you imagine that if two bodies are moving in the same direction, one slower, the other faster, the latter will soon overtake the former. It is not so, and can be proved impossible. Conceive the swift-footed Achilles trying to overtake a tortoise, and that he runs one hundred yards, while the other is crawling but ten. When he has completed his one hundred, the tortoise is still one ahead, when he has added this one, the tortoise is still 1/10 ahead, then 1/100, then 1/1000, and so on _ad infinitum_, for it is mathematically certain that neither series can ever reach the limit, in the one case of III, in the other of II yards. Therefore it is demonstrated that Achilles can never in all time overtake the tortoise. But we may go even farther and say that the very idea of motion is inconceivable. Every moving body must move in time, and time is divided into moments of time. At each moment the moving body must either be in the place where it is, or the place where it is not. The latter being manifestly absurd, the body must be in the place where it is. But then of course it is not moving, for motion can only be defined as a change of place. Continuous motion is therefore inconceivable. I need not do more than mention to you, that these very problems, handed down by Zeno to the schools, formed the subject of interminable disputes for centuries, and if you even now, with all your boasted progress, take them in hand, you will not easily find a logical solution. Happily we are no longer in the condition of those mediæval pedants, of whom we hear that not a few went mad, or died of brain fever, because they could not reconcile the foreknowledge and foreordaining of things by God with the absolute free will of men. Nor are any of you, I sincerely trust, encumbered with the extraordinary fairness of mind of the mediæval ass of Buridanus which being set between two bundles of hay exactly and precisely alike, died of starvation because it could see no possible reason for preferring to eat the one before the other. Nevertheless, I trust you will appreciate that the mental subtlety we inherit from the Greeks is no small part of our education.