than the other way; and the operations founded on fluxions, must be much more clear, accurate, and convincing, than those that are founded on the Differential Calculus. There is a great difference in operations, when quantities are rejected, because they really vanish; —and when they are rejected, because they are infinitely small: the latter method, which is the differential, must leave the mind in ambiguity and confusion, and cannot in many cases come up to the truth. It is a very great error then to call differentials, fluxions, and quite wrong to begin with the differential method, in order to learn the law or manner of flowing.
With amazement I heard his discourse, and requested to know by what master, and what method, she obtained these notions; for they were far beyond every thing on the subject that I had ever met with. What she said concerning the nature and idea of fluxions,

I though just and beautiful, and I believe it was in her power, to show the bases on which they are erected.
*My master, Sir, (Maria answered) was a poor traveller, a Scotchman, one Martin Murdoch, who came by accident to my father's house, to ask relief, when I was about fifteen years old. He told us, he was the son of one▪ of the ministers of Scotland, and came from the remotest part of the Highlands: that his father taught him mathematics, and left him, at his death, a little stock on a small farm; but misfortunes and accidents obliged him in a short time to break up house, and he was going to London, to try if he could get any thing there, by teaching arithmetic of every kind. My father, who was a hospitable man, invited him to stay with us a few days, and the parson of our parish soon found, that he had not only a very extraordinary understanding, but was particularly excellent at figures, and the other branches of the mathematics. My father upon this agreed with him to be my preceptor for five years, and during four years and nine months of that time, he took the greatest pains to make me as perfect as he could in arithmetic, trigonometry, geometry, algebra, and fluxions. As I delighted in the study above all things, I was a great proficient for so few years, and had Murdoch been longer with me, I should

have been well acquainted with the whole glorious structure: but towards the end of the fifth year, this poor Archimedes was unfortunately drowned, in crossing one of our