LAWS OF MATTER AND MOTION. 

 THE PENDULUM. 



This body, represented at fig. 27, depends for its motion upon the forces of 

 gravitation and persistence. The longer the pendulum the slower are its vibra- 

 tions, and. as the length is affected by temperature, various contrivances have 

 been, resorted to to correct this expansion and contraction ; these are termed 

 compensation pendulums (figs. 28, 29). Fig. 30 represents the balance wheel of 

 a watch, with a spring, which is expanded or contracted by the lever c, producing 

 a corresponding effect on the movement of the watch. 



CENTRAL FORCES. 



These are of two kinds, centripetal, or the force of gravity, tending towards 

 the centre ; and centrifugal, flying from it. The first may be illustrated by a 

 whirlpool at sea, or a whirlwind on land (figs. 31 and 32). Centrifugal force 

 may be illustrated in a variety of ways. If we whirl rapidly a sling with a stone 

 in it, and suddenly set free the stone, it will proceed in a straight line (fig. 33). 

 In turning rapidly a circular grindstone in contact with water, the latter will fly 

 off at right angles (fig. 34). A practical application of this power is seen in the 

 governor-balls of a steam engine (fig. 35). By any increase in the velocity in 

 the engine, the balls are thrown apart, and the levers draw down the collar, D, 

 and with it the end of the lever, F, which thus partially closes the throttle-valve 

 of the steam pipe. 



The centripetal and centrifugal forces are sublimely exemplified in the motions 

 of the planetary bodies ; the former in their attraction towards the central lumi- 

 nary by gravitation ; and the latter in their tendency to proceed in e straight 

 line by the force of persistence. 



The velocity of revolving bodies increases in proportion to the distance from 

 -**/ the centre of motion. The extremities of the vanes of the windmill move over 

 a much greater space than the parts near the axis, yet describe the circle in the 

 same space of time (fig. 36). In like manner, as our globe turns on its axis, 

 those parts nearer the poles describe smaller circles than those more remote -, 

 the equatorial regions describing the largest circles of all, hence, it follows, that 

 the equatorial regions move at a far greater velocity than the regions near the 

 poles (fig. 37). 



LAWS OF MOTION, 



A body projected by a single force naturally proceeds in the direction of that 

 force ; but if in its progress a new force acts upon it, it will then be sent in a 

 new direction. Thus, a ball projected in the line ABC (fig. 38), strikes obliquely 

 the ledge at c, there meeting an obstacle to its progress, which acts as a new 

 force, it is caused to rebound in the direction ODE, making the same angle 

 with the ledge as did the original path of the ball A B c. This effect is com 

 monly expressed by saying that the angle of incidence is. equal to the angle of 

 reflection, the former meaning the angle ABC, and the latter e D E ; and this 

 is a law that applies equally to the motions of sound, heat, and light ; and 

 therefore, is of the utmost importance throughout physics. If two or more 

 forces act upon a body at certain angles, a single force may be found which would 

 produce the same effect. This single force is called the resultant or equivalent. 

 In fig. 39 we have an example of this : a ball receiving a blow in the direction 

 A B, and at the same time a blow of equal force in the direction A D, does not 

 pursue either of those directions, but takes a diagonal course between them to c. 

 The effect being the same as if the ball had been sent in the direction A c, by a 

 single force. 



The process of finding a single fo*ee^quivalent to two or more forces is called 

 whe composition of forces, and the^orcss of finding forces which will produce a 

 motion equal to that of a single force, is called the resolution of forces. In fig. 

 40, this is illustrated in reference to the action of the wind upon the sail of a 

 ship, and of the tide upon the helm. Let A B represent the direction of the 

 wind acting upon the sail E F, placed obliquely to it, then, by drawing A c per- 

 pendicular to F E, and by completing the parallellogram D c; the diagonal A B is 

 resolvable into the adjacent sides A c and A D ; now, A c being at right angles to 

 E F, will have the effect of propelling the yessel, although not in a straight line; but 

 it may be guided in the desired direction by means of the helm, upon which the 

 water re-acts by the progressive motioa of the vessel 





