INCLINATION

, in Geometry, Mechanics, or Physics, denotes the mutual tendency of two lines, planes, or bodies, towards one another; so that their directions make at the point of concourse some certain angle.

Inclination of the Axis of the Earth, is the angle it makes with the plane of the ecliptic; or the angle between the planes of the equator and ecliptic.

Inclination of a Line to a plane, is the acute angle, as CDE, which the line CD makes with another line DE drawn in the plane through the incident point D and the foot of a perpendicular E from any point of the line upon the plane.

Inclination of an Incident ray, is the angle of inclination, or angle of incidence.

Inclination of the Magnetical needle. See Dipping Needle.

Inclination of Meridians, in Dialling, is the angle that the hour-line on the globe, which is perpendicular to the dial-plane, makes with the meridian.

Inclination of the Orbit of a planet, is the angle formed by the planes of the ecliptic and of the orbit of the planet. The quantity of this Inclination for the several planets, is as follows, viz.

Inclination of a Plane, in Dialling, is the arch of| a vertical circle, perpendicular both to the plane and the horizon, and intercepted between them.

Inclination of a Planet, is the arch or angle comprehended between the ecliptic and the place of the planet in its orbit. The greatest Inclination, or declination, is the same as the Inclination of the orbit; which see above.

Inclination of a Reflected ray, is the angle which a ray after reflection makes with the axis of Inclination; as the angle FBD, in the last fig. but one.

Inclination of Two Planes, is the angle made by two lines drawn in those planes perpendicular to their common intersection, and meeting in any point of that intersection.

Angle of Inclination, is the same as what is otherwise called the angle of incidence.

Argument of Inclination. See Argument.

Inclined Plan<*>, in Mechanics, is a plane inclined to the horizon, or making an angle with it. It is one of the simple mechanic powers, and the double inclined plane makes the wedge.

1. The power gained by the Inclined plane, is in proportion as the length of the plane is to its height, or as radius to the sine of its inclination; that is, a given weight hanging freely, will balance upon the plane another weight, that shall be greater in that proportion. So, when the greater weight W on the plane, is balanced by the less weight w hanging perpendicularly, then is w : W : : BC : AC : : sin. [angle]A : radius. Or, in other words, the relative gravity of a body upon the plane, or its force in descending down the plane, is to its absolute gravity or weight, in the same proportion of the height of the plane to its length, or of the sine of inclination to radius.

2. Hence therefore the relative gravities of the same body on different inclined planes, or their forces to descend down the planes, are to each other, as the sines of the angles of inclination, to radius 1, or directly as the heights of the planes, and inversely as their lengths.

3. Hence, if the planes have the same height, and absolute weights of the bodies be directly proportional to the lengths of the planes, then the forces to descend will be equal. Consequently, if the bodies be then connected by a string acting parallel to the planes, they will exactly balance each other; as in the annexed figure.

4. The relative force of gravity upon the plane being in a constant ratio to the absolute weight of the body, viz, as sine of inclination to radius; therefore all the laws relating to the perpendicular free descents of bodies by gravity, hold equally true for the descents on inclined planes; such as, that the motion is a uniformly accelerated one; that the velocities are directly as the times, and the spaces as the square of either of them; using only the relative force upon the plane for the absolute weight of the body, or instead of 32 1/6 feet, the velocity generated by gravity in the first second of time, using 32 1/6s, where s is the sine of the inclination to the radius 1.

5. The velocity acquired by a body in descending down an Inclined plane AC, when the body arrives at A, is the same as the velocity acqu<*>red by descending freely down the perpendicular altitude BC, when it arrives at B. But the times are very different; for the time of descending down the Inclined plane, is greater than down the perpendicular, in the same proportion as the length of the plane AC, is to the height CB : and so the time of descending from any point C to a horizontal line or plane ABG &c, down any oblique line, or Inclined plane, is directly proportional to the length of that plane, CA, or CD, or CE, or CB, or CF, &c.

6. Hence, if there be drawn AH perpendicular to AC, meeting CB produced in H; then the time of descending down any plane CA, is equal to the time of descending down the perpendicular CH. So that, if upon CH as a diameter a circle be described, the times of descent will be exactly equal, down every chord in the circle, beginning at C, and terminating any where in the circumference, as CI, CA, CK, CH, &c, or beginning any where in the circumference, and terminating at the lowest point of the circle, as CH, IH, AH, KH, &c.

7. When bodies ascend up Inclined planes, their motion is uniformly retarded; and all the former laws for descents, or the generation of motion, hold equally true for ascents, or the destruction of as much motion.

Inclined Towers, are towers inclined, or leaning out of the perpendicular. See Towers.