mm. These relations were determined by the size of the frame that had

already been used and by the desire to make the difference in area as marked as other necessary conditions would admit.) Each area was marked by a circle in each corner. The color of the compact group was the deepest shade of normal gray (Prang Normal Gray Darker); of scattered group the next higher shade (Normal Gray Dark). These dark grays were used in order to reduce to a minimum the tendency to produce after-images. The difference in the shades of the two groups was in the interest of avoiding the greater brightness due to the mass-effect of the compact group.

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

TABLE I

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

A B C D 274 248 120 132 _experiments_ _experiments_ _experiments_ _experiments_ _with each_ _with each_ _with each_ _with each_ _subject_ _subject_ _subject_ _subject_

_NS_ _AV%_ _NS_ _AV%_ _NS_ _AV%_ _NS_ _AV%_

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

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

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

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

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

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

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

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

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

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

TABLE II

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

A B C D 132 132 132 88 _Experiments_ _experiments_ _experiments_ _experiments_ _with each_ _with each_ _with each_ _with each_ _subject_ _subject_ _subject_ _subject_

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

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

3. _The Influence of Complexity in Group-Composition._

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

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

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

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

TABLE III

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

A B 132 132 _experiments_ _experiments_ _with each_ _with each_ _subject_ _subject_

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

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

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

4. _The Influence of Differences in the Kind of Objects._

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

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

TABLE IV

A1 A2 132 _experiments_ 132 _experiments_ _with each subject_ _with each subject_

_Gray_ _Red_ _No tendency_ _Gray_ _Red_ _No tendency_ Number of subjects 3 1 3 1

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

B C 132 _experiments_ 132 _experiments_ _with each subject_ _with each subject_

_Large_ _Small_ _No tendency_ _Circles_ _Squares_ _No tendency_ Number of subjects 8 3 5 8 4 4

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

D1 D2 88 _experiments_ 132 _experiments each_ _with two subjects_

_44 experiments_ _with two subjects_

_exposure_ = 1/25 _sec._ _exposure_ = 1/4 _sec._

_Simple_ _Complex_ _No tendency_ _Simple_ _Complex_ _No tendency_ Number of subjects 3 1 2

Av.% of difference in favor of 30.7 5.6 21.2

E 88 _experiments_ _with each subject_

_exposure_ = 1/25 _sec._

_Bright_ _Dark_ _No tendency_ Number of subjects 3

Av.% of difference in favor of 47.4

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

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

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

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

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

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

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

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

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

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

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

5. _The Influence of Complexity of Environment._

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

TABLE V

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

Exposure = 1/25 sec. _Simple_ _Complex_ _No_ _environment_ _environment_ _tendency_

Number of subjects 2 2

Av. % of difference in favor of 15.9 8.5

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

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

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

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

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

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

1. _The Influence of Active Pressure._

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

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

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

TABLE VI

A B 52 _experiments with_ 260 _experiments with_ _each subject_ _one and_ 208 _with the_ _other subject_

_No_ _No_ _No_ _Touch_ _touch_ _tendency_ _Uneven_ _Even_ _tendency_ Subjects 2 1 1

Av. % of difference in favor of 7.6 10 1

SPACE-ERROR

_No_ _No_ _Right_ _Left_ _tendency_ _Right_ _Left_ _tendency_

Subjects 1 1 1 1

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

C 145 _experiments with_ _one and_ 260 _with the_ _other subject_

_No Weight_ _No weight_ _No tendency_ Subjects 2 Av. % of difference in favor of 2.4

SPACE-ERROR

_Right_ _Left_ _No tendency_ 1 1 Av. % of difference in favor of 32 4.4

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

2. _The Influence of Unevenness in Active Pressure-Feeling._

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

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

3. _The Influence of Active Weight._

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

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

4. _The Influence of Muscular Strain in Observation._

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

(1) Equal strain (minimum). (_a_) Right--left. (_b_) Up--down. (2) Equal strain (maximum) eyes turned. (3) Strain _vs._ ease. (_a_) Head and eyes turned. (_b_) Eyes turned.

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

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

TABLE VII

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

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

C - 52 experiments Equal strain (maximum) Eyes Turned

D - 104 experiments with each subject Head and eyes turned

E - 52 experiments

A B C D E

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

Subjects Baldwin Hutchison 2 Bald. 2 Bald.

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

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

A B C D E

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

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

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

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

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

1. _The Influence of Touch._

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

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

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

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

TABLE VIII

A 88 _experiments with each of two subjects._ 132 _experiments with one subject._

B 198 _experiments with each of two subjects._ 110 _experiments with one subject._

C 44 _experiments with each subject._

D 88 _experiments with one subject and_ 44 _with the other_ _Exposure_ = 1/4 _sec._

A B _No _No _Touch_ _No touch_ tendency_ _Touch_ No touch_ tendency_

Subjects 3 3

Av.% of difference in favor of 3.2 5.7

C D _No _No _Touch_ _No touch_ tendency_ _Touch_ _No touch_ tendency_ Subjects 2 2

Av.% of difference in favor of 26.1 13.7

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

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

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

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

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

2. _The Influence of Hearing._

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

The sound for A was that of a small organ-pipe (Ut 4) blown by mouth. As in A of the preceding table the observers did not know in a given experiment with which group the sound would be given, but, as before, it was given the same number of times with the first as with the last. For B the multiplied sound was produced by an electric bell with a wooden gong. This was adopted in preference to metal because of the prompt ceasing of the sound after the stroke,--a very necessary condition when this sound accompanied the first group, that it might be clearly connected with its own group. A metal gong was used for the single sound, that the two might not be too unequal in loudness. Its vibrations were deadened by a rubber band, and each bell was controlled by a floor-button. For C and D a higher sound, from the same pipe unstopped, was used in preference to the former, for the reason that in certain experiments performed just previously the lower sound had been used and was presumably very familiar. So in order that the sound might be brought, if possible, afresh to the attention, the change was made.

TABLE IX

A B

132 _experiments_ 44 _experiments_ _each with_ 3 _each with_ 2 _subjects_. 180 _subjects_. 88 _with_ 1 _subject_ _with_ 1 _subject_

_Exposure_ = 1/25 _sec._ _Exposure_ = 1/25 _sec._

_Sound_\_No _No _Many _One _No Sound_ tendency- Sounds_ Sound_ tendency_ Subjects 4 1 2

Av.% of difference in favor of 5.4 18.2 2.2

C D

44 _experiments each_ 88 _experiments each_

_Exposure_ = 1/25 _sec._ _Exposure_ = 1/4 _sec._

Sound_ _No Sound_ _No_ _Sound_ _No Sound_ _No_ _tendency_ tendency_ Subjects 1 1 2

20.4 4.6 2.2

The results of these experiments may be summarized as follows: (1) The figures give evidence of but two cases out of eleven where sound was influential. (2) Duplication of groups is not effective in developing evidence of the influence of sound. (3) Increased length of exposure works, as in former cases, to lessen the influence of the modifying factor. (4) The introspections are to the effect that the sound seems to be entirely without influence upon the judgment, beyond the distraction it brings in the earlier stages of work. Sometimes it dropped wholly out of consciousness. Sometimes the distraction seemed to last longer. One observer reported, when D was taken, that he felt as if the sound sometimes increased and sometimes decreased the apparent numerousness. In some other experiments not directly upon this point, but later to be reported, a sound was used; and one observer reported that it seemed to become functionally connected with certain gaps in the groups, as though the puff had blown a hole in the group. Here its effect was of course to emphasize negative factors. It appears thus that the sound might function in opposite directions at different times, somewhat in accord with the particular character of the visual presentation. We should expect, then, to have percentages that look insignificant. (5) We shall not have failed to notice the difference between touch and auditory stimuli in the feeling of influence upon the number-judgment. If we seek a cause for the superior influence of touch, we may perhaps find it in the fact that practical experience has trained us to disregard in any case of judgment such simultaneous presentations as were employed for auditory stimuli; while a definite tap upon the brow is a rather unusual experience likely to attract notice to itself in spite of attempts at abstraction. As one observer said, who took part in both kinds of experiments, the touch seemed more "intimate."

3. _The Influence of Kinæsthetic Impression._

The method consisted in the employment of active effort upon a fist dynamometer or a wooden handle during the appearance of one of the groups. The handle was preferable because noiseless. The effort was made with the left hand because the right was used in recording. The amount of it was left to the observer's regulation, with the one instruction that its presence be made decidedly evident but without too great fatigue. The cards of Section IV 1 and 2 were used in the One-Group Apparatus. Similarly again the experiments were repeated with the duplicate-group cards. I present no table here because the figures show practically no influence of the effort. On one subject 176 experiments were made; on a second 132; on a third 88.

It is interesting to note here certain results obtained from one observer when he was in what he described as an active attitude toward the groups, in which he seemed to rouse himself to an unusual pitch of concentration upon the visual situation. This was evidently a condition of increased effort to abstract. Without abstraction he gave 26 to 6 in favor of the effort while with abstraction this tendency had fallen off to 30 to 17. The strength of the tendency is thus strongly indicated. Another observer felt a kind of motor difference between the groups; he expected the effort-group to look larger and felt additionally excited, a scattered activity, while he was passive toward the other group. Perhaps this account puts a little meaning into his small per cent. That his power of abstraction was effective here is hinted by his remark that he felt a difference in the groups even when he judged them equal. The third observer found no subjective evidence that effort modified his judgment.

V. THE "ERRORS" OF EXPERIMENTATION

Throughout the foregoing experiments has been involved the possibility of some one of the three "errors" of experimentation, those of time, space, and distribution, and sometimes all three. Their effect on the results, if it existed, was, to be sure, eliminated in the well-known way, but their existence, if actual, would raise an interesting problem. It was possible, in the case of every group of experiments, to rearrange the tables in such a way as to bring out the evidence for any tendency to overestimate, for instance, the first group as against the second, the right as against the left, or one kind of irregular distribution as against another.

The distribution-error must have a word of explanation. It refers to a tendency to give more wrong judgments in favor of one kind of irregular distribution than of the other kind with which, in a given card, it is mated. In the construction of a set of cards several forms of irregular internal arrangement were used, in order that the judgment might not be one merely of form, and of course on any given card the forms were not the same. Elimination of the effect of these form-differences from the results involved the appearance of any given one as many times in connection with one of the two contrasting factors studied in a given experiment as with the other. Thus two sets of forms were carried through an experimental series--a source of error indeed, but avoidable only by such means as were used to escape the effects of the space-error. Analysis would show which, if either, of the two sets received more judgments in its favor, resulting in further evidence as to the extent to which the judgment of relative number is a function of distribution, and as to the fineness of discrimination for such differences.

Now the tables, when thus rearranged, show that these errors exist to a surprisingly large extent. In many cases their causes, whatever they are, seem to be the controlling factors in the judgment of relative number.

Barring the experiments of Section III, in which the space-error has largely been accounted for, I now propose to gather in one survey all the results of those analyses that have given us the information of the existence of these errors, and all the material of later tables that bears on this point, and to test them by further experimentation. I will begin with the space-error.

TABLE X

_Av. % of _Av. % of _Av. % of difference in difference in difference in favor of_ favor of_ favor of_

_Cases_ _Right_ _Cases_ _Left_ _Cases_ _No tendency_

Angier 1 25 6 17.9 9 5.7 Davison 5 26.4 1 10.8 6 6.2 Dunlap 7 18.3 4 4.4 Holt 2 13.6 7 17.6 4 3.2 Hylan 8 23.6 7 6.7 Meakin 2 19.2 1 29.6 8 5.5 Meriam 2 16.5 2 12.9 7 6.8 Moore 2 11 3 16.6 7 3.1 Peterson 1 13.6 1 12.2 9 4.3 Rogers 4 21.9 2 15.9 6 4.5 Rouse 3 15.5 8 5.1 Shaw 3 20.9 5 18 7 6.1 Windate 1 22.8 4 19.5 7 4.5 Yerkes 6 26.6 8 5.2 Henry 1 10 2 16.6 3 8.1 Woods 3 19.3 3 4.8

1. _The Space-Error._

Table X presents to us a summary of the values of the space-error tendency. (1) Taken as a whole they fall into all the three classes that are possible; (_a_) favoring right; (_b_) favoring left; (_c_) no marked tendency. (2) There is no observer that does not at some time show a fairly marked tendency. (3) All the observers fall into (_c_) and all but five into both (_a_) and (_b_). (4) More favor the left than the right,--50 to 35. (5) This survey makes it clear that the observers agree neither with themselves nor with each other in the direction of influence exerted by the causes underlying the space-error.

_a. Special Experiments to establish the Facts._ It might be suspected that irregularities would be more apparent where other factors such as we have been studying enter to complicate the situation from the point of view of pure relative position of the two groups. Table XI presents the answer to this query. The cards used contained groups of gray circles (Gray Darker, Prang) arranged in equal areas of the usual size and shape. The distribution-error was eliminated, though not by duplication, and the small-difference cards were retained. The Two-Group Apparatus was used, with an exposure of 6/5 sec.

TABLE XI

88 _experiments with each_

_Right_ _Left_ _No tendency_

Subjects 4 7 3

Av. % of difference in favor of 25.6 23.1 3.4

The results give us again our inevitable three classes, and in many cases a difference-value surprisingly large when we reflect on the simplicity of the conditions. That the omission of complicating features was of importance is shown by the fact that more of the observers (11 out of 14) show a marked error than in any other case. Clearly enough the various factors introduced tend to eliminate the space-error, but when in any case it does enter, it is even then capable of rising to as high a degree on the whole as in the uncomplicated series, as is shown by the fact that in but four cases does the new value surpass the best of the old, and in three of these by a trifling amount.

It is interesting to note that the three cases of minimum space-error show a well-defined tendency to be determined by distribution.

_b. Possible Bases of this Error._ The outcome of these special experiments is that the factors found in the groups are at least not directly responsible for the situation that we are considering. The divergence among the observers shows this. In hunting after the cause for this apparent influence of side, we look first for changes in the peripheral, and then in the central, processes that precede the judgment. The material used for the experiments of Table XI seems approximately to have equalized all the objective factors in the two groups. How could there be anything further in the peripheral process whereby group could be differentiated from group? The most evident thing is that the visual stimulus is received in a different way from the two groups. There is a definite peripheral mechanism whose factors seem essentially to be two, however variously they may be combined: (_a_) The relative amount of time given to each group; (_b_) the order in which the groups are viewed.

The observers were instructed and continually reminded to equalize the amount of attention devoted to the group; but as this is not wholly a voluntary matter, the possibility of failure to conform has to be reckoned with. Experiment must therefore be employed to test the influence of these factors before one can fall back upon a central process as the cause for this tendency to favor a side.

_c. Its Relation to Differences between the Groups in Length of Look._ The material was the same used for the experiments of Table XI. The method was the same with the following necessary exceptions: The longer exposure was double the shorter (4/5 sec. to 2/5 sec.), and 2/5 sec. elapsed between the two. Further, the experiments were so arranged as to equalize the influence of the order of exposure with respect to both side and relative length. The means for effecting successive exposure took the earlier form described in the introduction to Section II.

TABLE XII

_88 experiments with each_

_Longer_ _Shorter_ _No tendency_

Subjects 6 7

Av. % of difference in favor of 18 6.5

These facts are yielded by Table XII: (1) There are but two classes of observers, as no tendency exists to favor the group of longer exposure. (2) The time-error shows a considerably more marked tendency than the length of look, which is indeed somewhat surpassed by the space-error. (3) The persistence of the space-error, even among those that reveal a tendency in length of exposure, shows that the factor of relative difference in length of look cannot account for it. The persistence of it, too, when the order of exposure is controlled, even though the conditions are not wholly adapted to the study of this latter factor, suggest at least that the space-error is independent of even that order; but into this we shall make special enquiry. (4) The judgment of number is independent of the amount of eye-movement devoted to the fixation of the objects in a group. This conclusion, so far as the actual movement is concerned, is established by the fact that so many observers favor the shorter look; and by all the experiments with the One-Group Apparatus where an exposure of 1/25 sec. was used, since that time was too short to admit of movement. That ideated movement is likewise insignificant appears from the fact of marked error arising in the material where the groups were duplicates. Here no motives to different movements could lie in the material.

_d. Its Relation to the Order in which the Groups are viewed._ Table XIII gives us the results of the enquiry. The experimental conditions were not changed except as to the length of exposure. Each group was given 3/5 sec.; and half the experiments were performed in the order right-left and half in the reverse order.

TABLE XIII

_88 experiments with each_

_First_ _Last_ _No tendency_

Subjects 3 9 2

Av. % of difference in favor of 17.5 28.3 1.7

The results may be thus summarized: (1) The order of exposure is notably influential upon the judgment of relative number, giving the usual three classes, with the tendency to overestimate the last group well in the lead. (2) The persistence of the space-error under these relatively simple conditions shows conclusively that it is not a function of the order of exposure. The two are independent variables.

2. _The Time-Error._

In pursuit of our enquiry we must survey the facts as they are given in the various experiments already reported and later to be reported. These facts are gathered into Table XIV, which furnishes the following items of significance: (1) All the observers, with the exception of Rouse, show at some time a definite tendency. One case only is given for him in this table, but other experiments not included in the tables from which the present is drawn confirm this fact by the ratio 29 to 30. (2) There is a rather striking consistency in the several observers. (3) The predominance of the last group is marked.

TABLE XIV

_Av. % of_ _Av. % of_ _Av. % of_ _difference_ _difference_ _difference_ _in favor of_ _in favor of_ _in favor of_

_Cases_ _First_ _Cases_ _Last_ _Cases_ _No tendency_

Angier 7 19.1 4 4.9 Baldwin 4 20.5 1 3.4 Bell 1 18.2 4 6.3 Davison 2 31.2 Dunlap 1 11.4 1 2.2 Holt 10 19 2 6 Hylan 2 16 5 25.4 5 4.9 Johnston 2 25.2 4 35.5 4 4.2 Meakin 2 39.7 Meriam 1 29.6 1 2.2 Miller 3 17.1 4 5.5 Moore 1 11.4 1 2.2 Olmsted 1 15.2 Peterson 1 17 1 9 Rogers 1 10.2 1 5.6 Rouse 1 1.2 Shaw 6 16.7 5 7 Windate 1 11.4 1 1.2 Yerkes 2 42.7

_a. Relation of the Error to the Absolute Length of the Total Exposure._ Table XV is set to answer this question. It is unsatisfactory in that but two observers took part in both XIII and XV. The material used for judgment consisted of the same cards used in the earlier experiment, but presented now in the One-Group Apparatus. The time of exposure was changed from 3/5 sec. to 1/25 sec. for each group. As the space-error was eliminated, the tendency to a time-error, if present at all, would presumably have freer play.

But the difference-values of the new table are for the most part very small. We have thus the further fact about the time-error that, under the conditions studied, it appears to be independent of the absolute length of exposure, when the groups are equal in this respect. To this we may add another fact drawn from Table XIV, that with the One-Group Apparatus the time-error is greater on the whole where the groups are differentiated by other factors. Thirdly, the values for Table XIII show that with all complicating factors withdrawn, except the differences in position, the error is at a maximum. This may be significant of the effect of space-differences upon that error, or, more probably, be due to the general difference between work by daylight and work in a dark room by artificial light. We shall be better able to consider this later.

TABLE XV

88 experiments with each of two subjects. 176 experiments with one subject. 154 experiments with one subject. 66 experiments with one subject.

Exposure = 1/25 sec.

_First_ _Last_ _No tendency_

Subjects 1 4 Av. % of difference in favor of 15.2 6.8

3. _The Distribution-Error._

The last of our three "errors" of experimentation is now before us. We may recall once more the meaning the term has had for us in these studies. It points to a tendency discovered by the use of those cards where all objective factors were in the course of a series equalized,--a tendency to mass one's judgments in favor of a particular arrangement of the circles; though each group had been constructed with a view to filling the given area as homogeneously as an irregular arrangement would allow.

As in the two "errors" preceding, so here we must get possession of the facts that gave rise to the present enquiry. Table XVI presents them to us, gathered out of all the tables wherein such a tendency has been technically reckoned with. But first a few words of explanation are needed to make the new table intelligible. Two sets of results are found in its two parts. In each set the particular group-arrangements employed and the frequency of their appearance are exactly the same. The two sets differ, as their headings suggest, in that the material for the second set was formed out of the first by replacing the small-difference cards by those having equal groups. Such a change as this might affect the proportion of judgments given in favor of the two sets of arrangements in a particular series, and these new results are, therefore, no longer fully comparable with the earlier ones. In presenting the directions of tendency in the results, it is impossible here, as in all the similar cases throughout the tables, to name a factor as a standard in whose favor all the judgments in the plus column should be understood as given,--impossible for this reason that, because the very method by which the circles were distributed in the groups, the experimenter was unable to satisfy himself as to the significant differences in the arrangements. All the results, however, when analyzed on this basis, were recorded consistently, so that consistencies and agreements among the observers might be readily apparent. We can now understand in part what Table XVI has to say to us.

TABLE XVI

A _No_ _Cases_ _Class 1_ _Cases_ _Class 2_ _Cases_ _tendency_

Angier 4 19.1 2 6.3 Davison 3 23.1 Dunlap 2 13.7 1 2.2 Holt 3 15.5 1 25 2 4.5 Hylan 1 11.4 2 14 3 6.7 Johnston 5 30.4 Meakin 3 34.9 Meriam 1 16 2 6.8 Miller 5 32.1 Moore 1 39.8 2 5.7 Olmsted 1 27.2 Peterson 3 42.1 Rogers 1 11.4 2 5.7 Rouse 2 14.2 Shaw 6 29.1 Windate 3 30 Yerkes 3 17.8

B _No_ _Cases_ _Class 1_ _Cases_ _Class 2_ _Cases_ _tendency_

Angier 3 2.9 Davison Dunlap Holt 1 22 1 21.6 2 3.1 Hylan 2 50.8 1 11.4 1 8.4 Johnston Meakin Meriam Miller Moore Olmsted Peterson Rogers Rouse Shaw 2 26 1 0 Windate Yerkes

Here as elsewhere the per cents recorded indicate the average per cent of difference in favor of a given class.

Here are the facts, first of A: (1) The only lapses from consistency are confined to two observers; and in both these cases there is but a single break in a uniform trend. (2) With three exceptions all agree in the trend of their difference-values. Of these three--Holt, Hylan, and Moore--the last furnishes but one significant value, and so must be left out of the reckoning on this point. (3) Of the 64 cases, 50 rise above 10%, some far beyond, showing the importance for the judgment of relative number of this factor of distribution. (4) Of the 50 cases, 45 agree in tendency. (5) That with this surprising agreement we have still a few exceptions, adds another item to the growing array of evidence on behalf of the importance of some subjective factor for the number-judgment. As to the nature of this factor we are yet in the dark. (6) To these facts B of this same table adds the further information that the observers inconsistent in the old are not consistent in the new, while the consistent still maintain their record.

_a. Analysis of the Experimental Conditions of Distribution._ At once we are interested to enquire for the factors underlying these results. To put ourselves upon the right track we must first consider what factors are involved in any such arrangement of objects as we have used in the material for these studies, and then, more precisely, we may ask in what way such arrangements could differ significantly. Finally, by an experimental trial-and-error process, we may solve our problem.

The groups of objects in our material were arranged in an area marked out in each corner by a circle. Within this area the circles were set irregularly, with the result that the group, as a mass of objects distinguished from a homogeneous background, had a more or less irregular outline whose irregularity varied with different internal arrangements. Within its outlines this area presented a mixed pattern of bright and dark. While the total enclosure marked off by the corner circles was always the same and theoretically the relative amounts of brightness and darkness in equal groups was likewise the same, yet practically differences, more or less slight, might enter through the changing character of the rude outlines whose ideal completeness could scarcely be brought out of a black background by the uninitiated. The amount of this difference is sometimes surprising to one whose chief thought of the group has been as vignetted in process of construction. As the objects are pushed toward the edges the central spaces open out; as they are withdrawn toward the interior gaps appear in the margin.

It is not a very easy task to fill an area with objects in irregular arrangement in such a way that no sections of vacancy or filling stand out by contrast against the remainder of the same element. To succeed in this is to fill the area homogeneously. But the chances are good that some vacant patch will get slightly the better of its neighbors or some section of circles will gather a little more closely than the surrounding circles; or perhaps a gap in the outline will be unexpectedly intrusive. Now in a given area the circles of one part cannot become more thickly massed without a corresponding enlargement of the vacancies of the other parts, and of course the converse is as true; but this theoretical situation may be quite out of ken at the moment when the group is seen. Either member of this pair of complements may stand out vividly in the field and its fellow quite escape perception. The very nicety with which in practical affairs we have to make a reliable comparison of this sort shows what suspicion of accuracy the off-hand judgment has bred. And further, the widening of a gap or thickening of the filling in one small part of a group may give a complementary loss to the rest of the group small enough to be unperceived when distributed throughout the larger section.

Two factors must therefore be considered as possibly significant in moving the judgment,--vacancies and filling; and with the former must be reckoned indrawing of the outline. Psychologically, increase in the prominence of either of these factors would be all one with their objective increase. With respect to the direction of their influence upon the judgment of number the increase of vacancies must signify the waning, and the increase of filling the waxing, of the objective number in the group.

It is in advance altogether probable that the results gathered into Table XVI were brought about by these two factors, at least in large part. And we have also in these factors the possibility of two types; for as we saw above, increased vacancies in one part involves increase of filling in another, and conversely. So the interesting question turns upon the altogether disproportional representation of types. Which is the type of the majority?

_b. Experimental Test of Hypotheses._ The question was put to the test of experiment. This was done by using groups in which now vacancies and now filling were objectively emphasized in contrast with the usual homogeneous group. First the vacancies. A set of cards was prepared after the method previously used to eliminate the distribution-error without duplication of groups on any one card. (See Section II.) In the present case, however, the two sets of arrangements were definitely differentiated as already indicated. One set had a homogeneously filled area, the other a prominent vacancy within or gap in the edge. The size of these variations was kept pretty close to the limit of noticeableness, that the increase in compactness of the other portions might be as slight as possible. It was experimentally necessary to free the material as far as might be from ambiguity, and practically important to avoid rousing the suspicions of the observers and the resulting reflections. It seemed very likely that the strength of the tendency shown by the distribution-error was due to its appearance in situations where the observers knew that other factors were being tested.

The general method already described was used in preparing the groups that gave objective prominence to compacted parts of the filling. To fulfil the conditions outlined above was here even more difficult than in the first set; and the cause will appear in the sequel. The small-difference cards were omitted and the One-Group Apparatus used.

A further attempt was made to head off reflection by a subterfuge. It had been found that, among the factors whose influence on the judgment had been studied, hearing had been as little effective as any. So the small stopped pipe used for those experiments was again brought into service and the error resulting eliminated in the usual way. Incidentally our new tables will thus give us further information about the effect of this factor, though of course under conditions that are theoretically highly unfavorable, since we are forcing upon the attention of the observers other factors that experience has shown them only too ready to seize upon. So if a tendency traceable to the factor of hearing should appear, we ought perhaps to give it somewhat more than its face value.

TABLE XVII

A.

_Exposure = 1/25 sec._

_Homogeneous_ _Vacant_ _No tendency_

Angier [1]50 Baldwin [2]53.4 Bell [1]52.2 Holt [2]44.4 Hylan [2]51.2 Johnston [1]56.8 Miller [2]4.2 Shaw [1]29.6

B.

_Exposure = 1/4 sec._

_Homogeneous_ _Vacant_ _No tendency_

Angier [2]51.2 Baldwin [2]55.6 Bell Holt [1]13.6 Hylan [1]52.2 Johnston [2]62.6 Miller [1]25 Shaw [2]14.8

C.

_88 experiments each_ _Exposure = 1/25 sec._

_Homogeneous_ _Compact_ _No tendency_

Angier 39.6 Baldwin 35.2 Bell 3.4 Holt 27.2 Hylan 39.6 Johnston 44.4 Miller 16 Shaw 2.2

[1] 44 Experiments. [2] 88 Experiments.

The per cents recorded indicate the average per cent of difference in favor of a given factor.

Now we are ready to inspect the results. Table XVII, A is the outcome of the attempt to emphasize vacancies. Its experiments with 1/25 sec. exposure were repeated with one of 1/4 sec. as Table XVII, B, shows. In Table XVII, C, the emphasis of compactness is concerned.

For convenience we may again resort to a summary outline in extracting the meaning from these tables. First Table XVII, A. (1) All the observers but one agree in favoring the homogeneous, most of them with very high difference-values. (2) Miller alone gives no tendency, and his notes show a conflict between the increased vacancy and the increased compactness. In other words, his discrimination was too keen for the material. Under the circumstances he constitutes no exception to the conclusion that the vacancy objectively emphasized was the cause for an underestimation of its group.

From Table XVII, B, we learn the following: (1) All the observers save one favor the homogeneous group, in most cases by large values. (2) The difference in the length of exposure seems to have no significance for this tendency, since, while Holt and Shaw decline, Miller rises in the scale.

Table XVII, C, gives us these facts: (1) The difference-values have noticeably fallen off. (2) We have again the customary three classes, but with homogeneous leading as in the earlier tables. (3) By his present favoring of the compact, Miller has now appeared in all three classes, while Holt has developed the preference for the compact that was budding in XVII, B. (4) The presence of four well-marked preferences for the homogeneous shows that the vacancies in the compact group were more significant for the number-judgment than was the increased compactness of the filling, and that in spite of the experimental effort to the contrary. (5) The decrease of this tendency and the growth of the opposing, indicates that the judgment is determined in either case by the more vivid factor.

The conclusions to be drawn from these facts lie close at hand. (_a_) The results in Table XVI, with their disproportionate division into classes, were evidently due to the tendency of three observers to note the filling and of the rest to be concerned with the vacancies. (_b_) The judgment of relative number under these conditions is primarily a judgment of vacancies. (_c_) The subjective factor of vividness determines the direction of error, and may attach to either vacancies or filling, though it usually attaches to the former.

It may not be out of place here to speculate a bit as to the probable cause for so close a dependence of the number-judgment upon what has no number, so to say; upon an object that has no standing in the official conclusion. The situation seems to be fundamentally based upon the conditions that determine contrast. In a homogeneous field no part stands out. Introduce a small object quite different in brightness or complementary in color and the attention is drawn instantly to it, but internal differences in its content are quite lost in the common quality by which it differs from the ground. A case somewhat analogous is furnished by our material, particularly in the One- and Two-Group Apparatus. The small group is so unified by its contrast with the field that internal differences must be made out with relative effort. Now internal differences are necessary to the numerical character demanded of it, and they can be brought out in no way save by attending to the vacancies and so isolating parts in the threatening unity, each in a kind of space-matrix. The most careful observer could not do better on his way to truth; and that is why the error was so much larger when the factor of space-differences was studied.

That group is normally the more numerous in which the vacancies are less completely developed under observation. We say "normally" here by virtue of the speculation just completed as to the best method of attaining a judgment objectively true. For a man thus proceeding, our proposition is a sound statement of fact, to which the following results of our experiments bear witness. (_a_) The experiments recorded in Table XII on Relative Difference in Length of Look shows no exception of a value equal to 10% to the general statement that all tendencies, when any existed, were in the direction of favoring the shorter group. The shorter the time of exposure the less completely would the vacancies develop. (_b_) Table IV, E, shows that without exception the darker group tends to be judged the more numerous. (_c_) Table XXI shows for each subject that in a shorter exposure the absolute number seems considerably greater than in a longer exposure.

No comment seems necessary to concentrate the force of such evidence. If we carry our proposition to the detailed results of our separate studies in factors of distribution, we shall find that it helps us to understand those few exceptions to the general trend of observers as they appear in Tables II and XVII. The exceptions there favored the groups in which compactness of parts went along with certain large vacancies. Possibly enough they refused to fall in with the objective analysis, and, disregarding the prominent vacancies, devoted themselves to a development of the vacancies within the compacted parts.

_c. The Factor of Hearing._ The time-error analyses of the experiments of Table XVII have already contributed their facts to the special section dealing with that error. But one or two interesting facts have remained unnoticed in the sound-analysis. In the experiments of Table XVII, A, there is a single case of marked tendency to favor the sound group. With the lengthened exposure of B, this tendency, as usual, disappears; but returns in C to some extent and two other observers share it. A fourth markedly favors the group without sound. So the experiments of this last table present as marked external evidence as we have for the influence of hearing upon the judgment. These facts are presented in Table XVIII.

TABLE XVIII

A _44 experiments with_ _each of 4 subjects,_ _88 with each of 3._

_Exposure = 1/25 sec._

_No-_ _No_ _Sound_ _Sound_ _tendency_ Subjects 1 6

Av. % of difference in favor of 27.2 4.1

B _88 experiments with_ _each of 3 subjects,_ _44 with each of 3._

_Exposure = 1/4 sec._

_No-_ _No_ _Sound_ _Sound_ _tendency_ Subjects 6

Av. % of difference in favor of 5.9

C _88 experiments each_

_Exposure = 1/25 sec._

_No-_ _No_ _Sound_ _Sound_ _tendency_ Subjects 3 1 3

Av. % of difference in favor of 12.9 20.4 4.5

It is a further curious fact, well sustained by these same experiments, that where there is some confusion, each of the factors present has a better chance to determine the judgment. The values for both time-error and sound rise higher for the majority in C than in A or B.

VI. THE INFLUENCE OF FACTORS IN THE SAME SENSE-FIELD UPON THE JUDGMENT OF ABSOLUTE NUMBER

The nature of the enquiry that we have been pursuing through so many pages is such that it may be raised exactly as well in the case of absolute as in that of relative number. There appears to be no reason why in this new field the results should not be exactly comparable with those in the old, to be taken indeed as a kind of test for the interpretation to be put upon the old. Without a single exception, unless it were imposed by a technical difficulty, all the earlier factors could be studied with the new purpose. Our practical interest to go to such lengths would depend pretty largely upon the results of first attempts. If wholly confirmatory, these would probably suffice.

The experimental conditions were of the simplest. The 3-8 in. steel balls of Section III were again pressed into service as objects for the number-judgment. They were thrown loosely into a fixed black frame, 20 cm. square. To avoid suggestive noises, its undersurface was made of a thick piece of felt covered with black cloth; and the whole rested of course on a black-topped table. The exposures were 2 sec. long, timed by watch-ticks. Between experiments the observer held a cardboard screen between him and the objects. When conditions were ready for a new judgment, closing his eyes he lowered the screen, opening his eyes again at the word of command and shutting them at the close of the experiment.

Of course the observers felt that their judgments were for the most part extremely vague. With small numbers they had a greater feeling of confidence. Yet altogether it was surprising with what readiness an absolute number-judgment would spring up in the presence of any given collection whatever within the limits set by the experimental series. Sometimes the observers thought that they made rough calculations on the basis of the filling in a unit of area. So far as this held it would tend to cut off the more astonishing departures from correctness, and it would probably advantage the smaller groups more than the large. Still it was entirely too rough a method to prevent the influence of the factors introduced, as the results will show. There was no time for systematic counting, which, in any case, the observers knew to be forbidden.

The figures in which the observers reported their judgments of absolute number have a value that is chiefly qualitative. The marked inconsistencies and disagreements are our guarantee for this statement. With all the observers there was but the loosest association between group-appearance and number-name. The innumerable variations in internal space-relations were of course responsible. For one observer a particular name probably had a quantitative significance far in excess of its value for another observer in this respect. To one man 100 might have meant about the same as 60, for example, to his neighbor. On the whole they were parsimonious; but Baldwin decidedly not.

A more or less constant influence was exerted on any given judgment by the comparison of the presented group with the traces of the preceding still in mind. The observers felt, however, that the judgment was largely independent of such comparison, and its fluctuations give some credence to this feeling.

The numbers chosen ranged by fives, from 25 to 100. In four cases a number was immediately repeated that rough suggestions as to the definiteness of the judgment and its dependence upon the actual number might be gained. These were indeed but rough suggestions, since, with certain exceptions to be noticed later, the arrangement was disturbed between times; but they made possible a closer watch upon the flickering of the judgment than could be kept by a mere repetition of the series. In the latter case it might be unstable and yet relatively firm in the other. A standard series is here recorded. Its order was determined by drawing the numbers out of a heap, but the repetitions were inserted arbitrarily.

1. 95 2. 25 3. 35 4. 65 5. No change 6. 30 7. 90 8. 85 9. 45 10. 100 11. 50 12. No change 13. 60 14. 40 15. No change 16. 70 17. 80 18. 55 19. 75 20. No change

1. _Absolute Number under Standard Conditions._

An indispensable preliminary for the present study is the establishment of a standard. Unless we know something in advance about the characteristics of the judgment of absolute number in relatively simple conditions, we shall be unable to tell what influence, if any, to attribute to the modifying factor in later experiments. Having then decided as to the general conditions under which we will study the problem we must make these the standard conditions of our work; and having discovered the nature of the judgments given under them, measure up to these results in all that is to follow. These standard conditions have already been set forth in the introduction to this section. The results are recorded in Tables XIX and XX.

TABLE XIX

KEY: St = Standard Sc = Scattered Co = Compact

_Subject_ = _Baldwin_ _Subject_ = _Miller_

_Trials with_ _each number_ 6 3 3 4 2 3

_Original_ _Numbers_ _St_ _Sc_ _Co_ _St_ _Sc_ _Co_

25 1 0 -6 -10 -6 -4 30 3 5 -5 -12 -7 -6 35 10 7 -3 -14 -4 -7 40 10 13 -8 -15 -8 -11 40 10 8 -8 -14 -10 -12 45 10 18 -3 -21 -13 -10 50 17 23 2 -19 -15 -17 50 15 22 2 -17 -15 -14 55 27 40 0 -18 -3 -12 60 19 33 5 -20 -23 -17 65 27 53 2 -18 -3 -7 65 24 57 5 -13 -13 2 70 38 77 0 -19 8 -8 75 31 73 0 -24 10 -20 75 28 78 -5 -24 8 -8 80 36 83 -5 -14 5 -18 85 54 85 5 -19 -8 0 90 54 90 5 -13 8 -3 95 48 73 5 -30 20 -15 100 61 87 7 -13 10 -7

The figures recorded are the average of the algebraic sums of other figures that represent the difference between the actual and the estimated number. Fractions are replaced by an added unit, if the value is 1/2 or over.

Baldwin never underestimated the scattered group, and only once the standard; but 31 times the compact. Miller only once overestimated the standard group, and but 6 times the compact; but 13 times the scattered.

Turning to these tables we notice at once, as characteristic of all the observers, the following facts: (1) Wide variation from objective correctness. (2) A far wider discrepancy with the larger numbers than with the smaller. Miller does not wholly agree here. His judgments by series show inconstancy, tending at first to follow the rule, but in the last two series to a maximum error near the middle. Certain remarks of this observer suggest that possibly in the latter case reflection as to the convenience of certain actual numbers for manipulation may have had influence. The three earlier series of Hutchison conform to the rule. The remainder, on the contrary, show no definite progression in tendency. It should be noted here that both Miller and Hutchison were more inclined than the other two observers to rough calculation. The effect of its adoption or of increased practice in it is shown by the disappearance of the characteristics of the earlier series. We have thus in these two cases a doubleness of standard that we must not fail to consider in our later comparisons. (3) There is a pronounced instability of judgment, as shown by the fluctuations for the same number in different series, and especially in successive judgments, of the same in any given series. (4) There is a general tendency to judge in multiples of five. That there should be any splitting of fives, particularly in the large numbers, might be regarded as mere caprice. Not so did it seem to the observers. They were conscious of an apparent absurdity in it where judgments were necessarily so vague; but they insisted that this stood for a kind of qualitative shading in the perception which threw out the choice of the round numbers just above and below. (5) The number is on the whole underestimated, three observers agreeing in this respect; but the fourth shows a very large and consistent tendency in the opposite direction.

In spite of the manifold special inconstancies and disagreements, these general tendencies are decidedly well-featured in the results. We may say that we have found a kind of standard illusion that will serve us for a guide through our later studies.

2. _The Influence of Distribution._

TABLE XX

_Subject_ = _Hutchison_ _Subject_ = _Olmsted_ _Trials_ _with_ _each_ _number_ 3 2 4 _First_ _Second_ _Original_ _Standard_ _Standard_ _Mixed_ _Small_ _numbers_ _Series_ _Series_ _Sizes_ _Sizes_ 25 -5 -2 -3 -1 30 -4 0 -5 0 35 -6 -5 10 1 40 -11 -5 -5 -13 40 -12 -9 -13 -11 45 -7 -4 -15 -10 50 -14 -10 -20 -12 50 -13 -8 -15 -15 55 -10 -7 -20 -11 60 -19 -18 -25 -20 65 -15 -7 -20 -5 65 -15 -10 -10 -18 70 -14 -3 -15 -20 75 -21 -17 -28 -23 75 -25 -20 -20 -24 80 -24 -17 -30 -19 85 -17 -13 -35 -13 90 -13 -7 -25 -20 95 -25 -13 -40 -23 100 -22 -13 -35 -24

6 2 3 _Mixed _Small_ _Standard_ _Sizes_ _Sizes_ -8 -8 -12 -11 -14 -16 -8 -5 -14 -18 -17 -20 -13 -18 -22 -18 -20 -18 -19 -18 -23 -22 -15 -27 -24 -28 -23 -22 -23 -27 -28 -28 -33 -22 -28 -23 -27 -30 -28 -32 -23 -27 -33 -25 -32 -27 -23 -33 -27 -38 -38 -33 -40 -37 -39 -55 -40 -36 -15 -37

For the meaning of these figures see under Table XIX. Hutchison overestimated the standard group only 5 times, never the mixed-size group, and 9 times the small-size group. Olmsted never overestimates at any time.

The first of the modifying factors to be considered has to do with the arrangement of the objects. Hitherto they had been thrown loosely into the frame. Now in successive studies they were, first, well scattered over the surface and, second, brought together into several compact nuclei. The last arrangement was adopted in preference to that of a single mass as being less open to comparison with preceding judgments and to judgment on the basis of form and size of group.

The results are shown in Table XIX: (1) The effect of scattering the objects is very markedly to raise the apparent number. Baldwin's preceding overestimations soar still higher; while Miller's former tendency to underestimation is checked to such an extent that 13 overestimations appear. (2) The effect of compacting the objects is just as markedly in the opposite direction. Baldwin gives 31 underestimations, and Miller reverts in a measure to his former type. (3) When similar arrangements were up for study in relative number we found two classes of observers, one favoring the compact, the other the scattered. The present results of Baldwin and Miller put them into the latter class.

3. _The Influence of Complexity of Group-Content._

This new factor of complexity in the content of the group was realized experimentally by making up the collection out of steel balls of two sizes, 1/8 in. and 3/8 in. The former looked almost infinitesimal beside the latter. The same objective numbers were still maintained and divided between the two sizes except where in so doing a five must be broken. In such a case the extra five went to the larger balls.

The results are found in Table XX. Olmsted shows no definite influence of the new factor. Hutchison, however, shows a very evident decrease in his estimations, when comparison is made with his second standard series. With the earlier series the new results rather closely correspond. That the latter are not simply a vacillating reversion seems fairly clear from this observer's account of his method. The small balls, he says, did not distinctly come in visually. To his judgment of the large he added an amount based on a very insecure estimate of the small. The number of the latter seemed from time to time pretty constant.

This situation corresponds very fully to that in the investigation of the same factor by use of a group of mixed colors, where relative number was in question. (Section II.) The tendency there discovered was to neglect the other colors in favor of one which thus surpassed the others in vividness. There as here the mixed group seemed smaller.

4. _The Influence of Size of Objects._

A study of this factor was made possible by substituting for the usual objects steel balls of a smaller size, 1-4 in. The results are contained in Table XX. They are not so striking as those obtained in our study of distribution. Still the influence of this new factor is evident, in the reduction of the apparent number. Olmsted shows this more generally for the smaller numbers. We find it in Hutchison when we compare the new results with the second standard series. This tendency to underestimation increases in the two final series of the present set. At the beginning of these two he remarked that he thought he had been overestimating the group. This tendency of smaller size to reduce apparent number was found true for the majority of observers in our earlier study of relative number.

5. _The Influence of the Length of Exposure._

I found that in relative number the shorter the look the more marked was the influence of certain factors. Reports of the observers making this seem highly probable happened in this way: When working with the One-Group Apparatus in relative number the shutter of the camera would occasionally stick, leaving a group exposed beyond its usual time. The effect of this upon some but not all the observers was to cause a noticeable shrinking in numerousness. Of those questioned, the only one failing to notice this effect is included among the observers in this new study.

To test this possibility resort was had to the One-Group Apparatus as affording a more satisfactory means for getting different lengths of exposure of small absolute magnitude. Cards were prepared containing a single group of larger area (67 × 82 mm.) than had been used for relative number. The objects were the usual white circles. Each corner was marked as usual; and, by reason of the number involved, the outline of the area was more regular than had been true in the earlier work. The number of circles on each card varied by steps of two from 16 to 30, giving eight cards in all. The series was arranged irregularly as before, and two of the cards repeated immediately upon their first presentation, making ten experiments in one set. The order of the series follows:

1. 24 2. 22 3. 26 4. No change 5. 18 6. 28 7. 16 8. 20 9. 30 10. No change

Two time-magnitudes were used for comparison,--1-25 sec. and 1 sec. The latter was managed with bulb exposure. All the experiments with the shorter time were made before those with the longer had been begun. The results are given in Table XXI. So far as the material is comparable, we may include in our comparison the standard experiments of Tables XIX and XX with 2 sec. exposure.

TABLE XXI

KEY: A = 1/25 sec. B = 1 sec.

_Baldwin_ _Miller_ _Hutchison_ _Olmsted_ _Actual_ _Numbers_ A B A B A B A B _Number of_ _trials with_ _each number_ 5 6 5 5 5 4 4 4 16 6 9 -2 -3 11 -1 2 -5 18 8 10 -4 -1 12 -1 -3 -5 20 34 19 1 3 19 1 1 1 22 37 17 6 6 14 6 4 -2 24 49 26 12 5 14 10 5 0 26 70 33 15 8 12 9 5 4 26 79 37 21 9 14 4 9 4 28 93 42 29 11 18 7 8 7 30 106 52 38 12 18 5 19 10 30 103 50 45 11 20 4 19 4

For the meaning of these figures see note under Table XIX.

The outcome may be thus summarized: (1) The apparent number is inversely proportional to the length of exposure. The tables show a perfectly clear progression from 2 sec. to 1-25 sec. All those that formerly underestimated are brought into the opposite class. (2) The results of the earlier experiments are confirmed on the whole with respect to the occurrence of greater errors with the larger numbers. (3) Baldwin's overestimation reaches astonishing heights. (4) These new facts for absolute number are quite in accord with Table XII, where, under the conditions of interpretation laid down, the tendencies were wholly in favor of the shorter look.

The issue of these tentative experiments in absolute number confirms the teaching of our studies in the related field. Absolute number, like relative, has been found largely subject to a modifying influence of certain factors. In the new field, too, distribution has asserted its supremacy among these, and similar effects of shortening exposure have been observed. There has been variation among the observers and some shifting of tendency, both of which point as before to the coöperation of some subjective factor in our results. Indeed the whole situation, as opened by these preliminary studies, indicates a theoretical interpretation that for both fields is at bottom one. So to an attempt to reach such an interpretation the next section will be devoted.

VII. THEORETICAL DISCUSSION

1. _The Fact of Modification._

That such an influence upon the judgment of number should have been exercised by the factors considered seems in many cases to receive an adequate account on the principle of association. Our practical experience in the simultaneous variability of number and certain other characteristics of a group of objects has been such as to lead us into illusions when the two no longer vary together. In such a case, when we have no time to count, we are actually led to _see_ a group as smaller or larger in accordance with the variations perceived in the associated factor. This interpretation is supported by the fact that on the whole the space-factors were more markedly influential in creating illusions than were any others. For those cases, however, in which the modification was effected by a factor unconnected with number, as color, or the simultaneous stimulation of other senses by irrelevant objects, it appears that the mere occurrence of greater total stimulation during the appearance of one group is sufficient to create illusion, either through failure of the observer to discriminate between the relevant and the irrelevant, or because he is led through fear of disturbance to overemphasize the other group.

2. _The Direction of Modification._

The foregoing account of the general fact throws no light upon the _direction_ of the influence. Why should a given factor make a group seem more numerous and not less? Why should it affect one man in one way and his neighbor in another? Why should it vary with the same man at different times? Appearances no less contradictory than these are what we must face in carrying a theoretical account to completion. The following propositions with appended commentary are offered in satisfaction of these requirements.

_a._ Differences in vividness among the factors determine differences in number.

Our study of the factor of distribution in Table XVII, where it was possible in a measure to control the vividness, furnishes evidence for this proposition. Introspective reports in other cases confirm this view by showing that the direction of the attention, the popular way of stating our proposition, was the determining feature. This will receive further support in our discussion of the following proposition.

_b._ If the vivid factor or complex be positive, _i. e._, associated in experience with the numerous, or if it be neutral, its group will seem the more numerous. If negative, _i. e._, associated in experience with the few, its group will seem the less numerous.

The experiments upon the effect of distribution support this proposition, especially as set out in Table XVII. When the vacancies in a given group were made vivid, the other group seemed more numerous; when its filling surpassed in vividness, the judgment was given for it. We have other confirmation in the fact that lengthening the time of exposure reduced the absolute number. Take also this note of one observer on the material in Table II, C:

"I noticed that I had set the open spaces in the outlined group over against the lack of them in the homogeneous, without paying much attention to the nearness together of the spots in the lines of the outlined. Then for a time my attitude was quite vacillating. I found my attention drawn to the nearness together of the spots in part of the outlined group so strongly that if I did not turn it voluntarily to the fact that the other was filled without any large open spaces, I was led to call almost any outlined group the larger. Toward the end of the experiment I got back into my original attitude, in which the outlined group seemed to have its spots hardly more thickly arranged in any part than the homogeneous, and to have also the bare spots and so to be the fewer."

That the vividness of a neutral factor or complex increases the apparent number was suggested by comments of the observers. One observer reported of the material in Table IV: "The greater brightness of red gave it more importance. The natural thing seemed to be to give the red the judgment. The gray fought more for recognition." And again: "The red seems a vitalized space and the dots more omnipresent, also the red lasts longer in memory and is there more vivid, so that often in cases of doubt, where the decisive comparison was made in memory, the red may have been given the vote. Often there was an immediate unanalyzed feeling that if the groups had been both of the same color, the judgment would have been for the gray." In both cases his results showed this tendency. Another observer, whose results agree with the former, found that his eye was directed involuntarily toward the red.

This fact was put to a special test. In the material of Table II, B, a card, in which the pattern group had an appearance strikingly different from the normal, was introduced, the two groups being objectively equal. With three observers the effect was overestimation of this group, and with a fourth, the suppression to equality of a previous overestimation of the opposite group. This fact, together with the observers' comments, seems to justify the conclusion that the vividness of a neutral factor or complex was the determining condition of the judgment. That the observers did not all show positive results in this experiment may be set down to the difficulty in controlling the subjective conditions of vividness. Of course the space-relations within the new pattern were different from those in the old. The only justification for taking no account of these is the character of the introspections themselves.

It should be said of the red group that beside its vividness it had characters mentioned by other observers that might independently have made its number seem greater. It was called "dazzling," "blurred," and its area seemed increased. In this respect the effect of the color should be discussed as a special case of distribution or object-size.

The vividness tested in this special way seems due to contrast, in the one case with surroundings, in the other case with the expected. Such a judgment is very far removed from the normal bases, rather more so, it would seem, than even those where a group had sound or touch accompaniment; for in the latter case there could be no question about the "moreness"; the only doubt could be about its legitimacy. Of the precise extent to which this cause of vividness has operated throughout our studies, even where spatial differences have been concerned, we cannot be sure. The patterns of the materials in B and C of Table II seem to offer that possibility. That it should enter anywhere opens, indeed, the entire field.

_c._ The observers fall into the following classes on the basis of the character of the association:

(1) Relatively fixed association,

(_a_) involving correct adjustment to objects (vividness of relevant factors);

(_b_) involving incorrect adjustment to objects (vividness of irrelevant factors).

(2) Relatively unstable association.

It will be remembered that in the case of nearly every factor studied under Relative Number, we found three classes of observers,--those favoring one group, those favoring the other group, and a so-called "no-tendency" class. The bases of classification were, first, the relative constancy in the character of the error, and, secondly, its direction. In this third or "no-tendency" class were really lumped off two kinds of observers, not separated at the time because our special interest did not demand it. Along with those that gave large errors in both directions was a much smaller class that gave a relatively large proportion of correct judgments; but could never claim any one observer all the time. In the new classification of Proposition _c_ this mixed composition is recognized by dividing it between (1) (_a_) and (2). The prime condition of correct judgment is asserted to be one in principle with that of the illusion,--namely, vividness, but in this case vividness of relevant factors. Our original "tendency" classes both fall under (1) (_b_).

Proposition _c_ is merely an attempt to apply the principles of association and vividness to an organization of our results. The types in question have no hard-and-fast connection with any particular observer; they rather represent a kind of ideal fixation of opposite tendencies playing through all.

3. _The Time-Error._

So far the time-error has been left without interpretation. The chief facts to be considered were: (_a_) Divergence of error and general trend in favor of last. (_b_) Individual inconsistencies. (_c_) Occasional absence.

We are in a position now to invoke at once the principle of vividness to account for the existence of the error and the vividness of recency to account for the predominant tendency to favor the last of the two groups exposed. In this respect this error may be classed with the effect of red. That is to say, a factor or complex, directly through its vividness and not indirectly through its association with the numerous or the few, draws the judgment after it. Here the content of the group is the effective thing, not the character of the vacancies.

But the observers do not all agree in the direction of the time-error nor are they always consistent. Here we shall get help from a proposition offered in the discussion of the distribution-error in which it is asserted that the group seems the more numerous in which the vacancies are less developed under observation. We have already noted a decided tendency to depend in judging upon the vacancies. Let us suppose that the two groups presented in succession differ with respect to the success of the observer in developing these vacancies. If this be true, that difference may well depend upon the occurrence of maximal attention during the exposure of but one of the groups. The tendency of the majority to overestimate the second group suggests that the attention is likely to be at a maximum when the experiment begins. If, on the other hand, it ripen later, or if the observer seek to rescue the second group from relative unclearness, then we should have the first group overestimated. The time-error would disappear for those that could attend alike to both. Clearly enough this account is decidedly hypothetical.

4. _The Space-Error._

Our attempt to reduce this error to one of time in some form was proven a failure. The facts brought out indicate that at the bottom is some subjective factor thus far not isolated. This factor is not a preference going directly with right- or left-handedness because on the surface at least it runs in the observers independent of such asymmetry. A single bit of available introspection would seem, however, to point to some relation of that sort; for one observer, who favored the left, felt that a group on that side gained an importance that was somehow due to the greater absolute value of a weight in the left than in the right hand. Even if this be decisive for him it will still be inapplicable to errors in the opposite direction unless we assume that with variations in bodily energy the emphasis is cast now in one, now in the other, direction, after the analogy of those two types of man to be found in our social experience, for whom respectively mountains are molehills and molehills mountains. Such successive differences in type in a single individual would then find an intelligible account in the shifting tides of that bodily energy. It is to be noted that the observer just quoted once, but only once, made a decisive reversal of his error from left to right.

It may occur to some one that the use of two observers sitting side by side may have given them a preference for one position of the groups. In the first place care was taken that both groups should be as readily seen from one point of view as from the other. Secondly and chiefly, there is no regularity among the observers in this respect.

It is not unlikely that a chance aspect of a particular group develops an emphasis that gives the mechanism of subjective adjustment a particular bent that for a time is relatively independent of the objective situation. Still the fact that there are some cases of persistence in type is rather damaging to this assumption and speaks rather for the earlier one. That one, if true, seems indeed adequate to account for the situation. As an hypothesis it accords with analogous physiological facts; but its weakness lies in imposing the burden of a strong tendency upon asymmetrical differences that may be in comparison relatively slight. Finally, these studies furnish no proof that the bodily condition of an observer of a particular type corresponds to the demands of the hypothesis.

_Summary:_ 1. The estimation of relative number in the visual field is modified by group-area, internal distribution, order, and complexity in group-composition; by the size, form, color, brightness, and complexity of the individual members; and by the character of the environment. It is further modified by factors contributed by the objects through other senses, as in active pressure, special differences in pressure character, active weight, and that complex of muscular and spatial factors arising when a group is observed under the condition of eye-muscle strain. The judgment is also influenced by factors outside the group in the field of touch, but not in that of kinæsthetic impressions.

2. On the whole the most influential factors were those lying in the space-characters of the groups; while those of least moment were contributed by other objects in other fields of sensation. Hearing was very nearly ineffectual.

3. In very many cases the observers fell into three groups, one of no-tendency, and a second and third showing opposite tendencies with respect to the factor investigated.

4. With a majority of observers there is a tendency to underestimation in the judgment of absolute number, though with a single observer the tendency is directly the reverse. Scattering the objects increases, and compacting diminishes, the apparent number. The smaller the size of the objects the fewer, under conditions, do they appear; while heterogeneity in group-composition lessens the number for one observer and has no apparent effect upon the other.

5. The apparent absolute number of objects is inversely proportional to the length of exposure of a group; and in relative number the influence of a factor was on the whole greater for shorter exposures.

6. The marked tendency to a space-error was found to be independent of differences between the groups in the length of look, and of the order in which they were viewed.

7. The distribution-error is grounded in a fundamental tendency to base the judgment of relative number upon the character of the vacancies in a group; though a secondary tendency to depend upon the filling was shown to exist. The subjective factor of vividness, attaching now to one and now to the other of the foregoing factors, determines which shall be operative, though it usually is joined to the first. The ground for the primary tendency may very well be the necessities imposed upon discrimination by the material. The contrast effect between the large black background and the brighter objects tends to unify the latter, which, to be discriminated as a number, must be split up by an emphasis of the vacancies.

8. The time-error is possibly due to differences in power to dismember the groups exposed in succession in one experiment, while its variations in direction seem adequately accounted for by differences in the time at which attention becomes maximal during the progress of a single test.

9. The ground for these facts of modification is found in the strength of the association between these several factors and the elements that signify number.

10. The basis for the different tendencies found among the observers is the differing vividness among several factors. If the vivid factor is associated with the idea of numerousness, or is in this respect neutral, its group will seem more numerous. If it has been associated with the idea of fewness, its group will seem less numerous. The difference between the two classes of "tendency" and "no-tendency" lies in the fact that for the latter either only correct clues are vivid, or else there is so frequent an alternation in vividness of opposing incorrect clues that through any given series no tendency appears, while for the "tendency" class misleading clues are without shifting in the ascendant.

At the time when these experiments were completed, no work precisely upon this problem had been published. Since then, however, Dr. J. F. Messenger has issued a monograph entitled The Perception of Number (Psych. Rev., Mono. Supp., vol. 5, no. 5), of which certain parts fall within the scope of the present studies. He was concerned with the estimation of absolute number and was primarily interested to discover the nature of the number-judgment. The reader of both articles will find agreement between the results and interpretations here recorded and such part of Messenger's work as has been a common object of study,--viz., the factors of distribution and size.

FOOTNOTES:

[Footnote 123: 44 experiments.]

[Footnote 124: 88 experiments.]

TIME-ESTIMATION IN ITS RELATIONS TO SEX, AGE, AND PHYSIOLOGICAL RHYTHMS

BY ROBERT M. YERKES AND F. M. URBAN

The desirability of a statistical study of time-estimation was suggested to us by a note concerning "sex-differences in the sense of time" which was published in Science recently by Prof. Robert MacDougall.[125] By comparing the time-estimates of groups of men and women consisting of fifteen individuals each, MacDougall discovered that for intervals of from one quarter of a minute to a minute and a half, the women exhibited a far stronger tendency to overestimate than did the men, and were at the same time markedly less accurate. The nature and extent of the overestimation discovered by MacDougall are indicated by the results presented in the accompanying table from Science. The numerals, 1, 2, 3, and 4 refer to different fillings of the intervals (listening to reading, marking letters, etc.), the signs + and - to over- and under-estimation respectively.

Period, One Minute.

Sex 1 2 3 4 Men +29" + 1.3" +22" - 3.5" Women +66 +22.0 +80 +24.0

These apparent sex-differences in time-estimation demand further attention, first, because the number of individuals studied by MacDougall, as he recognized, is too small to establish the fact of the existence of such differences, and, second, because if the differences really do exist they should be studied in their relations to age and the fundamental physiological rhythms.[126]

It seemed probable that further investigation of this subject might reveal some important facts concerning the development of the ability to estimate time in the individual, the significance of various conditions for time-estimation, the psychology of sex, and the relations of rhythms to personal affinities, antipathies, and motor capacities.

In this report the results of a statistical study of the sex-differences in time-estimation are discussed, and in later papers we shall present the results of investigations of the relations of time-estimation to age and to individual and sex rhythms, and attempt to work out a convenient and serviceable rhythm-formula. The need of such a formula for expressing individual rhythms is obvious, as is also the need of comparative studies of individual and sex rhythms.

TIME ESTIMATION

Name Place Age Date

ORDER OF TESTS TIME IN SECONDS

_Time of_ _Male_ _Female_ _Intervals._ (_17 years_) (_17 years_) No. 1 No. 9

1. Idleness _108̋_ _70̋_ _120̋_ 2. Reading _36_ _30_ _118_ 3. Writing _72_ _36_ _60_ 4. Estimating _18_ _15_ _30_ 5. Reading _108_ _90_ _68_ 6. Idleness _36_ _35_ _60_ 7. Writing _18_ _10_ _10_ 8. Estimating _108_ _100_ _125_ 9. Reading _72_ _100_ _66_ 10. Idleness _72_ _75_ _58_ 11. Writing _36_ _25_ _22_ 12. Estimating _72_ _60_ _60_ 13. Reading _18_ _14_ _15_ 14. Writing _108_ _130_ _59_ 15. Estimating _36_ _30_ _41_ 16. Idleness _18_ _10_ _18_

How did you estimate the interval when you were asked to estimate it as accurately as you could?

n o f e y m i q r s a d r g d e s t k n w e r a x u p x z y o n d f n o d c a e h p m a l g s r w y t b c k p s o n q a r v q c o m p v r i c p k t o s n q z r l x m i h u v o q g P p f u t o i c n g s c a r n o t c d a a o b i a r s a d e r w o a i e r g l c r t h f s o r a e n s i o c r b x g r z b h o w l t s

Number of letters counted 85 88 Pulse-rate 72 81

The experimental data now to be considered were obtained as follows. Record-sheets of the form reproduced above were printed, with blanks for age and name of subject, place, date, for sixteen judgments of time-intervals (numerals 1 to 16), for a statement of the subject's method of estimating time, for the number of letters counted in thirty seconds, and for the pulse-rate. Four intervals were used, 18, 36, 72, and 108 seconds, and for each of these intervals judgments were taken under the four conditions designated on the record-sheet as idleness, reading, writing, and estimating. In the experiments the intervals were not given in order of regular increase or decrease of the length of interval, nor were all the judgments for any one interval taken together, but instead, for the purpose of avoiding the influence of expectation of a particular interval or filling, they were arranged irregularly in the order of column two of the record-sheet. This column, as also columns three and four, which are specimen series of judgments for a male and a female respectively, of course were not printed on the record-sheets which were supplied to the subjects.

The experimental procedure was as follows:

(1) Each subject was given a record-sheet.

(2) The experimenter was provided with a record-sheet on which the time of the intervals numbered from 1 to 16 was given. Care was taken that the subjects should not know the length of the intervals before the experiments.

(3) The beginning of each interval was indicated to the subjects by the word "start" uttered distinctly by the experimenter; the end, by the word "stop."

(4) Before beginning the sixteen tests the experimenter gave a thirty-second interval as a standard of judgment. The experiment then proceeded with only sufficient pause between judgments to allow of the recording of estimates by the subjects.

(5) During the filling called "idleness" the subject did not pay special attention to the estimation of the time, but instead permitted his attention to wander.

(6) During "reading" the experimenter read aloud to the subjects.

(7) During "writing" the subjects wrote from the dictation of the experimenter.

(8) During "estimating" the subjects judged the interval as accurately as they could, by whatever method they chose except the use of a time-piece.

(9) Each subject recorded his judgment of the length of an interval in seconds at the appropriate place on the record-sheet as soon as the interval was ended.

(10) The question following judgment number 16 on the sheet was answered as soon as the sixteen judgments had been recorded.

(11) The number of letters counted in thirty seconds was determined by the use of the lines of letters at the bottom of the sheet. The subjects began at the left of each line and counted singly as many letters as they could between the "start" and "stop" signals of the experimenter. They then marked the last letter counted and immediately recorded, in the place provided on the record-sheet, the number of letters counted.

(12) The pulse was counted by the experimenter immediately after the experiment when possible and the rate recorded on the sheet.

(13) The experimenter avoided delays, interruptions, or other irregularities in the course of the series of experiments.

The materials for our discussion of the sex-differences in time-estimation consist of the judgments of 251 males and 274 females. The majority of the males were students in Harvard College, the majority of the females, in Radcliffe and Smith Colleges. The remainder of the records were obtained in Ohio State University, Pomona College, and West Chester State Normal School. The authors gratefully acknowledge their indebtedness for assistance in the obtaining of records to Professors A. H. Pierce, T. H. Haines, W. H. Scott, D. R. Major, A. M. Smith, H. A. Miller, and B. T. Baldwin. The males ranged in age from 17 to 23 years, the females from 17 to 20. The total number of judgments, the distribution of which among the various ages is shown in Table 1, is 4014 for the males, 4375 for the females.

Despite the fact that our experiments are open to the criticisms of all work done under variable conditions and by different experimenters, it cannot be doubted that the results indicate certain sex-differences in time-estimation which suggest additional problems. For the present we refrain from interpretations for the most part and state merely the statistical results of the investigation.

Previous studies of the "time-sense" and the conditions which influence time-estimation suggested to us the desirability of examining our data with reference to (1) sex-differences in estimates of intervals, (2) age-differences, (3) the influence of different fillings, and (4) differences dependent upon the length of the interval. The results have been studied, therefore, with reference to the significance of sex, age, filling, and length of interval, but as no marked age-differences appeared, the detailed tables which were constructed to exhibit the results for the subjects of each year of age have not been printed.

In all the tables the results for males and females are presented separately. The judgments for the sixteen intervals are arranged with reference to the length of the interval, not in the order in which they were taken; all the 18̋ intervals, for example, are grouped (Table 2). The letters I, E, R, W, refer to the fillings of the intervals.

TABLE 1

NUMBER OF SUBJECTS, AGE, SEX, AND NUMBER OF JUDGMENTS

_Males_

_Age_ _No. of subjects_ _No. of judgments_

17 yrs. 16 256 18 27 432 19 40 639 20 67 1071 21 50 800 22 35 560 23 16 256

Totals 251 4014

_Interval_ _No. of judgments_

18" 1004 36" 1003 72" 1003 108" 1004

Total 4014

_Females_

_Age_ _No. of subjects_ _No. of judgments_

17 yrs. 73 1160 18 57 911 19 64 1024 20 80 1280

Totals 274 4375

_Interval_ _No. of judgments_

18" 1092 36" 1094 72" 1096 108" 1093

Total 4375

A general survey of the individual records, all of which for any one year and sex were tabulated, for convenience of examination, on a single large sheet of coördinate paper, showed that the judgments vary within a wide range and are very inexact. Table 2 exhibits the number of correct judgments for each sex, interval, and filling. Of the 4014 male judgments only 96 (2.39%) were correct; of the 4375 female judgments only 46 (1.05%) were correct. The number of correct judgments decreases as the length of the interval increases. For the 18-second intervals there were 7.37% for the males, 2.48% for the females, while for the 108-second intervals there were only 0.10% and 0.37% respectively.

TABLE 2

FREQUENCY OF OCCURRENCE OF CORRECT JUDGMENTS

_Males_

18̋ 36̋ 72̋ 108̋ I E R W I E R W I E R W I E R W Σ % 29 26 11 8 5 6 3 0 3 3 0 1 0 1 0 0 96 2.39 Totals 74 = 7.37% 14 = 1.40% 7 = 0.70% 1 =0.10% 96 2.39

_Females_

7 15 1 4 2 4 1 0 2 5 0 1 2 1 0 1 46 1.05 Totals 27 = 2.48% 7 = 0.62% 8 = 0.73% 4 = 0.37% 46 1.05

_List of abbreviations which occur in the tables._

Σ always designates the sum of the results of the column which it heads.

I, E, R, W refer respectively to the intervals of idleness, estimating, reading, and writing.

The % sign refers to the value of the result in question in terms of the total number of judgments.

C refers to the results of the letter-counting test.

The male judgments for the 108-second intervals range from 11 to 300 seconds. If random guesses be made within these limits the probability of the occurrence of right guesses (108") would be 1 in 290; therefore among 1004 guesses (the number of male judgments for 108-second intervals) 3.5 would be right. In the experiment only one judgment of the 1004 was correct. For the other intervals, with the exception of 18 seconds, the number of correct judgments is only slightly greater than random guessing would have given. Both males and females, however, show considerably more correct judgments for 18-second intervals than the number of probable right guesses. Within the range of the male judgments and for their number 16.9 right guesses might be expected, for the females 10.9. In contrast with these numbers the experiments furnished 74 and 27 correct judgments respectively.

It is noteworthy that for those intervals which are most frequently correctly judged, not only is the number of correct judgments greater for the males than for the females (the ratio of the percentages is about 3 to 1), but the ratio of the number of correct judgments to the probable number of right guesses is also greater for the males.

The female judgments vary within a wider range and are less often correct than the male. For the latter the total number of correct judgments is more than twice that for the former.

Another interesting fact concerning the judgments of the time-intervals is that certain numerals occur in the last place of a judgment more frequently than we should expect if their occurrence depended on random guessing. Tables 3 and 4 exhibit the results of an analysis of the data made for the purpose of studying this fact. In Table 3 the frequency of occurrence of the digits 0, 1, 2, 3, etc., in the last place of the male judgments is given for each filling under the four intervals. For example, the digit 0 occurred in the last place of the male judgments for the interval reading 36 seconds 98 times, as we learn by referring to the first line and third row of the second column of Table 3.

Examination of Tables 3 and 4 shows at once the marked preference of the subjects for 0 and 5. The percentage of male judgments which end in 0 is 41.50; of female 58.51. Similarly the percentages of occurrence of the digit 5 for the males is 24.41, and for the females 23.11. Only two of the other digits (2 and 8) occur with a frequency of over 5%.

Among the 4014 male judgments 0 occurred as a final digit 1666 times, 5, 980 times. Among the 4375 female judgments 0 occurred 2560 times, 5, 1011 times. In the male judgments 0 occurred about four times as often as it would in random guessing; in the female, almost six times as often.

Comparison of Tables 3 and 4 indicates that the occurrence of 0 is 17.10% greater for the females, while that of 5 is 1.30% greater for the males. The sum of the percentages of occurrence of 0 and 5 for the males is 65.91, therefore the probability that a male judgment ends in one of these digits is almost twice that in favor of any other digit. For the females the sum of the same percentages is 81.62, and the probability of occurrence of 0 or 5 is therefore more than four times that of the other eight digits.

Tables 3 and 4 show that even numbers occur more frequently than uneven as final digits. Of the total number of judgments 2461 (3063)[127] end with even digits and 1553 (1312) with uneven.

TABLE 3. FREQUENCY OF OCCURRENCE OF THE NUMERALS (0 TO 9) AS FINAL DIGIT OF THE JUDGMENTS COMBINED RESULTS FOR ALL MALES

18̋ 36̋ 72̋ I E R W I E R W I E R W

0 70 57 72 76 131 77 98 90 124 74 120 125 1 5 11 9 9 10 9 8 7 1 18 5 2 2 20 15 21 18 5 19 16 15 11 20 5 14 3 9 17 14 10 8 11 10 8 6 14 12 4 4 8 12 14 9 3 14 12 3 4 14 8 7 5 67 58 56 63 62 54 60 85 72 59 62 73 6 13 17 12 13 9 14 11 6 10 9 7 7 7 15 22 14 12 6 15 11 10 5 14 13 4 8 36 30 29 31 15 19 16 20 11 17 11 11 9 8 12 10 10 2 18 9 7 7 12 8 3

108̋ I E R W Σ % C

0 151 121 127 153 1666 41.504 21.92 1 4 11 10 2 121 3.014 7.57 2 9 12 9 8 217 5.406 13.15 3 3 12 14 3 155 3.861 7.17 4 6 18 9 3 144 3.587 7.57 5 54 45 52 58 980 24.414 10.36 6 8 7 6 4 153 3.812 8.76 7 4 7 10 8 170 4.235 7.17 8 8 13 5 9 281 7.004 8.76 9 4 5 9 3 127 3.164 7.57

TABLE 4. FREQUENCY OF OCCURRENCE OF THE NUMERALS (0 TO 9) AS FINAL DIGIT OF THE JUDGMENTS COMBINED RESULTS FOR ALL FEMALES

18̋ 36̋ 72̋ I E R W I E R W I E R W

0 120 117 106 126 169 124 182 151 176 145 175 194 1 4 8 3 2 6 7 1 3 2 3 2 1 2 17 18 12 13 9 22 7 11 7 11 3 4 3 4 9 9 11 5 9 3 7 6 15 10 4 4 2 11 13 10 1 6 4 2 9 14 3 1 5 89 63 91 85 62 61 60 79 56 55 65 63 6 9 12 11 6 5 13 7 5 4 6 3 3 7 5 5 7 7 4 9 5 3 2 7 3 3 8 16 22 17 12 10 13 5 10 10 9 6 1 9 5 9 5 1 3 9 0 2 2 9 4 0

108̋ I E R W Σ % C

0 226 197 196 186 2560 58.515 26.14 1 1 5 2 0 50 1.143 9.09 2 4 11 6 3 158 3.611 5.30 3 3 7 4 7 113 2.583 5.68 4 2 4 2 2 86 1.966 11.36 5 32 44 49 57 1011 23.109 14.39 6 0 9 3 1 97 2.217 6.44 7 0 5 2 5 72 1.646 6.44 8 5 11 8 7 162 3.703 10.61 9 1 10 2 4 66 1.508 4.55

In order that the probability of the occurrence of even and uneven numbers may be calculated, those judgments which end in 0 and 5 must be subtracted from the total number of judgments, for the occurrence of these two digits is apparently due to a constant influence. The problem may be formulated thus. First, what is the probability that a judgment is determined by the constant influence in favor of 0 and 5? Second, what is the probability of even and uneven numbers, when the influence in favor of 0 and 5 is eliminated? The calculated probability of 0 or 5 is 0.65919 (0.81622) and therefore the probability that a given judgment is not determined by this influence is 0.34081 (0.18378). The probable limits of these numbers are 0.00505 (0.00395).

After the subtraction of those judgments which end in 0 or 5, there remain 1368 (804), of which 795 (503) are even and 573 (301) uneven. The probability of an even number is 0.58115 (0.62562) and the inverse probability of an uneven number is 0.41885 (0.37438). The probable limits of these numbers are 0.00900 (0.01027). There are therefore even chances that the percentage of occurrence of even numbers is between the limits 57.215 and 59.015 (61.535 and 63.589), or outside these limits.[128]

Statistical studies have already proved that in random guessing even numbers occur somewhat more frequently than uneven. It is therefore worthy of notice that in these results the frequencies of even numbers are not uniformly greater than that of uneven; for with the exception of the digit 6 in the female judgments, the digits next to 0 and 5, _i. e._, 9 and 1, 4 and 6, occur with least frequency.

In the case of the number of letters counted in a half minute, also, it appears (see last column (C) of Tables 3 and 4) that 0 and 5 occur more frequently in the last place than chance would lead us to expect. In contrast with the results for the time-judgments, in the same tables, the percentages of occurrence of the various digits in counting present less marked differences. For the males 3 and 7 occur least frequently, for the females 2 and 9.

To sum up the results of our examination of the materials with reference to the occurrence of digits in the final place of the judgments, the order of decreasing frequency of the various digits is 0, 5, 8, and 2. Of the others 3 and 7 occur more frequently than 4 and 6, with one exception. The statement that even numbers in general occur more frequently than odd must be modified by the statement that in these results the digits next to 0 and 5, namely, 9, 1, 4, and 6 occur with least frequency. These statements hold for both males and females, but for the latter the frequency of occurrence of 0 is far greater than for the males.

These results clearly indicate that the judgments are not random guesses. In seeking further for some explanation of the surprising frequency of occurrence of judgments which end in 0 or 5, we discovered that certain numbers occur very frequently, namely, the multiples of 15, 30, and 60. In order to exhibit this tendency quantitatively Tables 5 and 6 have been constructed.

In these tables will be found tabulated the number of times 15 and multiples of it which are not also multiples of 30 or 60 occur for any given interval and filling. Likewise are tabulated the frequencies of occurrence of 30 and multiples of it which are not multiples of 60, and finally, of 60 and its multiples. The numbers as they occurred in the three categories run as follows:

15 30 60 45 90 120 75 150 180 105 210 240 135 270 300 165 330 360 195 390 420

Fifteen and its multiples, as given above, are arranged in one division of the tables, thirty and sixty each in its own separate division. The line at the bottom of the tables marked Σ gives the frequency of occurrence of these three groups of numbers for all the subjects and for each interval and filling.

As is shown by the percentage of frequency columns of the tables, in no instance do the multiples of 15 constitute less than 19.52% of the male judgments and 23.81% of the female judgments. The lowest frequency for any of the four intervals is 20.32% of the total number of judgments. The maximum frequency for the males (43.03%) and for the females (56.57%) is for the interval idleness 108 seconds. That the male and female maxima should fall on the same interval is interesting.

TABLE 5

FREQUENCY OF OCCURRENCE OF 15, 30, 60, AND THEIR MULTIPLES

_Males_

15 30 60 Σ % _Average_

{I 48 5 0 53 21.12 {E 42 9 0 51 20.32 18̋ {R 43 8 0 51 20.32 20.32 {W 45 4 0 49 19.52

{I 29 60 7 96 38.25 {E 17 41 5 63 25.20 36̋ {R 22 41 6 69 27.41 29.57 {W 36 28 5 69 27.41

{I 29 18 46 93 37.05 {E 25 7 34 66 26.29 72̋ {R 28 26 33 87 34.66 34.70 {W 28 42 32 102 40.80

{I 25 31 52 108 43.03 {E 16 23 20 59 23.51 108̋ {R 22 30 39 91 36.25 36.16 {W 25 37 43 105 41.83

Σ 480 410 322 1212 % 11.96 10.21 8.02 30.12

TABLE 6

FREQUENCY OF OCCURRENCE OF 15, 30, 60, AND THEIR MULTIPLES

_Females_

15 30 60 Σ % _Average_

{I 58 30 0 88 32.47 {E 30 35 8 73 26.64 18̋ {R 56 26 3 85 31.02 28.48 {W 41 24 0 65 23.81

{I 31 55 39 125 45.62 {E 21 36 17 74 27.21 36̋ {R 31 63 33 127 46.35 38.86 {W 41 45 13 99 36.26

{I 29 28 60 117 42.70 {E 17 18 52 87 31.75 72̋ {R 26 37 52 115 41.97 41.60 {W 30 51 56 137 50.00

{I 12 45 98 155 56.57 {E 21 27 58 106 38.83 108̋ {R 23 36 84 143 52.19 47.83 {W 24 31 64 119 43.75

Σ 491 587 637 1715 % 11.22 13.42 14.56 39.22

If no influence worked in favor of the multiples of 15 in these experiments only one judgment in thirty would be 15 (3.33%) and only one in sixty, 30 or 60 (1.67%). For the probability of the occurrence of 15, 30, and 60 is 1/60 + 1/60 + 1/30 = 1/15, as is obvious from the fact that among sixty consecutive numbers (1 to 60) there are four which are multiples of 15. According to probability we should expect multiples of 15, 30, and 60 to occur 268 times among the 4014 male judgments and 292 times among the 4375 female judgments. As a matter of fact there are 1212 such judgments for the males, 1715 for the females. The probability that a male judgment is a multiple of 15, 30, or 60 is 0.3012 (probable error 0.0049); for a female judgment the probability is 0.39199 (probable error 0.0050).

These statistics indicate that the subjects are constantly and strongly influenced in favor of judgments which are simple fractions of a minute. Closer inspection of the tables gives some suggestion of the nature of this influence.

Comparison of the four intervals (Tables 5 and 6) with respect to the occurrence of simple fractions of a minute shows that the frequency of such numbers increases rapidly as the length of the interval increases. The various percentages of frequency for males and females and for the four intervals are again presented here for convenience of comparison.

18̋ 36̋ 72̋ 108̋

_Males_ 20.32% 29.57% 34.70% 36.16% _Females_ 28.48 38.86 41.60 47.83

As is obvious from these figures both frequency and rate of increase are far higher for the females than for the males.

Examination of the percentages (totals) at the bottom of Tables 5 and 6 reveals another remarkable sex-difference; for the frequency of occurrence of 15 and its multiples regularly decreases for males from the 15 to the 60 class, whereas for females it regularly increases.

Undoubtedly the time-judgments of these experiments were strongly influenced by thought of the conventional time-unit, the minute, for in all quantitative work there are errors in favor of the standard of measurement and simple fractions thereof. In the present instance this tendency to favor the unit was strengthened, perhaps, by the giving of a half-minute interval as a standard for comparison at the beginning of the tests.

Two explanations of the sex-differences above mentioned are suggested by our study of the data. One is the fact that the females are less exact than the males; the other that they generally overestimate the intervals, whereas the males often underestimate them. One's estimate of an interval is determined partly by confidence of accuracy. The longer an interval the less we feel able to estimate it accurately, and, as a consequence, the more frequently it is judged as the same as the time-unit or a simple fraction of that unit. The females are less exact in their estimates than the males, and less exact for long than for short intervals, and as an accompaniment of their inexactitude we find the frequent occurrence of multiples of 15, 30, and 60.

But confidence of ability to estimate accurately must be considered in connection with the fact which suggests our second explanation, namely, that the female estimates are higher than the male. Tables 7 and 8 show that the females almost invariably overestimate the intervals rather largely, while the males sometimes underestimate considerably. The range of the male judgments is from 1 to 300, of the female from 1 to 400. Obviously the chance of occurrence of 15, 30, 60, and their multiples varies with the range. The greater the range the greater the probable frequency of 30 and 60 in comparison with 15. In random guessing the probabilities of the occurrence of 15, 30, and 60 for long and short intervals is the same, but our results show that this is not true in the case of these time-estimation judgments. It seems possible, therefore, that the sex-differences referred to are due to the fact that the intervals seem longer to the females, and that, therefore, a feeling of greater inexactitude than would be felt for shorter intervals leads to the choice of simple fractions of a minute more frequently than in the male judgments and more frequently for the long than for the short intervals.

It is of interest in this connection to note that the length of a second is usually underestimated by females, overestimated by males. The average number of seconds counted in half a minute by twenty men and twenty women was as follows:

_Men._ M. 30.4, M.V. 8.7, R.V. 34.94. _Women._ M. 38.9, M.V. 10.6, R.V. 36.70

These figures would seem to indicate that the overestimation of the intervals of these experiments by the females is due to the use of a time-unit which is shorter than that of the males (although presumably of the same length).

We cannot with certainty say whether inaccuracy of judgment stands in the relation of condition or consequence of the occurrence of simple fractions of a minute, but it would appear that the female tendency to overestimate is responsible for the sex-differences already noted. For whatever be the facts concerning longer intervals the second as judged by the female is considerably shorter than that of the male.

Since a complicated periodicity of frequency in the distribution of the judgments is exhibited in the results of Tables 3-6 it is obvious that the distribution-curve will have a tertiary mode for each number ending in 0 or 5, a secondary mode for 15, 30, 60, and their multiples, and a primary mode which may or may not coincide with one of the secondary or tertiary modes. Extreme irregularity is characteristic of the distribution-curve. Different groups of judgments, as, for example, those for the two sexes, those for the different intervals, etc., give somewhat different forms of distribution, for the frequency of occurrence of 0 and 5, as well as of the multiples of 15, is variable.

These facts are important in connection with the selection of an interval for the construction of the distribution-curves, in that they indicate how large the interval or class of the distribution-curves and tables should be.

It is clear from the results of Tables 3 and 4 that the smallest interval which can be of value is 10 seconds, for a smaller interval would necessarily exhibit irregularities due to the greater frequency of 0 than of 5. The question is whether the interval can be so enlarged, without the loss of all details of the nature of the distribution, that every class will represent the influence of the same conditions. For this purpose only three intervals are possible: 10, 30, and 60 seconds. Of these 30 and 60 are undesirable because the interval 60 gives classes which are so large that all details of the distribution are lost, while 30 exhibits only a few details without doing away with the periodicity due to the preference for multiples of 60.

The further question remains, with which digit should the interval end, in order that uniformity of conditions for the various classes may be gained? Theoretically there are ten possibilities, but of these all except two, 0 and 5, are excluded by reason of the unequal frequency of the various digits already discussed. In favor of 0 is the fact that all the classes thus formed are of equal size, _i. e._ 1-10, 11-20, etc., whereas for 5 the first class would differ from the others in being only half as large, 1-5. This, however, is only a slight disadvantage, for there are very few judgments which fall in this class. On the other hand, since 0 is the final digit of most frequent occurrence, classes ending in 5 have the advantage of placing the value of greatest weight in the middle. On the whole it seemed desirable to arrange the judgments in 10 second classes, beginning with the class 1-10. But for purposes of comparison the male judgments have been distributed in classes of 10 seconds, which end in 5, 1-5, 6-15, 16-25, etc.[129]

TABLE 7

DISTRIBUTION OF MALE JUDGMENTS IN 10" CLASSES

_Classes_ 18̋ 36̋ 72̋ 108̋ C I E R W I E R W I E R W I E R W

1 - 10" 31 16 69 136 3 1 4 18 1 1 1 4 0 0 0 0 0 11 - 20 174 179 142 108 40 34 45 97 4 2 5 23 1 2 1 7 0 21 - 30 34 47 35 7 99 106 98 82 15 9 26 65 5 0 6 23 0 31 - 40 7 7 3 56 69 69 28 25 16 34 47 10 2 6 31 1 41 - 50 4 2 2 37 23 22 18 41 43 54 33 20 9 19 28 0 51 - 60 1 9 13 9 6 64 68 53 35 31 17 27 32 7 61 - 70 5 3 0 0 37 42 28 18 27 26 22 19 8 71 - 80 0 1 3 1 23 34 16 9 33 34 35 20 34 81 - 90 1 1 1 15 15 15 8 30 40 43 29 58 91 -100 0 9 8 7 1 23 35 25 17 65 101 -110 0 2 6 3 3 10 26 17 6 33 111 -120 0 8 5 5 2 29 16 17 16 29 121 -130 0 3 1 2 0 5 15 7 8 10 131 -140 0 1 1 1 1 6 9 5 0 4 141 -150 1 0 1 0 5 5 8 4 1 151 -160 1 0 2 3 2 2 1 161 -170 1 0 2 1 0 2 171 -180 1 1 5 4 5 2 181 -190 0 1 2 1 191 -200 3 2 2 2 201 -210 0 1 1 0 211 -220 0 0 0 0 221 -230 1 1 0 0 231 -240 2 0 1 0 241 -250 1 1 1 251 -260 0 0 261 -270 0 0 271 -280 0 0 281 -290 0 0 291 -300 1 1

Totals 251 251 251 251 251 250 251 251 251 251 251 250 251 251 251 251 251

As a result of these groupings of the male judgments it appeared that the former method gives a far more regular distribution than the latter. In view of this result and the above considerations, Tables 7 and 8 were constructed by the use of 10-second classes, beginning with 1-10. In these tables (column C) the distribution of the letter-counting results has been included for convenience of comparison of the two kinds of judgments as to form of distribution.

As instances of the general form of distribution of the judgments the curves have been plotted for letter-counting, Fig. 1 _A_. (Males ----, Females, ... ,) for idleness 36 seconds, Fig. 1 _B_, and for idleness 108 seconds, Fig. 2. The distribution of the letter-counting judgments in classes of 10 is very regular in comparison with that of the several time-estimation judgments. For idleness 36 seconds there are several fairly distinct modes, and for idleness 108 seconds the modes are still more numerous and more marked.

TABLE 8

DISTRIBUTION OF FEMALE JUDGMENTS IN 10̋ CLASSES

18̋ 36̋ 72̋ 108̋ _Classes_ I E R W I E R W I E R W I E R W C

1 - 10 72 20 88 133 5 6 5 33 2 0 1 6 0 1 0 2 0 11 - 20 114 119 109 94 33 29 40 83 7 5 15 25 2 2 7 10 0 21 - 30 50 87 54 29 70 57 73 74 16 13 25 52 4 1 3 27 0 31 - 40 17 17 10 6 51 87 53 30 24 21 24 30 2 1 11 14 0 41 - 50 10 14 7 4 40 35 39 20 35 18 37 32 14 6 17 34 2 51 - 60 2 10 3 1 43 30 40 14 48 44 47 53 30 18 35 36 5 61 - 70 1 3 0 3 11 7 5 2 28 50 20 21 8 11 23 22 18 71 - 80 3 2 1 2 5 8 2 10 29 32 23 14 14 21 20 14 57 81 - 90 0 0 1 1 9 3 6 2 27 29 28 14 41 35 35 19 67 91 -100 0 2 0 1 4 2 1 16 11 15 5 25 35 17 11 50 101 -110 0 0 0 1 1 1 4 7 6 0 9 24 7 6 25 111 -120 0 0 2 3 6 3 17 20 10 8 52 38 33 16 19 121 -130 2 0 0 1 0 3 4 3 3 4 15 6 8 13 131 -140 0 1 1 0 1 2 1 4 6 9 6 6 5 141 -150 0 1 0 1 5 4 4 2 15 13 16 7 1 151 -160 1 1 0 0 0 4 2 0 3 7 2 2 2 161 -170 0 0 0 1 1 0 0 3 2 0 1 171 -180 1 0 0 7 4 7 4 22 14 16 22 181 -190 0 0 1 0 1 0 2 2 3 0 191 -200 0 0 1 1 3 0 3 5 6 6 201 -210 1 0 0 0 0 0 1 0 1 0 211 -220 0 0 1 0 0 1 2 0 0 221 -230 0 0 1 0 0 1 0 6 2 231 -240 0 2 1 0 1 3 3 2 4 241 -250 0 1 0 0 3 0 0 251 -260 0 0 2 0 0 1 261 -270 0 0 1 0 0 0 271 -280 0 0 0 0 0 0 281 -290 0 0 0 0 0 0 291 -300 1 2 4 2 1 1 301 -310 0 0 0 0 311 -320 1 0 0 0 321 -330 0 0 0 0 331 -340 1 0 0 1 341 -350 0 0 351 -360 1 1 361 -370 0 371 -380 0 381 -390 0 391 -400 2

Totals 271 274 274 273 274 273 274 273 274 274 274 274 274 273 274 272 264

Tables 7 and 8 show that the range of the judgments increases with the length of the interval judged, and that the modal class is always much nearer the lower than the upper limit. Asymmetry is characteristic of the distribution of organic data, and in certain instances, as for example writing 18 seconds, males, the choice of a 10-second class interval results in extreme asymmetry, and one is reminded of the tables which Fechner gave as examples of his logarithmic method in statistics.[130]

It is not to be expected that a method of grouping should be found which will give regularity of distribution throughout, but it is important that there should be regularity about the mode. In the table of distribution for the males (Table 7) all the intervals from idleness 18 seconds to reading 72 seconds are regular.[131] The remaining intervals, with the exception of estimating 108 seconds, are irregular.

Trial proves that for these intervals increase of the size of the class to 30 seconds is sufficient to give regular distributions, as is obvious from Table 9. Grouping by 30-second classes gives regularity for most of the female judgments, but for idleness 108 seconds and writing 108 seconds there are still slight irregularities, as Table 10 indicates.

Tables 7 and 8 show that the distribution is far less regular for the females than for the males. The fact that it becomes regular when the class interval is increased to 30 seconds suggests that the irregularities of distribution which appear in the tables are due to those influences which favor simple fractions of a minute and not to the small number of judgments.

Having now noted certain important characteristics of the time-estimation judgments and the nature of their distribution, we may examine the arithmetical means and other statistical quantities which have been determined for our data. Those quantities which have been determined for the several ages, intervals, and fillings as well as for the sexes are: (1) The Mean (_M._ in tables), (2) the average variability (_M. V._), (3) the positive variability (+ _V._), (4) the number of judgments with positive variation (No. + _V._), (5) the negative variability (- _V._), (6) the number of judgments with negative variation (No. - _V._), (7) the relative variability (_R. V._) = _M_ + _V_/_M_ × 100.

Since the sums of the positive and the negative variations are equal, it is possible to make certain of the accuracy of the means and average variabilities by comparison of the + _V._ and - _V._ As this was done in all cases we feel confident of the reliability of the statistical quantities presented in the tables.

In Table 11 have been arranged the various quantities as determined for the males and females for each interval. The values given in this table are averages of the determinations made for the several ages separately.

TABLE 9

DISTRIBUTION OF CERTAIN MALE JUDGMENTS IN 30̋ CLASSES

_Classes._ W. 72̋ I. 108̋ R. 108̋ W. 108̋

1- 30 92 6 7 30 31- 60 115 61 52 91 61- 90 35 90 100 68 91-120 6 62 59 39 121-150 1 16 20 12 151-180 1 9 7 6 181-210 3 5 3 211-240 3 1 0 241-270 1 1 271-300 1

250 251 251 251

TABLE 10

DISTRIBUTION OF FEMALE JUDGMENTS IN 30̋ CLASSES

18̋ 36̋ 72̋ 108̋ _Classes_ I E R W I E R W I E R W I E R W 1- 30 236 226 251 256 108 92 118 190 25 18 41 83 6 4 10 39 31- 60 29 41 20 11 134 152 132 64 107 83 108 115 46 25 63 84 61- 90 4 5 2 6 25 18 13 14 84 111 71 49 63 67 78 55 91-120 0 2 0 3 8 9 5 37 38 31 13 86 97 57 33 121-150 2 0 2 2 1 9 10 8 9 25 37 28 21 151-180 1 2 0 0 8 9 9 4 28 23 18 25 181-210 1 0 2 1 4 0 6 7 10 6 211-240 0 2 3 0 1 5 5 8 6 241-270 0 1 0 3 3 0 1 271-300 1 2 4 2 1 1 301-330 1 0 0 0 331-360 1 1 1 1 361-390 0 391-420 2

Totals 271 274 274 273 274 273 274 273 274 274 274 274 274 273 274 272

TABLE 11

MEANS, ETC., FOR EACH SEX, INTERVAL AND FILLING

KEY: Ma. = _Males_ Fe. = _Females_

M. M. V. +V. No. +V. Ma. Fe. Ma. Fe. Ma. Fe. Ma. Fe.

{I 17.7 20.74 5.4 10.35 5.8 15.48 15.9 22.75 18" {E 19.5 25.55 4.9 9.84 6.0 13.98 16.9 23.75 {R 15.5 18.46 4.9 9.14 6.3 13.03 14.6 24.25 {W 11.5 15.58 3.7 8.56 4.6 11.83 14.3 25.75

{I 33.3 42.81 9.1 16.55 12.6 20.63 14.2 28.00 36" {E 33.1 41.54 8.4 15.23 10.7 23.34 14.2 23.00 {R 32.1 41.71 8.4 16.42 9.7 20.78 16.3 27.75 {W 24.7 30.10 9.0 14.71 10.9 22.08 14.4 23.50

{I 63.3 73.00 17.2 27.20 20.9 33.72 15.7 27.75 72" {E 63.1 77.13 16.0 26.56 18.8 37.27 16.9 24.75 {R 57.9 70.78 17.3 30.30 20.9 39.28 15.2 26.75 {W 51.2 54.93 19.8 24.21 23.7 29.47 15.0 38.25

{I 92.7 113.37 29.8 40.13 35.3 44.08 15.2 32.00 108"{E 99.8 114.88 26.3 36.38 29.3 49.26 14.9 26.25 {R 90.1 100.47 28.3 40.18 33.9 47.90 15.3 34.25 {W 75.5 87.45 32.4 45.33 40.8 61.12 14.9 34.25

-V. No. -V. R. V. Ma. Fe. Ma. Fe. Ma. Fe.

{I 5.7 7.78 20.0 45.00 30 49.83 18" {E 4.4 7.69 19.0 44.75 25 39.10 {R 4.4 7.07 21.2 44.25 31 49.26 {W 3.2 7.14 21.6 42.50 33 54.55

{I 8.1 14.01 21.7 40.50 27 38.32 36" {E 7.2 11.57 21.7 45.25 25 36.66 {R 7.5 13.84 19.6 40.75 26 38.84 {W 8.7 11.24 21.5 44.75 36 48.64

{I 15.5 22.83 20.2 40.75 27 36.87 72" {E 14.7 20.98 19.0 43.75 27 34.43 {R 15.7 24.91 20.7 41.75 30 42.77 {W 16.0 21.26 20.9 36.75 37 43.84

{I 25.9 37.87 20.7 36.50 32 35.34 108"{E 24.4 29.51 19.9 42.00 26 31.57 {R 24.8 34.60 20.6 39.75 31 39.95 {W 27.5 35.86 19.9 42.75 42 51.67

The following facts are revealed by comparison of the results for the two sexes.[132] Without exception the means for the females are larger than those for the males. All but one of the sixteen intervals (E 18̋) are underestimated by the males, whereas all but six are overestimated by the females. The amount of over- and under-estimation is given in Table 12. In every instance the females overestimate in comparison with the males. The mean variability is very much greater for the females, as is also the relative variability. If variability be taken as a measure of reliability of judgment the males are far superior to the females.

As is obvious from Table 12, both under- and over-estimation increase with increase in the length of the interval. For 18̋ intervals they are least, for 108" intervals greatest.

The influence of the fillings is marked. The writing intervals without exception are judged as shortest; reading gives the next shortest intervals, while sometimes idleness, sometimes estimating, comes third. In order of increasing length of average estimates of the intervals the fillings stand: writing, reading, idleness, estimating. As a rule the averages for the idleness and the estimating intervals are nearly the same, but it is worthy of note that the females always overestimate to a greater extent when estimating than when idle. This is another indication of the discrepancy between the female time-unit and the objective unit.

About ninety per cent of the subjects estimated by some counting method. The methods most frequently used were "counting seconds," counting "1 and 2 and 3 and 4, etc.," counting the swings of a pendulum, tapping, and counting imaginary watch-ticks.

The above statements might suggest that the overestimation characteristic of the female judgments is due to a more rapid counting rhythm. This, however, is not true, for the letter-counting tests indicate a slightly more rapid rhythm for the males, 93.42 as opposed to 91.89.

TABLE 12

AMOUNT OF OVER- AND UNDER-ESTIMATION OF INTERVALS

_Males._ _Females._ _Males._ {I - 0.3 + 2.74 Age 17 18 19 20 21 22 23 {E + 1.5 + 7.55 Over- or under- -8.55 18̋ {R - 2.5 + 0.46 estimation -3.60 -7.50 -13.02 -13.49 -8.71 -13.20 {W - 6.5 - 2.42 No. + 6 2 2 0 2 2 2

{I - 2.7 + 6.81 No. - 10 14 14 16 14 14 14 {E - 2.9 + 5.54 36̋ {R - 3.9 + 5.71 {W -11.3 - 5.90 _Females._

{I - 8.7 + 1.00 {E - 8.9 + 5.13 Age 17 18 19 20 72̋ {R -18.1 - 1.22 Over- or under- {W -24.8 -17.07 estimation + 2.38 - 4.16 - 2.57 + 2.55

{I -15.3 + 5.37 No. + 11 8 8 12 {E - 8.2 + 6.88 No. - 5 8 8 4 108̋{R -17.9 - 7.53 + = overestimation {W -32.5 -20.55 - = underestimation

In Table 13 are the means, variabilities, errors, etc., for the letter-counting tests. In this table we have presented the values of the various statistical quantities for the several ages of both males and females, for there are certain interesting differences which should be noted. Similar age-tables have been prepared for all of the other results, but in no case have noteworthy differences appeared. From Table 13 it will be observed that the males on the average count more letters in thirty seconds than do the females, and at the same time make more errors. The mean and relative variabilities for the sex-groups are almost the same. Curiously enough the number of letters counted as well as the accuracy of counting decrease for the females with age (17 to 20 years being the age-limits of the group under consideration). The males within the same age-limits increase in rapidity of counting, but decrease in accuracy. In the examination of Table 13 it is to be remembered that the 17 and 23 year groups of males contain only 16 individuals each, and therefore cannot be compared to advantage with the other groups. Both mean and relative variabilities decrease from 17 to 20 years for the females, whereas for the males there is no constancy in the direction of the change.

TABLE 13

MEANS, ETC., FOR LETTER-COUNTING

_Males._

_Age_ 17 18 19 20 21 22 23 _Average_ M. 92.81 92.48 94.00 95.87 92.66 97.06 89.06 93.42 M. V. 10.29 15.31 16.50 12.90 7.81 13.04 19.20 13.58 +V. 11.76 22.96 16.50 11.70 8.13 16.30 21.94 15.61 No. +V. 7 9 20 37 24 14 7 16.96 -V. 9.15 11.48 16.50 14.40 7.51 10.87 17.09 12.57 No. -V. 9 18 20 30 26 21 9 19.00 R. V. 11.1 16.5 17.6 13.5 8.4 13.4 21.6 14.59 Errors 0.88 1.04 2.10 3.03 1.70 0.89 2.75 1.77

_Females._

_Age_ 17 18 19 20 _Average_ M. 97.74 95.51 89.21 85.09 91.89 M. V. 17.06 14.56 11.30 11.28 13.55 +V 18.67 18.49 12.06 14.56 15.94 No. +V. 32 21 30 31 28.50 -V. 15.71 12.14 11.66 9.21 12.18 No. -V. 38 32 31 49 37.50 R. V. 17.5 15.2 12.7 13.3 14.70 Errors 1.35 1.46 1.49 1.65 1.47

SUMMARY

(1) The length of a second is slightly overestimated by men, greatly underestimated by women.

(2) Intervals of from 18 to 108 seconds are usually slightly underestimated by men (ages 17 to 23 years), and greatly overestimated by women (ages 17 to 20 years).

(3) The time-estimates of women are far more variable than those of men, and on the whole markedly less accurate.

(4) Both men and women favor estimates which end in 0 or 5, as well as simple fractions of a minute, but the tendency is stronger in women than in men. Over one third of the estimates reported in this paper were 15 seconds or simple multiples thereof.

(5) In letter-counting the groups of subjects studied (251 men and 274 women) exhibited differences just the opposite of those in time-estimation, for the men counted more rapidly and less accurately than did the women.

(6) Of the four fillings for the intervals used in the experiments, "writing" gave the smallest estimates of the intervals, listening to "reading" next, while "idleness" and "estimating" were conditions in which the intervals seemed much longer to both men and women.

(7) This preliminary study of sex-differences in time-estimation, by which it has been learned that women overestimate and are notably inaccurate in comparison with men, is to be followed and supplemented by the results of an investigation now in progress concerning the relations of sex-differences in time-estimation to age and physiological rhythms.

FOOTNOTES:

[Footnote 125: Science, N.S., vol. 19, pp. 708-709, 1904.]

[Footnote 126: E. Mach (Analyse der Empfindungen, 1900, p. 161) thinks that his physiological time-unit has become larger with age. And he has also noted that the time-sense differs in animals of the same species which differ in size.]

[Footnote 127: The unbracketed number is that for the males, the bracketed that for the females.]

[Footnote 128: It may be asked in connection with the above statistics, what is the probability that even and uneven digits have unequal chances of occurrence? The analytic treatment of this problem indicates that the probability is ½[1+φ(4.25)] = 0.99999999891 for the males and ½[1+φ(15.93)] for the females. It is therefore almost certain, theoretically, that even and uneven numbers have not the same frequency. See Czuber, Wahrscheinlichkeitsrechnung, 1903, pp. 158-161. The constants of this problem are in Czuber's denotation, _a_ = 52.308 and _b_ = 222.]

[Footnote 129: The judgments might be grouped in 10 second classes beginning with the lowest number in the experiments, but this would have the disadvantage of rendering the distribution tables or curves for different groups of judgments incomparable.]

[Footnote 130: G. Th. Fechner, Collectivmaasslehre, pp. 338-346, 1897. Compare the asymmetry of writing 18 seconds for both males and females with Fechner's Table III, p. 442.]

[Footnote 131: The distribution may be called regular if the classes increase to a maximum, the mode, and then decrease without interruption. (See Fechner, Collectivmaasslehre, pp. 121-122.)]

[Footnote 132: The values of the means and variabilities was determined to the second decimal for the females, but only to the first for the males; consequently the relative variability could be computed exactly to the first decimal for the females and to the unit only for the males.]

ASSOCIATIONS UNDER THE INFLUENCE OF DIFFERENT IDEAS

BY BIRD T. BALDWIN

The purpose of the following investigation was to study the influence of two or more starting-points on the train of associated ideas. It was begun in October, 1902, and concluded in January, 1905. Nineteen graduate students acted as subjects, and the experiments were conducted with each individually for one hour per week, except in a few instances where two subjects were present together. Occasionally the experimenter acted as subject in order to get a clearer insight into introspective data. There are recorded here thirteen groups of one hundred and eight sections, including eight hundred and fifty-five separate experiments, with a sum total of eleven thousand, one hundred and thirty-five named associations.

So far the field has not been studied experimentally, although Cordes,[133] while attempting to observe the effect of an unconscious intermediating factor in 'mediate association,' noticed that the accompanying factor (particularly with a tone) sometimes combined with the starting-point in determining the associated series. The fact is simply mentioned, and Scripture's[134] conclusions from the same are inadequate when he states, "In general we may say that two simultaneous ideas have an effect that depends on their relative masses; if one of the ideas is over-poweringly weighty the next idea will be chiefly influenced by it, but if the two are nearly balanced the next idea will be the result of the two." Miss Calkins[135] makes a near approach to the problem in a study of "Mental Combination," where auditory words were given as nearly simultaneously as possible and the subject was required to remain for four seconds in silence and then to write the train of imagery which passed in six following seconds; the words as auditory starting-points were finally excluded from the experiments "because the first word pronounced tends often to establish itself so firmly that its association-images are proof against the intrusion of the second word, which has therefore no chance to be grasped with the first." These results differ from the ones here recorded which were obtained independently and under different conditions. In her valuable monograph on Association[136] there is in one instance a suggestion of the problem, but no results are given.

The two or more starting-points were nonsense syllables, concrete or abstract words, pronounced by the investigator or shown on cards, or finally, pictures. The associations continued for a period of fifty seconds unless otherwise indicated. The same letters denote the same subjects throughout all the experiments, K. and R. being women. In the examples given, Roman numbers have been used, in place of the letters, as it was found impossible to get representative series which were entirely devoid of personal references.

After the associations had been "jotted down," the subjects in each case copied them, noting also the suggesting ideas, and giving, in many cases, a number of introspective notes. It is important to mention that in all of the work these records of suggesting ideas were made by the subjects without any questions on the part of the investigator.

GROUP I. TWO NONSENSE SYLLABLES

In order that a standard might be obtained that would serve as a basis for subsequent experiments, two nonsense syllables were pronounced with equal emphasis, as starting-points, and the subject was asked merely to wait until both had entered consciousness and not to favor nor inhibit either. If the subject stated that associations arose between the pronunciation of the starting-points the results were discarded.

Turning to the notes we find that K. reported, "The first just hovered around," and the associations followed the second, or as V. states it, "Sof was carried subconsciously for a while without influence," while By. frequently noticed that "The first may be in the background on the point of breaking in but be inhibited involuntarily," or in another, "It was frequently present but exerting no influence." A. "forgot what the other word was, but felt it trying to get a hand in." Ro. goes further and states in terms similar to A., "The words which might have been suggested by 'taf' were wholly inhibited, though I am sure 'taf' was present to me throughout the series, but was not efficacious as against the other syllable." It is unnecessary to multiply instances to show that the wraith, so to speak, of one may linger for a short time, or occasionally for the entire series, but that the associations are determined by the other. Or the lingering wraith of a starting-point may hover ineffectively in consciousness and exert no determining influence on the series until toward its close; then, however, although both starting-points still persist, they exchange places so far as effectiveness is concerned, and the former wraith becomes the primary factor in effecting the series of associations. For example, "The two syllables were present all the way through, but the former exhausted itself as a word-suggester after a few words." Again Ro. gives examples where "One alone may be in consciousness and determine the associations when the other may enter without effect upon the series, or may determine the series, the first persisting but losing its effect"; and a case of both ideas persisting and each alternately exerting an influence was noted by M. These last two conditions are exceptional.

Studying carefully the notes and graphic representations as given in the tables, it is apparent that one starting-point may be followed independently and exclusively; we find "'fef' suggesting 'theft,' and the subsequent associations monopolizing the field of consciousness and 'tuz' not again appearing." (V.) The results show that in the one hundred and seven experiments one was followed exclusively only twenty times. The following would be an example:

III. Naf-Tam

--tambour tam --experiment tambour --psychology experiment --laboratory experiment --space psychology --time space --ego space and time --Ebbinghaus ego --discussion psychology --posted notice psychology --door posted notice --gray door --stairs door --fishes laboratory --water fishes --decay fishes --animal fishes --meat fishes --odor meat

In other cases one starting-point may be followed and then the other for a few or many associations, each "occupying the mind to the exclusion of the other for a number of words, when suddenly the other appears and suggests a new series," which V. calls "a curious zigzagging in consciousness." This may take place at any point along the series. As Ro. indicates, "There was rivalry here; 'yud' wholly inhibited all the 'zid' associations, even 'zid' itself for the time, then, 'yud' apparently being exhausted, 'zid' entered again into the focus."

In contrast to the above forms, the tables indicate and the notes verify that while the associations primarily follow one there can be traced the modifying effect of the other; "The nature of the words was influenced by a fringe of consciousness which contains the other starting-point," M.'s comment runs, while J. adds, "The other helped in the mental picture but had no special significance." There are no experiments in the first group where this partial fusion took place throughout the series, and there are only six examples where it took place before the sixth word and continued to the end. While there are no cases here of alternating partial fusion, yet it sometimes happens, that is, the predominating influence is sometimes transferred from one to the other. The modifying influence may reach such a degree at any point in the series that the identity of each point of departure of the association is lost and there is total fusion, resulting in one idea or one train of thought. For example, 'rel' and 'mem' gave 'realm' for V.; for Ht. 'fef' and 'tuz' gave 'fezz'; for M. they gave 'fez'; for Ro. 'fuz.'

Of the twenty-one experiments where one starting-point was followed exclusively, there were two cases for the first and nineteen for the second. There were but two cases of alternating groups, a third one being unique in that after the first three words there was a persistent alternation between two apparently independent series of inter-related words and inter-related visual images. There were three cases of complete fusion throughout the series and nine where total fusion started before the fifth word and continued.

In a number of cases the initial starting-points were forgotten before the end of the series and the subjects were sometimes unable to recall them.

As the subjects were kept ignorant of the characteristic persistence of either starting-point in forming separate associations, and of the tendency towards fusion, as well as of the preponderance of influence of one over the other, it is to the tabulated results that we must look for quantitative measurement of these. 76.2% of the associations are due to the independent influence of one or the other of the starting-points; 23.9% are due to the combined influence; for the first starting-point we have 18.7%, for the second 57.5%. In 15.3% of all the associations the combined influence was the result of total fusion; in 4.1%, the result of a union where the first starting-point predominated in influence; in 4.4%, the second predominated. The following graphic representation indicates the order of influences for the first pair of syllables. The table gives the results for the ten pairs.

TABLE I. TWO NONSENSE SYLLABLES SPOKEN

Time--50 seconds.

Characters: | represents the influence of the first, - the second, + complete fusion, α fusion with the first predominating, β fusion with the second predominating.

1) Taf--Coz

M. | - - - - | | | | | - - - - F. - - | | + + + + | | | + + β β β β β β H. - | | | | | | | | | | | | | | | R. | - - - - - - - - - - - - - - - K. - - - - - - - V. | | - - - - | - - | + + + + Ro. | | | - - - - - - - - - - - - - - - - Bl. - - - - - - - - - - - - - - - By. | - | | | - - - - - - - - - - - - - - - - - - - Bs. - - - - - - - - - - - - - - - Ht. - - | | | | | | | | | | | | |

Starting-points:

(1) Taf--Coz. (2) Cim--Bef. (3) Yud--Zid. (4) Sof--Deb. (5) Naf--Tam. (6) Fef--Tuz. (7) Sar--Nef. (8) Sek--Lub. (9) Hov--Bes. (10) Rel--Mem.

| - + α β

M. { 20 69 26 4 3 { 16.5% 56.6% 21.2% 3.3% 2.4%

F. { 28 22 37 0 39 { 22.2% 17.5% 29.4% 30.9%

H. { 39 98 0 11 0 { 26.3% 66.2% 7.5%

R. { 9 102 32 0 0 { 6.3% 71.4% 22.3%

K. { 47 58 1 14 0 { 39.1% 48.3% .7% 11.9%

V. { 30 79 54 0 0 { 18.4% 48.4% 33.2%

Ro. { 32 111 0 5 0 { 21.4% 75.1% 3.5%

Bl. { 5 131 15 15 0 { 3.1% 78.9% 9.0% 9.0%

By. { 43 102 23 15 22 { 16.8% 52.6% 11.7% 7.7% 11.2%

Bs. { 9 72 31 0 6 { 11.4% 58.5% 25.3% 4.8%

Ht. { 32 58 20 0 0 { 29.0% 52.8% 18.2%

Totals{294 902 239 64 70 { 18.7% 57.5% 15.3% 4.1% 4.4%

Number of subjects, 11; number of sections, 10; number of experiments, 110; number of associations, 1569.

GROUP II

Two concrete nouns with apparently equivalent connotation were pronounced. In order that the subject get no clue as to the preponderance of one starting-point over the other, the nine sections were given at irregular intervals in connection with other experiments.

The tables show few cases of fusion, there being but one case in the eighty experiments where all the associations were the result of the combined influence of both starting-points. There was no other instance where complete fusion took place before the sixth association and continued throughout, and only six cases where any form of fusion took place in the eighty experiments within the first five words (7.6%), while in the one hundred and seven experiments of Group I there were twenty-five (23.9%).

The tables show a tendency which was noted when two syllables were used and which is emphatically brought out here, namely, it is the position or sequence which determines which of the two equivalent starting-points shall produce the greater influence. When the two starting-points are given in immediate succession, it is the second which predominates in influence. This preponderance may be clearly demonstrated by the tables alone, though there are many notes which show "the greater influence of one" (the second). A. seems to have realized this when he wrote, "While the first was uppermost the second hovered in subconsciousness, resting content, knowing that it would have its turn soon." In corroboration the tables give--abstracting from all cases of fusion--268 words (23.2%) for the first, 721 words (62.3%) for the second. In fifty-five of the eighty experiments the last had full control at the end of the series. Taking the cases where one was followed exclusively throughout the series, starting between the first and the sixth named association, we find eight for the first and twenty-nine for the second. This greater influence is again to be found in the cases of partial fusion; the first predominating in 2.6%, and the second in 4.3%.

The results of both groups show that the starting-points tend in a high degree toward independent influence, and also that such a method of presentation is one of sequence rather than simultaneity, as the two words show unequal influence. The former must in a manner be reproduced to become a point of departure for associations, while the latter acts directly. Is it then a condition of mind that when similar impressions are presented the one in the presence of which consciousness is reacting directly has a greater influence in arousing associations than one which is just past? This we are forced to conclude is the case, but the proof of the conclusion will be supplemented by later results.

TABLE II. TWO WORDS SPOKEN

Time--50 seconds. Characters--same as Table I.

(1) Library--River

M. | + + β - - - - - - - - - - - - F. | - - - - - - - - - | | | | H. - - - - - - - - - - - - - - - - Ro. | | | | - - - - - - - - - J. | - | | | | - - - - - - - - - - - - - - - Bl. | | - - - - | | | | | | | | | - - / By. - - - - - - - - - - - - - - - - - - - - - - Bos. | - - - - - - - Bur. - + - - - - - - - - - - -

(1) Library--River. (2) Hat--Road. (3) Newspaper--Medicine. (4) Bicycle--Drum. (5) Theatre--Magazine. (6) Store--Church. (7) Soldier--House. (8) Ship--Boy. (9) Furniture--Tree.

TABLE II.--_continued_

| - + α β

M. {32 66 26 0 13 {23.4% 48.2% 18.9% 9.5%

F. {32 67 13 5 1 {27.2% 56.7% 11.0% 4.3% .8%

H. {59 79 5 0 0 {41.3% 55.2% 3.5%

Ro. {44 85 0 0 0 {34.1% 65.9%

J. {21 121 8 5 0 {13.5% 78. % 5.3% 3.2%

Bl. {22 83 6 0 1 {19.7% 74.1% 5.4% .8%

By. {16 97 18 14 23 { 9.5% 57.8% 10.7% 8.3% 13.7%

Bs. {26 64 3 7 1 {25.8% 63.5% 2.9% 6.9% .9%

Bur. {16 59 8 0 10 {17.2% 63.4% 8.6% 0 10.8%

Total {268 721 87 31 49 { 23.2% 62.3% 7.6% 2.6% 4.3%

Number of subjects, 9; number of sections, 19; number of experiments, 80; number of associations, 1156.

GROUP III

For two syllables and like words the second strongly predominates in awakening associations; will the same be true when two simple outline pictures are shown in the same order? The following results show in attestation of the above conclusion percentages remarkably similar to those of the words. There are 23.7% for the first and 61% for the second; 84.7% of the associations show no sign of fusion and only 15.3% for fusion and the different forms of partial fusion, the second still holding the ascendency. When the two pictures did fuse, R. tells us, "All the associations were more elaborate pictures than when mere words were given."

A comparative study, inadequate though it is, offers a partial parallelism between the predominating memory type and stimulation. The subjects who are preëminently of the visual, K., visual motor, M., H., V., and visual lingual motor, Ht., find the pictures more suggestive than the syllables, while those of the pure motor, F. and By., reverse the order and find that the syllables offer more numerous and "more vivid" (F.) associations.

Common experience, however, immediately shows the limitations of reaching conclusions, when considering prolificacy as criteria of suggestiveness, inasmuch as starting-points which are abundantly rich in associations tend to produce so many points of departure that they tend to inhibit one another. Again there is to be considered the kind of associations, those of the syllables being of a very elementary character and in serial form.

A few experiments were given in which colored slips of paper were used as starting-points. These proved very suggestive for the subjects. Also a few tones were given, but these were soon discontinued, as other tones, which could not be recorded, were frequently suggested. The sentence which forms a very satisfactory starting-point where one is used could not be used to an advantage where several were given. As we are here interested in the mutual influence of the starting-points, our remaining study will be confined to a quantitative and qualitative variation of the forms used in the previous groups.

TABLE III. TWO PICTURES SHOWN

Time--50 seconds. Characters--same as Table I.

(1) Boy Rolling Hoop--Blacksmith

M. | | | - - - - - - | | | | | F. | | - - | + + H. - - - - - - - - - - - - R. - - - - - - - - - - - - - - - - K. - - - - - - - - - - - - - - - - - V. - - | | + + + + + + + + + + + + + + S. - - - - - - - - - | | | | | | | By. | - - - - - - - - - - - - - - - - - - - - - Bs. - - - - - - - - - Ht. | | - - - - - - - -

(1) Boy Rolling Hoop--Blacksmith. (2) Old Man With Umbrella--Bird House. (3) Carpenter--Mower. (4) Children Playing--Boy with Basket. (5) Horse--Dog House. (6) Shoemaker--Fisherman. (7) Little Girl--A Chicken. (8) Boy--A Sheep.

| - + α β

M. {41 65 2 0 1 {37.6% 59.7% 1.8% .9%

F. {11 42 21 0 5 {13.9% 53.2% 26.6% 6.3%

H. {37 52 11 26 9 {27.4% 38.5% 8.1% 19.3% 6.7%

R. {41 58 8 0 15 {33.4% 48% 6.5% 12.1%

K. {32 82 0 0 0 {27.1% 72.9%

V. {12 95 21 3 5 { 8.8% 70% 15.4% 2.1% 3.7%

S. {36 44 0 0 0 {45% 55%

By. { 8 111 12 0 13 { 5.4% 77.2% 8.3% 9.1%

Bs. {13 40 7 0 0 {21.7% 66.7% 11.6%

Ht. {22 72 7 0 4 {20.9% 68.6% 6.7% 3.8%

Totals {253 661 89 29 52 { 23.7% 61% 8.2% 2.7% 4.4%

Number of subjects, 10; number of sections, 8; number of experiments, 76; number of associations, 1084.

GROUP IV

The previous experiments suggest the conclusion that that starting-point in the presence of which consciousness is reacting exerts a greater influence than one just past. The proof of this anticipated result is supplemented by subsequent consectary data.

It is necessary to test the outcome when the nature of the impressions is varied and the starting-points are given simultaneously. An outline picture and a word may be so given. These experiments verify from a different standpoint the statement that the picture establishes itself more permanently and is more influential, there being 47.8% of the associations produced by the picture alone, 14.8% by the words alone, 25% of a fusion of the two, and 12.4% of a uniting influence with the first predominating. The subject R. is an exception in that she favors the word when not favoring a combination of the two, a fact which I am unable to explain except to add that the subject stated that the æsthetic pleasure connected with the picture was sufficient to inhibit the associations. K. has 100% for the pictures, which is partially explained by the fact that she is a remarkable visualizer who reproduces all situations in visual terms.

TABLE IV. PICTURE SHOWN AND WORD SPOKEN

Time--50 seconds. Characters same as Table I.

(1) (a rabbit)--Table

M. | - - | | | | | | | + - - - - R. + + + + + + + + + + + + + + + + + + K. | | | | | | | | | | | | | | | S. | | | | | - | | | | | J. | - - | | | | | | | | | - - - | | | | | | | | | Ht. | - | | | | | | | | | | | | - - - -

(1) (a rabbit)--Table. (2) (horse)--Book. (3) (boy)--Dish. (4) (duck)--Iron. (5) (dog)--Paper.

| - + α β M. { 38 9 16 6 0 { 55.0% 13.1% 23.3% 8.6%

R. { 1 20 55 0 0 { 1.3% 26.3% 72.4%

K. { 65 0 0 0 0 {100.0%

S. { 29 15 3 10 0 { 50.8% 26.3% 5.3% 17.6%

J. { 75 19 14 9 0 { 64.2% 16.3% 11.9% 7.6%

Ht. { 17 7 30 33 0 { 19.5% 8.1% 34.5% 37.9%

Totals {225 70 118 58 0 { 47.8% 14.8% 25.0% 12.4%

Number of subjects, 6; number of sections, 5; number of experiments, 30; number of associations, 471.

GROUP V

The character of the starting-points determines which shall be followed in a simultaneous presentation; can the character of two immediately successive starting-points be so varied as to overcome the factor of temporal difference? The few experiments in this group show an attempt to shift and measure this influence, selecting as variants words of general and specific character, the first being a term of everyday experience with the subjects, of wide connotation, and therefore presumably rich in associations, and the second, which had the advantage of position, one of more limited and specific connotation, thus in a measure making it possible to test the stability of the second in establishing itself as a word-suggester. For the words "Gymnasium--Stamens" the second still strongly predominates. There is a slight increase in the amount of fusion (24.5% in all), the explanation of which would probably lie in the fact that the first is more assertive than before and offers more elements common to the two. There was one case of total fusion, one case where fusion started before the sixth word and continued, no cases of alternating fusion, four cases of partial fusion, five cases where the second was followed throughout, no case where the first was followed throughout, five cases of alternation between the first and the second. In 75.5%, the influence was exerted without fusion. Eight of the nine subjects favor the specific term.

TABLE V. GENERAL AND FAMILIAR WORD--SPECIFIC WORD SPOKEN

Time--50 seconds. Characters--same as Table I.

(1) Laboratory--Rake

M. | | | | | - - - - - - - - - - - - - - - - F. | - - - - - - - - - H. + + + + + + + + + + + V. | - - - - - - - - - - - - - | | | | | S. - - - - - - - - - - | | | | Bl. - - - - - - - - - - - - - - - - - By. | - - | | | | | | | | | Bs. Ht. - - - - - - - - J. | | β β β β β β β β β β β β | | | | |

(1) Laboratory--Rake. (2) Experiment--Butterfly. (3) Gymnasium--Stamens.

TABLE V.--_continued_

{ 22 25 4 6 0 M. { 38.6% 43.9% 7.0% 10.5%

{ 4 19 0 0 0 F. { 17.4% 82.6%

{ 4 25 13 0 0 H. { 9.5% 59.6% 30.9%

{ 7 38 2 0 7 V. { 12.8% 70.7% 3.7% 12.8%

{ 11 34 0 0 0 S. { 24.4% 75.6%

{ 0 36 0 0 0 Bl. { 100.0%

{ 11 16 7 0 9 By. { 25.5% 37.1% 16.5% 20.9%

{ 0 9 12 2 Bs. { 39.1% 52.2% 8.7%

{ 10 11 10 Ht. { 32.3% 35.4% 32.3%

{ 17 8 15 0 13 J. { 32.1% 15.1% 28.3% 24.5%

{ 86 221 63 8 29 Totals { 21.2% 54.3% 15.4% 1.9% 7.2%

Number of subjects, 10; number of sections, 3; number of experiments, 27; number of associations, 407.

GROUP VI

What modification of influence takes place when an auditory impression in the form of a word of abstract nature (the pure abstract words are taken later) is given in comparison with a concrete noun? The tables indicate that we are now able partly to overcome the disadvantage of first position by the advantage of concrete content. 24% of the associations are the result of total fusion; there are eight cases of total fusion throughout the series, and seven where total fusion took place before the third word and continued. There are two cases where the first was followed throughout, and but one where the second was followed exclusively. The tables indicate that there were very few words. Some of the subjects claim, "These words did not seem equally rich in associations. I was not at all conscious of the one while the other was in consciousness." (H.) The most characteristic feature here was, as Br. also indicates, "Great amount of rivalry at the beginning of the series"; while Bs. states, "There was a lot of confusion and a feeling of groping for words." Br. adds later, "For some seconds association seemed obstructed. Then by an effort the process was started which followed an involuntary course. A kind of confused presence of both words." Another subject adds, "There was a long blank after the words were said in which both words were balancing off in the fringe of consciousness and the mind expectant, passively waiting for an association to turn up. The hesitant period seemed marked by an attempt at a synthesis of these two words in some way."

SUBJECT XIX

Lamp--Justice.

| chimney lamp. | white lamp chimney. | yellow white chimney. | flame yellow. | nickel lamp plus the other words. - scales justice. - purple robe justice.

As the tables indicate, there was frequently a strong tendency here for the abstract terms to fuse. As H. noticed, "It does not tend to call up associations of its own stripe, but in some way becomes concrete."

TABLE VI. TWO WORDS: CONCRETE--ABSTRACT SPOKEN

Time--15 seconds. Characters--same as Table I.

(I) Desert--Hate

A. | | | + + + M. | | | | - - F. + + + H. | - | | | | | | | Ro. | | - - | | | | Bl. + + + + + + + By. | | | + + + + + + Bs. - | | | | | Br. | | | + +

(1) Desert--Hate. (2) Lamp--Justice. (3) Pen--Fatigue, (4) Gate--Fear. TABLE VI--_continued_

| - + α β A. { 10 2 6 0 0 { 55.5% 11.2% 33.3%

M. { 7 8 10 0 0 { 28.0% 32.0% 40.0%

F. { 3 8 5 0 0 { 18.7% 50.1% 31.2%

H. { 17 16 1 0 0 { 50.0% 47.1% 2.9%

Ro. { 15 11 0 0 0 { 57.7% 42.3%

Bl. { 4 15 7 2 0 { 14.2% 53.5% 25.1% 7.2%

By. { 4 21 8 0 1 { 11.8% 61.8% 23.5% 2.9%

Bs. { 5 1 15 0 2 { 21.8% 4.3% 65.2% 8.7%

Br. { 11 8 2 0 0 { 52.3% 38.1% 9.6%

Totals { 76 90 54 2 3 { 33.8% 40.0% 24.0% .8% 1.4%

Number of subjects, 9; number of sections, 4; number of experiments, 34; number of associations, 225.

Reversing the order by placing the concrete noun second, it gains in influence. We are told by the subjects at this point, "The choice seems to be determined by the concreteness of the word." (H.) "The abstract soon exhausted itself as a word-suggester." (Ro.) There was fusion in 24% of the associations of the first group, and 22.2% in the second. There are six cases where the second alone prevails, two for the first starting-point and four for the second. There are eleven cases of fusion beginning before the sixth word and continuing throughout the series. There is much partial fusion, with the second predominating in influence.

The results again emphasize the fact that the influence is transferable, also that normally the second has the advantage; furthermore, they illustrate the preponderance of the concrete word as a starter of associations, and that the abstract term when it exerts an influence tends to fuse rather than persist in having separate associations; all of which shows that concrete terms produce more vivid impressions than abstract ones, and would, when it is possible to use them, be of direct aid to the learner.

TABLE VII. TWO WORDS: ABSTRACT--CONCRETE SPOKEN

Time--15 seconds. Characters--same as Table I.

(1) Honesty--Tide

A. - | - - - - M. - - - - | | | | F. | - - - - - H. | - - - Ro. | | - - - - Bl. | - - - - - - By. - - + + Bs. - - - - - - - J. - + + + + + +

(1) Honesty--Tide. (2) Skill--Coal. (3) Terror--Sky. (4) Refined--Flag.

| - + α β A. { 2 7 11 0 4 { 8.4% 29.2% 45.8% 16.6%

M. { 4 11 10 1 5 {12.9% 35.5% 32.3% 3.2% 16.1%

F. { 2 8 9 0 0 {10.5% 42.2% 47.3%

H. { 8 11 1 3 0 {39.2% 43.5% 4.1% 13.2%

Ro. {10 13 3 0 0 {38.4% 50.0% 11.6%

Bl. {15 10 0 0 0 {60.0% 40.0%

By. { 2 20 3 0 0 { 8.0% 80.0% 12.0%

Bs. { 1 11 6 0 2 { 5.0% 55.0% 30.0% 10.0%

J. { 6 16 6 0 0 {21.4% 57.2% 21.4%

Totals {50 107 49 4 11 {22.6% 48.4% 22.2% 1.9% 4.9%

Number of subjects, 9; number of sections, 4; number of experiments, 36; number of associations, 221.

Increasing the disparateness by making the one a proper name and the other a pure abstract noun, we find the name dominates consciousness, almost to the exclusion of the abstract term. The tables confirm the conclusions that the abstract term, even when given the advantage of position, exerts little influence, for in the first group of eighteen experiments of two hundred and eighty-four associations there are 13.4 times as many associations for the first as for the second, or two hundred and fifteen words for the first (75.8%) and sixteen (5.5%) for the second.

Reversing the order, the burden of influence swings back to thirty-eight (12.8%) for the first and one hundred and fifty-six (52.7%) for the second with an amount of fusion increased to ninety-nine (33.4%).

TABLE VIII. TWO WORDS: PROPER NOUN--ABSTRACT NOUN SPOKEN

Time--50 seconds. Characters--same as Table I.

(1) Lowell--Liberty

M. | | | | α α α | | | | | | R. | α α | | | | | | | | | | | | | K. | | | | | | | | | | | | | | J. | | | + + + α α α α α α α α α α α α α S. | | | | | - | | | | | | | Ht. - - | | | | | | | | | | | | | |

(1) Lowell--Liberty. (2) Roosevelt--Fidelity. (3) Eliot--Integrity.

| - + α β

M. { 29 3 2 7 0 { 70.7% 7.4% 4.8% 17.1%

R. { 30 0 17 2 0 { 61.2% 34.7% 4.1%

K. { 43 2 0 0 0 { 95.5% 4.5%

J. { 42 0 8 13 0 { 66.6% 12.7% 20.7%

S. { 40 2 0 0 0 { 95.2% 4.8%

Ht. { 31 9 3 1 0 { 70.4% 20.4% 6.9% 2.3%

Totals {215 16 30 23 0 { 75.8% 5.5% 10.7% 8.0%

Number of subjects, 6; number of sections, 3; number of experiments, 18; number of associations, 284.

TABLE IX. TWO WORDS: ABSTRACT NOUN--PROPER NOUN SPOKEN

Time--50 seconds. Characters--same as Table I.

(1) Individuality--Lincoln

M. | + | + + + + + + + + + + + + R. - - - - - - - - - - - - - - - - K. - - - - - - - - - - - - J. | - - - - - - - - - - - | | | | | | | | | | S. - - - - - - - - - - - - - - - Ht. - - - - - - - - - - - - - - - - - -

(1) Individuality--Lincoln. (2) Brevity--Webster. (3) Justice--Hanus.

| - + α β

M. { 4 19 25 0 0 { 8.3% 39.6% 52.1%

R. { 5 31 12 0 0 {10.4% 64.5% 25.1%

K. {14 31 0 0 0 {31.2% 68.8%

J. {13 11 44 0 0 {19.1% 16.1% 64.8%

S. { 2 40 0 0 0 { 4.8% 95.2%

Ht. { 0 24 18 0 3 { 53.4% 40.0% 6.6%

Totals {38 156 99 0 3 {12.8% 52.7% 33.4% 1.1%

Number of subjects, 6; number of sections, 3; number of experiments, 18; number of associations, 296.

GROUP VII

Occasional experiments of the previous groups indicated an abnormal influence of those ideas which were accentuated by the special interests of the subjects. We ask therefore: What is the relation of the newly aroused associations to the present content of consciousness? May the present content of consciousness be so varied as to reënforce or inhibit the characteristic influence of the individual impressions successively presented? In order to test this, words or a sentence were pronounced just previous to the presentation of the two starting-points related to them as follows; in the first divisions the preparatory words lead to the second, in the second divisions to the first, in the third divisions to neither, in the fourth divisions to both, and in the last we have a slight change in the marginal setting and a sentence leads to the second.

The following are examples of the first and second divisions:

Quartz--Granite--Shale. HORN--SLATE. Dog--Sheep--Horse. SQUIRREL--TELEGRAM.

SUBJECT XVIII

--slate slate --slate ledge (Col.) slate --Great Falls, Mont. quartz, granite, shale --geology quartz, granite, shale, G. F. --Will B. geology --State University Will B. --Sexton James State University --Mrs. J. Sexton James --C. S. J. Mrs. J. --Indian School C. S. J. --Fort Shaw School Indian School --Mrs. C. Ft. Shaw School --Mrs. E. Mrs. C. --Seattle, Wash Mrs. F. --Miss M. Seattle, Wash. --Everyman Miss M. --Cousin V. Everyman --theatre Cousin V.

SUBJECT XII

| hunt squirrel (and dog) | pasture sheep, horse, and hunt | yard squirrel and pasture | Harvard yard | Freshman Harvard | themes Freshman and squirrel | hunting themes, dog, " | George hunting | squirrel George | creatures squirrel | animals creatures | activity " animals | agility " " | grace " " | cuteness " " | pets " " | civilisation creatures | vs. cats " | enemies cats

That one starting-point establishes itself more firmly, and offers more dominant associations with an increased degree of suggestiveness is intimated by various expressions of the subjects who state, "the preparatory words called forth associations connected with this or that starting-point"; or "there was a felt fusion of all"; "a summation of all"; or "the preparatory words had an influence throughout"; "they strengthened this or that starting-point"; "they affected one and not the other"; and many similar expressions.

The influence of these preparatory marginal settings was also indicated very often by the nature or kind of words in the series.

Turning to the tables which collectively represent in a graphic and quantitative form the notes of the subject, and which are in harmony with the above, we find they demonstrate that there is a very intimate and definite relationship. When the state of mind immediately preceding the moment of the formation of the associated series is conditioned by the preparatory words leading to the second, the amount to which that starting-point dominates consciousness in arousing associations is greater than in any previous case where the words of like nature are pronounced.

With the preparatory words leading to the second starting-point, we have 11.5% of the influence for the first, 69.2% for the second; with them leading to the first, 58.2% for first, 17.2% for second; with them leading to neither, 40.6% for first, 44.2% for second; with them leading to both, 16.1% for first, 54.8% for second; with a preparatory sentence leading to second, 12.9% for first, 59.7% for second.

A few experiments were made where one word was given as a setting and four or eight starting-points were shown, but the starting-points were so numerous that they tended to confuse the subject's introspective account.

TABLE X. TWO WORDS SHOWN: THREE PREPARATORY WORDS SPOKEN LEADING TO THE SECOND

Time--50 seconds. Characters--same as Table I.

Corn, Wheat, Oats. (1) MOB--HAY

M. + + + - + + - - - - R. - - - | + + α + β - - - - - K. - - - - - - - - - - - - - - S. + + + + - - - - - - - - - - - - J. + + + + + + β β - - - - - - - Ht. - + + + + β β β β β β β β

(1) Corn, Wheat, Oats. MOB--HAY. (2) Cloud, Mist, Dew. ORATION--CANOE. (3) Turtle, Fish, Frog. KEY--NET. (4) Quartz, Granite, Shale. HORN--SLATE. (5) Geometry, Plane, Rectangle. CASE--CUBE.

| - + α β

{ 10 41 17 0 7 M. { 13.3% 54.7% 22.7% 9.3%

{ 15 37 21 1 4 R. { 19.3% 47.4% 26.9% 1.2% 5.2%

{ 0 55 0 0 0 K. { 100.0%

{ 8 64 4 0 0 S. { 10.5% 84.2% 5.3%

{ 17 69 6 0 2 J. { 18.1% 73.4% 6.3% 2.2%

{ 2 45 17 0 8 Ht. { 2.8% 62.5% 23.6% 11.1%

{ 52 311 65 1 21 Totals { 11.5% 69.2% 14.4% .2% 4.7%

Number of subjects, 6; number of sections, 5; number of experiments, 29; number of associations, 449.

TABLE XI. TWO WORDS SHOWN. THREE PREPARATORY WORDS SPOKEN LEADING TO THE FIRST

Time--50 seconds. Characters--same as Table I.

Dog, Sheep, Horse. (1) SQUIRREL--TELEGRAM

M. | | | | | | | | | | | | | | R. | | | | | | | | | | | | | | | K. | | | | | | | | | | | | | S. | | - - - - - - - - - - J. | | | | | | | | | | | | | | | | | | | Ht. | | | | | | | | | | - - - - - - - -

(1) Dog, Sheep, Horse. SQUIRREL--TELEGRAM. (2) Pineapple, Banana, Orange. FRUIT-STAND--ELECTRIC LIGHT. (3) Justice, Truth, Beauty. CHARITY--PHOTOGRAPH. (4) Gold, Copper, Silver. DIME--SKULL.

M. {28 3 15 0 8 {51.8% 5.5% 27.9% 14.8%

R. {16 9 23 0 11 {27.2% 15.3% 38.9% 18.6%

K. {56 2 0 0 0 {96.5% 3.5%

S. {36 24 0 0 0 {60.0% 40.0%

J. {38 4 24 1 7 {51.4% 5.4% 32.4% 1.4% 9.4%

Ht. {37 20 0 0 0 {64.9% 35.1%

Totals {211 62 62 1 26 {58.2% 17.2% 17.2% .2% 7.2%

Number of subjects, 6; number of sections, 4; number of experiments, 24; number of associations, 362.

TABLE XII. TWO WORDS SHOWN. THREE PREPARATORY WORDS SPOKEN LEADING TO NEITHER

Time--50 seconds. Characters--same as Table I.

Botany, Statue, Postal. (1) CHOCOLATE--BANNER

M. | | - - - - - - - - - - - - - | R. - | | | | | | | | | | | | | | | | | | | | K. | - | | | - | - | - | - | S. | | - - - - - - - - - - - - - - - - J. | | | | | | | - - - - - - - - - - - - - - - Ht. - - + + + - - - - - - - - - - -

(1) Botany, Statue, Postal. CHOCOLATE--BANNER. (2) Idea, Proposition, Syllogism. SILVER--GAME.

| - + α β

M. {3 28 0 0 0 {9.6% 90.4%

M. {22 1 2 0 14 {56.5% 2.5% 5.2% 35.8%

K. {28 5 0 0 0 {84.8% 15.2%

S. {13 20 0 0 0 {89.4% 60.6%

J. { 17 22 0 0 0 { 43.6% 56.4%

Ht. { 0 14 8 7 0 { 48.3% 27.6% 24.1%

Totals { 83 90 10 7 14 { 40.6% 44.2% 4.9% 3.4% 6.9%

Number of subjects, 6; number of sections, 2; number of experiments, 12; number of associations, 204.

TABLE XIII. TWO WORDS SHOWN. THREE PREPARATORY WORDS SPOKEN LEADING TO BOTH

Time--50 seconds. Characters--same as Table I.

Tree, Shrub, Grass. (1) TEA--FERN

M. + + α α α α α α α - - R. + + + + + + + + + + + + K. - - - - - - - - - - - - - - - - S. - - - - - - - - - - - - J. | - - - - - - - - - - - - - - - - - - - - Ht. + + α α α α α α | | | | |

(1) Tree, Shrub, Grass. TEA--FERN. (2) Fox, Wolf, Moose. DEER--DOVE.

| - + α β

M. { 2 12 4 8 0 { 7.6% 46.3% 15.3% 30.8%

R. { 0 0 25 0 0 { 100.0%

K. { 1 30 0 0 0 { 3.2% 96.8%

S. { 8 12 0 4 0 { 33.3% 50.0% 16.7%

J. { 8 26 0 0 0 { 23.5% 76.5%

Ht. { 8 12 2 6 0 { 28.5% 42.8% 7.2% 21.5%

Totals { 27 92 31 18 0 { 16.1% 54.8% 18.4% 10.7%

Number of subjects, 6; number of sections, 2; number of experiments, 12; number of associations, 168.

TABLE XIV. TWO WORDS SHOWN (AUTHORS)--WITH A PREPARATORY SENTENCE LEADING TO THE SECOND

Time--50 seconds. Characters--same as Table I.

"God's in His Heaven--all's right with the world."

(1) BURNS--BROWNING

M. + - - - - - - - - - | | | | | | R. | - - - - - - - - - - - K. + + + + + + + + + + + + + S. | - - - - - - - - - - - - - | | | J. | | - - - - - - - - - - - - - - - - - - Ht. - - - - - - - - - -

(1) "God's in His Heaven--all's right with the world." BURNS--BROWNING.

(2) "All that glistens is not gold." BYRON--SHAKSPERE.

(3) "Hitch your wagon to a star." SPENCER--EMERSON.

| - + α β

M. { 9 15 15 0 4 {20.9% 34.8% 34.8% 9.5%

R. { 1 47 0 0 0 { 2.1% 97.9%

K. {15 0 26 0 0 {36.5% 63.5%

S. { 6 34 0 0 0 {15.0% 85.0%

J. { 3 43 14 0 0 { 5.1% 71.6% 23.3%

Ht. { 0 18 13 0 0 { 58.1% 41.9%

Totals {34 157 68 0 4 {12.9% 59.7% 25.8% 1.6%

Number of subjects, 6; number of sections, 3; number of experiments, 18; number of associations, 263.

GROUP VIII

The aim here is to test the effect of interruption in the series of associations, and to throw further light on the relation of the series to the present content of consciousness when this content is a series of associations and the new content is a pronounced word which is to act as a point of departure for new associations.

There are three divisions. The time in all is fifty seconds; in the first a word of general connotation is given and after an interim of ten seconds a second more specific word is pronounced. In the second three similar words are given at an interval of fifteen seconds; the third four words with an interval of ten seconds. The following are examples of the first and third divisions:

SUBJECT III

Commencement--Sieve

commencement | college commencement | cap college | gown cap | boys commencement | confetti commencement

sieve - holes sieve - water sieve - flour sieve - space holes - concept space - Royce concept - time concept - eternity time - damnation eternity - Hamlet "Consummation," etc - Shakspere Hamlet

SUBJECT VII

Wax--Jug--Tar--Sod

wax | Charley wax | picnic Charley | horse Charley | saddle horse

jug - ink jug - clay jug - Hegel jug

tar / 'old tar' tar / ship 'old tar' / Bermuda 'old tar'

sod \ grave sod \ graveyard grave \ house graveyard \ church house \ music church \ white church

In all the experiments the subject simply knew that possibly more than one starting-point would be given. There was of course the conscious recognition on the part of the subjects that the pronounced words were starting-points, which would imply an attentive consciousness, but they were cautioned neither to favor nor inhibit the newly pronounced word nor an association in progress.

The notes are uniform in showing that often one, two or three words of the former association-series are written after the new word is pronounced. "The momentum," says F., "was great enough to carry the associations two or three words beyond the pronounced word"; while Bl. found "a tendency for the trend of associations to persist, though not strong enough to overcome the new influence." By.'s experience was slightly different. As stated before, he often wrote the word as it came into consciousness. "On hearing a new word it gets precedence over the next associations not yet formed, and there is considerable confusion and lost time unless the motor discharge of writing the pronounced word is permitted to have free expression." The tables verify the same, and also show that there are more associations during the first interval.

Does a former starting-point regain its influence? In the first division there are two cases where the first and second fuse, but no place where the first independently forms an association; in the second but one word for subject Bl. in "Quill--Bench--Chalk," and in the third not any. There was a small amount of fusion in all, since but two words are due to the combined influence of the first and third, five to the combined influence of the first and fourth, with three starting-points, and one to the combined influence of the first and third with four starting-points.

The train of associations is inhibited by a new starting-point which dominates in influence. No mention is made in any note that a former starting-point remains in consciousness for the series, but M. emphatically writes, "Absolutely no influence of the preceding word or words when the next is taken up"; and later, "As soon as the new one is pronounced the old word and the series it had brought up were immediately suppressed." Bl. comments, "How remarkable it is that each new word crowds the old trend of associations out and starts new ones"; and the graphic representation, one of which only is given here on account of lack of space, shows that there is no return to the original series.

The tables are indicative of the tendency. In the first division of the group there are three possible lines of fusion, in the second six possible lines, and in the third twelve possible lines, but we find only 13.2% for all forms of fusion in the first, 7.9% for the second, and 10.5% for the third. In the eighty-seven experiments of the series there is but one absolute return to the previous starting-point. (See Group IX, sec. 2, Bl.) The tables show the varying degrees of fusion, and while the percentages have little meaning, as there is a variable time-element, the numbers do show accurately the number of words and the relative and continued influence of each starting-point.

We conclude that, when the present content of consciousness is a series of associations, the newly given impression establishes itself sufficiently to inhibit the associations of the previous series.

TABLE XV. TWO WORDS--GENERAL AND PARTICULAR--SPOKEN

Time--50 seconds, with an interval of 10 seconds between 1 and 2. Characters--same as Table I.

(1) Commencement--Sieve

M. | | | - - - - - - - - - - - - - - F. | | | | | | + + + + + + + H. | | | | | - - - - - - - - - - - - V. | | | | | - - - - - - - - - - - - S. | | | | | | | | - - - - E. | | | - - - - - - - - - Bs.| | | - - - - - - - - - - - - - - Ht.| | - + + + + + + By.

| - + α β M. { 3 14 0 0 0 {17.6% 82.4%

F. { 6 7 {46.2% 0 53.8% 0 0

H. { 5 12 0 0 0 {29.4% 70.6%

V. { 5 12 0 0 0 {29.4% 70.6%

S. { 8 4 0 0 0 {66.6% 33.4%

E. { 3 9 0 0 0 {25.0% 75.0%

Bs. { 3 14 0 0 0 {17.6% 82.4%

Ht. { 2 1 6 0 0 {22.2% 11.2% 66.6%

By. 0 0 0 0 0

Totals {35 66 13 0 0 {31.4% 55.4% 13.2%

Number of subjects, 9; number of groups, 1; number of experiments, 8; number of associations, 114.

TABLE XVI. THREE WORDS SPOKEN

Time--50 seconds. Interval, 15 seconds.

Characters: | first, - second, / third, + partial fusion between first and second, α partial fusion between first and second with first predominating, β partial fusion between first and second with second predominating, γ partial fusion between first and third, δ partial fusion between second and third, ε partial fusion between first and third with third predominating.

(1) Gun--Bug--Jaw

M. | | | | | | | | - - - - - - / / / / / / F. | | | | | - - - δ δ δ H. | | | | | | - - - - / / / / / V. | | | | | | | | - - - - - - / / / / / / Bl. | | | | | | - - - - - / / / / / / / By. | | | | | | | | | - - - - - - / / / / / / Bs. | | | | | + + + + / / / / / Ht. | | | | | | | α | | | δ - - - - Ro. | | | | | | - - - - - - / / / / / /

(1) Gun--Bug--Jaw (2) Quill--Bench--Chalk (3) Hall--Moss--Leather

| - / + α β γ δ ε

M. {20 14 18 1 0 0 0 0 0 {37.8% 26.4% 33.9% 1.9%

F. {15 11 15 0 0 0 2 3 0 {32.6% 23.9% 32.6% 4.4% 6.5%

H. {19 11 15 0 0 0 0 0 0 {42.3% 24.4% 33.3%

V. {24 15 21 1 0 4 0 0 0 {36.9% 23.1% 32.3% 1.5% 6.2%

Bl. {15 9 9 0 0 0 0 0 0 {45.4% 27.3% 27.3%

By. {23 8 14 3 0 4 0 3 0 {41.8% 14.5% 25.5% 5.5% 7.2% 5.5%

Bs. {13 10 10 4 0 0 0 0 5 {30.9% 23.8% 23.8% 9.6% 11.9%

Ht. {23 11 10 1 1 2 0 1 0 {46.9% 22.5% 20.5% 2.0% 2.0% 4.1% 2.0%

Ro. {15 15 24 0 0 0 0 0 0 {27.8% 27.8% 44.4%

Totals {167 104 136 10 1 10 2 7 5 { 37.8% 23.5% 30.8% 2.3% .2% 2.3% .4% 1.5% 1.2%

Number of subjects, 9; number of sections, 3; number of experiments, 27; number of associations, 442.

TABLE XVII. FOUR WORDS SPOKEN

Time--50 seconds. Interval, 10 seconds.

Characters -- same as Table XVI, with addition of \ representing the fourth, ς partial fusion between first and fourth, η partial fusion between second and fourth, θ partial fusion between third and fourth, ☐ total fusion between first, second, third, and fourth, ι partial fusion between first, third, and fourth, κ partial fusion between second, third, and fourth, λ partial fusion between third and fourth, with fourth predominating, [ partial fusion between first, second, and third.

(1) Den--Nag--Cot--Fan

F. | | | | | | - - - - - - δ - - \ \ \ \ \ H. | | | | | - - - / / / / / / \ \ \ \ \ \ \ \ \ V. | | | | | - - - / / / / \ \ \ \ \ \ \ Bl. | | | | - - - - / / / \ \ \ \ By. | | | | | | - - - - - δ δ δ \ \ \ \ \ Bs. | | | - - / / / \ \ \ \ \ Ht. | | | | | - - - - - / / / / \ \ \ \ Ro. | | | | - - - - / / / / \ \ \ \ \

(1) Den--Nag--Cot--Fan (2) Tax--Fan--Map--Dog (3) Paw--Wand--Box--Mug (4) Bud--Car--Cub--Mat (5) Wax--Jug--Tar--Sod (6) Cur--Elk--Pug--Man (7) Rope--Wig--Ink--Grass

(_Table on page 460_)

GROUP IX

The aim here was to see if it were possible to have the first starting-point such that the conditions would be similar to the results obtained by using preparatory marginal settings, but include rather than inhibit the second starting-point. A review of the tendency toward mental combination in the former experiments suggested that the words be in the relation of the whole and part. The "part" was given the position of predominating influence in order to see to just what extent it would persist in combining.

| -- / \ + γ δ ς η θ

F. { 29 19 11 19 3 0 4 0 0 11 { 30.3% 19.8% 11.4% 19.8% 3.1% 4.2% 11.4%

H. { 31 18 24 25 3 0 0 0 0 8 { 28.5% 16.5% 22.1% 22.9% 2.7% 73%

V. { 28 28 21 50 0 0 0 0 0 0 { 22.0% 22.0% 16.6% 39.4%

Bl. { 18 17 17 29 0 0 0 0 0 0 { 21.6% 20.5% 20.5% 34.9%

By. { 36 22 9 24 2 4 3 0 6 2 { 32.1% 19.6% 8.0% 21.4% 1.8% 3.7% 2.6% 5.3% 1.8%

Bs. { 22 13 17 18 4 1 0 1 0 6 { 24.2% 14.3% 18.7% 19.8% 4.4% 1.1% 1.1% 6.6%

Ht. { 30 18 10 21 3 0 0 0 2 1 { 34.4% 20.6% 11.4% 24.2% 3.4% 2.4% 1.2%

Ro. { 24 22 16 48 0 0 3 0 0 0 { 21.3% 19.4% 14.2% 42.4% 2.7%

Totals{218 157 125 234 15 5 10 1 8 28 { 26.6% 19.2% 15.2% 28.5% 1.9% .6% 1.3% .2% .9% 3.4%

☐ ι β κ λ [

F. 0 0 0 0 0 0

H. 0 0 0 0 0 0

V. 0 0 0 0 0 0

Bl. 0 0 0 2 0 0 2.5%

By. 4 0 0 0 0 0

Bs. 0 3 1 0 5 0 3.3% 1.1% 0 5.4% 0

Ht. 0 0 0 0 0 2 2.4%

Ro. 0 0 0 0 0 0

Totals{ 4 3 1 2 5 2 { .4% .3% .2% .3% .7% .3%

Number of subjects, 8; number of sections, 7; number of experiments, 52; number of associations, 819.

In the light of the interpretation of previous facts and the subsequent results of this group of experiments, we are now in a position to conclude that, if the present content of consciousness on the reception of a new impression is such that the reactions are not antagonistic but reënforce each other, the second will not persist in independent influence, but will be rather included in and supplementary to the influence of the first, which otherwise would be less assertive. The results below show that while the first of the two starting-points has a decided disadvantage of position, and therefore has little influence in arousing associations, it here is responsible for 43.2% and the second for but 9.5%, while there is a combined influence of 47.3%, the first strongly predominating in partial fusion. There is but one case where the second was followed exclusively.

The explanation of this, extended to an hypothesis, would rest in the fact that each word has definite characteristic reactions and that the fusion of two words or lines of thought means that the motor accompaniments are such that they unite and reënforce each other, or that the one includes the other. There are few antagonistic impulses.

TABLE XVIII

TWO WORDS--WHOLE AND PART--SPOKEN

Time--15 seconds. Characters--same as Table I.

(1) Crowd--Man

A. | + + M. + + + + + + + + + F. + + + + + H. J. | | | | | | + + + S. - - - - V. + + + α α α α α α E. | + + + L. | | | | Bs. α α α α α α Br. | | | | | + +

(1) Crowd--Man (2) Ton--Pound (3) Moose--Horn (4) Engine--Whistle (5) Book--Page (6) Music--Octave

| - + α β

A. { 4 3 24 0 0 { 12.9% 9.6% 77.5%

M. { 13 0 27 2 0 { 30.9% 64.2% 4.9%

F. { 7 3 22 1 0 { 20.6% 8.8% 64.8% 5.8%

H. { 28 5 0 0 5 { 73.6% 13.2% 13.2%

J. { 21 1 17 6 0 { 46.6% 2.3% 37.8% 13.3%

S. { 25 12 0 0 0 { 67.5% 32.5%

V. { 4 2 16 10 0 { 12.5% 6.3% 50.1% 31.1%

E. { 11 3 9 5 0 { 39.2% 10.8% 32.2% 17.8%

L. { 14 6 4 0 0 { 58.4% 25.0% 16.6%

Bs. { 15 2 11 6 0 { 44.2% 5.8% 32.4% 17.6%

Br. { 25 0 9 9 0 { 58.2% 20.9% 20.9%

Totals { 167 37 139 39 5 { 43.2% 9.5% 35.9% 10.0% 1.4%

Number of subjects, 11; number of sections, 6; number of experiments, 62; number of associations, 387.

GROUP X

In the last group the words were called whole and part, although the reader no doubt observed that this was not always strictly the case, but rather that the more complex was more influential as a word-suggester than the simple and often tended to include it. Can this be demonstrated in another way? Attention was called in Group of Experiments IV (two pictures shown) that picture no. 3 (a man sawing wood), although first, had more than the normal number of associations, the explanation of which might lie in the fact that it contained more objects. We here attempt to test this by comparing a comparatively complex and a comparatively simple picture as starting-points. It has been clearly proven that the second picture to be presented has a decided advantage of position. The simple picture is here given the advantage of position. The notes show the first to be more important, while there is no suggestion of the first including the second, on account of there being less fusion than for words and more independent associations for the second starting-point; the averages are 38.5% for the first, 30.5% for the second, 31.0% fusion.

(a) Picture of Blacksmith shoeing horse (b) Picture of a Sheep. | shop (a) | nails shop | shoe shop and (a) | blacksmith shop and shoe and (a) | Longfellow blacksmith - pasture (b) - sheep pasture - lambs pasture and sheep - grass pasture and lambs - hillsides grass - brook pasture and hillsides | iron shop-shoe | hammering iron | soldier iron-hammering and first group | battle soldier | shoe battle | horse-shoe nail iron, hammering, soldier, battle | anvil horse-shoe nail

TABLE XIX. TWO PICTURES SHOWN

Time--50 seconds. Characters--same as Table I.

(1) (a) Blacksmith shoeing Horse (b) A Sheep

J. | | | | | - - - - - - | | | | | | | E. | + + - - | | | W. | - | - - - | | | | | | | V. | | + + + + + + + + + + + + + L. - | | | | | | | | Ht. - - α α | | | | - + + + + +

(1) (a) Blacksmith shoeing Horse (b) A Sheep

(2) (a) Girl and Boy (b) A Bird

(3) (a) Three Children (b) A Duck

(4) (a) A Sower (b) A Dog

| - + α β

J. { 30 23 9 18 0 { 37.5% 28.8% 11.2% 22.5%

E. { 28 10 2 0 0 { 70.0% 25.0% 5.0%

W. { 14 18 5 0 0 { 37.8% 48.7% 13.5%

V. { 6 11 37 0 13 { 8.9% 16.4% 55.3% 19.4%

L. { 27 4 1 0 0 { 84.3% 12.5% 3.2%

Ht. { 16 30 6 6 0 { 27.6% 51.8% 10.3% 10.3%

Totals {121 96 60 24 13 { 38.5% 30.5% 19.2% 7.6% 4.2%

Number of subjects, 6; number of sections, 4; number of experiments, 24; number of associations, 314.

GROUP XI

Three words spoken, one immediately following the other, are given in this group in order to test the span of consciousness and the influence of an immediate interruption, as one was given immediately following the other in such a way that all associations were checked until after the third starting-point. If we attempt to follow the initial starting-points we see they may disappear after the first few associations and reappear in the series; or each remain as initial starting-points for a few associations; or one alone control the whole series, while the others are present without influence; or there may be an alternation of independent influences; or an influence which shows a modifying effect of one or both of the other starting-points, which may reach such a degree that all fuse, and in so doing get an advantage over the single words. The starting-points are to a large extent disparate and there is very little fusion; we find only .5% total fusion and 18.7% partial fusion.

An example would be as follows:

SUBJECT VIII

FROG--ICE--TABLE

- snow ice | bench table | fish frog | pole fish | boat fish | line fish | bait fish | weeds fish - skating ice - sleds ice - coasting sleds - girls coasting

There were no cases of the total fusion of all the starting-points throughout the series, no cases of total fusion of the first and second, and two cases for the second and third. There were two cases of partial fusion of the first, second, and third throughout. The first was followed exclusively in two cases, the third in one. The first and third were followed intermittently in four cases, the second and third in eleven, the first, second, and third in thirty-five.

The second starting-point has the ascendency of influence. This is not due to habits formed in earlier experiments, as the two groups of experiments with two words were given in connection with other experiments. This group informs us that in immediate interruption the new impression has not sufficient power to establish itself more firmly than a past impression which is just past, and must in a manner be reproduced to start associations. The influence of the first has been somewhat destroyed, but the second is greater than the third.

TABLE XX. THREE WORDS SPOKEN

Time--50 seconds.

Characters--same as Table XVI, with the addition of [ representing total fusion between the first, second, and third, μ partial fusion between first, second, and third with first predominating, ν partial fusion between first, second, and third with first and third predominating.

(1) Frog--Ice--Table

A. / - - - - - M. - | | γ γ γ γ γ γ γ γ γ F. - - - - - / / | | | | / / / - - - H. | - - - - - | | | | / / / - - - J. | - - / / / / - + + + + + + + + Bl. - / | | | | | | - - - - By. | / / / / / / - - - - - - - - - - - - - - - - Bs. - | | | - - - / / Ro. | | - - / / / / / / / / / / / Br. - / / / δ δ δ δ δ δ

(1) Frog--Ice--Table (2) Key--Shoe--Knife (3) Desk--Park--Glove (4) College--Church--Cafe (5) Boston--Elevator--Lake (6) Skate--Book--Theatre (7) Bridge--Sleigh--Ticket (8) Gun--Lamp--Watch

| - / + α β γ δ [ μ ν A. { 26 32 30 0 0 0 0 0 2 10 0 { 26% 32% 30% 2% 10%

M. { 25 36 21 3 0 0 10 1 1 0 6 { 24.3% 34.9% 20.5% 2.9% 9.8% .9% .9% 5.8%

F. { 15 23 24 8 11 0 7 6 0 0 0 { 15.9% 24.5% 25.5% 8.5% 11.8% 7.4% 6.4%

H. { 31 68 31 0 0 0 0 0 0 0 0 { 23.8% 52.4% 23.8%

J. { 19 18 48 15 0 0 0 22 1 0 0 { 15.5% 14.6% 39.1% 12.2% 17.8% .8%

Bl. { 23 33 16 5 0 0 0 22 0 0 0 { 23.2% 33.2% 16.0% 5.0% 22.6%

By. { 13 56 48 15 0 1 17 2 0 0 0 { 8.7% 36.8% 31.5% 9.8% .6% 11.2% 1.4%

Bs. { 19 13 19 9 0 0 0 19 2 0 0 { 23.4% 16.0% 23.4% 11.2% 23.5% 2.5%

Ro. { 32 33 33 0 0 0 0 0 0 0 0 { 32.6% 33.7% 33.7%

Br. { 12 24 38 0 0 0 6 0 0 0 0 { 15.0% 30.0% 47.5% 7.5%

Totals{215 336 308 55 11 1 40 72 6 10 6 { 20.3% 31.1% 29.1% 5.2% 1.1% .9% 3.6% 6.8% .5% .9% .5%

Number of subjects, 10; number of sections, 8; number of experiments, 79; number of associations, 1060.

GROUP XII

In order to test the relative influence and to throw more light on the problem of immediate interruption four words were shown and the subject was directed to read from left to right. There were few experiments and most of the subjects were new. The results show that the third starting-point has a decided disadvantage, having an influence of only 7.8%. The second and fourth are almost equal, while the first is again less.

TABLE XXI. FOUR WORDS SHOWN

Time--50 seconds.

Characters--same as Table XVII, with the addition of ξ partial fusion between the second, third, and fourth with the second predominating.

(1) Gun--Car--Ink--Fan

M. \ \ \ - - - - - / / / / / / R. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ S. - | / - - - - - - - - J. | | | - - - - - - - - - - - Ht. + + α α α | | | | | | | | |

(1) Gun--Car--Ink--Fan (2) Brain--Umbrella--Telephone--Chain (3) Book--Money--Hour--Chart

| - / \ + γ θ α κ ξ M. {14 6 9 4 0 6 0 0 0 0 {35.9% 15.4% 23.0% 10.3% 15.4%

R. {16 0 0 30 0 0 0 0 0 0 {34.8% 65.2%

K. { 0 35 0 16 0 0 0 0 0 0 { 68.6% 31.4%

S. { 5 15 7 4 0 0 0 0 0 0 {16.2% 48.4% 22.5% 12.9%

J. {13 13 4 15 2 0 0 0 0 0 {27.7% 27.7% 8.5% 31.9% 4.2%

Ht. {15 9 0 5 2 0 7 3 1 1 {34.8% 20.9% 11.6% 4.7% 16.3% 6.9% 2.4% 2.4%

Totals{63 78 20 74 4 6 7 3 1 1 {24.5% 30.4% 7.8% 28.5% 1.6% 2.4% 2.6% 1.4% .4% .4%

Number of subjects, 6; number of sections, 3; number of experiments, 18; number of associations, 257.

GROUP XIII

Four similar words were pronounced in immediate succession, the results of which show that we are correct in calling the above a case of succession and also to establish clearly and definitely that there is a difference of degree between immediate and postponed interruption. The third starting-point has again a decided disadvantage of influence and exerts no apparent influence in thirty-seven of the fifty-two experiments. The last starting-point exerts the greatest influence.

TABLE XXII. FOUR WORDS SPOKEN

Time--50 seconds.

Characters--same as Table XVII with the addition of ο partial fusion between first, second, and third with first and second predominating.

(1) Cow--Roof--Fence--Girl (2) Cathedral--River--Elevator--Newspaper (3) Cane--Harness--Box--Coat (4) Book--Snow--Rope--Stone (5) Wire--Flower--Horse--Paper (6) Gun--Wharf--Chair--Stove

| - / \ + λ δ η θ ☐ ι ο ε β M. { 35 3 6 32 0 3 17 0 9 0 0 0 0 0 { 33.4% 2.8% 5.8% 30.4% 2.8% 16.2% 8.6%

F. { 16 11 1 35 0 3 0 0 1 2 1 0 5 0 { 21.3% 14.6% 1.4% 46.6% 4.0% 1.4% 2.7% 1.4% 6.6%

H. { 21 38 11 30 0 0 0 0 0 0 0 1 0 1 { 20.6% 37.3% 10.8% 29.5% .9% .9%

V. { 16 16 0 36 2 2 9 0 1 0 1 0 0 0 { 19.3% 19.3% 43.3% 2.4% 2.4% 10.9% 1.2% 1.2%

Bl.{ 36 8 10 19 0 0 4 0 0 0 0 0 0 0 { 46.8% 10.3% 12.9% 24.8% 5.2%

By.{ 23 30 3 36 1 0 0 0 1 0 0 0 0 0 {24.5% 31.9% 3.3% 38.3% 1.0% 1.0%

Bs.{ 22 14 1 20 1 0 0 7 0 1 0 0 0 0 {33.3% 21.3% 1.6% 30.0% 1.6% 10.6% 1.6%

Ht.{ 9 19 4 31 0 0 0 0 1 14 0 0 0 0 {11.5% 24.3% 5.2% 39.8% 1.3% 17.9%

Ro.{ 26 23 6 16 0 0 0 0 0 0 0 0 0 0 {36.6% 32.4% 8.4% 22.6%

Totals {204 162 42 255 4 8 30 7 13 17 2 1 5 1 {27.2% 21.6% 5.4% 33.9% .5% 1.1% 3.9% .9% 1.8% 2.3% .3% .2% .7% .2%

Number of subjects, 9; number of sections, 6; number of experiments, 52; number of associations, 751.

We ask finally how far our results and notes point to a theoretical understanding of the mechanism of associations. Previous work, especially that of James, Cordes, Calkins, and Scripture, as well as the accumulated notes of my subjects, confirm that the transition may be made by means of total, partial, and focal recall, and that in partial and focal recall the prominent persisting elements are surrounded in the formation of a new idea by other new elements.

If a latent idea remains in the margin of consciousness and exerts an influence, which not merely modifies but determines the series of associations, and leads up to the focalisation of the latent idea, we have a case of predetermined association, which, when noted by investigators, has invariably become confused with mediate association. Here there is an element or group of elements, persisting in the margin of consciousness, which is gradually maturing and becoming focalised into groups of elements comprising an idea which ultimately dominates consciousness. In some cases three, four, and five ideas have been named before this takes place, and we have here a reversed form of association. Four subjects noted the experience on different occasions, and it is not to be confused with the common experience of apprehending the present contents of consciousness as part of a larger whole where we are conscious of its existence but not of what it is.

The notes further show that the common conscious elements may be predominantly visual, auditory, olfactory, gustatory, or kinæsthetic, or a complex or compound of these in character, while to this may be added an indication of the fact that the transition, incipient as it is, may in many cases be reduced to a condition which is in the last analysis one of the motor nervous system. Ht., for instance, finds that the words all pass over into innervations of the organs of speech and "are accompanied by the impulse to make the sound," stating later, "they hang on the tongue." The following is one of the series given which represents rather an extreme case, Taft, taffy, toffy; tough, rough, ruff; buff, bluff, tough; muff, duff, tuff. Br., who also gave a large percentage of verbal associations, finds that "some part of each word seems to linger on the tongue with motor sensations till the next comes." "I am subject," he adds, "more or less frequently to verbal automatism of this auditory incipient motor type." Ro., who has many auditory associations, reports "they are always accompanied by motor images, together with many associations." A changing of orientation is a common accompaniment, with statements of the feeling of the impulse to turn in various directions. For F., who is predominantly of the motor type, we have an example where the rhythmic ticking of a clock fades into the rhythmic watching of a boat rising and falling on the water.

The notes would seem to indicate that there is no idea without a motor fringe, and also that these elements of incipient impulses to movement may accompany the elements of transition, and are observed introspectively by the subjects. They are therefore data for psychology. Do they influence or direct the associations? In short, are they the processes which connect and which determine the associations?

F. states, "There seem to have been waves of motor sensations. Such waves may start with a word and carry one in faint mimicry through the whole succession of bodily sensations that one experienced in that event, and then may come a relapse until other stronger currents appear." Here we are face to face with the dynamics of association, the most fundamental and important problem of brain association. Have these phenomena of ideational images "acquired by contact a kind of magnetism which causes the one to attract the other and have, so to speak, become magnetic?" (Zanotti.) Or are they on the other hand independent of all force and "merely ideas of antecedence and sequence only?" (Mill.) While there is no mention of a magnetic force, the notes and results all show that the ideas are systematically conditioned in a way which cannot be explained by the contiguity of the objects. The motor elements play the deciding role. Ht. emphasises the influence of ideated movement when he writes, "Kinæsthetic. Slow regular tramping on snowshoes brought up the characteristic swing of arms, and therewith the idea (sensations of weight) of the stick (or stock) which I have generally carried on Norwegian snowshoes. Transition from Vermont to the Black Forest by association with snowshoeing in both places. Real sensations in play were free breath, movements in chest (kinæsthetic), fresh air (olfactory), cold (thermal), and emotion of emotional strength." Again, "Looking up at sun suggested general ideas of expansion of attention and with this breath comes the idea, breezes"; another subject adds, "A tendency to imitate the sounds of syllables and this leads on to a train of associations"; another, "A slight feeling of sudden changed impulse"; another, "A sort of motor after-image came back and took the foreground"; and F. goes further when he states, "Ideationally my hand wandered to the upper right-hand corner of the page, then suddenly the auditory image of 47 came up as if whispered to me." All of which indicate that some ideas at least depend for their entrance into consciousness upon motor reactions.

Passing to the more refined reactions expressed in emotions we find that they are not merely accompanying coloring influences, but also often actual determining factors. All of the subjects notice at some time a coloring atmosphere from an emotion, but others find that "the growing word is rather felt emotionally than definitely formulated," and we have "a nameless idea, largely feeling-tone" (Ht.); or the words may "all come as parts of a growing feeling, an indistinct though strong state of mind." (J.) The same subject observed, "The previous word may create a mood or feeling which in the main determines the associations; a group of words is dependent upon strong accompanying feeling--there is a summation and a discharge while the next word has been accumulating force" (J.), and we have a form of summation; or in other words, "a general mood accumulated while several words were in mind at once, then all dropped and another general feeling came to the front with an accumulation of other words." (F.) Here we have a typical example of constellation where all the words and ideas are implicitly present as a total attitude or disposition, the elements of which become successively focalised into a series of associated images. The last subject finds that "the emotional atmosphere often controls the associations." Indeed, it would seem that occasionally for some subjects this strong accompanying undercurrent of undifferentiated emotional feeling is capable of bringing about trains of thought independent of any logical connection. K. finds "the feeling to carry one on"; H. finds the "point of departure the interesting idea"; all find that the words change with the disposition, as may be verified by a study of the lists of associations.

We are forced to conclude that the impulses to movement or other emotional attitudes may act as determining factors in association, which extended to an hypothesis would mean that the mode of transition in the associated series is in the last analysis to be found in delicate incipient motor tendencies to action, the psychic concomitants of which are observable; that psychic states are both as to their unity and organisation consequences of motor reactions which are implicitly present as parts of a total reaction to the present situation. It is these motor tendencies to action which determine what idea shall enter consciousness. Just in so far as they become released they become prolonged, accentuated, and form a nucleus for the new idea. To speak of association independent of motor elements is merely to make an empirical classification of successive states of consciousness.

There remains a psychical phenomenon which must be satisfactorily accounted for before we go farther. An element of an idea, an idea or a series of ideas may occupy consciousness to the exclusion of others. If the second starting-point were not given, the associations would undoubtedly follow the given one. Inhibition must then be one form of "obstructed association," the inhibiting ideas being present to the exclusion of the inhibited. But are we thus forced to say inhibition is the "negative side of the association process," claiming that all ideas not in consciousness are inhibited, and thus being forced to conclude the conscious idea is inhibiting an unconscious idea, which cannot exist (by the very definition and presuppositions of psychology) until it is an object of consciousness. This would mean that content of consciousness and inhibition are identical. On the other hand, the notes and exemplifying facts of the tables show Dr. Breese's fallacious position when he concludes that "because, obeying the laws of association, the train of ideas takes one direction rather than another can hardly be considered sufficient ground to hold that the other possible train of ideas is inhibited."[137] He has overlooked the possibility of two or more trains of associations having been started and the associations of one starting-point are excluded from entering the focus of consciousness by the direction of the given series. Inhibition would then be the negative side of fusion. The explanation must, as has already been demonstrated, be psycho-physical in character. If these impulses to action have actually been observed by the subjects we are justified in concluding that just as in physiological inhibition one action excludes another, so the correlative tendencies to movement of one idea exclude others.

By. observed that the image of the starting-point lingered and inhibited subsequent ideas. The implication here, from our previous reasoning, would be that not the ideational images, as such, but the physiological motor concomitants, persisted and excluded others, and this is why disparate terms give a "shock to the nervous system" (A.), "require different lines of expression" (A.); and "one has more momentum," as so many report. This would explain why the associations of a new starting-point inhibit the associations of a former one; for as the motor nervous impulses tend to work themselves out into action, the reaction of the previous impulse will be suppressed by those of a new impulse which enters, by the conditions of these experiments, an attentive consciousness. Thus the prepotent impulses to action are the conditioning factors in mental inhibition.

All this indicates that the basis of habit which has been the universal principle of explanation of associations is inadequate. As Münsterberg has pointed out, contrary to what we mean by habit, either idea may bring to consciousness the other, in a manner independent of the order of the original presentation. Extending our hypothesis to include the formation of associations, the conclusion will be that in order for two ideas to become associated they must be together in consciousness, each as parts of a total experience, a total attitude; the motor reactions of the ideas must be parts of a more comprehensive reaction which includes both as simultaneous correlated motor impulses: when, in future time, the reactions of the one are reëxperienced, there is a sequence of infinitely delicate and complex impulses to movement, and any tendency toward such reaction tends to reproduce the whole of which it is a part, as each reaction is more or less bound up in the integrity of the whole central nervous system.

FOOTNOTES:

[Footnote 133: Cordes, G.: Experimentelle Untersuchung über Association, Phil. Studien, vol. 17, p. 30.]

[Footnote 134: Scripture, E. W.: Elements of Experimental Phonetics, p. 142.]

[Footnote 135: Calkins, M. W.: Memory and Association, Psychol. Rev., vol. 5, p. 451.]

[Footnote 136: Calkins, M. W.: Association, Psy. Monograph, no. 2, p. 46.]

[Footnote 137: Breese, B. B.: On Inhibition, Psy. Rev. Monograph, vol. 3, p. 15.]

DISSOCIATION

BY C. H. TOLL

The purpose of this investigation, of which the following gives a preliminary report, was to compare the tendency to associate by contiguity, with the tendency to associate by similarity.

In every series of stimuli to which one gives attention there is tendency to association by contiguity. But some similarity among certain elements of the series may produce a dissociation of the given elements into two series with some bond of similarity in each. This is a matter of common experience, as when you find you can read your newspaper and listen to your neighbors' conversation at the same time, understanding both, although the actual order in which the several words are perceived would form a meaningless mixture.

We may say dissociation is always accomplished by a tendency to association by similarity overcoming the constant tendency to association by contiguity. Study of the relative efficacy of the two may therefore be called a study of dissociation. The tendency to associate by contiguity might be measured in two ways.

First, when one attempts to learn a series in exactly the given order, the number of errors in the series as recollected may be taken as an inverse indication of the strength of association by contiguity. The three kinds of error possible in nearly all of the experiments were Omissions, Displacements, and Imperfections. All of these three have been tabulated. But the number of elements omitted seems considerably the most reliable as an indication of the degree of inadequacy of the associative tendency. The cases of displaced or imperfect elements are comparatively few: moreover, Displacements and Imperfections are not mutually exclusive categories. A single element may be both imperfectly recollected and wrongly placed in the recollected series. On the whole, it seems that the number of given elements which were omitted in the recalled series is the most positive and reliable of the errors. Our conclusions are based on the Omissions.

Second, when one makes no attempt to learn the series, simply giving attention to each element as it comes, and afterward lets the elements recur spontaneously, the number of cases in which a recollected element is followed by an element given contiguously may be taken as a direct indication of the strength of association by contiguity.

Tendency to association by similarity can evidently be measured in the same two ways, by counting errors when one purposes to learn the series as two groups of similar elements, and by counting sequences of similar elements when one avoids any effort to learn the series and recollection is spontaneous.

In the first seven experiments we used the first method. The errors made when the purpose is to associate by contiguity can then be compared with the errors made when the purpose is to associate by similarity, an equal number of series, given under the same conditions, and of identical character, being given in each case.

In the last four experiments we have used the second method. The number of sequences of elements given contiguously can then be compared with the number of sequences of similar elements.

Five subjects have coöperated in this, but the experiments were strictly individual, one observer being alone in the room with the experimenter. Each test lasted about an hour. As a matter of course, the results have been calculated for each of the five subjects and their agreements and disagreements have been carefully considered. But as this first report is to indicate merely the general tendency, we give here at first only the average of the five persons.

The experiments have varied as to the kind of elements used, the manner of presentation, the time allowed, and the manner of recording the recollected series. But throughout each experiment the series were of one identical type, while the individual elements were altered in each series.

In the experiments where the series were to be learned, some in the given order, some dissociated by similarity, it was found rather confusing to turn from one method to the other; so several consecutive series were learned by one method, and then several by the other, four alternations being made each hour to neutralize any effect of practice or of fatigue.

The series were of course different in kind in the several experiments, but were usually of eight or of ten elements. Half of this number had some distinct characteristic in common, the other half some other characteristic. In some experiments these elements were alternated, in some arranged irregularly.

In the first eight experiments the subject wrote down the elements recalled, as soon as the series had been given. In the last three the subject spoke the elements recalled.

In all cases where the first method of measurement was used, the time allowed for learning the series was made a little too short to permit of learning the series perfectly. Since comparison of the number of mistakes was our method, we naturally had to make sure there would be mistakes to compare.

The details of the several experiments were as follows:

(1) The elements were letters and numbers. They were about 12×8 mm. in size and were printed on white cards 15×30 mm.

Five letters and five numbers were placed, alternately, in a straight row on a sheet of white cardboard. The series was then exposed to the subject by turning up the small tin shutter of a screen that was clamped to the table-edge.

The time of exposure was measured with a stop-watch and was constant throughout the hour for each individual subject. Four seconds proved the best time for most of them, but in one case it was necessary to allow only three seconds. Twenty series were presented during each hour, ten for each method of memorizing. There were duplicates of all the numbers, and of eight letters, but not more than two of any element. Selection in forming the series was by chance. In dissociating, the letters were separated from the numbers.

As soon as the exposure was ended, the subject wrote down the elements recollected, trying to preserve their relative order. This recollected list was then copied beside the operator's record of the given series, so making the errors apparent.

(2) The elements were all letters, printed as before, and the alternate cards were placed half their length out of alignment with the original row.

The method of presentation, the length of exposure, the number of elements presented, etc., were as in no. 1. In dissociating, the letters on one level were separated from those on the other.

(3) The elements were all letters, printed as before, and five of the ten elements presented were placed out of alignment. But the disaligned cards were at irregular intervals and often in groups, and were only a quarter of an inch out of alignment. This order was varied each time, but without any system.

The other details were as in no. 1.

During this experiment I came to notice the effect produced by the natural tendency to learn the five elements of the dissociated series in a rhythmical form, thereby increasing the ability to retain them; while there appeared to be no natural tendency to apply any such inclusive rhythm to the ten elements of the series when learned in the given order. To counteract this effect the subjects were instructed to consider the series, when learned in the given order, as two consecutive series of five elements each, and to use the same natural rhythm in learning these as they did in the dissociating. But this correction was not made in the first two hours, nor very perfectly in the rest.

(4) The elements were all numbers, printed as before, five of the ten being placed a quarter of an inch out of alignment, and in irregular groups, precisely as in the last experiment.

The time was reduced to three seconds for some and two seconds for the others. Details of presentation were as described in no. 1.

This time all the subjects tried to neutralize the effect of the instinctive rhythm for the five-element series by learning the ten-element series in two groups of five elements each.

(5) The elements were all nonsense syllables, each consisting of a vowel between two consonants, printed on white cards 20×20 mm. Eight of these were placed in an even row on a sheet of white cardboard, and four of them were marked by laying a quarter-inch strip of blue paper over the bottom of the card. The serial position of the marked cards was irregular, and was altered each time.

Ten seconds was given to some subjects, eight to the others. Other details of exposure, etc., were as in no. 1.

In learning the series in the given order, the blue markings were ignored; but in dissociating, the marked and unmarked syllables were learned in separate groups.

There seemed to be no rhythmical tendency; but to be safe the subjects were instructed to learn the straight series in groups of fours.

Seven series were given to be learned in each method during the hour with each subject.

(6) The elements were one-syllable nouns, alternated with nonsense syllables, all spoken by the operator. The nonsense syllables were all different from those used in the preceding experiment: the nouns were ordinary words, and were so arranged as to avoid any obvious sequence or relation among them. Very few, if any, were used twice in one hour. Five nouns and five syllables were given in each series.

The elements were spoken at the rate of forty-six a minute, timed by a metronome which was muffled in a heavily padded box so that its sound was no disturbing factor. The speaker sat within three feet of the subject and enunciated as distinctly as possible.

Dissociation was performed as previously: in each hour eight series were dissociated, and eight learned in the given order.

(7) The elements were one-syllable nouns, spoken as before, alternated with nonsense syllables, printed on small white cards. The nouns were all different from those used in the previous experiment: the nonsense syllables were the same, but were this time printed, in letters 10 mm. high, on cards 40 mm. square. They were exposed by sliding them, one at a time, in front of an opening in a cardboard screen which was fastened to the table-edge.

The optimum rate for presenting the elements was found to be about forty a minute, measured with the metronome.

Five nouns and five nonsense syllables were given in each series. Eight series were given to be learned in the given order, and eight to be dissociated into separate series of nouns and of syllables.

(8) The elements were names of mammals, alternated with names of cities of the United States, all spoken. The names were all fairly familiar. Ten elements were given in each series.

The interval in reading was planned to be long enough for some appreciation of the meaning of the words, but not enough to permit mental repetition of the preceding elements. Any mechanical time-measurement was found impracticable.

The subjects were instructed to avoid any effort to memorize the series, simply receiving each element as given.

After the last element there was a pause of about two seconds, to decrease the mere sound-recollection of the last few elements. Then the operator repeated, in an altered tone, one of the given elements. The subject at once wrote down the first element that came to mind, then the next, and so on.

In the seven preceding experiments the set of series presented had been different for each subject, though of course identical in character. But in this experiment and the following ones the lists of words were identical as read to each subject. The same element was repeated for each. Sixteen lists were given.

(9) The elements were nouns. In each series five names of similar objects were alternated with five names of a different sort of objects, _e. g._, names of fishes with names of poets. All were read, as before. In each series new sorts of objects were chosen. The subject never knew what sort of words were to be given; the subjects agreed this was not a disturbing factor to them, and it obviated the tendency to think what words would probably be given, as is natural when the general character of the series is announced beforehand.

The subjects were instructed to be passive during the reading, and during the four-second pause that followed, avoiding mental repetition of the words. Then the operator gave a signal and the subject repeated aloud the words as they happened to be remembered. The words being numbered on the list from which they were read, the operator was able to record the words as fast as spoken.

The subjects were instructed to give the word which they found to be foremost after they had spoken the preceding one, rather than to try to repeat a group of words which usually appeared simultaneously at the first effort of recollection, but which usually faded while one of them was being spoken.

The same sixteen series, of ten elements each, were given to each subject.

(10) The elements were nouns, the ten presented in each series all being names of similar objects, _e. g._, flowers. Five were spoken, alternated with five printed on small cards which were shoved in front of a 10×10 cm. opening in a cardboard screen fastened to the table-edge. Cards were 40 mm. square, the words printed by hand, but carefully, in letters 10 mm. high.

A series was given in about 13 seconds, but the time was not mechanically measured; it was at a rate which some practice showed to give a fair time to comprehend each element.

As before, the subjects were told to be passive until, after a four-second pause at the end of the series, the operator gave a signal. Then the recollected words were spoken.

The class of nouns was different in each series.

(11) The elements were nouns. In each series five of some familiar class were alternated with five of some other familiar class. The classes were different in each of the twelve series given.

From this regular series of ten, five were chosen irregularly, and were printed on cards as in no. 9. The remaining five, of course also irregularly placed in the series, were spoken. This irregularity was different in each series. Thus some words of one kind were spoken, the rest printed; some words of the other kind were spoken, the rest printed.

The other conditions were exactly as in the last experiment.

* * * * *

A table for the individual subjects, indicating not only the omitted but also the displaced and imperfect objects would have, for instance, the following character: C indicates that the effort was made to associate by Contiguity, S by Similarity.

SPOKEN NOUNS, ALTERNATED WITH PRINTED NONSENSE SYLLABLES

Nouns Omitted Syll. Omitted Displaced Imperfect C S C S C S C S Turley 13 16 21 14 7 13 6 10 Emerson 4 5 26 16 7 4 4 13 Miss Kent 5 8 15 8 18 5 9 4 Flexner 4 6 10 9 7 3 8 16 Toll 8 7 8 2 10 12 8 3

Total 34 42 80 49 49 37 35 46

If we consider total results only, and among them only the omitted elements, we come to the following percentages. They give the percentage of the errors of omissions among the elements recalled.

1. Letters and numbers alternated C 26. S 10.8 2. Letters, alternatingly disaligned C 21.2 S 15. 3. Letters irregularly disaligned C 23.8 S 22.4 4. Numbers irregularly disaligned C 7. S 20. 5. Nonsense Syllables, irregularly marked C 27.5 S 27.5 6. Nouns and Nonsense Syllables alternated, spoken C 35. S 37.2 7. Nouns and Nonsense Syllables alternated, nouns spoken, syllables printed C 28.5 S 22.7

In the second group, experiments 8 to 11, not the errors of omission, but, as explained above, the different kinds of reproduced elements, had to be analyzed with special reference to the question whether a sequence linked two contiguous or two similar objects. In the following table the total number of recalled sequences is taken as basis and the different kinds of sequences are given in percentages of it. The elements themselves are described above. B means a break, that is, a sequence without similarity or contiguity.

8. Dissimilar elements, similarly presented S 45 C 28 B 28 9. Dissimilar elements, different kind in each series S 53 C 25 B 21 10. Similar elements, dissimilarly presented S 54 C 20 B 26 11. Dissimilar elements, dissimilarly presented S (Meaning) 27 C 7 B 8 S (Presentation) 13.

The results by the first method of measurement may be summarized as follows, though the first and third conclusions are weakened by disagreement among the individual subjects.

_A._ When the only dissociating factor is some slight unessential feature (a bit of color on the card, a slight disalignment), this similarity and contiguity are nearly equally efficient. No. 3 and no. 5.

As this unessential feature is made more striking (disalignment half a card-length), the strength of similarity increases, only three fourths as many errors being made in dissociation as in contiguous association. No. 2.

The case of no. 4 (all numbers) is of little or no value. The time allowed for learning had to be made short enough to ensure the appearance of some errors; perfect recollection would obviously give no basis for comparison. And the time had to be so short in this case (only two seconds for some of the subjects) that the additional eye-motions and adjustments necessary in dissociating took time enough to spoil the results.

_B._ When the only dissociating factor is in the meaning of the elements (letters and numbers), this similarity is stronger than contiguity, only one half as many errors being made. No. 1.

The results of no. 6 do not support this proportion, but its results are not consistent, while those of no. 1 are.

_C._ When both meaning and manner of presentation are combined as dissociating factors (nouns and nonsense syllables, seen and heard), this similarity is stronger than contiguity, only three fourths as many errors being made.

But this method of measurement is not well adapted to series of auditory elements, so this experiment is unsatisfactory. No. 7.

The results by the second method of measurement may be summarized as follows:

_A._ When the only dissociating factor is in the meaning of the elements (names of different sorts of objects), this similarity is stronger than contiguity, twice as many similarity sequences as contiguity sequences being recalled. No. 8 and no. 9.

_B._ When the only dissociating factor is in the manner of presentation (to sight and hearing), this similarity is stronger than contiguity, nearly three times as many similarity sequences being recalled. No. 10.

_C._ When both meaning and manner of presentation are dissociating factors, these similarities are much stronger than contiguity, more than four times as many similarity sequences being recalled.

_D._ When these two dissociating factors are opposed to each other: (1) Four of the subjects show similarity of meaning much stronger than similarity of presentation, from two to five times as many similarity-of-meaning sequences being recalled. (2) One subject is strongly and consistently otherwise, giving nearly three times as many similarity-of-presentation sequences. No. 11.

MOTOR IMPULSES

THE ACCURACY OF LINEAR MOVEMENT

BY B.A. LENFEST

The starting-point for our investigation was the observation of Woodworth[138] that there is a certain rhythm in which a certain hand-movement is made with the maximum of exactitude, and which represents thus an optimum for the periodical discharge of the particular motor centre. Our question was whether this rhythm is a constant one for all parts of the body, or whether different groups of muscles produce the greatest exactitude in different periods; further, whether secondary factors, like complexity of movement, resistance by weight, fatigue, etc., influence this psycho-physiological optimum.

The investigation, however, showed soon the necessity to consider the whole problem of the accuracy of rhythmical linear movements, and the experiments are thus not always directly related to our starting-point.

There is very little material published that can be collected under the subject head, accuracy of voluntary movement, and still less when the enquiry is confined to the accuracy of straight lines or linear movements.

The most suggestive contribution is that of Dr. Woodworth on the accuracy of voluntary movement. He has collected consistently what can be found up to the date of his publication, and the reader is referred to pages 7-16 of his monograph for the most reliable collection of authorities.

It must be said, as we run over the list from Goldscheider on the threshold of perceptible movement, through the results of Hall, Hartwell, Loeb, and Delabarre on "bilateral asymmetry" and comparisons of right and left hands; consider Fullerton and Cattell in their suggestive results, and Münsterberg's studies of movements; and finally take the testimony of Bryan as to the growth of accuracy of movement in children, that the vast accumulation of material bearing on reaction time--and similar phenomena would be of more value if concerned more with the accuracy and less with the production or perception of movement.

A paper by Miss M. K. Smith, in the Philosophische Studien for 1900, with the title, Rhythmus und Arbeit, concerns the influence of rhythmical action upon the quality and quantity of work performed. The method was to commit to memory nonsense syllables and letters.

The results show a tendency to take up a certain rhythm, especially in the later results and after practice; easier memorizing if rhythm is present; motor reactions, as tapping, nodding, or swaying of body are noted frequently; the feeling of pleasure accompanies rhythmic reactions. While there are no data as to accuracy, there is suggestive matter bearing on the optimal rate and on the relations of compound and simple movements of the hand.

As far as the writer knows, he is the first to present systematic results as to the head and foot movement. The purposes of this enquiry may be briefly stated as

(1) the collection of a large body of facts, bearing on the actual and relative accuracy of straight-line movements possible with various parts of the body, such as hands, arms, head, legs, and feet;

(Something like 340,000 lines have been drawn and calculated.)

(2) to introduce certain variations in the conditions attending the production of ruled lines, such as

(_a_) to rule with the eyes opened and eyes closed, with other conditions the same;

(_b_) to change the rate of ruling or interval between the production of ruled lines; the rates chosen were 20, 30, 40, 50, 60, 70, 80, 100, 120, 140, 160, 180, and 200 beats per minute;

(_c_) to change the length of the normal or first line; the lengths used were 14, 10, and 1 cm.;

(_d_) to impose a weight on the ruling hand to either retard or accelerate the movement, choosing a weight of such magnitude that it would be perceptible, but would not have mass enough to cause pain or fatigue; 260 grams was used;

(_e_) to introduce a simultaneous movement of the free hand; _i. e._, the one that did not carry the recording pencil, of a similar character and extent but of opposite direction to the ruling hand;

(_f_) to record movements of both hands, of the head and of both feet;

(_g_) to conduct a series of experiments of similar character, as regards time-rate and extent of movement, to the series presented by Dr. Woodworth, with the idea of corroborating or disproving the results of his investigations; lines of 140 cm. were accordingly chosen;

(_h_) to conduct a series of experiments where the subject chooses his own rhythm or rate at which the easiest and best lines, subjectively speaking, could be ruled;

(_i_) to find the rates of respiration and pulse-beats and find the connection, if any, between them and the linear records.

(3) To examine, by variations of the number of lines ruled, the questions of fatigue and persistence of the memory-image; series of 50 lines for the first year and of 20 lines for the second year, were accordingly selected.

(4) To find the relations, if any, between constant errors and mean variations, so called.

THE APPARATUS

It is proposed to give the briefest possible discussion or explanation of the apparatus required for the investigation, it being desired at a later stage to enter into a comparison of the method adopted here with that of the only other investigation at all comparable to this one: the research problem of Dr. Woodworth, already referred to.

The underlying principle has been to avoid complication in apparatus, partly because of the delay and expense involved in working out, and making up elaborate schemes for apparatus, but mainly because of the advantage in duplicating this series of experiments, or of carrying on related investigations, to be derived from a choice of such parts, entering into the complete apparatus, as are at hand in any psychological laboratory, or that can be obtained and set up at small expense.

The use of smoked paper has been avoided, because a short preliminary series, using the usual smoked-paper records, was found to give no better results than did the method here adopted of ruling on white paper with a soft pencil, and the labor was thus considerably reduced.

To the objection that the pencil-ruling is more difficult, and involves more loss in friction and more complicated adjustments on the part of the subjects, only one of fourteen subjects admits that this is the case; and even if the testimony was unanimous as to the greater ease of production of the smoked records, it would be no reason for its adoption, since one of the first rules for all experimental work is uniformity of conditions, and this is equally well attained in either case.

The apparatus for free hand-movements and for the compound movements of both hands consists:

(1) Of an adjustable wooden rest (see Fig. _A_) with a base (_a_) about 40 × 60 cm. hinged to a vertically adjustable flat board (_b_), called the arm-rest, about 40 × 70 cm., and having on its upper edge two brass pins or plates (_c_) about 30 cm. apart.

The pencil is started from one of these pins, depending on the hand used, and moved until it comes in contact with a wooden rod that is held against the opposite pin and which is of the right length to give a movement of the pencil of 1, 10, or 14 cm., as desired.

The operator holds this rod in place for the first line ruled and then instantly removes it, so that the second and all later lines are ruled by memory of the first one, as closely in length to the first, or so-called normal line, as is possible.

(2) The apparatus for actuating and taking care of the paper.

This consists of two drums (_d_ and _d´_, Fig. _B_) 20 cm. diameter by 40 cm. wide, mounted on suitable supports about 1 metre apart, and fastened to a table, with axes parallel.

The drum upon which the record is to be made (_d_) is adjusted close to the arm-rest, so that each ruled line will be carried down and out of sight before the next one is ruled, the pencil being held in the position (_e_); note that the arrow shows the direction of rotation.

The second drum (_d´_) is actuated by a motor (_F_) through a round belt (_g_), this motor being a clockwork type, with gear-changes and adjustable vanes for varying the speed, and having the power derived from a suspended weight (_w_).

The recording paper (_h_) transmits motion from (_d´_) to (_d_). This paper consists of a strip about six metres long by twenty-eight cm. wide, with one end pasted to (_d_), and then wound upon (_d_), leaving enough to be carried to (_d´_) and pasted to the latter. As the paper is unwound from (_d_), it is wound upon (_d´_), and, both to keep the paper tight and to prevent too rapid unwinding of (_d_), it is necessary to apply a friction-brake to the shaft of (_d_).

(3) A metronome, capable of being used for a range of 20 to 200 beats, and a stop-watch, to enable the operator correctly to time the subject, are in constant use.

The metronome is set in vibration and the subject is permitted to take his own time to start the ruling, the operator holding the wooden rod in place with one hand, while the other hand holds the stop-watch ready to start it the instant the subject's pencil is moved. There is thus a personal equation for the length of period, but this is of no consequence, as will be apparent when the method of calculation and the use of the planimeter is considered.

In the series of records with the weight, it is impossible to run the speed about 80 to 100 beats, unless the modification in apparatus shown in Fig. _C_ is used; for the vibration of the string running from the hand to the weight around a pulley is violent enough either to throw the string off the pulley or cause the weight to jump so severely as to render the records useless.

This is entirely obviated by the given method of using a heavy weight acting with a small leverage (about 1 cm.) and thus moving only a short distance, so that it is capable of operating at the highest speeds with no perceptible shock or jump; the string is led to the hand or wrist from a grooved pulley of about 12 cm. radius, so the highest velocity of the weight is only about one twelfth that of the hand. This method makes it possible to carry the weighted records to the highest speeds.

This same method is used for the head and foot records, with the following additional apparatus; the string (Fig. _C_), shown leading to the hand, is led horizontally over to and around a similar large pulley on the opposite side of the table and either down to the foot or in a diagonally upward direction to the head; so that movements of the head or foot are faithfully recorded on the drum by means of a pencil held in a block of wood, this block of wood being fastened on the horizontal string in a suitable position for recording on the drum paper. The pencil is kept against the paper by a light spring or elastic band.

The foot is connected to the string by a stirrup that prevents any movement of the feet at all, unless the same is recorded by the pencil.

The head is furnished with a skull cap or harness consisting of non-elastic webbing and stiffened, where the string is attached, by a strip of sheet brass formed to fit the forehead or the back of the head, as the case may be. The object of the brass strip is to prevent a lost motion in the flexible webbing, that is found troublesome otherwise.

It will be evident, then, that the weight is continually acting as an accelerating or retarding influence in all records for head and feet, but it is not considered objectionable, for it is a constant throughout the series.

The other plan would require a circuit of cord leading in both directions from the head or feet in a complete circuit, and would cause in the opinion of the writer too much complication of apparatus.

The pulse-beats were taken by the stop-watch and wrist method so familiar to the physician, while the respiration results were obtained by the usual tambour apparatus for registering the chest expansion upon smoked paper.

THE METHOD OF CALCULATION

Suppose that the drums have been set in rotation and that the paper is unwinding from (_d_) and being wound on (_d´_), Fig. _B_, and suppose that the subject has ruled series of 20 to 50 lines, as may be desired, regulated by the stop-watch in the hands of the operator. The records will appear much as Fig. 5 under the planimeter discussion, there being for each speed one normal line to start and a series of lines following and intended to be of the same length as the normal line. A series of records, then, consists of 13 records of 20 or 50 lines, each running from 20 to 200 beats per minute, the complete series having not less than 260 and not more than 650 lines.

It should be added that the operator holds a pencil-point on the end of each normal line just after the record of 20 or 50 lines is made and turns the drum (_d_), thus marking a line nearly perpendicular to the ruled lines and at the average or normal distance from the starting-point; an absolutely correct record would show all ruled lines ending on this line.

The calculation of this series of records by the ordinary method of measuring each line, adding the lines of the series, averaging for the constant error, and repeating the operation in a slightly different form for the mean error or mean variation is of such enormous labor for an extended investigation as to be beyond the capacity of one or of several students; it is fortunate that the planimeter is at hand to be employed in averaging each series, and this instrument has therefore been selected as overcoming this difficulty.

It is desirable to consider the method employed by Dr. Woodworth to overcome this danger of excessive computation, and it will now be subjected to a critical and comparative examination.

He says, page 19 of his monograph on the Accuracy of Voluntary Movement, that the subject's sole duty was to make the present line equal to that immediately preceding, and the width of the slot was so adjusted that the subject could see only the line just ruled. After discussing certain matters of memory and its relation to the memory-image, in the attempt to support this changing normal plan, he confesses, on page 20, that this device is advantageous in much simplifying the most tedious part of the graphic method, that of computation.

While this is undoubtedly true, it needs careful scrutiny before adoption, for, on the same page, he says that one source of error in the method of making each line equal to the preceding one is that the different movements in the same series are not comparable, but the positive constant error is cumulative in its effect, and the normal tends to become longer and longer.

Some relation between this source of error and such a record as shown on page 29, Fig. 2, is evident, for, while it should be noted that this cumulative effect is peculiar to a series of lines for one speed, it has further a tendency to produce overruling at all speeds, and the natural result is to increase the error unduly and unnaturally for the higher speeds or as the speed increases, because there is then less time for the discrimination and choice that will tend to shorten the ruled line. It may be predicted, then, that Dr. Woodworth's method will show a slight lengthening of normal between lines at slow speeds and a much greater one at high speeds, the effect being to introduce a variable factor that would have no existence were a better plan adopted. The computation required for the average error is simple, being dependent only on the first and last lines of a series, and it is suspected that this very simplicity has led to its adoption and the consequent neglect of certain serious sources of error.

He tells us, on page 20, that the constant and variable error may well be isolated and studied separately, but indicates that they must "somehow" be considered combined as nature has made them; that is, analysis is desirable, but the synthetic method is more scientific.

This investigation will present data suggesting that

(1) Such a curve as that on page 29 of his monograph is not a characteristic one and relations of length of ruled line, as well as effects of weight, make it impossible to apply Weber's law or even the law of Fullerton and Cattell in the way proposed by Dr. Woodworth.

(2) There is no relation, mathematical or other, between constant and mean errors, and they not only may be but must be isolated and studied separately, if an investigation is to be conducted in the interests of scientific exactness.

It will be necessary to reject the method of Dr. Woodworth if the most reliable results are desired, in which case the planimeter is a necessity.

The theory of the planimeter cannot be developed at this place; every physicist and engineer is acquainted with it. The writer believes he was the first to apply the planimeter to the calculation of results from psycho-physical data for averaging both mean and variable errors. More than 340,000 lines were involved, each demanding two measurements. The best type of planimeter for general use and the one used here is the Amsler adjustable-arm form.

In Fig. _D_ is shown a record taken at twenty beats per minute that will both explain the method of computation and show how the planimeter has been used to find the constant and mean errors.

The record, as made and ready for computation, is not provided with the line _cd_ or with the dotted lines that connect the ends of the ruled lines. The line _ab_ is drawn by turning the drum of the apparatus with a pencil held at the end of the normal or left-hand line _af_, which was here 100 mm. long.

The tracing-point of the planimeter being placed at _a_, a reading is taken, which was in this case 1486; after following with the tracing-point the dotted path to _g_ and returning, via _gb_ and _ba_, a second reading is taken, which was 1248; subtracting gives 238, which should be read 2380 square mm. for the area of the space _agba;_ dividing by the distance _ab_, in this case 119 mm., gives the average height, which is + 20.0 mm., the plus sign suggesting that the distance thus found, which is the constant error for the series, be laid off in addition to or beyond _Fa_.

This being done, a line _cd_ is drawn parallel to and 20.0 mm. from _ab_, as the mean line of constant errors.

To find the mean error of the series a slightly different method is necessary.

Place the tracing-point of the planimeter at _c_ and read vernier, giving 1916; follow the dotted path from _c_ to _h_, the straight line from _h_ to _i_, the dotted path from _i_ to _k_, the straight line from _k_ to _l_, the dotted path from _l_ to _m_, the straight lines from _m_ to _n_ and _n_ to _g_, the dotted path from _g_ to _m_, the straight line from _m_ to _l_, the dotted path from _l_ to _k_, the straight line from _k_ to _i_, the dotted path from _i_ to _n_, and the straight line from _h_ to _c_, when a second reading is taken, which was in this case, 1806. Divide the difference of these two readings, 1100 mm., by the length of _cd_, 119 mm., and the result is 9.1 mm., or the mean error (mean variation).

It will be noted that this method gives the sum of the errors from the mean line _cd;_ that is, the same result would be obtained if the tracing-point were (1) carried from _c_ around all the area below _cd_, and this area were calculated as before; (2) carried from _c_ around all the area above _cd_ and the area measured as in other cases; and (3) these two results added and averaged.

To apply the method for _ab_, or constant error computation, to _cd_ should give equal readings at _c_ or a 0 mean error, a result evidently incorrect in the record selected.

After averaging results by the planimeter, the collection of data has been arranged by months; the record for one month only can be presented here, but the method of tabulation is the same throughout.

Each figure given for N, M, c and v, in the accompanying typical table for the month of May, 1904 (pages 495-499), is the average from 20 or 50 lines, ruled as already shown, Fig. _D_.

RESULTS

It is necessary to observe that the limits of space imposed on the writer preclude all but the barest outline of the deductions to be drawn from the investigation, and to this fact is due whatever of dogmatism is inherent in the argument; for it is manifestly impossible to present all the material, and the writer asks, then, the indulgence of the reader when he claims to have impartially examined and presented the evidence.

HAND MOVEMENTS

Simple movements Lines 14 cm. long.

TYPICAL SERIES FOR THE MONTH

Key. v = mean error. R.H. = right hand. R.F. = right foot. E.O. = eyes open. si. = simple motion N = normal line. Unit = 1 mm. L.H. = left hand. L.F. = left foot. E.C. = eyes closed. co. = compound motion. M = mean line. b = beats per minute. c = constant error.

See Beats per minute. Day. Subject. Key. 20 30 40 50 60 70 80 100 120

6 Hylan. N 10 10.5 11 11 10 10 10 12 10 L.F.E.O. M 16.1 13.5 12.1 13.8 13.1 10.0 10.0 11.2 12.5 c +6.1 +3.0 +1.1 +2.8 +3.1 0.0 0.0 -0.8 +2.5 v 2.8 3.5 1.9 0.9 1.6 4.6 2.0 2.7 1.2

140 160 180 200

12 10 11 11 12.0 6.1 11.0 14.21 0.0 -3.9 0.0 +3.2 1.0 1.3 2.1 4.0

Hylan. N 10 11 10 12 10 12 11 11 11 L.F.E.C. M 8.9 10.5 10.9 11.4 13.1 10.3 11.8 13.1 13.9 c -1.1 -0.5 +0.9 -0.6 +3.1 -1.3 +0.8 +2.1 +2.9 v 2.7 6.4 2.2 1.4 2.7 1.6 2.3 1.6 4.9

11 11.5 11 11 15.8 11.0 15.0 17.8 +4.8 -0.5 +4.0 +6.8 2.9 2.3 2.3 2.5

George. N 10.5 10 10 10 10 10 10 10 11 L.F.E.O. M 14.6 9.7 7.1 6.4 7.7 8.3 8.0 10.0 11.0 c +4.1 -0.3 -2.9 -3.6 -2.3 -1.7 -2.O 0.0 0.0 v 2.1 1.6 1.8 2.3 0.8 0.7 1.4 1.7 0.8

10 10 11 11 9.0 10.0 8.0 12.5 -1.0 0.0 -2.0 +1.5 1.0 1.3 1.6 0.4

George. N 10 9 9 10 11 9.5 9 10 8 L.F.E.C. M 11.7 9.2 10.2 12.6 13.2 11.5 12.2 6.6 5.0 c +1.7 +0.2 +1.2 +2.6 +2.2 +2.0 +3.2 -3.4 -3.0 v 2.0 2.9 2.5 0.7 0.5 1.0 0.8 2.0 4.1

10 9 9 10 8.0 7.6 8.0 11.0 -2.0 -1.4 -1.0 +1.0 3.1 2.5 2.1 3.7

Moore. N 10 10 10 10 11 11 11 10 10 L.F.E.O. M 15.7 18.8 17.7 16.7 18.3 18.5 16.5 15.6 16.0 c +5.7 +8.8 +7.7 +6.7 +7.3 +7.5 +5.5 +5.6 +6.0 v 3.5 3.8 1.1 0.8 3.6 2.1 2.7 0.6 2.4

10 11 10 10 16.2 16.3 16.4 18.8 +6.2 +5.3 +6.4 +3.8 0.5 3.5 2.2 3.8

N 10 10 10 10 11 10 10 9 Moore. M 19.6 15.3 15.3 14.3 14.9 13.5 6.7 13.4 L.F.E.C. c +9.6 +5.3 +5.3 +4.3 +3.9 +3.5 -3.3 +4.4 v 2.6 2.5 2.4 0.4 2.0 6.4 0.7 4.1

9.5 11 11 10 10.5 20.0 14.3 14.5 16.9 17.9 +10.5 +3.3 +3.5 +6.9 +7.4 2.6 3.8 1.1 3.1 2.8

N 10 10 9 10 10 9.5 10 10 9 Angier. M 13.6 12.5 11.6 11.6 11.5 11.7 13.0 12.9 R.F.E.O. c +3.6 +2.5 +2.6 +1.6 +1.5 +2.2 +3.0 +2.9 v 2.9 2.3 1.8 2.3 1.7 1.6 2.0 2.7

11 10 10 10 10 12.2 12.2 13.5 22.1 16.5 +1.2 +2.2 +3.5 +12.1 +6.5 3.3 1.5 1.5 6.7 1.5

N 10 10 10 9.5 10 9 10 10 Angier M 11.4 7.7 13.8 8.3 11.4 11.5 11.0 10.3 R.F.E.C. c +1.4 -2.3 +3.8 -1.2 +1.4 +2.5 +1.0 +0.3 v 4.8 1.3 3.0 2.6 1.4 1.7 1.8 1.7

140 beats

9 10 10 11 10 10 9.9 12.8 16.7 17.7 12.4 12.0 +0.9 +2.8 +6.7 +6.7 +2.4 +2.0 1.8 1.4 1.7 4.2 2.1 1.7

N 11 10 10 9 10 11 10 10 Huggins. M 12.5 8.5 12.6 9.7 9.7 16.6 15.7 18.7 R.F.E.O. c +1.5 -1.5 +2.6 +0.7 -0.3 +5.6 +5.7 +8.7 v 3.6 2.6 2.7 2.8 3.3 3.2 3.3 3.6

10 11 11 11 10 13.6 15.8 9.3 18.3 14.3 +3.6 +4.8 -0.7 +7.3 +4.3 3.1 2.7 2.9 3.8 3.0

N 11 8 10 10 11 10 10 10 Huggins. M 6.5 10.5 10.7 8.8 12.6 12.9 12.2 22.3 R.F.E.C. c -4.5 +2.5 +0.7 -1.2 +1.6 +2.9 +2.2 +12.3 v 1.4 2.1 1.8 1.6 3.7 3.1 2.0 4.1

10.5 10 10 10 10 9.9 21.8 12.0 12.5 16.3 -0.6 +11.8 +2.0 +2.5 +6.3 1.4 5.0 2.3 3.6 1.8

N 9 9 9 9 9.5 8 7 10 13 Lenfest. M 12.7 11.9 11.1 11.3 12.1 8.7 11.6 12.6 R.F.E.O. c +3.7 +2.9 +2.1 +2.3 +2.6 +0.7 +4.6 +2.6 v 3.7 2.4 1.9 2.3 2.8 0.2 2.8 2.1

10 10 9 8 10 9.0 8.6 11.7 7.0 11.8 -1.0 -1.4 +2.7 -1.0 +1.8 2.0 2.1 3.2 1.4 4.1

N 12 11 11 10 10 10.5 11 11 Lenfest. M 14.9 14.7 12.2 13.5 12.6 11.9 12.6 8.7 R.F.E.C. c +2.9 +3.7 +1.2 +3.5 +2.6 +1.4 +1.6 -2.3 v 3.3 2.2 3.5 3.5 3.2 3.0 2.6 1.7

11 11 10 10 10 9.1 8.9 8.4 14.1 6.9 -1.9 -3.1 -1.6 +4.1 -3.1 2.4 2.8 2.9 4.1 2.3

N 12 11 11 11 11 10 11 10 George. M 8.3 9.0 8.6 8.8 8.7 7.0 7.4 7.9 R.F.E.O. c -3.7 -2.0 -2.4 -2.2 -3.3 -3.0 -3.6 -2.1 v 5.0 3.3 2.3 0.1 3.3 2.9 2.4 3.1

11 10.5 11 10 10 6.8 9.7 9.0 5.8 11.0 -4.2 -0.8 -2.0 -4.2 +1.0 1.5 4.6 2.9 2.9 3.9

N 12 11 12 11 11 11 10.5 11 George. M 7.0 7.7 14.1 8.3 10.3 8.4 8.7 7.8 R.F.E.C. c -5.0 -3.3 +2.1 -2.7 -0.7 -2.6 -1.8 -3.2 v 2.5 2.6 2.4 3.7 2.9 2.3 1.6 2.1

10 10.5 11 10 10 6.4 10.0 9.0 7.9 7.3 -3.6 -0.5 -2.0 -2.1 -2.7 1.9 3.7 2.9 1.8 3.8

N 11 11 11 11 12 10 9 11 Moore. M 14.5 16.6 16.5 9.0 17.0 10.7 10.4 11.9 R.F.E.O. c +3.5 +5.6 +5.5 -2.0 +5.0 +0.7 +1.4 +0.9 v 1.7 2.2 1.9 1.8 1.3 2.2 2.6 2.2

10 10.0 10.5 11 9.5 11.5 12.5 12.5 15.1 12.6 +1.5 +2.5 +2.0 +4.1 +3.1 2.2 2.5 2.5 1.4 0.8

N 11 10 11 11 11 10 10 9 Moore. M 14.3 13.2 15.9 12.3 17.9 10.0 11.3 15.9 R.F.E.C. c +3.3 +3.2 +4.9 +1.3 +6.9 0.0 +1.3 +6.9 v 1.8 2.8 1.6 2.1 1.7 2.4 3.2 2.2

11 11.0 10 10 10 14.8 15.5 13.4 11.8 12.2 +3.8 +4.5 +3.4 +1.8 +2.2 2.7 1.4 2.2 1.8 2.2

N 11 11 10 11 10 10 10 11 16 Angier. M 14.3 13.5 9.3 14.4 14.1 9.5 15.1 12.7 R.F.E.O. c +3.3 +2.5 -0.7 +3.4 +4.1 -0.5 +5.1 +1.7 v 1.7 1.9 2.0 2.4 2.0 1.1 2.4 2.8

10 11 10 11 11 11.1 12.6 13.7 11.0 16.6 +1.1 +1.6 +3.7 0.0 +5.6 2.0 2.0 2.7 1.3 3.5

N 11 10 10 9 10 10.5 10 10 Angier. M 14.4 4.8 2.5 3.6 5.8 6.7 8.0 11.0 R.F.E.C. c +3.4 -5.2 -7.5 -5.4 -4.2 -3.8 -2.0 +1.0 v 3.2 2.7 2.3 3.6 2.7 2.3 1.3 2.8

11 10 11 11 11 13.5 11.1 13.9 10.1 11.0 +2.5 +1.1 +2.9 -0.9 0.0 2.8 1.4 2.4 1.8 2.2

N 97 97 98 97 98 99 97 98 Huggins. M 107.6 107.8 100.4 114.2 98.0 110.3 89.4 102.5 L.F.E.O. c +10.6 +10.8 +2.4 +17.2 0.0 +11.3 -7.6 +4.5 v 5.9 0.6 4.8 6.5 5.3 6.7 6.4 5.5

95 98 99 99 100 99.2 100.8 106.4 101.5 108.9 +4.2 +2.8 +7.4 +2.5 +8.9 7.8 6.0 4.7 7.0 12.7

N 97 98 100 97 95 95 99 99 Huggins. M 102.8 104.3 115.1 101.4 94.1 102.0 106.4 93.4 L.F.E.C. c +5.8 +6.3 +15.1 +4.4 -0.9 +7.0 +7.4 -5.6 v 5.8 8.6 10.8 9.9 7.9 10.4 8.1 6.8

97 98 99 99 100 87.7 98.7 108.4 97.7 110.8 -9.3 +0.7 +9.4 -1.3 +10.8 9.4 5.8 6.9 5.3 6.1

N 11 11 10 10 10 10 10 10 20 Lenfest. M 16.1 13.5 11.6 10.9 10.9 14.2 11.7 10.5 L.F.E.O. c +5.1 +2.5 +1.6 +0.9 +0.9 +4.2 +1.7 +0.5 v 2.8 3.0 3.0 3.0 1.2 1.9 1.0 1.6

11 10 11 11 10 12.4 11.1 12.2 8.7 12.9 +1.4 +1.1 +1.2 -2.3 +2.9 3.2 5.1 1.9 1.7 4.2

N 12 11 10 10 10 11 10 10 Lenfest. M 20.4 16.8 11.6 11.2 11.8 14.0 9.0 9.3 L.F.E.C. c +8.4 +5.8 +1.6 +1.2 +1.8 +3.0 -1.0 -0.7 v 2.5 3.6 3.0 1.9 1.6 2.0 3.0 1.2

10 10 11 11 10 6.2 10.0 8.5 5.1 8.3 -3.8 0.0 -1.5 -5.9 -1.7 1.9 0.3 1.8 1.7 0.8

N 98 97 94 98 98 97 98 98 George. M 104.0 100.4 102.6 99.3 105.1 111.1 101.9 100.5 L.F.E.O. c +6.0 +3.4 +8.6 +1.3 +7.1 +14.1 +3.9 +2.5 v 6.4 11.3 9.6 7.7 5.3 8.0 3.7 5.6

97 96 98 98 97 96.4 102.0 97.4 94.2 95.8 -0.6 +6.0 -0.6 -3.8 -1.2 5.7 5.7 9.1 7.8 3.6

N 98 97 94 97 97 98 98 97 George. M 93.6 81.2 94.7 92.7 104.2 99.3 93.4 89.6 L.F.E.C. c -4.4 -15.8 +0.7 -4.3 +7.2 +1.3 -4.6 -7.4 v 9.1 8.9 5.5 4.6 5.8 6.9 4.9 6.6

96 98 98 99 100 96.4 93.0 87.3 101.8 87.4 +0.4 -5.0 -9.7 +2.8 -12.6 7.8 4.8 7.7 5.6 5.7

N 97 99 98 97 96 96 97 98 Moore. M 106.1 106.9 105.2 103.0 104.7 108.6 102.7 106.9 L.F.E.O. c +9.1 +7.9 +7.2 +6.0 +8.7 +12.6 +5.7 +8.9 v 4.3 5.6 4.6 5.2 8.0 6.0 7.4 6.9

99 98 99 99 99 110.9 105.7 111.2 99.9 93.0 +11.9 +7.7 +12.2 +0.9 -6.0 4.8 9.0 4.7 11.4 1.8

N 96 97 97 97 96 97 96 97 Moore. M 119.2 79.8 87.3 79.6 81.6 91.2 96.5 106.2 L.F.E.C. c +23.2 -17.2 -9.7 -17.4 -14.4 -5.8 +0.5 +9.2 v 16.1 6.7 11.6 7.2 7.5 4.1 4.0 6.6

99 98 97 98 99 100.4 91.9 104.0 88.6 80.9 +1.4 -6.1 +7.0 -9.4 -18.1 4.0 6.1 5.4 6.6 8.2

N 98 97 95 96 96 97 99 97 23 Lenfest. M 105.7 110.8 97.4 93.8 97.8 100.2 99.9 92.9 L.F.E.O. c +7.7 +13.8 +2.4 -2.2 +1.8 +3.2 +0.9 -4.1 v 9.3 1.5 3.6 5.1 3.6 4.4 2.9 3.3

97 98 98 98 99 86.1 96.6 91.9 80.9 83.0 -10.9 -1.4 -6.1 -17.1 -16.0 6.7 5.0 8.2 6.0 7.8

N 96 94 96 96 96 94 96 97 Lenfest. M 111.3 95.0 98.3 101.7 101.7 110.1 98.8 79.0 L.F.E.C. c +15.3 +1.0 +2.3 +5.7 +5.7 +16.1 +2.8 -80.0 v 7.1 5.1 5.8 2.7 5.4 7.8 12.1 3.7

97 97 100 100 100 88.9 72.7 88.4 69.7 80.8 -8.1 -24.3 -11.6 -30.3 -19.2 5.6 8.0 7.4 8.4 7.0

N 96 97 96 96 98 98 97 97 Huggins. M 113.5 105.7 105.5 97.7 92.5 98.4 92.5 102.0 L.H.E.O. c +17.5 +8.7 +9.5 +1.7 -5.5 +0.4 -4.5 +5.0 v 4.2 2.4 3.6 5.0 3.5 3.1 4.2 5.8

95 98 98 99 97 95.0 112.3 104.5 108.7 95.7 0.0 +14.3 +6.5 +9.7 -1.3 4.7 6.4 5.8 7.1 4.4

N 98 97 97 97 97 99 99 97 Huggins. M 103.5 82.8 86.1 87.8 87.7 94.2 92.1 94.5 L.H.E.C. c +5.5 -14.2 -10.9 -9.2 -9.3 -4.8 -6.9 -2.5 v 8.4 6.7 5.4 3.5 6.7 5.4 6.0 5.8

97 97 98 98 96 99.9 111.5 101.3 113.7 95.1 +2.9 +14.5 +3.3 +15.7 -0.9 4.8 13.3 4.7 9.6 2.6

N 96 95 96 96 96 97 96 27 Lenfest. M 101.6 93.4 91.2 90.0 97.5 93.2 93.4 R.F.E.O. c +5.6 -1.6 -4.8 -6.0 +1.5 -3.8 -2.6 v 6.2 5.1 3.4 2.8 5.5 4.5 3.7

96 99 102 101 100 89.8 97.5 88.6 96.8 66.2 -6.2 -1.5 -13.4 -4.2 -33.8 5.5 3.6 4.3 4.9 8.1

N 96 96 97 97 97 98 98 Lenfest. M 103.8 101.2 94.0 100.3 96.4 101.2 105.0 R.F.E.C. c +7.8 +5.2 -3.0 +3.3 -2.6 +3.2 +7.0 v 6.2 7.4 4.5 3.8 3.5 4.7 2.4

95 98 100 99 100 78.0 98.5 88.8 85.1 65.8 -17.0 +0.5 -11.2 -13.9 -34.2 4.7 4.3 7.0 6.9 5.9

The records are averaged for nine subjects, three of them being left-handed. For the right hand we find, for mean error, a reduced error with visual control.

For constant errors, a similar result is apparent; when following the eyes-closed curve one may note a large negative error 20-50 beats, and a similar but larger positive error 70-160 beats, with a falling to a negative error again at 200 beats.

This may be interpreted to mean a groping for the correct length of line at the lower speeds when some time for reflective processes is allowed, and an inhibitory effect on the motor discharge; later the speed prevents this discrimination, and introspective testimony goes to show that a mental conception of a barrier, beyond which one cannot carry the pencil, is set up and kept more or less constant through the help of the joint and muscular sensations. It would follow, then, that this muscular stop is overestimated where reflection is not possible.

Finally, the falling-off of the length of the line is probably due to physical inability to rule a line of the full length of 140 mm. at 200 beats per minute and an examination of some individual cases confirms this opinion, for the lines may be started some distance away from the origin apparently in order to end them at the correct point.

Curve inclinations are upward, for mean errors, with visual control, while the eyes-closed records show no increase in error for the increased speeds.

For constant errors, with visual control, there is a similar inclination downward for both hands, with a 0 error at about 120 beats. It should be noted that this opposite tendency in mean and constant errors suggests that they should be kept separate in all computation.

The left-handed subjects have much better control of their left hand than have the right-handed subjects, and they may dispense with visual control to a large extent.

On the other hand, for right-hand records we find much the same increase in irregularity and error for both left- and right-handed subjects; they all must depend on visual control for reduction of errors.

It follows that the non-visual control exerted by the left-handed subjects on the right hand is as good or as great as for the right-handed subjects; while they have the hand in which they may be expected to excel under much better control.

It is not intended to present this as an argument for teaching left-handedness, but it is certainly suggestive when considering the question that ambidexterity be taught in early life.

It should be noted that two of the three left-handed subjects might be expected, because of special training, to show marked manual dexterity, while only one of the four right-handed subjects has had special training along this line.

No extended discussion is appropriate here as to the question of what portion of this extra ability of the left-handed subjects to react accurately is due to practice and habit, _i. e._, is automatic, and accomplished without reference to the sensory motor by-path to the cerebral cortex; and on the other hand, as to whether the direct sensory motor path via spinal cord or medulla is not cut off entirely.

For 140 mm. averages and free motion, we find in general

(1) a reduced error and greater uniformity of result at all speeds where visual control is added, in the case of both mean and constant errors and for all subjects;

(2) the mean errors for visual-control records show a rise along a line whose equation is approximately _y_ = _px_, or the equation of a straight line, where _p_ is an undetermined constant.

On the other hand,

(3) the eyes-closed mean errors show no increase or decrease in value during the entire series;

(4) the constant errors for visual-control records show a drop from positive errors to negative errors, along a line whose equation is approximately _y_ = _qx_ or the equation of a straight line, where _q_ is an unknown constant, somewhat less in value than _p_ in the case of mean errors; the constant error becomes 0 at about 120 beats;

(5) the eyes-closed constant errors follow the same equation for left-handed subjects, using the left hand, but all other cases suggest a curve of the parabolic form, having 0 constant errors at 60 and 180 beats and being convex upward.

Considering individual records for 14 cm.

A general survey of the charts suggests certain irregularities that call for explanation, for there will be sudden large increases in errors, that are explicable on the hypothesis that the subject has temporarily lost control of the moving hand, that is, that fatigue is to be noted.

While the purpose of the investigation has been to allow no lines to be ruled while the subject was conscious of any such feeling, there being a pause of any desired length to permit time for rest, it is to be noted that a considerable amount of recorded data as to fatigue shows that it is an unconscious or subconscious phenomena.

Further, the series of records have been arranged to occur from 20 to 200 beats and never in the reverse order, because of subjective limitations, so it is reasonable to expect that during the period of twenty minutes to one half an hour required for a series of records, there will be lapses of volitional control entirely beyond the ken of the subjects. It is to this cause rather than to pure chance that the results will be attributed. With this exception, the individual records show close agreement with their average.

The results obtained from a consideration of free hand-movements of 1, 10, and 14 cm. length are:

For 14 cm. lines

for the average of nine subjects:

The mean errors,

(1) increase with speed for eyes open;

(2) do not change in error with speed-change for eyes closed;

(3) visual control reduces errors for right hand, but does not for the left;

(4) right-handed subjects alone gain from visual control.

The constant errors,

(1) decrease with speed in visual cases;

(2) increase with speed to the middle and then reduce to 200 beats for eyes closed;

(3) left-handed subjects are more accurate for the left hand and can dispense with visual control;

(4) all subjects need visual control for the right hand;

(5) left-handed subjects show less error throughout for non-visual.

For the individual cases,

the mean errors

(1) show evidences of loss of control or fatigue for some speeds, and the average results are confirmed.

The constant errors show that the average deductions are confirmed.

Lines 10 cm. long:

Averages for seven subjects as regards mean errors have especial interest for l.h.e.c. records, which alone show a rise of error with speed-increase.

Noting that the records are overwhelmingly averages of right-handed subjects (six to one), it is of interest to examine this record.

We may say, then, that for right-handed subjects, the voluntary control for the right hand is not much improved by the introduction of visual assistance; it is more marked for speeds of 100 beats or less than for the high speeds. And in the latter case, it is under 10%; but when the left hand is considered, a marked gain or 40 or 50% is apparent, when the eyes are used except for the two lowest speeds.

As far as it is possible to offer any hypothesis from the few facts tabulated, it may be said that right-handedness implies a high development of muscular control, but slightly improved by the introduction of the visual element, as far as the right hand is concerned; but for the left hand muscular control comparable to the right-hand control can be obtained only with visual control; in short, I fail to find evidences of cross-education, where the visual element is absent, nearer than about 50% of the mean error.

No clearly marked gain through visual control can be pointed to in the case of constant errors; there is, to be sure, a slight gain in steadiness and error-reduction, where eyes help in the case of both hands, but not 5% in magnitude of the difference noted with mean errors.

Individual records show fatigue-points at 40 to 80 beats and again above 140 beats, but there is no perceptible loss of control during a series of lines ruled at only one speed.

It is apparent, when comparing with the 140 mm. records, that there is no physiological reason why the subjects may not rule the full length of a 10 cm. line at 200 beats, and the limit of movement for high speeds is probably between 10 and 14 cm.

The constant errors are in general positive and only Me. shows a tendency to underrule lines at high speeds.

For 10 cm. lines,

for the average record,

(1) the mean-error curve is horizontal for l.h.e.o., but otherwise rises with speed-increase;

(2) visual control is a 10% gain for right hand and 40 to 50% for the left, so right-handedness is prominent for the eyes-closed series;

(3) the constant-error curve for r.h.e.c. rises, but all others show reduction of error as rate increases;

(4) visual-control gains are not over 5%.

The individual curves show,

for mean errors,

(1) marked-fatigue points for l.h.e.o;

(2) r.h.e.o. curve is horizontal, but all others rise;

(3) l.h.e.o. curve is about the same as r.h.e.o., but there is more loss for non-visual series with left hand.

For constant errors,

(1) r.h.e.c. curve rises, but all others are horizontal;

(2) the eyes reduce errors especially for the left hand;

(3) overruling is prominent even at high speeds, for there is no evidence that the lines are shortened at high speeds.

Lines 1 cm. long:

Averages are made for nine subjects, three being left-handed.

The eyes are effective in reducing mean errors and to a less extent for constant errors.

A noteworthy feature of the constant-error record is that the errors are positive with one exception, that of 20 beats with l.h.e.c. and even this curve jumps rapidly above the 0 line.

In all cases the motor discharge is of sufficient magnitude to cause overruling in cases of normal lines of one cm. The assistance afforded by the eyes is not marked.

Certain evidence of an introspective character, that most of the subjects offer, is to the effect that, "when I would do good, evil is present with me"; that, where there is a decided feeling that the muscular limit, if such a term be permitted, is exceeded, yet the subject's will-power is not sufficient to inhibit the overruling; there is a more or less vivid conscious error in the 10 mm. series for the hands.

In regard to the relation of mean and constant errors, there is more close uniformity than with the 140 mm. lines, but it is to be noted that there is no comparison to be drawn between maximum or minimum points; for example, at 100 beats the minimum points for r.h.e.o. agree closely, but the maximum constant error matches the minimum mean error at 100 beats for r.h.e.c.

We cannot predict, then, that a subject capable of closely ruling to the normal will be able also to rule each line of the same length as the rest of the series, or _vice versa_.

As in the case of mean errors in general note that subjects show a less constant error and more regularity for their more dexterous member; it is not true for the left hand that for left-handed subjects visual control is a hindrance for accurate work; otherwise the same gain, by use of the eyes, is to be noted for the rest of the records.

Individual records show close correspondence with the average of results, and the latter may be considered fairly representative.

Almost the whole series shows the constant error positive, the most consistent example being for J. with l.h.e.o.; this tendency to overrun the 1 cm. lines is consistently uniform and has been elsewhere commented on, so it may be left with the observation that the log shows that the subjects were frequently conscious of this overruling, but confessed inability to correct it.

Only in the case of Y. for the three left-handed subjects and for W. among the six right-handed men does the left hand show less mean error than the right hand, and all other cases show such an interweaving of curves as to render it difficult to perceive any advantage that the more dexterous hand possesses on the score of accuracy.

For constant errors:

For individual cases it is to be noted that for the left-handed subjects J. is better for the right hand, Le. is indifferent, and Y. prefers the left hand; while three of the six right-handed subjects prefer the left hand and one is indifferent; thus giving still further proof that a more dexterous hand is a fiction on the score of the right or left-handed theory, when accuracy of straight-line movement is to be considered.

For 1 cm. lines, for the average, note for the mean errors:

(1) visual control reduces errors;

(2) errors increase for eyes open, but decrease for eyes closed, as speed increases when considering right hand, but left-hand errors are constant;

(3) as left-handed subjects are better for r.h.e.o. than right-handed subjects, but not for eyes closed, it is suggested that visual control equalizes differences in the subject's less trained hand.

For constant errors:

(1) visual control reduces errors;

(2) curves are horizontal in all cases;

(3) all errors are positive, showing consistent overruling;

(4) as visual control of the left hand is a gain for right-handed but a hindrance for the left-handed subjects, the more practised hand is probably able to dispense with visual control, and depend largely on the muscular sense.

Mean and constant errors are not comparable. For the individual cases we find a corroboration of the above and for mean errors: more dexterous hand does not excel, and evidence against ambidexterity is conflicting; for constant errors: overruling is consciously done.

Constrained hand-movements for lines 14 and 1 cm. long and for the weight, both accelerating and retarding the movement, are to be next considered.

Constrained motions are of two general types as examined by the writer. Series of the records for the hands were taken at 140 mm. and 10 mm. bases with a weight hung on the finger or fingers of the hand under investigation; in one series the weight acted as a pull or accelerating effect on the ruled line and in the other series the weight was imposed as a retarding effect, tending to restrain the movement of the hand.

This weight was in all cases 260 grams, this weight being chosen as of sufficient amount to have a perceptible effect, but not large enough to cause feelings of pain or fatigue in any case.

The average for seven subjects, three being left-handed, is as follows:

In general, the mean errors for the right hand are less, and less variable as compared with the left hand. The left-hand records are very close to the corresponding right-hand curves, especially the portions of the eyes-closed records 20 to 120 beats.

This may be said for both mean and constant errors. In general, mean errors are reduced, and curves are more nearly straight lines when the weight is added; also the weight reduces constant errors, and gains more regular records at all speeds. It is to be noted as a point of unusual interest that there is no apparent shortening of the line ruled when the weight is hung on the hand, for the negative errors are less, not more when the weight is applied.

In general, then, the imposition of a weight that will be small enough not to cause pain or fatigue shows that both mean and constant errors are reduced; that the amount of error is less variable over the range of speeds used; that the records show no retarding effect, but that the subject is both able to move the hand just as far as without the weight, and do it with much greater accuracy.

Individual records for 14 cm. and weight-retarding show a marked reduction in both mean and constant errors, and a less marked gain in uniformity in every case. This tends to confirm the introspective opinion of W. subject that the imposition of a retarding weight tends to reduce errors of both classes and to cause greater steadiness.

It should be added that there is evidence of an occasional letting-go of voluntary control, so to speak, resulting in a large increase in mean error, as already pointed out, or a large increase in negative constant error, as shown on all individual records, and it would seem then that the matter of cortical control is more vital and indispensable for the restricted movements.

The effect of weight-retardation on visual records is to reduce the error and steady the ruling of the less dexterous hand to a much more marked degree than for the well-trained hand.

In the l.h.e.c. records the lack of corrective effect of visual control is marked, as in the case of free movements, but the dip in the curve at 30 to 70 is not noted in the free ruling and should be considered as a distinct shortening due to weight-retardation before discriminative processes have oriented the subject.

Without considering the accelerating weight-records in detail note that:

The effect of weights (less than that necessary to cause pain or fatigue), either tending to accelerate or retard motions, is to reduce both mean and constant errors and to render more uniform or more uniformly increasing or decreasing such errors, except in the case of l.h.e.c., where constant errors are greater positively with the weight-pulling and greater negatively with the weight-retarding, than for free motions; that is, the effect of the weight is natural, and shows no signs of inhibition in this particular case.

There is no such marked fluctuation in error for the pull-records as was noted for the weighted curves, and it is further noted that the individual pull-records are more bunched or consolidated about some mean than are the free-movement curves. This suggests that the accelerating weight is a decided help for accuracy and regularity, and it would seem to call for less voluntary control than for either of the other movements.

Further, as the effect of pulling weights is to equalize the accuracy of movement of the hands, the hypothesis is proposed that weights either accelerating or retarding the movements of the hand tend to equalize their accuracy or to promote ambidexterity as far as accuracy of straight-line mean errors is concerned.

L.h.e.c. rise for Ha., are horizontal for J., W., and Y., and slope downward for the other subjects, the net effect being a slight downward slope. The loss of accuracy and regularity when the visual sense is inhibited is to be noted in every case, it being especially marked for Bo., Li., and W.

As compared with the r.h.e.c., there is not sufficient evidence to lead to the conclusion that the right hand is a more accurate member than the left, but on the contrary the left-hand record for non-visual control is lower for both weighted series than is the right-hand curve. Contrasting this with the eyes-open records for free and weighted movements, the visually aided results show a greater accuracy and regularity for the right hand.

This leads to a proposition that the greater dexterity on the line of accuracy, of one hand, that is the right hand for right-handed subjects, and the left hand for left-handed subjects, is a matter of visual control and is in no sense due to the muscular sense or to automatic action, for without eyes we are ambidextrous as far as accuracy of linear movements is concerned; the proposition needs careful scrutiny in application to the general question, but is held to be correct within the range of experiments.

We are tempted to extend this matter somewhat in the following way, by saying that there is no evidence deducible from this research that there is hereditary preponderance of activity or accuracy of one hand or one leg (as shown later) over its mate, and the baby is brought into the world with an equal capacity of accuracy of both members.

It is, then, an evolutionary matter, not racial but individualistic, and right-handedness or left-handedness is largely a development after birth. Our system of education is responsible for the over-development of one hand, and such a case as that of Dr. Anderson of the Yale University Gymnasium, who in class demonstration cannot instantly tell which hand is being used to actuate the chalk at the blackboard, is the normal symmetrically developed man.

The school reform for ambidextrous training is radical enough, but seems a logical conclusion of the argument. Apologies are appended for driving the argument beyond the limits of the investigation, but it is hoped that the enquiry is at least suggestive.

For 14 cm. lines,

weight-retarding movements:

For the average of nine subjects:

The weight reduces errors and promotes regularity in the case of both mean and constant errors, nor does it tend to cause underruling, save in the case of left-handed subjects for l.h.e.c. records. There is a gain, in general, when the visual factor is introduced.

For mean errors,

(1) right-hand curves are horizontal, while the visual records show increasing error and l.h.e.c. a reduction of errors;

(2) the right hand gives slightly better results;

(3) note that l.h.e.c. record is equally good for free or weighted movements.

For constant errors,

(1) r.h.e.o. and l.h.e.o. curve downward, while both non-visual curves slope upward;

(2) the left hand seems equally efficient, as compared with the right hand.

For individual cases,

note (1) fatigue-spots are more numerous than for free movements, especially for the left hand;

(2) weight reduces both mean and constant errors and to a less extent even records.

For mean errors,

(1) visual control reduces errors;

(2) the weight tends to equalize the accuracy of the right and left hands.

For constant errors,

(1) there is no general testimony showing shortening of lines at high speeds;

(2) the less trained hand is more helped by the weight, especially for non-visual work.

The evidence for right- and left-handed subjects is inconclusive, and we cannot finally say that the more trained hand is capable of greater accuracy.

Weight-accelerating movements:

The average of seven subjects:

The accelerating weight reduces mean and constant errors, and improves regularity of curves, except for l.h.e.c. constant-error record. There is some evidence that a pull causes overruling, while a retarding weight causes underruling, but there are exceptions enough to warrant care in finally accepting this statement. Visual control with accelerating weight reduces error more than the weight acting alone.

For mean errors,

(1) weight reduces errors for r.h.e.o. and l.h.e.c. as compared with free-movement records, while the other two curves are inconclusive;

(2) visual sense helps in accurate ruling;

(3) non-visual records are not reduced, as a rule, from the results of free motion.

For constant errors,

(1) the accelerating weight tends to greater accuracy, with an exception for the-non-visual records.

No testimony of marked importance is to be noted in comparison of right-handed and left-handed subjects; the more trained hand shows greater accuracy in some cases, but fails to excel in others; so the data is inconclusive.

For individual cases we find:

(1) the acceleration records are more accurate and regular, and present fewer lapses than the free or retardation results, suggesting greater ease with weight assisting;

(2) visual control is prominent throughout, and evidence shows that this sense is the greatest factor in the predominance of the more trained hand; the non-visual records should and do show no marked difference in the hands;

(3) a weight tends to equalize accuracy of hands;

(4) the overruling effect of weight is over-corrected in some cases for constant error of low rates.

Constrained movements of 1 cm.:

The average is of seven subjects, three of them being left-handed:

With weight-retarding movement, there is no reduction of mean error with visual control of right hand, but there is with the left. Constant errors show little reduction for either hand with eyes open.

The facts would seem to warrant the hypothesis that, for the left hand, a movement uncontrolled visually, whether restricted by a weight or not, can be made with greater accuracy, when time is permitted for discriminative and reflective processes and visual-control results in about the same error whatever the speed, while the right-hand motions show no such evening effect of visual control with the weight-records or even reduction of error; the free movement, however, does show a reduction of error.

A general statement may be deduced that, for lines of 10 mm. in length, there is no difference in either mean or constant errors, when a weight is imposed to cause retardation, provided the weight is not large enough to cause pain or fatigue.

By separating the averages for right- and left-handed subjects, it may be further said that:

Visual control is not efficient to reduce the error and no particular gain in regularity can be noted. The left-handed subjects show, for the left hand, much better results without visual control as far as the free motion is concerned.

While somewhat contradictory, it may be stated that constant errors are reduced by the weight addition, and there is some evidence leading to the belief that the ruled line is shorter when the weight acts as a retarding influence.

INDIVIDUAL RECORDS

Considering lines 10 mm. long with a retarding weight:

A glance over the seven individual records shows some considerable increase in both constant- and mean-error irregularities, as compared with the free-motion curves, as well as in actual errors; there are distinct losses of volitional control for both classes of errors, especially at or near the ends of the series.

There are cases of very low mean error to be found on all records, where the value is 1/4 mm. or less, and, while the same phenomenon is found with free motion, it is more marked here and occurs more frequently; in most cases it seems as a drop from errors of larger values rather than a gradual matter, as if the subject realized the large error and exerted unusual volitional control to correct and produce a very accurate record, but found that the attention needed was beyond his will-power, as shown by the immediate lapse of accuracy.

There is an indirect confirmation of this view from the introspective testimony of the subjects.

The visual element steadies but does not reduce mean errors when weight is retarding.

The general shape of curve for eyes closed is downward 20-40 beats, and rising for the rest of the series; it is less regular, but more accurate than the visual results.

The fact that constant errors are mostly positive leads to a denial of any inhibitory effect of the retarding weight.

For 1 cm. lines,

weight-retarding movements:

For the average of seven subjects we find:

(1) visual control does not improve accuracy or regularity as in free movements;

(2) a retarding weight tends to make errors constant whatever the speed-rate;

(3) the testimony goes to show that the free-movement records are more accurate than the retardation ones.

Mean errors are:

(1) no more accurate and perhaps less regular, when the weight is imposed;

(2) right- and left-handed subjects are equally accurate.

Constant errors:

(1) the more dexterous hand is superior for coördinations requiring accuracy;

(2) ruled lines are slightly shortened in some cases;

(3) weight-records do not give more accurate results as compared with free movements.

For individual records we find:

(1) retarding weights increase errors and irregularity;

(2) fatigue-points are more marked and frequent than for free movements.

Mean errors,

(1) the visual factor is of some value, but the testimony is varied; right hand for increased regularity only, and left hand for greater accuracy only;

(2) curves are horizontal or reducing with speed-increase.

Constant errors,

(1) the more dexterous hand coördinates better;

(2) all errors are positive;

(3) visual control helps only for regularity;

(4) curves are horizontal or rising.

With weight-accelerating movements, the average record shows a sudden rise in mean error at both ends, not in evidence with free or retardation results.

In general it is to be noted:

(1) that the visual element is of no value for reducing the error, and of little value for promoting regularity;

(2) that the pull-records are closely comparable to the free-motion records, and the accelerating influence of the weight is imperceptible;

(3) that the pull-records are more regular and closer to the free-motion curves than are the weighted records, especially at the ends of the left-hand curves.

For constant errors:

It is more in accord with the facts to say that the imposition of a weight tends to reduce the constant error, and this is more marked when the weight acts in pulling or to accelerate the motion.

Comparing with the weighted curve, we find the same general type of rising curve, similarly located, and the same is true when compared with the free-motion curve. Constant errors are reduced, but slightly, and visual control is rendered nil, when the weight acts either to accelerate or retard the movement, and of the two, the accelerating effect is more marked, as reducing errors and promoting regularity.

There is no appreciable tendency for the weight to reduce the ruled lines when retarding motion, nor is the weight as accelerating, able to extend the line beyond the point set in the free motion.

When contrasting averages from right- and left-handed subjects it may be said:

As compared with free motions there is a slight reduction of error and irregularity more marked with the left-handed subjects, but a general close correspondence of results.

The question is now appropriate, why should the right-handed men show a reduced error for speed-increase, while the left-handed subjects show the reverse? Bearing in mind that the right hand is the more dexterous or better trained in the former case, it may be suggested that the order of record from 20 toward 200 beats is such as to cause more accurate results at the upper limit, in spite of the fact that less time is allowed for discrimination and adjustments; on the other hand, left-handed subjects have much less advantage of practice and habit in their use of the right hand, and will show the predominance of error, when the ruling is too rapid for careful discrimination.

It becomes a struggle between automatism, or semi-automatism, on the one hand, and discriminative processes on the other.

Visual control is not an advantage in the case of accelerating weight, and the large reduction in error with visual control for the free movements is not evident with weighted motions.

For the left-handed subjects we find that the eyes-closed record shows closer work than does the eyes-open curve; it is lower and nearer the line of 0 error; in this respect, it shows the same effect as with the free-motion curve, and to a less extent as for the retardation weight-record. The accelerating record is, however, more accurate and regular than either of the other curves.

It will be clear, then, as observed, that for constant errors, visual control tends to reduce errors and steady records whatever the speed-increase, as far as right-handed subjects are concerned, but this effect is not noted for left-handed subjects using the right hand, and, with their left hand, visual control is a disturbing element.

Further this erratic effect of visual control is less marked but clear when the weight acts as a retarding factor, but is much more noticeable for the free-motion record.

Individual records show few lapses of control for either errors.

The bulk of the evidence is that the weight imposition, whether acting as a retarding or accelerating influence, is effective in rendering the results more accurate and regular, though at least one subject exhibits the opposite effect for the accelerating weight.

The left hand is better for J., Le., and W., but is less regular for all subjects, save Le. and W., showing again a somewhat complex mass of testimony, from which we may conclude that the right hand is the more accurate member for right-handed subjects, and to a much less extent the left hand is preferred by the left-handed subjects.

Visual control is to be noted as effective for accuracy and regularity, except for Ha., where the curves closely intertwine, and for J., where the eyes-closed record is much better.

Weight-accelerating movements:

For the average of seven subjects we find

visual control is of doubtful advantage, for left-handed subjects, but shows a clearly marked reduction of error for right-handed subjects.

Mean errors are:

(1) similar in all respects to free-movement results;

(2) acceleration-curves are closer to free-movement results than are retardation records;

(3) the more trained hand shows reducing error for speed-increase, while the other hand shows increasing errors, because of superiority of practice-effects over the native tendency to increase error as speed-rate rises, for the more dexterous hand alone.

Constant errors:

(1) there is no tendency to overrule, as compared with free movements, when weight acts to accelerate movements, for there are even cases of lines being shortened with accelerating weights;

(2) a weight seems to negate the results of visual control, as a rule.

For individual records we find:

(1) fatigue-points, for the right hand only, are to be found in a few cases;

(2) weight promotes regularity and accuracy;

(3) visual control is effective only for reducing variations of error;

(4) the better trained hand is the more accurate in the records, to a slight extent;

(5) there are evidences of semi-hypnotic or dreamy states in the non-visual series.

COMPOUND MOTIONS

Series of records were taken at 100 mm. and 10 mm. bases for the hands, with what is called compound motion. This consisted in an additional movement of the hand that was not ruling with the pencil, in a similar manner, as regards the amplitude and general character of the motion, but in an opposite direction.

For example, suppose the left hand is ruling a 100 mm. line outward, or to the left; coincident with this movement would be a similar motion of the right hand outward or to the right. The origin of both motions, or the starting-ends of actual and imaginary ruled lines, was optional, it being desired to bring out the effect of such additional motion, as little complicated as possible with restrictions, as to its position or extent. Actually this distance varied from about 10 mm. where both motions were outward to 600 mm. for inward motions.

A comparison of such compound motions with single-hand records shows in general the following:

For 10 cm. lines:

The case for mean errors may be summed up by saying:

(1) left-hand records are less accurate and regular than the right-hand curves;

(2) visual control reduces error and irregularity in all cases, but is more marked with the left hand;

(3) errors increase with speed-increase;

(4) compound-motion records show little increase in error or irregularity, as compared with the simple motions.

For constant errors:

No marked peculiarities are to be noted, but in general,

(1) left-hand records are less accurate and regular;

(2) visual control reduces errors and irregularity;

(3) errors reduce with increase of speed, except for compound motion uncontrolled visually;

(4) compound-motion errors are not much greater, nor is the irregularity increased.

INDIVIDUAL CASES

100 mm. hand with compound motions.

A glance at the charts shows for individual records a few examples of inhibition of voluntary control for both constant and mean errors, it being much more marked in the case of mean errors.

These lapses of control appear for constant errors for A. with l.h.e.c. at 160 and 180 beats, for mean errors for G. with l.h.e.c. at 200 and with r.h.e.c. at 180 beats; for Le. with l.h.e.c. at 50 and with r.h.e.c. at 160 beats; for A. with l.h.e.c. at 200 beats; thus giving evidence that the visual element has a steadying effect, and that the left hand is less reliable save for Le.

There seems reason for contending that the compound motion can be carried out, as arranged, without loss of accuracy or regularity on the part of the ruling hand, and further that the subjects are pretty generally apt to react to a given stimulus within certain rather narrow limits of accuracy.

The evidence is here pretty conclusive that the right-handed subjects, as a whole, show greater accuracy by about 25% for the more dexterous hand; but it will be wise to consider the individual cases on this point.

Greater regularity and accuracy for the right hand is attained by all right-handed subjects, while the preference of Le. for the left hand is clear but much less definite.

For individual cases:

The evidence again is fairly well marked that the more practised hand will give a better account of itself even when visual control is not called on.

The results for compound movements of the hand for 1 and 10 cm. lines are summarized as follows:

It should be kept in mind that the compound records were in all cases taken in connection with a duplicate series of lines for one hand, and called simple movements. These simple movements correspond with the free-movement records that have been considered already.

The purpose has been to bring out the modification of results that a compound movement introduces, rather than to bear heavily on intrinsic phenomena, _i. e._, comparison is deemed more important.

For lines 10 cm. long:

Average of seven subjects:

We find for mean and constant errors:

(1) left-hand records are less accurate and uniform;

(2) visual control increases accuracy and regularity, especially for the left hand;

(3) there is an increase as the speed increases for mean errors, and a decrease for constant errors;

(4) compound movements are practically as accurate and regular as the simple ones for constant errors.

For individual cases:

(1) a few lapses of control or fatigue-spots more marked for mean errors with the l.h.e.c., for the visual sense steadies ruling, and the left hand is less reliable;

(2) compound and simple records show close agreement;

(3) the more trained hand reacts more accurately, and with greater regularity;

(4) non-visual records show a cautionary shortening of line at low speeds, and another at the upper limit, the latter being due to physiological limitations.

For 1 cm. lines:

As far as averages are considered:

We may say, then, for mean errors:

(1) that visual control is effective for reducing errors, and increasing steadiness in both sets of records, being more marked with the less trained hand, the left;

(2) only in the case of the l.h.e.c. curves is the movement of the free hand noted as appreciably affecting the accuracy or steadiness of the record.

(3) eyes-closed records in general show a considerably greater error at 20 beats that practice rapidly reduces up to 40 to 60 beats.

We may note for constant errors:

(1) all errors are positive and confirm the earlier deductions on this point;

(2) visual control reduces error and improves steadiness of record;

(3) the free hand-movement does not affect either the accuracy or uniformity of results;

(4) errors do not increase with speed.

For individual records:

Comparing the individual cases of simple and compound movement, there is no particular reason for concluding that the compound movement is a disturbing influence as far as the records of all subjects are concerned, save possibly the lapse of G. at 20 beats, and on the other hand a case of greater accuracy and evenness for compound movements for Mo. with r.h.e.c. constant error.

It is, then, possible to extend the conclusion of the 10 cm. records, and say that both lengths of lines are ruled with a fairly constant limit of error, whether the movement be simple or complicated by movement of the free hand.

Individually there is testimony in favor of the gain in accuracy with visual control for Hu., Hy., and Le., while the crossing of curves for the other subjects shows that there is no difference in eyes-open and eyes-closed results, the general conclusion being in favor of the value of the eyes for accurate results.

For mean errors the right hand is more efficient in the case of A., Hu., Hy., and Me., while the reverse is the case for the rest, and the evidence goes to suggest that greater accuracy can be attained with the more practised hand.

For constant errors the right hand is more accurate in the case of A., G., Hy., only; Me. and Mo. are equally accurate with the hands, and the rest show a marked preference for the left hand, the evidence being thus conflicting, pointing to the theory of ambidextrous development on the lines of accuracy.

L.h.e.c. records are horizontal for all subjects except Hu., Me., and Mo., who show an upward slope to the curve. Evidences of visual control as giving greater accuracy are noted in general above 70 beats and individually for Hy. and Mo., only, the remaining records being so intertwined that no difference can be noted, all suggesting that the eyes are of but little assistance when the left hand is considered. The right hand is preferred with eyes closed by A., Hu., and Le., while four right-handed subjects testify that the less trained hand is more accurate.

The testimony here seems conclusive as pointing to a denial of the current notion as to the greater accuracy of the right hand for right-handed subjects, and of the left hand for left-handed subjects, and further suggests that visual control is a large factor in the supposed superior excellence of the hand mentioned.

SUMMARIZING

For lines 1 cm. long:

Average of seven subjects:

It may be said that:

(1) visual control reduces both mean and constant errors, especially for left hand;

(2) errors are constant whatever the speed;

(3) constant errors are positive showing overruling in all cases;

(4) there is no disturbance created by the second-hand movement, save for r.h.e.c. mean errors, where the accuracy is less for the compound records; this is probably due to the fact that this record shows the least evidence of voluntary control, and is thus most subject to disturbances;

(5) there is a marked reduction of mean error 20-50 beats, probably due to practice.

For individual cases note:

(1) fatigue-spots for non-visual mean errors only;

(2) the equality of result of both types of movements is noted for all cases;

(3) the non-visual right-hand records for some subjects are more accurate;

(4) the more trained hand is not, as a rule and subject to exceptions, the more accurate one, especially for the non-visual records; and

(5) there is evidence that the superior accuracy of the right hand for right-handed subjects is largely a matter of visual control.

HEAD-RECORDS

There was no attempt made to differentiate the visual element because the very movements of the head prevent the full use of the eyes; as a matter of fact, the subject's attempt to make use of the eyes and the aid is more marked at slow speeds and upon facing the apparatus. It is to be noted here that the visual element, as reducing the error at low speeds, is equally marked whether the eyes are directed toward the recording pencil or not. This raises an interesting question as to the direction the eyes must take for the optimal result; must the eyes be fixed on the moving pencil, on its immediate surroundings, or may they wander at will about the surrounding objects?

My own introspective testimony, corroborated by others, who have acted as subjects for this investigation, is that the eyes are most effective when gathering spatial relations in a gross way, and it may be expected that the effects of visual control as reducing errors will be equally efficient, whether the recording pencil be screened or visible, provided it be possible to bring on the retina objects that are grouped about the centre of attraction, the pencil, but not in its immediate neighborhood.

The records show that there is underruling at the higher speeds because of physiological limitations; but this shortening is greater for the backward movements, for the position of the subject is such as to lead to greater uncertainty as to the exact length of ruled line, and it is probable that a cautionary or inhibitory feeling is the cause of this shortening beyond what will be clearly due to inability to perform the desired movement.

Further, visual control is effective, in the case of constant errors, in lengthening the ruled lines at high speeds, and thus reducing the negative constant error.

While the muscular control of the head is a constant, whether the movement be forward or backward, it is less effective for constant error reduction when the head is moved backward. Consequently, while the backward and forward curves are fairly well in correspondence, there is some reason for offering the proposition that either the eyes are of assistance in forward movements to reduce mean errors at high speeds, and they are of no such value for backward movements, or the muscular control of the platysma myoides, trapezius and associated muscles of the neck group is more nearly perfect for movements of the head forward than for backward motions, the latter being to my mind the better hypothesis.

The results for head-movements for lines 1 and 10 cm. long are summarized:

For lines of 10 cm. length:

Average of six subjects:

For mean errors:

(1) the curve for head-forward and head-backward closely corresponds to l.h.e.c. record; the errors increase by 50% with increase of speed-rate, suggesting that

(_a_) visual control is negligible, as far as seeing the moving pencil is concerned;

(_b_) control of head for forward equals that for backward movements.

For constant errors:

(1) there is underruling at high speeds because of the usual physiological limitations, and this is more marked for head backward results, suggesting that

(_a_) spatial relations are obtained, when the apparatus is visible, that tend to correct underruling, or

(_b_) an extra inhibitory effect, due to lack of knowledge of spatial relations, is added to the normal physical shortening and the subject moves the head a less distance than is naturally possible; or

(_c_) the muscular control is less complete for movements of the head backward.

For individual cases we find:

(1) fatigue-lapses are less in magnitude than for the hands, because the head-movement can be only a fraction of the forearm-movement;

(2) mean errors increase and constant errors decrease with speed-rise;

(3) similarity of individual head-forward and head-backward curves is suggestive, taken with the fact that no typical form of curve is to be found;

(4) head-backward constant errors are greater and less regular in all cases, suggesting that the eyes, in head-forward records, by getting spatial relations, are more efficient.

For lines 1 cm. long:

Average of six subjects:

For mean errors note:

(1) the head-backward records are less regular than the head-forward ones, and rise a little with speed-increase, showing visual assistance for accuracy or better muscular control for the forward movements or both;

(2) the constant errors show shortening of ruled lines at high speeds a little more marked for the head-forward results;

(3) there is constant overruling.

Individual cases suggest:

(1) fatigue-spots are apparent, especially for head-backward movements;

(2) errors do not increase with speed;

(3) the movements of the head forward are under better control.

FOOT-RECORDS

10 cm. records show that

(1) the eyes are of no assistance as to increasing accuracy but help in promoting regularity of error;

(2) a shortening of ruled lines with speed-increase is noticeable, and is probably due to the usual physiological reason;

(3) the feet are capable of less accurate motion than the hands, but show better results than the head;

(4) mean errors increase but constant errors decrease with speed-increase.

Individual records show:

(1) less violent fluctuations of errors in all respects than do the results of head or hands, for vertical foot-movements are of less extreme extent than are arm- or head-motions;

(2) that for visual control with mean errors, no foot is the more accurate, and there is no reason to believe that the feet are unequally educated.

1 cm. records show, as far as mean errors are concerned, that:

(1) visual control is of no value as either reducing actual errors or as effecting greater regularity;

(2) Errors for foot-movements are no less, but considerably more regular than for head-motions;

(3) errors for hand-movements are more regular, and only 50% of the results for either head- or foot-movements;

(4) all curves are horizontal;

(5) there is no appreciable advantage as to accuracy or regularity that can be attributed to either foot. The evidence goes to show that the subjects are ambipedalous, if it be permitted to coin such a word.

In general, we find that, as far as constant errors are concerned,

(1) visual control does not help to reduce actual errors or promote uniformity;

(2) errors for foot-movements are less than the head records, and but little greater than the hand results, while the regularity for the feet is comparable to the hand, and much greater than for the head;

(3) all curves are horizontal;

(4) there is no particular advantage that either foot has over the other either as to accuracy or regularity.

The evidence is that the subjects were ambipedalous, as far as ability to reach a certain point equally well by either foot is concerned. The popular notion has been to the contrary, and it is a point of considerable importance to note the last point.

For example, in kicking, as developed by football trainers, it is commonly assumed that the right foot for right-handed subjects should be developed, and the opposite foot for left-handed men. Or again, in the case of a person lost in the woods and walking in a circle, it is observed that right-handed persons will turn to the left; probably because of the pace of the right foot being slightly longer than the left. My reply to this evidence will be that the data herein presented is for vertical movements of the foot, starting from the floor in every case, the subject being seated in a chair.

On the other hand, it is an entirely different movement, calling for a much different and greater muscular control in the case of kicking or walking that must be considered. For this reason the evidence, while conclusive within its range, is not offered as more than suggesting that the feet are equally well trained for the usual adjustments, and only an exhaustive investigation covering all possible foot-movements will settle the question.

The result for foot-movements for lines 1 and 10 cm. long is here summarized.

For lines 10 cm. in length:

Average of seven subjects:

Note in general that

(1) l.f.e.c. mean error is most erratic, while the same curve is the most accurate, as far as constant errors are concerned;

(2) the left foot mean and constant errors are slightly greater than those for the right foot, for visual records;

(3) mean errors increase and constant errors reduce with speed-increase;

(4) the visual sense improves regularity, but does not reduce errors;

(5) there is a physiological reason for the shortening of lines at high speeds;

(6) the feet are more under control than the head, but less than the hands.

For individual records:

(1) fatigue-lapses, all for non-visual, are less numerous and of less magnitude than for the hands and head, for the vertical movement of foot is likely to be of less extent than that of head and hands for the particular motion required here;

(2) there is no foot capable of being called more accurate than its mate;

(3) the eyes appear to be of no value for reducing or regulating errors for foot-movements.

For lines 1 cm. long:

Average of six subjects:

It may be said in general that

(1) the visual sense is valueless for promoting accuracy or regularity of curve;

(2) errors of foot-movements are more regular and, for the constant errors, more accurate than for the head-records;

(3) errors of foot-movements are less and less regular by 50% as compared with records for the hands;

(4) errors do not increase or decrease with speed-changes;

(5) the feet are equally accurate.

For individual results:

(1) fatigue-lapses and cases of large error-increases are noted in a number of subjects, both for visual and non-visual records;

(2) further, evidence is available as to the indifference to visual control;

(3) no preference for either foot is to be discovered.

The results for individual choice of rhythm.

In this series of records, the metronome was dispensed with, and the subject was permitted to react as he desired, taking the speed preferred because of ease, pleasure, or other reason.

Records were obtained for six subjects for feet, head, and hands, both single-hand and double-hand movements, all for lengths of line 1 and 10