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better not to make this distinction so pronounced.

Here again I have concerned myself primarily with only one illusion,

the illusion which deals with open and filled spaces. This is the

illusion to which Dresslar[12] devoted a considerable portion of his

essay on the ‘Psychology of Touch,’ and which he erroneously thought

to be the counterpart of the optical illusion for open and filled

spaces. One of the earliest notices of this illusion is that given by

James,[13] who says, “Divide a line on paper into two equal halves,

puncture the extremities, and make punctures all along one of the

halves; then, with the finger-tip on the opposite side of the paper,

follow the line of punctures; the empty half will seem much longer

than the punctured half.”

 

[12] Dresslar, F.B., Am. Journ. of Psy., 1894, VI., p. 313.

 

[13] James, W., ‘Principles of Psychology,’ New York, 1893,

II., p. 250.

 

James has given no detailed account of his experiments. He does not

tell us how many tests were made, nor how long the lines were, nor

whether the illusion was the same when the open half was presented

first. Dresslar took these important questions into consideration, and

arrived at a conclusion directly opposite to that of James, namely,

that the filled half of the line appears larger than the open half.

Dresslar’s conclusion is, therefore, that sight and touch function

alike. I have already said that I think that Parrish was entirely

right in saying that this is not the analogue of the familiar optical

illusion. Nevertheless, I felt sure that it would be quite worth the

while to make a more extensive study than that which Dresslar has

reported. Others besides James and Dresslar have experimented with

this illusion. As in the case of the illusion for passive touch, there

are not wanting champions of both opinions as to the direction in

which this illusion lies.

 

I may say in advance of the account of my experiments, that I have

here also found a ground of reconciliation for these two divergent

opinions. Just as in the case of the illusion for passive touch, there

are here also certain conditions under which the filled space seems

longer, and other conditions under which it appears shorter than the

open space. I feel warranted, therefore, in giving in some detail my

research on this illusion, which again has been an extended one. I

think that the results of this study are equally important with those

for passive touch, because of the further light which they throw on

the way in which our touch sense functions in the perception of the

geometrical illusions. Dresslar’s experiments, like those of James,

were made with cards in which one half was filled with punctures. The

number of punctures in each centimeter varied with the different

cards. Dresslar’s conclusion was not only that the filled space is

overestimated, but also that the overestimation varies, in a general

way, with the number of punctures in the filling. Up to a certain

point, the more holes there are in the card, the longer the space

appears.

 

I had at the onset of the present experiment the same feeling about

Dresslar’s work that I had about Parrish’s work, which I have already

criticised, namely, that a large number of experiments, in which many

variations were introduced, would bring to light facts that would

explain the variety of opinion that had hitherto been expressed. I was

confident, however, that what was most needed was a quantitative

determination of the illusion. Then, too, inasmuch as the illusion,

whatever direction it takes, is certainly due to some sort of

qualitative differences in the two kinds of touch sensations, those

from the punctured, and those from the smooth half, it seemed

especially desirable to introduce as many changes into the nature of

the filling as possible. The punctured cards I found very

unsatisfactory, because they rapidly wear off, and thus change the

quality of the sensations, even from judgment to judgment.

 

[Illustration: FIG. 7.]

 

The first piece of apparatus that I used in the investigation of the

illusion for open and filled space with active touch is shown in Fig.

7. A thimble A, in which the finger was carried, moved freely along

the rod B. The filled spaces were produced by rows of tacks on the

roller C. By turning the roller, different kinds of fillings were

brought into contact with the finger-tip. The paper D, on which the

judgments were recorded by the subject, could be slowly advanced under

the roller E. Underneath the thimble carrier there was a pin so

arranged that, by a slight depression of the finger, a mark was made

on the record paper beneath. A typical judgment was made as follows;

the subject inserted his finger in the thimble, slightly depressed the

carrier to record the starting points, then brought his finger-tip

into contact with the first point in the filled space. The subject

was, of course, all the while ignorant of the length or character of

the filling over which he was about to pass. The finger-tip was then

drawn along the points, and out over the smooth surface of the roller,

until the open space passed over was judged equal to the filled space.

Another slight depression of the finger registered the judgment on the

paper below. The paper was then moved forward by turning the roller

E, and, if desired, a different row of pins was put in place for

judgment by revolving the roller C. The dividing line between the

open and filled spaces was continuously recorded on the paper from

below by a pin not shown in the illustration.

 

The rollers, of which I had three, were easily removed or turned

about, so that the open space was presented first. In one of the

distances on each roller both spaces were unfilled. This was used at

frequent intervals in each series and served somewhat the same purpose

as reversing the order in which the open and filled spaces were

presented. With some subjects this was the only safe way of securing

accurate results. The absolute distances measured off were not always

a sure criterion as to whether the filled space was under-or

overestimated. For example, one rather erratic subject, who was,

however, very constant in his erratic judgments, as an average of

fifty judgments declared a filled space of 4 cm. to be equal to an

open space of 3.7 cm. This would seem, on the surface, to mean that

the filled space had been underestimated. But with these fifty

judgments there were alternated judgments on two open spaces, in which

the first open space was judged equal to the second open space of 3.2

cm. From this it is obvious that the effect of the filling was to

cause an overestimation—not underestimation as seemed at first sight

to be the case.

 

In another instance, this same subject judged a filled space of 12.0

cm. to be equal to an open space of 12.9 cm., which would seem to

indicate an overestimation of the filled space. But an average of the

judgments on two open spaces that were given in alternation shows that

an equivalence was set up between the two at 13.7 cm. for the second

open space. This would show that the filling of a space really

produced an underestimation.

 

The same results were obtained from other subjects. In my experiments

on the illusion for passive touch, I pointed out that it is unsafe to

draw any conclusion from a judgment of comparison between open and

filled cutaneous spaces, unless we had previously determined what

might be called a standard judgment of comparison between two open

spaces. The parts of our muscular space are quite as unsymmetrical as

the parts of our skin space. The difficulties arising from this lack

of symmetry can best be eliminated by introducing at frequent

intervals judgments on two open spaces. As I shall try to show later,

the psychological character of the judgment is entirely changed by

reversing the order in which the spaces are presented, and we cannot

in this way eliminate the errors due to fluctuations of the attention.

 

The apparatus which I used in these first experiments possesses

several manifest advantages. Chief among these was the rapidity with

which large numbers of judgments could be gathered and automatically

recorded. Then, in long distances, when the open space was presented

first, the subject found no difficulty in striking the first point of

the filled space. Dresslar mentioned this as one reason why in his

experiments he could not safely use long distances. His subjects

complained of an anxious straining of the attention in their efforts

to meet the first point of the filled space.

 

There are two defects manifest in this apparatus. In the first place,

the other tactual sensations that arise from contact with the thimble

and from the friction with the carrier moving along the sliding rod

cannot be disregarded as unimportant factors in the judgments.

Secondly, there is obviously a difference between a judgment that is

made by the subject’s stopping when he reaches a point which seems to

him to measure off equal spaces, and a judgment that is made by

sweeping the finger over a card, as in Dresslar’s experiments, with a

uniform motion, and then, after the movement has ceased, pronouncing

judgment upon the relative lengths of the two spaces. In the former

case the subject moves his finger uniformly until he approaches the

region of equality, and then slackens his speed and slowly comes to a

standstill. This of course changes the character of the judgments.

Both of these defects I remedied in another apparatus which will be

described later. For my present purpose I may disregard these

objections, as they affect alike all the judgments.

 

In making the tests for the first series, the subject removed his

finger after each judgment, so that the position of the apparatus

could be changed and the subject made to enter upon the new judgment

without knowing either the approximate length or the nature of the

filling of this new test. With this apparatus no attempt was made to

discover the effects of introducing changes in the rate of speed. The

only requirement was that the motion should be uniform. This does not

mean that I disregarded the factor of speed. On the contrary, this

time element I consider as of the highest consequence in the whole

of the present investigation. But I soon discovered, in these

experiments, that the subjects themselves varied the rate of speed

from judgment to judgment over a wide range of rates. There was no

difficulty in keeping track of these variations, by recording the

judgments under three groups, fast, slow and medium. But I found that

I could do this more conveniently with another apparatus, and will

tell at a later place of the results of introducing a time element. In

these first experiments the subject was allowed to use any rate of

speed which was convenient to him.

 

TABLE IX.

 

Subjects P R F Rr

2= 3.8 3.6 2.9 2.8

3= 4.1 4.1 4.2 3.9

4= 4.7 5.1 4.3 4.3

Filled 5= 5.2 5.6 5.8 6.0

Spaces. 6= 6.0 6.3 6.4 5.2

7= 6.8 6.5 6.6 7.0

8= 7.5 7.6 7.2 7.4

9= 8.3 8.1 8.2 8.6

10= 8.9 9.1 8.7 8.5

 

TABLE X.

 

Subjects P R F Rr

2= 4.0 3.8 3.2 2.6

3= 4.3 4.2 4.4 3.6

4= 4.6 5.6 4.6 4.8

Filled 5= 5.4 6.1 5.6 5.7

Spaces. 6= 6.2 6.4 6.8 6.9

7= 7.3 6.8 7.9 7.2

8= 7.8 7.4 7.3 7.8

9= 8.6 8.0 7.9 8.9

10= 9.3 9.1 8.9 8.5

 

TABLES IX. AND X.

 

First line reads: ‘When the finger-tip was drawn over a filled

distance

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