Chapter XXV: Section IV: , 1. The experiments of Table IX, C, repeat those of A with (5)

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

The details of the several experiments were as follows:

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

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

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

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

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

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

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

The other details were as in no. 1.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The interval in reading was planned to be long enough for some appreciation of the meaning of the words, but not enough to permit mental repetition of the preceding elements. Any mechanical time-measurement was found impracticable.

The subjects were instructed to avoid any effort to memorize the series, simply receiving each element as given.

After the last element there was a pause of about two seconds, to decrease the mere sound-recollection of the last few elements. Then the operator repeated, in an altered tone, one of the given elements. The subject at once wrote down the first element that came to mind, then the next, and so on.

In the seven preceding experiments the set of series presented had been different for each subject, though of course identical in character. But in this experiment and the following ones the lists of words were identical as read to each subject. The same element was repeated for each. Sixteen lists were given.

(9) The elements were nouns. In each series five names of similar objects were alternated with five names of a different sort of objects, _e. g._, names of fishes with names of poets. All were read, as before. In each series new sorts of objects were chosen. The subject never knew what sort of words were to be given; the subjects agreed this was not a disturbing factor to them, and it obviated the tendency to think what words would probably be given, as is natural when the general character of the series is announced beforehand.

The subjects were instructed to be passive during the reading, and during the four-second pause that followed, avoiding mental repetition of the words. Then the operator gave a signal and the subject repeated aloud the words as they happened to be remembered. The words being numbered on the list from which they were read, the operator was able to record the words as fast as spoken.

The subjects were instructed to give the word which they found to be foremost after they had spoken the preceding one, rather than to try to repeat a group of words which usually appeared simultaneously at the first effort of recollection, but which usually faded while one of them was being spoken.

The same sixteen series, of ten elements each, were given to each subject.

(10) The elements were nouns, the ten presented in each series all being names of similar objects, _e. g._, flowers. Five were spoken, alternated with five printed on small cards which were shoved in front of a 10×10 cm. opening in a cardboard screen fastened to the table-edge. Cards were 40 mm. square, the words printed by hand, but carefully, in letters 10 mm. high.

A series was given in about 13 seconds, but the time was not mechanically measured; it was at a rate which some practice showed to give a fair time to comprehend each element.

As before, the subjects were told to be passive until, after a four-second pause at the end of the series, the operator gave a signal. Then the recollected words were spoken.

The class of nouns was different in each series.

(11) The elements were nouns. In each series five of some familiar class were alternated with five of some other familiar class. The classes were different in each of the twelve series given.

From this regular series of ten, five were chosen irregularly, and were printed on cards as in no. 9. The remaining five, of course also irregularly placed in the series, were spoken. This irregularity was different in each series. Thus some words of one kind were spoken, the rest printed; some words of the other kind were spoken, the rest printed.

The other conditions were exactly as in the last experiment.

* * * * *

A table for the individual subjects, indicating not only the omitted but also the displaced and imperfect objects would have, for instance, the following character: C indicates that the effort was made to associate by Contiguity, S by Similarity.

SPOKEN NOUNS, ALTERNATED WITH PRINTED NONSENSE SYLLABLES

Nouns Omitted Syll. Omitted Displaced Imperfect
C S C S C S C S
Turley 13 16 21 14 7 13 6 10
Emerson 4 5 26 16 7 4 4 13
Miss Kent 5 8 15 8 18 5 9 4
Flexner 4 6 10 9 7 3 8 16
Toll 8 7 8 2 10 12 8 3

Total 34 42 80 49 49 37 35 46

If we consider total results only, and among them only the omitted elements, we come to the following percentages. They give the percentage of the errors of omissions among the elements recalled.

1. Letters and numbers alternated C 26. S 10.8
2. Letters, alternatingly disaligned C 21.2 S 15.
3. Letters irregularly disaligned C 23.8 S 22.4
4. Numbers irregularly disaligned C 7. S 20.
5. Nonsense Syllables, irregularly marked C 27.5 S 27.5
6. Nouns and Nonsense Syllables alternated, spoken C 35. S 37.2
7. Nouns and Nonsense Syllables alternated, nouns spoken,
syllables printed C 28.5 S 22.7

In the second group, experiments 8 to 11, not the errors of omission, but, as explained above, the different kinds of reproduced elements, had to be analyzed with special reference to the question whether a sequence linked two contiguous or two similar objects. In the following table the total number of recalled sequences is taken as basis and the different kinds of sequences are given in percentages of it. The elements themselves are described above. B means a break, that is, a sequence without similarity or contiguity.

8. Dissimilar elements, similarly presented S 45 C 28 B 28
9. Dissimilar elements, different kind in each series S 53 C 25 B 21
10. Similar elements, dissimilarly presented S 54 C 20 B 26
11. Dissimilar elements, dissimilarly presented
S (Meaning) 27 C 7 B 8
S (Presentation) 13.

The results by the first method of measurement may be summarized as follows, though the first and third conclusions are weakened by disagreement among the individual subjects.

_A._ When the only dissociating factor is some slight unessential feature (a bit of color on the card, a slight disalignment), this similarity and contiguity are nearly equally efficient. No. 3 and no. 5.

As this unessential feature is made more striking (disalignment half a card-length), the strength of similarity increases, only three fourths as many errors being made in dissociation as in contiguous association. No. 2.

The case of no. 4 (all numbers) is of little or no value. The time allowed for learning had to be made short enough to ensure the appearance of some errors; perfect recollection would obviously give no basis for comparison. And the time had to be so short in this case (only two seconds for some of the subjects) that the additional eye-motions and adjustments necessary in dissociating took time enough to spoil the results.

_B._ When the only dissociating factor is in the meaning of the elements (letters and numbers), this similarity is stronger than contiguity, only one half as many errors being made. No. 1.

The results of no. 6 do not support this proportion, but its results are not consistent, while those of no. 1 are.

_C._ When both meaning and manner of presentation are combined as dissociating factors (nouns and nonsense syllables, seen and heard), this similarity is stronger than contiguity, only three fourths as many errors being made.

But this method of measurement is not well adapted to series of auditory elements, so this experiment is unsatisfactory. No. 7.

The results by the second method of measurement may be summarized as follows:

_A._ When the only dissociating factor is in the meaning of the elements (names of different sorts of objects), this similarity is stronger than contiguity, twice as many similarity sequences as contiguity sequences being recalled. No. 8 and no. 9.

_B._ When the only dissociating factor is in the manner of presentation (to sight and hearing), this similarity is stronger than contiguity, nearly three times as many similarity sequences being recalled. No. 10.

_C._ When both meaning and manner of presentation are dissociating factors, these similarities are much stronger than contiguity, more than four times as many similarity sequences being recalled.

_D._ When these two dissociating factors are opposed to each other: (1) Four of the subjects show similarity of meaning much stronger than similarity of presentation, from two to five times as many similarity-of-meaning sequences being recalled. (2) One subject is strongly and consistently otherwise, giving nearly three times as many similarity-of-presentation sequences. No. 11.

MOTOR IMPULSES

THE ACCURACY OF LINEAR MOVEMENT

BY B.A. LENFEST

The starting-point for our investigation was the observation of Woodworth[138] that there is a certain rhythm in which a certain hand-movement is made with the maximum of exactitude, and which represents thus an optimum for the periodical discharge of the particular motor centre. Our question was whether this rhythm is a constant one for all parts of the body, or whether different groups of muscles produce the greatest exactitude in different periods; further, whether secondary factors, like complexity of movement, resistance by weight, fatigue, etc., influence this psycho-physiological optimum.

The investigation, however, showed soon the necessity to consider the whole problem of the accuracy of rhythmical linear movements, and the experiments are thus not always directly related to our starting-point.

There is very little material published that can be collected under the subject head, accuracy of voluntary movement, and still less when the enquiry is confined to the accuracy of straight lines or linear movements.

The most suggestive contribution is that of Dr. Woodworth on the accuracy of voluntary movement. He has collected consistently what can be found up to the date of his publication, and the reader is referred to pages 7-16 of his monograph for the most reliable collection of authorities.

It must be said, as we run over the list from Goldscheider on the threshold of perceptible movement, through the results of Hall, Hartwell, Loeb, and Delabarre on "bilateral asymmetry" and comparisons of right and left hands; consider Fullerton and Cattell in their suggestive results, and Münsterberg's studies of movements; and finally take the testimony of Bryan as to the growth of accuracy of movement in children, that the vast accumulation of material bearing on reaction time--and similar phenomena would be of more value if concerned more with the accuracy and less with the production or perception of movement.

A paper by Miss M. K. Smith, in the Philosophische Studien for 1900, with the title, Rhythmus und Arbeit, concerns the influence of rhythmical action upon the quality and quantity of work performed. The method was to commit to memory nonsense syllables and letters.

The results show a tendency to take up a certain rhythm, especially in the later results and after practice; easier memorizing if rhythm is present; motor reactions, as tapping, nodding, or swaying of body are noted frequently; the feeling of pleasure accompanies rhythmic reactions. While there are no data as to accuracy, there is suggestive matter bearing on the optimal rate and on the relations of compound and simple movements of the hand.

As far as the writer knows, he is the first to present systematic results as to the head and foot movement. The purposes of this enquiry may be briefly stated as

(1) the collection of a large body of facts, bearing on the actual and relative accuracy of straight-line movements possible with various parts of the body, such as hands, arms, head, legs, and feet;

(Something like 340,000 lines have been drawn and calculated.)

(2) to introduce certain variations in the conditions attending the production of ruled lines, such as

(_a_) to rule with the eyes opened and eyes closed, with other conditions the same;

(_b_) to change the rate of ruling or interval between the production of ruled lines; the rates chosen were 20, 30, 40, 50, 60, 70, 80, 100, 120, 140, 160, 180, and 200 beats per minute;

(_c_) to change the length of the normal or first line; the lengths used were 14, 10, and 1 cm.;

(_d_) to impose a weight on the ruling hand to either retard or accelerate the movement, choosing a weight of such magnitude that it would be perceptible, but would not have mass enough to cause pain or fatigue; 260 grams was used;

(_e_) to introduce a simultaneous movement of the free hand; _i. e._, the one that did not carry the recording pencil, of a similar character and extent but of opposite direction to the ruling hand;

(_f_) to record movements of both hands, of the head and of both feet;

(_g_) to conduct a series of experiments of similar character, as regards time-rate and extent of movement, to the series presented by Dr. Woodworth, with the idea of corroborating or disproving the results of his investigations; lines of 140 cm. were accordingly chosen;

(_h_) to conduct a series of experiments where the subject chooses his own rhythm or rate at which the easiest and best lines, subjectively speaking, could be ruled;

(_i_) to find the rates of respiration and pulse-beats and find the connection, if any, between them and the linear records.

(3) To examine, by variations of the number of lines ruled, the questions of fatigue and persistence of the memory-image; series of 50 lines for the first year and of 20 lines for the second year, were accordingly selected.

(4) To find the relations, if any, between constant errors and mean variations, so called.

THE APPARATUS

It is proposed to give the briefest possible discussion or explanation of the apparatus required for the investigation, it being desired at a later stage to enter into a comparison of the method adopted here with that of the only other investigation at all comparable to this one: the research problem of Dr. Woodworth, already referred to.

The underlying principle has been to avoid complication in apparatus, partly because of the delay and expense involved in working out, and making up elaborate schemes for apparatus, but mainly because of the advantage in duplicating this series of experiments, or of carrying on related investigations, to be derived from a choice of such parts, entering into the complete apparatus, as are at hand in any psychological laboratory, or that can be obtained and set up at small expense.

The use of smoked paper has been avoided, because a short preliminary series, using the usual smoked-paper records, was found to give no better results than did the method here adopted of ruling on white paper with a soft pencil, and the labor was thus considerably reduced.

To the objection that the pencil-ruling is more difficult, and involves more loss in friction and more complicated adjustments on the part of the subjects, only one of fourteen subjects admits that this is the case; and even if the testimony was unanimous as to the greater ease of production of the smoked records, it would be no reason for its adoption, since one of the first rules for all experimental work is uniformity of conditions, and this is equally well attained in either case.

The apparatus for free hand-movements and for the compound movements of both hands consists:

(1) Of an adjustable wooden rest (see Fig. _A_) with a base (_a_) about 40 × 60 cm. hinged to a vertically adjustable flat board (_b_), called the arm-rest, about 40 × 70 cm., and having on its upper edge two brass pins or plates (_c_) about 30 cm. apart.

The pencil is started from one of these pins, depending on the hand used, and moved until it comes in contact with a wooden rod that is held against the opposite pin and which is of the right length to give a movement of the pencil of 1, 10, or 14 cm., as desired.

The operator holds this rod in place for the first line ruled and then instantly removes it, so that the second and all later lines are ruled by memory of the first one, as closely in length to the first, or so-called normal line, as is possible.

(2) The apparatus for actuating and taking care of the paper.

This consists of two drums (_d_ and _d´_, Fig. _B_) 20 cm. diameter by 40 cm. wide, mounted on suitable supports about 1 metre apart, and fastened to a table, with axes parallel.

The drum upon which the record is to be made (_d_) is adjusted close to the arm-rest, so that each ruled line will be carried down and out of sight before the next one is ruled, the pencil being held in the position (_e_); note that the arrow shows the direction of rotation.

The second drum (_d´_) is actuated by a motor (_F_) through a round belt (_g_), this motor being a clockwork type, with gear-changes and adjustable vanes for varying the speed, and having the power derived from a suspended weight (_w_).

The recording paper (_h_) transmits motion from (_d´_) to (_d_). This paper consists of a strip about six metres long by twenty-eight cm. wide, with one end pasted to (_d_), and then wound upon (_d_), leaving enough to be carried to (_d´_) and pasted to the latter. As the paper is unwound from (_d_), it is wound upon (_d´_), and, both to keep the paper tight and to prevent too rapid unwinding of (_d_), it is necessary to apply a friction-brake to the shaft of (_d_).

(3) A metronome, capable of being used for a range of 20 to 200 beats, and a stop-watch, to enable the operator correctly to time the subject, are in constant use.

The metronome is set in vibration and the subject is permitted to take his own time to start the ruling, the operator holding the wooden rod in place with one hand, while the other hand holds the stop-watch ready to start it the instant the subject's pencil is moved. There is thus a personal equation for the length of period, but this is of no consequence, as will be apparent when the method of calculation and the use of the planimeter is considered.

In the series of records with the weight, it is impossible to run the speed about 80 to 100 beats, unless the modification in apparatus shown in Fig. _C_ is used; for the vibration of the string running from the hand to the weight around a pulley is violent enough either to throw the string off the pulley or cause the weight to jump so severely as to render the records useless.

This is entirely obviated by the given method of using a heavy weight acting with a small leverage (about 1 cm.) and thus moving only a short distance, so that it is capable of operating at the highest speeds with no perceptible shock or jump; the string is led to the hand or wrist from a grooved pulley of about 12 cm. radius, so the highest velocity of the weight is only about one twelfth that of the hand. This method makes it possible to carry the weighted records to the highest speeds.

This same method is used for the head and foot records, with the following additional apparatus; the string (Fig. _C_), shown leading to the hand, is led horizontally over to and around a similar large pulley on the opposite side of the table and either down to the foot or in a diagonally upward direction to the head; so that movements of the head or foot are faithfully recorded on the drum by means of a pencil held in a block of wood, this block of wood being fastened on the horizontal string in a suitable position for recording on the drum paper. The pencil is kept against the paper by a light spring or elastic band.

The foot is connected to the string by a stirrup that prevents any movement of the feet at all, unless the same is recorded by the pencil.

The head is furnished with a skull cap or harness consisting of non-elastic webbing and stiffened, where the string is attached, by a strip of sheet brass formed to fit the forehead or the back of the head, as the case may be. The object of the brass strip is to prevent a lost motion in the flexible webbing, that is found troublesome otherwise.

It will be evident, then, that the weight is continually acting as an accelerating or retarding influence in all records for head and feet, but it is not considered objectionable, for it is a constant throughout the series.

The other plan would require a circuit of cord leading in both directions from the head or feet in a complete circuit, and would cause in the opinion of the writer too much complication of apparatus.

The pulse-beats were taken by the stop-watch and wrist method so familiar to the physician, while the respiration results were obtained by the usual tambour apparatus for registering the chest expansion upon smoked paper.

THE METHOD OF CALCULATION

Suppose that the drums have been set in rotation and that the paper is unwinding from (_d_) and being wound on (_d´_), Fig. _B_, and suppose that the subject has ruled series of 20 to 50 lines, as may be desired, regulated by the stop-watch in the hands of the operator. The records will appear much as Fig. 5 under the planimeter discussion, there being for each speed one normal line to start and a series of lines following and intended to be of the same length as the normal line. A series of records, then, consists of 13 records of 20 or 50 lines, each running from 20 to 200 beats per minute, the complete series having not less than 260 and not more than 650 lines.

It should be added that the operator holds a pencil-point on the end of each normal line just after the record of 20 or 50 lines is made and turns the drum (_d_), thus marking a line nearly perpendicular to the ruled lines and at the average or normal distance from the starting-point; an absolutely correct record would show all ruled lines ending on this line.

The calculation of this series of records by the ordinary method of measuring each line, adding the lines of the series, averaging for the constant error, and repeating the operation in a slightly different form for the mean error or mean variation is of such enormous labor for an extended investigation as to be beyond the capacity of one or of several students; it is fortunate that the planimeter is at hand to be employed in averaging each series, and this instrument has therefore been selected as overcoming this difficulty.

It is desirable to consider the method employed by Dr. Woodworth to overcome this danger of excessive computation, and it will now be subjected to a critical and comparative examination.

He says, page 19 of his monograph on the Accuracy of Voluntary Movement, that the subject's sole duty was to make the present line equal to that immediately preceding, and the width of the slot was so adjusted that the subject could see only the line just ruled. After discussing certain matters of memory and its relation to the memory-image, in the attempt to support this changing normal plan, he confesses, on page 20, that this device is advantageous in much simplifying the most tedious part of the graphic method, that of computation.

While this is undoubtedly true, it needs careful scrutiny before adoption, for, on the same page, he says that one source of error in the method of making each line equal to the preceding one is that the different movements in the same series are not comparable, but the positive constant error is cumulative in its effect, and the normal tends to become longer and longer.

Some relation between this source of error and such a record as shown on page 29, Fig. 2, is evident, for, while it should be noted that this cumulative effect is peculiar to a series of lines for one speed, it has further a tendency to produce overruling at all speeds, and the natural result is to increase the error unduly and unnaturally for the higher speeds or as the speed increases, because there is then less time for the discrimination and choice that will tend to shorten the ruled line. It may be predicted, then, that Dr. Woodworth's method will show a slight lengthening of normal between lines at slow speeds and a much greater one at high speeds, the effect being to introduce a variable factor that would have no existence were a better plan adopted. The computation required for the average error is simple, being dependent only on the first and last lines of a series, and it is suspected that this very simplicity has led to its adoption and the consequent neglect of certain serious sources of error.

He tells us, on page 20, that the constant and variable error may well be isolated and studied separately, but indicates that they must "somehow" be considered combined as nature has made them; that is, analysis is desirable, but the synthetic method is more scientific.

This investigation will present data suggesting that

(1) Such a curve as that on page 29 of his monograph is not a characteristic one and relations of length of ruled line, as well as effects of weight, make it impossible to apply Weber's law or even the law of Fullerton and Cattell in the way proposed by Dr. Woodworth.

(2) There is no relation, mathematical or other, between constant and mean errors, and they not only may be but must be isolated and studied separately, if an investigation is to be conducted in the interests of scientific exactness.

It will be necessary to reject the method of Dr. Woodworth if the most reliable results are desired, in which case the planimeter is a necessity.

The theory of the planimeter cannot be developed at this place; every physicist and engineer is acquainted with it. The writer believes he was the first to apply the planimeter to the calculation of results from psycho-physical data for averaging both mean and variable errors. More than 340,000 lines were involved, each demanding two measurements. The best type of planimeter for general use and the one used here is the Amsler adjustable-arm form.

In Fig. _D_ is shown a record taken at twenty beats per minute that will both explain the method of computation and show how the planimeter has been used to find the constant and mean errors.

Hylan-20 beats. L.H.E.c.-2-13-Ό1.]

The record, as made and ready for computation, is not provided with the line _cd_ or with the dotted lines that connect the ends of the ruled lines. The line _ab_ is drawn by turning the drum of the apparatus with a pencil held at the end of the normal or left-hand line _af_, which was here 100 mm. long.

The tracing-point of the planimeter being placed at _a_, a reading is taken, which was in this case 1486; after following with the tracing-point the dotted path to _g_ and returning, via _gb_ and _ba_, a second reading is taken, which was 1248; subtracting gives 238, which should be read 2380 square mm. for the area of the space _agba;_ dividing by the distance _ab_, in this case 119 mm., gives the average height, which is + 20.0 mm., the plus sign suggesting that the distance thus found, which is the constant error for the series, be laid off in addition to or beyond _Fa_.

This being done, a line _cd_ is drawn parallel to and 20.0 mm. from _ab_, as the mean line of constant errors.

To find the mean error of the series a slightly different method is necessary.

Place the tracing-point of the planimeter at _c_ and read vernier, giving 1916; follow the dotted path from _c_ to _h_, the straight line from _h_ to _i_, the dotted path from _i_ to _k_, the straight line from _k_ to _l_, the dotted path from _l_ to _m_, the straight lines from _m_ to _n_ and _n_ to _g_, the dotted path from _g_ to _m_, the straight line from _m_ to _l_, the dotted path from _l_ to _k_, the straight line from _k_ to _i_, the dotted path from _i_ to _n_, and the straight line from _h_ to _c_, when a second reading is taken, which was in this case, 1806. Divide the difference of these two readings, 1100 mm., by the length of _cd_, 119 mm., and the result is 9.1 mm., or the mean error (mean variation).

It will be noted that this method gives the sum of the errors from the mean line _cd;_ that is, the same result would be obtained if the tracing-point were (1) carried from _c_ around all the area below _cd_, and this area were calculated as before; (2) carried from _c_ around all the area above _cd_ and the area measured as in other cases; and (3) these two results added and averaged.

To apply the method for _ab_, or constant error computation, to _cd_ should give equal readings at _c_ or a 0 mean error, a result evidently incorrect in the record selected.

After averaging results by the planimeter, the collection of data has been arranged by months; the record for one month only can be presented here, but the method of tabulation is the same throughout.

Each figure given for N, M, c and v, in the accompanying typical table for the month of May, 1904 (pages 495-499), is the average from 20 or 50 lines, ruled as already shown, Fig. _D_.

RESULTS

It is necessary to observe that the limits of space imposed on the writer preclude all but the barest outline of the deductions to be drawn from the investigation, and to this fact is due whatever of dogmatism is inherent in the argument; for it is manifestly impossible to present all the material, and the writer asks, then, the indulgence of the reader when he claims to have impartially examined and presented the evidence.

HAND MOVEMENTS

Simple movements
Lines 14 cm. long.

TYPICAL SERIES FOR THE MONTH

Key.
v = mean error.
R.H. = right hand.
R.F. = right foot.
E.O. = eyes open.
si. = simple motion
N = normal line.
Unit = 1 mm.
L.H. = left hand.
L.F. = left foot.
E.C. = eyes closed.
co. = compound motion.
M = mean line.
b = beats per minute.
c = constant error.

See Beats per minute.
Day. Subject. Key. 20 30 40 50 60 70 80 100 120

6 Hylan. N 10 10.5 11 11 10 10 10 12 10
L.F.E.O. M 16.1 13.5 12.1 13.8 13.1 10.0 10.0 11.2 12.5
c +6.1 +3.0 +1.1 +2.8 +3.1 0.0 0.0 -0.8 +2.5
v 2.8 3.5 1.9 0.9 1.6 4.6 2.0 2.7 1.2

140 160 180 200

12 10 11 11
12.0 6.1 11.0 14.21
0.0 -3.9 0.0 +3.2
1.0 1.3 2.1 4.0

Hylan. N 10 11 10 12 10 12 11 11 11
L.F.E.C. M 8.9 10.5 10.9 11.4 13.1 10.3 11.8 13.1 13.9
c -1.1 -0.5 +0.9 -0.6 +3.1 -1.3 +0.8 +2.1 +2.9
v 2.7 6.4 2.2 1.4 2.7 1.6 2.3 1.6 4.9

11 11.5 11 11
15.8 11.0 15.0 17.8
+4.8 -0.5 +4.0 +6.8
2.9 2.3 2.3 2.5

George. N 10.5 10 10 10 10 10 10 10 11
L.F.E.O. M 14.6 9.7 7.1 6.4 7.7 8.3 8.0 10.0 11.0
c +4.1 -0.3 -2.9 -3.6 -2.3 -1.7 -2.O 0.0 0.0
v 2.1 1.6 1.8 2.3 0.8 0.7 1.4 1.7 0.8

10 10 11 11
9.0 10.0 8.0 12.5
-1.0 0.0 -2.0 +1.5
1.0 1.3 1.6 0.4

George. N 10 9 9 10 11 9.5 9 10 8
L.F.E.C. M 11.7 9.2 10.2 12.6 13.2 11.5 12.2 6.6 5.0
c +1.7 +0.2 +1.2 +2.6 +2.2 +2.0 +3.2 -3.4 -3.0
v 2.0 2.9 2.5 0.7 0.5 1.0 0.8 2.0 4.1

10 9 9 10
8.0 7.6 8.0 11.0
-2.0 -1.4 -1.0 +1.0
3.1 2.5 2.1 3.7

Moore. N 10 10 10 10 11 11 11 10 10
L.F.E.O. M 15.7 18.8 17.7 16.7 18.3 18.5 16.5 15.6 16.0
c +5.7 +8.8 +7.7 +6.7 +7.3 +7.5 +5.5 +5.6 +6.0
v 3.5 3.8 1.1 0.8 3.6 2.1 2.7 0.6 2.4

10 11 10 10
16.2 16.3 16.4 18.8
+6.2 +5.3 +6.4 +3.8
0.5 3.5 2.2 3.8

N 10 10 10 10 11 10 10 9
Moore. M 19.6 15.3 15.3 14.3 14.9 13.5 6.7 13.4
L.F.E.C. c +9.6 +5.3 +5.3 +4.3 +3.9 +3.5 -3.3 +4.4
v 2.6 2.5 2.4 0.4 2.0 6.4 0.7 4.1

9.5 11 11 10 10.5
20.0 14.3 14.5 16.9 17.9
+10.5 +3.3 +3.5 +6.9 +7.4
2.6 3.8 1.1 3.1 2.8

N 10 10 9 10 10 9.5 10 10
9 Angier. M 13.6 12.5 11.6 11.6 11.5 11.7 13.0 12.9
R.F.E.O. c +3.6 +2.5 +2.6 +1.6 +1.5 +2.2 +3.0 +2.9
v 2.9 2.3 1.8 2.3 1.7 1.6 2.0 2.7

11 10 10 10 10
12.2 12.2 13.5 22.1 16.5
+1.2 +2.2 +3.5 +12.1 +6.5
3.3 1.5 1.5 6.7 1.5

N 10 10 10 9.5 10 9 10 10
Angier M 11.4 7.7 13.8 8.3 11.4 11.5 11.0 10.3
R.F.E.C. c +1.4 -2.3 +3.8 -1.2 +1.4 +2.5 +1.0 +0.3
v 4.8 1.3 3.0 2.6 1.4 1.7 1.8 1.7

140 beats

9 10 10 11 10 10
9.9 12.8 16.7 17.7 12.4 12.0
+0.9 +2.8 +6.7 +6.7 +2.4 +2.0
1.8 1.4 1.7 4.2 2.1 1.7

N 11 10 10 9 10 11 10 10
Huggins. M 12.5 8.5 12.6 9.7 9.7 16.6 15.7 18.7
R.F.E.O. c +1.5 -1.5 +2.6 +0.7 -0.3 +5.6 +5.7 +8.7
v 3.6 2.6 2.7 2.8 3.3 3.2 3.3 3.6

10 11 11 11 10
13.6 15.8 9.3 18.3 14.3
+3.6 +4.8 -0.7 +7.3 +4.3
3.1 2.7 2.9 3.8 3.0

N 11 8 10 10 11 10 10 10
Huggins. M 6.5 10.5 10.7 8.8 12.6 12.9 12.2 22.3
R.F.E.C. c -4.5 +2.5 +0.7 -1.2 +1.6 +2.9 +2.2 +12.3
v 1.4 2.1 1.8 1.6 3.7 3.1 2.0 4.1

10.5 10 10 10 10
9.9 21.8 12.0 12.5 16.3
-0.6 +11.8 +2.0 +2.5 +6.3
1.4 5.0 2.3 3.6 1.8

N 9 9 9 9 9.5 8 7 10
13 Lenfest. M 12.7 11.9 11.1 11.3 12.1 8.7 11.6 12.6
R.F.E.O. c +3.7 +2.9 +2.1 +2.3 +2.6 +0.7 +4.6 +2.6
v 3.7 2.4 1.9 2.3 2.8 0.2 2.8 2.1

10 10 9 8 10
9.0 8.6 11.7 7.0 11.8
-1.0 -1.4 +2.7 -1.0 +1.8
2.0 2.1 3.2 1.4 4.1

N 12 11 11 10 10 10.5 11 11
Lenfest. M 14.9 14.7 12.2 13.5 12.6 11.9 12.6 8.7
R.F.E.C. c +2.9 +3.7 +1.2 +3.5 +2.6 +1.4 +1.6 -2.3
v 3.3 2.2 3.5 3.5 3.2 3.0 2.6 1.7

11 11 10 10 10
9.1 8.9 8.4 14.1 6.9
-1.9 -3.1 -1.6 +4.1 -3.1
2.4 2.8 2.9 4.1 2.3

N 12 11 11 11 11 10 11 10
George. M 8.3 9.0 8.6 8.8 8.7 7.0 7.4 7.9
R.F.E.O. c -3.7 -2.0 -2.4 -2.2 -3.3 -3.0 -3.6 -2.1
v 5.0 3.3 2.3 0.1 3.3 2.9 2.4 3.1

11 10.5 11 10 10
6.8 9.7 9.0 5.8 11.0
-4.2 -0.8 -2.0 -4.2 +1.0
1.5 4.6 2.9 2.9 3.9

N 12 11 12 11 11 11 10.5 11
George. M 7.0 7.7 14.1 8.3 10.3 8.4 8.7 7.8
R.F.E.C. c -5.0 -3.3 +2.1 -2.7 -0.7 -2.6 -1.8 -3.2
v 2.5 2.6 2.4 3.7 2.9 2.3 1.6 2.1

10 10.5 11 10 10
6.4 10.0 9.0 7.9 7.3
-3.6 -0.5 -2.0 -2.1 -2.7
1.9 3.7 2.9 1.8 3.8

N 11 11 11 11 12 10 9 11
Moore. M 14.5 16.6 16.5 9.0 17.0 10.7 10.4 11.9
R.F.E.O. c +3.5 +5.6 +5.5 -2.0 +5.0 +0.7 +1.4 +0.9
v 1.7 2.2 1.9 1.8 1.3 2.2 2.6 2.2

10 10.0 10.5 11 9.5
11.5 12.5 12.5 15.1 12.6
+1.5 +2.5 +2.0 +4.1 +3.1
2.2 2.5 2.5 1.4 0.8

N 11 10 11 11 11 10 10 9
Moore. M 14.3 13.2 15.9 12.3 17.9 10.0 11.3 15.9
R.F.E.C. c +3.3 +3.2 +4.9 +1.3 +6.9 0.0 +1.3 +6.9
v 1.8 2.8 1.6 2.1 1.7 2.4 3.2 2.2

11 11.0 10 10 10
14.8 15.5 13.4 11.8 12.2
+3.8 +4.5 +3.4 +1.8 +2.2
2.7 1.4 2.2 1.8 2.2

N 11 11 10 11 10 10 10 11
16 Angier. M 14.3 13.5 9.3 14.4 14.1 9.5 15.1 12.7
R.F.E.O. c +3.3 +2.5 -0.7 +3.4 +4.1 -0.5 +5.1 +1.7
v 1.7 1.9 2.0 2.4 2.0 1.1 2.4 2.8

10 11 10 11 11
11.1 12.6 13.7 11.0 16.6
+1.1 +1.6 +3.7 0.0 +5.6
2.0 2.0 2.7 1.3 3.5

N 11 10 10 9 10 10.5 10 10
Angier. M 14.4 4.8 2.5 3.6 5.8 6.7 8.0 11.0
R.F.E.C. c +3.4 -5.2 -7.5 -5.4 -4.2 -3.8 -2.0 +1.0
v 3.2 2.7 2.3 3.6 2.7 2.3 1.3 2.8

11 10 11 11 11
13.5 11.1 13.9 10.1 11.0
+2.5 +1.1 +2.9 -0.9 0.0
2.8 1.4 2.4 1.8 2.2

N 97 97 98 97 98 99 97 98
Huggins. M 107.6 107.8 100.4 114.2 98.0 110.3 89.4 102.5
L.F.E.O. c +10.6 +10.8 +2.4 +17.2 0.0 +11.3 -7.6 +4.5
v 5.9 0.6 4.8 6.5 5.3 6.7 6.4 5.5

95 98 99 99 100
99.2 100.8 106.4 101.5 108.9
+4.2 +2.8 +7.4 +2.5 +8.9
7.8 6.0 4.7 7.0 12.7

N 97 98 100 97 95 95 99 99
Huggins. M 102.8 104.3 115.1 101.4 94.1 102.0 106.4 93.4
L.F.E.C. c +5.8 +6.3 +15.1 +4.4 -0.9 +7.0 +7.4 -5.6
v 5.8 8.6 10.8 9.9 7.9 10.4 8.1 6.8

97 98 99 99 100
87.7 98.7 108.4 97.7 110.8
-9.3 +0.7 +9.4 -1.3 +10.8
9.4 5.8 6.9 5.3 6.1

N 11 11 10 10 10 10 10 10
20 Lenfest. M 16.1 13.5 11.6 10.9 10.9 14.2 11.7 10.5
L.F.E.O. c +5.1 +2.5 +1.6 +0.9 +0.9 +4.2 +1.7 +0.5
v 2.8 3.0 3.0 3.0 1.2 1.9 1.0 1.6

11 10 11 11 10
12.4 11.1 12.2 8.7 12.9
+1.4 +1.1 +1.2 -2.3 +2.9
3.2 5.1 1.9 1.7 4.2

N 12 11 10 10 10 11 10 10
Lenfest. M 20.4 16.8 11.6 11.2 11.8 14.0 9.0 9.3
L.F.E.C. c +8.4 +5.8 +1.6 +1.2 +1.8 +3.0 -1.0 -0.7
v 2.5 3.6 3.0 1.9 1.6 2.0 3.0 1.2

10 10 11 11 10
6.2 10.0 8.5 5.1 8.3
-3.8 0.0 -1.5 -5.9 -1.7
1.9 0.3 1.8 1.7 0.8

N 98 97 94 98 98 97 98 98
George. M 104.0 100.4 102.6 99.3 105.1 111.1 101.9 100.5
L.F.E.O. c +6.0 +3.4 +8.6 +1.3 +7.1 +14.1 +3.9 +2.5
v 6.4 11.3 9.6 7.7 5.3 8.0 3.7 5.6

97 96 98 98 97
96.4 102.0 97.4 94.2 95.8
-0.6 +6.0 -0.6 -3.8 -1.2
5.7 5.7 9.1 7.8 3.6

N 98 97 94 97 97 98 98 97
George. M 93.6 81.2 94.7 92.7 104.2 99.3 93.4 89.6
L.F.E.C. c -4.4 -15.8 +0.7 -4.3 +7.2 +1.3 -4.6 -7.4
v 9.1 8.9 5.5 4.6 5.8 6.9 4.9 6.6

96 98 98 99 100
96.4 93.0 87.3 101.8 87.4
+0.4 -5.0 -9.7 +2.8 -12.6
7.8 4.8 7.7 5.6 5.7

N 97 99 98 97 96 96 97 98
Moore. M 106.1 106.9 105.2 103.0 104.7 108.6 102.7 106.9
L.F.E.O. c +9.1 +7.9 +7.2 +6.0 +8.7 +12.6 +5.7 +8.9
v 4.3 5.6 4.6 5.2 8.0 6.0 7.4 6.9

99 98 99 99 99
110.9 105.7 111.2 99.9 93.0
+11.9 +7.7 +12.2 +0.9 -6.0
4.8 9.0 4.7 11.4 1.8

N 96 97 97 97 96 97 96 97
Moore. M 119.2 79.8 87.3 79.6 81.6 91.2 96.5 106.2
L.F.E.C. c +23.2 -17.2 -9.7 -17.4 -14.4 -5.8 +0.5 +9.2
v 16.1 6.7 11.6 7.2 7.5 4.1 4.0 6.6

99 98 97 98 99
100.4 91.9 104.0 88.6 80.9
+1.4 -6.1 +7.0 -9.4 -18.1
4.0 6.1 5.4 6.6 8.2

N 98 97 95 96 96 97 99 97
23 Lenfest. M 105.7 110.8 97.4 93.8 97.8 100.2 99.9 92.9
L.F.E.O. c +7.7 +13.8 +2.4 -2.2 +1.8 +3.2 +0.9 -4.1
v 9.3 1.5 3.6 5.1 3.6 4.4 2.9 3.3

97 98 98 98 99
86.1 96.6 91.9 80.9 83.0
-10.9 -1.4 -6.1 -17.1 -16.0
6.7 5.0 8.2 6.0 7.8

N 96 94 96 96 96 94 96 97
Lenfest. M 111.3 95.0 98.3 101.7 101.7 110.1 98.8 79.0
L.F.E.C. c +15.3 +1.0 +2.3 +5.7 +5.7 +16.1 +2.8 -80.0
v 7.1 5.1 5.8 2.7 5.4 7.8 12.1 3.7

97 97 100 100 100
88.9 72.7 88.4 69.7 80.8
-8.1 -24.3 -11.6 -30.3 -19.2
5.6 8.0 7.4 8.4 7.0

N 96 97 96 96 98 98 97 97
Huggins. M 113.5 105.7 105.5 97.7 92.5 98.4 92.5 102.0
L.H.E.O. c +17.5 +8.7 +9.5 +1.7 -5.5 +0.4 -4.5 +5.0
v 4.2 2.4 3.6 5.0 3.5 3.1 4.2 5.8

95 98 98 99 97
95.0 112.3 104.5 108.7 95.7
0.0 +14.3 +6.5 +9.7 -1.3
4.7 6.4 5.8 7.1 4.4

N 98 97 97 97 97 99 99 97
Huggins. M 103.5 82.8 86.1 87.8 87.7 94.2 92.1 94.5
L.H.E.C. c +5.5 -14.2 -10.9 -9.2 -9.3 -4.8 -6.9 -2.5
v 8.4 6.7 5.4 3.5 6.7 5.4 6.0 5.8

97 97 98 98 96
99.9 111.5 101.3 113.7 95.1
+2.9 +14.5 +3.3 +15.7 -0.9
4.8 13.3 4.7 9.6 2.6

N 96 95 96 96 96 97 96
27 Lenfest. M 101.6 93.4 91.2 90.0 97.5 93.2 93.4
R.F.E.O. c +5.6 -1.6 -4.8 -6.0 +1.5 -3.8 -2.6
v 6.2 5.1 3.4 2.8 5.5 4.5 3.7

96 99 102 101 100
89.8 97.5 88.6 96.8 66.2
-6.2 -1.5 -13.4 -4.2 -33.8
5.5 3.6 4.3 4.9 8.1

N 96 96 97 97 97 98 98
Lenfest. M 103.8 101.2 94.0 100.3 96.4 101.2 105.0
R.F.E.C. c +7.8 +5.2 -3.0 +3.3 -2.6 +3.2 +7.0
v 6.2 7.4 4.5 3.8 3.5 4.7 2.4

95 98 100 99 100
78.0 98.5 88.8 85.1 65.8
-17.0 +0.5 -11.2 -13.9 -34.2
4.7 4.3 7.0 6.9 5.9

The records are averaged for nine subjects, three of them being left-handed. For the right hand we find, for mean error, a reduced error with visual control.

For constant errors, a similar result is apparent; when following the eyes-closed curve one may note a large negative error 20-50 beats, and a similar but larger positive error 70-160 beats, with a falling to a negative error again at 200 beats.

This may be interpreted to mean a groping for the correct length of line at the lower speeds when some time for reflective processes is allowed, and an inhibitory effect on the motor discharge; later the speed prevents this discrimination, and introspective testimony goes to show that a mental conception of a barrier, beyond which one cannot carry the pencil, is set up and kept more or less constant through the help of the joint and muscular sensations. It would follow, then, that this muscular stop is overestimated where reflection is not possible.

Finally, the falling-off of the length of the line is probably due to physical inability to rule a line of the full length of 140 mm. at 200 beats per minute and an examination of some individual cases confirms this opinion, for the lines may be started some distance away from the origin apparently in order to end them at the correct point.

Curve inclinations are upward, for mean errors, with visual control, while the eyes-closed records show no increase in error for the increased speeds.

For constant errors, with visual control, there is a similar inclination downward for both hands, with a 0 error at about 120 beats. It should be noted that this opposite tendency in mean and constant errors suggests that they should be kept separate in all computation.

The left-handed subjects have much better control of their left hand than have the right-handed subjects, and they may dispense with visual control to a large extent.

On the other hand, for right-hand records we find much the same increase in irregularity and error for both left- and right-handed subjects; they all must depend on visual control for reduction of errors.

It follows that the non-visual control exerted by the left-handed subjects on the right hand is as good or as great as for the right-handed subjects; while they have the hand in which they may be expected to excel under much better control.

It is not intended to present this as an argument for teaching left-handedness, but it is certainly suggestive when considering the question that ambidexterity be taught in early life.

It should be noted that two of the three left-handed subjects might be expected, because of special training, to show marked manual dexterity, while only one of the four right-handed subjects has had special training along this line.

No extended discussion is appropriate here as to the question of what portion of this extra ability of the left-handed subjects to react accurately is due to practice and habit, _i. e._, is automatic, and accomplished without reference to the sensory motor by-path to the cerebral cortex; and on the other hand, as to whether the direct sensory motor path via spinal cord or medulla is not cut off entirely.

For 140 mm. averages and free motion, we find in general

(1) a reduced error and greater uniformity of result at all speeds where visual control is added, in the case of both mean and constant errors and for all subjects;

(2) the mean errors for visual-control records show a rise along a line whose equation is approximately _y_ = _px_, or the equation of a straight line, where _p_ is an undetermined constant.

On the other hand,

(3) the eyes-closed mean errors show no increase or decrease in value during the entire series;

(4) the constant errors for visual-control records show a drop from positive errors to negative errors, along a line whose equation is approximately _y_ = _qx_ or the equation of a straight line, where _q_ is an unknown constant, somewhat less in value than _p_ in the case of mean errors; the constant error becomes 0 at about 120 beats;

(5) the eyes-closed constant errors follow the same equation for left-handed subjects, using the left hand, but all other cases suggest a curve of the parabolic form, having 0 constant errors at 60 and 180 beats and being convex upward.

Considering individual records for 14 cm.

A general survey of the charts suggests certain irregularities that call for explanation, for there will be sudden large increases in errors, that are explicable on the hypothesis that the subject has temporarily lost control of the moving hand, that is, that fatigue is to be noted.

While the purpose of the investigation has been to allow no lines to be ruled while the subject was conscious of any such feeling, there being a pause of any desired length to permit time for rest, it is to be noted that a considerable amount of recorded data as to fatigue shows that it is an unconscious or subconscious phenomena.

Further, the series of records have been arranged to occur from 20 to 200 beats and never in the reverse order, because of subjective limitations, so it is reasonable to expect that during the period of twenty minutes to one half an hour required for a series of records, there will be lapses of volitional control entirely beyond the ken of the subjects. It is to this cause rather than to pure chance that the results will be attributed. With this exception, the individual records show close agreement with their average.

The results obtained from a consideration of free hand-movements of 1, 10, and 14 cm. length are:

For 14 cm. lines

for the average of nine subjects:

The mean errors,