Centre

Centre, a term in general use in mathematics and dynamics, denoting a point possessing certain special properties. The centre of a circle is defined by Euclid as the point such that all lines drawn from it to the circumference of the circle are of equal length. More generally the centre of any conic section, whether circle, ellipse, parabola, hyperbola, or line-pair denotes that point which bisects all lines drawn through it and terminated by the curve. Similarly in solid geometry, since every section of any quadric surface (q.v.) is a conic, the centre of any such surface shall bisect all lines passing through it that are terminated by that surface. Centre of figure is also purely geometrical. The centre of figure of any aggregation of points is that point occupying the average position of all the given points. That is to say, its distance from any plane is the average distance of all the points in the figure from that plane. This applies to lines, areas, or solids, regarding any one of these entities as an aggregation of points. Centre of mass, or mass-centre of any number of masses, may be regarded as the centre of figure of a system of equal material points which give the same resultant mass-distribution as is presented by the given masses. Such a point always exists, and from its definition it is still geometrical. Centre of gravity of any system of material particles is a dynamical conception. It is the point through which passes the resultant pull of the earth's gravitation for all the particles. If the forces on all the particles were strictly parallel, a centre of gravity would always exist for a body of any shape, and would coincide with its mass-centre. But these forces are not strictly parallel, and as a consequence true centres of gravity only exist for special distributions of matter, such distributions being known as centrobaric. It is evident that the term centre of gravity should only be applied to mass distributions. The centre of suspension of a pendulum is that point by which it is hanging. If at rest, the centre of gravity will be vertically beneath. This line joining the centres is called the axis of the pendulum, and the centre of oscillation is that point in the axis where a mass might be concentrated so that if suspended by a weightless thread from the same point of support, it would swing in unison with the given pendulum. If the pendulum be rigid, and be struck horizontally at its centre of oscillation, no tendency to displace the centre of suspension will be observed. This is not the case for any other point of application of the blow. Hence the term centre of permission is applied to the centre of oscillation of any rigid body. In hydrodynamics the term centre of pressure denotes the point of application of the resultant fluid pressure on any plane area. Centre of buoyancy of a floating body denotes the mass-centre of the displaced liquid, and is practically the point through which passes the resultant upward pressure of the surrounding liquid.