method by which any person of average intellect can commence the shadow-study, and introduce children to it. The points of contact between us and the ancients, I shall (with one important exception) leave the reader to find out for himself. I will observe, however, that the shadow-study was a favourite amusement of George Boole; and it would appear from the Seventh Book of the Republic, that Socrates was familiar with it.[1]
Those who are only beginning the shadow-study can work most conveniently with a single light overhead. Later on, combined and crossed lights can be used, and in some cases it will be useful to have a movable light. Place on the table a sheet of white paper. Hold between the paper and the light a ring. Call attention to the fact that the same ring casts a circular or an oval shadow, or a straight line, according to the position in which it is held. Also that the same series of shadows is produced by an elliptical ring as by a circular one. Either can be made to cast a shadow resembling in shape the other. A straight line, however (a knitting-needle for instance), cannot be made to cast a curved shadow on a plane; its shadow is always a straight line, which becomes shorter as the needle is tilted up, till at last it resembles a mere dot.
If a circular disk of card-board be held horizontal under the light, it can be made to cast a series of shadows resembling in turn each of the conic sections (circle, ellipse, hyperbola, and parabola), by altering the position of the paper on which the shadow is cast. The same series of forms may be produced by placing a
- ↑ This detailed account of the use of these symbols for educational purposes will be found in "The Preparation of the Child for Science." (Oxford : Clarendon Press).
