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velocity, body, measure, vis, time, motion, viva and equal

FORCE, (from the Latin. fortis, strong) in philosophy, the cause of motion in a body, when it begins to move, or when it changes its direction from the course in which it was previously.moving. While a body remains in the same state, whether of rest or of uniform and rectilinear motion, the cause of its so remaining is in the nature of the body, which principle has received the name of inertia.

;Mechanical force is of two kinds : that of a body at rest, by which it pres.ses on whatever supports it. and that of a body in motion, by which it is impelled towards a certain point. The former is called by the names of pressure, tension, force, vis mortna, &c., the latter is known by the appellation of moving force, or vis viva. To the first of these are referred centrifugal and centripetal forces because, though they also reside in the vis viva, they are homogeneous to weights, pressures., or tensions of any kind. For want of a true k nowledge of the nature of force, we are accustomed to consider its measure by velocity, upon the supposItion that, under precisely similar circumstances, the velocity is equal to the force ; an hypothesis highly probable, though not easily demonstrable. Velocity itself is a compound idea, derived from a certain relation between time employed and space described. Thus, if two bodies be supposed to move unithrmly upon two different lines, the distances which they describe upon their respective lines in any given time, may be measured and represented by some standard measure, from which we acquire an idea of their relative velocity or force ; and considering velocity as an abstract number, it is said to be equal to the space, divided by the dine; and thus we are h d to consider velocity, or the space described in a given time, as the measure of force.

Force may also be expressed by other functions of velo city ; for it may be proportional to the square or cube of the velocity ; and La Place has very ingeniously proved that the difference between the proportionality of force to velocity, if any really exists, must be extremely small ; whence he argues it is highly improbable that any does exist. If there were any material variation in this law, the relative motions of bodies on the surface of the earth would be sensibly a&cted by the motion of the earth; in other words, the effect of a given force would vary considerably, accord ing as its direction coincided with, or was opposed to, that of the earth's motion. The effects of the state apparent forces would likewise vary in different seasons of the year ; the velocity of the earth being less by about one-thirtieth in summer than it is in winter. But as no such variation is

discernible, we nay justly conclude the proportion between force and velocity to be as 1 to I ; that is, there is no differ ence. Tu illustrate this, suppose two bodies moving upon one straight line with equal velocities; by impelling one of them with a force which increases its original force, its relative velocity to the other body remains the same as if both had been primitively in a quiescent state. The space described by the body, in consequence of its original force, and of that N‘Iiich has been added to it, becomes equal to the sum of what each of them would have caused it to have been, described in the same time ; therefore the force is propor tional to the velocity.

This law, and that of inertia above alluded to, may be considered as derived front observation and experiment: they are simple, and natural, and are sufficient to serve as a basis for the whole science of mechanics.

Early in the last. century, a warm controversy arose relatix e to the measure of force, which was carried on with considerable acrimony, though it now appears that the ques tion was rather about words than facts. Sir Isaac Newton had defined the measure of force to be " the mass of a body mutiplied into its velocity ;" which definition was not only convenient for the philosophical investigation in winch he was engaged ; but was really mathematically just. But in another point of view, in which the ell'ects of force may be said, without any impropriety, to depend on the mass multi plied into the square of the velocity, this product has been called the vis viva, and was considered by Bernouilli and Leibnitz as the true and universal measure of force, in oppo sition to Sir Isaac's definition ; though it now appears that they were led into an error by not duly considering all the circumstances of the question at issue. The measure adopted by them, the vis viva, merits attention, as in all cases of practical machinery it is frequently the most accurate, and always the most useful ; at the same time it implies no contradiction to the Newtonian definition. 13ut the force thus measured ought to be distinguished by some appropriate name, e. q. the vis nechanisu ; the Newtonian measure being applied to the vis motrix, as suggested by Mr. Wollas ton in the Bakerian Lecture fur 1805.