284 



THE POPULAR EDUCATOR. 



l>y the centrifugal force, and hence it remains in the can as if it 

 were a solid. So, too, when rapidly turning a corner or running 

 round the inside of a ring, we lean inwards. The body has a 

 tendency to move onwards in its previous direction, the feet 

 are, however, compelled to move in another, and thus the head 

 and body are thrown outward ; to obviate this we lean in the 

 contrary way. For the same reason, in a curve on a railway 

 the inner rails are lower than the outer, so that the carriage 

 inclines inwards, and thus removes the danger of its upsetting 

 or tearing up the rails. A carriage is not unfrequently upset in 

 this way while rapidly turning a corner. 



If a glass of water be placed on a small whirling table so 

 that it can be rapidly turned, the water will leave the centre 

 and rise towards the edges ; it may even be scattered over the 

 sides if the rotation be rapid enough. The same effect is see 

 if we rapidly stir a cup of tea, the level at the sides being abovf 

 that at the centre. 



A practical application of these principles is seen in the 

 entrifugal drying machine. This consists of a large hollow 

 cylinder, the bottom of which is perforated by a number of 

 holes. The linen is put into this, and it is then made to rotate 

 rapidly. In this way it is closely pressed against the sides, 

 and the water is given off and runs away through the holes in 

 the cylinder. Linen can thus be rendered almost dry in a very 

 short space of time. Another useful application of this force is 

 seen in the "governors" of a steam-engine. These consist of 

 two heavy balls sus- 

 pended by rods, and 

 when the speed of the 

 engine is increased be- 

 yond the proper degree 

 they fly apart, and in 

 so doing raise a loose 

 collar below them, and 

 by a series of levers 

 partly close the throttle 

 valve, and thus di- 

 minish the supply of <v 

 steam. 



In Fig. 105 a, a re- 

 present the balls sus- 

 pended by rods, which 

 are hinged at 6 to the 

 vertical shaft g. Mo- 

 tion is imparted to this by means of a strap, which passes 

 round the shaft of the fly-wheel, or some other convenient part 

 of the engine, and then round the driving-pulley, d. When tho 

 engine is moving too rapidly the balls fly further apart, and \ 

 by so doing raise the runner, e. This, by means of the bent 

 lever, k, works the rods, /, and thus partly closes the valve. 



Were it not for some such arrangement as, this, there would 

 be great danger of tho engine at times moving so rapidly, that 

 the fly-wheel would from the momentum of its particles le 

 shivered to pieces. These balls keep the speed nearly uni- 

 form ; for if it diminishes much they fall, and thus open the 

 throttle-valve to a greater extent and allow more steam to 

 pass. 



The laws of centrifugal force are important, because they 

 help to explain the motions of the heavenly bodies. The planets, 

 when first made, were started from the hand of their Creatoi 

 with a certain velocity. This produces a constant tendency 

 to fly off at a tangent from their orbits. They are, however, 

 restrained by another force, and that is the universal attraction 

 of all bodies for each other. Gravity is but one manifestation 

 of this : the earth draws the small bodies to it merely on account 

 of its superior weight, and for the same reason the sun attracts 

 all the planets ; or, to speak more accurately, all are attracted 

 to the common centre of gravity of our own solar system, 

 which is situated very near to the sun. 



This attraction, then, constantly deflects the planets from the 

 line in which they would otherwise move, and as a result of 

 these two forces they describe ellipses, in one focus of whi:L 

 the sun is situated. As this motion is through space, and not 

 through a resisting medium like the air, the retarding forces 

 which diminish the motion of bodies near the earth do not 

 affect them, and hence they move with undiminished speed. 

 This speed, however, varies with their distance from the sun, 

 and the following rule, discovered by Kepler, shows the rela- 



Fig. 105. 



tion that exists between the speed and the distance : The straight 

 line drawn from the planet to the sun always describes equal 

 areas in equal times. This law partly depends on another, 

 which teaches us that the attraction of any body for another 

 diminishes with the square of the distance. If, for instance, we 

 remove a body to double the distance, the attraction is |, if to 

 three times the distance, it is only A, and so on. This is an 

 experimental law, though by analogy with light we can easily 

 see why it should be so. If we take a piece of board, and 

 having cut out of it a piece a foot square, hold the board at any 

 distance from a bright light, and place a screen behind it at twice 

 the distance from the light, the illuminated space on the screen 

 will measure 2 feet each way, or 4 feet in all. . The light is thus 

 spread over four times the area, and therefore the illumination 

 at any point is only one-fourth as great. 



Similarly, if the distance of the screen from the light be three 

 times as great as that of the board, a space of 9 square feet will 

 be illuminated, and each part will have one-ninth of the 

 brilliancy. 



From this we see that when a planet is in the part of its 

 orbit most remote from the sun, it is attracted less powerfully, 

 and therefore its velocity must be less than when nearer the 

 Bun, or else it would fly out of its path. 



THE PENDULUM. 



We must now notice this very important instrument, so 

 valuable to us, not only as a regulating power for clocks, but 

 also for calculating the force of gravity and its variations in 

 different places. 



A simple pendulum is one all the weight of which is collected 

 at a single point. Such a one can, of course, only exist 

 theoretically ; but we may obtain a near approach to it by sus- 

 pending a small ball of some heavy substance, as lead or 

 platinum, by a very fine string. 



A common pendulum is called compound, for the weight ia 

 divided throughout it, and it may therefore be considered as a 

 number of simple pendulums connected together, so that all 

 swing at the same rate. All are familiar with its action, but 

 many do not know why it is used as a regulator. 



When a pendulum hangs freely, all its oscillations, if not of 

 wide extent, occupy exactly the same time. If the pendulum be 

 made to swing in a cycloidal curve, instead of an are of a circle, 

 then from whatever part of the arc it falls it always takes 

 exactly the same time. This remarkable property is called the 

 isochronism of the pendulum, this term being derived from two 

 Greek words, meaning "equal" and "time." Galileo was the 

 first to discover this law, and it is said his attention was called 

 to it by observing a chandelier in a cathedral. By some cause 

 it had been set swinging, and he noticed that however long tho 

 arc, it appeared to swing in exactly the same time. He ac- 

 cordingly tried some experiments on his return home, and found 

 that such was the case. 



In Fig. 10f> let o represent the point of suspension. When 

 o c is vertical the force of gravity is exactly 

 overcome by the tension of the cord, and thus 

 the pendulum serves as a plumb-line, for if c be 

 raised above the lowest point it will swing back- 

 wards and forwards till it settles at that point. 

 Now raise c to A. The same two forces act 

 upon it, namely, tension along A o and the force of 

 gravity acting vertically downwards along A x. 

 Produce o A to Y, and draw A z a tangent to the 

 arc. We can now resolve the force of gravity 

 into two, acting along A Y and A z. The former 

 of these will be overcome by the tension of the 

 string, the other part acting along A z will cause 

 the pendulum to move towards c. On arriving 

 there it will have acquired a velocity which 

 will carry it on over an arc nearly equal to c A, 

 and thus it will continue to oscillate till its 

 motion is stopped by the resistance it meets with. If we 

 now draw a line through Y parallel to A z, Y x will repre- 

 sent the portion of gravity which produces motion in the 

 pendulum, and A Y that which produces tension in the cord; 

 and it is clear that the smaller the arc A c, the less will Y x 

 be, and therefore the less the velocity of the pendulum. Thie 

 velocity ia found to decrease in the same proportion of the 



106. 



