_Answer._ Yes: models which show the working of the valve-gear have been constructed with a pencil, to which the reciprocating motion of the valve is imparted, and which traces a curve on a surface having the same motion as the piston. This method has been employed by the writer in an instrument which he has applied to the locomotive itself. The principle upon which it works will be understood by supposing that the steam and exhaust-ports as represented in the diagram for motion-curves, fig. 123, be drawn on a board, _A B C D_, fig. 126, but instead of standing vertical, as in fig. 123, they are represented in a horizontal position, and the board on which they are drawn is fastened to the cross-head, _L_, so that the former will move backward and forward simultaneously with the latter and the piston. A small shaft, _F_, is attached to suitable supports, _j_, which are fastened to the guides. This shaft has two arms, _G_ and _E_, one vertical and the other horizontal and of the same length. The upper end of the vertical one, _G_, is then attached to the valve-stem or rocker-arm by a short connecting-rod, _H_, or other suitable means, so that the movement of the valve-stem will be imparted to the arm and shaft. Of course the end of the horizontal shaft then has exactly the same motion vertically that the valve-stem and valve have horizontally, with the very trifling inaccuracy due to the fact that the movement of the one is in a straight line, whereas the other is in the arc of a circle. Now if a pencil, _P_, is attached to the end of the horizontal arm, _E_, and is set so that its point indicates the exact position of the steam edge, _h_, of the valve, as shown in fig. 123, it is obvious that when the piston and board have moved four inches, the pencil will have moved downward and have drawn the portion of the motion-curve from _h_ to _i_; and when the piston has moved eight inches the curve will be drawn to _j_, and at 12, 16, 20 and 24 inches of the stroke the curve will be drawn to _k_, _l_, _m_ and _n_. During the return stroke a corresponding curve, _n o h_, will, of course, be drawn. With such an instrument curves can be drawn for any position of the link, and they will show the exact movement of the valve during the whole stroke, and will indicate all the defects resulting from bad proportions or construction, lost motion in the parts, or other causes of error or irregularity. [Illustration: Fig. 126.--Scale ³⁄₄ in. = 1 foot.]