MOMENT
, in Time, is sometimes taken for an extremely small part of duration; but, more properly, it is only an instant or termination or limit in time, like a point in geometry. Maclaurin's Fluxions, vol. 1, pa. 245.
Moments, in the new Doctrine of Infinites, denote the indefinitely small parts of quantity; or they are the same with what are otherwise called infinitesimals, and differences, or increments and decrements; being the momentary increments-or decrements of quantity considered as in a continual flux.
Moments are the generative principles of magnitude: they have no determined magnitude of their own; but are only inceptive of magnitude.
Hence, as it is the same thing, if, instead of these Moments, the velocities of their increases and decreases be made use of, or the finite quantities that are proportional to such velocities; the method of proceeding which considers the motions, changes, or fluxions of quantities, is denominated, by Sir Isaac Newton, the Method of Fluxions.
Leibnitz, and most foreigners, considering these infinitely small parts, or insinitesimals, as the differences of two quantities; and thence endeavouring to find the differences of quantities, i. e. some Moments, or quantities indefinitely small, which taken an infinite number of times shall equal given quantities; call these Mo-| ments, Differences; and the method of procedure, the Differential Calculus.
Moment, or Momentum, in Mechanics, is the same thing with Impetus, or the quantity of motion in a moving body.
In comparing the motions of bodies, the ratio of their Momenta is always compounded of the quantity of matter and the celerity of the moving body: so that the momentum of any such body, may be considered as the rectangle or product of the quantity of matter and the velocity of the motion. As, if b denote any body, or the quantity or mass of matter, and v the velocity of its motion; then bv will express, or be proportional to, its Momentum m. Also if B be another body, and V its velocity; then its Momentum M, is as BV. So that, in general, , i. e. the Momenta are as the products of the mass and velocity. Hence, if the Momenta M and m be equal, then shall the two products BV and bv be equal also; and consequently , or the bodies will be to each other in the inverse or reciprocal ratio of their velocities; that is, either body is so much the greater as its velocity is less. And this force of Momentum is of a different kind from, and incomparably greater than, any mere dead weight, or pressure, whatever.
The Momentum also of any moving body, may be considered as the aggregate or sum of all the Momenta of the parts of that body; and therefore when the magnitudes and number of particles are the same, and also moved with the same celerity, then will the Momenta of the wholes be the same also.
MONADES. Digits.
