So far as the primary object of this part of the experiment is concerned the results are negative, but incidentally the process of training brought out some facts of a more positive nature. It was early noticed that some groups of four were much more readily recognized than others, and that some of them were either judged correctly or underestimated while others were either judged correctly or overestimated. For convenience the fingers were indicated by the letters A B C D, A being the index finger. The thumb was not used. Two weights were over each finger. The one near the base was called 1, the one toward the end 2. Thus A12 B1 C2 means two contacts on the index finger, one near the base of the second finger, and one near the end of the third finger. The possible arrangements of four may be divided into three types: (1) Two weights on each of two fingers, as A12 B12, C12 D12, etc., (2) four in a line across the fingers, A1 B1 C1 D1 or A2 B2 C2 D2, (3) unsymmetrical arrangements, as A1 B2 C1 D2, etc. Arrangements of the first type were practically never overestimated. B12 C12 was overestimated once and B12 D12 was overestimated once, but these two isolated cases need hardly be taken into account. Arrangements of the second type were but rarely overestimated—A2 B2 C2 D2 practically never, A1 B1 C1 D1 a few times. Once the latter was called eight. Apparently the subject perceived the line across the hand and thought there were two weights on each finger instead of one. Arrangements of the third type were practically never underestimated, but were overestimated in 68 per cent. of the cases.
These facts in themselves are suggestive, but equally so was the behavior of the subject while making the answers. It would have hardly done to ask the person if certain combinations were hard to judge, for the question would serve as a suggestion to him; but it was easy to tell when a combination was difficult without asking questions. When a symmetrical arrangement was given, the subject was usually composed and answered without much hesitation. When an unsymmetrical arrangement was given he often hesitated and knit his brows or perhaps used an exclamation of perplexity before answering, and after giving his answer he often fidgeted in his chair, drew a long breath, or in some way indicated that he had put forth more effort than usual. It might be expected that the same attitude would be taken when six or eight contacts were made at once, but in these cases the subject was likely either to fail to recognize that a large number was given or, if he did, he seemed to feel that it was too large for him to perceive at all and would guess at it as well as he could. But when only four were given, in a zigzag arrangement, he seemed to feel that he ought to be able to judge the number but to find it hard to do so, and knowing from experience that the larger the number the harder it is to judge he seemed to reason conversely that the more effort it takes to judge the more points there are, and hence he would overestimate the number.
The comments of the subjects are of especial value. One subject (Mr. Dunlap) reports that he easily loses the sense of location of his fingers, and the spaces in between them seem to belong to him as much as do his fingers themselves. When given one touch at a time and told to raise the finger touched he can do so readily, but he says he does not know which finger it is until he moves it. He feels as if he willed to move the place touched without reference to the finger occupying it. He sometimes hesitates in telling which finger it is, and sometimes he finds out when he moves a finger that it is not the one he thought it was.
Another subject (Dr. MacDougall) says that his fingers seem to him like a continuous surface, the same as the back of his hand. He usually named the outside points first. When asked about the order in which he named them, he said he named the most distinct ones first. Once he reported that he felt six things, but that two of them were in the same places as two others, and hence he concluded there were but four. This feeling in a less careful observer might lead to overestimation of number and be called diffusion, but all cases of overestimation cannot be explained that way, for it does not explain why certain combinations are so much more likely to lead to it than others.
In one subject (Mr. Swift) there was a marked tendency to locate points on the same fingers. He made many mistakes about fingers B and C even when he reported the number correctly. When B and D were touched at the same time he would often call it C and D, and when C and D were given immediately afterward he seemed to notice no difference. With various combinations he would report C when B was given, although C had not been touched at the same time. If B and C were touched at the same time he could perceive them well enough.
The next part of the research was an attempt to discover whether a person can perceive any difference between one point and two points which feel like one. A simple little experiment was tried with the æsthesiometer. The subjects did not know what was being used, and were asked to compare the relative size of two objects placed on the back of the hand in succession. One of these objects was one knob of the æsthesiometer and the other was two knobs near enough together to lie within the threshold. The distance of the points was varied from 10 to 15 mm. Part of the time the one was given first and part of the time both were given together. The one, whether given first or second, was always given about midway between the points touched by the two. If the subject is not told to look for some specific difference he will not notice any difference between the two knobs and the one, and he will say they are alike; but if he is told to give particular attention to the size there seems to be a slight tendency to perceive a difference. The subjects seem to feel very uncertain about their answers, and it looks very much like guess-work, but something caused the guesses to go more in one direction than in the other.
| Two were called | less than | one | 16% | of the times given. |
| " | equal to | " | 48% | " |
| " | greater than | " | 36% | " |
Approximately half of the time two were called equal to one, and if there had been no difference in the sensations half of the remaining judgments should have been that two was smaller than one, but two were called larger than one more than twice as many times as one was called larger than two. There was such uniformity in the reports of the different subjects that no one varied much from this average ratio.
This experiment seems to indicate a very slight power of discrimination of stimulations within the threshold. In striking contrast to this is the power to perceive variations of distance between two points outside the threshold. To test this the æsthesiometer was spread enough to bring the points outside the threshold. The back of the hand was then stimulated with the two points and then the distance varied slightly, the hand touched and the subject asked to tell which time the points were farther apart. A difference of 2 mm. was usually noticed, and one of from 3 to 5 mm. was noticed always very clearly.
I wondered then what would be the result if small cards set parallel to each other were used in place of the knobs of the æsthesiometer. I made an æsthesiometer with cards 4 mm. long in place of knobs. These cards could be set at any angle to each other. I set them at first 10 mm. apart and parallel to each other and asked the subjects to compare the contact made by them with a contact by one card of the same size. The point touched by the one card was always between the points touched by the two cards, and the one card was put down so that its edge would run in the same direction as the edges of the other cards. The result of this was that: