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

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

THE APPARATUS

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

THE METHOD OF CALCULATION

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

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

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

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

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

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

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

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

This investigation will present data suggesting that

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

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

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

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

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

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

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

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

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

Place the tracing-point of the planimeter at c and read vernier, giving 1916; follow the dotted path from c to h, the straight line from h to i, the dotted path from i to k, the straight line from k to l, the dotted path from l to m, the straight lines from m to n and n to g, the dotted path from g to m, the straight line from m to l, the dotted path from l to k, the straight line from k to i, the dotted path from i to n, and the straight line from h to c, when a second reading is taken, which was in this case, 1806. Divide the difference of these two readings, 1100 mm., by the length of cd, 119 mm., and the result is 9.1 mm., or the mean error (mean variation).

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

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

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

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

RESULTS

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

HAND MOVEMENTS

Simple movements
Lines 14 cm. long.

TYPICAL SERIES FOR THE MONTH

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