Page:Collier's New Encyclopedia v. 02.djvu/464

CENT  CENT, or CENTIME, the name of a small coin in various countries, so called as being equal to a 100th part of some other coin. In the United States and in Canada the cent is the 100th part of a dollar. In France the centime is the 100th part of a franc. Similar coins are the centavo of Chili, and the centesimo of Italy, Peru, etc. Cents or centimes, and their equivalents, are written simply as decimals of the unit of value.  CENTAUR, a mythical creature, half man, half horse, said to have sprung from the union of Ixion and a Cloud; the most celebrated was Chiron. They inhabited Thessaly, and were also called Hippocentaurs. The myth probably arose from some herdsman on horseback, who, being seen by individuals unacquainted with the uses of the horse, was supposed to form, together with his steed, one integral body.

It is also the name of a constellation in the Southern Hemisphere.  CENTER, a point equi-distant from the extremities of an object. Among its best known applications are:

Center of Inertia.—If m1 and m2 be the masses of two particles placed at the points A1 and A2, and if the right line A1A2 be divided in B1, so that

the point B2 is called the center of inertia, or center of mass, of the two particles. If m3 be a third mass at A3, and if AB1A3 be divided in B2, so that

B2 is called the center of inertia of the three particles. In general, if there be any number of particles, a continuation of the above process will enable us to

find their center of inertia. Every body may be supposed to be made up of a multitude of particles connected by cohesion. From this it is obvious that the center of inertia is a definite point for every piece of matter.



Center of Gravity.—If a body be sufficiently small, relatively to the earth, the weights of its particles may be considered as constituting a system of parallel forces acting on the body. Now, the magnitude of the weight of a particle is proportional to its mass. Hence, the line of action of the resultant of the parallel forces will approximately pass through the center of inertia. For this reason such bodies are said to have a center of gravity. Strictly speaking, there is no such point of necessity for every body, since the directions of the forces acting on the body are not accurately parallel. Hence, it is only approximately that we can say of a body that it has a center of gravity. On the other hand, every piece of matter has, as is shown above, a center of inertia. For all heavy bodies of moderate dimensions it is, however, sufficiently accurate to assume that the center of inertia and gravity coincide. For example, the center of gravity of a uniform homogeneous cylinder with parallel ends is the middle point of its axis, that of a uniformly thin circular lamina its center, and so on.

The center of gravity of a body of moderate dimensions may be approximately determined by suspending it by a single cord in two different positions, and finding the single point in the body which, in both positions, is intersected by the axis of the cord.

The term center of gravity is also used in a stricter sense than the one just explained. Thus, if a body attracts and is attracted by all other gravitating matter as if its whole mass were concentrated in one point, it is said to have a true center of gravity at that point, and the body itself is called a centrobaric body. A spherical shell of uniform gravitating matter attracts an external particle as if its whole mass were 