STATIC S. INTRODUCTION. 1. DEFINITIONS AND PRELIMINARY NOTIONS. 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 B 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. 6. With respect to the motion of a particle of matter, we conceive that it consists in the particle's being found to occupy different parts of space at successive instants, or epochs of time; but with respect to the motion of a rigid body we conceive, (1) That as a whole it may occupy the same portion of space at successive epochs, while some of its parts individually occupy different parts of space in successive in stants. This is called rotatory motion. * 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. (2) That as a whole it may occupy different parts of space at successive epochs, without having at the same time any rotatory motion. This is called a motion of translation. (3) That both these kinds of motion may exist together in the same body. This is the most general kind of motion of which we can form a notion. 7. From the preceding articles it will be perceived that we have taken motion as the characteristic effect of force. It will now be necessary to shew, that there exists another effect (and that more convenient for our present purpose) which may be taken as the measure or characteristic of force. If any portion of matter (a stone for instance) be held in the hand, it will be found to exert a pressure; and if the hand be suddenly removed, will fall. In its fall it may be caught, but the hand will again feel a pressure. This experiment informs us, that that which is the cause of motion, is likewise the cause of pressure. While the stone is held at rest, its continual tendency to fall is evidenced by the pressure which is exerted on the hand; hence, in all cases where motion is prevented, there is pressure. But further, the latter part of the experiment teaches us that, in all cases where motion is retarded, there is pressure. If when the stone is at rest, the hand exert a greater pressure upwards than is necessary to prevent it from falling, the stone will begin to move upwards. Hence we learn that pressure attends the production as well as the prevention and the destruction of motion. Thus it appears that pressure produces the same results as we have taken to be the characteristic effects of force. We may therefore take pressure as the measure of force, because both pressure and motion are effects of the same cause. 8. The Earth, in some unseen manner, exerts a pressure in a downwards direction upon all matter with which |