Question 182. What is meant by the valve-gear of a locomotive?

Answer. By the valve-gear is meant the arrangement of eccentrics, rods, links, rockers, etc., by which the valves are moved and their motion regulated.

Question 183. What is required of the valve-gear in working a locomotive?

Answer. It must be so arranged that the locomotive can be run either backward or forward, and so that the motion of the wheels can be reversed quickly and with certainty. It should enable the runner to employ the greatest power of the engine by admitting steam into the cylinders during the whole or nearly the whole of the stroke of the pistons, or when less power is required, to use the steam more economically by working it expansively, which latter is accomplished with the present appliances by changing the travel of the valve.

Question 184. How is the valve-gear constructed so as to run the engine either backward or forward?

Answer. As already explained, in answer to question 76, two eccentrics are provided for each cylinder. These are set so that one of each pair will run the locomotive in one direction, and the other two the reverse way.

Question 185. How must the eccentrics for each cylinder be set in order that the one may run the engine forward and the other backward?

Answer. This can be best explained by reference to fig. 100, in which the piston, P, is represented at the beginning of the backward stroke, and the valve V has the requisite lead and is just about to open the front steam-port. It is obvious that, in order to complete the backward stroke of the piston, the front port must be opened to admit steam into the front end of the cylinder, and therefore the valve must be moved in the direction indicated by the dart a. To do this, the upper arm of the rocker r must move in the same direction, and the lower arm must be moved the reverse way, as indicated by the dart e. If the crank is intended to move in the direction indicated by the dart N, then the centre of the eccentric must be above the centre of the shaft or axle, in order to move the rocker in the direction indicated by the dart e. Supposing, however, it was intended to move the crank the reverse direction, as shown by the dart N in fig. 101; it is evident in that case that the valve must be moved in the same direction as before, in order to open the front steam-port and thus admit steam to force the piston back. But if the crank turns in the direction shown by the dart N, fig. 101, then the centre of the eccentric must be placed below the centre of the axle in order to move the lower rocker arm in the direction of the dart e and the valve in that indicated by a. It will thus be seen that the centres of the eccentric for running forward and that of the one for running backward must be placed, the one above and the other below the centre of the axle at the beginning of the stroke of the piston, as shown in figure 101.

Question 186. Why is it that the centres of the eccentrics are not placed opposite to each other on the axle?

Answer. Because before the beginning of the stroke of the piston it is necessary to move the valve from its middle position a distance equal to the lap before the steam-port begins to open. If we have a valve like that shown in fig. 10—that is, without any lap—the centres of the eccentrics could be placed at right angles, or, as mechanics say, “square” with the crank, as was shown in fig. 11, and exactly opposite to each other, because such a valve begins to take steam as soon as it moves from the middle of the valve-face. If, however, we have a valve like that shown in fig. 27, it is plain that before it will admit or take steam, as it is called, in either of the steam-ports, it must be moved from the centre of the valve-face, or its middle position, a distance equal to the lap, L. For this reason, therefore, the eccentric, instead of being placed at half-throw,[49] as it is called, must be so far ahead of the middle position as to have moved the valve a distance equal to the lap, and if any lead is given to the valve, equal to the lap and lead together. In figs. 100 and 101, f g is a vertical line at right angles to the crank at the beginning of the stroke. It will be seen that the centre of each of the eccentrics is set far enough ahead of this line to give the valve the required lead. When the piston reaches the back end of the cylinder, the two eccentrics will occupy the position shown in fig. 102, in which position the lower one would move the valve so as to turn the crank in the direction of the dart N, and the upper one in the reverse direction. It will be seen that in this position both of the eccentrics are again ahead of half-throw, when the piston is at that end of its stroke.

Question 187. How is the motion of either eccentric communicated to the valve?

Answer. The ends of each pair of eccentric-rods are connected together by a link, a b, fig. 103. This link has a curved groove or slot, a b, in it, in which a block, B, fits accurately, so that it can slide freely from one end to the other. This block is attached to the lower rocker-arm by a pin, c, which works freely in the block. The two eccentric-rods C and D are attached to the ends of the link at e and f by pins and knuckle-joints. It is apparent that if the link is down, or in the position shown in fig. 103 and also on a smaller scale in fig. 104, the motion of the upper eccentric-rod, which is usually used for the forward motion, will be imparted to the rocker, and thus to the valve, and when the link is in the position shown in fig. 105, that the valve will be moved by the lower or backward eccentric-rod B. In order to reverse the engine, it is then only necessary to provide the means of raising and lowering the links. This is done by a shaft, A, fig. 103, called a lifting-shaft, which has two horizontal arms, E,[50] one for each link, and a vertical arm, F. The links are suspended from the ends of the horizontal arms by rods or bars, g h, called link-hangers, which are connected to the links and to the arms above by pins, which enable the hangers to vibrate freely. The lower pin is attached to a plate, L d, called a link-saddle, which is bolted to the link. The vertical arm of the lifting-shaft is connected by a rod, G G, called the reverse-rod, to a lever O, O, Plate II. in the cab called a reverse-lever, the construction of which will be explained hereafter. This lever is worked by the locomotive runner, and by moving the upper end of it forward, the link will be lowered, and the rocker and valve will be moved by the forward eccentric; and if the reverse-lever is moved back, the link will be raised, and the backward eccentric will move the valve. When this is done, the valve-gear is said to be thrown into the forward or backward motion, or forward or back gear.

Question 188. How is the travel of the valve changed by the motion of the link?

Answer. By either raising or lowering the link, so that the link-block and rocker-pin will be some distance above or below the eccentric-rods. Thus in fig. 104, the motion of the upper eccentric-rod, and in fig. 105 that of the lower or back eccentric-rod is communicated to the rocker-pin and the valve. If, however, the link should be raised so that the link-block and rocker-pin are somewhat below the upper or forward eccentric-rod, as shown in fig. 106, then the motion imparted to the rocker and valve will partake somewhat of that of the upper and also of the lower eccentric-rod. So long as the rocker-pin is above the centre of the link, the motion of the valve will partake most of that of the upper or forward rod, and the engine will then run forward, but when the rocker-pin is below the centre of the link, its motion will be influenced more by the back eccentric-rod, and the engine will then run backward.

The motion of the link, which is somewhat complex and difficult to understand clearly, will perhaps be understood better if we represent it in a number of successive positions of the whole stroke of the piston, as was done to show the motion of the eccentric in figs. 11 to 24. We will therefore suppose that the link is in what is called full gear forward, as shown in figs. 103 and 104. In fig. 108 the link is in the position it would occupy at the beginning of the stroke of the piston; in fig. 109 it is in that which it will be in when the piston has moved four inches; in fig. 110, when it has moved eight inches; in fig. 111, twelve; and in figs. 112, 113 and 114, sixteen, twenty and twenty-four inches. Figs. 114 to 119 represent the successive positions of the link during the return stroke. In order to show the different positions of the link we have represented on a larger scale, in fig. 120, the successive positions of the centre line of the link, which will indicate the motion imparted by it to the rocker. In order to designate each of these positions, the centre lines in fig. 120 are numbered + and -0, 4, 8, etc., etc., to correspond with similar numbers in figs. 108 to 119.

Thus the line -0 -0 represents the position of the centre of the link which it occupies at the beginning of the stroke as shown in fig. 108. The line -4 -4, that represented by fig. 109, when the piston has moved 4 in. The lines -8 -8, -12 -12, -16 -16, -20 -20, 24 24, +4 +4, etc., the successive positions of the centre of the link represented in figs. 108 to 119. The dotted lines h a and h b represent the two extreme positions into which the rocker-arm would be moved by the action of the link. It will be seen that when the link is in the position shown, it imparts the full stroke of the eccentrics to the rocker-pin and consequently to the valve. We will now suppose that the link is raised up as shown in fig. 106, so that the position of the rocker-pin is just half-way between the end of the eccentric-rod and the centre of the link. This position is called half-gear. In fig. 121 the different positions of the centre line of the link and of the rocker have been laid out for half-gear in the same way as was done for full-gear before. From this it will be seen that the travel, a b, imparted to the rocker-pin and valve by the link when it is in the position shown, instead of being 5 in. is only 3¹⁄₂ in. In fig. 107 the link is raised up, so that the rocker-pin is in the centre of it or midway between the eccentrics. This position is called mid-gear. The successive positions of the centre line of the link in this position have been laid down in fig. 122 in the same way as was done for full and half-gear. The movement of the rocker, it will be seen, is, for mid-gear, only 2¹⁄₂ in. These diagrams show that when the rocker-pin is opposite the eccentric-rod, the valve receives the full throw of the eccentric, and that the motion imparted by the eccentric diminishes as the rocker-pin approaches the centre of the link, so that, with eccentrics having 5 in. throw and a valve with ⁷⁄₈ lap and ¹⁄₈ in. lead, we can increase or diminish the travel of the valve from 2¹⁄₂ to 5 in. by simply raising or lowering the link, which is done by the reverse-lever.

Question 189. What is the effect of this variation of travel on the working of the valve and the admission and release of steam to and from the cylinder?

Answer. It is almost precisely the same as that which is effected by increasing or diminishing the throw of the eccentric, which was explained in the answer to Question 52. In order to show this effect more clearly, we have represented by motion-curves,[51] fig. 123, the movement imparted to the valve by the link when it is in full, half and mid-gear, as illustrated in the preceding figures. The curve for full-gear is engraved in full heavy lines; that for half-gear in lighter lines, and for mid-gear in dotted lines. From these curves it will be seen that when the valve is worked in full-gear the steam-port is opened wide at 2 in. of the stroke and steam cut off at 21 inches. When the valve is worked in half-gear the port is not at any time opened wide and steam is then cut off at 17¹⁄₂ in. of the stroke, and when worked in mid-gear the greatest opening of the steam-port is no greater than the lead and the cut-off occurs at 4 inches of the stroke.

It is of course possible to work the link in any intermediate position between those which we have represented. Usually the reverse-lever is arranged so that the steam will be cut off at 6, 8, 10, 12, 15, 18, and 20 inches of the stroke.

Question 190. What is the greatest and the least admission of steam possible with the ordinary link motion?

Answer. With 24 in. stroke of piston and 5 in. travel and ⁷⁄₈ in. lap, steam can be admitted as shown by the motion-curves during 21 in. or 87¹⁄₂ per cent. of the stroke, and can be cut off at about 4 in. or 16²⁄₃ per cent. It will be seen, however, that in mid-gear the motion-curve becomes a straight line, and that the pre-admission of steam, that is the admission of steam before the piston reaches the end of the stroke, is equal to that admitted after, so that it is impossible to work the locomotive with the link in that position. Practically it is found that no useful work can be done with a link if the steam is cut off at less than six inches, or one-fourth of the stroke. Even then the opening of the steam-ports is so small that the steam which enters the cylinders is very much wire-drawn.

Question 191. How are the curves drawn which represent the motion of the valve?

Answer. These motion-curves as produced by the link-motion are very difficult to draw, as the motion of the link is extremely complicated. It is doubtful, therefore, whether those who have no knowledge of mechanical drawing will be able to understand the following description of the method of doing it, which we will try to make as clear as possible.

In the first place, the centre S, fig. 124, of the axle, A, of the rocker, and B of the lifting-shaft, must be laid down in their proper positions. If, now, the valve has ⁷⁄₈ in. lap and ¹⁄₈ lead, the lower rocker-pin must be one inch ahead of its middle position when the piston is at the front end of the cylinder, and at the beginning of the backward stroke. We will, therefore, mark the centre, a, of the rocker-pin in this position. If from the centre of the axle a circle, c d e, be drawn whose diameter is equal to the throw of the eccentrics, this circle will represent the path in which the centres of the eccentrics will revolve. If, now, the distance from the centre of the axle to the centre of the lower rocker-pin, a, when the latter is in its middle position, be taken for a radius,[52] and from the position of the rocker-pin at the beginning of the stroke as a centre, the circle representing the path of the eccentrics be intersected at two points, c and d, the points of intersection will represent the positions of the centres of the forward and backward eccentrics. Having determined these positions, draw arcs of circles, f and g, from these centres with a radius equal to the distance from the centres of the eccentrics to the centres of the pins which connect the rods to the link. It is evident that at the beginning of the stroke the centres of the pins in the link must each be in one of these arcs. But the link is suspended by the hanger, i h, which oscillates from the end, i, of the lifting-arm, which for any one point of cut-off is stationary; and therefore the point of suspension of the link must always be in the arc, j k, described from the centre of the pin, i, in the lifting-arm, with a radius equal to the length of the hanger. There are, therefore, three points in the link, each of which must be in one of the arcs which have been drawn, and which will determine the position of the link. This can be done easiest by drawing the link, L, fig. 125, on a stiff piece of paper, m n, and cutting off the back, p q, of it through the centres of the pins, s and t, and also cutting out a triangular piece, u, the apex of which will correspond with the centre of the point of suspension, o. By placing this piece of paper on the drawing it can be moved, so that the three centre points, s, t and o, will respectively conform with the arcs, f g and j k, fig. 124. In this position the piece of paper will then be in the position of the link for the point of the stroke represented. By marking the centres of the link-pins on the arcs f and g, and from them as centres, with the length of the rods used to draw the arcs, two other arcs, v, w, be drawn intersecting each other, the point d, where they intersect will be the centre from which the centre line of the link can be drawn with a radius, l d, equal to the distance from the centre of the eccentrics to the centre of the link. This will give the first position -o -o, of the centre line of the link. As the rocker-pin must always be in the centre of the link, it is obvious that the point at which the centre-line of the link intersects the arc in which the rocker-pin oscillates must be the position of the centre of the rocker-pin. With this determined the position of the valve can easily be located.

In order to represent the link at any other point of the stroke, say after the piston has moved four inches, the position of the crank must first be laid down. To do this, allowance must be made for the irregularity due to the angularity of the connecting-rod, which was explained in answer to Question 54. From the centre of the axle, a circle, C D, whose diameter is equal to the stroke of the piston, is first drawn, which will represent the path of the crank-pin. A horizontal centre line, E F, should also be drawn through the centre of the axle and the centre of the cylinder. The intersection o of this line with the path of the crank-pin will be the position of the latter at the beginning of the stroke. If from this point a distance, o o, be laid off on the centre line equal to the length of the connecting-rod,[53] it will give the position of the wrist-pin at the beginning of the stroke, so that from this its successive positions for each inch of the stroke can be laid off. From its position after the piston has made say four inches of the stroke as a centre, and the length of the connecting-rod as a radius, if the path of the crank-pin be intersected at -4, the point of intersection will represent the position of the crank-pin at four inches of the stroke. The distance from o to -4 is equal to 44 degrees of the whole circle. The eccentrics, being attached to the axle, of course move the same number of degrees that the crank does, and therefore, in order to determine their position when the crank has moved any distance, it is only necessary to move them as many degrees as the crank has. This can be done very easily by extending the radii of the eccentrics, when they are in the first position, until they intersect the path of the crank-pin at c′ and d′. By stepping off from the latter points of intersection a distance c′ c‴ and d′ d‴, equal to o -4, which the crank has moved, and then drawing other radii from the two points c‴, d‴, their intersection, c″ d″, with the path of the eccentrics will represent the position of the centres of the eccentrics when the crank is at -4. Having determined the position of the eccentrics, the link can be laid down as before, that is, from c″ and d″ as centres and with the length of the eccentric-rods as a radius arcs, f″ and g″, are drawn. Then with the paper template the positions of the centres of the link-pins in these arcs are determined and marked, and from them with the length of the eccentric rods as a radius, two intersecting arcs, v″, w″, are drawn, whose intersection gives the centre of the link from which its centre line, -4 -4, is drawn. This will give the position of the rocker-pin for another point of the stroke. In a similar manner its position can be determined for any number of points of the stroke, from which the position of the valve can easily be determined and laid down on the diagram for the motion-curve as was described in the answer to Question 44. Of course the valve will be moved from its middle position the same distance that the rocker-pin is,[54] only in an opposite direction. In order to lay down the position of the valve on the diagram for motion-curves, it is, therefore, only necessary to draw it in the same relative position as that of the rocker-pin which is given by the point of intersection of the center line of the link with the path in which the rocker-pin oscillates. To construct the motion-curves it is necessary to determine the positions of the valve for different points of the stroke and mark them on the horizontal lines which represent the respective positions of the piston. Curves are then drawn through these points, either by hand or by constructing templates. The more points there are determined, the more accurate will be the curves. It is, therefore, best to lay down the position of the valve for each inch of the stroke of the piston. They should also be drawn full size, which of course was impossible for the illustrations which are given herewith.

Question 192. Is there any other method of drawing these motion curves?

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.

In using this instrument, however, it is impracticable to attach a board to the inside of the cross-head, and it must therefore be fastened to the outside. The horizontal arm E should be made of thin steel, so as to form a spring. The end has a small boss[55] with a hole in it ³⁄₁₆ of an inch in diameter. This hole has a screw thread cut in it, into which an ordinary hard drawing pencil is screwed. The spring is so arranged that the pencil will not be in contact with the board unless it be pressed against it. The locomotive is then placed on a smooth piece of track with steam on and run very slowly, so that a person walking alongside can press the pencil against the surface of the board, which should be covered with drawing paper. By watching the cross-head when it reaches the end of the stroke, the pencil can then be pressed against the paper and kept in contact through the whole stroke and instantly released when the motion-curve is completed. The link can then be placed in another position, and thus any number of curves can be drawn, which will furnish the most accurate means of analyzing the motion of the valve.

In practice it is best not to draw the lines which represent the edges of the ports, until after the curves are drawn and the paper removed from the board. A centre line must, however, be drawn on the engine from which to lay off the ports. This can be done by placing the valve in its middle position, and then fastening the shaft F in that position with a nut which should be provided for that purpose on the end of the shaft. After it is fastened in this position, detach the connecting-rod H, and with one stroke of the piston a centre line can be drawn with the pencil P. From this centre line the edges of the ports can easily be laid off and drawn on the paper after it is taken off the engine.

Question 193. Can the position of each edge of the valve, with any given amount of travel, be shown in its relation to the ports by one motion-curve, or is it necessary to draw such curves for each edge of the valve, as shown in fig. 28?

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.

If now we want to represent the motion and relative position of the back steam edge of the valve in relation to its port, it is only necessary to assume that the line t represents that edge, and that the curve h i j k l m n o h represents its motion, and to draw the back steam-port in its proper relation to it. When the valve is in its middle position, as shown in fig. 27, the outside edge of the port h is ⁷⁄₈ in., or a distance equal to the lap, from the steam edge q of the valve. As the center line a b, fig. 127, represents the middle position of the edge of the valve, it is only necessary to draw a line, n n′, ⁷⁄₈ in., or the same distance from the centre line a b that the outer edge of the port d is from q in fig. 28, to represent this edge of the port in fig. 127, and another b b′, at a distance from the former equal to the width of the port, to represent its inner edge. A line, q, below the line 0 24, will represent the edge of the valve at the beginning of the forward stroke. The curves in relation to the port d will then show the motion of the valve in relation to this port, in the same way that the dotted curve d f does in fig. 28.

If it is desired to represent the motion of the exhaust edge h′, fig. 28, of the valve, it is only necessary to imagine that the line t, fig. 127, represents that edge, and then draw in the port d in the same relation to it that it bears to the edge h′, in fig. 28. This has been done in dotted lines, c c′ and e e′, in fig. 127.

If the reader will cut a paper section of a valve like that shown in fig. 27 and place the different edges, h, i, h′ and q, so that they will successively correspond with the line t in fig. 127, the diagram will perhaps be more clear. If, for example, the paper section be placed to the right of the line t, so that the edge h will correspond with t, then it will be seen that the port c occupies the same relation to it that it does in fig. 28. If the valve be placed to the left, so that the edge q corresponds with t, then the port d will be in the same relation to it that it has in fig. 28. If the edges i and h′ be made to correspond with t, then the ports drawn in dotted lines in fig. 127 will represent the ports c and d in fig. 28.

The position of the ports in relation to the centre line of the motion-curve can be determined, if it is kept in mind that the centre line a b, fig. 127, represents the position of the different edges of the valve when the latter is in the middle of the valve-face as shown in fig. 27, and that the ports must be on the same side, and the same distance from the centre line that they are from the edge of the valve whose motion is represented. Thus if the movement of the steam edge h in relation to its port, c, was represented, the edge of the latter must be drawn on the motion diagram the same distance from the centre line that it is from h when the valve is in its middle position as shown in fig. 27. This distance is of course just equal to the lap of the valve. If the motion of the exhaust edge h′ was represented in relation to the steam port d, then the inside edge of the latter would be drawn the same distance from the centre line a b in the diagram that the inner edge of the port is from the edge h′ of the valve, which is equal to the inside lap. The exhaust port could also be drawn in the same way, but it would be liable to confuse a diagram made to so small a scale as that which has been employed for the accompanying illustrations, and it has therefore been omitted. Diagrams of this kind which are made full size will, of course, show the movement of the valve more distinctly than is possible in the space occupied by the illustrations herewith. When they are made of full size, the lines indicating the ports should be drawn of different colors, so as to distinguish them from each other easily. Such diagrams will show the position of the valve in relation to the ports, and indicate the distribution of the steam during the whole stroke. It is only necessary to refer the curve to the proper line to determine the position of the valve in relation to either of the ports for either the admission or release of the steam. If, for example, we want to observe how the admission of steam is governed by the valve, by referring to fig. 127 we see that at the beginning of the backward stroke the valve has ¹⁄₁₆ inch lead; that at 1³⁄₄ inches of the stroke the port c is wide open, as shown by the intersection of the motion-curve with the line m m′; that the valve has received its maximum backward travel at 9 inches of the stroke, and begins to close the port at 15¹⁄₂ inches, and completely closes it at 21 inches of the stroke. By referring the motion-curve to the lines n n′ and b b′, we see that the valve as shown by the line q at n′ again has ¹⁄₁₆ inch lead at the beginning of the forward stroke; that the steam port is wide open at 1³⁄₈ inches of the stroke; begins to close at 16¹⁄₄ inches, and is completely closed at 21 inches. By referring the curve to the lines e e′ and c c′ we see that the front port begins to open to the exhaust before the piston has completed its forward 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.