Suppose the weight be at s and moving towards p, and let a tangent to the circle be drawn at p. Take two points on the circle, a and B, very near p; the small arc a b does not differ perceptibly from the part a b on the tangent line; hence, when the particle arrives at a, it is a matter of indifference whether it travels in the arc a b, or along the line a b. Let us suppose it to move along the line. By the first law of motion, a particle moving in the line a b would continue to do so; hence, if the particle be allowed, it will move on to q: but the particle is not allowed to move to q; it is found at r. Hence it must have been withdrawn by some force.
565. This force is supplied by the string to which the weight is attached. The incessant change from the rectilinear motion of the weight requires a constantly applied force, and this is always directed to the centre. Should the string be released, the body flies off in the direction of the tangent to the circle at the point which the body occupied at the instant of release.
566. The central force increases in proportion to the square of the velocity. If I double the speed with which the weight is whirled round in the circle, I quadruple the force which the string must exert on the body. If the speed be trebled, the force is increased ninefold, and so on. When the speeds with which two equal masses are revolving in two circles are equal, the central force in the smaller circle is greater than that of the larger circle, in the proportion of the radius of the larger circle to that of the smaller.
THE ACTION OF CIRCULAR MOTION
UPON LIQUIDS.
567. I have here a small bucket nearly filled with water: to the handle a piece of string is attached. If I whirl the bucket round in a vertical plane sufficiently fast, you see no water escapes, although the bucket is turned upside down once in every revolution. This is because the water has not time to fall out during such a brief interval. A body would not fall half an inch from rest in the twentieth of a second.
568. The action of circular motion upon liquids is illustrated by the experiment which is represented in [Fig. 76].
Fig. 76.
A glass beaker about half full of water is mounted so that it can be spun round rapidly. The motion is given by means of a large wheel turned by a handle, as shown in the figure. When the rotation commences, the water is seen to rise up against the glass sides and form a hollow in the centre.
569. In order to demonstrate this clearly, I turn upon the vessel a beam from the lime-light. I have previously dissolved a little quinine in the water. The light from the lamp is transmitted through a piece of dense blue glass. When the light thus coloured falls on the water, the presence of the quinine makes the entire liquid glow with a bluish hue. This remarkable property of quinine, which is known as fluorescence, enables you to see distinctly the hollow form caused by the rotation.