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 of external nature. We have no power in our own consciousness to surmount the difficulties of conception to which I have referred. They arise from the conditions of our mental constitution, and reasoning about space will do no more to remove its mysteries than it will suffice to give to the man born blind a notion of the colour scarlet. But mathematicians, while fully aware of the imperfection of their powers of conception as regards the facts of space, are still enabled to frame a perfectly consistent theory according to which the observed phenomena of nature can be presented within a space which is finite in dimensions. They are even able, as it were, to lay their finger upon the exact point in which the subjective difficulty has arisen.

I must here be permitted to refer to a point in connection with the elements of Euclid. The beginner who studies that work commences, of course, by learning the axioms, and reads without any feeling of discontent or querulousness such venerable truths as that "the whole is greater than its part." But, after a number of propositions of this eminently unquestionable but somewhat puerile kind, he is suddenly brought up by the famous twelfth axiom in which Euclid lays down the theory of parallel lines. Here is a statement of a radically different kind from such assertions as that "if equals be added to equals the wholes are equal." In fact, Euclid's notion of parallel lines is so far from being an axiom of the same character as those other propositions that it is quite possible to doubt its truth without doing any violence to our consciousness.

The principle assumed in the twelfth axiom cannot be proved, and it has been well remarked, that it indicates