Social Psychology

Chapter 11: Response to Social Stimulation in the Group

Floyd Henry Allport

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The More Complex Social Situations. The forms of reaction described in the preceding chapter are the elementary responses which individuals make to one another. We now advance to the complex groupings in which those mechanisms are to be found at work. The pattern of social conditions in daily life is intricate. It involves varying numbers and arrangements of persons, attitudes of individuals toward one another, relations of personalities, and types of occupation or experience in which the various individuals share. Our present task is to trace the effect of these conditions upon the social behavior of the individual.

Two types of aggregation may be distinguished: the group and the crowd. The distinction between them is not sharply drawn, and one form is capable of passing into the other. For convenience, however, we may define a group as any aggregate consisting of two or more persons who are assembled to perform some task, to deliberate upon some proposal or topic of interest, or to share some affective experience of common appeal.[1] Groups may be organized or unorganized. The crowd we shall distinguish from such formations by the presence of emotional excitement and the replacing of the deliberate group activities by drives of the more primitive and prepotent level.

Groups, in turn, may be classified under two heads: co-acting groups and face-to-face groups. In the former the individuals are primarily occupied with some stimulus other than one another. The social stimuli in operation are therefore merely contributory. Pupils in a classroom reading a lesson in concert from the blackboard illustrate this type of group. In the face-to-face group,

(261) which is necessarily small, the individuals react mainly or entirely to one another. A committee of three or four directors discussing a business project is a group of this sort. The social stimulations in effect are of the direct order. Many groups, of course, combine the direct and contributory social influences, and are thus neither exclusively co-acting nor face-to-face. In the present chapter will be considered the behavior of the individual in response to stimulations from these two kinds of groups.


Social Facilitation: The Influence of the Group upon the Individual's Movements. In Chapter X there was described, under the general topic of suggestion, a two-fold effect of social stimulation in (1) releasing reactions for which the subject is in readiness, and (2) increasing these reactions once they have been initiated. This is precisely the effect of the co-acting group upon its members. The action prepared or in progress is some response participated in by all, and the social stimuli releasing or augmenting such response are the sight and sound of others doing the same thing.

A number of simple phenomena illustrate this law. It has been found that in lifting loads (weights of an ergograph) by bending the finger, the `maximum' weight that the subjects can lift while watching the similar movements of the experimenter's finger is greater than the maximum that can be lifted when the signal to lift is merely the beat of a metronome. In ergographic work and dynamometric tests of hand grip a better score is made when working with others than when working alone. Again, if one holds his hand in readiness for movement upon a freely moving writing board and attends to the hand of another while the latter traces curved designs, his own hand will follow automatically, producing similar tracings.

The most striking instances of social facilitation are to be found on the race track. It is a common maxim among bicyclist that, provided two riders are of equal ability, the one who starts out ahead and keeps ahead throughout most of the race will lose in the end. This is because the sight of his movements have afforded so great a contributory stimulus to the man behind that the latter's

(262) energy is materially increased and he is enabled to win. There is thus a 'competition for loafing' until the final spurt, each contestant striving to make his opponent pace him. Races paced by a faster multicycle are sometimes run in twenty-five per cent less time than those where competition alone is the spur. The well known effect of pacing in horse races is similar. An experiment was performed by Professor Triplett[2] in which forty children were tested, in a number of trials each, for their speed in turning fishing reels.

One half the trials were performed by the child alone, and one half in competition with another child. Although the instruction in each case was to "go as rapidly as possible so as to make a record" many of the subjects were able to exceed in their work in pairs the records they established as their maximum while working alone. Through the auditory sense as well as the visual, the performance of others increases that of the subject. Triplett found that children could be made to count at a faster rate by 'pacing' them; that is, by having the experimenter count at a faster rate than the child's maximum for five seconds just preceding the trial of the child himself.

In all kinds of competitive performance we may recognize two social factors. The first is social facilitation, which consists of an increase of response merely from the sight or sound of others making the same movements. The second is rivalry, an emotional reinforcement of movement accompanied by the consciousness of a desire to win. Although the effects of the two are difficult to distinguish, they are in reality distinct factors in the total response. That social facilitation may exist independently of rivalry is seen in such instances as paced running and the ergographic experiments, in which rivalry was fairly eliminated by the setting. Though these two factors are naturally supplementary, we shall try for the sake of clearness to separate them in the following discussions,

The Influence of the Group upon Attention and Mental Work. The pioneer investigation of the social influence by the method of comparing the individual's mental work in the group with his performance when working alone was carried out by Dr. August Mayer

(263) in 1903. His subjects were fourteen boys from the Volkschule of Wurzburg, Germany. Their average age was twelve years. Five types of test were selected as means of measuring reasoning, memory, and imagination. The tests involved writing from dictation, mental arithmetic, written arithmetic, learning nonsense syllables, and completing written sentences by supplying verbs which had been omitted. Five pairs of tests were used, one test in each pair being given in the classroom to all fourteen boys working simultaneously, and the other to each boy separately. No attempt was made to eliminate rivalry.[3] Three types of instruction were used in the various tests. The first was, "'You are to finish as quickly and yet do your work as well as you possibly can"; the second, "Go slowly but very carefully"; and the third, "Be as quick as you can quality does not count."

[Throughout this chapter the following terms will be used to express various phases of the social influence upon work. 'Social increment' will be used to indicate a gain in the average quantity of work done in the group over the average done alone. 'Social decrement' will denote a loss in quantity of work done in the group. Corresponding gains or losses in the quality of the work done in the group compared with the quality of that done alone will be termed 'social supervaluents' and 'subvaluents,' respectively.]

Under the instruction 'quickly but well,' which is the most natural and effective attitude for work, there was found a substantial social increment, amounting in some cases to from 30 to 50 per cent of the score made when working alone. There was also a social supervaluent; that is, there were fewer errors in the group performance than in the work done by the subjects when isolated. Another interesting result was the greater uniformity of the work of individuals when under the group condition. Working in the group produced a lower average deviation among the scores of the workers than did solitary work. The work of a single individual was also more constant under the social condition. Mayer speaks of this phenomenon as the ‘uniform tendency' of group work.


We thus find that social facilitation (sight and sounds of others working) combined with rivalry produces a distinct increase in the quantity and quality of the product of the individuals. In bringing the attainment of each more nearly to his maximum the social influence also brought them all more nearly to a common level. While working alone differences of energy, industry, and other traits produce wide deviations among individuals, deviations which are reduced when the common incitements of facilitation and rivalry are brought to bear.

Under the instruction `slowly but carefully' the effect, of the words was again reinforced by the social influence. That is, there was a social decrement (loss in speed), but a social supervaluent (gain in accuracy). When directed to work as 'quickly as possible without regard for quality,' there was a gain neither in the quantity nor the quality: only 40 per cent of the test pairs showed a social increment, as compared with 50 per cent which might have been expected by chance. This latter result is probably to be explained as follows. Social facilitation and rivalry were of themselves sufficient to bring the speed of performance almost to its maximum, so that the added verbal instruction to hurry brought about an over-stimulation. The result was a loss of muscular control. Over-stimulation through rivalry alone, a similar phenomenon, will be discussed presently.

In 1904 Dr. F. Schmidt published an account comparing the performance of children's tasks done at home with equivalent work done in the schoolroom. The work assigned included writing exercises, written arithmetic, and German composition. No measure of speed of work was obtainable for the home work, but certain comparisons of quality were made. It is fair to assume that the home work represents the solitary condition of working. There was found a distinct supervaluent for the work done together (that is, in the schoolroom).[4] A few individuals, however, did

(265) better at home. One group of subjects made 270 errors at home, and 184 at school. Schmidt found that omitted letters and words were characteristic of the home performance, while more superfluous letters and words were found in the exercises written at school. This seems to be another evidence of the heightened discharge of motor impulses under conditions of stimulation by the presence and similar movements of one's fellows. Periods of distraction, during which the errors were made, were in group work filled with impulsion to write on, thus producing the superfluous or 'group' type of mistake.

Professor Meumann (1904) carried on experiments, similar to those of Mayer, upon rote memory for words. Lists of disyllabic words, ranging from four to twelve words in number, were read aloud; and the subjects immediately afterward wrote down all the words they could remember. A significant age difference was found in the social increment. Children eight and nine years of age remembered more when tested in the group than when tested alone; while subjects thirteen and fourteen years of age were little affected by the social condition.

In the years 1916-1919 the writer conducted a series of experiments in the Harvard Psychological Laboratory comparable to those already described, but with the following differences of method. Instead of children the writer used as subjects adult graduate students, their average age being twenty-five. Both sexes were included. The work done together was performed in groups of four or five, seated around a table. In the solitary tasks the subjects all worked at the same time, but each in a separate room, the time signals being given by buzzers located in the various rooms. The two conditions T and A[5] were alternated in successive tests in such a way that the effects of practice, adaptation, and fatigue were equalized between them. An attempt also was made to eliminate rivalry, or at least to reduce it to its natural minimum, so that the pure effects of social facilitation could be measured. Several expedients were used for this purpose: First, a constant amount of time was given for each test; and the subject's speed was determined by the amount of the test completed. Hence no

(266) subject finished before the others. All comparisons of achievement and discussion of results were prohibited. Finally, it was emphasized that the test was in no way a competition, and that the records of the subjects would not be compared. All, however, were instructed to work in each test at their maximum speed consistent with accuracy. The subjects while working in the group were made aware that each was doing the same task as all the others.

A variety of mental functions was tested in these experiments. In this section will be described only the tests and results in the fields of attention and mental work. Three types of test were used for this purpose as follows:

(1) Vowel Cancellation Test. Columns of newspaper material were placed before the subjects, and they were instructed to cross out all the vowels, working as rapidly as possible.

Figure 23(2) Reversible Perspective Test of Attention. A twelve-inch figure, similar to that in Figure 23, was placed before the group (seated side by side), or before each subject in the solitary tests. In one set of tests the instruction was given to look first along the line bd, and try to see the face abed as nearer than the face efgh; and as soon as this was done to look at eg, and try to bring the face efgh nearer. When the control of the reversals was obtained, the subjects were required to perceive these two perspectives alternately, making as many of the reversals as they could in one minute. Their report of the number of reversals obtained served as a measure of the speed factor of attention, corresponding to the amount of mental work done in the given time. In another series the instructions required the subjects to fixate the dot in the center of the figure as steadfastly as possible mid try to keep the perspective from changing. Since the reversals are due mainly to eye movements, perfect fixation practically eliminates them. The number of changes occurring in spite of the effort to fixate was therefore used as a measure of the constancy of attention, or the aspect of

(267) attention concerned with accuracy or freedom from lapses in mental work. Two separate experiments were conducted with this test. In the first the data were secured from 7 subjects who were given 10 trials alone and 20 trials in the group. The second experiment employed 15 subjects, each of whom had at least 30 trials alone and 30 in the group.

(3) Multiplication Test. Horizontal rows of problems in multiplication were arranged on sheets, with ten problems in each row. Each problem consisted of the multiplication of a two-digit number by another two-digit number. At the signal the subject began at the left end of the row and performed as many of the problems as possible in one minute. Speed of the process was measured by the number of problems or part problems multiplied; constancy of attention by the freedom of the work from errors. Fifteen subjects were used, each of whom had approximately 30 tests alone and 30 in the group.

The main results of this investigation are summarized in Table VIII. The social increments, decrements, super-, and subvaluents in this table are based upon the average scores of individuals in tests given under the two social conditions, respectively.

The table shows that the presence of the co-working group tends to increase the quantity of work done by the individual members, but leaves the quality practically unaffected. In both vowel crossing and the two experiments with reversible perspective 71 per cent of the subjects affected by the group have a social increment in their work. The percentage for multiplying, though not so high, is also significant (66 per cent). The individual records (not shown in the table) furthermore indicated that the increments of those who did more work in the group were considerably larger than the decrements of those whose performance was greater alone.

The constant character of these results suggests that, for mental work involving close attention: (1) most individuals work at higher speed when stimulated by co-workers, and (2) a few individuals, on the contrary, are retarded by the social influence. These latter form a distinct type.

Turning now to the qualitative aspect, it might be inferred that, since the individuals having social supervaluents and subvaluents

(268) are about equal in number, group stimuli produce little effect upon the quality of individual work. This impression is incorrect; for while some subjects were little influenced by the group in their

  Speed (Quantity)
Indicated by number of vowels crossed, reversals of perspective produced, or problems multiplied
Constancy of Attention (Quality)
Indicated by number of reversals occurring with effort to fixate, or number of errors made in multiplying.
  No of subjects doing more work alone No. of subjects doing more work together No. of subjects doing equal work together and alone No. of subjects having greater constancy alone No of subjects having greater constancy together No. Of subjects having equal constancy together and alone
Crossing Vowels 2 5 0 Not recorded    
Reversible Perspective (1st exp) 2 5 0 3 3 0
Reversible Perspective
(2nd exp)
4 10 1 6 6 3
Multiplying 4 8 0 7 8 0

quality score, others showed marked increase or decrease. Introspective reports indicated the presence of conflicting influences. There was felt the urge toward greater speed and accuracy (facilitation) because of the activity of the others; but there was also dis-

(269) -traction through noise and emotional factors. In some individuals the facilitating influences outweighed the distracting, producing a social supervaluent; in others the distracting effects were stronger (social subvaluent). The subvaluents of the latter class were, on the whole, greater than the supervaluents of the former. One subject, rather asocial in habits, made 39 errors in his solitary multiplication, and 100 while working in the group. Judging from these considerations the advantage for quality of performance seems to be upon the side of the solitary condition.[6]

It is not difficult to understand why stimuli from the group should have a favorable effect upon the amount but not upon the quality of work. `Amount' represents speed of movement; whereas `quality' is determined, strictly speaking, not by movement at all, but by that fixity of the attention process which prevents any lapse or error. Our study of social facilitation has in all cases shown it to be a release or augmentation of some form of movement. The social stimuli reinforcing movement are more effective than those suggesting constancy of attention.

The distribution of the errors throughout the multiplication tests is significant for interpreting the distracting influence of the group. In the social setting the errors tended to be bunched together in successive problems of the test, while in solitary work they were more widely distributed. The index computed to express this tendency of the errors to be closely grouped we may call the cumulative error score. This score was larger in the group work of 10 subjects, and larger in the solitary work of only 3.[7] Distractions are stronger in the presence of co-workers, and lapses of attention involving errors are correspondingly lengthened. An emotional factor is also significant here. Probably many of the errors made were recognized, though both lack of time and the instructions forbade their correction. It is likely also that the subject was conscious that others were probably solving the problem correctly and that 1115 own performance w35 therefore inferior to that of his fellows. In consequence the recovery of composure was delayed

(270) and further mistakes made in problems immediately following. This interpretation, if correct, points to a deep-lying tendency to estimate one's own performance in relation to standards set by the group, and to be confused by comparisons which are unfavorable to one's self.

The Influence of the Group upon Association. The effect of stimulation from co-workers upon the free flow of associated word responses was studied by the writer in the following manner. The subjects in the two conditions, T and A, were given sheets of paper ruled with vertical columns on which to write successive words as rapidly as they came to mind. At the expiration of the first and second minutes (in some of the tests) a signal was given, and the subjects indicated by a line the last word written at that instant. At the end of three minutes the test was terminated. Immediately after each test the subjects were required to underscore on their papers all personal (ego-centric) associations, that is, all words derived from some definite personal experience of the individual concerned. Since speed of association is likely to be greater than the speed of writing and therefore to be hampered by the latter, the subjects were instructed in some of the experiments to write down only every third or every fourth word that came to them.

Table IX presents the number of subjects having social increments and decrements in the average number of words written under the various conditions.

An increase in speed and quantity of work under group influence seems to be as characteristic of free association as it is of other mental processes. In various experiments from 66 to 93 per cent of the subjects were facilitated by the stimulus of others doing the same task. In experiment 2 there were 14 social increments to 1 decrement. Where every third word was written (exp. 4) 75 per cent worked more rapidly in the group; while in the third experiment where every fourth word only was written the number of social increments fell to 66 per cent of those affected. This result shows clearly the nature of social facilitation. When the response of individuals is mainly implicit or internal (as in pronouncing two thirds of the words to one's self) facilitation is at its lowest. It is directly proportional to the amount of overt action through which

(271) the co-workers stimulate one another. The decrease in facilitation may also be partially explained by the fact that `to think to one's self' is generally more difficult when others are present than when alone.

Table IX. Influence of the Co-Working Group upon Speed of Association
Exp. No. Number of subjects Number of Tests Method No. Of subjects writing more words alone No. Of subjects writing more words together No of subjects writing an equal number of words alone and together
1 3 9 12 Every word written 1 2 0
2 15 11 13 Every word written 1 14 0
3 14 5 6 Every fourth word written 4 8 2
4 8 8 11 Every third word written 2 6 0

The qualitative aspects (not shown in the table) were also significant. In experiment 2 twelve subjects wrote a greater number of personal associations alone than they did in the group. Only three produced more in the group than alone. The introspection also verified this tendency to be `drawn out of one's self' in the play of word association in the presence of others. When alone there is a

(272) greater tendency toward the ego-centric type of response. Either the group directly affords many associations of a compelling sort, or else it inhibits the attitude of introversion and day-dreaming. It is harder to be ‘shut in' in our thoughts when we are in the presence of fellow workers. The decrease of personal associations in the group is of especial interest because it represents, not the result of face-to-face reactions, but an attitude unconsciously assumed upon working in the mere presence of others.

By counting the scores of the one-minute periods of the association tests separately the social facilitation was found to be greatest in the first minute and least in the third. That is to say, during the first minute, when associations come readily, social stimulation produces a greater addition of speed than toward the end of the test, when through fatigue and the exhaustion of ready responses, the facility of association has decreased. The greater the degree of activity in progress, the stronger the effect of social facilitation upon it.[8]

The Influence of the Group upon Thought. We have seen that the stimulation from the co-acting group facilitates the flow of free association. There now arises the question of its effect upon the more controlled process of reasoning. This problem was investigated by having the subjects write short arguments, during five-minute periods, in the group and alone. Didactic passages of uniform character were chosen from the writings of two ancient philosophers. In each test the subject was given a passage and was directed to write arguments, as many and as valid as possible, to disprove the statement of the passage. While working together the subjects were made aware that all were writing upon the same selection. Nine subjects were used, and seventeen tests given in each of the two conditions, A and T.

The effect upon quantity was again in favor of the group work. Fight out of the nine subjects produced a greater number of statements intended to disprove the passages in the social than in the solitary environment. The arguments written were next graded

(273) according to their value. The most cogent and relevant statements received a score of 3, those next in worth a score of 2, and the most superficial and unconvincing a value of only 1. Table X contains the result of this scoring.

Table X. Influence of the Co-Working Group Upon Quality of Thought
Quality of Arguments Number of subjects having higher percentage of arguments described in column at exteme left: Number of subjects having equal percentage alone and together
  Alone Together  
Arguments showing best reasoning (score 3) 6 3 0
Arguments showing reasoning of moderate value (score 2) 4 4 1
Arguments showing poorest reasoning (score 1) 3 6 0

It will be seen from the table that two thirds of the individuals produced a higher percentage of best arguments while working alone than while in the group; and that, by a reversal of the ratio, two 'thirds produced a higher percentage of poorest arguments while working in the group. The tendency toward reasoning of indifferent value was equal in the two conditions. There is thus indicated a social subvaluent for argumentative or discursive reasoning. This finding is in accord with commonly observed facts. Upon recalling speeches made under a strong social influence, such as that of a political rally or an oral debate, we are often surprised that we had not noticed the faulty logic upon which the arguments were

(274) based. There appears to be a spreading out or 'conversationalizing' of our thought in the social setting. We strive rather for convincing effect than for separate ideas of logical worth.

There is, in short, a kind of wordiness in the reasoning done in '' the group. Six out of nine subjects in the above investigation used more words in their arguments written with the others present than they did when alone.[9] The same law is here illustrated as in the experiments upon association: it is the overt responses, such as writing, which receive facilitation through the stimulus of coworkers. The intellectual or implicit responses of thought are hampered rather than facilitated .[10]

Although we have compared the results of the experiment just described with the quality of reasoning heard in a public debate, it must be remembered that in the group used there was no actual face-to-face contact of individuals. Such social stimuli as were present had only a contributory effect upon the subject's response to the task set. For this reason the tendency to write rather for conversational effect than for logical precision is the more interesting. As in the case of free association, merely being in the presence of others working upon the same problem places us in an attitude toward the task which is different from our approach to it in solitude. When working with others we respond in a measure as though we were reacting to them.

The Influence of the Group upon judgments of Comparison. A process allied to thought, namely, the evaluation and comparison of stimuli, has also been subjected experimentally to the group influence. In the first study of this sort the writer used judgments of pleasantness or unpleasantness of odors. Five series of ten different odors each were arranged in bottles, each series comprising a variety of affective values ranging from putrid odors to per-

(275) -fumes. Each subject was provided with a set of bottles, so that in the group work all were able to smell the same odor at the same time. The fact that each was judging the same odor at the same time as all the rest was further emphasized by interchanging the bottles among the subjects to show that their contents were identical. The subjects judged the pleasantness of the odors by drawing lines on standard strips of paper, a short line for an unpleasant odor and a longer one for a pleasant odor. The length of the line was proportional to the pleasantness which the subject experienced from the odor in question. In other trials the affective quality was expressed numerically on a subjective scale ranging from 0 to 100.

In each of the five series there were thus obtained ten judgments (one for each odor) while smelling the odors with the group, and ten judgments while working alone. This comprised the record of each individual for that series. The ten solitary judgments were now taken and arranged in a graph, the value of each judgment being laid off as distance from the base line upon a vertical ordinate. The ten odors were plotted in this way beginning with the most unpleasant at the extreme left. A line connecting the ten points thus plotted represents the curve of affective judgment for the ten odors in the solitary condition of judging. For an illustration of such a curve see the solid-line curve in Figure 24. The values of the same odors when smelled and judged in the group were plotted upon the same ordinates, and a curve thus described expressing the affective judgments of the same series made under the social condition (see dotted-line curve in Figure 24). The curves for the five series together and alone were then averaged for each subject and individual curves made whereby the social and solitary judgments of odors of various degrees of pleasantness could be readily compared for each subject. A final graph was made for the entire group of seventeen subjects based upon an average of the individual curves. This is the graph shown in Figure 24.

All inspection of Figure 24 shows that the curves representing the judgments under conditions A and T cross in their middle portions. For the unpleasant odors (at the left) the A curve is lower than the T curve; while for the pleasant odors (at the right) the reverse relation holds. The unpleasant odors therefore were

Figure 24. Influence of the Group upon Judgments of Pleasantness and Unpleasantness(276) estimated as less unpleasant in the group than when judging alone; and the pleasant were estimated as less pleasant in the group than. in the solitary judgments.[11] Expressed in other words there is a tendency toward moderation in judgments made in concert with others, the individual avoiding those extreme judgments at either end of the scale which he does not hesitate to make when judging alone.

Figure 24 is more than a mere average of the individual curves. It is a type to which the curves of the individual subjects closely conform. The same type of crossing of the T and A curves, indicating avoidance of extreme judgments in the group, was present in the graphs of 70 per cent of the subjects, while the graphs of 23 per cent more approximated this type.

The entire experiment was repeated using series of weights instead of odors. The subjects were required to estimate the weight of each of ten objects, identical in appearance, in relation to a light and a heavy standard given at the beginning of the test. Upon judging each weight they were asked to record their judg-

(277) -ments as they had done with the odors. The average curves for the judgments of all subjects, together and alone, are presented in Figure 25. This graph closely resembles that shown in Figure 24. When judging in the group the heavier weights were judged as lighter than when judging alone; and the lighter weights were judged as heavier. In sensory as well as affective judgments the individual avoids extreme opinions while working with others. Sixty-six per cent of the subjects had their T and A curves in the same relation as those in Figure 25; while 27 per cent more came fairly close to this type.

Figure 25 Influence of the Group Upon Judgments of WeightThe fact, therefore, of shunning extremes and expressing more moderate estimates when in the presence of other judges seems well established. How shall it be interpreted? In the writer's opinion it is the result of an attitude of submission which we assume, often unconsciously, in the presence of n. group. Where all are engaged upon the same sort of task this submission takes the character of conforming to the manner in which the other members are reacting. More specifically, upon approaching the extremes of the series, the question arises in the subject's consciousness, 'How extreme shall I make this judgment?' He feels that he is more likely to be at

(278) odds with the judgment of his associates if he goes too far than if not quite extreme enough. Hence he errs upon the side of moderation. In the introspective reports the subjects showed lively interest in how the others were judging the odors or weights. This interest took the form of imaginal comparisons, feelings of restraint upon their own judgments, and desire for corroboration. One subject noted that his social consciousness rose to a higher pitch as he neared the extremes of the series.

A social attitude of considerable importance is here revealed. Barring individual exceptions (a few of which were found in the experiments described), there is a basic human tendency to temper one's opinions and conduct by deference to the opinions and conduct of others. Early training and social contact have bred in us the avoidance of extremes of all sorts, whether of clothing, of manners, or of belief. This tendency is so fundamental that we are seldom conscious of it; yet we are seldom if ever without it. In the writer's experiment all discussion was prohibited. The individuals were aware that their judgments would not be compared and that there was no possible advantage in adhering in their reactions to an imagined group average. Yet, as in the case of association and reasoning, the mere proximity and co-working of other persons were stimuli which sufficed to evoke this modified form of response. To think and to judge with others is to submit one's self unconsciously to their standards. We may call this the attitude of social conformity.

Individual Differences in Social Facilitation. Individuals differ in their degree of susceptibility to the influence of the group. Children are more susceptible to the facilitating social influence than adults. But even among adults there are conspicuous differences. In the investigations described above certain individuals had a social decrement in their output, or failed to show the usual reaction to group stimulation in thought and conformity of judgment. Habit, customary work environment, nervousness and distractibility, as well as reclusiveness, negative suggestibility, attitudes of superiority, defect of sociality, and other traits are factors which may help us to account for these atypical reactions.

Another type of individual difference deserves special notice.

(279) The facilitating influence of the group is greatest for the slower and poorer workers and least for the more rapid and efficient. Mayer found a consistent relationship of this sort. It occurred also in the experiments upon mental work and association conducted by the writer: the correlation between speed of solitary work and gain through working in the group, though low, was always inverse. In certain instances it reached -.5 or -.6. The explanation of this phenomenon is partly as follows. The average speed of movement of the co-workers is less than that of the most rapid. Hence stimulation from the group would tend to retard rather than facilitate the movements of the latter. The effect would be similar to that of trying to pace a fast horse by a slower one. The slowest workers, on the other hand, would find the contributory stimuli rapid and hence facilitating. Rivalry also plays a part in this result, as will be later shown.

Social Consciousness in the Co-Working Group. The introspective reports of the subjects in these social experiments show practically always an awareness that the others 'are working hard and fast.' The individual is conscious of specific facilitating stimuli, such as the tapping of pencils, shuffling of feet; sounds of attentive respiration, peripheral vision of the speed, pauses, and degree of progress of one's neighbors. The facilitation consciousness resembles other forms of suggestion consciousness in the impulsion toward movement without adequate motive or reason. There was a scarcely articulated awareness that 'the others are writing rapidly, so I must write rapidly also.' Such conscious states may be quite independent of any feeling of rivalry. There was reported also a consciousness of impeding factors, including distraction and emotional inhibition resulting from imagined comparison of one's own achievements with those of others. Realization of inferior performance or of other discrepancies always brought a heightened self and social consciousness. Social consciousness varies according to the type of occupation in which the group is engaged. It is greater for work requiring overt and conspicuous movement than for the more intellectual tasks, which both demand closer concentration and afford fewer stimulations from the behavior of one's co-workers.


Rivalry. Rivalry works hand in hand with social facilitation in the production of the large social increments found both in experiment and practice. Industry, education, and sport are three of the many fields in which the direct spur of competition may be added to social facilitation for increasing the energy and accomplishment of the worker. Combined with the economic incentive of bonuses, rewards, and payment by piece-work, the drive to excel others is an effective tool in the hands of the factory supervisor.

There are limitations, however, to such methods. Rivalry, like social facilitation, increases the quantity, but does not improve the quality, of the output. There is likely in fact to be a deterioration in quality. This is the case in adult occupations even under the conventional instruction 'work as quickly as you can consistently with careful work.' The effect of competition is more favorable for speed of movement than for precision or constancy of attention. The laws of rivalry must be studied in relation to the individual. While competition is productive of speed in most persons it overexcites and retards the work of some. We may refer again to the experiment of Triplett upon rivalry in the turning of fishing reels (see p. 262). Forty subjects were used in this investigation. Twenty of them gained markedly in the competitive trials over their average for solitary work. Ten were little affected by the competition. These were for the most part older children. And ten actually lost in speed under the influence of rivalry. These last showed evidences of emotional excitement and a loss of motor control. Young, nervous, and excitable subjects are prone to over-stimulation through rivalry, with a consequent lowering of efficiency in competitive performance. Triplett found a higher percentage of girls than of boys susceptible to increase of performance through competition.

The effect of rivalry, like that of social facilitation, varies inversely with the ability of the worker. In 1914 Dr. W. Moede published an account of rivalry, in speed of tapping and strength of hand grip. Seventeen boys between twelve and fourteen years of age participated. The more rapid tappers made actually lower scores when tapping in competition with the others than when working alone. The speed of the nine slowest individuals, on the

(281) other hand, showed a distinct social increment. This increment was somewhat larger than the decrement of the more rapid half. By thus reducing the scores of the more rapid and increasing those of the slower workers the individual differences in performance were materially lessened. Moede thus found, like Mayer, that group work tends to bring the workers to a more nearly uniform rate of speed. This 'uniform' or `leveling' tendency we have already partially explained by facilitation or retardation through the tempo of other workers' movements (p. 279). The slower workers' reactions are facilitated because they are stimulated by movements made at a faster rate than their own. The more rapid lack such incitement. Rivalry also cooperates in the leveling tendency. The more rapid workers, realizing the ease with which they excel, lose interest in the competition and slacken their efforts; whereas the slower subjects, provided they are not hopelessly outclassed, are aroused to greater effort through their zeal to rival the others. This effect of rivalry must be regarded as distinct from that of the difference of social facilitation with which it is allied. The latter is merely the influence of external stimulations from the working of others, while the former represents a difference of attitude and incentive.

In the dual contest the situation is somewhat altered. Here greater ability and lesser ability become the basis of ascendance and submission, traits which are asserted early in the encounter (see p. 120). In contests in strength of hand grip between two boys Moede found that the rivalry attitude gave way almost immediately to an attitude on the part of the stronger to conquer his opponent, and on the part of the weaker merely to make the best showing he could. The more equally matched the two contestants the greater will be the effect of rivalry on both sides in the ensuing struggle. This is true also of work in groups. By separating the superior half of his group of tappers and allowing them to compete among themselves Moede found that a distinct social increment, instead of a decrement as formerly, was obtained.

Apart from ability, rivalry seems to be more a part of some personalities than of others. There are ascendant individuals who love a contest of any sort, and whose attitude is persistently to win,

(282) and to stand at the head of the list. Others find strenuous contests too exciting. They are of the despairing, less self-confident type. Their desire is merely to 'make a respectable showing,' and not to stand at the foot of the list. Continual defeat will usually break down the attitude to win, and reduce it to the less ambitious desire to make a good record. Athletes employ a deliberate device for this purpose. A runner allows his opponent to keep abreast of him for some time, pretending that he is running at his maximum speed and struggling to keep up the pace. He then suddenly darts ahead with a disconcerting burst of power. This discouraging process is known as 'running a man's head off.'

Auto-Rivalry, 'Team-Work,' and Esprit de Corps. There is a consolation for the individual who is outclassed in a competitive performance. Although he cannot equal his rivals' records he can improve upon his own. This is the well-known attitude of auto or self-competition. Its true origin in actual rivalry (hetero-competition) may be readily surmised; for it is by improving one's own score that one decreases the distance between self and the next higher competitor. Also, if one cannot excel his rivals, he can at least show a greater capacity for improvement. He can thus make a conquest in relative terms. The handicap and the children's maxim of 'taking a person your own size' are practical illustrations of this attitude. There is also less discomfort through emotional tension in the auto-rivalry than in the hetero-rivalry consciousness.

Competition between groups combines the attitude of cooperation with that of rivalry. The setting also favors auto-competition. Each member of the team tries to 'outdo himself' in order that his side may outdo the other. There is also an extension of the awareness of self to include the group; and an exhilarating excitement in the feeling of magnified conquest. It is pleasant to win a personal contest; but it is little short of sublime to be a member of a victorious group. Moede's researches included strength tests not only in dual contests, but between competing teams of five boys each. The records of the individuals in the group contests exceeded those in the dual contests, just as the latter excelled the records for the solitary tests.


A phenomenon closely allied to cooperation is that known as esprit de corps. The attitude of the individual is the same as in inter-group competition, except that the ideal is permanent excellence, or morale, rather than immediate victory. The soldier with this attitude strives to make his company the best in the regiment, and his regiment the best in the division.

The Physiological Basis of Social Facilitation and Rivalry. When, in the co-working group, rivalry enters and produces social increment, we may assume that the task is no longer simply a mechanical duty, facilitated by working with others, but a definite struggle in which each individual strives to prevent the others from beating him (that is from thwarting his habit of self-esteem). Whatever the competitive. occupation may be, it serves therefore as an efferent modification of the prepotent struggle response, that is, as a method of carrying on the struggle.

As introspectively reported, rivalry is emotional in character. It is a kind of mild anger which accompanies the modified struggle reaction. Its close relation to the stronger form of the anger emotion is shown by the fact that it passes readily into the latter. Competition in industry, scholarship, or other fields usually provides a successful method for use in the struggle to assert our prepotent interests. Rivalry is the emotion here aroused. Under some circumstances, however, more violent struggle responses are needed. Anger, for example, is quickly aroused by unsportsmanlike conduct on the football field, because without fair play it becomes impossible to win the struggle by the method of sport; and this outlet being blocked, the more primitive responses are called forth. Friendly boxing contests lead often to more serious blows, the rivalry and the anger emotions being fundamentally of the same character. The visceral reaction in rivalry, as in other emotions, probably liberates internal secretions, and involves other responses characteristic of the sympathetic system. By this means higher level of energy is provided fur the competitive exertion. Social facilitation without rivalry is more difficult to explain. Since we usually both hear and see ourselves work we might suppose that the sound and sight of our movements become conditioning stimuli; and that they tend to reevoke or augment in us these

(284) very movements from which they were derived. Similar movements made by others, since they give similar stimulations, would then serve the same purpose. When multiplied many fold by the co-working group these conditioning, contributory stimuli become important agents in facilitation. But on the other hand, there are many forms of task in which the explanation of conditioned response would scarcely apply. Attitudes of a more complex sort are also probable: knowing that those about us are to be doing the same task, we are disposed to work more rapidly from the start. Meumann ascribes social facilitation to an attitude of over-compensation. We work so hard to overcome the distraction incident to group activity that we actually accomplish more than we would without these hindrances.

Summary of the Experimental Study of the Group Influence. Groups in actual social life are far more complex in inter-relations of individuals than the experimental settings described above. For this reason, although the experimental findings are useful and important, generalizations from them must proceed with caution. We may summarize these results as follows:

The social stimulations present in the co-acting group bring about an increase in the speed and quantity of work produced by the individuals. This increase is more pronounced in work involving overt, physical movements than in purely intellectual tasks. In adults the group produces no improvement in the constancy of attention or the quality of the work performed. Some individuals in fact do inferior work in the presence of co-workers. There is a lowering of the logical value of reasoning carried out in the group; but an increase in the number of words by which such reasoning is expressed. In at least one type of work the tendency toward a social increment is strongest in the earlier part of the task.

The social increment is subject to individual differences in respect to age, ability, and personality traits. It is greatest for the least able workers and least for the most able. 

Two processes are accountable for the accelerating effect of the group upon the individual's work. The first of these is social facilitation. The movements made by others performing the same task as ourselves serve as contributory stimuli, and increase or has-

(285) -ten own responses. This process is accompanied by a consciousness of impulsion. The second process is rivalry Its occur' rice is in direct proportion to the competitive setting of the group occupation, though a certain degree of rivalry seems natural to all co-activity. Its effect is that of emotional reinforcement, the struggle to assert various prepotent needs or interests being the response which it reinforces. It improves the speed and quantity rather than the quality of the work in which it is operative. Rivalry, like social facilitation, varies with age, sex, and personality. Some persons are susceptible to an actual loss in performance through over-stimulation when the rivalry situation is stressed. In order to get the maximum effect from rivalry, two individuals must be about equally matched in ability. When rivalry produces a social increment in a group there is a tendency for the performances of the individuals to approach a common level. This is because the more rapid slacken their effort through absence of formidable competitors, while the slower increase their effort in the hope of excelling those above them. Auto-competition and rivalry between groups have their characteristic conscious attitudes, and are conducive to substantial gains in the output of the individuals.

Working in the presence of others, even though there is no direct contact nor communication, establishes certain fundamental attitudes. We are confused and distracted whenever we feel our reaction to be at variance with or inferior to the average behavior of those about us. In the association process we tend to inhibit ego-centric trends and personal complexes. In our thinking we assume a conversational attitude, becoming more expansive and less precise. And finally, we avoid extremes in passing judgment, tending, often unconsciously, toward conformity with what we think to be the opinion of those about us.


The Nature of Face-to-Face Groups. Direct social stimulation and response do not lend themselves to experimental control so readily as the contributory influences of the co-acting group. For this reason the investigation of responses in the face-to-face group has been neglected. Yet this is a large and important field. When-

(286) -ever two or more persons talk or otherwise react directly to one another we have a primary, or face-to-face, group.[12] The doorstep conversation of two housewives represents one of the simplest and most universal forms. Other examples of the `sociability' type are the children's party, the reunion, and the intimate afternoon tea. Pals, cronies, and cliques of three or four (rarely exceeding six) are common in childhood and youth, but are generally displaced in adult life by associations of vocation and family. Small discussion groups, literary and scientific societies, and committees, though including a higher degree of organization as well as factors of co-activity, retain also a certain face-to-face character. The consultation of doctors, lawyers, and financiers, councils of war, and deliberations of juries illustrate more imposing aggregations of the same type. In the governmental assembly, the convention, and the political rally the face-to-face relation, though present, tends to pass over into the situation of the audience, the co-acting group, and the crowd. The manner in which human beings react to one another under all these conditions presents a vast field of inquiry as yet scarcely touched by observation or experiment.

Social Control, Participation, and Sex as Drives in Primary Groups. In many face-to-face groups, such as committees and other constructive bodies, social behavior takes the form of securing adjustments of ascendance and submission among the members. Each asserts his opinion as to what should be done, and supports it by suggestion, by logic, or by the domination of his personality. Final decision in the adoption of a plan may come by discussion, persuasion, compromise, or sheer majority. In any case, however, the struggle for personal ascendancy looms large. The conclusion arrived at is as likely to be the result of control by ascendant personalities as of rational planning.

Face-to-face groups of the congeniality type are based upon the pleasure of responding to others and causing others to respond to us. The drive is for control of others, not to the extent of determining their reactions, but simply to make them react. Social behavior in itself is sought as an end. There is a universal tendency

(287) to produce reactions in others. It originates probably in the habit developed in early childhood of controlling parents and others in order to secure satisfaction of the bodily needs (cf. Chapter III) and of interests based upon these drives. Another probable source is the childish habit of doing things in order to attract attention (that is, to make others react to one).[13] As we grow up and become more self-sufficient the old habit persists as an inclination to control merely for the sake of controlling.

The reaction-getting habit is both striking and universal. The boy is not content with seeing a squirrel sitting in a tree; he must throw a stone at him to make him do something. The writer's three-year-old son made stealthy efforts to tread on his father's bandaged sore toe, looking meanwhile at his face in sober expectancy. A boy of eight did the same thing, except that it was a `make believe' attempt. Bullying and teasing is universal in childhood, and in maturity grows into badinage and practical joking. As the child treads on sore toes we grown-ups tread upon complexes and idiosyncrasies. Traveling salesmen contrive to get their interlocutor in a good light, and then try out various jokes and items of interest in order to make him reveal his personal traits. Reclusive persons irritate us, because it is difficult to get a response from them. The superiority of the mechanical toy and the talking doll to other playthings is based upon our reaction-getting drive. In all accounts of sensational trials, executions, and the like, the public demands to know just how the victim reacts when the sentence is passed or the noose adjusted. No newspaper account is complete without these details. The `close-up' of the actor's face in the `movie,' and the savage humor of the comic supplement indulge our craving to get a reaction, ludicrous or tragic, but always intense, from every situation.

Congenial face-to-face groups, to be sure, are not usually based on social participation in this elementary and savage form. Yet sociability, responding and producing responsive expressions in others, is a socialized form of the same drive. These groups afford

(288) also other pleasurable types of response. The facilitation of movement in co-activities such as dancing, card-playing, laughing, and experiencing pleasant emotions in the company of others are fundamental enjoyments of social gatherings. We derive an increase of'! pleasure in our drives and hobbies by discussing them with those whose interests are similar. Novel ideas, witty remarks, and personal gossip, diversions sanctioned for us because ethers indulge in them, release our inhibited sex attitudes and hostilities in an agreeable fashion. More than is generally recognized the popularity and animation of the face-to-face group is based upon sex attraction. This impulse usually remains unconscious, and we ascribe our pleasure to 'sociability' or to a `gregarious instinct.' But from the kissing games of pre-adolescents to the ballroom gayety of adults the mixed party is universally favored. The stag affair is sought only as a relief from the too rigorous strain of inhibitions made necessary by the presence of the opposite sex. Permanent face-to-face groups and 'crushes' among college girls depend to an unrecognized degree upon unconscious sexual fixation. Rivalry, display, and the prepotent habit of securing social approval add to the zest of the primary sociability group, and often ally themselves with the desire for sexual conquest.

Conversation and Discussion. Conversation, the outstanding form of social behavior and contact in primary groups, deserves a word of notice. Little need be said about its more obvious aspect, namely, that it is an interchange of stimulus and response by which thoughts and feelings are aroused in one's interlocutor. More fundamentally considered, it involves the opposed efforts of two persons for expansion and control through language, each being

only partially successful. A tries to control B by impressing upon him his (A's) knowledge, feelings, or beliefs; and B strives in the same manner to impress A; but neither succeeds to any marked extent. This fact can be readily observed by eavesdropping upon the conversation of others. It cannot be detected in our own conversations because we are so animated by our own narrative or viewpoint that we misjudge the other's sympathy with what we are saying. We think it to be as thoroughgoing as our own.[14] The

(289) attitude of the other speaker, however, might be put into words as follows: "What you say is interesting. But now listen to this that happened to me !" Since B's attitude is ascendant rather than passive and receptive he does not react to A's remark with serious or logical consideration. Often he does not fully understand it. Some word or phrase of it serves as a trigger to set off his own habit of thought or his own associated experiences. "That reminds me" is the frequent overt indication of this process.

In discussions, where one is not permitted to be `reminded of things' at random, but must stick to a point, there is still the most imperfect sort of contact. In formal debates the argument of one speaker will be taken up by the opponent, not for the purpose of giving a direct answer on the former's ground, but merely as an introduction from a new angle to the opponent's attack. So he reiterates his arguments with new variations upon the old theme. We go away from such gatherings disappointed that such good minds should have wholly failed to connect.

In spite of all this, discussion produces constructive results; for it brings new points of view to bear upon the thought habits of the participants. The writer has collected the written opinions of students upon debatable questions before and after a period of free discussion. In the reports written afterward there were instances where facts presented by others, though taken up in a sense different from that intended, had been worked into new and very substantial arguments. Conversation and discussion thus proceed by a series of mutual partial misunderstandings which may produce good results in directing old habits of thought along new channels. This is what is meant when we say that one's genius strikes fire from the words of another. If one is not too impervious to social stimuli, something great and even new may be produced by putting two or more heads together. From this standpoint it is as necessary also to have an opinion of one's own as it is to be willing to listen to others. Otherwise the result is simply a replica of the other's thought. To conceive a new idea we must have an old one to start with. This stimulation of new ways of conceiving old facts represents the profitable side of discussion. It is coming to be

(290) recognized in modern education in the 'socialized recitation' and the 'group game.' [15]

The good conversationalist is therefore one who can be a listener as well as a talker. In few human relations do personality traits count for so much. One must be ascendant, yet disciplined to alternate his ascendancy with attitudes of submissive and sympathetic attention. He must be expansive and still control his discourse by tact and an aesthetic understanding of proportion. He must be able and ready to respond to faint and even unconscious clues from the behavior of his fellows. His associative processes must be rapid and capable of following abrupt changes. And he must possess insight, humor, and a genuine love of social participation.


Burnham, W. H., "The Group as a Stimulus to Mental Activity," Science, N.S. 1910, XXXI, 761-67.

Triplett, N., "The Dynamogenic Factors in Pace-making and Competition," American Journal of Psychology, 1897, IX, 507-32.

Scherfig, F. E., Der psychische Wert des Einzel- and Klassen-unterrichtes. Leipzig, Dissert, 1882.

Mayer, A., "Ueber Einzel- and Gesamtleistung des Schulkindes," Archiv fur die Gesamte Psychologie, 1903, I, 276-416.

Meumann, E., Ham- and Schularbeit. Leipzig, Klinkhardt, 1914.

Schmidt, F., "Experimentelle Untersuchungen uber die Hausaufgaben des Schulkindes," Sammlung von Abhundlungen zur psychologische Pddagogie, 1904, I, 181-300.

Moede, W., "Der Wetteifer, Seine Struktur and sein Ausmass," Zeitschrift fur Padagogische Psychologie, 1914, xv, 353-68.

———, "Einzel- and Gruppenarbeit," Praktische Psychologie, 1920-21, u, 71-81; 108-15.

———, Experimentelle Massenpsychologie. Leipzig, Hirzel

Allport, F. H., "The Influence of the Group upon Association and Thought," Journal of Experimental Psychology, 1920, III, 159-82.

Munsterberg, H., Psychology, General and Applied, ch. 20. Psychology and Social Sanity, pp. 181-202.

Cooley, C. H., Human Nature and the Social Order, ch. R.


Clow, F. R., "Cooley's Doctrine of Primary Groups," American Journal of Sociology, 1919, XXV, 326-47.

Vincent, G. E., "The Rivalry of Social Groups," American Journal of Sociology, 1911, XVI, 469-82.

Smith, S., and Guthrie, E., "Exhibitionism," Journal of Abnormal Psychology and Social Psychology, 1922, XVII, 206-09.

Burtt, H. E., "Sex Differences in the Effect of Discussion," Journal of Experimental Psychology, 1920, III, 390-95.

Woolbert, C. H., "Conviction and Persuasion: Some Considerations of Theory," Quarterly Journal of Public Speaking, 1917, III, 250-64.

Williams, J. M., Principles of Social Psychology, ch. 2.

Ordahl, G., "Rivalry: Its Genetic Development and Pedagogy," Pedagogical Seminary, 1908, XV, 492-549.


  1. The word ‘group' is sometimes used in a sociological sense to denote a collection of individuals, not assembled in one another's presence, but joined by some common bond of interest or sympathy. In so far as the behavior of individuals in such groups may be termed social it has its original basis in the actual contacts described in this and the following chapters.
  2. Reference at the end of this chapter.
  3. The experimental situation in fact encouraged rivalry. Each subject was allowed to finish his test, and his time was then taken. The fact that some were finishing and ceasing their work before others was doubtless a spur to the competition of the remaining workers.
  4. More recent experiments tend to show that inferior performance is not the necessary outcome of assigning tasks for home work. Under proper direction work done out of school can be made as effective as work done in the classroom. It seems however that special devices must be used to offset the disadvantage of the lack of stimulation from the group. This is a problem which belongs rather to educational than to social psychology. See Heck, w. H., "Comparative Tests of Home Work and School Work," Journal of Educational Psychology, 1919, X, 153-62.
  5. That is, together and alone.
  6. The gross total of errors of all subjects supports this view. There were 683 errors made in group work as compared with 571 in work done alone.
  7. It was equal in T and A in two cases.
  8. Another possible interpretation is that the social stimulus when fresh adds to the signal for starting sufficient impetus for an 'initial spurt' which diminishes as the worker becomes more adapted to the presence of the others.
  9. The average of the six social increments was moreover many times greater than the average of the three social decrements.
  10. The researches of Mayer and Schmidt tend to corroborate this statement. Work requiring careful thought, such as written arithmetic, showed, in their experiments, a much smaller tendency to social increment and supervaluent than the more mechanical exercises. In the present writer's experiments a smaller proportion of subjects had a social increment in multiplying than in the simpler processes, and a smaller proportion in writing every third or fourth associated word than in writing every word.
  11. That this represents the social influence upon judgment, and not upon the pleasantness itself, is shown by a later experiment (vide infra) in which the same tendency was revealed in the judgment of non-affective stimuli (weights).
  12. A primary group, that is, in the psychological rather than the sociological sense (see footnote to p. 260).
  13. Professors Smith and Guthrie have suggested that the so-called perversion of exhibitionism (as well as boisterous, profane, or obscene behavior generally) is the persistence of a childhood method of gaining attention and producing reactions in adults.
  14. This is the phenomenon of social projection, a process which will be discussed more fully in later chapters.
  15. It is doubtful whether this advantage applies in judging between two clear-cut alternatives, such as the question of 'guilty or not guilty' which the jury tries to settle by discussion. Munsterberg found an increase in the accuracy of individual's judgments after such a discussion. These results, however, have been contradicted by the experiments of Professor Burtt (see references at the end of this chapter). Further experiment is needed upon the whole question.

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