HISTORICAL SKETCH.
The first mechanical problems solved were those dealing with the simple machines. Archi medes (me. 287-212) was acquainted with the law of the lever in its simplest form; and Leo nardo da Vinci (1432-1319) stated the law for the most general case, when the forces were in any directions and applied at any points. The principle of the inclined plane was known to Galileo ( 1564-1642) and to Stevinus Stevinus was the first to use a line to describe a force, and to make use of the principle of the composition and resolution of forces: he also discussed the properties of pulleys and com binations of pulleys. using the principle that if force applied to the cord (a weight) move down a certain distance, a weight fastened to the pul ley must move up a distance such that the product of each weight by its distance is the same. This principle is that of 'virtual velocities,' so called, which was applied also by Galileo, Torrieelli, Bernoulli, and Lagrange. In his treatment of the inclined plane Galileo made use of the gen eral principle that there is equilibrium in any case when the weight as a whole cannot descend farther; or, as Torricelli expressed it. when the 'centre of gravity' cannot descend.
Galileo was the founder of the science of dy • 'milks. He recognized the fact that if a piece of matter was in motion and was free from ex ternal action it would continue its motion un altered. He proved by experiment that all bodies fall with the same acceleration toward the earth, and proposed that the value of a force's act inn on a body be measured by the acceleration produced. Ile recognized the independence of different mo tions in discussing the =lion of a projectile. Ile was acquainted, too, with the general prop erties of a simple pendulum, especially its prop erty of having a definite period which varied with the length of the string.
Huygens (1629-95) did fully as important work as Galileo and deserves to rank with him. He de duced the formula for centrifugal motion, u He invented a pendulum clock and the 'escape ment' for it; he used a pendulum to determine g; and proposed a seconds pendulum as a stand ard of length. He solved the problem of deduc ing the length of a simple pendulum which would vibrate in the same period as a compound one, that is. be determined the position of the centre
of oscillation (q.v.). In this last deduction he made use of the principle that in whatever man ner the particles of a compound pendulum in fluenced each other, the velocities acquired in the descent of the pendulum are such that by virtue of them their centre of gravity rises just as high as the point from which it fell, whether the pendulum is considered a rigid body or as breaking up into particles each connected with the axis by a cord and thus forming a great num ber of simple pendulums. If p,. etc., are the weights of the particles, h„ etc.. are the dis tances they have fallen at any instant, and s„ etc.. are their speeds at that instant. 11 nygens's principle leads to the relation, + p + In the case of a rigid body turning around a fixed axis Mips', where w is the angular speed and r is the distance of the particle of weight p from the axis. Thus Huygens was led to the use of Zia' as a measure of the inertia of a rotating body. lie did not, however. realize the idea of mass as distinct from weight. The name •moment of inertia' was given by Euler.
Newton gave the principles of mechanics their final form. and since his day there have been no important additions to them. We owe to Newton (1642-1727) the recognition of other force than weight. the general idea of force, and in particu lar the conception of inertia or mass as a prop erty of matter distinct from its weight, the gen eral statement of the principle of the composition and resolution of forces, and the law of action and reaction being equal but opposite. Newton adopted as the proper measure of a force the ac celeration produced in a given portion of matter; or, in other words, the velocity produced in a given time. Aceording to Huygens the measure of the force is the square of the velocity produced in a given distance. Among the philosophers who came after Newton and there wins a school, following Descartes. who measured forces by the change in oar; another, following Leibnitz, who measured it by the Change in Thus. to a certain extent one school succeeded Newton; the other. Huygens. The two were shown by D'Alembert to be identical. although there was a great controversy for many years concerning their relative merits.