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PSYCHISM AND THE FOURTH DIMENSION 245 .conical mirror would serve this purpose. Now let four circles about half an inch in diameter be drawn at equal distances round the point of intersection, an inch or two from this point. Let a square be drawn round all the circles an inch or two outside them. We have here a two-dimensional counterpart of Zollner's room and table : and it will be manifest that the shadows from the two-dimensional table-legs,--the circles-will fall outwards on the walls, that these shadows will not be appreciably larger than the table-legs-since the rays casting them are sensibly parallel and that they will be sharply defined since the rays come from a point of light-the electric arc for example. Now in order that the light should produce this effect, it was necessary that it should fall from three-dimensional into twodimensional space, and that its source should be at a distance from that two-dimensional space. The only conception a two-dimensional being could form of this light, would be a beam going in all directions at once.
Now apply this by analogy to Zollner's table Suppose a beam, from a point of intense light, in four-dimensional space, to have fallen on the threedimensional space we are acquainted with at a point under Zollner's table, about equidistant from all the legs, and to be reflected in all the directions of threedimensional space by a suitable four-dimensional reflector--as we did with a conical mirror in the twodimensional space :-It is evident that it would have behaved exactly as the light Zollner observed did behave,
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