Decembee 9, 1898.] 



SCIENCE. 



821 



According to it the principal line of A in 

 the above figure is seen to be more distant 

 from the observer than the principal line of 

 B. The tiny obliques, that is, run forward 

 from the point of contact in the former 

 and backward in the latter. In consequence 

 of this difference in apparent distance be- 

 tween the two lines, the dimensions of the 

 figure must be apprehended in accordance 

 with the universal law, that of two objects 

 subtending the same visual angle that will 

 be perceived as the greater which is pro- 

 jected to the greater distance from the eye. 

 The perspective form, particularly of A, 

 can be most easily seen where the ends of 

 the obliques have been connected by straight 

 lines ; that is, when the whole figure has 

 been enclosed in a rectangle. But now im- 

 mediately the equivocal character of the fig- 

 ure becomes manifest. It may be seen, 

 namely, either as an oblong hip-roof in 

 miniature or as a hollowed out, crib-like 

 object. In other words, the principal line 

 may be made to appear now nearer, now 

 more remote from the observer. Though 

 less apparent, the same equivocal character 

 is to be observed in the normal figure, B, 

 But, whether nearer or more remote, the ap- 

 parent length of the prmcijjal line does not 

 change, and, since there are no compelling 

 grounds to determine once and for all that 

 A shall be seen in the distance and B in the 

 foreground, the perspective explanation 

 ignominiously fails, its whole structure be- 

 ing based, as we have seen, upon an iin- 

 equivocal perspective reference. 



The other theories mentioned are the 'con- 

 fluxion-contrast' theory of Miiller-Lyer, and 

 the ' muscular energy ' theory of Delbceuf 

 and Wundt. (6) Confluxion is the term used 

 to designate a class of facts where the esti- 

 mated lengths of lines partake of the nature 

 of the surrounding space in so far as this is 

 indicated by other lines lying immediatiBly 

 adjacent. That is, the principal line of A 

 is estimated as longer than that of B, be- 



cause the total space inclosed hy A is greater 

 than that inclosed by B. Confluxion differs 

 from contrast in that for the former any 

 line shares in the characteristics of its sur- 

 roundings, while for the latter any line as- 

 sumes characteristics opposite to those of its 

 surroundings. Here both motives are in- 

 fluential, confluxion as indicated, and con- 

 trast in so far as the principal line comes 

 into comparison with the short obliques. 

 This, in a word, is the ' confluxion-contrast ' 

 theory. Confluxion must evidently play 

 the more important role in the present case. 

 But an examination of this principle of ex- 

 planation reveals the fact that its unreliabil- 

 ity makes it very dangerous of acceptance. 

 Cases can readily be found where, if true, 

 the principle should be, but is not, effective. 

 The most simple case is perhaps that given 

 by Wundt (Fig. 6), where according to the 



theory i? s/iomM appear longer than A. Some 

 further theory seems requisite, therefore, to 

 satisfactorily account for the illusion. 



(c) Though the forms given to the * mus- 

 cular energy ' theory by Delbceuf and Wundt 

 are by no means identical in respect to de- 

 tails, yet for purposes of description they 

 may be brought together. Wundt has 

 given by far the best statement of the 

 theory. Its essence is that our visual spatial 

 estimates are always influenced, if not first 

 made possible at all, by the amount of 

 energy expended by the muscles of the eye 

 in running the point of regard over the fig- 

 ure viewed. The strength and range of this 

 theory we can first see when later we ex- 

 amine the several principles of explanation. 

 Meanwhile the statement will suffice that 

 the tendencies to move the ej'es beyond the 



