Page:The Kinematics of Machinery.djvu/53

 Rh examining, without regard to any existing machine-theories, one and the same motion as it appears in Nature and in the Machine.

Let us take the case of a, which shall be supposed to occur first as the motion of a  ; and then as the revolution of a.

Suppose that from any cause the satellite $$T$$ (Fig. 2) so move about the planet $$P$$ that its centre describes a circle about the centre of $$P$$ in a plane passing through that point. So long as the conditions remain unaltered the motion continues the same. So soon however as any external disturbing force $$Q_1$$ (shown here perpendicular to the plane of motion), begins to act upon one side of $$T$$, $$T$$ alters its path. If this is to be prevented, another external force $$Q_2$$, equal and opposite to $$Q_1$$, must be brought simultaneously into action. If $$Q_1$$ be a pound, $$Q_2$$ must be also a pound; if $$Q_l$$ increase to a ton, $$Q_2$$ must increase to a ton also; the absolute value of $$Q$$ does not further enter into the question, which is one solely of the equilibrium of the external disturbing forces acting upon $$T$$. The existence of such an equilibrium in nature would presuppose the existence always of equally divided causes of force; it probably does not once occur in the case of celestial bodies. We are however at liberty to assume its possibility in order to simplify the matter.

In the machine the case is quite different, and much more simple. In order that points of the wheel $$R$$, Fig. 3, may move in circles, let it be fixed upon a rigid shaft of which the ends at $$A$$ and $$B$$ are turned down and fitted in holes in fixed and rigid supports $$L L$$, the whole system having a common geometrical axis. If now the wheel be set in motion by some suitable handle, every point in it lying beyond its geometrical axis describes a circle about some point in that axis. If any disturbing force $$Q$$ act sideways upon the wheel, then (if we suppose the material of the wheel, shaft, and bearings to be completely rigid) no alteration of the circular motion occurs; and this is true equally whether $$Q$$ be great or small, continuous or intermittent, constant or changing in direction. There is nevertheless continuous equilibrium here, but in