THE PEECEPTION OF SPACE. (IV.) 527

We need only attend to one of the angles represented, and imagine it either solid or hollow pulled towards us out of the plane of the paper, or pushed back behind the same and the whole figure obeys the cue and is instantaneously transformed beneath our gaze. The peculiarity of all these cases is the ambiguity of the perception to which the fixed retinal impression gives rise. With our retina excited in exactly the same way, whether by after-image, mask or diagram, we see now this object and now that, as if the retinal image per se had no essential space-import. Surely if form and length were originally retinal sensations, retinal rectangles ought not to become acute or obtuse, and lines ought not to alter their relative lengths as they do. If relief were an optical feeling, it ought not to flap to and fro, with every optical condition unchanged. Here, if anywhere, the deniers of space-sensation ought to be able to make their final stand. 1 It must be confessed that their plea is plausible at first sight. But it is one thing to throw out retinal sensibility altogether as a space-yielding function the moment we find an ambiguity in its deliverances, and another thing to examine candidly the conditions which may have brought the ambiguity about. The former way is cheap, wholesale, shallow; the latter difficult and complicated, but full of instruction in the end. Let us try it for ourselves. In the case of the diagrams 17, 18, 19, 20, 21, the real object, lines meeting or crossing each other on a plane, is replaced by an imagined solid, which we describe as seen. Really it is not seen, but only so vividly conceived as to approach a vision of reality. We feel all the while, however, that the solid suggested is not solidly there. The reason why one solid may seem more easily suggested than another, and why it is easier in general to perceive the diagram solid than flat, seems due to probability. 2 Those lines have count- less times in our past experience been drawn on our retina by solids for once that we have seen them flat on paper. And hundreds of times we have looked down upon the upper surface of parallelepipeds, stairs and glasses, for once that 1 The strongest passage in Helmholtz's argument against sensations r.f space is relative to these fluctuations of seen . relief : " Ought one not to conclude that if sensations of relief exist at all, they must be so faint and vague as to have no influence compared with that of past experience 1 Ought we not to believe that the perception of the third dimension may have arisen without them, since we now see it taking place as well against them, as with them?" (Physiol. Optik., p. 817). 2 Cp. E. Mach, Beitrcige, &c., p. 90.