it the body would proceed, if gravity acted no longer on the body's arrival at A.
•	2. Take a glass tube open at both ends, whose concavity is of different diameters in different places, and immerse it in a stream, till the water fills the tube, and flows through it. Then, in different parts of the tube, the velocity of the water will be as the squares Page  297
of the diameters, and of consequence different. Suppose then, in any marked place, a plane to pass through the tube perpendicular to the axis, or to the motion of the water, and of consequence, the water will pass through this section with a certain determinate velocity: But if another section be drawn ever so near the former, the water, by reason of the different diameters, will flow through this with a velocity different from what it did at the former, and therefore to one section of the tube, or single point only, the determinate velocity belongs. It is the fluxion of the space which the fluid describes at that section; and with that uniform velocity the fluid would continue to move, if the diameter was the same to the end of the tube.
•	3. If a hollow cylinder be filled with water, to flow freely out through a hole at the bottom, the velocity of the effluent will be as the height of the water, and since the surface of the incubent fluid descends without stop, the velocity of the stream will decrease, till the effluent be all out. There can then be no two moments of time, succeeding each other ever so nearly, wherein the velocity of the water is the same; and of consequence, the velocity, at any given point, belongs only to that particular indivisible moment of time. Now this is accurately the fluxion of the fluid then flowing; and if, at that instant, more Page  298
water was poured into the cylinder, to make the surface keep its place, the effluent would retain its velocity, and still be the fluxion of the fluid. Such are the operations of nature, and they visibly confirm the nature of Fluxion. It is from hence quite clear, that the fluxion of a generated quantity, cannot retain any one determined value for the least space of time whatever, but the moment it arrives at that value, the same moment it loses it again. The fluxion of such quantity can only pass gradually and successively thro' the indefinite degrees contained between the two extreme values, which are the limits thereof, during the generation of the fluent, in case the fluxion be