their fundamental principles and operations, and could investigate, and give the solution of the most general and useful problems in the mathematics; but likewise, solve several problems that occur in the phaenomena of nature. Here Maria stopped, and as soon as astonishment would permit me to speak, I proposed to her several difficult questions, I had heard, but was not then able to answer. I requested her, in the first place, to inform me, how the time of a body's descending through any arch of a cycloid was found: and if ten hundred weight avoirdupoise, hanging on a bar of steel perfectly elastic, and supported at both ends, will just break the bar, what must be the weight of a globe, falling perpendicular 185 feet on the middle of the bar, to have the same effect? — My next questions were, how long, and how far, ought a given globe to descend by its comparative weight in a medium of a given density, but without resistance, to acquire the greatest velocity it is capable of in descending with the same weight, and in the same medium, with resistance? — And how are we to find the value of a solid formed by the rotation of this curvilinear space, A C D about the axis A D, the general equation, expressing the nature of the curve, being 〈 math 〉— How is the centre of gravity to be found of the space enclosed by an hyperbola, and its asymptete? And how are we to find the centre of oscillation of a sphere revolving about the line P A M, a tangent, to the generating circle F A H, in the point A, as an axis?—These questions Maria answered with a celerity and elegance that again amazed me, and convinced me that, notwithstanding the Right Rev. metaphysical disputant, Dr. Berkley, late Bishop of Cloyne in Ireland, could not understand the doctrine of fluxions, and therefore did all he could to disgrace them, and the few mathematicians who have studied magnitudes as generated by motion; yet, the doctrine, as delivered by the divine Newton, may be clearly conceived, and distinctly comprehended; that the principles upon which it is founded, are true, and the demonstrations of its rules conclusive. No opposition can hurt it. When I observed, that some learned men will not allow that a velocity which continues for no time at all, can possibly describe any space at all: its effect, they say, is absolutely nothing, and instead of satisfying reason with truth and precision, the human faculties are quite confounded, lost