The crossed lines in Fig. 29 can be seen as right angles in perspective with two different spatial arrangements of one or both lines. In fact there is quite a tendency to see such crossed lines as right angles in perspective. The two groups on the right represent a simplified Zöllner's illusion (Fig. 37). The reader may find it interesting to spend some time viewing these figures and in exercising his ability to fluctuate his attention. In fact, he must call upon his imagination in these cases. Sometimes the changes are rapid and easy to bring about. At other moments he will encounter an aggravating stubbornness. Occasionally there may appear a conflict of two appearances simultaneously in the same figure. The latter may be observed occasionally in Fig. 30. Eye-movements are brought forward by some to aid in explaining the changes. [Illustration: Fig. 30.--Reversible cubes.] In Fig. 30 a reversal of the aspect of the individual cubes or of their perspective is very apparent. At rare moments the effect of perspective may be completely vanquished and the figure be made to appear as a plane crossed by strings of white diamonds and zigzag black strips. The illusion of the bent card or partially open book is seen in Fig. 31. The tetrahedron in Fig. 32 may appear either as erect on its base or as leaning backward with its base seen from underneath. [Illustration: Fig. 31.--The reversible "open book" (after Mach).] [Illustration: Fig. 32.--A reversible tetrahedron.] The series of rings in Fig. 33 may be imagined to form a tube such as a sheet-metal pipe with its axis lying in either of two directions. Sometimes by closing one eye the two changes in this type of illusion are more readily brought about. It is also interesting to close and open each eye alternately, at the same time trying to note just where the attention is fixed. The familiar staircase is represented in Fig. 34. It is likely to appear in its usual position and then suddenly to invert. It may aid in bringing about the reversal to insist that one end of a step is first nearer than the other and then farther away. By focusing the attention in this manner the fluctuation becomes an easy matter to obtain. [Illustration: Fig. 33.--Reversible perspective of a group of rings or of a tube.] [Illustration: Fig. 34.--Schröder's reversible staircase.] In Fig. 35 is a similar example. First one part will appear solid and the other an empty corner, then suddenly both are reversed. However, it is striking to note one half changes while the other remains unchanged, thus producing momentarily a rather peculiar figure consisting of two solids, for example, attached by necessarily warped surfaces. [Illustration: Fig. 35.--Thiéry's figure.]