December 9, 1898.] 



SCIENCE. 



819 



the transversal would result iu an apparent 

 narrowing of the vertical strip and a con- 

 sequent increase of the illusion. But this 

 latter factor is probably effective here in a 

 minimum degree. 



Somewhat more interesting is the per- 

 spective explanation. This we meet under 

 two different forms. The first employs the 

 usual perspective argument. Carefully 

 viewed, the ends of the transversal may be 

 seen to issue from the plane. This becomes 

 especially evident if the figure be made of 

 wire and suspended before a uniform back- 

 ground. In consequence of this perspective 

 quality of the figure the visual angle made 

 by the transversal and the vertical is inter- 

 preted as representing an angle of greater 

 magnitude than that seen, just as in the 

 case of all angles seen perspectively in ob- 

 jective vision, and the illusion results. This, 

 if I rightly understand him, is the argu- 

 ment of Thi^ry. The second form of the 

 perspective explanation differs quite ma- 

 terially from this. It is the explanation of 

 Filehne. According to this the vertical 

 strip of the Poggendorff figure serves prin- 

 cipally to sunder the two ends of the trans- 

 versal to such a degree that there is no 

 longer any sufficient reason for regarding 

 them as belonging together. Now, remem- 

 bering that, in accordance with the per- 

 spective theory in general, the lines of a 

 plane geometrical figure act chiefly as the 

 means of suggesting real objects of actual 

 experience, we can easily see the line of 

 thought. For there is not the remotest ne- 

 cessity that two detached portions of a 

 straight line represent objects whose bound- 

 ing edges should appear continuous, merely 

 because they would meet and form a con- 

 tinuous line in the linear drawing that 

 represents them. It can be most readily 

 and graphically shown by straight-line 

 drawings of objects that two detached por- 

 tions of one and the same line may repre- 

 sent objects in totally different planes of 



space, so that if the objects represented 

 were to be prolonged in their own direction 

 they might never meet at all, or at best 

 only at an oblique angle. In the figure be- 

 fore us, consequently, it is highly probable 

 that the sundered portions of the oblique 

 recall some real experience, or set of experi- 

 ences, in which the objects represented are 

 absolutely unconnected. Such an experience 

 may be suggested by a finger-post, an arm 

 upon one side pointing obliquely towards 

 the observer, an arm upon the other side — 

 lower or higher, as the case may be — point- 

 ing obliquely away. Herr Filehne finds 

 great support for this view in the alleged 

 observation that every trace of the illusion 

 vanishes in the above figure if only the two 

 verticals be somehow united, or if some in- 

 dications be present to show that the ends 

 of the tiansversal are portions of a continu- 

 ous whole, the missing part of which is hid- 

 den behind the vertical strip. The first con- 

 dition can be secured by drawing within 

 the latter a short line which shall be oblique 

 to the transversal and meet the edges of the 

 strip at points opposite those in which the 

 ends of the transversal terminate. The 

 second condition can be readily secured by 

 making the transversal represent a pointed 

 stick, or by placing at the outer ends of the 

 transversal the drawing of some such de- 

 vice as weights and pulleys, which shall 

 make it clear that the two ends are really 

 acting in unity. But though these condi- 

 tions be fulfilled to perfection, the illusion 

 simply does not vanish, despite the asser- 

 tion of Filehne to the contrary, nor would 

 one expect it to do so. For what these par- 

 ticular devices are expected to accomplish 

 is the closer approach to the actual condi- 

 tions of tri-dimensional vision, where only 

 one interpretation of the lines is possible. 

 The best conditions for testing the theory 

 would be found, therefore, in normal objec- 

 tive experience. Stretch a rope obliquely 

 behind a tree trunk and at a distance of 



