cover its former position. If, then, the axis be passed through B, the body will be in a state of indifferent equilibrium; for the point of support corresponding with the centre of gravity, it will remain at rest in whatever position it be placed. Lastly, if an axis be passed through c, the body will be in a state of unstable equilibrium, for it can only retain this position as long as a perpendicular from B passes through c; and as soon as the slightest deviation occurs, on the application of the smallest force the body will move round, until в falls under the point of support. Thus, for a body to be in a state of steady equilibrium, its centre of gravity must occupy the lowest possible point.

CHAPTER III.

ON MOTION. (GENERAL DYNAMICS.)

Species of Motion, 38. Newtonian Laws, 40-46. Centrifugal Motion, 41. Figure of the Earth, 43. Action and Reaction, 45. Reflexion of Motion, 46. Composition of two Forces, 47-48-of several Forces, 49. Resolution of Motion, 50. Velocities of moving Bodies, 53. Formula for uniformly accelerated Motion, 54.

38. In the preceding chapters we have confined ourselves to the consideration of matter in a state of rest; we have next to investigate the properties of matter in motion, constituting part of the science of Dynamics.

By motion we understand the act by which a body changes its position; it has been divided into several species: thus a body is said to be in absolute motion when it is actually moving from one part of space to another, instanced in the movements of the planets; and to be in a state of relative motion when it is moving with respect to some other body and at rest with regard to another: thus a man standing in a sailing vessel is in motion with relation to the shore, and at rest in relation to the several parts of the ship; in this case also his motion is said to be common with that of the vessel. Besides these, there are some other divisions of motion of importance to understand: thus the motion of a body is uniform when it passes over equal portions of space in equal times; it is accelerated when the successive portions of space passed over increase, and when they diminish it is said to be retarded, and when this increase or decrease of movement is

constant, the motion is said to be uniformly accelerated or retarded. The motion of any body is swifter or slower in proportion as the space passed over in a given time is greater or less. The degree of rapidity with which a body moves is termed its velocity, and is measured by the space passed over in a given time.

39. In consequence of the inertia of all bodies, force must be applied to cause them to assume motion; if it be merely intended to cause the body to move in the same horizontal plane which it previously occupied, the applied force must be sufficient to overcome the innate resistance of the body to any alteration in position, or inertia, and the friction of the supporting body; but if it be intended to place the body on a higher horizontal plane than it previously occupied, the applied force must be sufficient to overcome also the attraction of the earth, or force of gravity.

40. The simplest principles to which the phenomenon of motion could be reduced have been arranged by Newton in the form of three axioms or laws; well known as the Newtonian laws of motion.

LAW I.

A body at rest will continue at rest; and if in motion, will continue to move in a right line, unless acted upon by some external force.

This law is a necessary consequence of the inertia of matter (10); the second part, however, referring to a moving body never assuming a state of rest until acted upon by external force, might at first be doubted; but a little reflection on the commonest phenomena of moving bodies will dispel this doubt and demonstrate the truth of the Newtonian axiom. The chief invisible external causes checking the motion of bodies are, 1. Friction. If a ball be thrown along a common road, its motion from its encountering so many obstacles, be

comes obstructed and it soon stops; on a smooth bowling-green, there being less friction, the ball moves to a longer distance; and still farther on a smooth sheet of ice or level pavement, from the great diminution of friction. 2. Resistance of the atmosphere. This has been already referred to as a powerful cause in checking motion (28); it may be very satisfactorily proved by causing a wheel accurately balanced to rotate in air, and in the vacuum of an air-pump; and it will be found to continue in motion for a much longer time in the latter than the former. 3. Gravitation. This is by far the most important source of opposition to the continuance of motion, for whether a body be projected vertically upwards, or horizontally the attraction of gravitation will ultimately cause it to stop and fall towards the earth.

41. In consequence of the inertia of bodies causing them to persevere in rectilinear motion, it is found that when revolving in a circle they constantly endeavour to recede from the centre: this is termed the centrifugal or centre-flying

B

force. If a ball fixed to a cord, c, be made to revolve rapidly in a circle from a fixed point, s, as a centre, it will describe the circle ABE; if whilst rapidly moving, the cord c be cut with a sharp knife, the inertia of the ball will cause it to continue in motion, not however in a circle but in a right line corresponding to a tangent to the circular orb it described whilst the line c was entire. The force which caused a to fly off in the direction of a tangent is the centrifugal force; and the cord c, represents the direction of the centripetal or centreseeking force. Thus, considering the circle to be composed of an infinity of planes, the ball will tend to follow the direction of one of these planes and rush off at a tangent to the curve; this circumstance taking place the instant the force which binds A to the centre is overcome.

42. We see magnificent examples of this force in the revo

lution of the spheres of our universe: here the earth and other planets revolve round the sun as a centre with enormous velocity, everywhere tending to rush off into infinite space in the direction of a tangent to their circular orbits, a state of things of course equivalent to universal desolation and destruction, and prevented only by a powerful centripetal force; here represented by the gravitative attraction of the sun by which all the planets tend to gravitate towards his centre. Equally balanced between these opposing forces, the elements of our universe have revolved for myriads of ages around the great centre of our system, presenting a spectacle of infinite harmony and wisdom.

43. On our own globe we have a remarkable instance of the effects of this force, from its revolving on its own axis at the rate of 13.5 miles in a minute; an energetic centrifugal force becomes generated at the equator, by which portions of the earth tend to rush off into space; this is prevented by the centripetal force of gravitation acting from the centre of the earth. Still this has not been without its influence, for at an early epoch, probably during a semi-fluid state of our globe, a considerable bulging out occurred at the equator, and a corresponding flattening at the poles; so that the equatorial diameter of the earth is 17 miles greater than its polar diameter. On this account bodies weigh less at the equator than at the poles, 1000 pounds at the latter corresponding to 995 at the equator, from the increased distance. from the centre of the globe.

The projection of a stone by a sling; heaving the lead at sea; the scattering of drops of water from the wet revolving carriage wheel, or housemaid's mop; are so many familiar examples of this force.