.......... -ell ...... ........... eighth of this, or a bushel, was equivalent Egyptian stadium......... 750.8 to a cubic foot of water. A chaldron of Greek foot.......... 1.009 coals weighed 2000 pounds, and was a phyletarian foot ......... 1.167 ton. Hebrew foot......... 1.212 The French, acting upon a general system cubit...... 1.817 of innovation during the late Revolution in - sacred cubit............ 2.002 that country, formed new measures, the great cubit =six commou cubits. nomenclature of which is generally disap- Natural foot........ .814 proved of by the learned of Englaud, and Roman foot.. .970 Dr. Yonng ventures to give them, in some ..(after Titus) .965 degree amended, as follow: (from rules) ,9672 English inches. ..(from buildings) .9681 Millometre.. ,03937 ...(from a stone) .9696 Centimetre .39571 Roman mile of Pliny.. 4840.5 Decimetre... 3.93710 - of Strabo..... 4903. Metre....... 39.37100 Sicilian foot of Archimedes...... ,730 Decametre.. 393.71000 MODERN MEASURES. Amsterdam foot.......... .927 Myriometre. S93710.00000 2.233 The metre is 1.09364 yards, or nearly Antwerp foot.... 6940 1 yard, 14 nail, or 443.2959 lines French, or Barcelova foot..... .992 ..513074 toises. Basle foot...... .944 A decametre is 10 yards, 2 feet, 9.7 Bavarian foot... .968 inches. Berlin foot.... .992 A hecatometre, 109 yards, i foot, 1 inch, Bologna foot...... 1.244 A chiliometre, 4 furlongs, 213 yards, 1 Brabant ell in Germany. 2.268 foot, 10.2 inches. Brescia foot......... 1.560 A micrometre, 6 miles, 1 furlong, 156 Brescian braccio.. 2.099 yards, 6 inches. Brussels foot........ .902 Eight chiliometres are nearly 5 miles, greater ell.... 2.278 An inch is .0254 metre; 2441 inches, 62 lesser ell... 2.245 metres; 1000 feet, nearly 305 metres. China mathematical foot..... 1.127 An arc, a square decametre, is 3.95 Imperial foot.......... 1.051 perches, Chinese li........... 606. A hecatre, 2 acres, 1 rood, 35.4 perches. Constautinople foot........ 2.195 Cubic inches English. Copenhagen foot..... 1.049 | Millilitre .06103 .929 Centilitre .61028 1.857 Decilitre. 6.10280 Florence foot.. .995 Litre, a cubic decimitre 61.02800 braccio... 1.900 Decalitre... 610.28000 .812 Hecatolitre... 6102.80000 7.300 Chiliolitre........... 61028.00000 Geneva foot..... 1.919 Myriolitre... 610280.00000 .933 Lisbon foot..... .952 Two and fth wine pints are about a Madrid foot........ .915 litre; 3 wine pints are nearly 14 decilitres ; -- vara.. 3.263 a chiliolitre is one tun, 12.75 wine gallons, Malta palm...... .915 3,5317 cubic feet make a decistere, a Moscow foot........ .928 measure for fiie-wood. Naples palm......... .861 A sterc, a cubic metre, 35.3171. canna. 6.908 We shall now present the reader of thiş Paris foot.......... 1.066 article with various ancient and modern Paris metre....... 3.281 measures, which were selected from the best Rome palm... .733 authorities, foot....... .966 deto...... .6foot)... .0604 ANCIENT MEASURES, oncio ...........(11 foot)... 0805 Arabian foot......... 1.095 .2515 Egyptian foot.......... 1.421 palmo di architettura ... .7325 cauna.... ras...... ell......... post mile. Rome canna di architettura..... 7.325 modern geometricians use a decempeda, or staiolo...... 4.212 perch, divided into ten equal parts, called canna dei mericanti(8 palms) 6.5365 feet; the feet they subdivide into ten dibraccio dei mercanti (4 palms) 2.7876' gits, and the digit into ten lines, &c. braccio di tessitor di tela 2.0868 MEASURE of the mass, or quantity of matbraccio di architettura., 2.561 · ter, in mechanics, is its weight; it being apRussian archine......... 2.3625' parent that all the matter which colieres arschin. 2.3333 and moves with a body, gravitates with it, verschuck, ta arschin... .1458 and it being found by experiment that the Stockholm foot..... 1.073 gravities of homogeneal bodies are in proTurin foot...... 1.676 portion to their bulks, hence, while the 1.958 mass continues the same, the weight will trabuco 10.085 be the same, whatever figure it put on; by Tyrot foot....... 1.096 which is meant its absolute weight, for as 2.639 to its specific, that varies as the quantity of Venice foot.... 1.137 the surface varies. braccio of silk.. 2.108 MEASURE of a number, in arithmetic, ell............ 2.089 such a number as divides another without braccio of cloth..... 2.250 leaving any fraction : thus 9 is a measure Vienna foot ..... 1.036 of 27. ell........ 2.557 MEASURE of a solid, is a cube whose side 24888, is one inch, foot, yard, or any other deterWarsaw foot....... 1.169 minate length. In geometry, it is a cubic The yoke of land, a description of mea- perch, divided into cubic feet, digits, &c.: bure 'in Austria, contains 1600 sqnare fa. hence cubic measures, or measures of capa. thoms : “ 1 metz, or bushel, 1.9471 cubic city. feet. 1 eimer = 40 kannen = 1.792 cubio MEASURE of, velocity, in mechanics, the feet, of Vienna ; 1 fass = 10 einer." space passed over by a moving body in a In Sweden, a kanne contains 106 cubic given time. To measure a velocity thereSwedish inches. fore, the space must be divided into as MEASURE, in geometry, denotes any many equal parts as the time is conceived quantity assumed as one, or unity, to which to be divided into; the quantity of space the ratio of other homogeneous or similar answering to such an article of time is the quantities is expressed. This definition is measure of the velocity. somewhat more agreeable to practice than MeaśURE for horses, is the hand, which, that of Euclid, who defines measure, a quan- by statute, contains four inches. tity which being repeated any number of Measure is also used to signify the ca. times becomes equal to another. This lat- dence and time observed in poetry, danc. ter definition answers only to the idea of an ing, and music, to render thein regular and arithmetical measure, or quota-part. agreeable. See METRE. MEASURE of an angle, is an arch des MEASURE, in music, the interval or space scribed from the vertex in any place be. of time which the person who beats time tween its legs. Hence angles are distin- takes between the rising and falling of his guishod by the ratio of the arches, described hand, in order to conduct the movement from the vertex between the legs to the pe- sometimes quicker and sometimes slower, ripberies. Angles then are distinguished according to the music or subject that is to by those arches; and the arches are distin- be sung or played. See TIME. guished by their ratio to the periphery: thus MECHANICAL, in mathematics, dean angle is said to be of so many degrees notes a construction of some problem, by as there are in the said arch. See ANGLE. the assistance of instruments, as the dupli. MBASURE of a figure, or plane surface, is cature of the cube and quadrature of the a square wliose side is one inch, foot, yard, circle, in contradistinction to that which is or some other determinate length. Among done in an accurate and geometrical geometricians, it is usually a rod called a manner. square rod, divided into ten square feet, MECHANICAL curve, is a curve, accord. and the square feet into ten square digits ; ing to Des Cartes, which cannot be defined hence square measures. by any algebraic equation; and so stands MEASURE of a line, any right line taken contra-distinguished from algebraic or geoat pleasure, and considered as unity. The metrical curves. Leibnitz and others call these mechani- there is in every combination of bodies, cal curves transcendental, and dissent from and in every single body which may be Des Cartes in excluding them out of geome. considered as made up of a number of try. Leibnitz found a new kind of trans- lesser bodies, a centre of pressure or gracendental equations, whereby these curves vity. This discovery Archimedes applied are defined; but they do not continue con- to particular cases, and pointed out the mestantly the same in all points of the curve, thod of finding the centre of gravity of as algebraic ones do, plane surfaces, whether bounded by a paMECHANICS, is the science which rallellogram, a triangle, a trapesium, or a treats of the laws of the equilibrium and parabola. See CENTRE of gravity. motion of solid bodies; of the forces by Galileo, towards the close of the sixteenth which bodies, whether animate or inani- century, made many important discoveries mate, may be made to act upon one ano- on this subject. In a small treatise on statics, ther; and of the means by which these may he proved that it required an equal power to be increased, so as to overcome such as are raise two different bodies to altitudes, in most powerful. As this science is closely the inverse ratio of their weights, or that connected with the arts of life, and particu- the same power is requisite to raise ten larly with those which existed even in the pounds to the height of one hundred feet, rudest ages of society, the construction of and twenty pounds fifty feet. It is imposmachines must have been practised long be- sible for us to follow this great inan in all fore the theory upon which their principles his discoveries. In his works, which were depend conld have been understood. Hence published early in the seventeenth century, we find in use among the ancients, the le- he discusses the doctrine of equable mo. ver, the pulley, the crane, the capstan, and tions in various theorems, containing the many other simple machines, at a period different relations between the velocity of when mechanics, as a science, were un- the moving body, the space which it de. known. In the remains of Egyptian archi- scribes, and the time employed in its detectire are beheld the most surprising scription. He treats also of accelerated marks of mechanical genius. The eleva. motion, considers all bodies as heavy, and tion of immense and ponderous masses of composed of heavy parts, and infers that stone to the tops of their stupendous fa- the total weight of the body is proportional brics, must have required an accumulation to the number of the particles of which it of mechanical power, which is not in the is composed. On this subject he reasons possession of modern architects. We are in the following manner : “As the weight indebted to Archimedes for the foundation of a body is a power always the same in of this science : he demonstrated, that when qnantity, and as it constantly acts without a balance with unequal arms is in equilibrio, interruption, the body must be continually by means of two weights in its opposite receiving from it equal impulses in equal scales, these weights must be reciprocally and successive instants of time. When the proportional to the arms of the balance. body is prevented from falling, by being From this general principle the mathemati. placed on a table, its weight is incessantly cian might have deduced all the other pro- impelling it downwards ; but these impulses perties of the lever, but he did not follow are destroyed by the resistance of the ta. the discovery through all its consequences. ble, which prevents it from yielding to In demonstrating the leading property of them. But where the body falls freely, the lever, he lays it down as an axiom, that the impulses which it perpetually receives if the two arms of the balance are equal, are perpetually accumulating, and remain the weights must be equal, to give an equi- in the body unchanged in every respect, librinm. Reflecting on the construction of except the diminution which they expe. the balance, which moved upon a fulcrum, rience from the resistance of the air : hence he perceived that the two weights exerted it follows, that a body falling freely is unithe same pressure on the fulcrum as if they formly accelerated, or receives equal incre. had both rested on it. He then advanced ments of velocity in equal times. He then another step, and considered the sum of demonstrated that the time in which any these two weights as combined with a third, space is described by a motion uniformly and then the sum of the three, with a fourth, accelerated from rest, is equal to the time and so on, and perceived that in every such in which the same space would be describ. combination the fulcrum must supported by an uniform equable motion, with half their united weight; and, therefore, that the final velocity of the accelerated motion, and that in every motion uniformly accele- sustained. The points of suspension are rated from rest, the spaces described are those points where the weights really are, in the duplicate ratio of the times of de- or from which they hang freely. The scription: after this he applied the doctrine power and the weight are always supposed to the ascent and descent of bodies on in. to act at right angles to the lever, except clined planes. For a more particular ac- it be otherwise expressed. The lever is count we may refer to Dr. Keil's “ Phy- distinguished into three sorts, according to sics.” Under the articles CENTRE of gra- the different situations of the fulcrum, or vity, DYNAMICS, Elasticity, Force, prop, and the power, with respect to each GRAVITATION, MOTION, &c. will be other. 1. When the prop is placed be. found much relating to the doctrine of tween the power and the weight, as in steel. mechanics; we shall therefore in this place · yards, scissars, pincers, &c. 2. When the chiefly treat of the mechanical powers, prop is at one end of the lever, the power which are usually reckoned six in pumber : at the other, and the weight between them, viz. the lever; the wheel and axis, or, as it as in cutting knives fastened at, or near is frequently called, " the axis in peritro- the point of the blade ; also in oars moving chio;" the pulley ; tbe inclined plane; the a boat, the water being the fulcrum. 3. wedge; and the screw. Some writers on When the prop is at one end, the weight this subject reduce the six to two, riz. the at the other, and the power applied belever, and the inclined plane; the pulley, tween them, as in tongs, sheers, &c. and wheel and axis being, in their estima. The lever of the first kind is principally tion, assemblages of the lever; and the used for loosening large stones ; or to raise wedge and the screw being modifications great weights to small heights, in order to of the inclined plane. get ropes under them, or other means of When two forces act against each other, raising them to still greater heights: it is by the intervention of a machine, the one the most common species of lever. ABC is denominated the power, and the other (Plate I, Mechanics, fig. 1.) is a lever of this the weight. The weight is the resistance kind, in which F is the fulcrum, A the end to be overcome, or the effect to be pro- at which the power is applied, and the duced. The power is the force, whether end where the weight acts. To find when animate or inanimate, which is employed an equilibrium will take place between the to overcome that resistance, or to produce power and the weight, in this as well as in the required effect. every other species of lever, we must ob. The power and weight are said to ba. serve that when the momenta, or quantities lance each other, or to be in equilibrio, of force, in two bodies are equal, they will when the effort of the one to produce mo. balance each other. Now, let us consider tion in one direction, is equal to the effort when this will take place in the lever. of the other to produce it in the opposite Suppose the lever AB, fig. 2, to be turned directiou; or when the weight opposes that on its axis, or fulcrum, so as to come into degree of resistance which is precisely re- the situation DC; as the end D is farthest quired to destroy the action of the power. from the centre of m and as it has The power of a machine is calculated when moved through the arch AD in the same it is in a state of equilibrium. Having dis- time as the end B moved through the arch covered what quantity of power will be re- BC, it is evident that the velocity of AB quisite for this purpose, it will then be ne. must have been greater than that of B. cessary to add so much more, viz. one. But the momenta being the products of the fourth, or, perhaps, one-third, to overcome quantities of matter multiplied into the velothe friction of the machine, and give it mo- cities, the greater the velocity, the less the tion. quantity of matter to obtain the same proThe lever is the simplest of all machines, duct. Therefore, as the velocity of A is and is a straight bar of iron, wood, or other the greatest, it will require less matter to material, supported on, and moveable about produce an equilibrium than B. a prop called the fulcrum. In the lever, Let us now examine how much more there are three circumstances to be prin- weight B will require than A, to balance. cipally attended to: 1. The fulerum, or As the radii of circles are in proportion to prop, by which it is supported, or on which their circumferences, they are also proporit turns as a centre of motion : 2. The tionate to similar parts of them; therefore, power to raise and support the weight: 3. as the arches, AD, CB, are similar, the The resistance or weight to be raised or radius, or arm, DE, bears the same proportion to E C that the arch A D bears to CB. weight to change places, so that the power But the arches A D and C B represent the may be between the weight and the prop, velocities of the ends of the lever, because it will become a lever of the third kind; they are the spaces which they moved over in which, that there may be a balance bein the same time; therefore the arms DE tween the power and the weight, the in. and EC may also represent these velocities. tensity of the power must exceed the inHence, an equilibrium will take place, when tensity of the weight just as much as the the length of the arm A E, multiplied into distance of the weight from the prop exthe power A, shall equal ER, multiplied ceeds the distance of the power. Thus, into the weight B; and consequently, that let E, fig. 4, be the prop of the lever E F, the shorter E B is, the greater must be the and w, a weight of one pound, placed three weight B; that is, the power and the times as far from the prop as the power P weight must be to each other inversely, as acts at F, by the cord going over the fixed their distances from the fulcrum. Thus, pulley D: in this case, the power must be suppose A E, the distance of the power equal to three pounds, in order 10 support from the prop, to be twenty inches, and the weight of one pound. To this sort of EB, the distance of the weight from the lever are generally referred the bones of a prop, to be eight inches, also the weight man's arm; for when he lifts a weiglit by to be raised at B to be tive pounds; then the hand, the muscle that exerts its force the power to be applied at A, must be two to raise that weighit, is fixed to the bone pounds; because the distance of the weight about one tentli part as far below the from the fulcrum eight, multiplied into the elbow as the liand is. And the elbow being weight tive, makes forty; therefore twenty, the centre round which the lower part of the distance of the power from the prop, the arm turns, the muscle must therefore must be multiplied by two, to get an equal exert a force ten times as great as the product; which will produce an equili. weight that is raised. As this kind of lever brium. is a disadvantage to the moving power, it The second kind of lever, when the is used as little as possible; but in some weight is between the fulcrum and the power, cases it cannot be avoided; such as that is represented by fig. 3, in which A is the of a ladder, which being fixed at one end, fulcrum, B the weight, and C the power. is by the strength of a man's arms reared The advantage gained by this lever, as in against a wall. the first, is as great as the distance of the What is called the hammer-lever, differs power from the prop exceeds the distance in nothing but its form from a lever of the of the weight from it. Thus, if the point tirst kind. Its name is derived from its use, a, on wbich the power acts, be seven times that of drawing a nail out of wood by a as far from A as the point b, on which the hammer. Suppose the shaft of a hammer weight acts, then one pound applied at C to be five times as long as the iron part will raise seven pounds at B. This lever which draws the nail, the lower part resting shews the reason why two men carrying a on the board, as a fulcrum; then, by pullburden upon a stick between them, bearing backwards the end of the shaft, a man shares of the hurden which are to one ano- will draw a pail with one-fifth part of the ther in the inverse proportion of their dis- power that he must use to pull it out with tances from it. a pair of pincers; in which case, the pail It is likewise applicable to the case of would move as fast as his hand; but with two horses of unequal strength to be so the hammer, the hand moves five times as yoked, as that each horse may draw a part much as the nail, by the time that the nail proportionable to his strength; which is is drawn out. Hence it is evident, dat done by so dividing the beam they pull, in every species of lever there will be an that the point of traction may be as much equilibrium, when the power is to the weight nearer to the stronger horse than to the as the distance of the weight from the fulweaker, as the strength of the former ex. crum is to the distance of the power from ceeds that of the latter. To this kind of the fulcrum, In experiments with the lever may be reduced rudders of ships, lever we take care that the parts are per. doors turning upon hinges, &c. The hinges fectly balanced before the weights and being the centre of motion, the hand ap- powers are applied. The bar, therefore, plied to the lock is the power, while the has the short end so much thicker than the door is the weight to be moved. long arm, as will be sufficient to balance If in this lever we suppose the power and it on the prop, |