NATURAL PHILOSOPHY MATTER, MOTION, AND HEAT. 



Fig. 17. 





the times are thus exactly equalised would be out 

 of place here. 



It is only short oscillations that are thus isoch- 

 ronous, as it is called ; when the arcs are large, 

 the steepness does not increase in exact proportion 

 to the length, and therefore the isochronism is 

 not perfect. Accordingly, pendulums are made to 

 swing in short arcs ; and then, though no con- 

 trivance could make the extent of the oscillations 

 exactly uniform, the times are virtually equal. 



But though the time of oscillation is not affected 

 by the largeness of the arc, it is by the length of 

 the pendulum itself. Long pendulums vibrate 

 more slowly than short ones. Though the balls 

 B and D in the fig. have the same 

 amplitude of vibration, or go over 

 corresponding arcs, the journey of 

 the one is longer than that of the 

 other. But the steepness of descent, 

 or inclination of the path, is the 

 same in both ; therefore B must 

 take longer time to perform its jour- 

 ney than D. We must not, how- 

 ever, conclude that when the length 

 of the arc, or, which is the same 

 thing, of the pendulum, is doubled, 

 the time of oscillation is also 

 doubled. The motion of the pen- 

 dulum is an accelerated motion ; 

 and, as in all other uniformly accelerated motions, 

 the spaces described are as the squares of the 

 times. To give double the time of vibration, then, 

 requires the pendulum to be four times as long ; 

 treble the time, nine times as long ; and so on. 

 A pendulum of a little more than 39 inches beats 

 seconds, and one of one-fourth that length beats 

 half-seconds. 



When we say that the seconds pendulum is 

 always of the same length, we must be understood 

 to speak of the same place. In different places, 

 its length varies. At the equator, owing to the 

 shape of the earth, we are thirteen miles further 

 from the centre than at the poles ; the force of 

 gravity is therefore less, and thus the seconds 

 pendulum must be somewhat shorter at the equa- 

 tor, and grow gradually longer as the latitude 

 increases. 



The length of a pendulum is measured from 

 the point of suspension, not to the bottom, or even 

 the centre of the ball, but to a point called the 

 centre of oscillation, where the whole mass of the 

 swinging body rod and ball together may be 

 supposed concentrated. The determination of this 

 point is a matter of some difficulty. The use of 

 the pendulum in regulating clocks is considered 

 in the number on HOROLOGY. 



CENTRIFUGAL FORCE AND CIRCULAR MOTION. 



Motion in a circle, or in .any other curve, is 

 something constrained. When we make a ball 

 whirl round rapidly at the end of a cord, we feel 

 the cord stretched with a sensible force ; the ball 

 is pulling outwards, and the hand is pulling in- 

 wards. The outward pull of the ball is called the 

 centrifugal, or centre-flying force ; the inward pull 

 of the hand, the centripetal, or centre-seeking force. 

 The tension of the cord is the measure of both 

 forces. 



When a body, constrained to move in a circle, 



Fig. 1 8. 



is released from the restraint, what is the result ? 

 Suppose the ball B re- 

 tained by the cord AB, 

 and moving in the direc- 

 tion C EG, &c. ; if relieved 

 from the restraint of the 

 cord, it does not fly di- 

 rectly away from the 

 centre, in the line AB 

 prolonged. It has still 

 its onward motion in the 

 direction of the curve, and 

 the only effect of the re- 

 lease from the centripetal 

 force is, that that motion 

 ceases to be bent, and goes on straight in the direc- 

 tion it had at the instant. Now, at any point in a 

 circle, the direction of the curve is that of a straight 

 line drawn through the point at right angles to the 

 diameter. Such a straight line is called a tangent; 

 and thus motion in a circle, when released from 

 the constraining force, becomes motion in the 

 tangent, or flies off at a tangent At C, for in- 

 stance, the direction of the ball, when set free, 

 would be CD ; at I it would be IK. 



The tendency to fly off from the centre and at 

 a tangent, is exemplified in a multitude of phe- 

 nomena. A stone let go from a sling is the most 

 familiar instance. When a vessel with water in it 

 is rapidly turned round like a horizontal wheel, 

 the water recedes from the centre, and rises up 

 round the sides. 



In equestrian performances in a circus, both 

 rider and horse incline their bodies inwards ; they 

 are leaning against a force which is impelling 

 them outwards, and which thus sustains a part of 

 their weight. A skater must do the same in 

 describing a curve. If a round ball of soft clay be 

 turned rapidly on a spindle, it ceases to be per- 

 fectly round in all directions : it bulges out at the 

 middle and shortens in the direction of the spindle. 

 This has happened to our earth ; and to a still 

 greater degree to Jupiter and Saturn, which have 

 a more rapid rotation on their axes. 



The centrifugal force of a body moving in a 

 circle increases as the mass of the body, and as 

 the square of the velocity. It is calculated that if 

 the rotation of the earth were seventeen times 

 faster than it is, centrifugal force at the equator 

 would be equal to gravity; in other words, all 

 bodies would be completely without weight, and a 

 little increase of velocity would throw them off, to 

 circle round like small satellites. 



HEAT. 



To account for the appearances presented by 

 matter in its several forms of solid, liquid, and gas, 

 we have seen it necessary (p. 195) to assume that 

 there is a repulsive force at work among its mole- 

 cules, counteracting and modifying the attractive 

 forces. This repulsive force would seem to be 

 identical with heat Heat expands bodies ; it 

 overcomes the cohesion of their particles, con- 

 verting solids into liquids, and liquids into gases ; 

 without it, there would be only one form of matter, 

 the solid, and all life would cease on the earth. 



203 



