RETARDATION

, in Physics, the act of retarding, that is, of delaying the motion or progress of a body, or of diminishing its velocity.

The Retardation of moving bodies arises from two great causes, the resistance of the medium, and the force of gravity.

The Retardation from the Resistance is often confounded with the resistance itself; because, with respect to the same moving body, they are in the same proportion.

But with respect to different bodies, the same resistance often generates different Retardations. For if bodies of equal bulk, but different densities, be moved through the same fluid with equal velocity, the fluid will act equally on each; so that they will have equal resistances, but different Retardations; and the Retardations will be to each other, as the velocities which might be generated by the same forces in the bodies proposed; that is, they are inversely as the quantities of matter in the bodies, or inversely as the densities.

Suppose then bodies of equal density, but of unequal bulk, to move equally fast through the same fluid; then their resistances increase according to their superficies, that is as the squares of their diameters; but the quantities of matter are increased according to their mass or magnitude, that is as the cubes of their diameters: the resistances are the quantities of motion; | the Retardations are the celerities arising from them; and dividing the quantities of motion by the quantities of matter, we shall have the celerities; therefore the Retardations are directly as the squares of the diameters, and inversely as the cubes of the diameters, that is inversely as the diameters themselves.

If the bodies be of equal magnitude and density, and moved through different fluids, with equal celerity, their Retardations are as the densities of the fluids. And when equal bodies are carried through the same fluid with different velocities, the Retardations are as the squares of the velocities.

So that, if s denote the superficies of a body, w its weight, d its diameter, v the velocity, and n the density of the fluid medium, and N that of the body; then, in similar bodies, the resistance is as nsv² or as nd²v², and the Retardation, or retarding force, as (nsv²)/w, or as .

The Retardation from Gravity is peculiar to bodies projected upwards. A body thrown upwards is retarded after the same manner as a falling body is accelerated; only in the one case the force of gravity conspires with the motion acquired, and in the other it acts contrary to it.

As the force of gravity is uniform, the Retardation from that cause will be equal in equal times. Hence, as it is the same force which generates motion in the falling body, and diminishes it in the rising one, a body rises till it lose all its motion; which it does in the same time in which a body falling would have acquired a velocity equal to that with which the body was thrown up.

Also, a body thrown up, will rise to the same height from which, in falling, it would acquire the same velocity with which it was thrown up: therefore the heights which bodies can rise to, when thrown up with different velocities, are to each other as the squares of the velocities.

Hence, the Retardations of motions may be compared together. For they are, first, as the squares of the velocities; 2dly, as the densities of the fluids through which the bodies are moved; 3dly, inversely as the diameters of those bodies; 4thly, inversely as the densities of the bodies themselves; as expressed by the theorem above, viz, (nv²)/(Nd).

The Laws of Retardation, are the very same as those for acceleration; motion and velocity being destroyed in the one case, in the very same quantity and proportion as it is generated in the other.