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

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

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

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

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)

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)

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

TABLE XIV

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

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,[122] 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.

THE ESTIMATION OF NUMBER

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 126 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: 12 upon groups objectively equal; 512 upon those differing by one from each other, where half each went to (20 to 19) and (19 to 20); 112 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 ( 13 to 12 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