NewThoughtLibrary.com / DivineLibrary.org

fleeting moment the present, as if it were a node jointing the past to the future. A hemisphere is not a sphere because it meets on one side the conditions of the definition. A true infinite must be irnmeasureable in all the directions in which measurement can be applied. A forward or a backward stretch, leaving a definite, finite period in the opposite direction, constitutes no true infinite; the lines which pass out from any given point are not infinite, they lack an essential feature of the infinite, interminableness. They are limited in one direction. "We are always to distinguish between the indefinitely great and the infinite. Mathematics deals with the one, metaphysics with the other. A series of figures increased as you please, can never express an infinite amount, and therefore no infinite can be twice or thrice as great as another infinite. This borne constantly in mind, and we shall easily dispose of a portion of the perplexities Sir William Hamilton has thrown around the subject.

"A quantity, say a foot, has an infinity of parts. Any part of this quantity, say an inch, has also an infinity. But one infinity is not larger than another. Therefore an inch is equal to a foot." Neither an inch, nor a foot, nor any other definite quantity, has an infinity of parts parts that are parts, that have any size, will exhaust any dimensions short of the infinite, and the quotient still remain finite. "A wheel turned with quickest motion; if a spoke be prolonged, it will therefore be moved with a motion quicker than the quickest."

This example and similar examples, are mere riddles arising under a play of words. There is no absolutely quickest motion, and no motion that is infinitely rapid. The perplexity in these cases does not all spring from the notion of the infinite, but from the effort of the imagination to transcend its own conditions in a false search by a