_Answer._ One motion-curve is sufficient to represent the position of any part of the valve during the entire stroke. This will be apparent if it is remembered that each motion-curve is exactly like the others, as shown in fig. 28, the only difference being that the ports occupy different positions in relation to the curves. It is, therefore, only necessary to draw lines to represent the relative positions of the ports to the other curves to show the entire motion of the valve by one curve. To illustrate this it will be assumed that a motion-curve, _h i j k l m n o p_, and a centre line, _a b_, fig. 127, have been drawn with the instrument described in the answer to the previous question. The centre line _a b_, which will be equal in length to the stroke of the piston, should then be divided into inches, and lines _ff_, 23 1, 22 2, etc., should be drawn through the points of division and at right angles to _a b_. If, now, we want to show the movement of the front steam edge of the valve in relation to the corresponding steam port, a line, _t_, should be drawn perpendicular to _f f_, to represent that edge of the valve at the beginning of the stroke. As it is impossible to determine accurately the position of this steam edge at the beginning of the stroke from the motion-curve, which is then _tangent_[56] to the line _f f_, we must lay it off from the centre line, _a b_. This can readily be done if we remember that if a valve has ⁷⁄₈ in. lap when it is in the middle position, as shown in fig. 27, and ¹⁄₁₆ in. lead at the beginning of the stroke, it must have moved ¹⁵⁄₁₆ in. from the middle position at the beginning of the stroke as shown in fig. 28. The line _t_ must therefore be drawn ¹⁵⁄₁₆ in. from _a b_ to represent its proper position in relation to the motion-curve, and as it has ¹⁄₁₆ in. lead, the steam edge, _h h′_, of the steam-port must be drawn at that distance from _t_. Another line, _m m′_, can then be drawn to represent the width of the front steam-port, _c c′_. From these lines the movement of the valve in relation to the front port, _c c′_, and the admission of steam are shown as clearly as in fig. 28. [56] A curve is said to be _tangent_ to another carve or to a straight line when the two just touch, but do not intersect or cross each other.