MECHANICAL UNITS. 243 MECHANICS. 'P. S. 1844, 1 pound,' and deposited at the office of the Kxchequer." Both the standard yard and pound are now preserved at the Standards Office of the Board of Trade, London. Still another system is based upon the foot (one-third of the yard), the mean solar second, and the u-ciylit of one pound at sea-level and latitude .'/-i" as the unit of force. (A unit mass is yiven an accelera- tion unity by a unit force; hence, since the unit force K'^** P^i' second an acceleration 32.172 feet per second to a mass of one pound, it will give an acceleration 1 to 32.172 pounds; tljerefore. on this system, the unit of mass is 32.172 pounds.) The relations between these units is as follows : 1 centinietiT = 0,3937079 inches = 0.01093633 yards. 1 vftrd = yl. 43835 centimeter. 1 griltn =- 0.002'2046212.5 lb. = 16.43235 grains. 1 pound = 453.59205 grams. The units for the various important mechanical quantities are derived from them. These de- rived units and a few others are given in the following seetioas:
clocity. — One centimeter per second; one
yard (or foot) per second; one nautical mile, knot (0080 feet), per hour. Acceleration. — Unit Telocity per second. Force. — One gram with unit C. G. S. accelera- tion = rfy/ic; one pound with unit (ft.-lb.-see.) acceleration = poundul = 13,825 dynes. Weight of one pound = 44,520 dynes. ll"oc7,-. — One dyne acting through one centi- meter = cry ; 10' ergs :=joule. One pound raised one foot = foot-pound — 1.326 joules. One kilo- gram raised one meter = kilogram-meter = 9.81 joules. (The last two relations are approxi- mate.) Power. — One joule per second = icatt ; 33,000 foot - pounds per minute = horse - power = 746 watts: 'force de cheval'^ 75 kilogram-meters per second := 730 watts. Pressure. — One dyne per square centimeter = •barie.' One megadyne (10° dynes) per square centimeter = 'mcgabarie.' 'Weight of one pound per square foot' = 47.9 dynes per scjuare centi- meter; one poundal per square foot = 14.88 dynes per square centimeter; 'one centimeter of mercury' = 13.5950 X 980.692 dynes per square centimeter = 13,332.5 dynes per square centi- meter ; lience 75 centimeters of mercury = 1 niegabarie (very closely) ; 70 centimeters of mer- cury, 'one atmosphere' = 1.0133 megabarics. MECHANICS (Lat. mechaniea, from Gk. IJi.r]xo.vtKa., nifchanika, fn]xa.viKri, mcchanikc, me- chanics, from ix7]xa.rfi, vierliniie, device). The science which is concerned with the motion of matter; the possible kinds of motion, the condi- tions under which the motion remains unchanged, and those under which it changes. That branch of mechanics which discusses the possiljle kinds of motion is called kinematics; while that which discusses the properties of matter in motion is called diinamics. Dynamics is divided also into two parts — statics and kinetics — the former treating the conditions under which there is no change in the motion; the latter, those under which there is chanse. niSTORIC.L SKETCH. The first mechanical problems solved were those dealing with the simple machines. Archi- medes (B.C. 287-212) was acquainted with the law of the lever in its simplest form ; and Leo- nardo da Vinci (1452-1519) 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 (1.504-1042) and to Stevinus (1548- 1620). Stevinus was Jhe iirst to u.so 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, TorriccUi, Bernoulli, and Lagrange. In his treatment of the inclined plane Galileo made use of the gen- ei'al principle that there is equilibrium in any case when the weight as a wliole cannot descend farther; or, as Torricelli expressed it, when the ■ 'centre of gravity' cannot descend. Galileo was the founder of the science of dy^ namics. He recognized the fact that if a piece of matter was in motion and was free from ex- tei-nal action it would continue its motion un- altered. He proved by experiment that all l)odie3 fall with the same acceleration toward the earth, and proposed that the value of a force's action on a body be measured by the acceleration produced. He recognized the independence of different mo- tions in discussing the motion of a projectile. He 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, « =.s"r. He invented a pendulum clock and the 'escape- ment' for it; he used a pendulum to determine <;; and proposed a seconds pendulum as a stand- ard of length. He solved the problem of deduc- ing the length of a simple pendulmu which would vibrate in the same period as a compound one, that is, he determined the position of the centre of oscillation (q.v. ). In tliis last deduction he made use of the principle that in whatever man- ner the particles of a compound pendulum in- fluenced each othei', 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 forTuing a great num- ber of simple pendulums. If ;),, p,, etc., are the treights of the particles, ft,, ft,, etc., arc the dis- tances they have fallen at any instant, and s,, .Sg, etc., are their speeds at that instant. Huygens's principle leads to the relation, ip,.s,^ + i/JjS.' -|- etc. = (pifti -|- pJi; -- etc.) - or 2 Jp.s2 = - SpA. In the case of a rigid body turning around a fixed axis Xips' = W-Xpr", 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 S/u- as a measure of the inertia of a rotating body. He did not. however, realize the idea of mass as distinct from weight. The
