PHYSIOLOGICAL AND METRIC SPACE 9
nize the circular form of the cross-section of a tube 2 mm. in diameter.
The space of the skin is the analogue of a two-dimensional, finite, unbounded and closed Rieman-nian space. Through the sensations induced by the
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Figs. 1 and 2.
movements of the various members of the body (notably the arms, the hands, and the fingers) something analogous to a third dimension is superposed. Gradually we are led to the interpretation of this system of sensations by the simpler and more salient relations of the physical world. Thus we the upper and lower lips, appears sensibly to shut when moved horizontally towards the side of the face (Fig. i). If the points of the dividers be placed on two adjacent finger-tips and thence carried over the fingers, the palm of the hand, and down the forearm, they will appear at the latter point to close completely (Fig. 2). (The real path of the points is dotted in the figure; the apparent, marked by lines.) The forms of bodies that touch the skin are indeed distinguished;2 but the spatial sense of the skin is nevertheless greatly inferior to that of the eye, although the tip of the tongue will recog-