stroke and when it has nearly an inch to move, that it is wide open almost immediately after the piston begins its stroke, does not begin to close until the piston has moved 19¹⁄₂ inches of its stroke, and is completely closed at 23 inches of the stroke. By referring the curve to the lines _d d′_ and _g g′_, almost the same phenomena will be observed for the forward stroke. In fact from such a diagram the whole motion of the valve can be studied and analyzed with the greatest accuracy; and, as has already been shown, the motion imparted to a slide valve by a link is of so complicated a nature that it is almost or quite impossible to observe its exact nature without such diagrams. QUESTION 194. _Can a motion diagram be constructed to represent the motion of the valve with different amounts of travel?_ _Answer._ Yes; it is only necessary to construct motion-curves for the same diagram for each distance traveled, and they will show the movement of the valve for the given amount of travel represented by the curves. This has been done in fig. 128, which is a reduced copy of a series of motion-curves taken from a locomotive. From this diagram the movement of a slide-valve worked by the link-motion can be seen from the highest to the lowest practicable point of cut-off. For convenience of reference the curves have been numbered. [Illustration: _Fig. 128._ Scale ³⁄₁₆ inch = 1 inch.] The smallest travel of the valve represented by curve No. 1 is a little less than 2¹⁄₂ in., and the ports are then opened only about ⁵⁄₁₆ in., and the steam is cut off at 8 in. on the backward and 6³⁄₄ in. on the forward stroke. The exhaust is opened or the steam is released during the backward stroke at 17 in., and during the forward stroke at 16⁵⁄₈. When the valve works with its greatest travel, as represented by curve 8, it travels 5 in., and opens the steam port wide at 3 in. of the backward stroke and 2¹⁄₄ in. of the forward stroke. The steam is cut off at 20³⁄₄ and 20¹⁄₂ in., and its release takes place at 23¹⁄₈ in. of each stroke. The following table gives the greatest width of opening, the point of cut-off, the point of release, and the lead for each motion-curve on the diagram. This table has been made up from the motion-curves drawn with the instrument described in answer to Question 191, on a locomotive which had been running about eighteen months and whose valve-gear consequently was considerably worn, as s indicated by the flatness of the motion-curves on each side at the point when the motion of the valve was reversed. This flatness was caused by the lost motion in the valve-gear, the pencil remaining for a time stationary when the motion was reversed and while the parts were moving from their bearings on one side to those on the other. The curves and the table therefore show the operation not of a theoretically perfect valve-gear, but are examples of actual practice, with such imperfections as are incidental to ordinary locomotives.