It has been found more convenient to neglect these formal distinctions in the very brief presentation of the subject which will be given in this book.
11. Configuration and Displacement.— An assemblage of points may be completely described by selecting some one point as a point of reference and assigning to each of the others a definite distance and direction measured from this fixed point. Such a set of points is called a system of points, and the assemblage of distances and directions which characterize it is called its configuration. The motion of one or more of the points is recognized by a change in the configuration. The change in position of any one point, determined by the distance between its initial and final positions and the direction of the line drawn between those positions, is called the displacement of the point.
Any particle in the system may be taken as the fixed point of reference, and the motion of the others may be measured from it. Thus, for example, high-water mark on the shore may be taken as the fixed point in determining the rise and fall of the tides; or, the sun may be assumed to be at rest in computing the orbital motions of the planets. We can have no assurance that the particle which we assume as fixed is not really in motion as a part of some larger system; indeed, in almost every case we know that it is thus in motion. As it is impossible to conceive of a point in space recognizable as fixed and determined in position, our measurements of motion must always be relative.
12. Composition and Resolution of Displacements.— If a point undergo two or more successive displacements, the final displacement is obviously given by the line joining its initial to its final position. This displacement is called the resultant of the others. If the point considered be referred to a point which is itself displaced relative to a third point taken as fixed, the motion of the moving point relative to the fixed point may be considered as resulting from a combination of the displacement of the first point, relative to the second point, and the displacement of the second point relative to the third or fixed point. These simultaneous
