A Treatise on Statics: Containing the Theory of the Equilibrium of Forces; and Numerous Examples Illustrative of the General Principles of the Science

An excerpt from the INTRODUCTION.DEFINITIONS AND PRELIMINARY NOTIONS. 1. In the Science of Mechanics of which Statics forms a part, matter is considered as essentially possessing extension, figure and impenetrability. The least conceivable portion of matter is called a particle. 2. We conceive of matter that it can exist either in a state of rest, or motion. If then matter, once at rest, pass into a state of motion, the change, not being essential to the existence or nature of matter, is of necessity ascribed to some agent, which, as to its nature, is essentially independent of the matter influenced. Whether this agent reside in the matter influenced, or in external objects, or in both, are questions which can only be answered after experimental investigation. This agent is called force; and it will be perceived from this statement, that a force is judged of entirely by the effects which it produces: and hence, if in the same circumstances two forces produce equal effects, we infer that the forces are equal. 3. It is assumed, that the effect of two equal forces acting in concert, is double the effect of one of them three, treble; and so on. The reason of its being necessary to make this an assumption is, that in our ignorance of the nature of force, we are compelled to judge of it by the change which it produces in the state of rest or motion of matter; and it is obvious, that we can no more judge that one such change is twice as great as another, than we can affirm that one candle is twice as bright, or one substance twice as sweet, or one noise twice as loud as another. 4. A force is considered as having magnitude and direction, and a point of application. When these three are known, the force is said to be known. From Art. 2, it will be seen that, by the magnitude of a force, we mean the degree of motion which it is capable of producing in matter previously at rest; and by the direction of a force, we mean the direction in which a particle of matter, under the influence of that force, would begin to move; and by the point of application of a force, we mean that particular particle of a mass of matter on which the force immediately exerts its influence. 5. If one particle of a rigid* mass of matter be acted upon by a force, it cannot obey the influence of the force without dragging with it the other matter with which it is connected; the motion therefore which it would receive, if free, is in some manner distributed among the whole mass of which it is a part. It is clear, therefore, that the subject of which we are treating, naturally divides itself into two distinct parts, according as the forces act on a free particle, or on a rigid body. * We define a rigid body to be an assemblage of particles of matter, connected together in such a manner that their relative places never change.