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G40

given them, I suppose by P. G. Tait): they express the four most fundamental classes of characters of all geometrical figures that are possible in a space confined to three dimensions. It is a pity that Listing never investigated spaces of higher dimensionality. Nor did he pay attention to "singularities," or "singular characters"; that is characters of exceptional parts of figures. He should have done so; but the omission is of no very great importance. Every general character of a figure is either topical, graphical (Clifford's word; "projective" is much more usual,) or metrical. The least im-

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