574. The explanation of the development of the ring involves some additional principles: as the sphere of oil spins round in the liquid, its surface is retarded by friction; so that when the velocity attains a certain amount, the internal portions of the sphere, which are in the neighbourhood of the spindle, are driven from the centre into the outer portions, but the full account of the phenomenon cannot be given here.
575. The earth was, we believe, originally in a fluid condition. It had then, as it has now, a diurnal rotation, and one of the consequences of this rotation has been to cause the form to be slightly protuberant at the equator, just as we have seen the sphere of oil to bulge out under similar conditions.
576. Bodies lying on the earth are whirled around in a great circle every day. Hence, if there were not some force drawing them to the centre, they would fly off at a tangent. A part of the earth’s attraction goes for this purpose, and the remainder, which is the apparent weight, is thus diminished by a quantity increasing from the pole to the equator ([Art. 86]).
THE APPLICATIONS OF CIRCULAR MOTION.
577. These principles have many applications in the mechanical arts; we shall mention two of them. The first is to the governor-balls of a steam-engine; the second is to the process of sugar refining.
An engine which turns a number of machines in a factory should work uniformly. Irregularities of motion may be productive of loss and various inconveniences. An engine would work irregularly either from variation in the production of steam, or from the demands upon the power being lessened or increased. Even if the first of these sources of irregularity could be avoided by care, it is clear that the second could not. Some machines in the mill are occasionally stopped, others occasionally set in motion, and the engine generally tends to go faster the less it has to do. It is therefore necessary to provide means by which the speed shall be restrained within narrow limits, and it is obviously desirable that the contrivance used for this purpose should be self-acting. We must, therefore, have some arrangement which shall admit more steam to the cylinder when the engine is moving too slowly, and less steam when it is moving too quickly. The valve which is to regulate this must be worked by some agent which depends upon the velocity of the engine; this at once points to circular motion because the force acting on the revolving body depends upon its velocity. Such was the train of reasoning which led to the happy invention of the governor-balls: these are shown in [Fig. 79].
Fig. 79.
a b is a vertical spindle which is turned by the engine. p p is a piece firmly attached to the spindle and turning with it. p w, p w are arms terminating in weights w w; these are balls of iron, generally very massive: the arms are free to turn round pins at p p. At q q links are placed, attached to another piece r r, which is free to slide up and down the spindle. When a b rotates, w and w are carried round, and therefore fly outwards from the spindle; to do this they must evidently pull the piece r r up the shaft. We can easily imagine an arrangement by which r r shall be made to shut or open the steam-valve according as it ascends or descends. The problem is then solved, for if the engine begin to go too rapidly, the balls fly out further just as they did in [Fig. 74]: this movement raises the piece r r, which diminishes the supply of steam, and consequently checks the speed. On the other hand, when the engine works too slowly, the balls fall in towards the spindle, the piece r r descends, the valve is opened, and a greater supply of steam is admitted. The objection to this governor is that though it moderates, it does not completely check irregularity. There are other governors occasionally employed which depend also on circular motion; some of these are more sensitive than the governor-balls; but they are elaborate machines, only to be employed under exceptional circumstances.
578. The application of circular motion to sugar refining is a very beautiful invention. To explain it I must briefly describe the process of refining.