520 w. JAMES :

That small angles look proportionally larger than larger ones is, in brief, the fundamental illusion to which almost all authors would reduce the peculiarity of Fig. 12, as of Figs. 7, 8, 9 (pp. 343, 344). This peculiarity of small angles is by Wundt treated as the case of a rilled space seeming larger than an empty one as in Fig. 13 ; and this, according Fi. 13. a to both Delboeuf and Wundt, is owing to the fact that more muscular innervation is needed for the eye to traverse a rilled space than an empty one, because the points and lines in the filled space inevitably arrest and constrain the eye, and this makes us feel as if it were doing more work, i.e., traversing a longer distance. 1 When, however, we recollect that muscular movements are positively proved to have no share in the waterfall and revolving-spiral illusions, and that it is hard to see how Wundt's and Delboeuf's particular form of muscle-explanation can possibly apply to the compass-point illusion considered a moment ago, we must conclude that these writers have probably exaggerated, to say the least, the reach of their muscle-explanation in the case of the sub- divided angles and lines. Never do we get such strong mus- cular feelings as when, against the course of nature, we oblige our eyes to be still ; but fixing the eyes on one point of the figure, so far from making that part of the latter seem larger, dispels, in most persons, the illusion of these diagrams altogether. As for Helmholtz, he invokes, to explain the enlargement of small angles, 2 what he calls a " law of con- trast " between directions and distances of lines, analogous to that between colours and intensities of light. Lines cutting another line make the latter seem more inclined away from them than it really is. Moreover, clearly recognisable magnitudes appear greater than equal magnitudes which we but vaguely apprehend. But this is surely a sensationalistic law, a native function of our seeing-apparatus. Quite as little as the negative after-image of the revolving-spiral could such contrast be deduced from any association of ideas or recall of past objects. The principle of contrast is criticised by Wundt, 3 who says that by it small spaces ought to appear to us smaller, and not larger, than they really are. 1 Bulletins de FAcad. de Belgique, xix., 2, Revue Philosophique, vi., pp. 223-5 ; Physiologische Psychologic, 2te Aufl., p. 103. 2 Physiol Optik., pp. 562-71. 3 Pliysiol. Psych., pp. 107-8.