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28 the point where we introduce into our reasoning considerations derived from an order of thought higher than that whose relations we are investigating.

Now the present condition of moral and religious reasoning is about on a level with that of mathematical reasoning at the time when a few bold spirits were proposing to look for an equation between lines in the region of non-linear surface; and the majority were expressing scepticism and indulging in sneers. The parallel is perhaps all the more accurate, because reasoning about lines as lines is in itself, and necessarily, in a sense illusory. There is no such thing in Nature as a line, except the edge of a surface (nor, indeed, can there be any surface except the boundary of a solid).

Thousands of years before any such definite conception dawned in mathematics as that to which the name "dimensions" attaches itself now, it must have occurred to thoughtful men to study the shadows cast by solid objects. The duration of the shadow, it would be observed, is not coeval with that of the substance from which it is projected; a passing cloud is sufficient to obliterate it. Nor is its form solely determined by that of the solid object, but partly by the position of the latter relatively to the Source of Light. Pondering on this would lead to experiments in shadow-producing. Of the exact course of the shadow-study carried on by wise men of old we have no accurate record; but whoever is engaged in prosecuting similar investigations now, is sometimes irresistibly made to feel that he is going over the same ground as has been trodden by some "inspired" writer of the olden time. To avoid controversy, I propose here only to indicate a simple