeling. Neither was he sure that the degree of certainty varied exactly with the degree of distinctness. Subject D found that all objects about which he made judgments of which he was certain were present to his mind in the form of distinct images; but did not feel that that covered all that was to be said of the feeling of certainty. The number of images present, as visual and auditory, seemed to increase the degree of certainty for him. Subject F could give no characterization of his feeling of psychological certainty. His feeling of logical certainty seemed to spring largely from a feeling of consistency between the present experience and his past experiences. With subjects A, B, and K the vividness of an image was a strong determining factor in the degree of certainty felt in any judgment, but again was not the whole story. Something they could not characterize was also present for A and B, and, as well, a feeling of more or less perfect congruence between an image and the general character of a field. (This introspection developed in connection with the visual experiments.) Among these eight subjects we have but one (K) who is satisfied with reducing certainty to a set of elements.

To my mind the most valuable thing to be gained from this division of the experiment is the suggestion that there are definite types of certainty, and that people may be classified by these. There are obviously marked individual variations as to the characteristics of this feeling. I should expect from my work this year that two pretty distinct types could be discovered. For one of these, certainty in a judgment as to an experience would rest very largely upon the vividness of an image; for the other, upon the congruence of an image with other previously accepted images, that is, the absence of conflicting images when the experience judged about is imagined part of a wide setting of past experiences. I should not expect either element of certainty to appear absolutely, without the other form. For many people one element would predominate in certain fields, as in judgments regarding sense-experiences, the other in the more logical fields. For some, again, perhaps, the two would be nearly coördinate in every experience of certainty. But for some subjects, as, I think, for subject K here, the vividness of the image would always be the determining factor, while for others, as for subject H, congruence with wider experience would be much more important. This classification of subjects according to their types of certainty might develop into a much more complicated affair. The experiments described here have gone no farther than to suggest lines along which it may perhaps run. There may be other elements equally important with these two. A set of experiments consisting of attempts to raise uncertainty to certainty would bring out the essentials of certainty from a new point of view, and would, perhaps, test this theory that individuals may be classified according to the types of their certainty, in the most satisfactory manner.

II. THE EFFECT OF VOLUNTARILY ATTENDING TO CERTAIN ASPECTS OF A TOTAL EXPERIENCE UPON CERTAINTY IN THE JUDGMENTS AS TO THE CONSTITUTION OF THAT TOTAL EXPERIENCE.

As has been said, judgments as to the elements of visual fields were tested for this part of the experiment. The apparatus used was the following: The subject was seated before a low table which was shut from his view by curtains and boards. He looked down upon the table through an opening into which a camera-shutter had been fitted. This shutter was set for a two seconds' exposure and opened by means of a bulb which the subject held in his hand. Just before each exposure, the experimenter placed a card on the table below the camera-shutter. The set of twenty cards so used were alike in that the background for all was gray and the objects pasted upon the cards black letters and numerals and simple geometrical figures of chosen shapes and colors. No color was repeated on any one card. The cards were different in the choice and arrangement and in the number of objects used. The number of letters and numerals on any one card varied from two to five, the total number of objects from eight to twelve. A white card on which were pasted dark gray samples of each of the eleven shapes used, together with a card of the background of those shown in the experiment on which were pasted torn scraps of the eleven colored papers used, was always in sight at the subject's side. A camera-shutter, experiment cards and sample cards thus made up the apparatus.

The presence of the sample cards needs explanation. They stood for the attempt to place the colors and shapes on the same footing as the letters and numerals. Their presence, in the first place, and, as well, the limitation of the number of letters and numerals used, did away somewhat with the advantage that letters and numerals naturally have for ease of naming. In the second place, the use of a new color for the sample shapes and the absence of definite shape in the sample colors helped to keep the colors and shapes more distinct. With the help of these cards it seemed that we could properly hold we had a a visual field of three very nearly coördinate sets of elements.

The experiment as a whole, as conducted, had four phases which, except for one particular, were exactly alike. The subject's attention was directed toward a certain aspect of the field by (1) asking him before each exposure (or less often if that appeared unnecessary) to attend to that aspect, as, for instance, to the colors present, and (2) taking care that any questions asked should tend to strengthen rather than counteract the effect of that voluntary attention. At a given signal the subject pressed the bulb which opened the shutter. On the closing of the shutter he reported what he had seen. This report the experimenter recorded almost in the subject's own words, and later tabulated in the manner described presently. So far as giving the objects present was concerned, the report was given almost invariably without any suggestion by the experimenter as to the possibilities of the field. To help the subject distinguish the amount of confidence which he had in the judgments that such or such objects were present, however, the experimenter frequently asked such questions as, "Would you risk more on the fact that there was a square in the field than on the fact there was something blue there?" In giving his report the subject pointed to the sample cards or spoke, as he might wish. He was also allowed to be as leisurely or as rapid in giving it as he chose. A half-minute interval elapsed between the end of each report and the signal that the shutter be opened again. No persistent effort to distract the subject's attention was made then, though conversation on other topics was frequently carried on. The point in which the phases of the experiment differed was in the aspect of the field to which attention was called. In the first, this was the shapes, in the second, the colors, in the third, the letters and numerals, and in the fourth, the number of objects in the field. Fixing the attention upon the number of objects in the field served to distribute it equally over all the groups represented there. The general method of calling attention to the different aspects and of learning the effect of such attention was, as has just been said, the same for all phases.

As a preliminary to making up the tables here given, from which we are to answer our problems, the experimenter first tabulated the reports of the subjects in such a way as to show how many judgments (correct and incorrect) of each of the four grades of certainty adopted for this division of the experiment were made by each subject on each card for each group on the card (shape, color, or letter or numeral). From these tabulations the tables that follow were in turn compiled.

The number of grades of certainty adopted for this division of the experiment is obviously decidedly arbitrary. Grades of certainty there surely are. The introspection of the subjects develops that clearly, as has been stated. But there is no reason in the conditions of the case for holding to the number four, as is done here. In giving the results for which the experiment was undertaken, I shall, indeed, confine myself to studying the range of the judgments made with as high a grade of confidence as the subject believed he should ever have. This is called certainty (1) or certainty proper. But for the tributary discussion on the relation of certainty and error, the consideration of three other grades used in the report and early tabulation, is also introduced. This lowest grade (4) might better be named "as complete uncertainty as will admit of one's making any judgment." The other two are intermediate. It was at first intended to give the results with regard to the effect of voluntary attention upon the place of these grades of certainty, also, but such a discussion has been omitted because it promised to add very little more than complexity to the report. Besides this, the classification into these lower grades is too purely approximate to make the distinction there of great value. For judgments of the order certainty (1) we have the test, "Are you as certain of this as you can imagine being in an experiment of this sort?" but no such test for the other grades could be found. Yet, though he tended to omit judgments of the lower grades of certainty, each subject seemed to find four grades a convenient number to use in giving his report.

The number of experiment cards used varied with the subjects. E had so clear a memory of the cards that after as many as ten had been shown, he found difficulty in distinguishing his memory of the one which he had just seen from that of others seen earlier. Ten cards only were used in his case. A, B, D, and F showed signs of fatigue after fifteen cards which made the value of any later results questionable. C and K showed no such signs of fatigue. The same set of cards was, of course, shown any one subject for all four phases of the experiment. Those omitted were the last ten or the last five of the complete set as the case might be.

TABLE I

% of cards where % of cards where % of cards where % of cards where certainty (1) certainty (1) certainty (1) certainty (1) is appears in the appears elsewhere in attended-to stronger outside attended-to than in the group only. than within the group. attended-to attended-to group. group.

A 91% 49% 49% 13.3% B 97 91 83 28 C 95 67 30 16.6 D 93.3 69 24.5 11.2 E 96.6 83.3 13.3 26.6 F 88.8 30 53.3 8.3 H 91.6 70 26.6 10

Table I answers the first part of our first problem promptly. Every subject gave judgments of the order certainty (1) about groups other than that attended to, in the case of a very considerable percentage of the cards. True, again in the case of a considerable (though generally smaller) percentage of those cards, each subject confined his judgments to the group attended to. The fact of individual variation stands out again here; and, moreover, the conclusions drawn should be qualified slightly because of the fact that it was often possible for the subjects to give all the letters and numerals on the cards, and still have, as it were, some attention left over for the other, supposedly non-attended-to groups. Such reaching beyond the properly attended-to group never seemed to be possible with either shapes or colors. Aside from this, however, it is clear that judgments of the highest grade of certainty were by no means limited to the group attended to.

This same table answers, also, the second part of the problem. Each subject found certainty of the highest grade sometimes stronger outside than within the group which held his attention. It is, of course, practically impossible to make absolutely certain that each subject's attention was invariably held to the group toward which it was turned, yet the percentage where certainty was stronger outside than within such groups seems large enough, in some cases, at least, as with subjects A, B, and H, to warrant our answering this second part of the problem in the negative. I should feel, however, that this was answered less definitely than was the first part of the problem. We may say, then, that the judgments made with the highest degree of certainty about a visual field will not be confined to the group attended to, and that we have strong evidence pointing toward the belief that we cannot expect there will invariably be more of such judgments within the group attended to than outside it.

TABLE II

# 1: % of judgments of certainty (1) given to each group in phase I (or when shapes were attended to).

# 2: % of judgments of certainty (1) given to each group in phase II (or when colors were attended to).

# 3: % of judgments of certainty (1) given to each group in phase III (or when letters and numerals were attended to).

# 4: % of judgments of certainty (1) given to each group in phase IV (or when the attention was equally distributed over all the groups).

1 2 3 4

Subject Shapes (a) 94% 38% 18% 31% A Colors (b) 5 61 20 59 Letters and (c) Numerals 0 0 61 9

Subject (a) 48 39 21 33 B (b) 43 60 29 38 (c) 8 0 51 28

Subject (a) 88 15 26 34 C (b) 8 77 28 8 (c) 5 7 47 58

Subject (a) 60 13 11 40 D (b) 19 67 2 37 (c) 19 19 86 23

Subject (a) 51 15 0 37 E (b) 22 56 8 29 (c) 26 28 91 34

Subject (a) 66 12 0 50 F (b) 14 77 0 27 (c) 19 10 100 23

Subject (a) 43 21 7 24 H (b) 29 52 4 19 (c) 27 26 88 57

The most interesting part of this division of the experiment is brought out in Table II in answer to the problem, "Will the place of voluntary attention materially alter the distribution of judgments of the highest order of certainty among the given groups?" In every case the percentage is affected, in most cases, greatly affected. Take the case of subject A, for instance. Although, when his attention is equally distributed over the field 59% of the judgments we consider were of colors, yet when his attention was fixed on shapes and on letters and numerals this fell to 5% and 20% respectively. When it was fixed on colors, it rose, indeed, only to 61%. When, however, subject A fixed his attention upon the letters and numerals, 61% of the judgments were confined to the group attended to,--the same percentage as when colors were the attended-to group,--although, when his attention was distributed over the whole field, the percentage of these judgments about the group of letters and numerals was 9% only. When shapes were attended to, the 31% of the fourth phase of the experiment rose to 94%,--almost all of the judgments of the highest grade of certainty that were given were judgments about shapes. A similar study of the results given in the table can be made for the other subjects. The degree of change varies with the subject and with the group, but always there is some change, and often a very marked one. In this experiment the place of voluntary attention clearly did alter, and alter materially, the proportion of judgments of the highest order of certainty made about any given group.

That, indeed, would seem to me to be the answer of this experiment to the question as to the effect of voluntary attention upon certainty in one's judgments. Every subject showed a tendency to have more certainty in those judgments which were made about that aspect of the field toward which his attention was directed. Yet, on the other hand, this was a tendency only, one not strong enough to make it possible to predict beforehand exactly how great a proportion of the judgments in which he had the highest degree of confidence would be limited to that field, or even to be sure in every case that the greater proportion of those judgments would be so limited. The place of voluntary attention has an influence upon the subject-matter of the judgments made with certainty about a visual field just seen, but an influence of varying and uncertain strength.

TABLE III

1 = % of mistakes in judgments of certainty (1). 2 = % of mistakes in judgments of certainty (2). 3 = % of mistakes in judgments of certainty (3). 4 = % of mistakes in judgments of certainty (4). x = no judgments of that kind given. 1 2 3 4

Subject A (in giving shapes) (a) 7% 10% 0% 100% (in giving colors) (b) 2 14 23 0 (in giving letters and numerals) (c) 0 0 x x

Subject B (a) 2 10 10 0 (b) 3 6 20 25 (c) 4 50 0 x

Subject C (a) 1 8 10 0 (b) 4 14 14 0 (c) 1 0 16 0

Subject D (a) 3 4 0 16 (b) 1 6 0 0 (c) 5 0 0 0

Subject E (a) 2 10 25 50 (b) 1 33 40 0 (c) 0 0 0 0

Subject F (a) 1 25 7 25 (b) 4 15 29 26 (c) 3 0 0 x

Subject H (a) 3 6 5 0 (b) 6 2 15 15 (c) 4 0 0 20

TABLE IV

Label 1: General % of mistakes in judgments of certainty (1).

Label 2: % of mistakes in judgments of certainty (1) about attended-to groups.

Label 3: General % of mistakes in judgments not of certainty (1).

Label 4: % of mistakes in judgments not of certainty (1) about attended-to groups.

1 2 3 4

Subject A 4% 1% 17% 27%

Subject B 3 2 10 7

Subject C 2 3 9 24

Subject D 3 4 4 0

Subject E 1 2 22 34

Subject F 3 1 21 23

Subject H 4 6 6 10

The results given in Tables III and IV were compiled from the same records as those of the two Tables just discussed. They give the relation of error to certainty and to attention, as that relation was developed in this experiment. No experiments were conducted with these relations of error primarily in view, but the results developed in connection with the problem of the effect of attention upon certainty in one's judgments.

Both Tables show again marked individual variation. They suggest to me, in the first place, a further line of investigation in the same field and for the same purpose as those investigations which L. William Stern outlines in an article entitled Aussagestudium. This further line is the testing subjects to learn the probable relative correctness of the judgments made with different degrees of confidence. Although a comparison of the first and third columns in Table IV makes it clear that the proportion of mistakes for the highest grade of confidence is lower than for the other grades taken together, there is a very marked difference among the subjects to be noticed. The difference in the two percentages is, for instance, very slight in the cases of D and H, and very great in the case of E. It is interesting to notice with regard to E that while he has the lowest percentage of mistakes for certainty (1), he has the highest percentage for the group of certainties (2), (3), and (4). In the more detailed percentages given in Table III we see further that in certain fields and sometimes in all fields (as with subject C) judgments made with the lowest grade of confidence were invariably correct. Such Tables might be of help in a case where the evidence of eye-witnesses conflicted. We might perhaps learn that witness N made a large proportion of mistakes where he was absolutely certain, whereas witness M was seldom wrong in judgments in which he had a low degree of confidence. Even when the probity of both was unquestioned, we should not then assume that N was more probably right because he had so much more confidence in his judgments than M had in his. A much longer and more comprehensive set of experiments would be necessary before we could feel that we had at hand a table from which to work in this way.

The question of the effect of voluntary attention upon error, for answering which Table IV was compiled, brings out again the marked individual variation among these seven subjects which has shown itself in practically all parts of the experiment. Some effect seems to have been produced always, but this was sometimes to give a larger percentage of mistakes in the attended-to groups and sometimes a smaller. With A, B, and F the percentage of mistakes in certainty (1) was lower for the groups attended to than for the total number of judgments of that order. Only with subject B, however, is this true of the group of lower grades of certainties also. On the other hand, with subjects C, D, E, and H the percentage is greater for certainty (1) in the groups attended to than for certainty (1) in the collection of all the judgments of certainty (1) taken together. Here, too, in the case of subject D, the results with regard to the lower grades of certainty reverse those for certainty (1). Thus all four possibilities as to the kind of influence of voluntary attention upon certainty appear. We cannot say that the place of voluntary attention will tend to affect the percentage of error in any given way. We can only say that apparently it made some difference with each subject. It might be found by further experimenting that the character of this difference is associated with some other characteristic of either attention or the feeling of certainty, as, for instance, with the ease with which attention is held to the chosen field or with the type of the subject's certainty.

Like all experiments, these open up further questions quite as much as they answer those toward which they are aimed. To repeat something of what has already been said, I feel that what it has established is (1) that introspection develops distinct grades of certainty in the case of every individual, (2) that the particular characteristics of the feeling of certainty vary markedly among individuals; (3) that the feelings of certainty associated with the different senses are not, as feelings of certainty, to be distinguished from each other; (4) that the judgments of the highest degree of certainty which are made about the constitution of any visual field just seen will not be confined to the group in that field toward which the attention is directed; and (5) that such fixing of the attention will, nevertheless, materially alter the subject-matter of such judgments of greatest certainty. The rather vague statement that the percentage of error is not surely less with the judgments of a group because attention is fixed on that group may perhaps be added as a sixth conclusion. The most interesting and promising of the problems which the experiments seem to me to raise are: (1) the problem, are there such definite types of the feeling of certainty that people may be classified according to their types, and, if so, what are the types and what their relation to other psychological characteristics of the individual? (2) the problem, what will be the result of careful and trained introspection as to the relation of so-called logical and psychological certainty and in what fields do these appear for different individuals? (3) the problem, how can a test for grading the probable percentage of error in the judgments of different grades of certainty made by any one person be constructed? and (4) the problem, how are such facts as those given in Table IV to be connected with the effort required for attention, the type of certainty of each subject, etc.? Other problems could, of course, be suggested, but these, I feel, mark the steps that naturally follow the experiments described here.

FOOTNOTE:

INHIBITION AND REËNFORCEMENT

BY LOUIS A. TURLEY

Experiments made by Ranschburg on the significance of similars in the process of learning and remembering determined that when duplicates occur within a series of stimuli, one either totally or very greatly inhibits the perception of the other according as they are contiguous or are separated by other stimuli. Dr. Yerkes, in testing the effect of auditory on visual and tactual stimuli in frogs, found that if the auditory stimulus preceded another stimulus by various time-intervals, it had an alternating reënforcing and inhibitory effect. A similar result was obtained by Hofbauer in a similar experiment on human subjects. The question now arises,--if the time-interval were increased between a stimulus and its duplicate in a series would the inhibitory effect gradually approach zero where all effect of the preceding stimulus ceased, to which Ranschburg's experiments point, or would the inhibitory effect be alternated with one of reënforcement as the experiments of Dr. Yerkes and Hofbauer would indicate? This problem--the effect of a stimulus on its duplicate in a succeeding series of stimuli--is the problem I undertook to solve. For this purpose, it was necessary to introduce exactly determinable time-intervals between the stimulus and its duplicate. Therefore I used--as Miss Kleinknecht did for other purposes--a stroboscopic arrangement instead of simultaneous presentation which Ranschburg used.

My apparatus was Professor Münsterberg's Stereoscope without Prisms or Lenses, a description and photograph of which was published in the article by that title in Psychological Review, vol. 1; or rather, I used Professor Münsterberg's attachment to Kohl's centrifugal machine, since my apparatus was not identical, except in principle, with the "Stereoscope." The "attachment" consists of two black discs about thirty inches in diameter, mounted about eight inches apart on the disc-shaft of the centrifugal machine. The back disc is of wood. The outer three inches of its face is furnished with thirty-six equidistant strips of black tin, one end of each of which is bent so as to grip a groove in the rim of the disc, and the other end of each is gripped by tiny thumb-screws so that the strips lie along radii of the face of the disc. The front disc, slightly smaller than the back disc, is of pasteboard. Between the two discs a stationary black screen with a short narrow slit was placed so that the slit revealed only the strip on the horizontal radius of the back disc. Behind this screen an eight-candle-power electric light was placed to illuminate the back disc,--as the experiment was carried on in a darkened room. By moving this light I was enabled to vary the intensity of illumination to offset the skill of the observer.

For my purpose, a small white figure--one of the ten characters of the Arabic notation--was stuck on about the middle of each of the tin strips on the back disc; and radial slits, one millimetre wide and an inch long, were cut from one sixth of the circumference of the front disc so as to come opposite six of the strips on the back disc. Similar radial slits were cut at various intervals from the remaining five sixths of the circumference of the front disc. These were covered by small pieces of cardboard fastened to niagara clips, thus making them readily removeable. By this means any desired figure could be exposed in the same revolution with the series exposed by the six slits above mentioned.

The thirty-six strips were divided into six series of six each, indicated by chalk-marks on the disc. Each of the series was often changed in whole or in part by shifting and interchanging the strips.

The figure on which the effect of a preceding stimulus was tested occupied the fourth place in the series, since this is the place where the greatest number of errors occur, as is shown by the experiments of Ranschburg and previous investigators in the Harvard Laboratory. In my experiment, 4, 5, 6, 7, 8, and 9 occupied the fourth place in the 1st, 2d, 3d, 4th, 5th, and 6th series respectively, and the effect of a preceding stimulus was tried on each of these figures for each time-interval. The preceding stimulus in each case was a duplicate of the fourth member of a series, and was a member of some other series. Thus the fourth member of each series was at all times fixed and constant while the preceding stimulus occupied successive progressive positions round the disc. The other members of each series were chosen at random, care being taken that the fourth figure was not duplicated within its series, since it would then have taken part in inhibition within the series.

By adjusting the front disc, I exposed any one of the series desired, and by removing the cardboard blind from one of the suggestion slits, I gave a stimulus at the desired time-interval in advance of the fourth member of the series. The first interval I used was 1.11 sec. as Miss Kleinknecht had tried intervals up to 1 sec. My second interval was 1.39 sec., the third 1.8 sec., and then every .277 sec. up to 4.3 sec. In performing the experiment I exposed alternately a series without and a series with a preceding stimulus--taking from the observer three reports of each--until the six series had been seen. I then repeated this, exposing with a preceding stimulus those series that had been exposed without preceding stimulus, and without preceding stimulus those series that had been exposed with a preceding stimulus in the first instance. In this way I equalized and minimized the effects of novelty and memory.

At 1.11 sec. there was considerable inhibition in five out of six cases. In the sixth case there was slight reënforcement at this interval. With an interval of 1.39 sec., with one exception,--not the exception above mentioned,--there was a stronger inhibition than at 1.11 sec. Inhibition in all cases began to decrease from 1.39 sec. until it ceased at about 1.8 sec. The preceding stimulus then had a reënforcing effect which reached a maximum in four cases at 2.08 sec., one at 2.36 sec., and one at 2.64 sec. Then, in all cases, there was a decrease of the reënforcing effect which in three cases amounted to inhibition. In the other three cases, the preceding stimulus had no inhibitory effect for an interval greater than 1.8 sec. For one of these, Fig. 5, the preceding stimulus had a reënforcing effect for all the intervals beyond 1.8 sec. The second trough in the wave or interval of maximum inhibition was at either 2.64 sec. or 2.92 sec., except for the person for whom there was constant reënforcement beyond 1.8 sec., in which case the first interval of least reënforcement or second trough was at 3.19 sec. This was the second interval of greatest enhancement, or second crest, for four of the others. Then followed a third point of no effect or inhibition, which was 3.75 sec. or 4.03 sec. For the person for whom the preceding stimulus had least enhancing effect at 3.19 sec., the second interval of greatest reënforcement coincided with the interval of greatest inhibition for the majority of the other observers. For four of the six observers, the third interval of greatest reënforcement was 4.3 sec. In this, the observer agreed for whom the last interval of greatest reënforcement was 3.75 sec. Thus while, for this observer, the first two points of greatest reënforcement were separated by an interval of 1.11 sec., the second and third points were separated by an interval of only .55 sec. This same thing occurred in the records of two other observers, for one at this point, and for the other at another point. Of the two dissenters from the opinion of the majority that the third crest was at 4.3 sec., one was an erratic observer; and for the other, there was a slight reënforcement at 4.03 sec. and no effect at all at 4.3 sec.

Fig. 1 represents the average of the records of the six observers. The curve is based on the difference between the number of times the fourth members of the series were seen with and without preceding stimulus. The base-line represents the number of times the figure was seen without preceding stimulus, taken each day as the normal for that day. Figures above the base-line represent the greater, and those below the line, the less number of times the figure was seen with preceding stimulus, or reënforcement and inhibition, respectively. The first two points are the average of fifty-four observations; each point beyond the second is the average of 108 observations. Figs. 2, 3, 4, and 5 represent individual records constructed as Fig. 1, each point being the average of eighteen observations.

The curve in Fig. 1 is somewhat misleading in showing points of maximum reënforcement at 3.19 sec., 3.75 sec., and 4.3 sec. In no individual case was this true. The reason for the crest at 3.75 sec., or at least for its height, is that in two cases reënforcement was considerable at this interval, and there was little inhibition to offset this in the general average. At 3.19 sec., which was the second interval of greatest reënforcement, for four out of the six observers, owing to practice, the reënforcement was not great (Fig. 4), but in no case was there inhibition at this point. Thus for the lack of strong positive effect at 3.19 sec. and the lack of strong negative effect at 3.75 sec., the two crests are the same height, while the first represents the maximum effect for four and the second for two observers.

From these results, taking everything into consideration, my conclusions are:

(1) If a stimulus precedes at various time-intervals its duplicate in a series of stimuli, it will alternately inhibit and reënforce the perceiving of the duplicate stimulus.

(2) Within 4.5 sec. there are at least three points each of maximum inhibition and maximum reënforcement.

(3) The points of maximum inhibition and likewise those of maximum reënforcement are separated by intervals of from .55 sec. to 1.2 sec.--more often by one of the two extremes than by any mean.

(4) Up to 4.5 sec., as the time-interval increases, the maximum inhibition generally decreases, while the maximum enhancement correspondingly increases.

What the limit of this periodic effect is, I cannot as yet say, as up to the present I have not used time-intervals beyond 4.3 sec. But from the intensity of the effect at this interval, I do not expect the limit to be within several seconds.

FOOTNOTES:

THE INTERFERENCE OF OPTICAL STIMULI

BY H. KLEINKNECHT

The purpose of this investigation is the determination of the location, extent, nature, and cause of the interference of optical stimuli. Ranschburg studied the phenomena carefully in using optical stimuli which were spread over the retinal field, for instance, a series of letters or figures one beside the other. But if we are to experiment on the inhibitory influence of a certain qualitative impression, we must try to eliminate the local difference; the letters or figures ought to be seen at the same spot.

This became possible by a stroboscopic arrangement, consisting of two parallel circular discs one foot apart on the same axis, whose motion was controlled by an electric current.

The discs were 60 cm. in diameter. Thirty-six radii were drawn equidistant on the farther disc, and on these were clasped black tin strips bearing letters or numbers or colors. The nearer disc was similarly divided and an opening, 3 mm. in width, was cut at each radius. This exposed the number. A cardboard placed between the discs limited the range of vision, its opening being 4 × 5 cm.

The figures were 10 mm. high, white, and placed on a dark background.

Preparatory stimuli were given to enable the subject to adjust his eye to the farther disc. They were so placed as to fall on different retinal points, thus avoiding fatigue.

Many of the tests employed by Ranschburg were used again to ascertain the influence of the change in method and with the hope that such differences might throw some light on the nature of the interference. At first there were six subjects, afterwards eight--all graduate students and trained in laboratory work. The experiment was carried on in the morning. Numbers consisting of six digits were exposed on a dark background. The time of exposure varied with the subject, but was constant throughout the experiment. The subject was asked to record the number immediately after perceiving it, but in almost every case it was read verbally (its retention being thus facilitated) and then recorded.

For the first few weeks letters were used. But since subjects found it very difficult to distinguish these, a change was made to figures. For a month and a half numbers were given for the purpose of training the subjects and of ascertaining the speed best adapted to each. This varied from 5-1/2" to 8" a revolution, each figure being exposed from 115 to 166 sigma.

Three series of numbers were given: (1) Homogeneous, containing a repeated figure, as, 495851. (2) Heterogeneous; as, 708654. (3) Similar, that is, in construction; as, 813470 (8 and 3 being easily substituted for each other). Other similars given by Ranschburg are 9 and 0, 9 and 6, 9 and 2, and 5 and 3.

In order to determine the place of greatest interference, the repeated figures were located in all possible positions, while the preceding and succeeding figures were left unaltered, so as to obviate any new influences which might result from a change of relations. There are fifteen possible variations of the series: mabcdm, ambcdm, abmcdm, abcmdm, abcdmm, etc.

The following table, illustrative of the scheme ambmcd, will show the character of the results obtained. Only the numbers in which errors occur are here recorded, those figures which were incorrectly perceived being printed in heavy type. The dash is used when the location of the figure omitted is known, and the interrogation mark when the reply is doubtful.

8" 8" 5-1/2" 5-1/2" 5-1/2" 8" V. R. S. M. H. E. 708025 70625 76082 ..... 70825 7082-5 70285 958564 95584 ..... ..... 95864 985 ? 4 958-54 281845 281485 ..... 20861 28185 281-54 436392 43632 43636 436932 436924 43632 43632 526273 526723 5257 572673 52763 ..... 52623 940469 94069 940465 ..... 94069 94640 940-69

The interference may result in permutation, substitution, or inhibition. The latter two may take several forms; as, inhibition of identicals, of similars, of dissimilars, the location of the omitted figure being known or unknown; also, substitution of an identical, similar, or dissimilar figure which precedes or follows.

The homogeneous series (540 tests) gives results as follows:

HOMOGENEOUS SERIES

Inhibition of Inhibition of Inhibition Identicals. Similars. due to Location. Location of the Spot Spot Spot Spot Spot Spot Identicals. Known Unknown Known Unknown Known Unknown

mabcdm 1 1=6 1 1 4 5 ambcdm 2 2=6 5 2 1 3 3 3=6 2 3 5 4 4=6 3 3 4 2 5 5=6 6 15(?) 4 5 6 1=5 1 2 1 2 1 3 7 2=5 5 3 3 8 3=5 3 7 2 1 9 4=5 2 21(?) 2 5 3 10 1=4 9 4 3 11 2=4 3 9 4 1 7 12 3=4 3 19(?) 1 2 4 13 1=3 5+3(?) 2 1 10 14 2=3 1 11(?) 3 8 15 1=2 6(?) 1 4 9

Total 19 48+75(?) 6 38 17 71

I. Inhibition

(1) There is considerable inhibition only when identicals are next to each other.

(2) There is but little difference in the amount of inhibition when identicals are removed two and when removed three places.

(3) The interference is greatest when 3d = 4th, 4th = 5th, and 5th = 6th figures, in which schemes it is almost equal in amount.

(4) When identicals are adjacent, it is impossible to decide whether there be inhibition or fusion, i. e., whether one be inhibited and the other appear, or whether the figure seen be a fusion of the two (unless there is an omitted figure whose location is known to the subject). Its intensity does not serve as a clue, for the perception of the number demands the full concentration of the attention.

II. Substitution

When the interference is not sufficiently great to cause inhibition, substitution may result.

(1) In the majority of cases the substituted figure is a dissimilar not occurring in the number.

(2) A preceding figure is frequently substituted.

(3) Occasionally a figure is replaced by its similar, but this is not true of the homogeneous element. (Cf. with Ranschburg.)

(4) Sometimes the next figure in the natural number series is substituted; as, 9 for 8, 6 for 5.

(5) The figures containing straight lines (4, 7, and especially 1) are less subject to illusion; likewise the smaller numbers (1, 2, 3, 4).

III. Permutation

The permutation represents the least interference.

(1) The 4th and 5th figures are most often exchanged.

(2) The figure is seldom permuted more than two places, and generally but one.

The recording of the number was most interesting. Generally the first few figures and the last were written without comment, but the 4th and 5th often called forth an expression of doubt, which was immediately followed by an exclamation at the coming of the figure into consciousness as if by "inspiration." The experience was extremely peculiar. The figure, fully as distinct as those already perceived, was always from 5″ to 10″ late, and seemed to "pop in unannounced"--to "come from nowhere." A substitution or permutation occurred without this lapse of time.

HETEROGENEOUS SERIES

(1) There are less than half as many inhibitions as in the homogeneous series, the largest number being in the 4th and 5th places.

(2) The number of substitutions is decreased by a fourth, the identicals and similars remaining the same.

(3) There are no fusions.

(4) Fewer permutations are found in this series. The 4th and 5th figures are most often permuted. In a very few cases the figure is permuted four and five places.

(5) There are an equal number of doubtful perceptions in both series.

SIMILAR SERIES

(1) There are few cases of inhibition, and even more surprising is the small number of cases in which a figure is inhibited by its similar.

(2) There are more substitutions, 6 being very often substituted for 5, generally in the 6th place and when preceded by 0 or 9, often by both. Similars are never replaced by identicals (69 by 66 or 99) as Ranschburg found in his experiments.

(3) The fusion of similars equals that of identicals in the homogeneous series.

(4) The number of permutations is the same as in the homogeneous series and less than in the heterogeneous.

(5) The doubtful perceptions have decreased by half.

That there are fewer errors in this series than in the homogeneous or heterogeneous, may be due to the fact that it was given last, especially since one subject showed marked improvement in the entire series and another during the last half. These subjects suddenly began to see six figures, while previously they had seen but five and those contained errors.

In the above 1620 tests, 9 and 0, and 8 and 3, are sometimes inhibited by and substituted for each other, but the remaining similars mentioned by Ranschburg seldom have any such effect.

It is impossible to determine definitely the nature of the interference, the greatest uncertainty existing in the homogeneous series when two identicals are adjacent. But the interference is dependent not only upon the identity or similarity of the figures of which the number is composed but also upon their location.

INHIBITIONS

1 2 3 4 5 6 Total Place Place known unknown K. U. K. U. K. U. K. U. K. U. K. U.

Homogeneous 1 13 2 28 9 41 15 31 15 44 42 157 6(?) 14(?) 19(?) 21(?) 15(?) 75(?)

Heterogeneous 2 5 1 8 2 15 4 36 5 34 2 25 16 123

Similar 4 4 5 3 6 2 13 5 32

Total excluding(?) 2 5 2 25 4 47 13 82 23 71 19 82 63 312

Total of Known + Unknown 7 27 51 95 94 101 375

(?) Inhibition or fusion.

SUBSTITUTIONS

1 2 3 4 5 6 Total

Homogeneous 8 12 26 27 38 14 125 Heterogeneous 4 4 14 21 30 20 93 Similar 1 5 9 25 33 27 100

Total 13 21 49 73 101 61 318

FUSIONS [See (?) under Inhibitions]

1 2 3 4 5 6 Total

Homogeneous 1 2 1 3 10 17 Heterogeneous 0 0 0 0 Similar 3 3 6 6 18

Total 1 5 4 9 16 35

Note. There were no clear cases of fusion, but the evidence favored fusion rather than inhibition.

PERMUTATIONS

1 2 3 4 5 6 Total

Homogeneous (a) 6 29 46 56 30 167 (b) 5 21 45 68 35 174 Heterogeneous (a) 15 25 60 62 28 190 (b) 14 23 51 82 44 214 Similar (a) 13 20 37 78 16 164 (b) 12 17 26 75 28 158

Total (a) 34 74 143 196 74 521 (b) 31 61 122 225 107 546

(a) forward, (b) backward

Note. The permutation of an inhibited figure was not noted unless its location was known: hence the difference in the number of forward and backward permutations.

1 2 3 4 5 6 Total

Total Interferences 54 160 323 509 524 300 1870 % 3% 9% 17% 27% 28% 16% Absolute Errors (excluding 20 55 119 191 225 103 713 Permutations) 3% 8% 17% 27% 31% 14%

ABSOLUTE ERRORS (excluding Permutations)

Homogeneous Heterogeneous Similar Inhibitions 199 139 37 Substitutions 129 93 101 Fusions 17 18 (?) 75

Total 420 232 156 52% 29% 19%

Over 50% of the errors were found in the 4th and 5th places.

In 1620 tests, the homogeneous series contained 52% of the absolute errors, the heterogeneous 29%, and the similar 19%.

COLORS

In the hope that some light might be thrown upon the main question at issue, the writer changed the stimuli, using colors instead of numbers.

It was important that the colors should be of the same or only slightly varying intensity and that they should be easily distinguishable. In a series of preliminary experiments in which red, blue, yellow, green, brown, gray, pink, and violet were used, red was lost in 8% of the tests, and gray in 25%.

Colors 1×4 cm. in size "ran into each other," while those which were 1×1 cm. remained distinct.

Here it was found necessary to distinguish between the various factors which might cause inhibition. Three factors entered into each test--perceiving, naming, remembering.

Four subjects found difficulty in naming, especially at first. The various methods of naming are given below in detail. M. says: "The name of the color is localized in my mouth. Generally there is no movement of the tongue--an impulse only; and the name is felt in that part of the mouth where the sound would be reflected, as, red in the upper part, blue near the front, etc."

S.: "Usually there is no apparent tendency to pronounce. Occasionally, naming them over inaudibly before recording is found advantageous."

E., V., and H.: "The naming is mental, but is accompanied by a slight movement of the tongue and throat."

684 heterogeneous and 200 homogeneous tests showed that greatest inhibition occurred in the following order: 4th place (27%), 3d (26%), 5th (24%), 2d (11%), 6th (8%), 1st (4%). There was but little difference in the 3d, 4th, and 5th places.

During first tests subjects were allowed only one exposure, but later it was thought best to eliminate all omissions resulting from inability to name colors perceived, and hence they were asked to record only when able to name all colors perceived during that exposure. However several required but one exposure.

Preliminary drill was given for two weeks. Since no clear cases of fusion had been obtained in the entire number-series, the one aim of the experimenter was to ascertain whether fusion of colors, even though of heterogeneous, be possible. Eight hundred heterogeneous tests gave 927 cases of inhibition, 7 of fusion, and 18 which, though somewhat doubtful, yet gave more evidence of fusion than of inhibition. Yellow (3d place) and brown (6th place) were seen as yellowish-brown, brown and pink as pinkish-brown, etc. Gray was seen several times instead of a color and its complementary when these were in immediate succession. This was true of both red and blue. Half of the total number of substitutions was due to the displacement of yellow by brown. And a color not in the series was as likely to be substituted as one preceding or following the displaced color.

Two hundred and fifty-two homogeneous tests showed that there is greatest interference when identicals are in immediate succession, and least, when removed two places. The doubtful (fusion?) cases number one third of the inhibited. The 4th and 5th colors are permuted most often, as was found to be the case in the heterogeneous series also. The element is generally permuted but one place.

The heterogeneous color-tests show three times as much interference as the corresponding number-tests, and the homogeneous twice as much. The discrepancy in the amount of variation may be due to the experiments with the heterogeneous colors being earlier, when naturally more errors would be made.

However, a comparison of 252 homogeneous with the same number of heterogeneous tests, taken at the same time, shows that there is a much larger difference in the number of absolute errors between the heterogeneous and the homogeneous number-series than there is, proportionately, between the two series of color-tests.

Lest the want of correspondence in the results might have been due to the comparatively small number of immediately successive identicals in the color-tests, 90 homogeneous tests, equally distributed among all possible variations in the location of the identical elements, were compared with 90 heterogeneous, and it was unexpectedly found that the absolute errors as well as the permutations were almost equal in the two series. Nevertheless, the validity of a conclusion based on so few tests may well be questioned.

Ranschburg found that simultaneous homogeneous stimuli interfere with one another; while simultaneous heterogeneous stimuli clear the way for one another. On the basis of the experiments with numbers, the writer would amend the conclusion reached in the earlier research to read thus: Homogeneous optical stimuli, whether occurring simultaneously in different positions, or in immediate succession in the same positions, interfere with one another; while heterogeneous stimuli clear the way for one another.

FOOTNOTES:

SUBJECTIVE AND OBJECTIVE SIMULTANEITY

BY THOMAS H. HAINES

This investigation finds its starting-points in two widely separated lines of experimentation in the problems of attention. These two lines are the "scope-of-attention" experiment with the tachistoscope, and the "time-displacement" experiment with the pendulum apparatus. It seems to me these two can be brought into relation to each other to the help of each of them individually, and that an investigation taking these wide relations within its scope may reasonably be expected to throw new light upon the manner in which mental processes are related to each other when they are together in consciousness at the same time. The first of these experiments (tachistoscopic) is concerned with the number and relative clearness of the processes which go on at the same time. The second (displacement) is concerned with the conditions of the subjective displacement of one of two objectively simultaneous stimuli with reference to the other. Its problem is the essential psychological problem involved in the astronomer's error in transit observations by the eye-and-ear method, for the personal equation arising in these observations is more a matter of the reciprocal relations among the processes which are together in consciousness at the moment of observation than it is of mere reaction time. It is primarily more a matter of relative clearness, as controlled probably through interference of one with another, than it is of the more or less temperamental facility of converting ideas into action.

The psychological question at the heart of the observation-error, called the personal equation, is this,--What are the conditions which hinder such a division of attention among the parts of the complex operation of coördinating sense-stimulations, that the processes which start simultaneously may proceed to equal clearness at the same time, and so be perceived as simultaneous? The facts sought in order to answer this question are the very same as some of those, at least, demanded by the "scope-of-attention" investigation when it really opens up to its true problem. W. Wirth has recently shown, in an exhaustive criticism of the tachistoscopic method, that "scope of attention" is primarily concerned with the relations of the processes present together, and that this demands a previous exhaustive study of their relative clearnesses. Earlier studies by the tachistoscopic method, as, for example those of Cattell on the relatively short time for the perception of letters in words, as compared with that for separate letters, and the overlapping of processes in continuous reading, showed that the important question is, what are the processes which may go on at the same time. Leaving out a statement of the nature of the processes is equivalent to leaving out one of the dimensions when endeavoring to state the contents of a solid. The scope of attention can be defined adequately only when one knows fully what the separate processes are as well as how many there are. This analysis, which the scope-of-attention problem demands, cannot fail to be directly fruitful for the solution of the time-displacement problem. The analysis of this larger problem directly involves the former. Any attempt to investigate the time-displacement of sense-impressions from simultaneous stimuli must inevitably place the highest value upon the whole detailed analysis of any moment of attentive effort.

The present investigation, starting with the facts of time-displacement, and taking the hint offered by Gonnessiat, attempts to show, by a more complete analysis, the effects of the various relations within each series,--the visual within which the sounds are to be placed, and the auditory series itself, and also relations existing between the two series. In other words, the attempt is made to strip the "displacement" experiment until nothing more remains to be coördinated than a single pair of simultaneous stimuli. This was the experiment of Exner. He investigated the shortest discriminable interval marked off by various pairs of stimuli, addressed to the same sense and to different senses. From this coördination of a visual and an auditory stimulus, where the limits of the "specious present" are obtained, I make a turn into the realm of the scope of attention. By a new method, whereby impairment of accuracy of processes is made the test as to whether the processes have proceeded together, it is shown that two such perceptual processes can go on just about as well at the same time as separately. Since this test is subject to the objection that the visual and auditory processes may really be successive, though seemingly at the same time, owing to retinal inertia, the same question is removed to an entirely different plane in a further and more detailed set of experiments where the processes combined are judgments of comparison based upon one and the same visual sensation.

EXPERIMENTS IN TIME-DISPLACEMENT

The Leipsic Complication Experiment with the pendulum apparatus (for description of this see Wundt's Physiol. Psy., 5th ed., vol. 3, p. 82) was an early adaptation of the astronomers' eye-and-ear method to the purposes of psychological experimentation. Instead of localizing a visual stimulus (star on meridian) in an auditory series (clicks of a chronoscope) as in the eye-and-ear method, this adaptation localized an auditory stimulus (bell-stroke) in a visual series (successive positions of a pointer on a graduated circle). This pointer passed around to the right and to the left from the position of rest, in which it pointed vertically upward, as the pendulum, to which it was connected by clockwork, swung back and forth. By a simple adjustment the bell-stroke could be made to come at any point in the complete double swing of the pendulum, and so anywhere in the arc over which the pointer moved. This machine makes an additional problem as to the effects upon displacement of the increasing and decreasing speed. My aim being to simplify as much as possible the displacement-error and so reduce it to its elements, this feature was not only not of direct interest, but it was very desirable to dispense with it altogether. This was done by arranging the visual series so that the members were shown in perfectly regular order, i. e. with equal time-intervals, throughout the series. These equal intervals were secured by the rotation of a disc at a uniform rate.

My method also gave a more distinctly serial character to the visual stimuli, in that they were separated by blank periods. The series consisted of letters in alphabetical order. Denison's smallest white letters, about six millimetres in height, were pasted upon a disc of black cardboard, near the circumference and perpendicular to radii, so that they would appear in succession and right side up, to an observer looking through a slit at the peripheral region of the disc, as it rotated. The letters were placed in three concentric rows, so that as the disc rotated they appeared in three different places. The disc was 56.5 cm. in diameter. As a further aid in securing separate exhibitions of letters, another black disc of the same size as the one bearing the letters, with radial slits 2 mm. wide and cut in from the edge 4 cm., opposite each letter on the other disc, was mounted on the same shaft, six inches from the first, and between it and the observer. A short observation-tube was placed at the same height as the axis of the discs parallel to this axis, and opposite the slits when they were at this elevation. Looking through this, as the discs were rotated, one would see the letters right side up and in serial succession. Uniform illumination was secured by working in a dark room with artificial light. An electric lamp was hung between the discs. Uniform motion was secured by an automatic control gravity motor, connected by belt with a pulley on the disc-shaft.

The auditory stimulus, a click, adjustable to any part of the series, was made as follows: A wooden shaft, mounted on the same axle as the discs, and beyond the discs from the observer, could be rotated freely around the axle when the nut securing it was loosened. This shaft extended beyond the edge of the disc. It carried a copper wire which was in contact with the axle. A mercury cup was placed on the table, upon which the machine rested, in such position that the copper tip passed through the mercury when the discs rotated. It was thus a very simple matter to connect an electric sounder so that it would click every time the circuit was made by the copper passing through the mercury. And, by the adjustment of the wooden shaft, the click was readily placed anywhere in the visual series.

As already suggested above, the length of interval between members of the visual series, and also the time between clicks, seem to be important factors in determining the amount, and perhaps also the direction of the displacement. Bessel found his personal equation was considerably diminished when he used a clock marking half-seconds instead of one marking seconds. Wolf also diminished his error by using a clock beating one hundred times a minute instead of one beating seconds, which he was accustomed to use. Wundt found his customary negative displacement on the pendulum apparatus (coördinating the sound with a position of the index earlier than that with which it was actually simultaneous) disappeared when he had members of the visual series one thirty-sixth second apart and the auditory stimuli one second apart. It seemed important at the outset, therefore, to determine, if possible, the effects of each of these factors.

BOTH INTERVALS PROGRESSIVELY VARIED

In each experiment the observer was allowed to observe as many complications (coincidences of click and letter) as he desired, in order to assure himself of his judgment. The experimenter counted and recorded the number observed in each experiment. Experiments were made in series of ten. Six different combinations of intervals were used in this first group of experiments. The auditory intervals (time between successive clicks) and visual intervals (time between successive members of the visual series) are given at the tops of the columns in Table I. This table is a summary presentation of the results of this group. There were three observers. During each hour of experimentation with a given observer, at least one series with each of the first four time-interval combinations was tried out. "Aver. num. Trials" means the average number of complications observed in the whole number of tests averaged. "Num. Series av." means the number of series of ten experiments each averaged to give the displacement results below. "Aver. Error" is the average of all the displacements of the auditory impression, irrespective of the direction of the displacement. "Mean Displacement" is the actual mean displacement as obtained by dividing the algebraic sum of all displacements, positive and negative, by the number of experiments. The plus sign indicates a positive displacement, and the minus sign, a negative. Negative and positive are here used in the sense customary in similar experiments,--namely, the click, being heard as simultaneous with a visual impression which actually came before it, was said to be displaced negatively, and the click, being heard as simultaneous with a visual impression coming in fact later than it did, was said to be displaced positively. Average errors and mean displacements are given in the table in thousandths of seconds. Observers were asked to locate the click in the visual series in terms of one tenth the distance or time between the letters.

TABLE I

Aud. Interval (sec.) 1.28 2.56 4.04 8.40 1.28 2.02 Vis. Interval (sec.) .040 .080 .120 .260 .080 .120

Obs. B Av. num. Trials 13.9 5.8 3.8 2.1 9.8 13.9 Num. Series av. 8 13 13 8 2 2 Aver. Error (sec.) .056 .064 .077 .164´ .045 .067 Mean Displac'mt (sec.) +.045 -.040 -.067 -.152 +.045 +.067

Bo Av. num. Trials 9.4 4.1 3.0 2.0 5.5 3.5 Num Series av. 6 10 11 8 3 2 Aver. Error. (sec.) .114 .060 .054 .049 .05 .082 Mean Displac'mt (sec.) +.114 +.045 +.033 .000 +.045 +.082

M Av. num. Trials 6.3 3.1 2.5 2.2 5.3 4.4 Num. Series av. 9 12 12 10 3 2 Aver. Error (sec.) .09 .07 .076 .110 .067 .172 Mean Displac'mt (sec.) +.089 -.058´ -.058 -.104 +.062 +.168

The first four combinations of intervals above, with which the major part of the results was obtained, it will be noticed, are approximately proportionate increases in each interval, column by column. These conditions were planned with a view to revealing the conditions, most favorable for coördinating the auditory and visual impressions, for each observer, so that his displacement would disappear, or show a tendency to disappear. So far as is shown by these results, there are here two types of observer. Bo has no mean displacement for the 8.40-.260 sec. combination, and it steadily decreases toward this point as the two intervals increase. Both B and M, on the other hand, have a considerable positive mean displacement for the 1.28-.040 sec. combination, and a considerable negative mean displacement for the 2.56-.080 sec. combination, and there is a further increase in the negative displacement as the intervals increase from this point. It seems as though these observers would give a mean displacement of zero for some combination of intervals between these first two. It will be noticed that the average number of trials is exceptionally large for all three of the observers in the first combination. This seemed to be pretty clearly due to the very short interval separating visual impressions.

THE AUDITORY INTERVAL alone VARYING

In order more certainly to isolate the influence of the time-interval between successive auditory impressions, another series of experiments was performed, in which this interval between clicks, alone, was varied from series to series. The visual interval was kept at .083 sec. throughout. This seemed to be about the shortest time-separation at which the successive impressions were perfectly distinct. The auditory impressions were at 1, 1-1/2, 2, 3, and 4 sec. intervals. The additional observer, H, was myself. I obtained these results by experimenting alone. I adjusted the wooden shaft carelessly to a new position and started the machine. When speed was attained, I would make the observation just as an observer for whom the adjustment had been made. I would have as little idea beforehand as he with regard to the position of the click in the series of letters. Having made the observation, however, I measured the actual place of the sound and recorded it, as well as my judgment. In this way, of course, I had some idea, all the time, as to what kind of displacements I was making and how large. I was as careless of this knowledge as possible, and the records were laid aside absolutely, until I was through with the whole experiment. Terms used in Table II are the same as in Table I.

TABLE II

Aud. Interval (sec.) 1 1-1/2 2 3 4 Vis. Interval (sec.) .083 .083 .083 .083 .083

Obs. B Av. num. Trials 8.5 6.8 6.2 4.8 4.8 Num. Series av. 10 10 10 10 10 Aver. Error (sec.) .097 .108 .106 .097 .101 Mean Displacement (sec.) +.097 +.108 +.106 +.097 +.101

Bo Av. num. Trials 6.0 5.0 4.2 3.2 3.1 Num. Series av. 10 10 10 10 10 Aver. Error (sec.) .103 .080 .081 .092 .082 Mean Displacement (sec.) +.102 +.073 +.078 +.089 +.075

M Av. num. Trials 4.4 3.8 3.4 3.0 2.8 Num. Series av. 10 10 10 10 10 Aver. Error (sec.) .088 .084 .081 .068 .052 Mean Displacement (sec.) +.086 +.079 +.072 +.051 +.048

H Av. num. Trials Num. Series av. 10 10 10 10 10 Aver. Error (sec.) .043 .036 .047 .040 .037 Mean Displacement (sec.) -.022 -.012 -.027 -.017 -.013

One series of ten of each of these combinations was given during each hour of experimentation with each observer. These were also given in a different order each day, so that no combination should have the advantage, by practice or lack of fatigue, in the average of the ten series. Here again it was evident, in the records of each of the observers for whom the count was made, that the largest number of trials was necessary in the 1-.083 sec. combination. It thus appears that it was not the short visual interval, .040, in Table I, that was responsible for the large number of trials necessary in the first combination. Here, where there is the same visual interval of .083 sec. throughout, it must be the short auditory interval which makes particularly difficult conditions for attention. This agreement between the results in both groups of experiments seems to indicate unfavorable conditions for accurate coördination at auditory intervals as short as one second. The large changes in the mean displacement for B and M between the first two combinations in the first group (Table I) was kept especially in mind in planning this second series of combined intervals. It was presumed from the results given by these observers in Table I that they would each, with the range of auditory interval presented them in these experiments, show a point of no displacement, or a very slight one, and an increasing displacement on each side of this point. They both seemed to indicate a time-interval favorable for the "ripening of apperception" as Wundt and Von Tschisch call it, and I planned these experiments especially to bring it out more clearly. But there is far less indication of a time most favorable for "ripening" than in the previous group of experiments. B and M both give all mean displacements as positive, and decidedly small differences in displacement for the various combinations. Results of Bo are, however, entirely consistent with those of Table I. H gives a very small negative mean displacement throughout. This, as well as the smallness of the average error, may be due to the knowledge of results which I had.

An examination of the detailed daily results, which cannot be exhibited here, shows considerable change in the direction of the displacements as the work proceeded. This is especially marked in the case of B, who, during the first two hours of experimentation, gave only negative displacements. Through the rest of the first group there was a gradual increase of positive displacements, and in the last two hours about 90% were positive. In the second group he did not give a single negative displacement. The same change is manifested in the results of M for the first group; but he did not change over nearly so completely. In the five hundred experiments of Table II, for M, there are three hundred and ninety-two positive, sixty-seven negative, and forty-one no displacements. Bo gave a number of positive displacements from the start. These increased considerably in the second over the first group, showing only thirty-seven negative displacements in the second group. This change in the direction of the displacement, rather independently of the intervals, is an interference with the main purpose of the experiment. It may represent the effect of practice.

Angell and Pierce found the same progressive change from negative to positive displacements. They explained it as a change in the focus of attention. The visual series is focal at first, and the sound becomes focal in later experiments. Negative displacements result from fixing the last possible point in the visual series before the sound is heard, while positive displacements result from getting the first letter possible after the sound. The method of my observers, with the large numbers of trials at their disposal, was to "let the sound announce the letter" on the first trial, and then to "lie in wait for the letter" so announced, and to "see whether it was too late or too early." It was found to be too late usually, for this was the second method of Angell and Pierce, which gave positive displacements.

So at the next trial the preceding letter would be waited for, and tested in the same way. The first trial was thus auditory-visual attention and the second was visual-auditory, and there was a striving after a balance where neither auditory nor visual impression had the preference.

As soon as adjustment to the conditions of a given combination had been secured, it was a simple matter to anticipate, with a fair degree of accuracy, both a given letter and the recurrence of the sound. The attention could thus be pretty accurately divided between the two, and a very small time-displacement was the result. When I was acting as observer, a change of the auditory interval upset the whole plan of procedure for a short time. I had to accustom myself to the new rhythm. But as soon as this adjustment was made, it was just as easy to make the judgment at one rate as at another, barring variations which might be called fortuitous, since they were so small. This experience with the conditions here under consideration, as well as the introspections of the other observers, convinces me that the conception of an apperception-ripening time has been overworked.

It is true that I find here, just as Pflaum found, displacements in both directions with every observer. It seems very doubtful to me, however, whether these are in any sense due to what may be considered a fixed apperception-time for a given observer, under fixed objective conditions. The facility with which adaptation is made to the changed conditions of a new combination of intervals, so that just as small displacements are made under one as another, indicates to my mind that one can control the conditions so that the apperception shall ripen quickly or slowly, depending upon the warmth of the interest, and the concentration or division of the attention,--that there is a capacity in the ordinary individual so to adapt himself to the conditions as to do equally good work in coördinating two sense-impressions anywhere within a wide range of intervals. The influence of the length of the interval separating succeeding clicks, in determining displacements, has been considerably overestimated. I should state here that no one of the three observers had any specific training to reduce the displacement. The results were not discussed with them. They had no means of knowing what displacements they were making. This certainly adds strength to the inference, from these results, that there are adaptable apperceptive conditions for coördinating sense-impressions.

THE INFLUENCE OF THE LENGTH OF THE SERIES OF VISUAL IMPRESSIONS

The next step in the analysis of the complication experiment, bringing it into relation with the simple coördination of two disparate stimuli, is to show, if possible, the influence of the series of visual impressions. This naturally divides into two lines, namely, (1) the length of the series as such, and (2) the relative influence, in case of a given kind of displacement, of the part of the series coming after the auditory stimulus, and the part preceding it. For the first, I used in comparison, a series of twelve letters, a series of three, and a single letter. For the second, the letter, whose coördination with the click was set as the task of the observer, was made successively the first, the last, and the middle member of a series of five letters.

During each hour of experimentation, the observer was tested as to his accuracy of localization of the click, (1) in a series of twelve letters at intervals of .083 sec., (2) in a series of three at the same interval, and (3) with reference to a single letter. The method for the first two was exactly as in the preceding experiments. In the case of the single letter, he was asked to localize as accurately as possible in terms of the intervals as he remembered them from the series. This introduced an element of uncertainty. One observer, St, would not give any judgments as to time-differences in the case of the single letter. Another method had to be adopted in order to obtain more comparable results. These results (Table III) are presented as showing, by comparison with the following table, the transition from one method to the other. Clicks were at 2-sec. intervals. Each number in the table is the average result of fifty or more experiments. They are in thousandths of seconds, and the plus and minus signs indicate positive and negative displacements.

TABLE III

Observer Twelve Letters Three Letters One Letter. A +.012 sec. -.029 sec. -.010 sec. G -.022 sec. +.004 sec. -.004 sec. Sh +.028 sec. -.079 sec. -.057 sec. St -.050 sec. -.036 sec. Bo +.029 sec. -.015 sec. -.022 sec.

The method of right and wrong cases was used in the next group of experiments, to secure the same conditions of making the judgment in each of the three cases used above. Selecting a letter near the middle of each series, I asked the observer, in each of these cases, just as in that of the single letter, to say whether the click was before, on, or after the letter. I worked out, in successive experiments by successive adjustments, from the position of apparent simultaneity of click and letter, in both directions, to a point where in 75% of the cases the click seemed to come before; and also to one where it seemed to come after, in 75% of the cases. So also I worked in both ways, by successive adjustments, from regions of clear discrimination of time-difference and direction, to points where the time-relation was uncertain or wrong in 75% of the trials. By averaging the just perceptible and the just not perceptible, in each case, the thresholds were obtained for "click first" and "click last." The time between these thresholds I call the "range." It is really a measure of James's "specious present" and of Stern's "Präsenzzeit." (An admirable presentation of similar results by Wilhelm Peters has appeared since this work was done.) The best means of comparing these results, for our present purposes, and also of bringing them into relation with the complication-results already obtained, is to take the mean point between these thresholds, and state its position, in time, relative to the time of the visual stimulus (letter) just before or after which the click came. This mean point is called the "Threshold Mean" in the following tables. In Table IV, for example, "After Letter .026 sec." means that the mean point between the thresholds, "click first" and "click last" falls twenty-six sigmas after the time of the exposure of the letter. These results are readily comparable with those of Peters. By dividing the "range" by two, and adding the "threshold mean" to one half, and subtracting it from the other, one has the total interval between "click first" and "click last" and its place with reference to the time of the visual stimulus.

TABLE IV

Obs. Twelve Letters Three Letters One Letter

A Threshold Mean After After Letter .026 sec. On Letter .041 sec. Letter .020 sec. Range .093 sec. .062 sec.

G Threshold Mean Before Before After Letter .015 sec. Letter .020 sec. Letter .062 sec. Range .072 sec. .083 sec. .304 sec.

Sh Threshold Mean Before After After Letter .003 sec. Letter .027 sec. Letter .003 sec. Range .172 sec. .111 sec. .241 sec.

It must be distinctly understood that these "threshold means" are not displacements, and that the two cannot be compared as if they were statements of the same facts. These means indicate the centre of gravity of the "click first" "click last" interval with respect to the visual stimulus. Changes in this centre of gravity may reasonably be expected to approximate a variation inverse to that of the displacements of the auditory stimulus. For example, any change in the conditions which would tend to increase a negative displacement would tend also to put the centre of gravity of the "click first" "click last" interval after the visual stimulus, or, if it were already after, to increase its time after. So also the positive displacement and the position of the threshold mean before the visual stimulus may be considered similar indications. For a click given at the time of the threshold mean of a given observer, in connection with the same visual stimulus, would certainly be judged by that observer as simultaneous with the visual stimulus. If, then, this mean is before the visual stimulus, the sound will be displaced positively, i. e., coördinated with a visual stimulus coming later. If the mean is after the visual stimulus, the sound will be displaced negatively, i. e., coördinated with a visual stimulus coming earlier. The position of the mean of the thresholds indicates a tendency toward the displacement of the auditory impression in the opposite direction.

In Table III, three out of five observers, A, Sh, and Bo, show a change from a negative displacement in the series of three to a positive displacement in the series of twelve. If this were the effect of the series, the same should show in the series of three as compared with the single letter. Such a change is manifest in the results of Bo. It is, however, very slight. The others increase the negative displacement from the single letter to three letters. In Table IV, of the same three observers represented, Sh changes the threshold mean from after in the three-letter series to before in the twelve-letter series, and A changes from after in one letter to on in three letters. These changes correspond to changes from negative to positive displacements for increase of series and introduction of series. G shows the same change from one letter to three, in both tables. These changes, in 55% of the cases offered for comparison in the two tables, indicate a decrease of negative displacement and an introduction of positive displacement as the effect of the visual series. The visual element is made more focal in expectant attention as it is more isolated, and so the tendency toward negative displacement and increasing negative displacement as the serial character of the visual impressions is stripped off. But there are strong counteractive tendencies, which control the 45% of comparisons not mentioned above, where the increasing series shows increasing negative displacement.

In the series all the observers adopted the method which has been outlined above, that of letting the click pick out the letter, or letting the letter announce itself. One said "the letter hits the sound." After this sorting-out of the letter, they resorted to the system of tests and counter-tests, in succeeding trials, to correct the first impression. One can readily understand, then, that when they were taken off the series altogether, an entirely different kind of adjustment had to be made. G did not succeed in making this new adjustment very well, as is shown by his exceptionally large range under one letter. He could not get the two impressions to come together. In attending to either one, he could not get the other in relation to it. There was something in the visual series which enabled him to get the visual impression in line with the auditory, and when this was absent the same kind of work could not be done.

St had also a peculiar method, which was directly dependent upon the serial character of the visual stimuli and impressions. He allowed the series of clicks and the series of visual impressions to establish themselves as a complex rhythm. Each series was rhythmic independently. The two got connection by means of the click appearing as an "after-strike," as on the piano, to a member of the visual series. The letter "flashes out" for him as that of which the click was the "after-strike." The click was thus between two letters. But there was no amount of before or after about it. It was a general quality of the whole complex which was taken to mean such and such a position of click in the series. What he thus translated into temporal judgments, were qualitative aspects of the rhythmic experience, to which he usually attached no temporal meaning whatever. Learning how so to translate them into temporal terms was a definite process of training for him. Under these circumstances, he of course had an entirely new lesson to learn when the visual series was taken away. In fact, it might be, he would now find no visual impression to which the click could be an after-strike, and so he would be entirely without material to translate into temporal terms.

Under these circumstances it is not surprising to find G and St exceptions to the majority of the observers in this experiment. This makes more probable the effect of the series, inferred above for the other observers,--namely, series decreases negative displacement.

THE INFLUENCE OF THE Position OF THE Series OF Visual IMPRESSIONS

It was noticed in the series of the three letters, particularly, that some observers were much more accurate in their work when the click was near one end of the series. In this experimental group, the comparison is between cases where the click is coördinated with (1) the first member of a visual series of five, (2) the middle member of a series of five, and (3) the last of such a series. The method was the same as that used in obtaining the results of Table IV. H was the letter used in each case for coördination. Results follow in Table V.

TABLE V

Obs. H first H middle H last A Threshold Mean After Letter After Letter After Letter .010 (sec.) .021 (sec.) .025 (sec.) Range .072 (sec.) .085 (sec.) .093 (sec.) G Threshold Mean Before Letter On Letter Before Letter .007 (sec.) .007 (sec.) Range .124 (sec.) .083 (sec.) .151 (sec.) R Threshold Mean After Letter After Letter After Letter .032 (sec.) .016 (sec.) .042 (sec.) Range .464 (sec.) .398 (sec.) .369 (sec.) Sh Threshold Mean After Letter After Letter After Letter .025 (sec.) .015 (sec.) .030 (sec.) Range (sec.) .176 .176 .166 St Threshold Mean After Letter After Letter After Letter .050 (sec.) .062 (sec.) .078 (sec.) Range (sec.) .140 (sec.) .108 (sec.) .108 (sec.)

Under these conditions, whatever the effect of the visual series, if it has any effect, opposite tendencies in direction of displacement ought to be shown in the "H last" from those in the "H first," results, as each is contrasted with "H middle." Contrasted in this way, these results, for A and St, show a relative approach of the mean to zero for "H first," and a relative departure from zero for "H last," or a decrease of a negative displacement for "H first" and an increase of the same for "H last." In other words, the series draws the displacement of the click toward itself. A negative displacement is increased by a series coming before the visual stimulus in question, and decreased by such a series coming after. For R and Sh, the negative displacement is increased in both H first and H last as compared with H middle, but relatively the most for H last in both observers. For G there is the same positive displacement introduced by both H first and H last, but it is less than in any of the other cases. The drift of the evidence here, then, is that the visual series draws the displacement in its own direction. Each observer who has a negative displacement (Threshold mean after) with "H middle" increases this when the series all comes before (H last) and two decrease it when the series comes after (H first).

THE EFFECT OF RHYTHM (Repetition of Auditory and of Both Stimuli)

It is very evident to any one who has worked at all in the complication experiment, that rhythm plays an important part in the displacement. Witness also the astronomers' experience cited above, St's waiting for the rhythm to establish itself, and my own readjustment to the new conditions when a new combination of intervals was given in the experiment with varying auditory intervals. In order to show the part played by rhythm, I tested each one of five observers on several different days, to fix for each of them both the "click first" and the "click last" thresholds, as above, under each of the following conditions: (1) one visual (single letter) and one auditory stimulus (one pair), (2) one visual (single letter) and many auditory stimuli, and (3) many visual (single letter repeated) and many auditory stimuli (many pairs). For visual fixation, the observer had a very dim light at the end of the observation-tube. The visual stimulus was a flash of red in the place thus fixated. It had a total duration of less than .005 sec. The surface exposed subtended a vertical visual angle of about seven tenths of a degree. In the case of one visual and many auditory stimuli, the visual stimulus was given when the observer had heard the recurring auditory stimuli several times and had himself given the "ready" signal. The results follow in Table VI.

TABLE VI

Obs. One Visual and One Pair Many Auditory Many Pairs A Threshold Mean After Letter (sec.) .005 After Letter .022 After Letter .042 Range (sec.) .021 .024 .039 G Threshold Mean After Letter (sec.) .022 After Letter .009 After Letter .005 Range (sec.) .078 .083 .084 H Threshold Mean Before Letter (sec.) .011 After Letter .006 After Letter .012 Range (sec.) .035 .035 .039 Hy Threshold Mean After Letter (sec.) .034 After Letter .030 After Letter .046 Range (sec.) .089 .074 .072 St Threshold Mean After Letter (sec.) .054 After Letter .037 After Letter .041 Range (sec.) .096 .080 .083

In this experiment, the observers A, H, and Hy, show an increasing distance of the threshold mean after the visual stimulus, with the successive introductions of the auditory series and the combined series. In other words, the second column negative displacement is larger than that of the first, and the third column has a still larger. G and St are again exceptions, as they would be expected to be from the above analysis of their methods. Each did his most accurate work in a case where there was some rhythm present. St said in regard to this work "the one pair abolishes the sound as a standard." The rhythmic factor most missed by these observers, in the case of the single pair, was the sound; for their results are almost the same in the second and third columns. Introduction of the repetition of the visual series does not make any decided difference. A, H, and Hy were able so to adjust their attention as to get the best results in the case of the single pair. The rhythm seemed to introduce for them a subjective rhythm which upset the nice adjustment of attention and so increased the displacement or the time between the threshold mean and the visual stimulus. The negative displacement was increased under these circumstances, probably as a result of the facilitation of the auditory perceptive process. It has an opened path. It is a case of pre-perception. Even when both were repeated (many pairs) the auditory dominated, and so did the most at opening its path. But it seems more likely to me that the rhythm, as such, whether auditory or auditory and visual, claimed the attention and so proved a distraction from the work of accurately discriminating the times of the impressions. And this exaggerated the displacement or lack of discrimination in whichever direction it was tending before.

In the successive stages of the investigation thus far, the complication experiment has been stripped down by degrees to the simple problem of the shortest possible interval between two disparate stimuli,--in this case shortest auditory-visual and visual-auditory intervals, as in the one-letter experiment of Table IV and the one-pair experiment of Table VI. The various factors in the complication experiment which have been successively analyzed out--the interval between members of the auditory series, the length of the visual series, the position of the visual series in relation to the auditory stimulus, and the auditory series itself--have all been shown to be factors intimately connected with the way the observer attends to the stimuli in question. From the present standpoint, it may be said they are all factors which, being introduced into the simple interval discrimination experiment, modify the resulting judgment with regard to the interval, by an interference with the normal attention-processes in the discrimination of intervals.

INTERVAL DISCRIMINATION

The method of interval discrimination deserves special consideration. Some of the introspective observations made by observers while engaged in the work, already reported, are instructive in this connection. In the case of a single pair, one observer said, "I know which is first because it gets hit first." This remark is a very apt expression of my own experience in trying to answer the same question. "Getting hit first" clearly means, to my mind, some kind of action on the part of the observer. He was ready, in the moment of preparation for the experiment, to see a flash of red with his right eye (either eye could have been used) and to hear a click with his left ear. (The stimuli were each produced 25 cm. from the respective sense-organs.) His preparation consisted in securing the "hair-trigger" condition in the two parts of the cortex and conduction apparatus immediately in question in the sensing of the two expected stimuli, and other parts are in a shut-off-from-discharge condition. This is the interpretation which seems to me an appropriate explanation of the feeling of special readiness to discharge in these two directions, when the expected stimuli shall come. The eye- and ear-muscles, in such case, are held tense on the sides (in the organs) where the stimuli are expected. The breath is held, and the whole trunk is under a strain. All bodily processes, in so far as they are controlled, are directed in such wise as to get whichever of these expected impressions shall come first, in as short time as possible, in order to know that it is first.

The reaction which gives the basis for the judgment may be a conscious "hitting" of the first. Or it may be a reaction, ostensibly as a part of the whole apperceptive process of which the auditory and visual processes are parts. This reaction may be any one of many kinds. Often it is a letting-go of the held breath. The exhalation or other reaction comes in response to the whole stimulating or "setting-off" process, and the one or the other of the two stimuli is judged to be first by certain peculiar relations within the experience of the moment. Such an explanation is in part suggested by the expression of St, that the visual impression when it came before the auditory, appeared as a "grace-note," and when it came after the auditory, as an "after-strike." St played the piano. He himself thought that this discrimination was a motor affair, i. e., a difference judged on the basis of a difference in the motor response. The judgment of the temporal order of the two impressions seemed to be an interpretation or translation of the different motor responses.

A, whose method brought the shortest range in Tables IV, V, and VI, said, "I hold my breath at the moment of expected stimulation, and it goes at the first impression." At another time he said, "When I say 'click first' I have the feeling that the click is left, and when I say 'click last,' that the click is on the right." He interpreted this to mean that when the click sounded first, he had moved slightly toward it, that is, to the left, and that when the visual stimulus had come first, he had moved slightly toward it (it was sensed by his left eye), and this was rather away from the sound, which would have come before the movement could have been more than initiated.

In my own case, I felt distinctly different motor responses in the two cases. There was an immediate feeling of release in whichever organ the stimulus first reached. A little involuntary jerk occurred in the musculature of this sense-organ, and sometimes the head moved slightly in the direction of the first stimulus. The condition of the next moment from which the judgment proceeded seemed to be best expressed thus, "I had it at a time when the other was not there." The attention was accurately set for both. Right eye and left ear were both distinctly innervated. The first stimulus "struck" the appropriate organ, and the "set" of the organ was released.

I am persuaded that the difference in sensitivity to intervals between auditory and visual impressions is due, in part, to a difference in the power of "cocking the ear" to hear, as one fixates the eye to see. The observers who got the smallest ranges between upper and lower thresholds had the most distinct kinæsthetic sensations in the moment of preparation, in the middle ear and about the external meatus. All had some sensations from the side of the head in question. The less accurate had a general feeling in the neck-muscles. Accuracy of discrimination was in no wise connected with voluntary control of the musculature moving the pinna. This was subject of careful enquiry with all observers.

If this introspective evidence leads me aright, it seems that the non-discriminable interval between auditory and visual impressions is due principally to two things, (1) the impossibility of perfect balance in the preparation of the attention for two expected stimuli, and (2) the possible difference in time it takes to react to the different impressions. The various complicating conditions which are added to the simple interval discrimination in the cases of a complication experiment, such as we started with in this investigation, are chiefly interferences with the first-named factor. They disturb the nice balances of attention. In this simple discrimination experiment, under favorable conditions, a close approximation to a balance can be attained. Any difference in the reaction-times to different stimuli will remain as a constant error of displacement. It is well known that reaction-times to visual stimuli are longer than those to auditory. There is a retinal inertia which delays the perception of the visual impression, in comparison with the auditory, coming from exactly simultaneous stimuli. Having this physiological basis, it will be relatively constant, as compared with the ever-varying attention-differences.

THE COEXISTENCE OF MENTAL PROCESSES

Having given, then, these relatively fixed temperamental conditions of reactions to different stimuli, which remain after practice (training in the control of attention) has reduced the reactions to their lowest terms, and has secured the conditions which are favorable for the best balancing of the attention, there is yet one other question very germane to the subject. It will have occurred already to any one reading the above, that while the response to one stimulus is being made, the other may be held in abeyance in the fringe region of the attention-field, and that it is only brought up to clear perception when the first has been disposed of. In other words, it may well be that the first of two simultaneous but disparate stimuli, which gets a start at setting-off its appropriate response in its sense-organ, will bring out this response and be perceived before the other one gets started,--that we do only one thing at a time,--that even in such minute processes as this there is no possibility of division of attention. It is hardly probable on the basis of the experimentation already reported, that this is the case. There is some division of attention. Otherwise there would be an equal certainty of judgment in every case, no matter how small the separating interval. But still the question as to how two mental processes, starting at the same moment of time, do proceed, as compared to the progress of each of the same processes when it holds the field alone, is very vital to the understanding of the psychology of interval-discrimination. And thus the question of objective time-relations is necessarily involved in that of making judgments of the time-relations of simple mental processes (subjective time-relations). The question is, Do these processes, starting simultaneously, proceed just as freely as if they were the sole occupants of the field of attention and so had the whole energy of attention concentrated upon the single process, or do they interfere with each other?

Distribution of attention, of some sort, is granted. It is generally conceded that there must be some sort of overlapping of the processes in any complex mental operation. But there is the greatest lack of information as to how this overlapping takes place,--as to the mechanism of the distribution of attention. Fechner held to the notion of a fixed maximum of available psychophysical energy. If this energy is being consumed in a single process, that process is very vivid, and all other processes are below the threshold. If, on the other hand, it is distributed over several simultaneous processes, they are all of diminished vividness. Distribution of attention always means diminution of vividness, and concentration of attention, increase of vividness. (See Elemente der Psychophysik, vol. 2, p. 451, 1860.) There is no question of the truth of the last statement, and very likely Fechner's fundamental concept is a true one; but there is need of more definite data on the conditions and nature of simple mental processes occurring at the same time, before it is considered proved.

Such researches as those of Paulhan, Jastrow, Loeb, and De Sanctis all dealt with the combination of processes which were themselves quite complex. It may well be that such processes as reciting a poem, performing a subtraction or multiplication of long numbers on paper, or keeping time with a metronome with the hand, seem to go along together when combined, so that the time taken to do the two of them together is much less than the sum of the times required for their separate performance, and, in some cases, no greater than the time required for either alone, and yet there may be no real proceeding together. The apparent saving of time may be due, as Paulhan suggested, to a rapid oscillation from one to the other of the two complex processes which are largely automatic and can proceed, to such extent as they are automatic, without any attention. This illustrates how these investigations have probably missed the real point at issue with regard to the division and distribution of attention. The attention might be distributed over several of the minuter part-processes of these processes so that many were proceeding at the same time, and yet the method of these experiments would not reveal it. They were not planned with sufficient precision. There is a problem in the division of attention which they did not come within sight of, and this is the real question of division in case of the simplest processes.

This problem is really that of the mechanism of mental assimilation. The process it investigates is illustrated by the maturing collective idea, as a melody or a spoken sentence. There is a gradual enrichment or growth in meaning, as such a process goes on toward its completion. At any instant during the process, implicit associative and nascent perceptive elements are working together to their own mutual clarification and explication. All focal content is the result of complicated interworkings of such fringe material. It is impossible, it seems to me, to question the causal relation of the fringe elements or processes of one moment to the focal of the next; and it is equally impossible to deny the complication of these same fringe processes. They must go on at the same time in order to enter into one and the same resultant process. The question of direct interest at this point in the discussion is, To what extent do they proceed at the same time?

It would seem from the way in which this question, of the relationship and interference of mental processes which proceed or start to proceed at the same time, has come up in this investigation, that the natural method of pursuing it would be that of comparing reaction times for cognition reactions to the single and combined stimuli. But we are warned against this by very clear inferences from an investigation of Professor Münsterberg's in which he used the reaction method. By an ingenious use of the reaction experiment, the author shows that two-part processes in a reaction, as, for example, a restricted judgment of class and a subjective preference, occupy about the same time when combined in a single reaction as when either is performed in a separate reaction. In other words, two judgments of distinctly different kinds can be made in the same time as either can be made when it has all the attention concentrated upon it. The conclusion that these elementary processes go on together--that at least there is some degree of overlapping--seems unavoidable.

But when the first part of the same report is considered in relation to the second, it is clearly shown that the reaction experiment is not adapted to the finer investigation of this problem. For the first part shows that no matter how much a motor reaction is complicated by choices or other judgments, it always takes place in just about the same time as the simple reaction. The complications may be such as actually to double the reaction time in the case of a sensory reaction, and yet a motor reaction, under precisely the same conditions as far as they may be the same for a motor, shows no increase in time. The "set" of the attention in the motor reaction is, no doubt, such a change in the order of succession of the parts of the process that some of those, which come after the stimulus is received in the case of the sensory reaction, are made to come before the stimulus in the motor. When, however, it is found that the motor response to the question, "Is this the name of a scientist, philosopher, poet, statesman, or musician,--Sappho?" is made by the appropriate finger, as previously agreed upon, in just as short a time as the observer can make a motor response with any finger to a simple auditory stimulus, it indicates, either that the whole of the choice judgment has been made before the stimulus was received, or that the judgment itself is so automatic that it is practically a reflex. This latter cannot be true. The judgment, as conscious choice, cannot be made before the stimulus is given, i. e., until the question is completed. And judgment cannot be made automatic and yet be a judgment. In fact both alternatives are untenable, and there is no other course than to hold the situation which gave rise to them at fault. If the judgment process here required previous to the reaction does take time apart from the processes of the simple reaction, the reaction process is shown by these experiments to be unable to exhibit it. A more microscopic method is demanded before the matter can be settled.

The Leipsic method of measuring the scope of attention by means of the tachistoscope is the standard means of securing data as to the number of elementary processes which can go on at the same time in consciousness. The same question, with which we are here concerned, grows directly out of the investigation of the number of processes which can go on together. Wundt acknowledges the great difficulty which inheres in the investigation of this problem. Cattell's early work with the tachistoscope showing the numbers of letters, syllables, and words, which could be apperceived under the same objective conditions, indicated the great importance of what we may best call meaning, in apperception, and its influence on the number of different processes which may proceed together. In fact the number depends upon the definition of the unit with which the investigator starts out. Wirth, the latest emendator of the tachistoscopic method, has shown, in a very thoroughgoing and genuinely constructive criticism of earlier work, that the one question of primary importance in investigations of the content of the moment of consciousness, i. e., scope of attention, is to set forth the relative clearnesses of the elementary processes there proceeding together. He shows that the different grades of clearness which may present themselves in the field of consciousness of a momentary act indicate, on the one hand, the impossibility of sharply distinguishing the "scope of attention" from the "scope of consciousness" as Wundt uses these terms, and, on the other, the serious indefiniteness of any merely numerical statement of the scope of attention. His main purpose is to set forth a method by which this field can be enriched by exhaustive statements of the relative clearnesses of the processes going on at the same time. All the work of the present study had been performed before the publication of Wirth's work. Otherwise some of his suggestions would have been used in the plan of the experiments following. I may say, however, that I believe the method here used has its own distinctive merits.

GENERAL METHOD FOR TESTS IN COEXISTENCE

Taking the suggestions offered by Professor Münsterberg's study of apperceptive and associative processes, I selected simple judgments of comparison as the best means of trying-out this question of coexistence. The perceptive act itself is made up of judgments, and these may very properly be the processes studied in combination as in the tachistoscopic experiment. But the judgment which has a previous perceptive act as its condition, determining its start, seems to be better under control. It is itself a central process, not dependent upon the variations of the objective factors in sensation. My plan was to have the stimuli so arranged as to give rise to two or more perceived conditions at the same moment, and so have one or more judgments of comparison between the perceived features made at the moment the perceptions were completed and immediately stated. If one makes two series of single judgments of comparison, and a series wherein these two judgments are combined in a single act, all three under precisely the same objective conditions, and the same subjective conditions, saving only the necessary changes in the direction of the attention, and the percentage of correct judgments is recorded in each case, providing always that in no single series of judgments were the conditions such that all judgments could be correctly given, he would then have reasonable grounds for making inferences with respect to the interference of simple mental processes going on at the same time,--whether there is any, and, if there is, how much there is. Interference would be indicated by the falling-off in percentage of correct judgments as the combinations were increased.

Such relative accuracy of judgments, single and combined, was the test sought after and relied upon in the following experiments. It was very necessary to have the objective conditions such that the results in cases of single judgments, later to be combined, should be short of absolute correctness, in order that interference from the combination should show itself in impaired accuracy. Otherwise there might be some free energy of attention, which could readily take up the extra work when the judgments were combined, and so there would be no impairment of accuracy. It was the aim to have the objective conditions, such as duration and extent, so regulated that about ninety per cent correct judgments resulted in the series of single judgments. If, then, when two were combined, eighty per cent were given correctly, and when three were combined, seventy per cent, the inference would seem reasonable that this falling-off in correctness was due to interference. The failure of the perceptive process, indicated by the ten per cent incorrect judgments in the series of singles, would remain a constant source of error throughout.

There is, however, one other source of increasing error, with the increasing combination of judgments, supposed above. The judgment processes might go on at the same time without any impairment of the accuracy of the single judgment, and yet the results, as expressed, might show a falling-off in accuracy. This imperfection would then be due to a partial failure of the retentive and reproductive processes, and not to the imperfection of the judgment processes. I have found no sure means of separating this factor and excluding it. As the experiments were arranged and conducted, though, I believe any impairment in accuracy resulting from combination is more likely due to interference of the judgment processes.

If neither of these factors is efficient, on the other hand, there will result no falling-off in accuracy of results when single judgments are combined. To be sure the conditions of the experiment, as outlined so far, do not preclude the possibility of the combined judgments occurring in succession, and so giving rise to as large a percentage of correct results as when occurring singly. That is, while one of the so-called combined judgments was in process, the latent conditions of the other would remain for the moment as mere physiological or possibly psychical dispositions, and to these one would "hark back" in the next moment. Here the reaction method is suggested as the means of assurance that this is not the case. But this method, we have already seen, will not lend itself to work of such precision as this. The probability of this succession of judgments is reduced to a minimum in the experimental groups following.

It can be practically precluded by a prevention of all sensory images. In these experiments every precaution was used to prevent them. In all cases where visual stimuli were used, for instance, a brightly illuminated blue field immediately succeeded the momentary stimulus, while comparative darkness preceded it. I cannot be so sure that there were no memory images functioning. But all observers were carefully questioned on this point at frequent intervals during the experiments, and no evidence of their existence was found in any case. I feel sure sensory images were excluded and think memory images very improbable.

SINGLE AND COMBINED JUDGMENTS FROM VISUAL AND TACTUAL STIMULI

In this group of experiments, I used judgments from visual and tactual stimuli, singly and in combination. Both stimuli were given by means of a large pendulum in the Harvard laboratory, specially constructed for Professor Münsterberg. This pendulum is about one and a half metres in length. It is hung in a heavy steel frame which rests upon a large table. A curved steel bar, concentric with the swing of the pendulum, and ninety degrees in extent, is so set to the frame that it serves as the attachment for an electro-magnet, at any point in the swing of the pendulum. The pendulum-rod carries an armature which fits this magnet. By means of this magnet, the pendulum may be held at any point between the position of rest and forty-five degrees out in either direction; and it may be released by breaking the circuit through the magnet. The pendulum also carries a segmental screen of about seventy degrees extent. An opening about nine by eight centimetres near the centre of the screen affords means of tachistoscopic observations. A sliding shutter makes the slit as narrow as may be desired. In these experiments a black tube was set up, at right angles to the direction of the motion of the pendulum, and at the height of the slit in the screen. On the other side of the pendulum screen, and directly opposite the tube, was placed a support for holding the object to be shown.

The object for the visual stimulus was one of two light gray lines on a black background. These lines were 4 mm. wide, and one 44 mm. long, and the other 40 mm. The work was done in a dark room. The stimulus card was illuminated by an electric light hanging between it and the screen. Both cards were shown the observer several times, before experimenting, till he was sure of their lengths. Upon one being shown, in experiment, he was asked to say whether it was the longer or shorter. The touch apparatus was so arranged that the experimenter could at will give the observer one or two contacts on the back of his right hand. The contacts were made by means of an electro-magnet. This was actuated by a current which was made by the closing of a switch which was secured by a set-screw to the same curved steel bar as bore the pendulum magnet. This switch was closed by the pendulum in passing. It was adjustable on the bar. Another similar switch, opened by the falling pendulum the next instant, removed the tactual stimuli. These switches were so placed in the course of the pendulum fall that the tactual and visual stimuli were exactly simultaneous. The tactual judgments were, one or two points touched. Results are presented in Table VII for three observers, A, B, and Bo. The number of series which were averaged in each case is given, in order properly to weight the results.

TABLE VII

Combined Single Single Tactual Obs. Tactual Visual and Visual A Number of series averaged 3 3 3 Per cent Correct 80 89 79 Judgments \-------\/-------/ Average 84

B Number of series averaged 5 5 5 Per cent Correct 72 78 78 Judgments \-------\/-------/ Average 75

Bo Number of series averaged 5 5 5 Per cent Correct 88 71 78 Judgments \-------\/-------/ Average 79

In Table VIII are given A's results for further experimentation under the same conditions, also for a pair of visual judgments, a pair of tactual, and all four combined. One series of each of the five was given each hour of experimentation. For the additional visual judgment, the observer was required to say whether the line was high or low. It was of two heights from the lower edge of the card, 17 mm. and 20 mm. For the other tactual judgment, he reported the point or points touched on the hand, as on the right or left side. The middle line was traced by the experimenter, before tests, as often as the observer wished to be reassured of its position.

TABLE VIII

Tact. Two Tact. Obs. Sing. Sing. and Two Two and Tact Vis. Vis. Tact. Vis. Two Vis. A Number of series averaged 6 6 6 6 6 6 Per cent Correct Judgments 87 88 83 9 81 83

The next additional combination was a pair of judgments based upon auditory stimuli. Four electric clickers were placed on the wall behind the observer. Two were loud and two faint. Each pair was accurately adjusted so they were of the same intensity and quality. One of each pair, i. e., one loud and one faint, were hung about four feet to the left of the observer's median plane. The other two were hung at an equal distance to the right of this plane. The circuit making the click was made by a switch closed by the pendulum as it fell. The experimenter by pressing any one of four buttons gave the one of the clicks he desired. The observer's two judgments were as to the loudness and the position of the click.

TABLE IX

Two Vis. Two Tact. Two Aud. Obs. Lgth. Pos. Num. Pos. Inten. Pos. B Number of series averaged 8 8 8 8 8 8 Per cent Correct 82 94 89 100 94 92 Judgments \----------------\ /----------------/ Average 91.7

Bo Number of series averaged 12 12 12 12 12 12 Per cent Correct 77 91 87 97 81 82 Judgments \----------------\ /----------------/ Average 85.8

Six Judgments Together Visual Tactual Auditory Obs. Lgth. Pos. Num. Pos. Inten. Pos. B Number of series averaged 14 14 14 14 14 14 Per cent Correct 89 97 86 96 70 86 Judgments \----------------\ /----------------/ Average 87.3

Bo Number of series averaged 20 20 20 20 20 20 Per cent Correct 77 93 85 98 81 80 Judgments \----------------\ /----------------/ Average 85.7

It is evident, on the face of these returns, that there is no positive assurance of interference. Each of these observers had been in some part of the complication work. And so the inference from lack of evidence here can be carried back to that work, and we may rest assured that the lack of accuracy in interval discrimination work by these observers was due in minimal measure, if in any, to interference of the mental processes, auditory and visual, tending to proceed at the same time. Some parts of the results here presented look like evidence for interference. But there is, on the whole, just as much evidence of what one might call facilitation, in combination, as there is of interference.

There is one source of possible explanation for the non-appearance of evidence of interference in these results: that is the fact that the stimuli are disparate, and so probably take different times for maturing. Thus the judgment processes, so far as they thus start from disparate sensations, may start at different times. There was good reason for using disparate stimuli first for the combination of two mental processes, as this was the closest related to the simple interval discrimination experiment to which the complication experiment had been reduced. But this objection is now easily overridden by making the conditions of experiment such that all judgments start from one and the same perceptual process.

ONE, TWO, AND THREE JUDGMENTS BASED UPON A SINGLE SENSE-PERCEPTION

The conditions here were such that the perceptual basis for any one of the single judgments was at the same time the possible basis for any other single judgment and also for any or all of them combined. What judgment or judgments were given depended entirely upon the directions given, and the consequent preparation of the attention. Under these conditions, there could no longer be any doubt about the even start of all judgments, so far as outer conditions were concerned. The only remaining cause of an uneven finish--lagging of a process, as shown by its increased inaccuracy when combined--must be interference with its progress by other processes going on at the same time.

Visual stimuli were used. The objects to give the perceptual basis for the judgments were small rectangular openings in cardboard seen, on exposure, by transmitted light. These rectangular windows in the cardboard were 2 cm. by 1 cm. and stood in the vertical position 1 cm. apart. The judgments were all based upon differences existing between these rectangles as shown. One of these differences was in length. They might be of the same length, or either the right or left might be 2 mm. longer than the other. Another difference was in shade. This was secured by different thicknesses of paper, pasted over the openings. Two shades were used. The opening on one side might be shown as either the same brightness, brighter, or less bright. The third difference was in the number of lines which crossed the rectangles. Two or three wires were placed across them horizontally and about 5 mm. apart. Thus they had the same number of lines, or one had fewer or more than the other.

The same large pendulum was used in these experiments. The moveable magnet on the curved steel bar was kept in one position throughout. It held the pendulum, ready for release, at twenty degrees from the position of rest. The adjustable weight on the pendulum was also kept in one position. The only adjustment which was changed during this series of experiments was the width of the slit in the window of the screen. This was varied from one millimetre to five. The whole time during which any part of the two rectangles was in view (the total exposure) with a 5 mm. slit was .033 sec.; with a 3 mm. slit .031 sec.; with a 1 mm. slit .029 sec. These times were measured with a Hipp's chronoscope. The entire visual field, embracing the two rectangles, was about 2 cm. by 3 cm., and was about three fourths of a metre from the observer's eye. It could be accurately fixated beforehand and fully exploited during the moment of exposure.

The observer was always instructed to give his judgments in terms of one of the two rectangles. If, for example, length was in question, he should say of the left-hand rectangle that it was longer, shorter, or of the same length as the right-hand one. The process of expressing the judgments was also facilitated by using the terms plus, minus, and equal, for all three sorts of judgments. This was a special aid to expression where two or more judgments were in question at the same time. In these cases the observer was always given an order beforehand, in which the judgments were to be given. This order for the three combined, for example, was always, "length, lines, shade," as in the following tables. If, then, the judgments were given "plus, minus, minus," it meant that the left-hand rectangle was longer, had fewer lines, and was less bright than the right. The process of making these interpretations, as well as the order, was made automatic with the observer, by practice, before experimenting.

Three observers, A, B, and Y, were used in this experiment. The judgments were made in series of ten. Each hour's work was distributed over (1) several series of single judgments, (2) two at a time, and (3) three at a time, the aim being to get an equal number of judgments of each kind, length, lines, and shade, under each of the three conditions. The results are given as general percentages of correct results. To properly weight these averages, the number of series (of ten judgments each) which are included in making up any average, is given just above the average.

TABLE X

KEY: Lth = Length Ln = Lines Sh = Shade

Single Judgment Two Judgments Three Judgments Obs. Lth Ln Sh Lth Ln Sh Lth Ln Sh A Number of series averaged 11 12 10 15 17 14 11 11 11 Per cent Correct Judgments 95 93 96 90 91 83 94 91 89 \----\/----/ \----\/----/ \----\/----/ Average 95 88 91

B Number of series averaged 8 8 7 9 10 9 7 7 7 Per cent Correct Judgments 93 80 90 76 77 90 75 70 75 \----\/----/ \----\/----/ \----\/----/ Average 88 81 73

Y Number of series averaged 12 13 13 19 19 16 13 13 13 Per cent Correct Judgments 76 80 58 72 76 61 72 74 58 \----\/----/ \----\/----/ \----\/----/ Average 71 70 68

Since these general averages for the single judgments are so close to those in pairs, it seemed possible that the presence of objective differences, other than the single one asked for, might be a distracting agent, and really interfere with the judgment process in question. For example, when judgment on length was in question, it might be possible to give it correctly a larger number of times, if there were no differences in shade or lines, than if these were present. Some careful test experiments were made with a view to clearing up this situation. The observers in no case knew the nature of the investigation, nor were they aware that other differences were absent in some of the cases. The results presented in Table XI certainly show that the presence of other differences than the one in question is no cause of interference.

TABLE XI

Length Lines Shade With With With Obs. Diffs. Alone Diffs. Alone Diffs. Alone A Number of series averaged 5 5 5 5 5 5 Per cent Correct Judgments 98 96 96 96 98 94

B Number of series averaged 5 5 5 5 5 5 Per cent Correct Judgments 90 92 96 94 78 84

Y Number of series averaged 7 8 8 8 7 8 Per cent Correct Judgments 73 76 75 64 88 67

Notwithstanding the precautions taken to secure the full energy of attention for the single judgment process, as already indicated in the discussion preliminary to these experiments,--namely, by making the stimulation conditions so near the threshold that only a part of the judgments could be given correctly,--there still appeared a probability that there was free energy of attention during the single judgment process. The observers seemed to do more work when more judgments were asked for. If this is true, the results of Table X are not a true index of interference. If there is free energy during the moment of making the single judgment, this may readily be used for another process when combined with the first, and so there will be no interference. This is a sufficient proof so far as it has immediate bearing upon the interval discrimination experiment, but the further question as to what will take place if we can use this free energy, if it exists, in both processes alike, is an important one for the question of the relation of two processes going on together in consciousness.

To ascertain the fact in this matter, I performed a series of experiments with the same observers, in which previous occupation of the mind served as a distraction. The distraction consisted in a simple arithmetical operation,--addition or subtraction. The moment before giving the stimulus for the judgment processes,--in the place of the "ready" signal, I would call out some numbers, as, for example, "twenty-four from sixty-three" or "fifty-seven and fifteen," the first indicating subtraction and the second addition. The answer to the addition or subtraction was always given before the judgment or judgments, to make sure that it was performed. And in any case where the observer knew that the addition or subtraction was done before he attended to the stimulus for the judgment, that particular test was thrown out. The results are given in the same form as in Table X.

TABLE XII

(Addition and Subtraction as a Distraction)

KEY: Lth = Length Ln = Lines Sh = Shade

Single Judgment Two Judgments Three Judgments Obs. Lth Ln Sh Lth Ln Sh Lth Ln Sh A Number of series averaged 8 8 8 15 15 16 15 15 15 Per cent Correct Judgments 79 84 67 66 68 66 53 69 59 \----\/----/ \----\/----/ \----\/----/ Average 77 67 60

B Number of series averaged 6 4 5 8 7 11 7 7 7 Per cent Correct Judgments 57 70 60 66 44 53 51 50 44 \----\/----/ \----\/----/ \----\/----/ Average 62 54 52

Y Number of series averaged 8 8 7 15 16 15 14 14 14 Per cent Correct Judgments 66 60 51 56 62 56 66 57 55 \----\/----/ \----\/----/ \----\/----/ Average 59 58 59

These results (general average percentages) show, for observer A, a more regular and somewhat larger falling-off with combination than in Table X, for B and for Y, a diminished falling-off, and relatively less for the three than for the two combined judgments. The percentages are lower throughout. This is a result to be expected. But there is no notable change in the relative lowering of two judgments in comparison with single judgments, or of three in comparison with two, such as should appear if, as supposed, in the experiment resulting in Table X, there had been free energy of attention in the case of the single judgment.

It was my aim in these experiments, with distraction through another simultaneous process, to secure a uniform residue of attention for the judgment processes, whether single, in twos, or in threes. The arithmetical operations were therefore as uniform as possible. But it may readily be that very unequal demands were made upon a given observer by successive operations, one's automatisations in number-work may be so various. These would no doubt tend to average up in the course of the whole work running through several weeks. But in order to make more sure of the point, I tried another means of using the free energy of attention which may exist in the case of the single judgment, namely, by suggesting a judgment or series of judgments just before an exposure. It will be recalled that the order of judgments was always the same as that of the tables, and that all were expressed as minus, plus, or equal. So if the experimenter called out before a three-judgment exposure, "plus, equal, minus," it would be in the nature of a challenge to the observer to assure himself beyond a doubt whether or not the exposure showed the left-hand rectangle as longer than the right, having the same number of lines, and being less bright. The so-called suggestion was a distinct factor in heightening attention. This is shown especially in Y's case by the larger percentage of correct judgments. Results are averaged in Table XIII.

TABLE XIII

(Attention heightened by Suggested Judgments)

KEY: Lth = Length Ln = Lines Sh = Shade

Single Judgments Two Judgments Three Judgments Obs. Lth Ln Sh Lth Ln Sh Lth Ln Sh A Number of series averaged 2 4 2 6 7 7 8 8 8 Per cent Correct Judgments 90 89 85 87 81 76 92 72 77 \----\/----/ \----\/----/ \----\/----/ Average 87 81 80

B Number of series averaged 4 3 4 8 9 7 8 8 8 Per cent Correct Judgments 85 70 92 84 80 83 84 74 81 \----\/----/ \----\/----/ \----\/----/ Average 82 82 80

Y Number of series averaged 6 6 5 11 13 12 16 16 16 Per cent Correct Judgments 88 75 94 90 81 77 89 74 70 \----\/----/ \----\/----/ \----\/----/ Average 86 83 78

An analysis of the results obtained from B to show the effect of the suggestions is given in Table XIV.

TABLE XIV

Single Two Three Judgments Judgments Judgments Per cent of right suggs. judged correctly 87 85 79 Per cent of wrong suggs. judged correctly 73 77 80

The effect of the so-called suggestions in making for correct judgments was then quite noticeable in the case of single judgments, less so in two judgments, and none whatever in three. This observer was able to overcome 73% to 80% of the wrong so-called suggestions. Now, when it is considered that only 80% to 82% of all the judgments given by B (see Table XIII) are correct, it is very clear that their action as suggestions was very slight. They had an influence, however. It was shown, as expected, in a heightened attention. This was especially the case with Y. Compare his general averages in Table XIII with those in Table X. This rise in general averages coincides with the impression of the experimenter during the experiment. It seemed then that this was a distinct challenge to keen attention on the part of Y. He is a man who intends to make impartial observations for himself, and has no notion of being told what he is to see. That his general averages of correct judgments stand so much farther apart in this case with heightened attention than in either of the others (see Tables X and XII) is indicative of an interference of the judgment processes themselves.

Such a series of general averages as those of Y in Table XIII, as those of B in Table X, or as those of A in Table XII, seem, in themselves, and under the conditions of the experiment, to be pretty clear indication of an interference of simple mental processes carried on at the same time. The only other explanation is that suggested above, namely, an interference of the processes of reproduction and expression. The conditions of the experiment seem to reduce the probability of this to a minimum. But the centre of interest, in considering the results, does not lie in the question as to whether it is interference of the judgment processes themselves or the processes of their reproduction. The foreground is occupied by a prior question, namely, whether there is any evidence here presented for interference. For if there is interference of such processes, why does it not show up in the results for each of the observers in each of the Tables X, XII, and XIII? Of the nine cases here offered for comparison, only the three above designated show what may be called clear evidence of progressively increasing interference with increase of combined processes proceeding at the same time.

Under these circumstances this cannot be accepted as indisputable evidence of interference. Such results as those of A in Table X, where correct judgments, two at the same time, are given in 88% of the cases, and three at the same time, in 91% of the cases, stand directly opposed to interference. They seem to show a facilitation by combination. This is indeed possible where three and only three sorts of judgment are worked with. It is the limiting case, and if more than one is asked for it is really easier to give three than to select two. A himself remarked that this was the case. A similar explanation holds concerning the results of B in Table XII, and those of A in Table XIII. If such an explanation is the true one, it is manifest that the "limit of attention," of which mention has been made above, has probably not been reached in any of these cases. On the whole, these experiments seem to indicate a small degree of interference of simple mental processes going on at the same time. But such interference cannot be considered proved by these experiments.

THE QUESTION OF SYNERGY

In connection with these last experiments, where the comparative judgments all proceed from one definite perceptive act, and where therefore the conditions are most accurately controlled for showing the effect of interference, if it is a fact, there is yet another means of looking into that question. This is afforded by the similarity of the means of expressing the different kinds of judgment. In connection with the current emphasis given to the motor side of mental processes, it is often urged that mental processes go on at the same time when they are working together toward one and the same motor out-go. Otherwise they are likely, at least, to hinder each other, and to take their turns. If such is the case, the similarity of motor out-go which is present in these cases, where all three judgments are plus, or all minus, or all equal, ought to produce a larger percentage of correct judgments than is found in cases where there are two or three kinds of expression. Furthermore, if there is no interference of the judgment processes as such, but, as supposed possible above, the impaired accuracy of judgment in the combination of judgments is due to the imperfection of the memory, this too will be diminished by similarity of expression of the three judgments. In fact similarity should reduce this source of error to a minimum. The results presented in Tables X, XII, and XIII, for three combined judgments, were worked over, so far as possible, and all cases where the three judgments, if correctly made, would have been expressed similarly, were separated out. The total number of such cases, and all those where the judgments would have been properly expressed dissimilarly, are recorded for each observer in Table XV. The number actually given correctly under each class is also recorded, as well as the percentage of correct judgments in each class for each observer.

TABLE XV

KEY: TN = Total Number CJ = Correct Judgments N = Number % = Per cent

Judgments expressed Judgments expressed Similarly Dissimilarly Obs. TN CJ TN CJ N % N % A 222 172 77 561 479 85 B 195 153 78 498 356 71 Y 372 277 74 863 572 66

If the results of B and Y were presented alone, they would seem to indicate synergy of similarly expressed judgments. But those of A are most strongly contradictory of such a working together of such judgments. This is very surprising to me, as A had such a facility in expressing these similar judgments, especially "equal, equal, equal," that it suggested this comparison. But the apparent facile expression is here shown to have attended a diminished accuracy. No conclusion can be drawn with respect to synergic influence from the similarity of expression of judgments.

RELATION OF OBJECTIVE AND SUBJECTIVE SIMULTANEITY

Reviewing this work in combination of judgments with reference to its bearing upon the complication results, and the interval discrimination results, it seems that interference of simple mental processes going on at the same time, though it appears to be a fact, showing itself in impaired accuracy of processes combined, is yet quite inadequate to explain the whole, or indeed, any considerable part of the synchronism, as we may call the "click first" "click last" interval of Tables IV, V, and VI. The slight amount of interference of such processes as the auditory and visual perceptions, tending to proceed at the same time, would tend to a very slight displacement of one with regard to the other. It is true, for reasons already discussed, that this time-difference is so slight and so difficult of seizure that it cannot be measured, and so no measure is offered. We cannot, therefore, be certain how much of the non-detectable interval is due to this cause. But the evidence offered in the above tables of results is ample justification for the statement that interference can be responsible for only a very small part of the "click first" "click last" interval.

In the case of this interval, as in that of an interval between any disparate stimuli, a part of it must be due to the different resistance or inertia of the sense-organs. The eye is undoubtedly slower than the ear. This would at once suggest itself as the cause of the interval between the threshold mean and the visual stimulus in the results shown in Tables IV, V, and VI above. That is, vision being slower, an auditory stimulus given at the same time as a visual will appear to be earlier, and it may be given considerably later and yet appear earlier. In general, therefore, so far as this cause is active, one would expect that the interval, at which a sound must precede a visual stimulus in order to be certainly distinguished as coming before the latter, would be much shorter than the interval, at which a sound coming after a visual stimulus could be unfailingly distinguished as coming later. In other words, the centre of gravity of the "click first" "click last" interval, so far as this visual inertia is the cause of its displacement with reference to the visual stimulus time, will be after the visual stimulus.

In one case in my results, Table V, St, H middle, there is presented an extreme where not only the centre of gravity (threshold mean) is placed after the visual stimulus (letter), but the whole synchronous period ("click first" "click last" interval) is after the visual stimulus, so that a sound coming .008 sec. after the visual stimulus is distinguished with certainty as coming before it. So also St, in Table VI, one pair, the sound coming .006 sec. after is judged as coming before the visual stimulus.

But the variety of displacements of the threshold mean in different observers, and more particularly in the same observer under different experimental conditions, indicates very clearly that there are factors other than visual inertia which are quite as important, and perhaps equally responsible for this displacement. In Table VI, H, one pair, for example, the threshold mean is before the visual stimulus .011 sec. So in Table V, G, H first, and also H last, it is before the letter .005 sec. In these cases there must be some factor or factors quite as strong as this visual inertia, and counteractive to it. These are, in part, the complex attention factors which have been referred to already. Prominent among them are the rhythmic perception which is so marked in St; the movement toward the first stimulus and the "letting-go" of the breath, of A; the passive "striking" of the letter by the sound, in the case of some of the observers; and the "cocking" of the eye and the ear, of others. These all have to do with the length and place of the "click first" "click last" interval quite as much as does the visual inertia. But however this may be, of this inertia and the other factors just now named, probably each has more to do with it than does the interference of the perception processes themselves.

But after eliminating the parts played by each and all of these agencies in the determination of the interval, there will remain a period of "present time," in which there are no time-differences, and no qualitative differences which lead the subject to suspect the existence of time-differences. The mental content of this reduced synchronous period in experience is one experience. The sound was heard and the letter was seen, but they came together as aspects of one experience. In the moment of perceiving either one, it was not possible to say that the other was already a memory. In other words, the primary memory of either, whichever came first, had lasted over into the perception of the second. There had been no perceivable transformation of the first since the instant of its perception. At the moment of the inception of the second process, the first was still, to the perceiving subject, what it was at the moment of its own inception. Though change was probably going on in the physiological substrata of the mental process in question, in every minutest moment of the interval, yet a certain amount of effect of this change had to accumulate before the observer could become aware of the change, and so be aware of the passing of time or of temporal difference. This was, then, only a case of the working of the law of relativity. And the perception of time is a function of the duration and amount of change of mental process.

Looked at from this point of view, we see the whole explanation of the existence, the amount, and the position of this synchronous period under one rubric, if only we could grant the combination of mental processes without interference. If mental processes go on together, the sole ground of the imperceptibility of short periods of time separating mental processes is in the fact that the first of these processes has not changed sufficiently to be known as different, to the perceiving subject. The minimal perceivable interval will vary from man to man, and in the same man from time to time, inversely as the amount of change per unit of time, in the process itself. The same statement could be made in terms of vividness or relative clearness. The more focal the idea or process, i. e., the more vivid or relatively clear it is, the more rapid will be the changes and the perception of those changes. Professor Münsterberg's physiological explanation of vividness, as due to the facilitation of the motor discharge, has already found confirmation in the method of keenest interval discrimination as outlined above. The more rapidly the first process can get into action, the more is the discriminated interval shortened. So in Exner's experiments, where it was known which of two stimuli would come first, the interval was very much shorter than any of my results, for the motor preparation could be made very complete beforehand, as in a muscular reaction. Therefore the perceptible change, upon perception of the stimulus, occurred in a shorter time. Under any circumstances, the conditions, subjective or objective, which make for rapid maturing (and by the principle of dynamogenesis maturing means going over into action) of the mental process, make also for the shortening of the least perceptible interval.

These conditions are as various as the gamut of human experience is wide. There is nothing, from the primary temperamental characteristics to the passing wave of feeling of the present moment, which does not affect it. Most particularly, though, is it a matter of the relations existing among the elementary processes striving to go on together. Among the focal and fringe elements of a given moment of experience, no matter how carefully the practised introspectionist may strive after an ideal condition of monoideism, there is an incessant interaction. There are all sorts of hindrances and facilitations. Herein is the justification of Stern's statement that the "praesenzzeit," as he calls it, "varies with the quantity and quality of conscious content, the direction of attention, and the strength of psychical energy," and that it cannot be assigned a maximal value but rather what he calls an "optimal value." All that is included, in fact, in the complex rubrics, attention and interest, has to do with the length of this indiscriminable interval.

Time-difference in consciousness is the very simplest thing in mental life, for it is a case of the bare awareness of change. The elementary time-judgment is mere judgment of change in content of consciousness. In the experiment where one is asked to say which of two expected stimuli comes first, however, the case is already complicated. There must be a double preparation to react and to note the change characteristic of each case, and so convert it into a time-judgment. In the combination of two judgments, there is the same double expectancy, preparation to react in two ways at once. In each experiment, the preparation and shaping of expectation is the same as in reaction experiments. In all reaction work, the short reaction comes as the result of catching the attention wave at its most favorable point. If the signal to react catches the idea of reaction in the mind of the observer at the very focal point in consciousness, the shortest reaction possible under the given conditions results. So in both the combination experiment and the interval discrimination experiment, it is very necessary to catch the attention wave, equally prepared for both or all the processes, and at the highest crest of advancement. Both demand the same preparation as a compound reaction. I believe it is this inequality of balance of the attention between the various processes that is responsible for the interference which is evidenced in my results. This is my explanation of the appearance of impaired accuracy for combinations for a given observer under some conditions and the failure of any sign of impaired accuracy for the same observer under other experimental conditions, or even under the same experimental conditions at different times.

In the time-interval discrimination experiment the evenness of balance in the attention wave will make for the shortest interval discrimination, and the proportion between the two will be direct, so far as other factors do not interfere. But there are special interferences here. One of these is the fact that the two mental processes do not set off at the same moment. No matter how even the balance in attention at the moment of impact of the first of the two stimuli, the preparation for the other, not yet set off, cannot be held in equal readiness while this is going off. This discharge has already disturbed the preparation to discharge in the other direction. In the case of a given pair of stimuli of definite qualities and intensities, the relation will be one of mutual facilitation for one interval of separation and one of inhibition for another interval. In one case the first opens the path for the second, being a case similar to the summation of stimuli, and in the other, it draws all the available energy in its own direction.

FOOTNOTES:

THE ESTIMATION OF NUMBER

BY C. T. BURNETT

I. There are situations not a few in life in which we find ourselves estimating the number of objects in some group. Sometimes we desire to know merely whether the group is large or small. Sometimes we try to reach an absolute number that shall approximate roughly to the real number. Sometimes, again, we only care to know whether the group in question is more or less numerous than some other group that we have before us or perhaps recall in memory. The public speaker finds himself wondering whether this present scattering audience is larger than the one that last night crowded into the front seats. The farmer riding between adjoining orchards judges roughly the prospective yield by a comparative estimate of the fruit in sight. The politician too has an interest that is very notable indeed in such rough numerical estimates. He asks himself, for example, whether the voters will be more influenced by reports favorable to his party sent in from numerous small towns or by such reports from a few large centres. Or perhaps he is planning a demonstration in favor of his candidate. His problem then is so to arrange his procession that five hundred men will look like five thousand. Turning to another field, how is it that the enrolment in some institutions of learning seems larger and the size of the faculty more portentous than in other similar institutions that are really of about the same size?

These examples bring to mind our interest in rough numerical estimates and at the same time suggest the probability that we are swayed back and forth in these estimations without ever a numerical difference occurring in the objects of our judgment. These considerations lead us on, then, to an enquiry about the factors that can thus influence our estimation of number.

II. INFLUENCE OF FACTORS IN THE SAME SENSE-FIELD AS THE OBJECTS WHOSE RELATIVE NUMEROUSNESS IS IN QUESTION.

The experiments described in the following pages are concerned with the influence exerted on the judgment of a given factor by other factors presented at the same time. The object of judgment in these studies is visual number, which is to be submitted under varying conditions of the objects whose number is in question, for example, varying conditions of form, size, distribution, with the intent to discover whether this judgment is a function of these other factors as well as of the numerical. The scope of the enquiry includes both relative and absolute number.

The objects chosen as a basis for the number-judgment were bits of paper pasted in two well-defined groups side by side upon a background of black cardboard. This card fitted into an upright frame where it was held in place by a pivoted spring, which allowed easy adjustment and removal of the card. The opening of the frame, 15×20 cm. was concealed at will from the observer by a black wooden screen that played up and down on guiding posts, when released by a cord and lever from the catch that held it in place before the card. It fell by gravity upon a cushion that deadened the sound; and it was restored to its position by the operator's thrusting his fingers beneath and lifting it till the catch above caught and held. The entire apparatus, as well as the operator's movements, was concealed from the observer by a large black cardboard screen resting upon a black-covered table. The one opening in this screen was just large enough to allow a full view of the card when the inner wooden screen fell from sight.

This apparatus which we will call the Two-Group Apparatus, admitted of simultaneous exposure of the two groups of objects, and that only. At first, to make successive exposure possible, a light wooden frame was constructed in whose grooves two leaves of black cardboard ran like sliding doors. By means of rods fastened to their outer edges these leaves could be pulled apart or thrust together till their inner edges met. When this apparatus was placed between the outer screen and the frame bearing the card, and the inner wooden screen had been dropped out of the way, this substitute divided screen was sufficient roughly to accomplish the end in view.

With this apparatus the illumination was daylight, coming through a very large window at the back of the observers. By means of a curtain, marked variations in the light could be prevented.

For the length of simultaneous exposure of the groups the following rule was adopted: Each observer was to be allowed time enough to get a satisfactory feeling of relative number, but not time enough to admit of counting. This time was kept constant during the work of any one sitting. As the weeks went on, it was found possible, under the rule laid down above, to shorten the time for some of the observers, and to use with all the same length of exposure that had sufficed for the speediest. The range of variation was from 1.2 sec. to 1.6 sec. Time was measured by the ticks of a watch. Later tests showed for the time studied that, where effective at all, the longer exposure diminished a given tendency. Often it had no apparent effect.

The method of control already described is not only rather rough but does not exclude the possibility of a space error. This possibility proved actual by experiment. So an apparatus was contrived that should present the groups in succession at approximately the same place and should shorten the exposure, if desirable, to a small fraction of a second.

This new apparatus, which we will call the One-Group Apparatus, required artificial light and a dark room. By means of a 125 cp. incandescent electric lamp, images of the groups of objects were reflected through the lens of a camera and came to a focus upon its ground-glass screen. A second screen of ground glass was placed in front of the first and as close to it as possible, that an even distribution of light might be obtained. The cards containing the objects were of the same general character as in the earlier experiments. They were held in a moveable slide whereby each group in succession could be brought before the lens. When the slide was drawn to the limit in one direction a single circle appeared in a black field. This circle was used as a signal and a means for directing the eye in the dark to that region where the groups were to appear. The exposures were made with a camera bulb, the shutter being set for instantaneous movement, with diaphragm 22 and length of exposure 1/26 sec. A shorter time was thought on trial to make perception too difficult. The apparatus rested upon a table of special construction and was enclosed as far as the glass screen with a wooden frame covered with denim. Double curtains of this material formed this enclosure on one side and made possible an easy adjustment of the cards between exposures, as well as the admission of the operator's hand during a given experiment for the adjustment of the shutter. This had to be set, of course, before each of the three exposures constituting one experiment. During its progress the hand was not removed at all, the curtains falling about the arm in such a way that little light escaped. The other hand managed the moveable slide from behind the enclosure.

Time was measured by watch-ticks. The three exposures--dot-signal, Group 1, Group 2--were separated from each other by intervals of 1.6 sec. This was fixed upon as the minimum for convenient operation of the apparatus.

In much of the experimentation on relative number two observers were employed at once. Their chairs were placed closely side by side on a line about 150 cm. from the plane in which the groups appeared. These groups were not very far from being on a level with the eye. Each observer recorded his own judgment, against the number of that experiment. There were three possible kinds of judgments,--equality or either group larger. If the judgment was of difference it was recorded in terms of the larger.

When the dark room was used, special arrangements were required, for convenience of the observers in making their record. After several schemes were tested the following was adopted as least trying to their eyes: A large, black-topped table was placed before them, bearing an electric lamp enclosed in a black box with a small aperture that could be closed at pleasure; or, if left open, did not let enough light escape to disturb the perception of the groups.

The absolute number of objects in the groups was determined, first, by the character of the problem, and then by convenience. If we are to learn anything about the influence exerted upon the number-judgment by other factors than the numerical, we must eliminate all influence of the latter. Correct judgments may be determined by this factor alone; erroneous judgments must have been otherwise conditioned; and these conditions it is the task of our method to isolate and study, as modifying factors. From correct judgments we learn nothing definite about our problem, but from erroneous everything. Other things being equal, it is preferable to eliminate from the results the influence of this numerical factor, just as one handles any other disturbing, unavoidable element, by equalizing the numbers in the two groups.

What may be called the standard number of objects in each is twenty. This choice was governed by the purpose of using a number large enough to make counting impossible in a brief time and yet not so large as unnecessarily to increase the labor of preparation and the difficulty, for the observer, of getting an idea of the groups as a whole. To the cards containing equal groups, 20 to 20, were added others, 20 to 19, 19 to 20, for the purpose of easy variation in arrangement, by omitting one object from a group, without making the actual numerical difference easily perceivable. In later work these small objective differences were dropped. Yet other cards, 23 to 17, 17 to 23, were added, to the end that the observers might find unmistakeable number-differences, and so not be bothered by the suspicion that the groups were all equal. The reversal of the number-relations, as indicated above, was in the interest of equalizing the influence of the actual numerical factor in the two groups.

The following proportion was kept among the numbers of observations made upon each kind of card: 1/2 upon groups objectively equal; 5/12 upon those differing by one from each other, where half each went to (20 to 19) and (19 to 20); 1/12 to those showing the maximum objective difference of six, where again half went to (17 to 23) and half to (23 to 17). Of course the observations upon cards of this last sort are excluded from the tables.

As to the number of cards employed for each series of experiments, it was found at first convenient to use seven,--3 (20 to 20), 1 (20 to 19), 1 (19 to 20), 1 (17 to 23), 1 (23 to 17). In each group the arrangement of objects was irregular. The use of three of the first sort was to encourage freshness of judgment, each having its particular irregularity. Cards were but rarely remembered, practically never except in the case of groups differing widely in number. So far as the observers could tell, judgment was formed afresh in all these cases. In later experiments eight cards were used. This number was in the interest of avoiding the distribution-error. At first it was thought sufficient that all the groups should be merely irregular. Later it became evident that discrimination was very fine here and so that this factor must be eliminated by the usual precise method.

The space- and time-errors, where likely to be present, were eliminated in the usual way by performing an equal number of experiments with the groups in reversed arrangement. Several methods of doing this were at first tried; but these were all abandoned in favor of the following: The experiments were arranged in sets of 24, in each of which the proportion of kinds of cards was kept as indicated above. Each set with one space- or time-order of the groups was repeated with that arrangement reversed.

A word must be added as to the arrangement of results in the tables. Judgments of equality upon objectively unequal groups are entered as overestimations of the smaller groups. The per cent of correct judgments is equally divided between the two other classes, and for this reason that interest centres, not in correctness at all, but in the difference between the tendency of error in one direction and that in the other direction. No doubtful judgments were admitted, but in such cases another trial was allowed later, usually when the observer was not aware that he was being given a new chance. The subjects are divided into three classes according as the results show a tendency to favor one or the other group or no tendency either way. A difference of 10% is arbitrarily taken as significant.

1. The Influence of Group-Area. The Two-Group Apparatus was employed. The four sets of experiments carried out with this factor differed primarily in the material upon which the observer's judgment was based, and secondarily in certain matters of method. The attempt in them all was to approximate more completely to the isolation of the factor under investigation. They are numbered in the order of approximation. As marked results were obtained from each, they have all been offered for consideration in the four parts of Table I. A description of the material used in each case follows.

A. Squares (1 cm.) Neutral Gray no. 1. (Bradley), arranged irregularly in two groups with irregular outlines on a background of black cardboard. One group was large in area, the other small, the attempt being made to fill each space homogeneously. Groups were not proportional in shape of area.

B. As above, save that circles (11 mm. approx. in diameter) were substituted for squares, in the interest of distinctness for the several objects.

C. The area of the groups was oblong and regular, and the sides were proportional. (Compact 72.5 mm.: 58 mm.; scattered 110 mm.: 88 mm. These relations were determined by the size of the frame that had already been used and by the desire to make the difference in area as marked as other necessary conditions would admit.) Each area was marked by a circle in each corner. The color of the compact group was the deepest shade of normal gray (Prang Normal Gray Darker); of scattered group the next higher shade (Normal Gray Dark). These dark grays were used in order to reduce to a minimum the tendency to produce after-images. The difference in the shades of the two groups was in the interest of avoiding the greater brightness due to the mass-effect of the compact group.

D. As in C, except that India ink outline circles (1/3 to 1/2 mm. line) were used on a background of granite cardboard. This change was made to avoid, as far as possible, the greater mass-stimulation due to the reënforcing effect of the compact arrangement. The size of circles remained as before.

TABLE I

KEY: NS = Number of Subjects AV% = Av. % of difference in favor of

A B C D 274 248 120 132 experiments experiments experiments experiments with each with each with each with each subject subject subject subject

NS AV% NS AV% NS AV% NS AV%

Small 5 31.5 10 34.6 7 44.1 10 46 Large 3 35.1 4 44.1 5 41.5 3 26.3 No tendency 1 8.8 2 4.2 4 5.7 3 6.6

The per cent recorded in the no-tendency class is an average of all per cents below 10, whether in favor of the one or the other of the two remaining classes. This is true for all the following tables.

The following facts are presented by the several parts of Table I: (1) The large per cents of difference show that area is to a large extent a determinant of the judgment of relative number. (2) Different subjects show opposite tendencies. (3) A comparison of the results of individual subjects through the four series shows that this opposition in tendency occurs in the same subject at different times. The introspective notes of one of these subjects show the internal process of change from one tendency to the other. It consists in a gradual increase of analytic activity toward the compact group. At first glance the composition of the scattered group was more evident; but when attention was fairly turned toward the compact, the inability to isolate objects made them seem very numerous. The importance of a coöperating subjective factor is here evident. (4) Out of a possible 57 cases there are but 10 showing no tendency.

2. The Influence of the Internal Arrangement. As before, the Two-Group Apparatus was employed; and the factor was studied in three aspects.

A. The material consisted of two groups of gray circles (Normal Gray Darker, Prang) covering equal areas. In one group this area was filled homogeneously, in the other the circles were gathered into nuclei. In order that there might be exactly the same relation of parts when the cards were reversed, each group was so arranged on a diagonal axis of symmetry from upper left to lower right corner that each half repeated the other in reverse order. Otherwise the arrangement of circles was irregular.

Six cards only were used,--four (20 to 20), one (17 to 23), and one (23 to 17). Slight differences among them occurred in the arrangement of the equality-cards, which might help to counteract any incipient reasoning from sameness of appearance to sameness of number. The large increase in the difference-values is accounted for in part by the fact that the cards (19 to 20) and (20 to 19) were omitted, and for this reason: that when an observer tended largely to favor a particular group, the introduction of a card in which that group was objectively greater would mean an increase in the number of correct judgments; whereas the introduction of two objectively equal groups for the others would increase considerably the number of erroneous judgments.

B. The numerical character of the cards here used shows a return to the usual. The material was like that of A, except for a new internal arrangement. Here the area of one group was filled homogeneously, while that of the other contained a pattern of this sort: An ellipse just contained within the boundaries of the normal area; a circle in each of the four corners of that area; and in the centre a diamond formed of four circles. Numerical changes were always confined to the ellipse, as less open to counting than the rest of the figure.

C. Material and method repeat B but with another internal arrangement. One group, as before, showed an area homogeneously filled, and irregularly, as usual. The other group carries to an extreme the distinction of open and filled space made prominent in the other groups of this table by massing the circles in an outline completely enclosing the area and in a diagonal from upper left to lower right corner. The outline did not show even spacing; more circles were crowded in one part than in others, that counting might be more difficult.

That there might be no attempt to remember cards, in all cases where there were twenty objects in the homogeneous group the same kind of irregular arrangement was repeated. This is a different method from that employed in A. Since the length of exposure was so short and the arrangement in the group irregular, either one is probably as good as the other.

D. The material used for B and C had a kind of regularity, since definite patterns were used. The introspection of the observers showed, however, that the patterns as such were not in question in the judgment, but rather the vacancies and the crowding. With the Two-Group Apparatus an arrangement in parallel lines could rather easily be counted, but with the One-Group Apparatus and its means for instantaneous exposure this difficulty was to some extent overcome. The arrangement of the objects in parallel lines was therefore adopted and matched against the irregularity of an accompanying group. The same size of group-area was kept, but the small difference-cards were omitted. There was no other change beyond those made necessary by the apparatus and already indicated on an earlier page. The length of exposure was 1/25 sec. The bearing of this time-factor on the results will be considered in a later section.

TABLE II

KEY: H = Homogeneous N = Nucleated P = Pattern O = Outlined R = Regular I = Irregular NT = No tendency

A B C D 132 132 132 88 Experiments experiments experiments experiments with each with each with each with each subject subject subject subject

H N NT H P NT H O NT R I NT Number of subjects 10 2 2 10 1 3 7 5 2 2 1 Av. % of difference in favor of 53.23 1.5 6.1 35.7 52.8 5.3 42.7 34.8 7.9 40.3 1.2

The several parts of Table II give us the following facts: (1) The judgment of relative number is very markedly a function of the internal arrangement. (2) The marked tendency among the observers to favor the homogeneous in A and B meets a check in C. Recalling the direction of difference between C and the other sets, that in C the gradually increasing contrast between the inner vacancies and the filling reaches a maximum, we may suspect that these vacancies begin to seem no longer a part of the group-situation, while the compactness of the filling, where it does occur, is thrust prominently forward. The notes of the observers confirm this suspicion. (3) The results of the different subjects show that the shifting of tendencies occurs as before. (4) As to the way in which regularity functions in the judgment, the notes of one observer are very clear. The blank spaces in the irregular are noticeable, he says, which is not true of the regular, where, on the contrary, one has a feeling of compactness of figure. I am able to confirm this character of the spaces by my experience outside this experiment. A simple pattern is very easily apprehended and irrelevancies of the background dismissed. Increase its complexity to a maximum, as in the case of an irregular group, and I am almost at a halt to isolate objects from their fellows and maintain them apart, yet together. The background is hardly to be shut out. This is probably due to the absence of a centrally excited image of the group. The object and the not-object run together. (5) The position of the single observer in the no-tendency class of D was marked subjectively by great difficulty in forming a judgment. The groups seemed incomparable, the vividness of form excluding the perception of number.

3. The Influence of Complexity in Group-Composition.

Complexity of group-content was attained by introducing objects of different colors; so there was not a clean isolation of factors. By comparing these results with those recorded in Table IV, A, we shall be able somewhat roughly to make allowance for the factor of mere color.

Sets of 132 experiments each from sixteen observers were obtained for each of these factors. Unfortunately the distribution-error was not eliminated. Later experiments showed the importance of this factor, and, in consequence, the impossibility of interpreting the results under consideration. So new experiments were performed under the proper conditions, but at a time when only a few of the first observers could be used. Their results from the earlier series are given in Table III, A. The exclusion of the small-difference cards from the later series (Table III, B) and the consequent increase of the number of experiments on objective equality prevent comparison.

The material in A consisted of two groups of circles of the usual size, one Normal Gray (Prang), the other of three colors--Red, Yellow Orange Shade 2 (Bradley), Light Blue Blue Green (Prang). The intent was to equalize the two groups in brightness. When the observers were questioned about the relative brightness, supporters were found for all three possible opinions. So it seems probable that the groups did not differ widely in this respect. As nearly as the number-condition would allow, the three colors were represented equally in the group; and they were distributed so as to make the whole as homogeneous as possible.

In B the changes were the correction for distribution as described in the introduction to this section, and the substitution of equality-cards for those of slight numerical difference. In addition, three other colors replaced those of A, in the interest of regulated brightness and more pleasing æsthetic effect. These were, in the Bradley system of broken spectrum scales, A-Red, medium; A-Yellow Orange, dark; A-Blue Green, dark. With these exceptions B was like A. The observers were all inclined to consider the gray brighter than the mixed. The Two-Group Apparatus was used.

TABLE III

KEY: G = Gray MC = Mixed Colors NT = No Tendency

A B 132 132 experiments experiments with each with each subject subject

G MC NT G MC NT Number of subjects 3 1 3 1

Av. % of difference in favor of 17.7 2.2 19.9 6.8

The following facts may be gathered from Table III: (1) The tendency to overestimate the gray is due in part at least to the additional factor of complexity in the other group, as is shown by the markedly changed tendencies in Table IV, A, where a solid color takes the place of the mixed colors. The actual colors involved in the two cases are different, to be sure, and necessarily so, and this difference may of course be invoked as the cause, as well as a possible difference in brightness between the gray and mixed in III, B. The introspective notes help us here. One observer felt that he favored the gray primarily because there was a tendency to consider but one color in the mixed. Another was drawn toward the gray because it seemed definite and consistent. For both of these observers æsthetic elements were involved in favor of the gray. The latter found also that the greater brightness of the gray gave it a larger area. With a third subject the fact of variety was felt as decidedly important; but his notes show a conflict between this factor and that of distribution which was the conscious basis for his normal judgment.

4. The Influence of Differences in the Kind of Objects.

A. The Factor of Color. The material in A 1 consisted of two groups of circles of the usual size, one Normal Gray (Prang), the other Red (Bradley). The attempt was made by this choice to equalize the brightness. The size and shape of the group-area were those of the smaller area of Table I, C and D. In A 2 the only changes were the correction for distribution, as described in the introduction to this section, and the substitution of equality-cards for those of slight numerical difference. The Two-Group Apparatus was used.

The following results appear in Table IV, A 1 and A 2: (1) While complexity seemed on the whole to diminish apparent number, red noticeably increases it. Some of the observers report that group as more vivid and interesting. One observer compensated by emphasizing the gray in attention, as his results showed. (2) If one ask how the color red functioned in the judgment, the reply must apparently be, by its brightness and vividness. The mixed group functioned in a double way, as vivid and so more numerous, as fragmentary and so fewer.

TABLE IV

A1 A2 132 experiments 132 experiments with each subject with each subject

Gray Red No tendency Gray Red No tendency Number of subjects 3 1 3 1

Av.% of difference in favor of 18.3 5.4 30.3 9

B C 132 experiments 132 experiments with each subject with each subject

Large Small No tendency Circles Squares No tendency Number of subjects 8 3 5 8 4 4

Av.% of difference in favor of 33.6 27.5 6 28.4 18.8 3.5

D1 D2 88 experiments 132 experiments each with two subjects

44 experiments with two subjects

exposure = 1/25 sec. exposure = 1/4 sec.

Simple Complex No tendency Simple Complex No tendency Number of subjects 3 1 2

Av.% of difference in favor of 30.7 5.6 21.2

E 88 experiments with each subject

exposure = 1/25 sec.

Bright Dark No tendency Number of subjects 3

Av.% of difference in favor of 47.4

B. The Factor of Size. The Two-Group Apparatus was used, the material consisting of India ink circles (1/3 to 1/2 mm. line) on a background of granite paper. This paper was chosen here and for the experiments of Table I, D, to get a suitable mean between too sharp contrast and sufficient distinctness. The circles in the one group were ten mm. in diameter; in the other seven mm. The two areas were approximately equal, and of the same size as that of the more compact group in Table I. This is in fact the standard size throughout these studies in Relative Number, wherever area is not in question. The small-difference cards were included.

Two sources of possible complication must be considered. It is unavoidable that the factor of differences in compactness should enter and that clean results on the basis of object-size be denied. Our interpretation must not fail to consider this fact. Because of this, it seems unlikely that a distribution-error should arise; so the usual precaution to eliminate it was omitted both here and in the study of area (Table I). Distribution affects the appearance of the vacant spaces. When differences in the amount are by the conditions inevitably prominent, differences in the conformation may be safely regarded as of minimal vividness.

The following results appear in Table IV, B: (1) The illusion of numerical inequality is marked for many subjects. (2) The judgment is quite possibly a function of the two factors--object-size and group-vacancies. If we recall the fact that the small-object group is more scattered than the other, we shall note that the leading class here is like the leading class in Table I, and we may fairly reckon this factor as of importance in the issue. Of the incomplete introspective notes on this question, those of only one observer speak clearly for the size. He says: "There is an overpowering feeling of predominance in case of the large and I must judge for them. The large space covered seems an important factor. The longer I reflect upon the relative numbers the more numerous seem the larger, that is, they appear to increase over the small after the exposure. It is hard to give judgments of equal in most cases."

C. The Factor of Form. The material consisted of a group of circles, each of the same size as in former material; and a group of squares, each approximately equal to a circle of the other group. These were made of Prang's gray paper (Normal Gray Darker) and pasted upon a black background. The areas of the two groups were approximately equal. The squares were set irregularly except for those in the corners, where the edges were placed parallel to the edges of the card. The Two-Group Apparatus was used and the small-difference cards included.

In this material, again, the formal elimination of the distribution-error was not attempted. The striking difference in the conformation of the vacancies through the form-differences of the objects probably makes the repetition of the exact positions insignificant. Still the fact must be noted.

The results appear in Table IV, C. (1) The illusion of numerical inequality is here again marked for many observers. (2) The introspective notes are not on the whole very illuminating as to the basis of judgment. One observer, who favored circles, found that the appearance of more orderly arrangement in squares made them seem few. Another, who favored squares, found, on the contrary, the more regular the more numerous, and thought that the squares may have seemed more regular. A third, who favored circles, found the squares better individualized, with whom a fourth agreed in both respects, who also was influenced by the apparently greater bulkiness of the squares. Fewer could go into a given area. A fifth, on the other hand, who found the circles better individualized, still favored them. So we have these observers apparently doing the same thing under opposite conditions, and the opposite thing under the same conditions. Here indeed is a situation for any theory. So far as we can learn from the foregoing, the form may influence the judgment merely through its space-characteristics, but possibly also through the vividness of intrinsic interest.

D. The Factor of Complexity. The One-Group Apparatus was used in this work and results were obtained for two different lengths of exposure, 1/25 sec. and 1/4 sec. The material differed, in that to the centres of the circles of one group were added small Red (Bradley) circles (6 mm.). With the apparatus used, the color was not very effective, the brightness contrast between dark centres and white periphery being chiefly prominent. The total group-brightness was of course diminished by those centres. The small-difference cards were omitted.

The results are recorded in Table IV, D 1 and D 2. (1) The illusion is apparently strong. (2) The amounts of the difference-values show that the shorter exposure is more favorable to the illusion. (3) The introspective notes indicate that both brightness and complexity functioned in the judgment. Two observers, both of whom show large tendencies, were not conscious of any influence of complexity. One of these did find differences in brightness important; and in favoring the darker group his results exactly coincide with those of Table IV, E, where this factor is under direct consideration. A third found the complex group interesting. With a fourth the complex group developed in number amazingly during the few moments after exposure and had an appearance of great intricacy, often seeming to be in active movement. A fifth observer too felt that its numerical character depended on its complexity.

E. The Factor of Brightness. Hitherto the absolute arrangement of the objects in any two groups compared, where this factor has not been the object of enquiry, has been in the two cases different, though with respect to irregularity alike. This course was governed by a desire to avoid the substitution of a form-judgment for one on number, through recognition of the fact that both groups had identical forms. The resulting distribution-error I tried to eliminate in the usual way. Tests toward the end of these studies showed that there was no danger from this source. Errors seemed about as frequent as before. No observer made any comment on the fact, except one who through his official connection with the laboratory work knew that the test would be made sometime, but not exactly when. During many of the experiments he did not perceive the likeness of form; and when he did the numerical judgment arose without connection with that factor, as was shown by the feeling that the two groups were unequal in number. He called the relative fewness of the first group a case of "perspective effect." This must have significance for any account of the time-error; but by no means carries with it its own interpretation.

One welcome result of these tests was their assurance that I might without fear further simplify the experimental conditions by avoiding the possibility of a distribution-error. The material for these experiments on brightness therefore profited by this possibility. Each card had a different specific irregularity, but always in duplicate. In choosing the degree of brightness-difference Prang's brightest shade of normal gray was found as dark as could be conveniently perceived with the artificial light of the One-Group Apparatus. The contrast between this shade and white was quite evident enough for the purpose. The small-difference cards were omitted.

Table IV, E, shows the decisive character of the results. The observers fall all into one class in favoring the darker group, and by a large difference-value. The following introspection of one observer shows the extent to which the factors of brightness and number fuse: "I frequently lose sight of time-order. It is a question of number and not one of light-intensity, and if called upon to state which group came first I might not be able to answer. In equality-judgments the difference of light comes out distinctly."

5. The Influence of Complexity of Environment.

The material prepared for these experiments certainly lays stress upon relative, not absolute, complexity; for the conditions were satisfied by placing 5 mm. strips of white paper, equal in length to the width of a group, a few millimetres off at the top and the bottom of the groups that were on one side of the cards. The One-Group Apparatus was used and the small-difference cards omitted.

TABLE V

44 experiments with two subjects. 88 experiments with two subjects.

Exposure = 1/25 sec. Simple Complex No environment environment tendency

Number of subjects 2 2

Av. % of difference in favor of 15.9 8.5

The results are recorded in Table V. (1) The drift of tendency is toward the group with the more complex environment. No one markedly favors the other group. (2) The notes of the observers indicate that the added strips functioned through their effect upon the apparent area of their group. The observers all found the dimensions increased; but with some, apparently by contrast, the added height brought out sharply the narrowness. One observer found this true in general; another, when the barred group came first. The latter says: "The unbarred group, coming first, appears to reflect its compact character on the barred one, when it comes, so that it does not look so attenuated and strange." Here the image brought over to the second took the width of the second somewhat out of relation to its illusory height, whereas in the reverse order the contrast relation was fully maintained.

III. THE INFLUENCE OF FACTORS PRESENTED IN OTHER SENSE-FIELDS BY THE OBJECTS WHOSE NUMBER IS IN QUESTION

A very simple apparatus was employed. The objects whose number was in question were bright steel balls (3/8 inch) thrown loosely into square black frames, 13 cm. inside, placed side by side on a black-topped table. The experiments were performed in series of 30. The groups were kept equal numerically, with this exception, that into each series were introduced four experiments where the groups were so unequal that the observer could have no question as to the correctness of his judgment and the existence of objective differences. This numerical superiority was given to each group alternately, and judgments on it were, of course, excluded from the results. The actual numbers employed in a series varied between 35 and 60 in accordance with the following scheme:

1. 50 each 2. 45 " 3. 50 " 4. 55 " 5. 60 to 40 6. 50 each 7. 45 " 8. 40 " 9. 45 " 10. 50 " 11. 55 " 12. 60 " 13. 40 to 60 14. 50 each 15. 45 " 16. 40 " 17. 35 " 18. 40 " 19. 45 " 20. 50 " 21. 55 " 22. 60 " 23. 60 to 45 24. 50 each 25. 45 " 26. 50 " 27. 60 " 28. 55 " 29. 50 " 30. 45 to 60

The time of a single exposure--in this case two groups at once--was 3 sec. measured by a stop-watch. As to the arrangement of the balls, care was taken that they should not be massed in one place, but scattered somewhat homogeneously over the space within the frames. The illumination was daylight, so managed that shadows cast by the balls were reduced to a minimum. The observer sat close to the table with the groups directly in front of him. He either kept his eyes closed between experiments or held a small screen before them. Sometimes he merely turned away. The operator worked from the opposite side of the table, taking care to make the necessary noises as little suggestive as possible. The observers agreed that they were not consciously influenced by the manipulation.

The progress of these experiments disclosed an astonishing space-error. So far as was conveniently possible the usual technique of elimination was employed.

1. The Influence of Active Pressure.

In this study the groups were differentiated in this way: With one hand the observer rolled the balls of one group under his fingers, while the other group was presented to vision only. The method of observation consisted in rapidly and lightly rolling the balls under the fingers a few times and then surveying both groups visually for the remainder of the exposure, judgment being given on the visual number.

Evidently there is much that is rough about this procedure. Pressure and kinæsthetic factors are lumped off together; the length of the touch-stimulus was not exactly determined; and there is the possibility that the visual stimulation from the group touched is weakened. To be sure the method prevents any great difference in the latter respect; and if we are guarded in our interpretation, something of interest may be learned.

There appeared to be no convenient way to eliminate the space-error. The right hand was used with the right group and the left with the left. So here again interpretation must be circumspect.

TABLE VI

A B 52 experiments with 260 experiments with each subject one and 208 with the other subject

No No No Touch touch tendency Uneven Even tendency Subjects 2 1 1

Av. % of difference in favor of 7.6 10 1

SPACE-ERROR

No No Right Left tendency Right Left tendency

Subjects 1 1 1 1

Av. % of difference in favor of 69.2 23 30.8 20.2

C 145 experiments with one and 260 with the other subject

No Weight No weight No tendency Subjects 2 Av. % of difference in favor of 2.4

SPACE-ERROR

Right Left No tendency 1 1 Av. % of difference in favor of 32 4.4

Turning to the results in Table VI, A, we find the following: (1) The influence of the pressure-kinæsthetic complex practically does not appear; while the space-error shows a marked tendency that, for the two observers, is in opposite directions. (2) On the other hand, the notes of one observer show that in his case at least the face value of the table is erroneous. To this effect he says in substance that he can make a more accurate estimate of the number in the group touched. He tries to ignore these sensations of touch, but with ill success in the case of the left hand, where clumsiness not only makes it difficult to touch the balls gently but also to keep them under the fingers, which often feel the ground-space. For this cause the group seems small in number. Clearly enough, then, it is the space-error that tells the story of the effect of the added stimuli on this observer, only it must not be interpreted as space-error. The pressure functioned in the judgment through its numerical aspect. But the positive effect with the right hand was turned to a negative with the left through its emphasis of vacancies. The high difference-value in the space-column becomes thus a striking evidence of the effect of pressure, and the results are accounted for without reference to the kinæsthetic factor. The other observer felt that the active pressure was relatively indifferent. (3) The entire absence of correct judgments on the objectively equal groups shows to what a surprising extent other factors have modified the numerical.

2. The Influence of Unevenness in Active Pressure-Feeling.

In the experiments of this section the groups differed in this way, that one rested on the smooth table-top while the other had for its bottom a coarse wire mesh covered with black cloth. The balls of the one rolled smoothly beneath the fingers while the other balls moved lumpily over their mesh. Both hands were used--each for the group on its side; and the method of observation and length of exposure agreed with those conditions in the preceding section, except that the balls were rolled a little more vigorously that the factor studied might come clearly into consciousness. The groups were interchanged for half the number of series. This could not of course completely eliminate the space-error, since kinæsthetic differences in the limbs remained uncompensated. In general the criticism in the preceding section is again applicable.

The results appear in Table VI, B. (1) One observer shows a tendency to favor the smoothly rolling group, while the other again shows no tendency. Both have large space-errors of the same character as in A of this table. (2) The introspection of the observer showing no tendency is to the effect that touch plays little or no conscious part in the situation. The other's notes give no hint that the factor studied here was influential; but to the effect on the judgment of touch in general, especially with the right hand, they give clear witness. The touch-sensations, he says, were difficult to ignore. Those from the right hand were more vivid than those from the left; and the right hand seemed more sensitive. Judgment was based on a general feeling of "moreishness" which came promptly. There is nothing to contradict the evidence of the earlier experiments that touch is again influential through its numerical character. (3) Both observers regard factors of distribution as of fundamental importance, though one was inclined at first to insist that there was nothing but number in his judgment. The significance of this unanalyzed feeling will appear in a later section. (4) These results agree with the preceding in the approximate exclusion of correct judgments.

3. The Influence of Active Weight.

The variation here in question consisted in lifting one of the groups during judgment of the relative number in the two groups. The apparatus was made by transforming into trays the frames containing the balls, by putting into these frames wire-mesh bottoms covered with black cloth. They were set each upon four small wooden pillars so that the hand could be easily thrust under the tray. At the signal a given tray was several times raised a little way and lowered, and the judgment formed on the same factor as before. Here again the space-error was not entirely eliminated. Each hand was used with the group on its side, but kinæsthetic differences peculiar to each of the limbs remained. There was always some motion among the balls in the lifted tray, though the gentleness of the lifting prevented the existence of much. This is a radical defect, but one not easily avoided with maintenance of other desirable conditions. Even more serious, as the issue proved, was the failure to control the lifting impulse; yet, as it happens, we are not prevented from getting an experimental answer to our question.

The results are recorded in Table VI, C. (1) They show no apparent effect of the weight, and with one observer the further unusual fact of no space-error. This error is marked enough in the case of the other, and, conforming in direction to that of the preceding sections of this table, allows us in so far to adopt the same interpretation of his results. (2) The introspection of one observer was to the effect that he felt a tendency toward a modification of the number-judgment by weight. It was especially strong when the group was lighter or heavier than was anticipated, the light group seeming less numerous, and the heavy group more. Occasionally he caught himself weighing the second group mentally; and sometimes he had to recover himself from a tendency to make judgments on a wrong basis, presumably that of mere weight. With such a conflict of tendencies the character of the results is not surprising. Particularly important are the opposing tendencies lying in the factor of weight itself. The other observer reported that a very heavy weight exerted an influence that it was hard but not impossible to ignore, while a lighter weight did not effectively enter the situation at all. His earlier inclination to say that there was nothing but number in his judgment inclines one to believe that fusion of factors may have passed beyond the stage of ready analysis. (3) Our analysis has given us reason to believe that active weight has a definite tendency to modify the judgment of relative number.

4. The Influence of Muscular Strain in Observation.

The study was made from the point of view of more than one set of experimental conditions, viz.:

(1) Equal strain (minimum). (a) Right--left. (b) Up--down. (2) Equal strain (maximum) eyes turned. (3) Strain vs. ease. (a) Head and eyes turned. (b) Eyes turned.

The conditions of (1) (a) were exactly those of the earlier experiments with the exception that the groups were undistinguished save by position. In (1) (b) one group was so placed between the other and the observer that there might be as little increased effort as possible in viewing the farther. In the up-down movement more muscles are involved in the lift than in the fall of the eye. So really we have here a case of (3) but not so marked. In (2) the groups were put to the right and left at such distances that, when sitting between, the observer could just take each one in without turning his head. This brought a decided strain upon the eye-muscles. In (3) (a) the groups were separated by the length of the table--a distance of 90 cm.; and the observer placed in alternate series before each; as he was in (3) (b) where the farther group was carried to the limit of vision to be reached without turning the head. Here the strain was like that in (2), but for one group only.

An incompleteness in experimental analysis lies in the impossibility of separating the factors of distance and strain.

TABLE VII

A - Baldwin 46 experiments Hutchinson 78 experiments Equal strain (minimum)

B - 52 experiments with each subject Equal strain (minimum)

C - 52 experiments Equal strain (maximum) Eyes Turned

D - 104 experiments with each subject Head and eyes turned

E - 52 experiments

A B C D E

Right Left Lower Upper R. L. Ease Strain E. St.

Subjects Baldwin Hutchison 2 Bald. 2 Bald.

Av.% of difference in favor of 30.4 28.2 68.3 71.2 52.4 80.8

Here are the facts of chief interest: (1) The following tabulation gives us a ready view of the character of the results in Table VII; and shows the extent to which they are consistent:

A B C D E

Baldwin favors right {upper left {farther {nearer {strain {strain {no-strain left left

Hutchison favors left {upper {farther {strain {strain left

(2) The only inconsistency in the strain-distance complex is with Baldwin in E. He reported that the more distant group appeared rather as an undifferentiated mass whose number was not so well obtained, while in the near the individuals were significant. He seemed to be in the midst of these. The case seems analogous to that of the observer whose introspection was reported under Table I, and who at first accepted what we may call the objective analysis, by which the scattered group gave up more distinct objects than the compact; but later attempting voluntarily to disintegrate the compact, found a bewildering confusion in the task that made this group seem very numerous, and brought about in the end an exact reversal of tendency. (3) Can we now separate in the results between the influences of strain and of distance? So far we have regarded them as one complex. But the introspections speak merely of the space-characters of the objects, Hutchison agreeing with Baldwin that the more remote group is judged as an area rather than as a collection of definite objects. (4) The almost entire absence of correct judgments in these experiments adds new evidence to that of the immediately preceding experiments in proof of the insignificance of the actual numerical relation for the judgment of relative number.

IV. THE INFLUENCE OF FACTORS OUTSIDE OF THE OBJECTS AND IN OTHER SENSE-FIELDS

The One-Group Apparatus was employed, and cards in general corresponding to those where area was not in question,--white-circle groups equal in size and irregular in inner distribution, which was not duplicated on the same card, though the resulting distribution-error was formally eliminated in the usual way. The usual care was taken to fill the group-area homogeneously. The small-difference cards were retained at first; but on later discovering the possibility of duplication a few supplementary experiments were added.

1. The Influence of Touch.

The apparatus employed to give the touch-stimulus consisted in a long lever attached to the armature of a small electro-magnet. In the end of the lever was inserted at right angles a wooden peg, cork-tipped. In view of the other conditions of the experiment a convenient spot for the application of the stimulus was found to be the forehead where it curves backward above the right eye. The apparatus was supported by rods and clamps upon a long upright steel rod set in an iron base and placed behind the chairs of the observers. The same rod carried a head-rest, designed not as a support but merely to show the observer that he had returned to the original position after he had bent forward to record judgment. Where two observers were used at once two sets of this apparatus were employed, with the magnets in a single circuit governed by a floor-button. The touch-stimulus was made to coincide as closely as possible with the appearance of a given group.

In view of the practical remoteness of this factor from the object of judgment the experimentation here took two forms,--one in which the observer was passive toward the touch-stimulus; the other in which the effort was made closely to associate the touch with the visual group by imagining the group to be responsible for the touch. For the passive method the touch was given irregularly now on the first and now on the last, but as many times on one as on the other.

For the active method, it was given always on the last group. This constancy was held to favor the active association of touch and particular group. The constant time-error was guarded against by experiments in which no modifying factor was introduced. A and B of Table VIII present the results of the passive and active methods respectively. C and D repeat A with duplication of groups,--C with the usual (1/25 sec.), D with a longer, exposure. These last sets were taken that the factor of touch might be studied when the objective conditions of the strong distribution influence should have been removed. It might prove that a factor swamped in the former situation might emerge into effectiveness.

The following summary gathers the chief facts of Table VIII: (1) Touch appears practically without effect in A. (2) In B, the results for touch seem again insignificant; but comparison with the control-results, to isolate touch from time-order, while it shows no marked change for Angier, does show for the others that touch was effective in determining the direction of error by difference-values, in the two cases of 10.2 and 14 per cent. The active method seems to be slightly more favorable to the influence of touch. (3) The duplication of the groups in C gives a large increase to the apparent effectiveness of touch, which is considerably diminished but not destroyed by the lengthening of the exposure in D. (4) The introspection for A indicates that touch under these experimental conditions has little subjective importance for the judgment of number. It is sometimes quite unnoticed. Angier made a possible exception in its favor in cases of great hesitancy where it added "importance" to the group with which it occurred. Usually he felt little doubt. With Shaw the touch was at first distracting but later indifferent. Johnston's notes indicate rather more effect. The touch prevented strict attention to the figure impression whereby the space-intervals in that group lost in value. Later it lost its confusing effect. Here seems to be subjective tendency, but not enough to predominate in results.

TABLE VIII

A 88 experiments with each of two subjects. 132 experiments with one subject.

B 198 experiments with each of two subjects. 110 experiments with one subject.

C 44 experiments with each subject.

D 88 experiments with one subject and 44 with the other Exposure = 1/4 sec.

A B No No Touch No touch tendency Touch No touch tendency_

Subjects 3 3

Av.% of difference in favor of 3.2 5.7

C D No No Touch No touch tendency Touch No touch tendency Subjects 2 2

Av.% of difference in favor of 26.1 13.7

Results in B for the subjects separately were as follows: Angier 4%, Johnston 8.2%, Shaw 5%, all, so far as they went, in favor of the touch-group. Control experiments to determine the time-error gave the following results: Angier 6.8% in favor of the group last seen, Johnston 2.2%, and Shaw 9% in favor of the first group.

Some further introspective evidence appears in connection with the active method of B. Angier confirms his earlier account exactly. Usually the factors of distribution practically associated with number determine the judgment promptly; but in cases of doubt the touch is felt to add to its group something that appears as number-value. Johnston's subjective situation seems a little complicated. I may summarize thus: (a) The connection between the touch and its group being established, that group seems smaller, as being, together with the touch, somewhere nearly equal to the first. (b) The connection established and touch failing to come, that group seems smaller. (c) The connection not established and attention being concentrated on the visual impression, the touch-group feels much larger. The curious attitude in (a) results in a discounting in advance of the actual number. This done, the touch adds numerical value to its group. In (c) the effort at abstraction appears to emphasize the second (touch) group. Later, he reported similarly that the touch-stimulus seemed to add to the number of circles in its group even when the judgment favored the other group; and that "any outside stimulus connected with the one of two exposures tends to lose its own significance and be translated into number of dots to help the accompanying exposure to equal or exceed the first." The touch-group is felt to have more significance through association with an idea of superior energy or greater motor impulse.

Of the character of the influence exerted by the touch, Shaw reported that there seemed to be a diminution in the size of the first group and something extra in the second. More specifically, this effect appeared at times as an added circle at the right of the second (touch) group. He thought that this effect was overruled by the real bases of number-judgment which he summarized as "size, regularity, density, etc."

These notes show a definite tendency on the part of the touch-stimulus to break in upon the course of the number-judgment ordinarily determined by the practical association of a specific group of factors with number. That this result gets no more marked registration in the percentages is apparently due to the strength of these customary associations.

(5) The extent to which the distribution-error complicates the present study is shown by the prompt increase in effectiveness of the touch-stimulus when the groups were duplicated, as in C and D.

2. The Influence of Hearing.

The scheme of the experimentation upon this factor conformed in general to that of Section IV, 1. But a new sort of differentiation was possible in the auditory field, and one more readily suggestive of numerousness, perhaps, in that by use of an electric bell a rapid succession of sounds could be given with one group while with the other a single sound could be produced. An actual numerical difference in the auditory field might fuse with the factor of relative visual number and determine the judgment to its direction. These results are set down in B of Table IX. The same set of cards was used in the One-Group Apparatus for these experiments as for those of Section IV, 1. In these two sections of Table IX the observers did not know on which group the sound or the particular sound would be given; but any possible disturbing effect of this irregularity was formally eliminated as in