genius, and the noblest thought that ever entered the human mind. It must be so (Maria replied): As the case is stated, Sir Isaac Newton was most certainly the inventor of the method of fluxions: And supposing Leibnitz had been able to discover and work the differential calculus, without the lights he received from Newton, it would not from thence follow, that he understood the true method of fluxions: for, though a differential has been, and to this day is, by many, called a fluxion, and a fluxion a differential, yet it is an abuse of terms. A fluxion has no relation to a differential, nor a differential to a fluxion, The principles upon which the methods are founded show them to be very different; notwithstanding the way of investigation in each be the same, and that both centre in the same conclusions: nor can the differential method perform what the fluxionary method can. The excellency of the fluxionary method is far above the differential. This remark on the two methods surprised me very much, and especially as it was made by a young lady. I had not then a notion of the difference, and had been taught by my master to proceed on the principles of the Differential Calculus. This made me request an explication of the matter, and Maria went on in the following manner. Magnitudes, as made up of an infinite number of very small constituent parts put together, are the work of the Differential Calculus; but by the fluxionary method, we are taught to consider magnitudes as generated by motion. A described line in this way, is not generated by an apposition of points, or differentials, but by the motion or flux of a point; and the velocity of the generating point in the first moment of its formation, or generation, is called its fluxion. In forming magnitudes after the differential way, we conceive them as made up of an infinite number of small constituent parts, so disposed as to produce a magnitude of a given form; that these parts are to each other as the magnitudes of which they are differentials; and that one infinitely small part, or differential, must be infinitely great, with respect to another other differential, or infinitely small part: but by fluxion, or the law of flowing, we determine the proportion of magnitudes one to another, from the celerities of the motions by which they are generated. This most certainly is the purest abstracted way of reasoning. Our considering the different degrees of magnitude, as arising from an increasing series of mutations of velocity, is much more simple, and less perplexed