The criticism may be made on these experiments that the subject has not in reality been obliged to rely entirely upon the time sense, but that he has equated the two spaces as the basis of equivalent muscle or joint sensation, which might be considered independent of the sensations which yield the notion of time. I made some experiments, however, to prove that this criticism would not be well founded. By arranging the apparatus so that the finger-tip could be held stationary, and the block with the open and filled spaces moved back and forth under it, the measurement by joint and muscle sensations was eliminated.
It will be observed that no uniform motion could be secured by simply manipulating the lever with the hand. But uniformity of motion was not necessary for the results at which I aimed here. Dresslar has laid great stress on the desirability of having uniform motion in his similar experiments. But this, it seems to me, is precisely what is not wanted. With my apparatus, I was able to give widely different rates of speed to the block as it passed under the finger-tip. By giving a slow rate for the filled space and a much more rapid rate for the open space, I found again that the subject relied hardly at all on the touch sensations that came from the finger-tip, but almost entirely on the consciousness of the amount of time consumed in passing over the spaces. The judgments were made as in the previous experiments with this apparatus. When the subject reached the point in the open space which he judged equal to the filled space, he slightly depressed his finger and stopped the moving block. In this way, the subject was deprived of any assistance from arm-movements in his judgments, and was obliged to rely on the tactual impressions received at the finger-tip, or on his time sense. That these tactual sensations played here also a very minor part in the judgment of the distance was shown by the fact that these sensations could be doubled or trebled by doubling or trebling the amount of space traversed, without perceptibly changing the judgment, provided the rate of speed was increased proportionately. Spaces that required the same amount of time in traversing were judged equal.
In all these experiments the filled space was presented first. When the open space was presented first, the results for four out of five subjects were just reversed. For short distances the filled space was underestimated, for long distances the filled space was overestimated. A very plausible explanation for these anomalous results is again to be found in the influence of the time factor. The open space seemed longer while it was being traversed, but rapidly foreshortened after it was left for the filled space. While on the other hand, if the judgment was pronounced while the subject was still in the midst of the filled space, it seemed shorter than it really was. The combination of these two illusions is plainly again responsible for the underestimation of the short filled spaces. The same double illusion may be taken to explain the opposite tendency for the longer distances.