Apparently Zöllner was the first to describe an illusion which is illustrated in simple form in Fig. 29 and more elaborately in Figs. 37 to 40. The two figures at the right of Fig. 29 were drawn for another purpose and are not designed favorably for the effect, although it may be detected when the figure is held at a distance. Zöllner accidentally noticed the illusion on a pattern designed for a print for dress-goods. The illusion is but slightly noticeable in Fig. 29, but by multiplying the number of lines (and angles) the long parallel lines appear to diverge in the direction that the crossing lines converge. Zöllner studied the case thoroughly and established various facts. He found that the illusion is greatest when the long parallel lines are inclined about 45 degrees to the horizontal. This may be accomplished for Fig. 37, by turning the page (held in a vertical plane) through an angle of 45 degrees from normal. The illusion vanishes when held too far from the eye to distinguish the short crossing lines, and its strength varies with the inclination of the oblique lines to the main parallels. The most effective angle between the short crossing lines and the main parallels appears to be approximately 30 degrees. In Fig. 37 there are two illusions of direction. The parallel vertical strips appear unparallel and the right and left portions of the oblique cross-lines appear to be shifted vertically. It is interesting to note that steady fixation diminishes and even destroys the illusion. [Illustration: Fig. 37.--Zöllner's illusion of direction.] The maximum effectiveness of the illusion, when the figure is held so that the main parallel lines are at an inclination of about 45 degrees to the horizontal was accounted for by Zöllner as the result of less visual experience in oblique directions. He insisted that it takes less time and is easier to infer divergence or convergence than parallelism. This explanation appears to be disproved by a figure in which slightly divergent lines are used instead of parallel ones. Owing to the effect of the oblique crossing lines, the diverging lines may be made to appear parallel. Furthermore it is difficult to attach much importance to Zöllner's explanation because the illusion is visible under the extremely brief illumination provided by one electric spark. Of course, the duration of the physiological reaction is doubtless greater than that of the spark, but at best the time is very short. Hering explained the Zöllner illusion as due to the curvature of the retina, and the resulting difference in the retinal images, and held that acute angles appear relatively too large and obtuse ones too small. The latter has been found to have limitations in the explanation of certain illusions.