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weight of 40 gr. for the filled space, as against 20 gr.

for the open space. In E the weight of each was 20 gr.,

making the total weight of the filled space 80 gr.

 

TABLE V.

 

6 Centimeters.

 

A B C D E

less = gr. less = gr. less = gr. less = gr. less = gr.

R. (a) 10 8 2 12 0 8 14 6 0 9 6 5 8 2 10

F. (a) 12 4 4 12 6 2 12 4 4 8 3 9 6 3 11

K. (a) 10 2 8 12 6 2 14 2 4 6 4 10 7 2 11

––— ––— ––— ––— ––—

32 14 14 36 12 12 40 12 8 23 13 24 21 7 32

 

TABLE VI.

 

8 Centimeters.

 

A B C D E

less = gr. less = gr. less = gr. less = gr. less = gr.

R. (a) 4 1 5 5 1 4 7 0 3 4 0 6 3 0 7

(b) 4 0 6 5 1 4 6 1 3 4 1 5 2 1 7

F. (a) 5 0 5 5 0 5 6 0 4 3 0 7 4 0 6

(b) 5 1 4 6 1 3 8 0 2 4 1 5 2 3 5

K. (a) 4 1 5 6 1 3 7 1 2 3 2 5 1 3 6

(b) 4 0 6 7 0 3 6 1 3 4 0 6 3 0 7

––- ––- ––- ––- ––-

26 3 31 34 4 22 40 3 17 22 4 34 15 7 38

 

TABLE VII.

 

12 Centimeters.

 

A B C D E

less = gr. less = gr. less = gr. less = gr. less = gr.

R. (a) 3 6 16 8 3 14 10 8 7 6 3 16 3 4 18

F. (a) 5 7 13 10 5 10 9 6 10 6 4 15 5 1 19

K. (a) 8 2 15 8 4 13 13 9 3 3 7 15 3 0 22

––— ––— ––- ––— –––

16 15 44 26 12 37 32 23 20 15 14 46 11 5 59

 

TABLE VIII.

 

18 Centimeters.

 

A B C D E

less = gr. less = gr. less = gr. less = gr. less = gr.

R. (a) 2 0 23 0 0 25 4 4 17 3 1 21 0 1 24

(b) 3 1 21 1 0 24 5 3 17 1 6 18 0 2 23

F. (a) 1 4 20 3 0 22 8 6 11 0 5 20 2 0 23

(b) 2 3 20 2 1 22 6 7 12 1 4 20 0 3 22

K. (a) 4 2 19 4 0 21 2 7 16 0 7 18 0 0 25

(b) 1 0 24 2 6 17 8 0 17 2 6 17 1 0 24

––— ––— ––— ––— ––—

13 10 127 12 7 131 33 27 90 7 29 114 3 6 141

 

TABLES IV.-VIII.

 

The first line in column A (Table IV.) signifies that out of 10

judgments, comparing an open space 4 cm., total weight 20 gr., with a

filled space of 4 points, total weight also 20 gr., the filled space

was judged less 7 times, equal 2 times, and greater once.

 

III.

 

The results of the investigation, thus far, point to the conclusion

that short filled spaces are underestimated, that long spaces are

overestimated, and that between the two there lies what might be

called an ‘indifference zone.’ This unexpected outcome explains, I

think, the divergent opinions of the earlier investigators of this

problem. Each theory is right in what it affirms, but wrong in what it

implicitly or openly denies.

 

I next set out to determine as precisely as possible how far the

factor of fusion, or what Parrish has called irradiation, enters into

the judgments. It was evident from the beginning of this whole

investigation that fusion or displacement of the points was very

common. The term ‘irradiation’ is, however, too specific a term to

describe a process that works in these two opposite directions. The

primary concern of these next experiments was, therefore, to devise

means for preventing fusion among the points before the subject

pronounced his judgment. With our apparatus we were able to make a

number of experiments that show, in an interesting way, the results

that follow when the sensations are not permitted to fuse. It is only

the shorter distances that concern us here. The longer distances have

already been shown to follow the law of optical illusion, that is,

that filled space is overestimated. The object of the present

experiments is to bring the shorter distances under the same law, by

showing, first, that the objective conditions as they have existed in

our experiments thus far are not parallel to those which we find in

the optical illusion. Second, that when the objective conditions are

the same, the illusion for the shorter distances follows the law just

stated.

 

In repeating some of the experiments reported in Tables IV.-VIII. with

varying conditions, I first tried the plan of using metallic points at

the ends of the spaces. Thus, by an apparent difference in the

temperature between the end points and the filling, the sensations

from the end points, which play the most important part in the

judgment of the length, were to a certain extent kept from fusing with

the rest. The figures in Table II. have already shown what may be

expected when the points are kept from fusing. Here, also, a marked

tendency in the direction of apparent lengthening of the distance was

at once observed. These short filled distances, which had before been

underestimated, were now overestimated. The same results follow when

metallic points are alternated with hard rubber points in the filling

itself.

 

This changing of the apparent temperature of the end points has, it

must be admitted, introduced another factor; and it might be objected

that it was not so much the prevention of fusion as the change in the

temperature that caused the judgments to drift towards overestimation.

I have statistics to show that this observation is in a way just.

Extremes in temperature, whether hot or cold, are interpreted as an

increase in the amount of space. This conclusion has also been

reported from a number of other laboratories. My contention at this

point is simply that there are certain conditions under which these

distances will be overestimated and that these are the very conditions

which bring the phenomenon into closer correspondence with the optical

illusion, both as to the stimuli and the subjective experience. Then,

aside from this, such an objection will be seen to be quite irrelevant

if we bear in mind that when the end points in the filled distance

were replaced by metallic points, metallic points were also employed

in the open distance. The temperature factor, therefore, entered into

both spaces alike. By approaching the problem from still another point

of view, I obtained even more conclusive evidence that it is the

fusion of the end points with the adjacent points in the short

distances that leads to the underestimation of these. I have several

series in which the end points were prevented from fusing into the

filling, by raising or lowering them in the apparatus, so that they

came in contact with the skin just after or before the intermediate

points. When the contacts were arranged in this way, the tendency to

underestimate the filled spaces was very much lessened, and with some

subjects the tendency passed over into a decided overestimation. This,

it will be seen, is a confirmation of the results in Table II.

 

I have already stated that the two series of experiments reported in

Section II. throughout point to the conclusion that an increase of

pressure is taken to mean an increase in the distance. I now carried

on some further experiments with short filled distances, making

variations in the place at which the pressure was increased. I found a

maximum tendency to underestimate when the central points in the

filled space were weighted more than the end points. A strong drift in

the opposite direction was noticed when the end points were heavier

than the intermediate ones. It is not so much the pressure as a whole,

as the place at which it is applied, that causes the variations in the

judgments of length. In these experiments the total weights of the

points were the same in both cases. An increase of the weight on the

end points with an equivalent diminution of the weights on the

intervening points gave the end points greater distinctness apparently

and rendered them less likely to disappear from the judgments.

 

At this stage in the inquiry as to the cause of the underestimation of

short distances, I began some auxiliary experiments on the problem of

the localization of cutaneous impressions, which I hoped would throw

light on the way in which the fusion or displacement that I have just

described takes place. These studies in the localization of touch

sensations were made partly with a modification of the Jastrow

æsthesiometer and partly with an attachment to the apparatus before

described (Fig. 1). In the first case, the arm upon which the

impressions were given was screened from the subject’s view, and he

made a record of his judgments on a drawing of the arm. The criticism

made by Pillsbury[6] upon this method of recording the judgments in

the localization of touch sensations will not apply to my experiments,

for I was concerned only with the relative, not with the absolute

position of the points. In the case of the other experiments, a card

with a single line of numbered points was placed as nearly as possible

over the line along which the contacts had been made on the arm. The

subject then named those points on the card which seemed directly over

the points which had been touched.

 

[6] Pillsbury, W.B.: Amer. Journ. of Psy., 1895, Vol. VII., p.

42.

The results from these two methods were practically the same. But the

second method, although it obviously permitted the determination of

the displacements in one dimension only, was in the end regarded as

the more reliable method. With this apparatus I could be more certain

that the contacts were made simultaneously, which was soon seen to be

of the utmost importance for these particular experiments. Then, too,

by means of this æsthesiometer, all movement of the points after the

contact was made was prevented. This also was an advantage in the use

of this apparatus, here and elsewhere, which can hardly be

overestimated. With any æsthesiometer that is operated directly by the

hand, it is impossible to avoid imparting a slight motion to the

points and thus changing altogether the character of the impression.

The importance of this consideration for my work was brought forcibly

to my attention in this way. One of the results of these tests was

that when two simultaneous contacts are made differing in weight, if

only one is recognized it is invariably located in the region of the

contact with the heavier point. But now if, while the points were in

contact with the skin and before the judgment was pronounced, I gave

the lighter point a slight jar, its presence and location were thereby

revealed to the subject. Then, too, it was found to be an advantage

that the judgments were thus confined to the longitudinal displacement

only; for, as I have before insisted, it was the relative, not the

absolute position that I wished to determine, since my object in all

these experiments in localization was to determine what connection, if

any, exists between judgments upon

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