A Mathematical and Philosphical Dictionary
, a mixed mathematical science, that treats of forces, motion, and moving powers, with their effects in machines, &c. The science of Mechanics is distinguished, by Sir Isaac Newton, into Prac- tical and Rational: the former treats of the Mechanical Powers, and of their various combinations; the latter, or Rational Mechanics, comprehends the whole theory and doctrine of forces, with the motions and effects produced by them.
That part of Mechanics, which treats of the weight, gravity, and equilibrium of bodies and powers, is called Statics; as distinguished from that part which considers the Mechanical powers, and their application, which is properly called Mechanics.
Some of the principles of Statics were established by Archimedes, in his Treatise on the Centre of Gravity of Plane Figures: besides which, little more upon Mechanics is to be found in the writings of the Ancients, except what is contained in the 8th book of Pappus's Mathematical Collections, concerning the five Mechanical Powers. Galileo laid the best foundation of Mechanics, when he investigated the descent of heavy bodies; and since his time, by the assistance of the new methods of computation, a great progress has been made, especially by Newton, in his Principia, which is a general treatise on Rational and Physical Mechanics, in its largest extent. Other writers on this science, or some branch of it, are, Guido Ubaldus, in his Liber Mechanicorum; Torricelli, Libri de Motu Gravium naturaliter Descendentium & Projectorum; Balianus, Tractatus de Motu naturali Gravium; Huygens, Horologium Oscillatorium, and Tractatus de Motu Corporum ex Percussione; Leibnitz, Resistentia Solidorum in Acta Eruditor. an. 1684; Guldinus, De Centro Gravitatis; Wallis, Tractatus de Mechanica; Varignon, Projet d'une Nouvelle Mechanique, and his papers in the Memoir. Acad. an. 1702; Borelli, Tractatus De Vi Percussionis, De Motionibus Naturalibus a Gravitate pendentibus, and De Motu Animalium; De Chales, Treatise on Motion; Pardies, Discourse of Local Motion; Parent, Elements of Mechanics and Physics; Casatus, Mechanica; Oughtred, Mechanical Institutions; Rohault, Tractatus de Mechanica; Lamy, Mechanique; Keill, Introduction to true Philosophy; De la Hire, Mechanique; Mariotte, Traité du Choc des Corps; Ditton, Laws of Motion; Herman, Phoronomia; Gravesande, Physics: Euler, Tractatus de Motu; Musschenbroek, Physics; Bossu, Mechanique; Desaguliers, Mechanics; Rowning, Natural Philosophy; Emerson, Mechanics; Parkinson, Mechanics; La Grange, Mechanique Analytique; Nicholson, Introduction to Natural Philosophy; Enfield, Institutes of Natural Philosophy, &c, &c. As to the Deseription of Machines, see Strada, Zeisingius, Besson, Augustine de Ramellis, Boetler, Leopold, Sturmy, Perrault, Limberg, Emerson, Royal Academy of Scicnces, &c.
In treating of machines, we should consider the weight that is to be raised, the power by which it is to be raised, and the instrument or engine by which this effect is to be produced. And, in treating of these, there are two principal problems that present themselves: the first is, to determine the proportion which the power and weight ought to have to each other, that they may just be in equilibrio; the second is, to determine what ought to be the proportion between the power and weight, that a machine may produce the greatest effect in a given time. All writers on Mechanics treat on the first of these problems, but few have considered the second, though not less useful than the other.
As to the first problem, this general rule holds in all powers; namely, that when the power and weight are reciprocally proportional to the distances of the directions in which they act, from the centre of motion; or when the product of the power by the distance of its direction, is equal to the product of the weight by the distance of its direction; this is the case in which the power and weight sustain each other, and are in equilibrio; so that the one would not prevail over the other, if the engine were at rest; and if it were in motion, it would continue to proceed uniformly, if it were not for the friction of its parts, and other resistances. And, in general, the effect of any power, or force, is as the product of that force multiplied by the distance of its direction from the centre of motion, o<*> the product of the power and its velocity when in motion, since this velocity is proportional to the distance from that centre.
The second general problem in Mechanics, is, to determine the proportion between the power and weight, so that when the power prevails, and the machine is in motion, the greatest effect possible may be produced by it in a given time. It is manifest, that this is an enquiry of the greatest importance, though few have treated of it. When the power is only a little greater than what is sufficient to sustain the weight, the motion usually is too slow; and though a greater weight be raised in this case, it is not sufficient to compensate for the loss of time. On the other hand, when the power is much greater than what is sufficient to sustain the weight, this is raised in less time; but it may happen that this is not sufficient to compensate for the loss arising from the smallness of the load. It ought therefore to be determined when the product of the weight multiplied by its velocity, is the greatest possible; for this product measures the effect of the engine in a given time, which is always the greater in proportion both as the weight is greater, and as its velocity is greater. For some calculations on this problem, see Maclaurin's Account of Newton's Discoveries, p. 171, &c; also his Fluxions, art. 908 &c. And, for the various properties in Mechanics, see the several terms Motion, Force, Mechanical Powers, Lever, &c.