[Footnote 21: Strictly speaking, this is only true when the divergence of the rods from the spindle is not very great, and, in practice, this divergence is never sufficient to render the above assertion untrue. This property of the conical pendulum arises from the circumstance of the centrifugal force, in this instance, varying as the radius of the circle in which the balls are moved; and when this is the case, as is well known, the _periodic time_ is constant. The time of one revolution of the balls is equal to twice the time in which either ball, as a common pendulum, would vibrate on the centre, and as all its vibrations, though the arcs be unequal, are equal in time, provided those arcs be small, so also is the periodic time of the revolving ball invariable. These observations, however, only apply when the balls settle themselves steadily into a circular motion; for while they are ascending they describe a spiral curve with double curvature, and the period will vary. This takes place during the momentary changes in the velocity of the engine.] We have thus described the principal parts of the double-acting steam engine. The valves and the methods of working them have been reserved for the next chapter, as they admit of considerable variety, and will be better treated of separately. We have also reserved the consideration of the boiler, which is far from being the least interesting part of the modern steam engine, for a future chapter. CHAPTER VII. DOUBLE-ACTING STEAM ENGINE (_continued_.) On the Valves of the Double-Acting Steam Engine. -- Original Valves. -- Spindle Valves. -- Sliding Valve. -- D Valve. -- Four-Way Cock.