Page:Mind (Old Series) Volume 11.djvu/549

 548 j. JASTBOW : small a space. 1 On the average, the distance between thumb and forefinger will be reproduced by a movement 68 per cent, of its true length. It is not possible to combine the last two state- ments, for the substitution of Eye for Hand as the receiving sense changes the error from an underestimation to an exaggera- tion. A comparison of the conclusions thus far reached will bring to light a few general laws applicable to all three senses. A. The error decreases as the length (to be repro- duced) increases. This means that (within the limits of the lengths experimented upon) a larger length is reproduced more accurately than a smaller one. It is expressed in Fig 5 by the fact that the direction of all the curves is towards the central line, following one or other of the arrows. 2 B. If reproducing one sense by another results in an exaggeration (or underestimation), then repro- ducing the second sense by the first will result in an underestimation (or exaggeration) to about the same extent. In attempting to move over a space equal to the length of a line seen I move over much too large a space, and w r hen I select by sight a line equal to a space moved over by my arm I select much too short a line. Thus the curves expressing the space- relations of the three senses are grouped in pairs [Fig. 5, 1-2 and 2-1 ; 1-3 and 3-1 ; 3-2 and 2-3], one of each pair being above the central line, the other (in which the receiving and expressing senses have changed places) below it. This law confirms one's a priori expectations on the assumption that the processes involved are rational and regular ; for to say that the eye 'draws' a sni; line than the arm is the same as to say that the arm dravs a larger line than the eye. A result of this law is that in the three pairs of operations, Eye to Hand and Hand to Eye (1-2 and 2-1), Eye to Arm and Arm to Eye (1-3 and 3-1), Arm to Hand and Hand to Arm (3-2 and 2-3), the mean proportional 3 between the exaggerated reproduction by the first and the underestimated reproduction by the second of each pair of operations will give 1 The foot-note on page 547 is equally applicable here. 5 The law is applicable to the curves in which the receiving ami e. ing senses arc the same, if we measure the error by ordinates upon a horizontal line drawn through the origin of the curve. 3 Not the 'mean' but the 'mean proportional,' because the same absolute error i.- a im-ater error as an underestimation than as an exaggeration. Doubling a length is as far from the truth as halving it; but then- is an error of 100 per cent, in the first case and of 50 per cent, in the second. The two appear alike when we compare the exaggerated reproduction with the reciprocal of the underestimated reproduction. To make the curves above, and below the central line (Fig. 5) absolutely comparable as they stand, the percentages below the central line are plotted in terms of their