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THE PERCEPTION OF FORCE1

BY JOHN J. B. MORGAN

Psychological Examiner for the War Department

I. INTRODUCTION

(a) Statement of the Problem.—If an individual is askedto pull a spring to a point where the tension will amount totwenty pounds he will very probably make a large error. Ifhe is permitted to repeat the pull after being told the amountand direction of his error he will probably either reverse thedirection of the error or approach nearer to the requiredtwenty pounds. Succeeding corrections and trials will enablehim to reduce the size of his errors; and they will, if tabulated,give an approximation to the normal probability curve withthe twenty pounds as a mean.2 To delineate the mechanismwhich makes such learning possible and to describe the modi-fications involved would be no simple task; evidence forwhich is given in the antagonistic results of previous investi-gations on this subject.3

Disagreement in the findings of science is due either tofaulty experimental control, to incorrect interpretation ofresults, or to both; hence when one meets contradiction inthe results of different experiments it is first necessary to seewhether the conclusions as stated by the investigators neces-sarily follow from their experimental data, and if the trouble

1 The experiment of which this article is a report was made possible through aCutting Travelling Fellowship granted the writer by the trustees of Columbia Univer-sity in the spring of 1916. The apparatus was made and the experimenting largelydone in the psychological laboratory of the Johns Hopkins University under thesupervision and with the generous assistance of Professor John B. Watson. Theexperimenting was completed in the Princeton psychological laboratory and the dataput in shape while the writer was instructor in psychology in Princeton University.

1 Fullerton, G. S., and Cattell, J. McK., 'On the Perception of Small Differences,'Publ. of the Univ. of Penna. Philos. Series, 1892, No. 2.

• Sherrington, C. S., 'The Muscular Sense,' Shafer's 'Text-book of Physiology,'1002-1025. James, Wm., 'Principles of Psychology,' Vol. II., 486-520. Woodworth,R. S., 'Le Mouvement.'

21

22 JOHN J. B. MORGAN

cannot be located there to repeat and modify the experimentalconditions in order to obtain supplementary information onthe subject. Our problem will therefore be to investigatethe nature of the conflicts in previous experiments on theperception of force and then after we have clearly formulatedthe point at issue to attempt to supply data based on experi-mental modifications of such a nature as to give them strongevidential character.

(b) Some of the Points at Issue.—In connection with thisproblem one fact that previous investigations have demon-strated is that the 'sense of tension,' 'sense of resistance,'or 'sense of force' is a very complex affair. If there were aunitary sensation of innervation accompanying the dischargeof motor impulses; if there were a simple sensation of tension,of energy expended, or of muscle change accompanying move-ments of the body; if extent or time were the fundamentalthing in the perception of movement;—if any one of thesewere the irreducible element, no such discordant results ashave been obtained would have confused investigators andno doubt the problem would long ago have been settled.Different investigators have as the result of different experi-ments argued for the importance of each of these factors inthe production and perception of movement, and each newexperiment seems to bring to light some new phenomenonwhich contradicts what some previous investigator has found.One factor among those mentioned that seems to have beendiscredited by recent experiments is the sense of innervation.1

At least there are such strong arguments against it that weneed not consider it here. If then kinesthesis depends whollyupon afferent impulses, the question is left as to whether it isdetermined principally by the quality or intensity of theseimpulses or by their spatial or temporal relations, or by allthese combined. Under certain conditions it has been shownthat one judges force by movement speeds,2 in other condi-tions extent has been shown to be important, while in othersthe criterion is the latent time required to overcome the

1 Of. cit.•Muller and Schumann, Arch.j. d. ges. Phystol., 1889, 45.

THE PERCEPTION OF FORCE 23

opposing resistance.1 Clinical experiments on the effect ofanesthetizing the superficial areas on the perception of liftedweights have given discordant results.2

Fullerton and Cattell give three arguments against thecontention of Muller and Schumann that force is judged byspeed. (1) The force of a movement can be judged betterthan its time. (2) The judgment of time follows Weber'slaw more nearly than the judgment of force. (3) When therate is altered so that the one is lifted four times as rapidlyas the other, either by being lifted higher in the same timeor the same distance more quickly, the probable error is notincreased. They state that this latter unexpected resultproves conclusively that we do not judge of difference inweights by the rate at which they are lifted. They are ofthe opinion that lifted weights are judged by a combinationof skin, pressure and muscle sensations.3

(c) Previous Work Leading to the Present Paper.—Thethesis which led to the experiments to be reported in thispaper was that the perception of force is very crude and itsseeming accuracy in certain instances depends upon theadoption of secondary criteria. We will first refer verybriefly to the facts which led to this thesis, show how theuse of secondary criteria could have entered into Fullertonand Cattell's experiments on the perception of force, andthis will bring us to an explanation of the method and planof our experiments.

It has been found that when a person is told to raise aweight with all the force he can, if the weight is changed hewill tend to pull varying masses with the same speed, whichmeans that the force of the muscular contraction must varywith the different weights.4 The time required for this ad-justment of force has been found to be fifty sigma or less,in no case more than 100 sigma. It must therefore be eithera reflex or a local muscular phenomenon. Further, when the

'See discussion of the experiments of Jacobi in Woodworth's 'Le Mouvement.'2 Sherrington, op. cit.* Op. at.* Morgan, J. J. B., 'The Overcoming of Distraction and Other Resistances,'

Jrch. of Psychol., No. 35, 1916.


subject is told to pull several weights with the same forcehe can make but crudely the time adjustment that is neces-sary.1

These facts show that if one has any elementary sensationof force it is not the same thing we have to deal with inphysics. In physics, if we have a certain force acting againsta certain mass we will get a definite acceleration, the forcebeing equal to the mass multiplied by the acceleration. Ifthe mass is changed and the force kept the same the accelera-tion can be determined from the equation and is found tobe borne out by experiment. If we tell a subject to set hisown force in pulling a certain weight we can measure theacceleration and can determine the amount of physical forceused. If we change the mass and tell him to use the sameforce as before we find that acceleration is but little changedbut that the resultant physical force is. Certainly this showsthat the subject has no unitary sensation of physical force;or, if he has, he is grossly ignorant of its relation to accelera-tion. The force of a spring, of an explosion, or of gravity isvastly more accurate in its adjustments than the humanmuscle.

Over against these facts stand the experiments of Fullertonand Cattell which showed that force can be judged moreaccurately than time, although somewhat less accuratelythan extent. In all their experiments, except in one withextent, they used the following procedure: The subject wasgiven a practice series in which to learn the standard magni-tude, whether extent, time, or force. After the practiceseries the movements were made in pairs. The first of eachpair was an attempt to approximate the standard magnitude,the second of the pair was an attempt to equal the first. Inthis way the subject made his own standard which he usedfor comparison. The average errors were taken from thedifferences between the two movements of the pairs. Thesubject was told at the end of each ten pairs how much hewas above or below the standard magnitude, and thus could

1 Ibid., 'The Speed and Accuracy of Motor Adjustments,' J. OF EXPER. PSYCHOL.,June, 1917.


attempt to make the necessary correction. In the experi-ments on extent they used standard magnitudes of ioo, 300,500 and 700 mm.; in the experiments on time they had thesubjects make a 50 cm. movement in minimum time, in 250sigma, in 500 sigma and 1,000 sigma; in the experiments onforce the subjects endeavored to pull the handle of a springdynamometer with a force of 2, 4, 8 and 16 kg. In theexperiments on extent no record was taken of the time of themovements, in the experiments on force no record was takenof the time, and in all except the 16 kg. pull the force was adirect function of the extent of the pull. For these reasonswe believe that a comparison of the relative accuracy of theperception of time, force and extent cannot be derived fromtheir experiments.

Since we are mainly interested in the force of movementswe will study a little more closely their experiments on thisphase of the subject. The dynamometer they used moved6.4 mm. for every kg. up to 10 kg., for pulls of 10 kg. or morethey changed the apparatus so that movement began at10 kg. and for each kg. above 10 the handle moved 6.4 mm.This means that in pulling a standard of 2,000 grams thesubject had a standard extent of 12.8 mm. to strive for; inpulling a standard of 4,000 grams he had an extent standardof 25.6 mm.; in pulling a standard of 8,000 grams he hadan extent standard of 51.2 mm.; and, in pulling a standardof 16,000 grams he had an extent standard of 38.4 mm.

We have no way of telling what the variable errors ofFullerton and Cattell's subjects would have been had theybeen given extent standards of these values. If they hadexperimented with such extent standards we could comparethem with the extent errors when they used 2, 4, 8 and 16kilograms as standards and might thus ascertain whetherthe force pulls were influenced by the extent of the movementsmade.

It might nevertheless be interesting to determine whatthe extent errors for the 12.8 mm., 25.6 mm., 51.2 mm. and38.4 mm. standards would have been on the basis of theirextent experiments with 100, 300, 500 and 700 mm. standards,


if calculated by Weber's or Cattell's psycho-physical laws.1

The ratio of error for the ioo mm. movement was for theirsubject F. one to 18.9.2 If this ratio were to hold accordingto Weber's law this subject would have scored a variableerror of .676 mm. with the standard of 51.2 mm., 1.42 mm.with the standard of 25.6 mm., 2.84 mm. with the standardof 51.2 mm. and 2.13 mm. with the standard of 38.4 mm.If on the other hand Cattell's square root law held good thissubject's variable errors for the several linear magnitudeswould have been respectively 1.90, 2.69, 3.79 and 3.29 mm.Now in their force experiments a pull of one mm. on thedynamometer which they used equalled nearly 156 grams.If then we transmute the linear errors into gram errors wewill get the result shown in Table I. By comparing these

TABLE I

T H E RELATION BETWEEN THE VARIABLE ERRORS OBTAINED FROM SUBJECT F IN

FULLERTON AND CATTELL'S FORCE EXPERIMENTS AND THE VARIABLE

ERRORS AS COMPUTED FOR MOVEMENTS OF SIMILAR

EXTENT FROM THEIR EXPERIMENTS ON EXTENT

Force StandardsExtent Standards

V. E. Subject F in force expV. E. Weber's law from extent expV. E. Cattell's law from extent exp

3,00013.8

183ios296

4,00035.6

280221420

8.000jr.a

373443S9i

16,000 Grams38.4 Mm.

434 grams332 grams513 grams

two sets of computed variable errors with the actual variableerrors made by this same subject in the force experiment itwill be seen that for the most part the actual force errorsfall between the force errors computed from the 100 mm.standard by the two methods. This is evidence enough atleast to suggest to one the hypothesis that the force pullswere in large part guided by extent, and Fullerton andCattell could have secured the results they did if theirsubjects possessed only a very crude perception of force assuch. Theoretically this removes the disparity between the

1 Cattell, J. McK., 'On Errors of Observation,' Am. Jour, of Psychol., 1893, $>285-293.

* Fullerton and Cattell, 'On the Perception of Small Differences,' Univ. of Penna.Publ. Philos. Series, 1892, p. 48.


results of our experiments and those of Fullerton and Cattell.We found that the force a person exerted was determinedby the resistance encountered and that the subjects couldnot consciously adjust the speed of their movements so asto use the same force in moving different masses. Fullertonand Cattell found that force could be judged better than time;but, as their subjects may have been judging by extent, an/comparison of force with time or extent is ruled out. Itremains for experiment to show whether this hypothesis,that the perception of force is largely dependent on otherfactors, can be proven and it is this we have attempted to doin the experiment we are about to report.

An observation made by Professor Woodworth has abearing on the problem.1 He has shown that if the severalfactors that enter into a perception are perfectly correlatedthe variable error will increase in direct proportion to thestimulus (Weber's law), while if the factors are not at allcorrelated but are operative in a purely chance way thevariable error will increase in proportion to the square rootof the stimulus (Cattell's law). Where there is some correla-tion the error of observation will fall between the errorrequired by the two laws. Now if all the causal factors ofany perception are directly correlated, by the very nature ofthe case these factors must be relatively few, for by chancewe mean a number of factors working indiscriminately, hencethe larger the number of factors the greater the likelihood ofa pure chance series. In Fullerton and Cattell's experimentsthe variable error in time followed Weber's law very closely,the variable error in extent followed Cattell's square rootlaw, and the variable error of force fell between. This wouldindicate that the perception of time is relatively simplecompared with that of extent or force regardless of theirrelative accuracy, and we believe our experiments will showthe complex nature of the perception of force and extent.This lack of correlation between the factors controlling theforce of movements may account for the conflicting results

1 Professor Cattell's Psychophysical Contributions, in the Psychological Researchesof James McKeen Cattell, Arch, of Psycho!., 1914, No. 30, pp. 70-72.


obtained in experiments on the perception of force. Miillerand Schumann found that under certain conditions the per-ception of lifted weights correlated with the speed with whichthey were lifted. Cattell varied the speed and found per-ception as accurate as before. If weights are judged by anumber of non-correlated factors, a subject could readilyshift from one basis of judgment to another. We feel thatin the study of the subject this fact should receive strongemphasis. If we are studying a form of perception whichdepends upon, let us say, five correlated factors and weexperimentally interfere with one factor, the total perceptionwill be changed more radically than would be the case if wewere to interfere with one element in a perception thatdepended on five factors operating in a purely chance manner.Translated into the terms of our problem this would meanthat, if the perception of force depends on several non-correlated factors, under normal conditions the subject willjudge the force of his movements; or, in objective terms, theerror in his movements will be determined by all, several orperhaps only one of these factors. Suppose his force move-ments are determined largely by time; then, if time is variedhe might shift to extent. If extent were varied or eliminatedhe might revert back to time unless it were still controlled.If both time and extent were eliminated, skin and musclesensations might be called upon to bear the larger part inthe force control and judgment. If, therefore, force dependsupon one factor the control of this would perfectly controlthe error of a force movement. If it depends on severalpartially correlated factors the relative importance of thedifferent factors could be determined experimentally. If itdepends on several chance factors the only way to changethe error and judgment of force would be to have adequatecontrol of all the factors. We believe our results will showthat Woodworth was right in his theory, and that forcedepends on a number of partially correlated factors. Wemay also be able to show the relative importance of someof them.

If it is possible to show that this is the case it may shed


some light on what we mean by adaptation. It is possiblynothing more than an evidence of the multiplicity of causesunderlying activity of any sort. If the causes of an act arefew or closely correlated, adaptation will be less completethan if the causes are numerous and related only in a randomway.

II. GENERAL PLAN OF THE EXPERIMENT

To arrange an experimental procedure which would showwhat determines the control and judgment of the force ofmovements was our problem. Three major experimentalvariations were used, the same general procedure being usedin all. The general procedure was to inform the subject ofthe task; that is, whether to attempt to make a movementof a certain length or to pull with a certain force. Havingreceived his instructions he was given twenty-five practicetrials, the amount and direction of his error being givenafter each trial. After this practice series the movementswere made in pairs. In the first of each pair the subjecttried to produce the standard, while in the second he tried toreproduce the first. This is the procedure devised by Cattelland Fullerton and it permits the subject to make his ownstandard for each movement and gives a much more accuraterecord of the subject's perception and control than if thearbitrary standard was used as a base from which to computethe errors. After the second movement of each pair thethe subject gave a judgment as to the direction of the dif-ference between the two. After he had given this reportthe experimenter told him the direction and amount of errorof the second of the pair when compared with the arbitrarystandard given at the beginning. He was thus enabled tomake an intelligent effort to correct the first movement ofthe next pair which we will call the standard. He was nottold whether his judgment as to the direction of the errorbetween the two pulls was correct or not. Fifty pairs inaddition to the twenty-five practice movements constitutedone experimental sitting.

The experimental variations were as follows:1. The subject was instructed to pull with a certain force


and corrections were given him in terms of the number ofgrams too heavy or too light. In all these experiments theextent of the pulls was the same for each standard forcefrom 2 to 16 kg. Time records were taken for each pull, thechronoscope starting when the pull began and stopping theinstant the return stroke was initiated.

2. With a change in the arrangement of springs on thedynamometer between experimental sittings the subject wasgiven instructions to pull a certain distance and correctionswere given in terms of millimeters too long or short. Timerecords were taken for each pull, as in the previous procedure.

3. The subject held his arm as nearly stationary as possibleand the experimenter increased the tension, the subject callingout when he judged that the tension had reached the requiredamount.

An experimental sitting consisted of 25 practice pullsfollowed by 100 paired pulls with one set of springs. Aset of experiments included experiments with 2, 4, 6, 8, 10,12, 14 and 16 springs. Including the 3,200 practice pullsthe experiments to be reported are based upon 16,000 pullsand 6,400 judgments.

The sequence of the experiments was varied with thedifferent subjects so that when averaged together practiceeffect was eliminated in the average scores. Subjects A, B,C and D had an entirely different order from E, F, G and H.In addition the sequence for A and B was exactly the reverseof that for C and D, and that for E and H the exact reverseof that for F and G.

The subjects in the experiment ranged from those whowere highly trained in experimental psychology and labora-tory procedure to those distinctly untrained. We could findno tendency for the untrained to differ specifically from thetrained.

III. DESCRIPTION OF APPARATUS

The dynamometer consisted of a handle connected to arod which ran on roller bearings so as to minimize friction.From this rod projected a smaller rod at right angles whichmoved an indicator before it as it made the forward stroke.

THE PERCEPTION OF FORCE 3 1

On the return stroke this rod left the indicator, thus givingthe experimenter an opportunity to read the extent of themovement from a millimeter scale which was attached to the

T

TFIG. 1. Outline of Dynamometer and Dunlap Chronoscope with Electrical

Connections. A is the handle of the dynamometer which connects with the rod Bwhich in responding to pulls on the handle works on roller bearings at C and D. Eand F are plates each equipped with 16 hooks upon which may be fastened 16 springsin parallel. H and / are the two sets of magnets in the Dunlap chronoscope. Themagnets H are connected to the armature of a synchronous motor which is in motionthroughout the experiment. When everything is set for a pull the rod at M is con-nected both through the magnets / by a contact which breaks as soon as the handlemoves forward and through the magnets / / by a contact with the marker which rideson the scale A7. At L is inserted a Dunlap key (omitted in the drawing for the sakeof clearness) which closes the contact through / an instant before it closes that throughH, thus making certain that the armature J is against the stationary magnets / .The breaking of the contact through the magnet / at the beginning of a pull permitsthe armature to be pulled away from the stationary magnets / to the revolving magnetsH and the indicator K begins to revolve. The beginning of a pull likewise breaks acontact at 0 which breaks an independent circuit through the relay P. The armatureof the relay being released falls back and makes a contact at Q which reconnects thecircuit through the magnets / of the chronoscope. The armature of the relay is soadjusted that the remaking of the current would not be strong enough to pull it upand so the breaking of the contact at Q is not accomplished until the experimenterpushes it up with his hand. This prevents any inadvertent starting of the chrono-scope. The forward movement of the handle moves the indicator along the scale Nand as soon as the return stroke is initiated the contact through it and the rod Mthrough the revolving magnets of the chronoscope H is broken, thus allowing themagnets / to pull the armature J forward and stop the chronoscope.


dynamometer. After reading the indicator was returned to0. An electrical contact was broken when the arm left itsback stop at the beginning of a pull and a second contactbroken when the rod left the indicator at the beginning of thereturn stroke. These two break contacts operated the mag-nets of a Dunlap chronoscope. The details of the chronoscopeconnections and operation are shown in Fig. I. The rodattached to the handle of the dynamometer had at its otherend a plate upon which were 16 hooks. This plate facedanother similar plate which was fixed to the other end of thedynamometer. Between each of these 16 pairs of hookssprings could be placed or removed as desired. They werehowever always used in pairs so as to prevent lateral torsion.This was accomplished by using together two springs on aline with the center of the rod and equidistant from it. Thesprings were as nearly alike as possible but were carefullycalibrated and the variations that were found were takeninto consideration in the records. An extension of 175 mm.required a pull of one kilogram on a single spring. Byarranging, in different experiments, 2, 4, 6, 8, 10, 12, 14 and16 springs in parallel we were enabled to use standards of 2,4, 6, 8, 10, 12, 14 and 16 kilograms and in each case keep theextent of the movement the same.

In the experiment where the subject held his arm sta-tionary a second handle was attached by a wire to the rearend of the dynamometer, which in this case was suspendedfrom two standards and the movable end connected to awindlass which the experimenter operated to tighten thesprings. The subject held the handle as near to an indexpoint as possible throughout the experiment and consequentlythe dynamometer and the handle he held only moved withthe waverings of his hand. In every case the dynamometerwas screened from the subject, and when he made arm move-ments a screen was placed between his arm and body sothat he could not observe his movements.

IV. RESULTS

In the first experiment the subjects were required to pull2, 4, 6, 8, 10, 12, 14 and 16 kilograms, a different force being


asked for at each experimental sitting, the sequence of thedifferent forces being determined by chance. Records weretaken of the extent error and the time of each pull. Theforce errors were later computed from the extent error. Inthis series four subjects A, B, C and D were used and their

FIG. Z.

force, extent and time errors are given in Tables II., I II .and IV. In each of the tables four records are given foreach subject for each set of springs used. The first is theaverage force, time or extent of the first pull of each pair,called the standard. The second score is the average error,that is, the average difference between the first and secondpulls. The third score is the variable error showing thevariability in the size of the error between the first and secondpulls. The last record is the ratio of the variable error tothe standard.

In this experiment the extent factor was the same withall the various forces used. The subject could pull the handledifferent distances, as there was nothing on the apparatus toprevent this (except that a stop was arranged so that hecould not pull hard enough to damage the springs), but ifhe pulled the exact force standard the extent of the movementwould be the same for each force standard. The time factor


was not controlled in any way, the subject being left free topull as quickly or as slowly as he pleased.

TABLE II

FORCE RECORDS IN MM. OF I,6OO EXPERIMENTS IN WHICH THE SUBJECTS AT-TEMPTED TO PRODUCE TWO MOVEMENTS OF EQUAL FORCE, AND IN WHICH CORREC-TIONS WERE GIVEN IN GRAMS.

Set Standard ...

Subject A:Av. of stand-

ard pull ..A. DAverage error.Variable errorRatio V. E. to

standSubject B:

Av. of stand-ard pull

A. D. .Average errorVariable errorRatio V. E. to

stand. . .Subject C:

Av. of stand-ard pull.

A. DAverage errorVariable errorRatio V. E. to

stand.. .Subject D:

Av. of stand-ard pull

A. D. .Average errorVariable errorRatio V. E. to

standAverages:

Standard pullA. D.Average errorVariable errorRatio. . .

I,98o107102

64

3°-9

2,02046

'3485

23.8

1.94389

11765

29-9

2,008738660

33-4

i,987-778.7

109.768.529.0

4

3,910162

246138

29-3

4,1261002 3 2

156

26.4

3,9461012 5 1138

286

4,O93154126

78

63-3

174.2213.7127-5

6

5.766244264162

35-6

6,0123 / r

330189

31,8

5.902250

395167

253

5.980197237•45

41.2

5.915251-5306.5165733-5

8

7.97O562304188

42.4

8,008

388192

42.1

7.9723583 1 0181

44.1

8,094237274156

5'-8

8,011380.5319179.245.1

10

9,8933043252 1 0

47.1

9,8854186502 3 0

43.0

10,099434479334

JO.O

9,789560418266

36.8

9,9165*P4682 6 0

39-2

Z3

I1,9O636O354234

50-9

11,460A%6666324

ii,974446492278

4J

12,026i 6 7516396

3°-4

11,841407.350730839-9

14

13,923

469245

569

14.091182560329

428

13,780476549311

44-3

13.789

6 0 0358

38.4

13.896548.7544-5310.7

•tf-<5

16 Kg.

15.744618584344

« • *

15.984

si*496

32.2

15,887

507288

55-1

16,025464507294

54'5

15,91056/7605.5355-546.9

Before we examine the experimental results in detailit may be well to consider the relation of some of the factorsinvolved and what certain results would mean. This willgive a point to the presentation of the results, and give theirexposition greater clearness. If the subject used extent as


a basis of control the extent errors should have been nearlythe same in all cases, which would of course mean that theforce errors would vary in conformity with Weber's law.If the time errors appear the same with all forces, it wouldindicate that time might help the subject to control force.

TABLE III

EXTENT RECORDS IN GRAMS OF I,6OO EXPERIMENTS IN WHICH THE SUBJECTS

ATTEMPTED TO PRODUCE TWO MOVEMENTS OF EQUAL FORCE, AND IN WHICH CORREC-

TIONS WERE GIVEN THEM IN GRAMS.

Set Standard.

Subject A:Av. of standard pull.A.DAverage errorVariable errorRatio V. E. to stand.

Subject B:Av. of standard pull.A.DAverage errorVariable errorRatio V. E. to stand.

Subject C:Av. of standard pull.A.DAverage errorVariable errorRatio V. E. to stand.

Subject D:Av. of standard pullA. DAverage error . . . .Variable errorRatio V. E. to stand.

Averages:Standard pullA. DAverage errorVariable errorRatio

2

171.9210.68IO.26.4

26.0

176.044.6

13-48-5

20.7

168.288.Q2

II.666.52

25-8

174-87.278.645-97

29-3

172.6

10976.85

25.68

4

168.54<?.o£

12.36-9

24.4

179.28P-52

11.67.8

23.0

170.289-56

12.566.92

24.7

177.647.726.33-88

« • *

173-93

10.696.37

29-47

6

164.2£ . «8.85-4

304

172.4

II .O

6-327.4

168.74<y.j2

13.165.56

30-3

171.346.567-94.84

35-5

169 17<?-5<?

10.215-52

30-9

8

171.2614.047.64-7

56.4

172.29.129-74.8

55 P

I7I-3S.967-744.52

38.0

174.365-926.863-9

•«-7

172.289-5'7-974.48

5<?-75

xo

169.866.086.54.2

40-4

169.79.16

13.04.6

5<5p

I73-988.689-586.68

25-9

167.787-28.365.32

5'-5"

170.337.789-3°5.20

55-67

12

174-446.0

5-93-9

44-7

167.627.6

11.15-4

31-0

175.567-W8.24.64

37.8

176.44- d./2

8.66.6

26.7

I73-5I6"7P8.455-13

35-05

>4

173.927-56-73-5

4P-<5

176.3

8.04-7

37-5

171.86

7.844-44

38.7

171.98£•458.565.12

55-<5

173.517.847-774-44

39.85

16

172.87.727-34-3

40.2

175.89.2

10.36.2

*?.J

174-545-366.34

176.325-«6.343.68

47.6

174.867.057-574-44

41.15

If the subject were ignorant of the relation of force andextent and could only judge time, the force and extent errorsmight show an interrelation and the time errors be the same.

In the actual experimental results the force errors (TableII.) increase with the size of the stimulus, not as rapidly aswould be required by Weber's law and more rapidly thanwould be required by Cattell's square root law (see Fig. 3).


TABLE IV

TIME RECORDS IN SIGMA OF I,6OO EXPERIMENTS IN WHICH THE SUBJECTS AT-TEMPTED TO PRODUCE TWO MOVEMENTS OF EQUAL FORCE, AND IN WHICH THECORRECTIONS WERE GIVEN IN GRAMS.

Set Standard . .

Subject A:Av. of standard

pullA. DAverage error.Variable error.Ratio V. E. to

standSubject B:

Av. of standardpull

A. DAverage errorVariable errorRatio V E. to

stand. .. .Subject C:

Av. of standardpull

A. DAverage error..Variable error..Ratio V. E. to

standSubject D:

Av. of standardpull

A. DAverage error..Variable error.Ratio V. E. to

standAverages:

Standard pullA.D. . . ..Average error. .Variable error .Ratio.. .

2

1.393174H 783

16.8

516

57Si31

16.6

918777144

po.p

44120J9JI

40.0

81782644223.6

4

1,235

9711664

19-3

430253322

10.6

9458486So

18.9

447'P2414

31.8

764566537224

6

1.485I08Il884

I7.7

46240

3924

19-3

1,105978647

23-5

442

n24IS

20.4

87365674222.5

8

1.725266201112

15-4

527S35231

17.0

827464730

27.6

438132212

36.5

87994804624.1

10

1.42599"379

18.1

562374128

20.1

891446141

21.7

439J51911

39-9

82949584025.0

22

1,2241279152

2J.6

432304227

/<5.o

916617540

22.p

4131922IS

27.<5

74659573322.5

1,163<?56842

27.7

492

5231

15-9

1,012657648

21.1

433/61811

39-4

77552S33320.0

967

81

55

17.6

601

42

H-3

782

4329

27.0

455242714

32-5

7015952

According to Woodworth's interpretation referred to abovethis would mean that force is not controlled by factorsperfectly correlated nor operating by pure chance. Timeseems to have some part to play (Table IV.), since the ratioof the errors to the standard time (that is, the time of thefirst pull) is about the same with all forces. It cannot,however, be the controlling factor, since the relative error isgreater than either force or extent.


An examination of the average and variable error records(Table III.) shows that as the resistance to a movement isincreased the ability to make two movements of the sameextent is increased while on the other hand the ability toreproduce a standard pull (shown by the average deviationof the standard) is the same regardless of the resistanceopposed to the movement, which means that the productionof a standard force increases in direct proportion to themagnitude of the force (Weber's law). This together withevidence we will presently adduce points to the importanceof extent in judging force.

TABLE V

EXTENT RECORDS IN MM. OF I,6OO EXPERIMENTS IN WHICH THE SUBJECTS AT-

TEMPTED TO PRODUCE TWO MOVEMENTS OF EQUAL EXTENT, AND IN WHICH THE

CORRECTIONS WERE GIVEN IN MM.

Number of Springs 6

173-028.729-4S.68

30-5

I7S-47-34

10.05.6

3^-3

160.6211.7610.526.55

24-5

181.97-329.725-03

36.1

172-738.789.91S-7i

30.6

8

168.226.72

IO.45-7

29.7

179.27.029-2

35-8

174.886.765.83.8

4.6.0

173-886.98

10.046.55

26.5

174.046.878.865.26

34 5

I O

171.946.646.94.2

40.9

178.727.217-13-3

54-i

173.528.089.145-56

31-3

178.048.048.75.28

33-8

175-557-497.964.58

40.02

173-44-035.02.9

59-9

172.868.888.92-3

75.0

166.488.489.285.24

31-8

174.688.18-345-12

34-i

171.857-377.883-89

50.2

4

171.626.245.263.24

S3

172.725-566.34-4

39-2

168.068.29-76-75

24.9

i75-°25-i8.945-36

32-7

171.856.277-554.94

37-45

Subject A:Av. of standard pull.A . DAverage errorVariable error.. . .Ratio V. E. to stand.

Subject B:Av. of standard pull.A . DAverage errorVariable errorRatio V. E. to stand.

Subject C:Av. of standard pull.A .DAverage errorVariable errorRatio V. E. to stand.

Subject D:Av. of standard pull.A . DAverage errorVariable errorRatio V. E. to stand.

Averages:Standard pullA . DAverage errorVariable errorRatio

172.186.16

1005.8

29.7

182.5813.1215-77-i

25-7

168.786.27-12.1

80.3

177-311.867.924-4

40-3

167.68 J163.5611.9613.046.6

25.4

174.247-99.585.56

174.179.78

12.086.26

28.05

9-412.627.48

21.9

175.468.32

10.445-85

30.0

171.278-949-524.96

43-r2

174.066.246.73-9

44-7

171.785-36

5-1

63.6

177.128.889-345-0

35-4

169.447-569.286.32

26.9

173-17.017.614.48

42.65

With the same subjects another experiment was tried inwhich they were told to pull the handle a certain distance


and corrections made in terms of millimeters. A sitting wasgiven with each group of springs used in the force standardexperiments. Here an error of ioo grams with two springs

TABLE VI

TIME RECORDS IN SIGMA OP 1600 EXPERIMENTS IN WHICH THE SUBJECTS A T -

TEMPTED TO PRODUCE TWO MOVEMENTS OF EQUAL EXTENT, AND IN WHICH THE

CORRECTIONS WERE GIVEN IN MM.

Number of Sprtbgs..

Subject A:Av. of stand-

ard p u l l . . . .A. DAverage error.Variable error.Ratio V. E. to

standSubject B:

Av. of stand-ard p u l l . . . .

A. DAverage errorVariable error.Ratio V. E. to

stand.Subject C:

Av. of stand-ard pull.. .

A. DAverage error.Variable error.Ratio V. E. to

standSubject D:

Av. of stand-ard pull. . . .

A. DAverage error.Variable errorRatio V. E. to

standAverages:

Standard pull.A. DAverage error.Variable error.R a t i o . . . .

1,0156860.239.1

26.0

503?ojy44.826.7

18.9

95584.4.T'T

70.I48

19.9

47925.431-416.4

20.2— y.—

738^4.251.632.5

4

1.149106

87.425.8

44-?TT V

488

Of

3820.3

2d

9427064.237-3

2?.?

42827.930.720.6

20.8

75260.2552628.6

1,400171

1 *

13892.5

15.2

43224. T33-623-3

18.6

54584.7TV

53-331

17.6

51214.1

JT

34-122.9

22.4.

72278.664.742.418.4

8

1.37414.712565.4

21.0

47641.2tf.+ .*.

33420.3

i??.4*• j"r

1,155J0J.C** "j'J37.856.8

2O.dt-u.tf.

44120. <32.51 9 4

22 7

8617857-240.521.9

1 0

1,2129285.644-2

27.4t v

6162J.640.325-5

24..1

1,04570 061737-3

28

41819.630.019.7

21.2

82351

54-43i-725./

1 2

1,031

4852.537-2

27.71 t

51328.240-323.8

27.6

92471.7/ /72.341.8

22.1

50427.0

/ y25.019.4

26.O

74344.TT

47-530.524-3

14

1,3457P99.851-7

2(5./

49726.S28.616.7

20.8

762*y.<557-338.5

19.8

4704.7.245-730

X? 7

768

57-834-222.8

16

1,35210096.858.3

21.2*-J'—

550

26!620.5

2<5.£

1,03566.789.05i-7

2 0

44816 829.718.9

22 7

846Kd.60.537-3

would involve the same extent error as an error of 800 gramswith 16 springs. The records of this experiment are howevernot materially different from the records when a force standardwas used (Tables V. and VI.). When identical conditionsexist efforts to reproduce a standard force or a standard


extent produce identical results (see Fig. 3). When statedin terms of force we have found that as the magnitude of thestimulus increases the variable error increases more slowlythan in direct proportion to the stimulus, but more rapidlythan in proportion to the square root of the stimulus. When

FIG. 3. This graph shows the force records of subjects A, B, C and D, whenthey were guided by both a force and an extent standard, compared with the recordsthat would be expected from Weber'6 and Cattell's psycho-physical laws.

stated in terms of extent we have found that as the resistanceoffered to a movement of the same extent increases theaccuracy with which the movement can be reproduced in-creases. We cannot however make too much of this pointbecause, as we shall show later, our other four subjects donot show this reaction. We may suggest as an explanationthat our later four subjects may have used extent as a basisof judgment to a greater extent than did our first four.

With the end in view of examining further this relationbetween force and extent, it was planned to eliminate extentaltogether and to see what effect this would have upon thesubject's judgment and control of force. The dynamometerwas suspended so that it would swing freely, the subjectgrasped a handle fastened to the rear of the dynamometer,and the experimenter increased or decreased the tension bymeans of a windlass attached by a cord to the handle. Inthis experiment, as before, twenty-five practice trials were

4° JOHN J. B. MORGAN

given, after which the pulls were made in pairs. The springwas tightened until the subject gave a vocal signal that whathe deemed was the standard had been reached. All the ten-sion was then removed and again the spring tightened untilthe subject gave the signal. The spring was tightened withapproximately the same speed that the subjects used inmaking the movement themselves. Of course with such aprocedure a greater variability would appear in the resultsdue to the introduction of the reaction time of the experi-menter. However, this increase in the error records wouldbe the same regardless of the amount of the force standardand so would not prevent a study of the relations of thedifferent force standards.

FIG. 4. This graph shows the force records of subjects E, F, G and H when theywere guided by a force standard in pulling the dynamometer compared with therecords that would be expected from Weber's and Cattell's laws.

As new subjects (E, F, G and H) were used in this experi-ment, additional experiments were made with them usingthe same procedure as with the subjects A, B, C and D, withthe exception that no time records were taken. Contraryto the former results, the variable errors (Table VII.) fol-lowed very closely Weber's law (Fig. 4). This means thatthese subjects made errors of approximately the same extentwhen pulling with a standard force of 16 kilograms as with aforce standard of 2 kilograms, indicating that they werelargely influenced by extent. The records where extent was

THE PERCEPTION OF FORCE

TABLE VII

FORCE RECORDS IN GRAMS OF 1600 EXPERIMENTS IN WHICH THE SUBJECTS,

ATTEMPTED TO PRODUCE TWO MOVEMENTS OF EQUAL FORCE, AND IN WHICH COR-

RECTIONS WERE GIVEN THEM IN GRAMS.

Set Standard, . a 4 6 8 ro xa 14 x6

Subject E:Av. of stand-

ard pul l . . . . 1,981 4,027 5,910 7,634 9.718 12,520 13,427 15,819A. D 46 122 199 3Si 470 478 636 S98Average error 49 142 263 546 649 439 593 544Variable error 28 72 150 290 298 249 291 326Ratio V. E. to

stand 70.7 29 39.4 26.3 32.6 s°-3 46.2 48.3Subject F:

Av. of stand-ard pull . . . 2,033 3,992 6,134 8,162 9,900 12,275 13,744 l6,495

A. D 13s 144 297 349 382 508 683 60sAverage error 85 109 180 246 296 374 424 366Variable error 51 73 80 104 109 170 272 221Ratio V. E. to

stand 39.8 $4-6 7^-6 78. $ 90.8 72.2 50.6 74-6Subject G:

Av. of stand-ard pa l l . . . . 2,095 3,972 5,771 7,700 9,643 11,506 13,581 15,086

A. D 107 160 288 372 362 S77 5i8 828Average error 108 236 431 510 467 1,120 794 1,374Variable error 70 133 204 254 263 552 369 544Ratio V. E. to

stand 42.2 29.7 28 30.3 40.8 20.9 36.8 27.7Subject H:

Av. of stand-ard pull . . . . 1,999 4,090 5.969 7,992 10,275 12,149 14,270 16,210

A. D 80 93 175 262 354 316 siS S28Average error 71 107 159 259 286 253 335 466Variable error 34 73 100 141 163 168 231 330Ratio V. E. to

stand s8-8 S&-1 S&-7 5^-7 63.4 72.3 61.8 49.2Averages:

Standard pull 2,027 4,020 5,946 7,872 9,884 12,112 13,755 I5,°O2A. D 92 130 240 333 392 470 s88 640Average error 78 148 258 390 424 546 536 687Variable error 46 88 133 197 201 285 291 355Ratio . . 52.9 42.3 50.2 480 S6-0 S3 9 488 s°-°

eliminated do not follow Weber's law but fall between Weber'slaw and Cattell's law (Table VIII. and Fig. 5). This resultis not merely a result of the difference in method, but a resultof the elimination of extent. Evidence for this is given bya study of the judgment thresholds. As we noted aboveafter each pair of pulls the subject gave his judgment as towhether the second was heavier or lighter than the first.From these judgments thresholds were calculated and are

JOHN J. B. MORGAN

TABLE VIIIEXTENT RECORDS IN M M . OF I,6OO EXPERIMENTS IN WHICH THE SUBJECTS

ATTEMPTED TO PRODUCE TWO MOVEMENTS OF EQUAL FORCE, AND IN WHICH CORREC-

TIONS WERE GIVEN IN GRAMS.

Set Standard a

172. i4.644.922.8

61.5

177.2813.528.525.14

34-5

183.5410.7210.847.04

26.1

173-98.027.063-4

5i-i

176.69.227.834.6

43-3

4

174-346.127-13-6

48.5

172.567-25-443.64

47-4

171.628.02

11.86.68

2.T-7

177-524.645-363.64

174.016.497.424-39

42.0

6

169.046.648.78S-O

33-8

176.46p.p.?5.982.68

65-5

164.389.6

H-346.8

24.2

170.985-*45-33-32

51.8

170.09£.08.64-45

43-82

8

162.86<J.7O

13.667.24

22-5

176.04<y.72

6.14

2.667.6

164.50 J 2

I2.766.4

25-7

171.86.566-343-52

48.8

168.8

<y-5*9.72

4-9441-^5

JO

166.36p-4

12.985-06

27.P

170.00

5-922.18

78.0

164.867-249-364.72

34-8

177.77.o55-723.26

545

169.737-*48-54.03

*?.(?

X2

I84.667-967.324-16

«"#

I8O.588.646.242.84

63.6

I67.769.64

18.669.2

Jtf.2

I78485-284-222.8

65.7

177.877.889.II4-75

166.829.088.464.16

40.2

171-349.766.063.88

44.2

169.027-4

11.365.28

J2-0

178.867-364.783-3

54-2

I7I-5I*.«7.664-15

4205

16

Av. of standard pull. . .A. DAverage errorVariable errorRatio V. E. to stand...

Subject F:Av. of standard pull. . .A. DAverage errorVariable errorRatio V. E. to stand. .

Subject G:Av. of standard pull. . .A. DAverage errorVariable errorRatio V. E. to stand. ..

Subject H:Av. of standard pull. . .A. DAverage errorVariable errorRatio V. E. to stand. ..

Averages:Standard pullA. DAverage errorVariable errorRatio

173-747.486.84.08

42.6

182.187-564.582.76

66.0

164.5810.3617.186.92

23.8

178.626.65.844-13

43-2

I74-788.08.64-47

43-9

FIG. 5. This graph shows the force records of subjects E, F, G and H whenthey held the arm stationary in judging the tension of the spring compared with therecords that would be expected from Weber's and Cattell's laws.


given in Table IX. In the experiments where the subjectsmade arm movements in pulling the dynamometer thethreshold follows Weber's law (Fig. 6); where the subjectheld his arm stationary it falls between Weber's law and

TABLE IXFORCE RECORDS IN GRAMS OF I,6OO EXPERIMENTS IN WHICH THE SUBJECTS

ATTEMPTED TO JUDGE THE POINTS IN TWO SUCCESSIVE TRIALS WHEN THE TENSIONON A HANDLE, WHICH WAS HELD STATIONARY, WAS EQUAL.

Set Standard....

Subject E:Av. of stand-

ard tensionA. DAverage errorVariable errorRatio V. E. to

standSubject F:

Av. of stand-ard tension.

A. D..Average errorVariable errorRatio V. E. to

standSubject C:

Av. of stand-ard tension

A DAverage errorVariable errorRatio V. E. to

standSubject H:

Av. of stand-ard tension.

A. D.Average errorVariable errorRatio V. E. to

standAverages:

Standard ten-sion

A. DAverage errorVariable errorRatio.. . .

a

1,992

* J

15780

24.0x y

2,141IAO1 0 9

56

38.2

2,18496

172102

21.4

2,125III

JIO954

W.4

2,111125'377331.0

3,986164188n o

36.2

4.1J3

2OI105

d2.0

4,000lS2190123

52.5

4>»33181199131

31.5

4.133IQI

»9411735-5

6

6,006208

350228

26.3

6,464

361190

34-o

5,9962804 0 12 0 8

28.8

6,2782<;6416224

2S.0

6,i862733822 0 2

29-3

8

7,623102

543254

10.0

8,422422

343192

43-8

8,280363354181

45-7

8,26802134872 1 8

37-9

8,1483524322 1 1

39-3

2 O

9,973

J

3372 1 2

47.0T /

IO,224AC2

581286

35-8

10,542338498306

32.8

10,451124.

J T

3O92 0 2

Si-8

10,29735843i25141.8

1 3

11,0694S2605341

12.4J T

12,814io6433199

64.4

12,24545'4582 1 4

57-2

12,6324828 1 2

518

24.4

12,19045357731844.6

14

13.846.7 J

690448

?/.o

"4,38461768635°

41.0

H,475484663624

23.2

14.437392434235

61.4

14,285

618414JP-f

16

16,470106jy w

4002 0 2

16,357607694358

45-7

16,90675P

1.133560

30J

16,741595940509

33-0

16,61860779240747.°-

Cattell's law (Fig. 7). Referring again to Woodworth's inter-pretation this means that when the subject makes the armmovement the judgment of force depends on a factor or


factors closely correlated with force. When extent is ruledout the judgment of force is determined by factors relatedmore by chance. This indicates that with some subjectsat least the judgment of force is closely correlated withjudgment of extent.

FIG. 6. This graph shows the judgment thresholds of subjects E, F, G and Hwhen they had a force standard in pulling the dynamometer compared with whatwould be expected from Weber's and Cattell's laws.

FIG. 7. This graph shows the judgment thresholds of subjects E, F, G and Hwhen they held their arm stationary while the experimenter changed the tension ofthe dynamometer spring compared with what would be expected from Weber's andCattcll'8 laws.

In Table X. we have assembled the judgment thresholdsderived from the different experiments. In part A are giventhe judgment thresholds when the subjects attempted to

THE PERCEPTION OF FORCE

TABLE X

45

A. EXTENT THRESHOLDS BASED ON THE JUDGMENTS OF THE SUBJECTS IN I,6OO

EXPERIMENTS IN WHICH THE ATTEMPT WAS MADE TO PRODUCE TWO MOVEMENTS

OF EQUAL FORCE. UNIT I MM.

Set Standard-

SubjectsAB

cDAverage.. ..

3

9II7

24

12.75

4

II137

22

13-25

6

813II3°

13

8

141296

10.25

I O

IO16168

12.5

X2

11

92419

IS-7S

14

8101427

14-75

16

8161917

15

B. EXTENT THRESHOLDS BASED ON THE JUDGMENTS OF THE SUBJECTS IN 1,600


OF EQUAL EXTENT. UNIT I MM.

Set Standard

SubjectsAB

cD

Average.. .

2

13181313

14.25

4

II101417

13

6

II12IS12

12.5

8

II138

11

10.75

I O

13IS7

10

11.25

77

1210

9

97

1714

n-75

x6

128

1015

11.25

C. FORCE THRESHOLDS BASED ON THE JUDGMENTS OF THE SUBJECTS IN 1,600


OF EQUAL FORCE. UNIT I GRAM.

Set Standard-

SubjectsE....F . ..G/ / . . .

Average....

3

SO18090

no

107-5

4

IOOIOO200180

145

6

27O2IO330300

277-5

8

84O320240680

520

1 0

5O0300300350

3625

1 2

42072O36O300

450

14

630910560

1,120

805

16

1,040I,O4O

8801,120

I,O2O

D. FORCE THRESHOLDS BASED ON THE JUDGMENTS OF THE SUBJECTS IN 1,600

EXPERIMENTS IN WHICH THE ATTEMPT WAS MADE TO INDICATE THE POINTS IN TWO

SUCCESSIVE TRIALS WHEN THE TENSION ON A HANDLE, WHICH WAS HELD STATIONARY,

WAS EQUAL. UNIT I GRAM.

Set Standard.

SubjectsEF .G

Average.. . .

a

25021052OI4O

2 8 0

4

560280340420

400

6

90027048O570

S5S

8

1,240680720

1,040

92O

1 0

500750

1,2005OO

737-5

1 2

1,440780840

1,200

1,065

14

2,170980

1,050980

1,295

16

1,5201,5201,5202,240

1,700


pull with a given force and were corrected in terms of grams;in part B are the records from the experiments where thesubjects attempted to pull a certain extent and were givencorrections in millimeters. When they had the force standardthe errors in judgment increased as the size of the standardincreased. When they had the extent standard the errorsin judgment became smaller as the resistance to be overcomeincreased. This is interesting when we consider that in eachof these cases the subject had the same sensation complex.If he was told to pull 16 kilograms and had to make a move-ment 175 millimeters long to do so, or if he was told to pullthe handle 175 millimeters and had to pull 16 kilograms to dothis, the only factor changed was the difference in instruc-tions. In some way the difference in the two standardsstriven for must have changed his interpretation of the samesensation complex. As we have shown above the variableerrors in the two experiments were not materially different(Tables II., III., V. and Fig. 3). There must therefore havebeen something in the experiment that rendered their judg-ments different in the two cases while it did not change theiraccuracy of movement. In all probability this was the natureof the corrections given. When a subject made an extenterror of 1 millimeter and was told that he had made anerror of 80 grams in one case (with a 16 kilogram standard),and 10 grams (2 kilogram standard) in another, the effectwould be different from that induced if with two similarpulls with different forces he was told that in each case hehad made an error of 1 millimeter. It must be rememberedthat in no case was the subject told whether he had made acorrect or false judgment, but after he had made two pullshe was told how the latter pull differed from the arbitrarystandard of the experiment. When a subject had made twopulls which he thought were both near the standard and wastold that in one case the latter pull was 80 grams heavy andin the other 1 millimeter long he would in the first instancebe led to make a larger correction, or at least have his con-fidence in his accuracy shaken, while in the latter case hewould think he had done well and attempt to do the samethe next time.


Part D of Table X. is a tabulation of the judgmentthresholds when the subject merely held his arm stationaryand the tension on the handle was changed by the experi-menter. Part C is a tabulation of the judgments of thesesame subjects when they made arm movements. We havesaid above that the reaction time of the experimenter in theformer situation probably made the variable errors larger,but there is no reason why this .should have made the judg-ment thresholds differ. Yet we find that when the extentfactor is eliminated the thresholds are from 1.6 to 2.75(average 2.1) times as large as when the extent element waspresent. It seems unquestionable that when a subject couldhe used sensations of extent to help him judge the force of amovement just made by him, when extent was eliminated hecould judge with less accuracy the force of his movementsalthough he could judge them with some degree of accuracy.

We have seen that whether an extent or force standardwere used the subjects kept their time fairly uniform. Whilethe ratio of the variable error in time to the total time ofthe pull shows that taken by itself it is more variable thaneither extent or force, it may nevertheless play a large partin the control and judgment of the other two factors. Wetherefore tried a short supplementary experiment to ascertainthe effect of radical variations in time.

The procedure last described was used, namely that ofhaving the subject hold the handle while the experimenterchanged the tension of the springs; and, as these subjectshad no previous knowledge of the experiments, they weregiven a series of trials with the arm movement procedurefor comparison. The standard used was 10,000 grams.When the subjects made arm movements the judgmentthresholds of the two subjects were (/) 650 grams and (/)350 grams. When they held the handle in a fixed positionand the speed with which the springs were tightened wasradically different in the two trials of each pair according toa prearranged schedule, the thresholds were (7) 1,050 and(/) I4S°« When the speed of release was changed as wellas the speed of tightening, that is, when the spring was

48 JOHN ]. B. MORGAN

tightened quickly, care was taken to release it quickly andvice versa; the thresholds were respectively 1,250 and 2,200grams. Here where extent was eliminated and time so variedas to eliminate it as a help the judgment threshold showed aratio of I to 8 and 1 to 4.5. Where extent was eliminatedand no attempt was made to change radically the time thejudgment thresholds averaged 1 to 10.8, and when the subjectmade the movement and so could have the benefit of extentand time the average judgment ratio was 1 to 21.3.

V. CONCLUSIONS

An outstanding feature of these experiments is the adap-tation of the subjects to changed conditions. Adaptation infairly complex situations is generally recognized under thename of learning and an individual's intelligence is judgedby the extent to which and the speed with which he makes aselection of the most favorable reaction toward any givensituation. If he makes the most intelligent reaction he willrespond in such a way as to produce a certain result in themost efficient way. If after he has learned this most expedi-tious form of reaction some block is put in his way or thismode of action prevented in any way, he does not then andthere give up all effort to attain the end in view but triessome new method of attack. All this is perfectly obviousand well recognized. That the same thing holds in moreelementary fields has likewise been recognized by biologistsand psychologists, but it has not received the emphasiswhich it deserves.

It is clear from our experiments that to execute a move-ment of a certain force is a learned act and that to make ajudgment of the force of a movement that has been made isalso a learned act. Like every learned act it requires practicefor one to become at all skilled in it and like any complexprocess it is easily interfered with by a change in the circum-stances surrounding the act. The subject when asked topull a handle 175 millimeters, when asked to pull with a forceof 8 kilograms, or when asked to hold his arm stationaryand signal when the tension has reached 8 kilograms, must


in the first instance make a random reaction just as onedoes in learning a strange puzzle or a maze. This randomreaction produces a certain complex of sensations, and whenhe is told that he has made an error he tries to change hisnext movement so as to make the correction and is guidedin this attempted correction by a comparison of the secondsensation complex with the memory of the first. Theremay be various elements that he uses in successive trials,just as one makes various efforts to solve any new situation,and the final result of the elimination process is to selectthat element which will give him the best results.

It is important that the complex nature of the perceptionof force be clearly recognized. Investigators have spokenof it as though it were some simple sensation and statementshave been made that weights were judged not by force butby the distance to which they were raised, by the speed ofthe movement, or by the latent time between the initiationof effort and the actual movement of the weight. Othershave contended that weights are judged by sensations offorce. The parties on both sides of the argument seemedto consider force as an elementary process, and throughfailure to analyze it as a complex process, could not agree.

We have shown that one is best able to learn to producea movement of a certain force when extent and time are bothinvolved. The elimination of extent greatly interferes withthe act, as does any radical variation in the time. Whenthese modifications are introduced, however, one can learnto produce movements approximating the desired force, butwith less efficiency than when the extent and time factorsare present.

We believe that the evidence herein adduced is sufficientto prove that the force of a movement is controlled by anumber of factors; that extent is for most individuals adominant factor and, though with less certainty, that timeis an important factor. Besides these two there are a numberof less closely correlated factors that an individual uses whenhe is prevented from using extent and time. That there isa simple sensation of force seems out of the question.

the perception of forcewexler.free.fr/library/files/morgan (1918) the perception... ·...

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