Page:The Kinematics of Machinery.djvu/106

 Every motion which occurs in the machine thus connects itself with one leading idea, of which the single propositions considered contain special applications. Just as the old philosopher compared the constant gradual alteration of things to a flowing, and condensed it into the sentence: " Every thing flows;" so we may express the numberless motions in that wonderful production of the human brain which we call a machine in one word, " Everything rolls." Through the whole machine, hidden or apparent, the same funda- mental law of rolling applies to the mutual motions of the parts. The same idea, as we have already seen occasionally, can be extended to all the phenomena of kosmic motion, for our investigations do not merely cover the movements of the different parts of a machine, but are applicable generally to all moving bodies.

But the rolling geometrical figures which we can imagine to connect themselves with kosmic bodies are not in themselves constant. They are parts ' of the universal " flowing ;" they alter themselves incessantly as the motions vary, now disappearing into nothing, now remodelling themselves into other continually changing forms, exactly determinable at every instant only in the rolling point itself. In the planetary motions also, that regu- larity which is capable of exact representation by axoids exists only approximately. In the machine, on the other hand, the rolling figures are rendered constant by artificial limitations of the motions, this end at least is sought by all possible means, and practically attained, so that, considered in the abstract, we are entitled to say that here this constancy exists.

Here these figures pass periodically through their mutual changes of position unnumbered times; they rest when the machine stops, and commence their play anew exactly as before so soon as the driving force again infuses life into the whole; one part only remains stationary, that which serves as a connecting piece between the machine itself and the unmoving space surrounding it.

For the practical mechanician, who has made himself familiar with modern Phoronomy, and still more for the theorist, the machine becomes instinct with a life of its own through the rolling geometrical forms everywhere connected with it. Some of these stand out in bodily form, as in belt-pullies or friction- wheels (as for example those of a railway carriage); others, such