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. kinds of treatments to finish a series.
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.
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.
PLATE V.
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.
PLATE VI.
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.
PLATE VII.
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.
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 JUDGEMENTS 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