[Illustration: JOY'S REVERSING AND EXPANDING VALVE GEAR.] The former of these is constant and unalterable, the latter is controllable by the angle at which the curved slide, J, may be set with the vertical. It will further be evident that if the lever, E, were pinned direct to the connecting rod at the point, A, which passes through a practically true ellipse, it would vibrate its fulcrum, F, unequally on either side of the center of the curved slide, J, by the amount of the versed sine of the arc of the lever, E, from F D; it is to correct this error that the lever, E, is pinned at the point, D, to a parallel motion formed by the parts, B and C. The point, D, performing a figure which is equal to an ellipse, with the error to be eliminated added, so neutralizing its effect on the motion of the fulcrum, F. The "lap" and "lead" are opened by the action of the valve lever acting as a lever, and the port opening is given by the incline of the curved slide in which the center of that lever slides, and the amount of this opening depends upon the angle given to that incline. When these two actions are in unison, the motion of the valve is very rapid, and this occurs when the steam is being admitted. Then follows a period of opposition of these motions, during which time the valve pauses momentarily, this corresponding to the time when the port is fully open. Further periods of unison follow, at which time the sharp "cut-off" is obtained. The "compression" resulting with this gear is also reduced to a minimum, owing to the peculiar movement given to the valves (_i. e._, the series of accelerations and retardations referred to), as, while the "lead" is obtained later and quicker, the port is also shut for "compression" later and quicker, doing away with the necessity for a special expansion valve, with its complicated and expensive machinery, and allowing the main valve to be used for expansion, as the "compression" is not of an injurious amount, even with a "cut-off" reduced to 15 per cent., or about 1/6 of the stroke. Thus, so far as the distribution of the steam and its treatment in the cylinder is concerned, a marked advantage is shown in favor of this valve gear. But next in its favor, as before said, is that the above advantages are not gained at the cost of added complication of parts or increased cost of machinery, but the reverse, as this gear can be built at a less cost than link gear, varying according to the circumstances, but reaching as high as a saving of 25 per cent., or, if it be compared with a link gear supplemented by the usual special expansion valve and gear as employed on marine engines, then the total saving is fully 50 per cent., and an equally good result is obtained as to the distribution and subsequent treatment of the steam.