The material needed for these discs is cardboard, covered with white paper on one side, or the Bristol board used by artists.  The discs on which the designs are drawn should be made as large as the gramophone table will take conveniently, so as to be viewed by a number of people at once.  To encourage readers who do not possess a gramophone, it may be pointed out that a gramophone, is merely a convenience, and not indispensable for turning the discs, which may be revolved on a sharpened pencil or any other spindle with pointed ends.

The Vanishing Spirals (Fig. 137).—­This design, if spun slowly in a clockwise direction, gives one the impression that the lines all move in towards the centre.  If the disc is turned in an anti-clockwise direction, the lines seem to move towards the circumference and disappear.  To get the proper effect the gaze should be fixed and not attempt to follow the lines round.

[Illustration:  Fig. 137.]

[Illustration:  Fig. 138.]

The Rolling Circles.—­Figs. 138 and 139 are variations of the same idea.  In Fig. 138 two large circles are described cutting one another and enclosing a smaller circle concentric with the disc.  When spun at a certain rate the larger circles will appear to run independently round the small.  The effect is heightened if the circles are given different colours.  If black only is used for the large circles, the eyes should be kept half closed.  In Fig. 139 two pairs of circles are described about two centres, neither of which is the centre of the disc.  The pairs appear to roll independently.

[Illustration:  Fig. 139.]

[Illustration:  Fig. 140.]

The Wriggling Line (Fig. 140).—­If this design is revolved at a low speed and the eye is fixed on a point, the white (or coloured) line will seem to undulate in a very extraordinary manner.  The line is made up of arcs of circles, and as the marking out is somewhat of a geometrical problem, a diagram (Fig. 141) is added to show how it is done.  The dotted curves are those parts of the circles which do not enter into the design.

Begin by marking out the big circle A for the disc.  The circumference of this is divided into six equal parts (chord equal to radius), and through the points of division are drawn the six lines from the centre.  Describe circles aaa, each half the diameter of A. The circles bbb are then drawn from centres on the lines RRR, and with the same radius as aaa., The same centres are used for describing the circles a1 a1 a1 and b1 b1 b1, parts of which form the inner boundary of the line.  The background should be blackened and the belt left white or be painted some bright colour.

[Illustration:  Fig. 141.]

Another optical illusion is afforded by Fig. 142.  Two sets of circles are described about different centres, and the crescent-shaped areas between them coloured, the remainder of the disc being left white.  The disc is revolved about the centre of the white areas, and one gets the impression that the coloured parts are portions of separate discs separated by white discs.