Cornell XHntverstt^ 
 
 Xibrar^ 
 
 OF THE 
 
 mew IPorft State College of agriculture 
 
 J\cj..3k3n,:a^. 
 
Cornell University Library 
 TJ 545.H19 
 
 Slide valve gears; an explanation of the 
 
 3 1924 001 075 047 
 
Cornell University 
 Library 
 
 The original of tliis book is in 
 tine Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924001075047 
 
SLIDE VALVE 'GEA'RS.v 
 
 ^A^ EXPLANATION OF THE ACTION AND '/ 
 CONSTRUCTION OF PLAIN AND ' 
 
 CUT-OFF SLIDE VALVES. •^iS'X. 
 
 
 ■s-^f'" 
 
 BY 
 
 FREDERIC A. HALSEY, 
 
 ENGINEER OF THE RAND DRILL COMPANY; 
 
 Member of the American Society op Mechanical Engineers : Member of 
 
 THE American Institute of Mining Engineers ; Graduate 
 
 OF THE Sibley College, Cornell University. 
 
 analsBis \fs tSe asilgram JSiasram 
 
 NEW YORK : 
 D. VAN NOSTRAND COMPANY, 
 
 23 Murray and 27 Warren Streets. 
 i8g6. 
 
Copyright, 1889, 
 
 BY 
 
 L), VAN NOSTEAND CoMPAHft 
 
TO 
 
 iProfeeeor Jobu E. Sweet, 
 
 TO HAVE BEEN WHOSE PUPIL I CONSIDER ONE OF THE 
 
 GREATEST PRIVILEGES OF MY LIFE, 
 
 THIS LITTLE VOLUME IS GRATEFULLY INSCRIBED. 
 
PREFACE. 
 
 This work has been prepared to meet what the author 
 considers a real want. It has been written with the aim 
 of making it intelligible to any one who might be will- 
 ing to make a serious effort to understand it. High 
 authority exists for a mathematical treatment of the 
 subject, but with this the author has no sympathy. 
 Designing a valve gear is essentially a drawing board 
 process, and a mathematical treatment of it is' simply 
 an uncalled for use of heavy artillery. The graphical 
 treatment is therefore adopted throughout. 
 
 Acknowledgment is due to Mr. Hugo Bilgram for 
 his courtesy in kindly permitting the use of his valve 
 diagram. The author has all due respect for the Zeu- 
 ner diagram, but that respect is not incompatible with 
 the conviction that Mr. Bilgram's method is a marked 
 improvement upon it. Valve diagrams are used for two 
 purposes — to analyze existing valve motions and to de- 
 sign new ones. The Zeuner diagram fulfils the first pur- 
 pose perfectly, but is unsatisfactory when applied to 
 the second. The leading data that are given in design- 
 ing a valve motion are the point of cut-off, the port open- 
 ing, and the lead of the valve (not the lead angle of the 
 crank, as is often conveniently assumed). It is the radi- 
 
 ili 
 
IV PREFACE. 
 
 cal defect of the Zeuner diagram that none of these di- 
 mensions can be laid off from known points. The lead 
 must be laid off from an unknown point of the centre 
 line, and the port opening from an unknown point on 
 an unknown line. Finally, through these unknown 
 points and the centre of the shaft the valve circle is to 
 be drawn from an unknown centre and with an unknown 
 radius. Under these circumstances the result sought 
 is found only through blind trial. With Mr. Bilgram's 
 method all this is changed. The lead is laid off from a 
 fixed line, the port opening from a fixed point, and the 
 cut-off position of the crank is located. The lap circle 
 is then drawn tangent to these lines, and the problem 
 is solved. Moreover, the awkward conception of the 
 backward rotation of the crank is obviated. Finally, 
 these marked advantages are not accompanied by any 
 compensating disadvantages whatever. 
 
 Acknowledgment is also due to the American Ma- 
 chinist for the use of a number of engravings originally 
 prepared to illustrate some of the author's articles in 
 that paper. 
 
 The irregularities due to the connecting rod introduce 
 peculiar difficulties into the study of the first principles 
 of the slide valve, which difificulties were first overcome 
 by the happy expedient of using the slotted cross-head 
 instead of the connecting rod in the preliminary study. 
 For this, together with many other original and highly 
 valuable contributions to the subject, we are indebted 
 to Mr. W. S. Auchincloss, who first published them in 
 his well-known and standard work entitled Link and 
 Valve Motions, to which those who wish to prosecute 
 their studies beyond the scope of this work are referred. 
 
PREFACE. V 
 
 The author has gone more fully than is customary 
 into the methods of equalizing the various events of 
 the stroke. The sections relating to these methods 
 will be found more difficult to follow than the others, 
 while at the same time they form no necessary part of 
 a general treatment of the subject. Those who be- 
 gin their studies of valve motions with this book, may 
 find these chapters too difficult for the first reading. 
 They have, therefore, been marked with a star (*) in the 
 Table of Contents and in the body of the book, in order 
 that they may be omitted, if desired, in the first reading; 
 and it should be understood that the chapters not so 
 marked form of themselves a complete connected trea- 
 tise, of a more elementary character than the book as a 
 whole. 
 
 Philadelphia, Oct. ig, 1889. 
 
TABLE OF CONTENTS. 
 
 The chapters with an asterisk (*) prefixed may be omitted in the first reading 
 without brealdng the continuity of the subject. 
 
 PART I. 
 The Slide Valve with Fixed Eccentric. 
 
 PAGE 
 
 The Plain Slide Valve 3 
 
 The Eccentric 4 
 
 The Scotch Yoke or Slotted Cross-head, ..... 5 
 
 The Primitive Engine, ........ 7 
 
 Defects of the Primitive Engine 13 
 
 Lap, . , 15 
 
 Angular Advance, 18 
 
 Lead, ,...,..,,... 21 
 
 Exhaust Lap, .......... 25 
 
 Backward Rotation, ......... 26 
 
 The Bilgrara Diagram, ........ 28 
 
 Laying out the Slide Valve, ....... 38 
 
 * Velocity of the Valve, ........ 39 
 
 Limitations of the Plain Slide Valve, 40 
 
 The Areas of the Ports and Pipes, 42 
 
 * The Angular Vibration of the Connecting Rod, ... 45 
 
 * " " " " Eccentric Rod, .... 49 
 
 * Equalized Exhaust, 50 
 
 * Equalized Cut-off, 54 
 
 Setting the Slide Valve, 59 
 
 vii 
 
VIU TABLE OF CONTENTS. 
 
 PART II. 
 The Slide Valve with Shifting and Swinging Eccentric. 
 
 PAGE 
 
 The Slide Valve at Short Cut-off, 67 
 
 * Equal Lead and Constant Lead, 77 
 
 The Shifting Eccentric 78 
 
 The Swinging Eccentric 80 
 
 * The Angularity of the Eccentric Rod, ..... 85 
 
 * Equalized Lead, 8g 
 
 * Equalized Lead and Cut-off, 95 
 
 PART III. 
 
 The Slide Valve with Independent Cut- off. 
 
 Introductory Remarks loi 
 
 The Gonzenbach Valve Gear 102 
 
 The Meyer Valve Gear, ........ 109 
 
 The Buckeye Valve Gear, 116 
 
 The Straight Line Independent Cut-off Valve Gear, . . . 120 
 
 The Bilgram Valve Gear, 122 
 
PART I. 
 
 THE SLIDE VALVE WITH FIXED 
 ECCENTRIC. 
 
The Slide Valve with Fixed Eccentric. 
 
 THE PLAIN SLIDE VALVE. 
 
 Fig. I is a sectional view of a plain slide valve and 
 its seat, the valve being shown in its central position, 
 with the ports completely covered by it. The distance 
 
 Fig.l 
 
 a, by which the valve extends beyond the steam edge 
 of the port, is called the outside lap, steam lap, or more 
 usually, simply lap of the valve. The distance b, by 
 which it extends beyond the exhaust edge of the port, 
 is called the inside lap or exhaust lap.* The exhaust 
 
 *As will be more fully shown later on, valves are sometimes so made 
 that the steam is admitted by the inside and exhausted by the outside 
 edges. Hence the terms inside and outside lap are somewhat am- 
 biguous. The terms steam lap and exhaust lap avoid this ambiguity, 
 and are to be preferred. 
 3 
 
4 SLIDE VALVE GEAIiS. 
 
 lap is always much smaller than the steam lap. It is 
 frequently absent, and frequently the exhaust edge of 
 the valve does not reach the exhaust edge of the port, 
 being made as shown by the dotted lines. In that 
 case the distance c is usually called inside clearance, 
 though a better name is negative inside or exhaust lap. 
 It is sometimes called inside lead or exhaust lead ; but 
 these terms should not be applied here, as they have 
 properly another definite meaning, which will be ex- 
 plained farther on. The measurement for both steam 
 and exhaust lap is made for one end of the valve only. 
 Thus if a valve is said to have f inch lap, the meaning 
 is that it has that much at each end. 
 
 THE ECCENTRIC. 
 
 The slide valve is usually driven by means of an eccen- 
 tric on the crank shaft, and it becomes necessary at the 
 outset to obtain a clear conception of the motion which 
 the eccentric gives. In brief, the eccentric is a short 
 crank with a large crank pin. It is obvious that the 
 motion of,,juGfess-kead_ would not be changed by in- 
 creasing the size of the crank pin. If a crank pin were 
 enlarged until the crank shaft came within the cir- 
 cumference of the pin, the result would be an eccen- 
 tric. The arm of a crank is the distance from the 
 centre of the shaft to the centre of the crank pin, and 
 similarly the " throw" of an eccentric is the distance 
 from the centre of the shaft to the centre of the eccen- 
 tric disc. Usually the centre of the disc is within 
 the circumference of the shaft ; but this does not alter 
 
THE SCOTCH YOKE OR SLOTTED CROSS-HEAD. S 
 
 the nature of the device, which remains simply a short 
 crank with a large crank pin. 
 
 THE SCOTCH YOKE OR SLOTTED CROSS-HEAD. 
 
 The usual method of connecting the cross-head to 
 the crank pin by means of a connecting rod introduces 
 certain distortions and irregularities into the relative 
 motions of the piston and crank. These will be more 
 fully explained farther on, but it is desirable in the 
 first instance to avoid the necessity for considering 
 them, as they greatly complicate the subject. This is 
 accomplished by considering in the first instance an 
 engine having the piston and crank connected by 
 means of the device called the Scotch yoke or slotted 
 cross-head, since that connection is without the distor- 
 tions mentioned.* As has been explained, the eccen- 
 tric is essentially a crank ; and it follows that the dis- 
 tortions which are introduced by the connecting rod 
 into the motions of the piston and crank, are also in- 
 troduced by the eccentric rod into the motions of the 
 valve and eccentric. The reasons which lead to the 
 adoption of the slotted cross-head in place of the con- 
 necting rod also require its use in place of the eccen- 
 tric rod. An engine fitted with slotted cross-heads is 
 illustrated in Figs. 2-ii. The slotted cross-head will 
 be recognized at once, and is too familiar a device to 
 need further description. 
 
 * The slotted cross-head is employed here with the permission of 
 Mr. W. S. Auchincloss, to whom the thanks of the author are due. 
 
6 
 
 SLIDE VALVE GEARS. 
 
 
7'HE PRIMITIVE ENGINE. 7 
 
 THE PRIMITIVE ENGINE. 
 
 When illustrating the action of the valve of a steam 
 engine, it is essential for clearness that the valve be 
 shown on the top of the cylinder. A valve so located 
 in an actual engine would require the use of a rock 
 shaft to communicate the motion of the eccentric rod 
 to the valve rod — a construction which finds use in. 
 American locomotives. This rock shaft complicates 
 the action of the parts, and it is desirable in this pre- 
 liminary work to avoid it. To accomplish this the 
 unmechanical arrangement of Figs. 2-11 is adopted. 
 
 Figs. 2-6 represent the primitive engine with the 
 parts in a number of successive positions. The valve 
 has no lap on either steam or exhaust side, and the 
 eccentric is set at right angles to the crank, and in ad- 
 vance of it in the direction of the rotation. The ec- 
 centric, being in fact a crank, is represented as such, 
 and the valve is driven from it by a slotted cross-head, 
 which is secured to the valve stem by the bracket 
 shown. In Figs;.3'f6;the slotted cross-heads are rep- 
 resented by their centre lines only, for greater clearness 
 and simplicity. 
 
 Referring to Fig. 2, the crank is on the " centre," 
 and the parts are ready to begin movement, the direc- 
 tion of rotation being as shown by the arrow. In Fig. 
 3 the crank shaft has turned through an angle of forty 
 five degrees, carrying the parts to the positions shown. 
 Considering Figs. 2 and 3, it is clear that the first move- 
 ment of the crank shaft carried the valve to the right, 
 and thereby opened port x to steam and y to exhaust. 
 Opening port x admitted steam behind the piston to 
 
SLIDE VALVE GEARS. 
 
THE PRIMITIVE ENGINE. 
 
IC lO 
 
 SLIDE VALVE GEARS. 
 
THE PRIMITIVE EMGINE. II 
 
 drive it forward, and opening y enabled the stearti 
 which previously filled the space in front of the piston 
 to escape to the cavity s, which communicates through 
 the exhaust pipe with the atmosphere or condenser, as 
 the case maybe. In Fig. 4, the crank shaft has turned 
 through an additional angle of forty five degrees, bring- 
 ing it at right angles to its initial position. The pis- 
 ton is now at the centre of its travel, and the valve at 
 its extreme right hand position. As the rotation con- 
 tinues, the piston continues to advance ; but the valve 
 reverses its motion, and gradually closes its ports, until 
 when the crank completes a half revolution, as shown 
 in Fig. 5, the valve reaches its middle position at which 
 it stood in Fig. 2, with all ports closed. Continuing 
 the motion, the valve is carried to the left, opening 
 port y to steam and x to exhaust, as shown in Fig. 6, 
 and the piston is driven back to its original position ; 
 and this sequence of operations will obviously continue 
 indefinitely. 
 
 With the eccentric located as in the figures, the di- 
 rection of rotation must be as described. This will be 
 apparent if, starting with Fig. 2, rotation in the opposite 
 direction be imagined. The effect of this would be to 
 open port x to exhaust and j/ to steam, thereby effectu- 
 ally stopping the rotation in the direction imagined. 
 To effect this reverse rotation the eccentric must be 
 located diametrically opposite to the position shown in 
 the figures.* The student should satisfy himself of 
 
 * This is true with the primitive form of valve only. With valves 
 having lap, as actually used, the eccentric position for reverse rota- 
 tion is not diametrically opposite from the position required for for- 
 ward rotation. This subject will be referred to again. 
 
tii 
 
 ^LiDE Valve dEARS. 
 
DEPECfs OP THE PliiMiTivE eMginE. i5 
 
 the correctness of this fact by supposing the eccentric 
 so located, and then following the' motion through a 
 revolution. 
 
 Throughout this book, whether shown or not, it will 
 be understood that tht cylinder is located as in the 
 figures already explained, i.e., to the left of the shaft ; 
 and unless otherwise specified, that the direction of 
 rotation is the same as in these figures, i.e., " over." 
 
 DEFECTS OF THE PRIMITIVE ENGINE. 
 
 With the construction of Figs. 2-6 the opening and 
 closing of the ports are coincident with the passing of 
 the centre by the crank. Economy of steam and suc- 
 cessful running require that the following changes be 
 made in this distribution of the steam : 
 
 I. The opening of the steam port or "admission" 
 should occur slightly before the crank reaches the cen- 
 tre.* In a general sense this is called giving the valve 
 steam lead or simply lead. In a more strict sense, that 
 term means the width of opening in fractions of an 
 inch which the valve has given to the steam port at the 
 instant the crank passes the centre. 
 
 II. The closing of the steam port or " cut-off " should 
 occur a good deal before the crank passes the centre. 
 
 III. The opening of the exhaust port or "release," 
 
 * Of late years a difference in practice has arisen in this respect. 
 Some makers now set their valves to open the port just as the crank 
 passes the centre, and in some cases the admission is delayed until 
 after that event. The statement in the text, however, represents 
 general practice. This subject will be referred to again farther on. 
 
u 
 
 ^LIDE VALV£ GEARS. 
 
 i? 
 
 /^' 
 
LAP. IS 
 
 and its closing or " compression," should occur earlier 
 than the opening of the steam port, but not so early as 
 its closing. As the width of port opening to steam as 
 the crank passes the centre is called steam lead, so the 
 width of opening to the exhaust at the same instant is 
 called exhaust lead or inside lead (compare page 4). 
 
 These changes in the steam distribution are brought 
 about by two changes in the valve gear : (1.) The valve 
 is given lap, and (II.) The eccentric is advanced on the 
 shaft ahead of the position given. 
 
 LAP. 
 
 Fig. 7 is a reproduction of Fig. 2, with the addition 
 of outside or steam lap to the valve. There is no' 
 change in the exhaust side of the valve nor in the 
 angular position of the eccentric, and it is obvious that 
 the ports will be opened and closed to the exhaust as 
 the crank passes the centre exactly as before ; but the 
 port X will not be opened to steam until the valve has 
 been carried to the right an amount equal to its lap. 
 
 This will happen as shown in Fig. 8, when the shaft 
 has turned through an angle def, such that df, or what 
 is the same thing, eg, is equal to the lap. This angle 
 def is called the lap angle. The valve opens port x to 
 steam when the edge of the valve passes the edge of 
 the port going to the right, and it closes it when the 
 edge of the valve passes the edge of the port going to 
 the left. The position of the valve is the same at clos- 
 ing as at opening, the only difference between the two 
 acts being in the direction of the valve's motion ; con- 
 
i6 
 
 SLIDE VALVE GEARS. 
 
LAP. 
 
 i; 
 
l8 SLIDE VALVE GEARS. 
 
 sequently the port must close with the eccentric at h, 
 vertically below _/", as shown in Fig. 9. From this, two 
 important and fundamental facts can be learned : 
 
 I. During the time that steam was being admitted 
 the eccentric (and with it the shaft and crank) turned 
 through the angle fch. Now feh is equal to a semi- 
 circle less def and less hei^ that is, a semicircle less twice 
 the lap angle, and this is the first result of the addition 
 of lap to the steam side of the valve. During the 
 admission of steam the crank turns through an angle 
 equal to a semicircle less twice the lap angle. 
 
 IJr4a-thc case of the pr-ifrntive Vahre of Figs. 2-6, the 
 port began to open with the eccentric in the position of 
 Fig. 2. It attained its greatest opening in the position 
 of Fig. 4, and the maximum width of port opening was 
 equal to the throw of the eccentric. With the valve of 
 Figs. 7-9, however, the port does not begin to open 
 until the eccentric reaches the point f, and the remain- 
 ing travel gk only is available as port opening. This 
 width of opening, ^^, is equal to ek less eg, that is, to 
 the throw of the eccentric less the lap of the valve ; and 
 it follows at once that if a valve with lap is to give the 
 same port opening as another without lap, the eccentric 
 throw of the former must exceed thaf of the latter, and 
 the greater the lap the greater must be the throw. 
 
 ANGULAR ADVANCE. 
 
 The last section has shown how, by the addition of 
 lap, the period of port opening may be shortened as 
 desired. While, however, the method of regulating 
 
ANGULAR ADVANCE. I9 
 
 the length of period of port opening was pointed out, 
 nothing was said about properly timing the opening 
 or closing of a valve having lap with reference to the 
 position of .the piston, and in point of fact in Fig. 8 
 the port opening to steam occurred long after the 
 crank had passed the centre. The correct timing of 
 the events of the stroke,- and especially of the admis- 
 sion of steam, is obtained by advancing the eccentric 
 around the' shaft from the position thus far shown. 
 In order to give admission to the steam at the instant 
 the crank passes the centre, it is necessary to first 
 locate the crank on the centre, then to advance the 
 eccentric around the shaft such an amount as to 
 draw the valve to the right a distance equal to the 
 steam lap, and finally to secure the eccentric in that 
 position. Such a setting of the eccentric is shown in 
 Fig. 10, in which the eccentric has been turned forward 
 until the distance df ox its equal, eg, is equal to the lap. 
 Such advance of the eccentric on the shaft is called the 
 angular advance or the advance angle of the eccentric ; 
 and if the admission is to occur with the crank on the 
 centre, as in this instance, the advance angle of Fig. lO 
 is equal to the lap angle of Fig. 8. Having secured a 
 proper admission to the steam, it is proper to inquire 
 next into the effect which this change in the angular 
 position of the eccentric has had on the other events of 
 the stroke. It is sufficiently obvious that turning the 
 eccentric forward a given angle would simply cause 
 each event to occur that much earlier in the rotation 
 of the crank. After steam lap had been added, and 
 before the advance of the eccentric, the cut-off occurred 
 with the crank lacking one lap angle of having reached 
 
20 
 
 SLIDE VALVE GEARS. 
 
 V 
 
 
 v?S 
 
 iF 
 
 / 
 
 y 
 
LEAD. 21 
 
 the centre (see Fig: 9). Advancing the eccentric one 
 lap angle will cause cut-off to occur one lap angle earlier 
 still, or with the crank lacking two lap angles of having 
 reached the centre. Before the advance of the eccen- 
 tric, the opening and closing of the ports to the exhaust 
 occurred as the crank passed the centre (see Figs. S and 
 7). Advancing the eccentric one lap angle will there- 
 fore cause both release and compresssion to occur with 
 the crank lacking one lap angle of having reached the 
 centre. 
 
 Summarizing then,- the valve has had steam lap 
 added to it, and the eccentric has been advanced by 
 an angle equal to the lap angle, and the resulting steam 
 distribution is as follows : Admission occurs as the crank 
 passes the centre ; cut-off occurs two lap angles before 
 the centre ; and release and compression occur one lap 
 angle before the centre. 
 
 Throughout this book the advance angle will be 
 designated on the diagrams by the letter S (delta). 
 
 LEAD. 
 
 It was explained on page 13 that the admission of 
 steam should take place slightly before the crank 
 reached the centre, and that such early admission was 
 called lead. In the last section, for the sake of sim- 
 plicity, the admission was supposed to occur as the 
 crank passed the centre. In other words, the lead was 
 made zero. It now becomes in order to examine the 
 method for the introduction of lead, and the changes 
 in the other events of the stroke which follow. In Fig. 
 
22 
 
 SLIDE VALVE GEARS. 
 
LEAD. 23 
 
 10 the eccentric was advanced to cause admission to 
 occur on the centre. If it is proposed to give the valve 
 lead, the eccentric must be advanced still further, so as 
 to draw the valve to the right an additional amount 
 equal to the lead desired. In Fig. 1 1 this additional 
 advance has been made, the eccentric having been 
 moved from /of Fig. 10 (reproduced in Fig. 1 1) to /. 
 The angle/>/ is called the lead angle, and it follows that 
 in all cases the angular advance is equal to the lap angle 
 plus the lead angle. If the lead is zero, then, as be- 
 fore found, the angular advance is equal to the lap an- 
 gle. If in Fig. 1 1 the crank shaft be turned backward, 
 the valve will close the port when the eccentric reaches 
 point f and the crank stands at m, the angle nem being 
 equal to the angle fel. In other words, the lead angle 
 is equal to the angular distance which the crank lacks 
 of having reached the centre when admission occurs. 
 
 It was found on page ig that advancing the eccentric 
 on the shaft a given angle advanced all the events of 
 the stroke correspondingly, and the resulting distribu- 
 tion of steam with no lead was summarized on page 21. 
 If now the valve have lead so that the angular ad- 
 vance be greater than the lap angle, the steam dis- 
 tribution given on page 21 is changed as follows : 
 
 Admission occurs with the crank lacking the lead 
 angle of having reached the centre. 
 
 Cut-off occurs with the crank lacking two lap angles 
 and one lead angle of having reached the centre. 
 
 Release and compression occur with the crank lack 
 ing one lap angle and one lead angle of having reached 
 the centre. 
 
 An application of the above principles is all that is 
 
24 
 
 SLIDE VALVE GEARS. 
 
 necessary for the analysis of the steam side of any exist- 
 ing plain slide valve, as will be seen from the following 
 example : 
 
 An eccentric has a throw of i|", the valve has one- 
 
 --tfv 
 
 Fig. 12 
 
 inch steam lap, no exhaust lap, and the eccentric is set 
 to giveyij^" lead. Required the greatest port opening, 
 and the crank positions for admission, cut-off, release, 
 and compression. 
 
 In Fig. 12 strike the circle with a radius equal to the 
 
EXHAUST LAP. 2$ 
 
 throw of the eccentric, and lay off Oa equal to the lap 
 of the valve and a b equal to the lead. Erect perpen- 
 diculars from points a, b, giving points c, d. Now eOc is 
 the lap angle, cOd is the lead angle, and eOd is the an- 
 gular advance. Lay off fg equal to cd, giving Og the 
 crank position for admission. Make hi equal to twice ec 
 plus cd, giving the crank position Oi for cut-off. Make 
 kk equal to ec plus cd, giving Ok the crank position for 
 release and compression. Finally, ak is the greatest 
 steam port opening. 
 
 The student should familiarize himself with the prin- 
 ciples thus far treated, by the solution of a variety of 
 problems similar to the following : 
 
 Problem I. Eccentric throw if, lap J, lead j^. Re- 
 quired crank positions for lead, cut-off, compression and 
 release, and port opening to steam. 
 
 Problem II. Eccentric throw ij, lap |f, lead^|-. Re- 
 quired as before. 
 
 EXHAUST LAP. 
 
 The addition of lap to the inside of the valve has the 
 same effect upon the opening and closing of the port 
 to the exhaust that steam lap has upon opening and 
 closing it to steam, i.e., it delays the opening and 
 hastens the closing, and it delays the opening and has- 
 tens the closing by an angle of rotation of the crank 
 equal to the exhaust lap angle — that angle being found 
 exactly as was the steam lap angle in Figs. 8 and 12. 
 Returning to Fig. 12, if the valve were to have an ad 
 dition of -^ inch inside lap, its effect upon the release 
 
26 SLIDE VALVE GEARS. 
 
 and compression could be found as follows : Make 01 
 equal the inside lap, and by the line /w2 find the exhaust 
 lap angle eOm. From k lay ofT em both upward and 
 downward. Draw the radii On and Op, and the results 
 are On for the crank position at release, and Op for com- 
 pression. It is unnecessary to go in detail through the 
 results following the introduction of negative inside 
 lap. It will be seen at once that its results are the di- 
 rect reverse of the preceding, i.e., to hasten the opening 
 and delay the closing of the ports. If in the illustration 
 preceding, the valve had been given ■§• negative inside 
 lap, the crank positions found for release and compres- 
 sion would have changed places. 
 
 It was shown on page i8 that the steam port open- 
 ing given by a valve having steam lap is equal to the 
 throw of the eccentric less the steam lap, and it follows 
 by the same course of reasoning that the exhaust 
 opening is equal to the throw less the exhaust lap. 
 Since the exhaust lap is always less than the steam lap, 
 it follows that the. port opening to exhaust is always 
 greater than to steam. 
 
 BACKWARD ROTATION. 
 
 It was explained on page 1 1 that with a primitive 
 valve the eccentric location for rotation in the reverse 
 direction would be diametrically opposite that shown 
 in Figs. 2-6. For a valve having lap, the position for 
 reverse rotation is found by laying off the advance 
 angle in the direction of the proposed rotation from the 
 position for a primitive valve. The effect of a rock 
 
BACKWARD ROTATION. 27 
 
 shaft in the valve motion (for an example of which see 
 any American locomotive) is to reverse the motion of 
 the valve as compared with the eccentric, and hence to 
 require a location of the eccentric which will provide 
 for this reversal. The position of the eccentric for 
 either direction of rotation, and with or without a rocker, 
 may be located from the following facts : 
 
 I. Without a rocker the eccentric for a primitive 
 valve is 90° in advance of the crank in the direction 
 of the rotation. With a rocker the eccentric is behind 
 the crank. 
 
 II. The advance angle is laid off in all cases in the 
 direction of the rotation from the position for a primi- 
 tive valve. 
 
 One qualification should be added to the above, as 
 follows : In all the cases thus far shown, the location of 
 the eccentric for the primitive valve is as stated at right 
 angles to the crank. In certain cases, owing ta the 
 character of the connections between the eccentric and 
 valve, this is not true. For an example see Figs. 58 
 and 59. In cases of this kind the location of the ec- 
 centric can be found as follows : Carry the centre of 
 the eccentric strap to the centre of the crank shaft. 
 Through the centre of the shaft draw a line perpen- 
 dicular to the location of the eccentric rod thus found. 
 This perpendicular gives the location of the eccentric 
 for the primitive valve, and the angular advance is to 
 be laid off from it in the direction of the rotation. 
 
28 SLIDE VALVE GEARS. 
 
 THE BILGRAM DIAGRAM. 
 
 Any existing slide valve can be analyzed by the 
 methods that have been followed in explaining the 
 action of the valve, and new valves could be designed 
 by a tentative application of the same methods. Such 
 a plan of procedure, however, would be exceedingly 
 tedious, and much ingenuity has been expended in de- 
 vising briefer and better methods. Of these, by far 
 the best is the diagram devised by Mr. Hugo Bilgram, 
 and explained below. The chief office of such a dia- 
 gram is to show briefly and accurately the position of 
 the valve for any and every position of the crank. 
 
 A 
 
 B 
 
 Fig. 13 
 
 The demonstration of the Bilgram diagram depends 
 upon the following theorem of geometry: In Fig. 13 
 let ABC and abc be two triangles, such that any two 
 of their angles, as those a.t A, C and a, c, and any one 
 side, as BC and be, are respectively equal. Then this 
 theorem asserts that all of the other parts of the tri- 
 angles are equal, i.e., angle B to b, side AC to ac, and 
 side AB to ab. 
 
 In Fig. 14 let A be the dead-point location of the 
 crank, and B be the corresponding position of the ec- 
 
THE BILGRAM DIAGRAM. 
 
 29 
 
 centric centre, S being the angle of advance. It is 
 obvious enough that the valve is now located a dis- 
 tance Bb (equal to the sum of the lap and lead) to the 
 right of its middle position. Imagine the crank to 
 turn through the angle a to a new position A' . The 
 eccentric will turn through an equal angle a to its new 
 
 Fig. U 
 
 position B', and the valve will then be located a dis- 
 tance B'b' to the right of its middle position. Lay 
 off the angle S upward from OX, and thus locate a 
 fixed point, Q. From Q drop Qq perpendicular to the 
 new crank position extended. There are thus formed 
 two triangles, B'b'O and QqO, and in them B'O equals 
 
30 SLIDE VALVE GEARS. 
 
 QO, since both are radii of the same circle. Angles 
 B'b'O, QqO are equal, because both are right angles; 
 and finally, angle B'Ob' equals QOq, since each is equal 
 to d plus a. The two triangles have thus two angles 
 and a side of one, respectively equal to two angles and 
 a side of the other, and it follows that the triangles are 
 equal in all their parts, and hence Qg equals B'b'. B'b' 
 is the distance which the valve has travelled from its 
 central position for crank position A' , and it hence 
 follows that Qq likewise equals that distance. The 
 same demonstration can be made for any other crank 
 position as well as for A' , and the following general 
 fact is thus established : Lay off the advance angle 
 above the centre line, and thus locate the fixed point 
 Q. Draw any crank position desired, and extend it if 
 necessary. From the fixed point Q drop a perpendic- 
 ular to the crank line, and the length of the perpendic- 
 ular will be equal to the distance of the valve from its 
 central position for the crank position taken. For ro- 
 tation in the reverse direction, points B and Q would fall 
 below instead of above the centre line. 
 
 The length of the perpendicular Qq gives the dis- 
 tance of the valve from its central position, but it does 
 not of itself show whether the valve is located to the 
 right or to the left of its middle position. That fact 
 will be determined instinctively after a little practice 
 in the, use of the diagram ; but if desired it can be 
 determined by the following consideration : Referring 
 to Fig. 14, that side of the crank and of its imaginary 
 extension facing the space toward which the crank is 
 revolving may be called the face side of the crank, and 
 the opposite side may be called the rear side. If the 
 
THE BILGRAM DIAGRAM. 3 1 
 
 perpendicular Qq falls upon the face side of the crank, 
 the valve is to the right of its middle position ; if the 
 perpendicular falls upon the rear side, the valve is to 
 the left of its middle position.* As has been explained, 
 the greatest port opening is equal to the throw of the 
 eccentric 0Q-, Fig. 14, less the lap ; and it is also true 
 that for any position of the crank, the port opening 
 which exists at that position is equal to the displace- 
 ment of the valve from its "central position less the lap, 
 i.e., to the value of Qq for that position, less the lap. In 
 other words, if for any crank jiosition the value of Qq 
 be found, and from it the steam lap be taken, the result 
 will be the distance which the steam port stands open for 
 that crank position. If, on the other hand, the exhaust 
 lap be taken from it, the result will be the distance which 
 the exhaust port stands open. This subtraction can 
 be conveniently made by striking two circles L, I from 
 (2 as a centre, and with radii equal to the steam and 
 exhaust laps respectively, as is done in Fig. 15. In 
 case the inside lap is negative, it of course increases 
 instead of decreases the port opening to exhaust. 
 Throughout this book, positive lap will be shown by 
 full circles, and negative lap by dotted circles. 
 
 Starting with the position A, Fig. 15, the length of 
 the perpendicular which locates the valve is Qq, and the 
 width of opening of the port to steam is «^ ; A being 
 the dead-point position of the crank, aq is the lead of 
 the valve. Similarly, 3^ is the exhaust lead. In Fig. 16 
 the valve is shown in position for crank position A. 
 
 * This takes it for granted, as explained on page 13, tliat the posi 
 lion of the cylinder is to the left of the shaft. 
 
32 
 
 SLIDE VALVE GEARS. 
 
 The opening of the port c to steam is equal to aq of 
 Fig. 15, and the opening of port ^to exhaust is equal 
 to bq. Similarly, the displacement e of the valve from 
 its centre is equal to Qq* As the crank revolves, Qq 
 gradually lengthens until the crank reaches position B 
 perpendicular to OQ, when Qq becomes QO, which is its 
 
 vB 
 
 -K6^ 
 
 _G 
 H 
 
 ^U 
 
 y 
 
 ,.^' 
 
 m 
 
 Fig. 15 
 
 greatest value. The valve now stands at its extreme 
 right hand position as shown in Fig. 17, the ports being 
 open to their greatest amount — the steam port by a 
 
 * It will be understood that the distances stated as equal are not so 
 shown in the cuts, as they are necessarily drawn to different scales. 
 
THE BILGRAM DIAGRAM. 
 
 33 
 
 width a'O, and the exhaust port b'O. Passing B, the 
 valve returns towards its central position, and at C the 
 
 Fi3. 16 
 
 displacement has been reduced to equality with the 
 steam lap. The port c is therefore closed to steam, and 
 
 cut-off takes place as shown in Fig. i8. At D, port d 
 is closed to the exhaust, Fig. 19, and compression be- 
 
 Fig. 18 
 
 gins. At F, port c is opened to exhaust. Fig. 20, and 
 release occurs. At G the valve is ready to open port 
 d for the return stroke. Fig. 21 ; and at H the valve has 
 
34 
 
 SLIDE VALVE GEARS. 
 
 opened port d by the amount of the lead. The posi- 
 tions of the crank for the return stroke are readily found 
 
 Fig. 19 
 
 by extending the crank lines beyond the centre. Thus 
 / is the lead position, ^ the release, Afthe compression, 
 
 Fig. 20 
 
 and iVthe cut-off. Had there been no exhaust lap, re- 
 lease and compression would have occurred simultane- 
 
 Fig. 21 
 
 ously at E ; and had the exhaust lap been negative, re- 
 lease and compression would have exchanged places, 
 and the maximum opening to exhaust would have been 
 Ob". 
 
THE BILGRAM DIAGRAM. 3S 
 
 Consideration of this diagram will recall and enforce 
 the essential effect of lap, as stated on page i8 ; i.e., to 
 shorten the period during which the port is open. Thus 
 with steam lap the steam port is open when the crank 
 is moving from / to Cand from G to N, and with exhaust ■ 
 lap the exhaust port is open from K to D and from F 
 to M. With negative inside lap, on the other hand, 
 the port is open during more than half a revolution, 
 i.e., from M to F. 
 
 The principles laid down should be fixed in the mind 
 by the solution of practical problems . similar to the 
 following : 
 
 Problem III. Throw of eccentric 2", steam lap i\, 
 exhaust lap |-, lead \. Required port opening and 
 points of cut-off, release, and compression. 
 
 Problem IV. Travel of valve 3", steam lap |-, nega- 
 ' five exhaust lap -f^, lead ^. Required as in the last 
 problem. 
 
 This diagram is of use not only in analyzing existing 
 valve motions as in the preceding problems, but also in 
 designing new ones to meet required conditions. The 
 method of using it for this purpose is best shown by an 
 illustrative example, as follows : 
 
 The valve for a certain engine is to have a steam- 
 port opening of |", a lead of 3^ ; is to cut off the steam 
 at I of the stroke, and open the exhaust at 95 per cent 
 of the stroke. Required the inside and outside lap, the 
 throw and advance angle of the eccentric, and the point 
 of exhaust closure. 
 
 In Fig. 22 make AB equal to the length of the stroke, 
 using a scale of three inches to the foot. Make Aa 
 
36 
 
 sLit)E Valve gears. 
 
 equal | of AB, and Ab equal .95 of /i^. Draw the 
 semicircle A'a'b'B' to represent the path of the crank, 
 and project to it the points a, b. Draw Oa' and Ob', 
 which are the crank positions for cut-off and release. 
 Draw cd such that de is equal to the lead opening, ^ 
 
 inch ; and strike the arc fg with radius equal to the 
 port opening. Find by trial the centre and radius of 
 the steam lap circle such that it shall be tangent to Oa', 
 cd, and fg. From the same centre strike the exhaust 
 lap circle tangent to Ob'. Draw Oh' tangent to the ex- 
 haust lap circle and project h' to the stroke line, giving h. 
 
THE BILGliAM DIAGRAM. 37 
 
 Measuring the diagram, the results sought are, outside 
 lap y\ inch, inside lap \ inch, throw of eccentric ly*^ 
 inch, advance-angle iOB' , point of exhaust closure h, 
 which is 90 per cent of the stroke. It may be observed 
 further, that the exhaust port opening is Ok ; in this 
 
 case and in all others this is more than sufficient for 
 the purpose, and hence no particular care is necessary 
 in relation to it. 
 
 An interesting and profitable exercise in this connec- 
 tion is to make a diagram showing by a continuous line 
 the varying width of port opening throughout the 
 stroke. This is illustrated in Fig. 23, in which the con- 
 tinuous base line represents the stroke of the piston of 
 Fig. 22 divided into tenths. At each division a per- 
 pendicular is erected, and on this perpendicular is laid 
 off the opening of the ports to steam and exhaust for 
 that position of the piston — this opening being obtained 
 from Fig. 22. Through the points thus found the 
 
38 SLIDE VALVE GEARS. 
 
 curved lines are drawn — the upper one for the exhaust 
 port and the lower one for the steam port. The cross- 
 ing of the base line by the curved lines shows the points 
 of cutting off and compression, respectively; and the 
 extension of the curved lines below the base line shows 
 the distances by which the edges of the valve have 
 closed the ports. This diagram shows at a glance how 
 gradual is the cutting off of the steam. Such diagrams 
 are exceedingly useful in connection with the study of 
 independent cut-ofi valves, many of which will not give 
 flattering results when subjected to this analysis. 
 
 LAYING OUT THE SLIDE VALVE. 
 
 The diagram Fig. 22 gives all the dimensions neces- 
 sary for laying out its valve, except the width of the ex- 
 haust cavity, and that is determined at once by draw- 
 ing the valve and its seat with the valve at one extreme 
 of its travel, that is, in the position already shown in 
 Fig. 17. Referring to Fig. i, it is clear that the width 
 of the acting face of the valve is equal to the outside 
 Jap plus the width of the port plus the inside lap. In 
 order to determine all the dimensions of the valve face 
 and seat proceed as follows : Lay down the width of 
 the left hand port (rules for which will be given farther 
 on) and the width of the bridge (usually made equal to 
 the thickness of the cylinder). On these locate the 
 acting face of the valve with the port open to steam to 
 the greatest amount intended. From the exhaust 
 edge of the acting face lay off the distance /, Fig. 17, to 
 equal or slightly exceed the width of the port, thus com- 
 pletely determining the exhaust cavity in the cylinder. 
 
VELOCITY OF TwA VALVE(//\ 39 
 
 From the right hand edge of i\\\f cay^ty the remaining 
 bridge and port are to be laid off, the same as the 
 left hand side. The valve seat being completed, and 
 the steam and exhaust laps being RHl>lvn,,it is easy to 
 complete the drawing of the valve. The proper deter- 
 mination of the distance/", Fig.' if, as aboye, is all that 
 need be considered in designing the exhaust cavity in 
 the cyhnder. If this cavity be made too narrow, it will 
 cramp the exhaust ; if too wide, it will add unnecessari- 
 ly to the size of the valve and to the steam pressure 
 upon it, and hence to the friction and wear and tear on 
 all the valve gear. Further than this, the size of the 
 exhaust cavity has no influence on the valve motion. 
 
 It will be observed that in the valve diagram Fig. 22, 
 the lines for the piston and crank circle are drawn to a 
 reduced scale, but the lines for the valve and eccentric 
 are full size. The reduced scale for the crank dimen- 
 sions is for convenience. The valve dimensions should 
 always be made full size. 
 
 * VELOCITY OF THE VALVE. 
 
 Referring to Fig. 14, it is obvious that the valve 
 will move with its greatest velocity when the eccentric 
 is at P. At this point its velocity may be represented 
 by the eccentric throw OP. At any other position of the 
 eccentric as B, the valve will move with a velocity pro- 
 portional to the leverage with which the eccentric acts 
 upon it, that is, Ob. Similarly at B' the velocity of the 
 valve will be represented by Ob'. In the original dem- 
 onstration of this diagram it was shown that the tri- 
 angles B'b'O and QqO are equal in all their parts. It 
 
40 '■■^'(^^ ' stW'E VALVE GEARS. 
 
 hence follows that- (9g equals Ob' . In other words, if a 
 perpendicular be drawn from the point Q to any crank 
 line, tht distance from the centre of the shaft to the 
 foot of "that perp^ridfcular.' will represent the velocity 
 with which the valve, is moving with the crank in that 
 position. Quic^ elo^uiS^ of the port in cutting off steam 
 is considered a merit in a valve motion, and this prop- 
 erty of the Bilgram diagram furnishes a ready means 
 of comparing the merits of different valve gears in this 
 respect. In Fig. 15 the perpendicular Qc will deter- 
 mine the distance Oc, which represents the velocity 
 with which the valve is moving at the instant of 
 cutting off. 
 
 LIMITATIONS OF THE PLAIN SLIDE VALVE. 
 
 Careful study of the Bilgram diagram will explain 
 the features of the common slide valve which have usu- 
 ally been considered to limit its application to cases 
 where a comparatively late cut-off was to be employed. 
 Thus, in the example of Fig. 22, let the given condi- 
 tions be the same, except that cut-off is to be at half 
 stroke instead of three quarters, and let there be no 
 inside lap. The results are shown in Fig. 24, where 
 it will be seen that the throw has increased to two 
 inches and the steam lap to one and three eighths 
 inches, while the common point of compression and re- 
 lease has gone back to bh — 85 per cent of the stroke. 
 At still earlier points of cut-off these features become 
 still more marked, the travel of the valve rapidly in- 
 creasing and the release and compression becoming 
 more and more premature. The increased lap and 
 travel increase directly the size and duty which the 
 
LIMITATIONS OP THE PLAIN SLIDE VALVE. 4I 
 
 parts have to perform. Further, as will be seen by re- 
 ferring to the section on laying out the slide valve, 
 and to Fig. 17, they increase the size of the exhaust 
 cavity, and so add to the size of the valve and to the 
 steam pressure upon it. The release can be made later 
 
 Fig. 24 
 
 by the addition of exhaust lap, but this involves a still 
 earlier compression. From these considerations it has 
 been generally held and taught that the plain slide 
 valve could not be profitably employed for cut-offs 
 shorter than one half or five eighths stroke. The 
 
42 SLIDE VALVE GEARS. 
 
 methods which have been adopted to overcome the 
 above difficulties will form the subject of a later chapter, 
 
 THE AREAS OF THE PORTS AND PIPES. 
 
 It will be seen from the foregoing that the width of 
 port opening is an essential factor in the design of a 
 valve motion. The exact meaning of the term port 
 opening in this connection should be clearly under- 
 stood. By that term is to be understood the extreme 
 distance of the steam edge of the valve from the steam 
 edge of the port. This distance may, and often does, 
 exceed the width of the port — that is, the valve may 
 have over-travel to secure certain real or fancied advan- 
 tages. In engines with fixed eccentric, which are now 
 under consideration, the only benefit of such over-travel 
 is to increase the sharpness of the cutting off. This, in 
 the author's opinion, is not worth its cost, and hence he 
 does not practise nor recommend it. In locomotives 
 and shifting eccentric engines the travel of the valve is 
 shortened at the early cutoffs, and in such engines, in 
 order to secure sufficient port opening at the early cut- 
 offs, it is proper and necessary to ^\v^ over-travel at the 
 late ones. 
 
 It is clear that the area of the port opening should 
 have a proper relation to the size and speed of the en- 
 gine. It will be furthernfore clear without extended 
 explanation, that in engines having separate admission 
 and exhaust ports (for example, the Corliss) the exhaust 
 passage should have a greater area than the admission 
 passage. In engines using the same passage for both 
 purposes, to which this book relates, that passage 
 should be proportioned to meet the requirements of 
 
THE AREAS OF THE PORTS AND PIPES. 
 
 43 
 
 the exhaust, and then, if desired, it need not be opened 
 to steam any wider than is necessary for its use as a 
 steam port, 
 
 In determining the area of a pipe or passage it is 
 treated as though the velocity of the steam through it 
 were equal to the velocity of the piston multiplied by 
 the ratio of the area of the piston to the area of the 
 port or pipe. Of course, owing to the expansion of 
 the steam at release, this is not strictly true, but it 
 simplifies the determination of the dimensions, and as 
 long as the rules and tables make allowance for its lack 
 of precision, the results are the same as though a more 
 complicated process were gone through. 
 
 As the result of experience and experiments, the 
 proper velocities of the steam through the various pas- 
 sageways are as follows : 
 
 Through the steam pipe 8000 feet per minute. 
 
 Through the exhaust port 6000 feet per minute. 
 
 Through the exhaust pipe 4000 feet per minute. 
 
 For free admission of steam the port should be opened 
 three fourths of its width. From the above data the 
 following table is constructed for convenient use : 
 
 Piston Speed, 
 Feet per Minute. 
 
 Diameter of Steam 
 
 Diameter of Exhaust 
 
 Area of Exhaust 
 
 Pipe (Diameter of 
 Piston = i). 
 
 Pipe (Diameter 
 of Piston = j). 
 
 Passage (Area of 
 Piston = 1). 
 
 200 
 
 .158 
 
 .223 
 
 .033 
 
 250 
 
 .176 
 
 
 248 
 
 .042 
 
 300 
 
 .194 
 
 
 272 
 
 .050 
 
 350 
 
 .209 
 
 
 294 
 
 .058 
 
 400 
 
 .224 
 
 
 314 
 
 .067 
 
 450 
 
 ■237 
 
 
 333 
 
 •075 
 
 500 
 
 .250 
 
 
 353 
 
 .083 
 
 550 
 
 .260 
 
 
 368 
 
 .092 
 
 600 
 
 .274 
 
 
 385 
 
 . 100 
 
44 SLIDE VALVE GEARS. 
 
 The table determines the diameters of the steam 
 and exhaust pipes at once, but it gives the area only 
 of the port, leaving its length and breadth to be de- 
 termined by the designer. The practice in this par. 
 ticular is very diverse. In shifting eccentric automa- 
 tic engines, which form the subject of Part II, and in 
 which every expedient must be employed to secure 
 sufficient port opening, the length of the ports is often 
 made to equal or even exceed the diameter of the cyl- 
 inder ; but in plain slide valve engines of the usual type, 
 a length of about three quarters the cylinder diameter 
 more nearly represents average practice. This length 
 determined, it is only necessary to divide the area of 
 the passage by it to determine the width of the port, 
 and three fourths o£ this will give the port opening to 
 be used in laying out the diagram. 
 
 A " rule of thumb" which is in very common use is 
 to make the steam pipe one fourth the diameter of the 
 cylinder, and the exhaust pipe one third. At slow 
 speeds this rule gives an excess of capacity over the re- 
 quirements, to which of course there is no objection ; 
 but at high speeds it gives a deficiency. On high grade 
 engines, where the best results are sought, steam pipes 
 are seen as large as one third and exhaust pipes one 
 half the cylinder diameter. 
 
 All the principles thus far given will be found re- 
 quired in the solution of the following 
 
 Problem V. — An engine with a lo" X 15" cylinder 
 is to run at 200 revolutions per minute. Cut-off is to 
 be at I stroke, release at .93 stroke, and lead is to be ^^'. 
 Required the diameters of steam and exhaust pipes, the 
 
ANGULAR VIBRA T-ION OF THE CONNECTING ROD. 45 
 
 dimensions of the ports, the travel, and the steam and 
 exhaust laps of the valve. 
 
 * THE ANGULAR VIBRATION OF THE CONNECTING ROD. 
 
 As has been explained, the slotted cross-head was 
 adopted in the preceding to avoid certain distortions 
 which are incident to the use of the connecting rod. It 
 is now proper to discuss these distortions, and explain 
 the methods for neutralizing their effects. 
 
 With the slotted cross-head the position of the piston 
 
 or cross-head in its stroke for any crank position is found 
 by simply projecting the crank position to its horizontal 
 diameter, or a line parallel thereto, by means of a straight 
 projecting line, as was done in Figs. 12, 22, and 24. Fig. 
 25 is a skeleton diagram of the usual connecting rod 
 and crank. It is obvious that if the crank pin end of 
 the connecting rod be disconnected from the crank pin 
 and carried to the centre of the crank shaft the cross- 
 head pin will occupy its central position a. If from 
 this position the crank pin end be carried to either 
 " quarter" position of the crank pin b, c, the cross-head 
 
46 SLIDE VALVE GEARS. 
 
 pin will be drawn toward the shaft and will occupy the 
 position d. For the forward stroke the position of the 
 cross-head is measured from ^ as a starting point, and 
 hence the cross-head and piston have moved too far 
 by the distance ad. For the return stroke the position 
 is measured from / as a starting point, and hence the 
 cross-head and piston have not moved far enough by 
 the same distance. If the valve motion were laid out 
 by the preceding methods to cut off steam at half stroke, 
 it would in fact cut off later than half stroke for the 
 forward stroke and earlier for the return. The same 
 distortion takes place at all other positions of the crank 
 except at the centres, though to a less degree ; and it 
 follows that all the events of the stroke except the lead 
 occur too late in the forward stroke and too early in 
 the return. The amount of this distortion can be found 
 for any position of the parts, as is done in Fig. 25, for 
 the position shown, by striking an arc with radius equal 
 to the length of the connecting rod, the distance gh be- 
 ing equal to ad. Striking this arc is, in fact, projecting 
 the point b to the centre line with the circular arc in- 
 stead of a straight line, as has heretofore been done ; 
 and in order to find the true relation between the posi- 
 tions of the piston and crank, it is only necessary to 
 project the one to the other by means of such circular 
 arcs with radius equal to the length of the connecting 
 rod. It is often convenient to measure the piston posi- 
 tions for the forward and return strokes from the same 
 starting point as i, and in order to do this it is only 
 necessary to strike the arcs for the forward and return 
 strokes from opposite sides of the shaft. Thus, with 
 the crank on the quarter, the piston will have moved 
 
AXGULAR VIBRA TION OF THE CONNECTING ROD. 47 
 
 through the distance ih for the forward stroke and ik for 
 the return. Similarly, if the crank move through an angle 
 ibl for the forward stroke, the piston will have moved 
 through the distance io ; and if the crank move through 
 the same angle from p on the return stroke the piston 
 will have moved through the distance iq. The directions 
 of these distortions for the two strokes are best distin- 
 guished by remembering that the effect of the connect- 
 ing rod is always to draw the piston too near the crank. 
 
 The amount of these distortions will diminish if the 
 length of the connecting rod be increased, and if a con- 
 necting rod of infinite length be conceived, the distor- 
 tions will disappear. Hence a piston motion without 
 distortion, such as is given by the slotted cross-head, is 
 often called the motion due to a connecting rod of in- 
 finite length. 
 
 Since the speed of the crank's rotation is uniform, 
 and the piston must travel farther for a given angle of 
 crank rotation in the forward than in the return stroke, 
 it follows that the speed of the piston's motion is greater 
 in the forward than in the return stroke. 
 
 These principles can be applied to the problems al- 
 ready given, and thereby determine the actual positions 
 at which the various events occur. Fig. 26 is a repro- 
 duction of Fig. 22, but with the projections made by 
 circular arcs instead of straight lines. It thus appears 
 that with the valve there designed, the cut-off, instead 
 of taking place as intended in Fig. 22, will really take 
 place after a piston travel Aa' , Fig. 26, in the forward 
 stroke and Aa" in the return. Similarl}', the compres- 
 sion will take place after travels Ah' and Ah" , and the 
 release after Ab' and Ab" . If preferred, the construe- 
 
48 
 
 SLIDE VALVE GEARS. 
 
 tion may be made by repeating the lap circles below 
 the centre line in position for the return stroke, as is 
 
 Fig. 26 
 
 done in Fig. 27. With this construction the measure- 
 ments are necessarily made from A for the forward 
 stroke and B for the return. Of these two plans that 
 of Fig. 26 possesses the advantage that it shows at a 
 glance the difference between the points of cut-off, etc., 
 in the two strokes. 
 
 Problem VI. It is required to find the true positions 
 for cut-off, release, and compression of the valve of 
 
ANGULAR VJBRA TION OF THE ECCENTRIC ROD. 49 
 
 Fia. 27 
 
 Problem III. Length of connecting rod five times the 
 crank. 
 
 * THE ANGULAR VIBRATION OF THE ECCENTRIC ROD. 
 
 As has been explained, the eccentric is in effect a 
 crank and the distortions introduced by the connecting 
 rod into the motion of the piston are likewise intro- 
 duced by the eccentric rod into the motion of the valve. 
 
so SLIDE VALVE GEARS. 
 
 In other words, if the distortions are not corrected, the 
 valve, like the piston, will always be too near the crank. 
 The throw of the eccentric is much less than the arm 
 of the crank, and the eccentric rod is proportionately 
 longer than the connecting rod ; hence the distortions 
 in the positions of the valve are absolutely and relatively 
 smaller than those in the positions of the piston. Since 
 the effect of these distortions is to draw the valve too 
 near the crank, it follows that if they are not provided 
 for, the lead of the valve at the back end f of the cylinder 
 will be increased and for the front end diminished. The 
 greatest port openings are measured with the eccentric 
 on the centre line of the engine, when these distortions 
 vanish ; and hence the two port openings will be equal. 
 It is important that the lead openings be equal, while 
 it is not particularly important that the maximum port 
 openings be equal, provided the smaller one be large 
 enough. Hence in practice the eccentric rod or valve 
 rod is slightly lengthened to give equal lead at the two 
 ends, and the result is that the port opening is slightly 
 diminished for the forward stroke and slightly increased 
 for the return. This lengthening of the eccentric rod 
 is effected in setting the valve for equal lead, and it 
 practically corrects the effects of the angular vibration 
 of the eccentric rod. 
 
 "^ " * EQUALIZED EXHAUST. 
 
 As has been explained, the setting of the valve for 
 equal lead practically neutralizes the effect of the an- 
 
 \ With apologies to the locomotive fraternity.the end of the cylinder 
 farthest from the crank will be called the back end. 
 
EQUALIZED EXHAUST. 
 
 51 
 
 gularity of the eccentric rod. Nothing, however, has 
 yet been done toward correcting the irregularities due 
 to the connecting rod, and that is the next subject to 
 be discussed. 
 
 If the valve has no inside lap, compression and re- 
 
 
 
 ____^— 
 
 
 
 
 ^-•' 
 
 ""^^^^ 
 
 
 ^ 
 
 
 
 
 X 
 
 ^. 
 
 N 
 
 
 / 
 
 ^ 
 
 "^■v, v^""^^ \ ^^**\. 
 
 
 / 
 
 ^ 
 
 
 
 / .^' 
 
 
 / X \ a'\ 
 
 
 / y 
 
 
 / \ j-'^X \ 
 
 
 / / 
 
 
 / \<;^'\ \ 
 
 
 / / 
 
 
 
 
 / / 
 
 
 1 y^'^y^J n \ 1 
 
 
 / / 
 / / 
 
 
 \y^ \ 1| \/ 
 
 
 / / 
 
 
 vrSr \ r v 
 
 
 
 
 
 ' 1 
 
 
 
 
 1 / 
 
 
 
 
 
 
 
 
 I h 
 
 
 y^ ^ ii 1 
 
 
 1 ^^^ — \ 
 
 ^^ 
 
 la 1 
 
 
 1 / ', \ 
 
 j>^^ 
 
 / ' 
 
 
 '/ \ 
 
 
 / / 
 
 
 X \ / 
 
 '>\ ^ 
 
 / / 
 
 / 
 
 ^\ \ ^^ 
 
 "A 
 
 / / 
 
 / 
 
 \ ^^^^ 
 
 \ 
 
 / / 
 
 
 6V- ^N 
 
 1 
 
 / / 
 
 \ 
 
 I \ N 
 
 
 / / 
 
 
 \ \ "^ 
 
 / 
 
 / / 
 
 
 
 \^ 
 
 
 q 
 
 
 r*'- 
 
 t\a 
 
 Fig. 28 
 
 lease are coincident, and the correction of one will like- 
 wise correct the other. It is desired to cause both these 
 events to occur earlier in the forward stroke and later 
 in the return stroke, and to accomplish this, it is only 
 necessary to give an appropriate exhaust lap to the end 
 of the valve nearest the crank shaft, and an equal nega- 
 
52 
 
 SLIDE VALVE GEARS. 
 
 tive exhaust lap to the other end. In applying this cor- 
 rection, it should be remembered that the Bilgram dia- 
 gram gives the true relation between the positions of 
 the crank and eccentric, and that the distortions under 
 discussion are given to the piston through the connect- 
 ing rod. In Fig. 28 it is proposed to correct the release 
 and compression of the valve shown, which, in the first 
 instance, has no exhaust lap. By the vertical projec- 
 tion lines the points of release a, b are found in the usual 
 way, and by means of the curved projection lines points 
 a! , ^'are found for the correct crank positionscorrespond- 
 ing to piston positions a, b. If the release and compres- 
 sion are to take place at piston positions a, b, they must 
 take place at the crank positions a', b' . Drawing the 
 crank lines fl'Oand b'0,\.\. is easy to add the exhaust lap 
 circles shown, from which measurement shows that for 
 that edge which effects exhaust at a' a positive lap of 
 ■^" is required, and for b' a negative lap of the same 
 amount. The resulting valve is shown in Fig. 29. Had 
 
 Fig, 29 
 
 the valve originally possessed exhaust lap, as in Fig. 
 30, exact equalization would have been impossible, al- 
 though a result could have been reached sufificientlynear- 
 ly correct for all practical purposes. The piston positions 
 
EQUALIZED EXHAUST. 
 
 53 
 
 for compression a, b and release c, da.re projected to the 
 crank circle by circular arcs, as shown, giving the corre- 
 sponding crank positions a', b' , c', d' . It is apparent at 
 once that the change of lap to give compression at a' is 
 greater than the change to give release at d' , and simi- 
 
 Fig. 30 
 
 larly for c' and b'. In such a case the best that can be 
 done is to divide the difference, making the alteration in 
 the lap half way between that called for by a' and d' for 
 their end of the valve, and half way between that called 
 for by c' and b' for their end of the valve. This sub- 
 ject wil4 be returned to at the close of the next section. 
 
54 SLIDE VALVE GEARS. 
 
 * EQUALIZED CUT-OFF. 
 
 It was shown in the last section that by introducing 
 inequality in the inside laps, the inequality of release 
 or compression could be equalized — a change in one 
 event being, however, accompanied by a change in the 
 other. It is obviously possible to equalize the cut-off 
 in a similar manner by making the outside laps un- 
 equal. As a change in the inside laps involved both 
 release and compression, so will a change in the outside 
 laps involve both admission and cut-off; and since the 
 valve, as thus far described, gives equal lead at the two 
 ends of the cylinder, it follows that increasing one lap 
 and decreasing the other would result in an unequal 
 lead — in other words, cut-off equalized by such a 
 method would involve unequal lead. Such a method 
 is usually explained in detail in books of this character. 
 Equality of lead is, however, of more importance than 
 equality of cut-off, and hence the method is of no prac- 
 tical importance, and is not introduced here. 
 
 The following method f secures equality of cut-off 
 without affecting the equality of the lead. It has 
 no objectionable features, and is of general utility. 
 Throughout the discussion, one fundamental fact must 
 be kept in mind, viz. : The acts of opening and closing 
 a port by a slide valve differ only in the direction of 
 motion of the valve. The port is opened or closed, as 
 the case may be, by the edge of the valve passing the 
 
 f First published by the author in the American Machinist for 
 March 14, 1889. It was invented independently by Professor Sweet 
 and the author, — first, however, by the Professor. 
 
EQUALIZED CUT-OFF. 
 
 55 
 
 edge of the port, and the position of the valve when 
 cut-off takes place is the same as when adniission takes 
 place. Since the valve is mechanically connected to 
 the eccentric rod pin, it follows that the position of that 
 pin must be the same at cut-off as at admission. 
 
 Let it be proposed to design a slide valve to cut off 
 steam at half stroke, with equal lead and cut-off. 
 
 First design the valve by the methods already ex- 
 plained, then strike the crank and eccentric circles of 
 Fig. 31.* Locate points A, B, the positions of the crank 
 pin for admission of steam, and the corresponding 
 positions a, b for the eccentric centre. With radius 
 equal to the length of the connecting rod, and with 
 
 * In this and the following diagrams the throw of the eccentric is 
 made disproportionately large, and the eccentric rods disproportion- 
 ately short, to add to the clearness of the constructions without un- 
 necessarily large diagrams. This gives the appearance of a distorted 
 valve movement ; but with working proportions these apparent dis- 
 tortions are no greater than with the usual construction, and are not 
 objectionable. 
 
S6 SLIDE VALVE GEARS. 
 
 centre at the middle position of the cross-head pin, 
 strike arcs cutting the crank circle at c and d. Before 
 cut-off in the forward stroke, the crank shaft, and with 
 it the eccentric, must turn through the angle Ac, and 
 in the return stroke Bd. Space off a'e equal to Ac, 
 and b'f equal to Bd. Draw eg and fg, and we have 
 point h, where the eccentric centre must be for cut-oft , 
 at c, and i where it must be for cut-off at d. With 
 radius equal to the length of the eccentric rod, and with 
 centres at b, i, strike arcs meeting at k, and with same 
 radius and centres a, h, strike arcs meeting at /. Npw 
 for admission at A and cut-off at c, the eccentric rod pin 
 must be in the same position, and as the eccentric rod 
 is of fixed length, this position must be /, that being 
 the only point whose distance from both a and h equals 
 the length of the eccentric rod. Similarly for admission 
 at B and cut-off at d, the pin must be at k. The pin 
 can be brought to these positions at the proper time by 
 introducing a rock shaft in the valve motion having its 
 centre at any point o ; such that an arc struck from it 
 shall pass through k and /, and then connecting the 
 eccentric rod to it as shown. The valve stem should 
 then be connected to the rocker, as shown at m, n. 
 The eccentric rod positions for crank positions A, B 
 are shown at al, bk. The rocker fulcrum might be 
 located above the centre line, if preferred, at o'. 
 
 In cases where the valve chest is located on the top 
 of the cylinder, a rocker of different type, with the arms 
 on opposite sides of the fulcrum, becomes necessary. 
 The construction for this type of rocker is essentially 
 the same as shown in Fig. 32, which is lettered to cor- 
 respond with Fig. 31. Of course, with this type of 
 
EQUALIZED CUT-OFF. 
 
 57 
 
 rocker the eccentric positions a, b change places as 
 shown. One result of the equaHzation growing out of 
 the inequaHty of the rocker arms is to alter the port 
 opening from that determined upon in the original de- 
 signing of the valve. The motion as thus far deter- 
 mined should therefore be treated as a trial result only, 
 and the dimensions of the valve and eccentric should 
 be altered in the light of the experience gained. 
 
 n m 
 
 At the close of the description of Fig. 31 it was 
 stated that the rocker fulcrum might be located indif- 
 ferently at either or 0' of that figure. This is strictly 
 true so far as relates to equal lead and cut-off, but there 
 is still a difference in the effect of the two positions. 
 By suitably locating the fulcrum the compression and 
 exhaust can be equalized for the two ends of the cylin- 
 
58 
 
 SLIDE VALVE GEARS. 
 
 der — exactly if the valve have no inside lap, and ap- 
 proximately if it have such lap. This has not the 
 unique interest which belongs to the equalization of lead 
 and cut-off, since it can be accomplished by other 
 means ; but it forms an interesting study, nevertheless. 
 The method of accomplishing this equalization is 
 shown in Fig. 33, which follows the construction of Fig. 
 
 31 up to and including the finding of k, /, but with lead 
 zero. Suppose, in the first instance, that the valve has 
 no inside lap, and by the methods already described 
 find the points of the piston stroke in, n, where release 
 and compression should occur, and by arcs whose com- 
 mon radius is equal to the length of the connecting rod 
 find the corresponding crank positions j,/. Layoff 
 Acs from a' giving q, and Bdp from b' giving r. Draw qg 
 and r^ giving /and u, where the eccentric must be for 
 the two equalized compressions. With radius equal to 
 the eccentric rod, and centres t, u, strike arcs meeting in 
 
SETTING THE SLIDE VALVE. 59 
 
 V. Now locate the rock shaft fulcrum at o, such that 
 the eccentric rod pin shall pass through k, I, and v, and 
 the result will be a valve motion giving equal lead, cut- 
 off, release, and compression. If the valve have inside 
 lap, then, instead of one point, v, there will be two, . 
 just as with outside lap there are two points, k, I. In 
 that case it will be found impossible to so locate o that 
 the eccentric rod pin shall pass exactly through all four 
 points. It should be then made to pass through k and 
 /, and the difference be divided between the two points 
 V. The release and compression will then be as nearly- 
 equalized as is possible. 
 
 SETTING THE SLIDE VALVE. 
 
 As the parts of an engine valve motion are assem- 
 bled two dimensions are lacking: ist, the angular loca- 
 tion of the eccentric relative to the crank ; and, 2d, the 
 length of the valve rod. The eccentric is capable of 
 being located in any angular position, and the length of 
 the valve rod is usually capable of adjustment by means 
 of jamb nuts each side of the valve, or some equiva- 
 lent means. The setting of the valve involves locating 
 the eccentric and fixing the valve at the proper point 
 on the rod. There are two distinct steps to the process : 
 I. Locating the engine exactly on the centre ; 
 
 II. Locating the eccentric and valve. 
 
 To locate the engine on the centre, proceed as fol- 
 lows : Turn the crank to any convenient distance 
 above the centre. Fig. 34. Upon the side or face of the 
 crank disc or fly-wheel, as most convenient, scribe an 
 arc a by means of a tram b swinging from any conven- 
 
6o 
 
 SLIDE VALVM GEAHS. 
 
SETTING THE SLIDM VALVE. DI 
 
 ient fixed point on the engine frame or floor. Also 
 scribe a line c on cross-head and guides. Turn the crank 
 below the centre as shown by Fig. 35, the cross-head 
 line receding from its mate on the guide and approach- 
 ing it again. When these lines are exactly fair, stop 
 the motion and scribe a second line d on the wheel,' line 
 a, now occupying the position shown in Fig. 35. With 
 the dividers find point e, dividing the arc ad in halves. 
 When point e is brought fair with the point of the tram, 
 Fig. 36, it is clear that the engine will be on the centre. 
 Repeat this construction for the other centre. One pre. 
 caution is necessary in relation to the above, in order to 
 obviate any error that might arise from looseness in the 
 crank pin and cross-head pin bearings : In scribing the 
 lines a and d have the crank pin pressing against the 
 same brass for both lines. It matters not which brass 
 be used, but the same one must be used for both lines. 
 To locate the eccentric and valve proceed as follows : 
 Locate the eccentric by the eye as near as may be, 
 and ahead of its correct position rather than behind it. 
 Bring the engine to either centre, as found above, turn- 
 ing it in doing so in the direction of the proposed rotation 
 in order to neutralize any looseness in the connections. 
 With the engine on the centre, locate the valve to give 
 the required lead, after which turn the engine in the 
 directio7i of its future rotation to the opposite centre. If 
 the eccentric is ahead of its correct position, the lead 
 for this position will be greater than the first ; if the 
 eccentric is behind, the second lead will be less than 
 the first, and probably negative. In either case the 
 valve is to be adjusted on the rod to divide the differ- 
 ences in the lead. This being done, the valve is cor- 
 
62 
 
 SLIDE VALVE GEARS. 
 
SETTING TffE SLIDE VALVE. 63 
 
 rectly located on the rod, the lead is equal at the two 
 ends of the cylinder, but is too large or too small at 
 both. To correct this it only remains to adjust the 
 eccentric, moving it in the direction of the rotation until 
 the valve have the proper lead. Verify the results, 
 and the work is done. 
 
PART II. 
 
 THE SLIDE VALVE WITH SHIFTING 
 AND SWINGING ECCENTRIC. 
 
The Slide Valve with Shifting and 
 Swinging Eccentric. 
 
 THE SLIDE VALVE AT SHORT CUT-OFF. 
 
 The difficulties which impede the use of the plain 
 slide valve at short cut-off have been explained at 
 length in Part L Before explaining the shifting eccen- 
 tric automatic valve gear, it is necessary to show how 
 these difficulties have been surmounted. By referring 
 to the section on the Limitations of the Plain Slide 
 Valve those difficulties will be seen to be — 
 
 L Premature release and compression^either of 
 which, however, can be made later at the expense of 
 making the other earlier still. 
 
 n. Inadequate port opening to steam or, in lieu of 
 that, excessive size and travel of valve. 
 
 The first difficulty has been met by increasing the 
 speed of the engine. All of the engines employing 
 this description of valve gear are of the "high speed" 
 type. In such engines a heavy cushion is appropriate 
 and necessary to bring the reciprocating parts quietly 
 to rest at the centres, and hence the early compression 
 ceases to be a radical objection. Indeed, inside lap is 
 
 67 
 
68 SLIDE VALVE GEARS. 
 
 given to the valve in order to delay the release — there- 
 by, as has been explained, still further increasing the 
 compression. 
 
 The second difficulty is met by two expedients, the 
 first being sometimes employed alone, but more often 
 in connection with the second. These expedients are, 
 1st, the use of balanced valves, usually of the true pis- 
 ton type or of the " pressure plate" type, both being 
 perfectly balanced against the steam pressure ; 2d, the 
 use of valves having multiple ports, by which the neces- 
 sary throw of eccentric is halved or even quartered. 
 The use of balanced valves permits the use of valves of 
 large size and great throw ; and the use of multiple 
 ports gives sufficiently large openings with such throws 
 as it is practicable to use. 
 
 It is believed that the first engine to embody the 
 above features in connection with a shifting eccentric 
 and a shaft governor was the Straight Line ; and hence 
 that engine is entitled to be recognized as the progeni- 
 tor of a large and vigorous family. So far as known, 
 these features were first combined in an engine designed 
 by Professor John E. Sweet, built at the Cornell Uni- 
 versity shops, and exhibited at the Centennial Exhibi- 
 tion. 
 
 That the difficulty of restricted port opening is a real 
 one, maybe gathered from any indicator diagram from 
 a locomotive with plain valve at good speed and well 
 "notched up." Such diagrams invariably show a 
 marked fall in the steam pressure on entering the cyl- 
 inder ; and it is largely on this account that such per- 
 sistent attempts have been made to improve the loco- 
 motive valve motion. An appropriate introduction to 
 
THE SLIDE VALVE AT SHORT CUT-OFF. 
 
 69 
 
 the study of multiple ported valves is found in one not 
 necessarily balanced, which was designed more especial- 
 ly for use on locomotives, — to which it has been large- 
 ly applied, — namely, the Allen valve, shown in Fig. 37. 
 In this valve the seat is shortened and a supplement- 
 ary port aa is cast through the valve. This port regis- 
 ters with the end of the seat as shown in the figure, 
 which represents the valve open by the amount of its 
 lead. The course of the steam is shown by the arrows, 
 from which it will be seen that the opening at b is added 
 
 Fig. 37 
 
 The Allen Valve. 
 
 to the usual one at c ; and that up to the point where 
 the opening at c is equal to the width of passage a, 
 the total opening is just twice what it would be with 
 the usual form of valve. 
 
 The " pressure plate" type of valve is well shown in 
 Fig. 38, which represents the valve of the Straight Line 
 engine. The pressure plate AA receives the pressure 
 of steam upon its back. It is prevented from pressing 
 the valve proper to its seat by means of distance pieces 
 above and below the valve, and slightly thicker than the 
 valve. Recesses in the plate form in it an exact coun- 
 
70 
 
 SLIDE VALVE GEARS. 
 
 terpart to the valve seat. The valve slides between 
 the seat and plate like a square piston relieved of all 
 pressure. This valve, like those that follow, is shown 
 
 FI3. 38 
 
 The Straight Line Valve. 
 
 open to its lead ; and the manner in which the recesses 
 in the plate and the passages aa through the valve 
 combine to give a double port opening will be seen 
 
 Fig. 39 
 
 The Woodbury Valve. 
 
 from the arrows. The ledges bb are for the purpose of 
 protecting the finished surfaces of the pressure plate 
 from the cutting action of the exhaust steam. Some 
 designers of double ported valves have thought it best 
 to provide double ports for the exhaust, while others 
 
THE SLIDE VALVE AT SHORT CUT-OFF. 
 
 71 
 
 have not. The illustrations of both the Allen and 
 Straight Line valves will show that the opening to ex- 
 haust is amply large without double ports ; but such 
 ports increase the quickness of opening to exhaust, and 
 so secure a desirable advantage. The valve under dis- 
 cussion is provided with them at c, c. Their action is 
 
 Fig. 40 
 
 precisely the same as that of the steam passages a, a, and 
 need not be explained further. 
 
 Fig. 39 shows the valve of the Woodbury Engine Com- 
 pany. It combines the method of action of the Allen and 
 Straight Line valves, and so secures four port openings 
 to steam and two to exhaust. Openings a, b act pre- 
 cisely like those of the Straight Line valve, and open- 
 ings c, dad substantially like the supplementary port of 
 the Allen valve. This will be seen more clearly by re- 
 
^2 
 
 SLIDE VALVE GEARS. 
 
 ferring to Fig. 40, which represents a plan of the Wood- 
 bury valve. Passages e,faxe cast through the valve to 
 act in conjunction with the openings c, d of Fig. 39, in 
 the same manner that the passage aa of Fig. 37 oper- 
 ates in conjunction with opening b of the same figure. 
 Ledge g acts to protect the finished surfaces of the 
 cover plate from the action of the exhaust in the same 
 manner as ledges b, b of the Straight Line valve. 
 
 Fig. 41 illustrates the valve of the Armstrong engine, 
 
 Fig. 41 
 
 The Armstrong Valve. 
 
 in which the action of the steam and exhaust edges of 
 the valve is reversed from the usual practice. The 
 steam enters at a, and the outer edges of the valve con- 
 trol the exhaust. The steam pressure tends to lift the 
 cover plate, and it is therefore held down to its seat by 
 means of the bridle b. The action of the steam ports 
 will be seen from the arrows. This valve gives four 
 openings to steam and two to exhaust. 
 
 The Rice valve (Fig. 42), like the last example, takes 
 
THE SLIDE VALVE AT SHORT CUT-OFF. 
 
 73 
 
 steam from the inside. It gives two openings to steam 
 and two to exhaust. The relief plate aa is in this in- 
 stance a piston fitting the cylinder bb, this cylinder be- 
 
 Fig. 42 
 
 The Rice Valve, 
 
 ing bolted to the floor of the steam chest. The pres- 
 sure of steam within this cylinder forces the piston 
 toward the valve, which, however, it is prevented from 
 
 ^^^^^^^y-^^^^^y^y-^^^^^^^^^^M'yyyy^^ ^M^-'M^Ml 
 
 ■^^^^^^^^y^y^yyy^y^^M'y^^^^^^y^^y^^^^^^^^^^^^ t^ 
 
 Fig. 43 
 
 The Armington and Sims Valve. 
 
 touching .by means of distance pieces slightly thicker 
 than the valve, and similar to those already described 
 in connection with the Straight Line valve. 
 
74 
 
 SLIDE VALVE GEARS. 
 
 Fig. 43 illustrates the Armington and Sims valve, 
 which is a true piston valve with double ports. The 
 course of the steam is shown as heretofore by the 
 arrows. 
 
 Fig. 44 shows the Ide double ported valve, which, 
 like the last, is a piston valve. 
 
 Fig. 44 
 
 The Ide Valve. 
 
 Of an entirely different type is the Giddings valve as 
 used in the Russell & Company engine. This valv:; is 
 shown in Fig. 45. Steam enters at a and exhausts at bb. 
 Each end of the valve acts in much the same manner 
 as the Allen valvepas will be understood from the arrows, 
 while over all is cast a case c. The steam entering from 
 the inside of the valve, its pressure would, if not coun- 
 teracted, lift the valve from its seat. This is prevented 
 by the use of "needle ports" (not shown), one connecting 
 the live steam space within the valve to the body of 
 the valve chest, and the second connecting the chest to 
 the exhaust. The action of these ports is explained by 
 Mr. Giddings as follows : " The steam is taken under 
 the valve, which would result in throwing the valve off 
 
THE SLIDE VALVE AT SHORT CUTOFF. 
 
 75 
 
 the seat. This must be counteracted by pressure on 
 the back of the valve sufficient to overcome the ten- 
 dency to leave the seat. This I obtain by the small 
 needle port communicating with the live steam passage 
 on the inside of the valve. If there were no outlet 
 this would soon result in an excess of pressure nearly 
 equivalent to steam pipe pressure on the back of the 
 valve, which would produce a hard working valve. To 
 avoid this, I put another needle port opening, commu- 
 nicating with one of the exhaust ' D's ' of the valve. 
 • C 
 
 Fig. 45 
 
 The Giddings Valve. 
 
 The resulting pressure due to these two openings is 
 just sufficient to overcome the tendency to leave the 
 seat." 
 
 A remarkable feature of this valve, not attained by 
 any other so far as known to the author, is the use 
 made of the supplementary passage d. After the com- 
 pression has commenced, and before opening to admit 
 live steam from the steam supply, this passage opens 
 into communication with the regular steam port. This 
 increases the volume into which the steam is compressed, 
 without, however, increasing the clearance space from 
 which the steam is exhausted, since this supplementary 
 
76 SLIDE VALVE GEARS. 
 
 port is never in communication with the exhaust." This 
 is described by Mr. Giddings as follows : 
 
 " We find by increasing the capacity of the carry over 
 port or portchamber, that we can use it as a reservoir 
 or port into which to pack the surplus compression of 
 a single valve automatic movement, thereby giving us 
 a peculiar offset in the compression curve, and giving 
 us from lo to I2 per cent increase of area, and a con- 
 sequent increase of power from a given sized engine. 
 The amount of this is entirely within our control by a 
 
 Fig. 46 
 
 variation of the cubical capacity of this passage way, 
 thereby enabling us to get the compression curve down 
 in the corner, something after the manner of the four 
 valve engine cards." 
 
 This feature is of such unique interest that indicator- 
 cards from one of these engines (Fig. 46) are introduced 
 to illustrate it. The offset mentioned will be seen at 
 aa, the dotted line b representing the compression 
 curve that would have resulted but for this provision. 
 
 The shifting eccentric valve gear, in connection with 
 which all these valves are used, requires that the valve 
 
EQUAL LEAD AND CONSTANT LEAD. 77 
 
 shall have an excess of port opening and travel at the 
 late cut-offs in order that they may be sufficient at the 
 early cut-offs. Inspection of any of the valves illustrated 
 will show that with large travels the supplementary port 
 becomes closed after the main port is well opened ; and 
 with such travels the effect of the supplementary port is 
 merely to increase the quickness of port opening and 
 closing. 
 
 * EQUAL LEAD AND CONSTANT LEAD. 
 
 The lead of a valve may vary in two ways, and to 
 prevent ambiguity it is necessary to define and follow 
 an exact use of terms. The reader is asked to note 
 carefully the following explanations of the terms equal 
 lead and constant lead. They will be used hereafter 
 strictly as defined, and it is necessary that they be 
 clearly understood. 
 
 Equal lead implies that the lead is alike at the two 
 ends of the cylinder. Constant lead implies that the 
 lead does not change for different grades of expansion. 
 An engine might have equal lead for one grade of ex- 
 pansion and unequal lead for another grade, or the 
 lead might be equal at all grades without being con- 
 stant ; that is, the lead at the two ends of the cylin- 
 der might be always alike, but larger at both ends for 
 three quarters cut-off than for one quarter. So, also, 
 an engine might have constant lead without equal lead ; 
 that is, the lead might not change for different grades 
 of expansion, but at the same time be always larger 
 for one end of the cylinder than for the other. 
 
 The above distinctions are radical and important, 
 
78 SLIDE VALVE GEARS. 
 
 and it is necessary that they be clearly seen in order to 
 understand what follows. 
 
 THE SHIFTING ECCENTRIC.f 
 
 s 
 
 The expedients which are employed for making what 
 is geometrically the plain slide valve available for early 
 cut-offs having been explained, it remains to describe 
 how the same valve can be made available for different 
 cut-offs. 
 
 In Fig. 47 let the circle abc represent the eccentric 
 path of a given eccentric in the Bilgram diagram, the 
 eccentric centre being at d, and L and / being, as usual, 
 the steam and exhaust lap circles. Let the centre of 
 the eccentric be shifted from d to d' , dd' being a 
 straight line perpendicular to ac. There will thus be 
 formed a new eccentric path a'b'c' . Laying off b'd' up- 
 ward from c' , will locate Q' , the new centre of the lap 
 circles. From this centre the lap circles maybe drawn 
 in the usual way, and from them the crank positions A 
 for the new point of cut-off, B for exhaust closure, and 
 C for release may be found. Since bd equals cQ, and 
 b'd' equals c'Q' , and since dd' is perpendicular to ac, it 
 follows that QQ' is parallel to ac : hence the lead open- 
 ing has not been changed. The lead angle, however, 
 has clearly been increased, and the port opening has 
 been reduced. In the same way, the eccentric may be 
 shifted still further on the line dd', and new points of 
 cut-off, release, and compression, and new values of the 
 
 f Throughout this and the following section the angularity of the 
 connecting and eccentric rods is neglected, 
 
THE SHIFTING ECCENTRIC. 
 
 79 
 
 port opening, found. Finally, if the eccentric be shifted 
 to the position d° on the line ac, the point Q will be lo- 
 cated at Q °, when the port opening will be reduced to 
 the lead opening and the cut-off will take place as much 
 after the centre as the lead did before it. In all posi- 
 
 Fig. 47 
 
 tions the lead opening will be constant. If the valve 
 have multiple ports, when the travel becomes so reduced 
 as to bring them into action, the result will be to give 
 double or quadruple the opening shown by the diagram, 
 as the case may be. Should the movement of the ec- 
 centric be continued below the Hne ac, the result wouid 
 
80 SLIDE VALVE GEARS. 
 
 be to reverse the direction of the rotation. The study 
 of reversing engines is, however, beyond the scope of 
 the present work. 
 
 An eccentric arranged for adjustment on straight 
 line dd°, as in this illustration, is called by the author a 
 shifting eccentric* 
 
 So far as known to the writer, there are but two en- ' 
 gines in the American market which employ a shifting- 
 eccentric. These are the Armington and Sims and the 
 Russell (Giddings) engines. The former obtains prac- 
 tically a straight line motion of the eccentric centre by 
 means of a combination of two eccentrics, while in the 
 Russell engine the required motion is obtained by means 
 of a straight guide keyed to the shaft and appropriate 
 wings attached to the eccentric. 
 
 THE SWINGING ECCENTRIC. 
 
 Instead of shifting the eccentric across the shaft in a 
 straight line as in the last examples, most designers have 
 preferred to swing it by an arm cast in one with itself, 
 and pivoted to an arm in the fly-wheel or other con- 
 venient piece. Such an eccentric is called by the author 
 a swinging eccentric, and its effect upon the steam dis- 
 tribution, as distinguished from the shifting eccentric, 
 is to vary the lead opening at different points of cut-off. 
 The nature and degree of this variability depends in 
 large degree upon the location of the pin from which 
 
 * For want of another word, the term shifting eccentric is also used 
 as a general expression which includes both shifting and swinging 
 eccentrics. This double use of the ivord will not, however, cause con- 
 fusion. 
 
THE SWINGING ECCENTRIC. 
 
 the eccentric is swung. If the pin is on the same side 
 of the shaft as the crank, and in the centre line of the 
 crank, as in Fig. 48, the path of the eccentric across the 
 shaft is the arc dd° . The path of the point Q will then 
 be a similar arc QQ° , with the same radius and with its 
 centre located in the line ef. It is clear from the posi- 
 tions of the various lap circles that the lead opening 
 
 / 
 Fig. 48 
 
 will not be constant with this arrangement, but will be 
 greater in the early cut-offs than in the late ones. The 
 action upon the other events of the stroke is substan- 
 tially the same as that of the shifting eccentric. With 
 the pin located in the centre line on the opposite side 
 of the shaft from the crank, as in Fig. 49, the arc in 
 which the eccentric swings has its convexity reversed 
 
82 
 
 SLIDE VALVE GEARS. 
 
 from the last figure. The path of the point Q will also 
 be reversed, and instead of receding from the centre- 
 line in the early cut-offs, it will approach it, thus dimin- 
 ishing the lead opening in those cut-offs. This diminu- 
 tion of lead may be carried so far as to make the lead 
 zero or even negative in the early cut-offs — a fact which 
 
 Fig. 49 
 
 will be shown on the diagram by the earlier steam lap 
 circles crossing the horizontal centre line. The same 
 result of a decreasing lead in the early cut-offs can be 
 obtained with the eccentric swing pin on the same side 
 of the shaft as the crank, but raised above the centre 
 line as in Fig. 50, in which the swing pin is located on 
 the line dg extended. Similarly, by raising this pin 
 when located opposite to the crank, an increasing lead 
 can be obtained. By locating the pin half way between 
 
the: swinging ^ccenthic. 
 
 83 
 
 Fig. 50 
 
 
 ■■-(4 
 
 
 1 
 I 
 
 Fig 
 
 51 
 
§4 
 
 Slide vaLVe GEaHS. 
 
 the positions of Figs. 48 and 50, on the line hi of Fig. 
 5 1 the lead will be the same at the smallest as at the 
 greatest throw ; and by suitably placing it as in Fig. 52, 
 the lead can be made alike for any two expansions de- 
 sired. In this construction the two points of cut-off. 
 
 A 
 
 for which equal lead is desired are decided upon, and 
 the corresponding crank positions ^, B are drawn. The 
 lap circles are drawn in the usual way for A and B, 
 the lead being made the same for both. Points Q and 
 Q' are then transferred to d and d', and the eccentric is 
 so hung that its centre shall pass through the points 
 d and d' . 
 
filM aMgVlaRity oP The eccentric rod. 8s 
 
 As has been pointed out, if the valve have a negative 
 lead in the early cut-offs, it will be shown in the diagram 
 by the lap circle going below the horizontal centre- 
 line. In this case if the cut-off be made early enough 
 the lap circle will pass through the centre of the shaft. 
 This marks the point where the port opening becomes 
 zero by reason of the eccentric throw becoming re- 
 duced to equality with the lap. For any smaller throw 
 there is no admission whatever. 
 
 Designers have usually endeavored to obtain as nearly 
 a constant lead as possible. The author considers, how- 
 ever, that for stationary engines, where the speed is 
 fixed, a lead decreasing in the early cut-offs is more 
 suitable. That the lead should be equal at the two 
 ends of the cylinder, there is, however, no question. 
 This entire subject will be discussed at greater length 
 in the section on Equalized Lead. 
 
 *THE ANGULARITY OF THE ECCENTRIC ROD. 
 
 Thus far in Part II the influence of the angular vi- 
 bration of both connecting and eccentric rods has been 
 ignored. • It will be understood that primarily both 
 connecting and eccentric rods produce the same distor- 
 tions with the shifting as with the fixed eccentric. 
 There is, however, with the shifting or swinging eccen- 
 tric an additional distortion produced by the angularity 
 of the eccentric rod growing out of the fact that the 
 vibration of that rod varies in amount with the varying 
 throw of the eccentric — the small throw due to an early 
 cut-off giving a small angular vibration, and the large 
 throw due to a late cut-off giving a larger vibration. 
 
»D SLIDE VALVE GEARS. 
 
 Taking up first the case of the shifting eccentric in 
 Fig. S3,* let A, B represent the crank pin of a shifting 
 eccentric engine when on the dead centres, a, b being 
 the corresponding positions of the eccentric centre at its 
 greatest throw, h, i at its mean throw, and e,fa.t its 
 smallest throw. The positions of the eccentric rod for 
 mean throw of the eccentric are shown at ch, di, and 
 the valve in both positions is open by the amount of 
 its lead, as shown by the upper valve sketch for c, and 
 the lower one for d. Let the path of the eccentric 
 
 centre, when shifted across the shaft to change the ex- 
 pansion, be a straight line occupying the position ae 
 for crank position A, and 4/^ for crank position B. Im- 
 agine the crank on the centre A, and shift the eccen- 
 tric toward e. Obviously point c will be moved to the 
 left, and the lead will be disturbed. For crank posi- 
 tion B the same is true ; and what is still worse, while 
 the movement for crank position A decreases the lead, 
 that for B increases it. If, with crank at A, the eccen- 
 tric be shifted towards a, and with crank at B towards 
 
 * See foot-note, page 55. 
 
 This feature of the present diagrams shows a greater irregularity in 
 the lead in the usual form of construction, as well as in the form to be 
 described, than actually obtains with working proportions. This, how- 
 ever, for the present purpose, is rather an advantage than otherwise. 
 
THE ANGULARITY OF THE ECCENTRIC ROD. 87 
 
 b, the lead at the two points will be disturbed in the op- 
 posite directions; i.e., for position^ the lead will be in- 
 creased, and for B decreased. The broad fact is evi- 
 dent, that, owing to the varying angularity of the ec- 
 centric rod, an engine laid out as shown in Fig. 53 could 
 not have a constant lead, and it could only have an 
 equal lead for some one (selected) grade of expansion. 
 With a swinging eccentric, the simplest case is where 
 the eccentric swings about a point which, with crank 
 at A, Fig. 54, coincides with c. Thus, suppose a 
 
 Fig. 54 
 
 large disc keyed to the shaft, and arrange the ec- 
 centric to swing about a pin fixed to the disc, the 
 centre of the pin for crank position A coinciding 
 with c, Fig. 54. Now shift the eccentric from h to- 
 wards e or a, and c will not be disturbed. When, 
 however, the crank is at B, the pin c will be at ^ ; and 
 if the eccentric be shifted from i towards /or b, point d 
 will obviously be disturbed more than in the corre- 
 sponding movement of Fig. 53; and it may be said in 
 general, that with the eccentric rod arranged in the 
 common way, as shown in Fig. 53, any change in the 
 path of the eccentric across the shaft, to correct the in- 
 constant lead at one dead centre, will only make mat- 
 ters worse at the other, and by no possible modifica- 
 
SLIDE VALVE GEARS. 
 
 ti'on can the lead be made equal for more than one 
 grade of expansion. 
 
 The arrangement of Fig. 54, however, while of inter- 
 est and value in a theoretical study of the subject, is of 
 no practical importance, because its use would require 
 so large a disc for the attachment of the eccentric 
 swing pin as to be impracticable. It therefore be- 
 comes necessary to examine the situation with the ec- 
 centric swung from a position nearer the shaft. Let 
 the pin be located at the centre of the crank pin — a 
 common position — as in Fig. 55, the eccentric rod 
 being much longer than the crank, as it always is in 
 practice. In that case the actual path of the eccentric 
 
 Fig. 55 
 
 for crank at A will be to the right of ae of Fig. 54, and 
 to the left of bf; consequently the lead will increase 
 at both ends of the cylinder for short cut-offs, but the 
 increase will plainly be greater for crank position B 
 than for A. The result is a lead increasing in the early 
 cut-offs, but increasing much faster for one end of the 
 cylinder than for the other, and hence equal at the two 
 ends of the cylinder for one grade of expansion only. 
 Similarly it might be shown that by swinging the ec- 
 centric from a point diametrically opposite the crank 
 pin the lead would decrease in the early cut-offs (see 
 Fig. 49), but decrease much more rapidly for one end 
 
EQUALIZED LEAD. 89 
 
 of the cylinder than for the other ; and it is clear that 
 whatever quality is sought for in the lead, and deter- 
 mined so far as the Bijgram diagram can do it, it "will 
 in fact be modified by the angular vibration of the ec- 
 centric rod. It seems unnecessary, however, to exam- 
 ine the subject in detail further. 
 
 * EQUALIZED LEAD. 
 
 So far as known to the author, the only engine in 
 which any attempt is made to correct the distortions 
 which have just been explained is the Straight Line. 
 The valve motion of this engine, like its mechanical 
 details, is an exhibition of refined ingenuity which it 
 would be dififiicult to surpass. In the following it will 
 first be explained how the engine was originally built 
 to secure a substantially constant lead, and after that 
 the present construction will be shown. The con- 
 struction to be described is essentially the same as that 
 already used in equalizing the cut-off of fixed-eccentric 
 engines (page 54), and it should be understood that 
 the present use of that construction was the original 
 one — its use for equalizing the cut-off being in fact 
 an offshoot of its original use for equalizing the lead. 
 In equalizing the lead as well as the cut-off, two 
 types of rocker are possible. The first type of rocker 
 is shown in Fig. 56, the parts being lettered as in 
 the three preceding figures. From h and i, he and id 
 are drawn parallel to the centre line, and each is 
 made equal to the length of the eccentric rod. The 
 rocker fulcrum is then so located at o that the pin 
 for the eccentric-rod shall describe an arc passing 
 
90 
 
 SLIDE VALVE GEARS. 
 
 through c and d. The pin for the valve rod is located 
 as usual, m belonging with c, and n with d. The eccen- 
 tric is shifted by being swung- from a pin, whose loca- 
 tion for crank position A coincides with c. As ex- 
 plained in connection with Fig. 54, the disturbance of 
 the lead for crank position A is thus eliminated. When 
 the crank is at B, t is at ^ in line with id. In this 
 position of the parts, shifting the eccentric on the line 
 
 ^/will disturb the lead a trifle, though much less than 
 in the constructions of Fig. 53 or 54. We have here, 
 then, a construction which eliminates the disturbance 
 for crank position A, and practically eliminates it for 5, 
 and thus secures substantially a constant lead. Com- 
 paring Figs. 54 and 56, the essential diff^erence in the 
 two plans is apparent. In Fig. 56, ch and di are par- 
 allel, and hence both c and g are in line with the eccen- 
 tric rod position to which each belongs ; whereas in Fig. 
 54 ch and di are not parallel, and hence, while c is in line, 
 g is not, and cannot be made so. The construction so 
 far explained, would, however, lead to inconvenient 
 dimensions of some of the parts. The centre of motion 
 for shifting the eccentric is therefore in practice moved 
 
EQUALIZED LEAD. 
 
 91 
 
 inward from c to some convenient point k on the line 
 ch, the eccentric rod pin still remaining at c. The po- 
 sition of k for crank at B is of course /. This change- 
 introduces a trifling error for crank position A, and by 
 an equal amount increases the existing error for B; but 
 the final irregularity is infinitesimal as compared with 
 Fig. 53 or 54, and the mechanism accompHshes its ob- 
 
 Fig. 57 ** 
 
 ject — obtaining a practically constant and equal lead 
 at all grades of expansion. 
 
 The second type of rocker introduces no material 
 change in the lay-out. For an engine with the steam 
 chest on top of the cylinder it is illustrated in Fig. 57, 
 the parts being lettered to correspond with Fig. 56. 
 This type of rocker reverses the motion of the eccen. 
 trie, and hence positions «, b, change places as shown. 
 
92 
 
 SLIDE VALVE GEARS. 
 
 As the Straight Line engine is actually built, how- 
 ever, the steam chest is on the side of the cylinder, and 
 hen^e the second type of rocker takes the unusual 
 form of Fig. 58. There is, however, no change in the 
 essential principle of the construction, which is, that the 
 two positions of the eccentric rods which belong with 
 crank positions A, B shall be parallel to one another. 
 The object of using this form of rocker is as follows: 
 
 This valve motion, like the usual form, when set for 
 equal lead, gives a larger port opening for one end of 
 the cylinder than for the other. It is well known that 
 the speed of the piston is faster in the end of the cylin- 
 der farthest from the crank shaft. Now the second 
 type of rocker gives the large port opening to that end 
 of the cylinder in which the piston travels the faster, 
 
EQUALIZED LEAD. . 93 
 
 while the first form gives the reverse relation. Hence 
 the choice in the construction. 
 
 As now built, however, the Straight Line engine has a 
 decreasing lead in the early cut-offs, becoming in fact 
 negative in the earliest grades. The reason for this 
 change in practice is as follows : In shifting eccentric 
 engines, as is well known, the compression increases as 
 the cut-off grows shorter. The total cushion by which 
 the momentum of the reciprocating parts is arrested 
 is the sum of the exhaust cushion and the lead cushion. 
 Now if the total cushion is to be constant at all points 
 of cut-off, as it should be, the lead must decrease as the 
 compression increases, and at the early cut-offs the lead 
 should be negative. Furthermore, in such engines, as 
 has been explained, both the release and compression 
 for early cut-offs occur earlier than is desirable. Now 
 by laying out two valves for the same cut-off, one with 
 positive and the other with negative lead, it will be 
 found that the valve with negative lead gives consid- 
 erably later release and compression than does the one 
 with positive lead. In other words, the introduction 
 of negative lead at the early cut-offs, in addition to off- 
 setting in a measure the increasing compression, pro- 
 longs the expansion, thereby getting more work out 
 of the steam, and also delays the compression, thereby 
 still further reducing the cushion. The result is accom- 
 plished as shown in Fig. 59, which is a modification of 
 Fig. 58. The point k, instead of being on the line di, 
 is placed above it. This brings / equally below ch, ex- 
 tended ; and, as will be seen by referring to the upper 
 valve sketch for m and the lower one for n, reduces 
 the lead for both crank positions A and B, as the eccen- 
 
94 
 
 SLIDE VALVE GEARS. 
 
 trie is shifted inward towards e and f. If the elevation 
 of k above di is suiificient, the lead at the early cut-offs 
 will obviously be negative. To fully appreciate the 
 merit of this construction, Fig. 59 should be compared 
 with Fig. 53, when it will be seen that while in Fig. 53 
 shifting the eccentric inward from h, i, decreases the 
 lead in the upper valve sketch, it increases it in the 
 lower one ; in Fig. 59, on the other hand, shifting the 
 
 ®? 
 
 eccentric inward from h, i, decreases the lead in both 
 valve sketches. 
 
 Again, Fig. 59 should be compared with Fig. 55, and 
 with the suggested companion to it having a decreasing 
 lead in the early cut-offs, when it will be seen that 
 while the plans are essentially alike in having an incon- 
 stant lead, they are unlike in that in Fig. 59 the lead 
 is substantially equal at both ends of the cylinder 
 
EQUALIZED LEAD AND CUT-OFF. 9S 
 
 throughout the range, but in Fig. 55 it is equal at one 
 grade of expansion only. 
 
 * EQUALIZED LEAD AND CUT-OFF. f 
 
 It has been shown how, by different methods of pro- 
 portioning the parts, the same mechanism can be laid 
 out at will to give either exact equalization of the cut- 
 off in fixed eccentric engines, or approximate equaliza- 
 tion of the lead in shifting eccentric engines. It re- 
 mains to be shown how a proportion of parts can be 
 found which will satisfy both constructions, and thus 
 obtain a practically constant and equal lead, an ex- 
 actly equal cut-off for any chosen grade of expansion, 
 and approximately equal cut-offs for all grades. 
 
 Referring again to Fig. 56, it appears that the funda- 
 mental principle of its construction is the diminution 
 of the inclination to one another of the lead positions of 
 the eccentric rod; and, referring to Fig. 31, it appears 
 that the fundamental principle of its construction is 
 the direct reverse of this, i.e., the increase of this incli- 
 nation. It hence appears at once that the construc- 
 tions of Figs. 56 and 31 are incompatible, and cannot 
 be reconciled with one another. Comparing Figs. 57, 
 and 32, on the contrary, it appears that in this general 
 way they agree ; but while in Fig. 57 the inchnation of 
 he and id is reduced to actual zero, i.e., the rods are 
 made parallel, in Fig. 32 al and bk are still inclined at 
 an appreciable angle. Now the inclination of al and 
 bk to one another in Fig. 32 can be varied at will by 
 
 f First published by the author in the American Machinist for 
 March 14, i88g. 
 
96 SLIDE VALVE GEARS. 
 
 changing the length of the eccentric rod ; and by 
 choosing a proper length they can be made parallel, 
 and the proportions so found will satisfy the construc- 
 tion for equal lead, and for the particular grade of ex- 
 pansion for which it should be drawn for equal cut-off 
 likewise. For other grades it will, of course, satisfy the 
 construction for equal cut-off only approximately. One 
 qualification must, however, be made. In Fig. 57, A 
 and B are located at the dead points, while in Fig. 32 
 they are located at the points where admission occurs, 
 and these are not usually the dead points. It will 
 simplify matters to make these points coincide by con- 
 sidering, in the first instance, an engine with a lead of 
 zero. In Fig. 60 the construction of Fig. 32 is repeated 
 for the mean throw of the eccentric and with lead zero, 
 but with several lengths of eccentric-rod, giving a cor- 
 responding number of points k' , k", k'", I ', I", I'". It is 
 plain that the inclination to one another of k'b and 
 I' a is less than that of k"b and I" a, which in turn is 
 less than ^'"3 and /'"«, the degree of inclination de- 
 pending on the length of rod. used. If a length of rod 
 can be found such that its two positions shall be paral- 
 lel to one another, the rod so found will obviously sat- 
 isfy the constructions for both equal lead and equal 
 cut-off. This length is found in the following manner: 
 It is obvious that all the points k', k", etc., are on the 
 straight line pg, and similarly /', /", etc., are on gg\ 
 therefore, draw pg and qg. Assume a trial length of 
 eccentric-rod, and with centres a, b, strike arcs giving 
 k, I, such that bk and al are parallel, repeating the 
 construction with different lengths of rod until the 
 correct length is found. Locate the rocker fulcrum so 
 
EQUALIZED LEAD AND CUT-OFF. 
 
 97 
 
 that the eccentric rod pin shall pass through k and /. 
 Now positions al, bk obviously satisfy the construc- 
 tion for equal cut-off, and, being parallel, they also sat- 
 isfy that for equal lead ; and an engine with its valve- 
 motion laid out in this manner will have approximately 
 equal and constant lead, equal cut-off for that eccen- 
 tric throw for which the construction is made, and an 
 
 approximately equal cut-off for other positions of the 
 eccentric. 
 
 The construction of Figs. 56, 57, and 58 was made 
 with the crank on the centre, while that for Figs. 31 
 and 32 was made with the crank in position for ad- 
 mission of steam, and in Fig. 60 these methods were 
 reconciled by supposing the admission to occur on the 
 centre. No material error would be introduced if this 
 
98 
 
 SLIDE VALVE GEARS. 
 
 method were followed in all cases ; but if it is desired 
 to follow the strictly correct method, it can be done in 
 the following manner : Fig. 6i is a reproduction of Fig. 
 32, constructed for the mean throw of the eccentric, 
 with some additions. Find points b^ , «, and k^ , /j cor- 
 o 
 
 responding with crank positions A', B', and draw kj)^ 
 and /,«, . Now the construction of Fig. 32 gives the 
 positions of kb and la, while it is desired to make k^b^ 
 and /,«, parallel by suitably selecting the eccentric rod 
 length. This should be done by trial, as before, re- 
 peating the trial until the desired result is reached. 
 
F»ARX III. 
 
 THE SLIDE VALVE WITH INDEPENDENT 
 CUT-OFF. 
 
The Slide Valve with Independent 
 Cut-off, 
 
 INTRODUCTORY REMARKS. 
 
 An early cut-off being a necessity for an economical 
 use of steam, it comes about that with valves of the 
 construction previously described the leading consider- 
 ations in their design are those pertaining to the steam 
 side of the valve. The valve and eccentric being de- 
 signed with reference to the steam side, so as to secure 
 an early cut-off, there is little that can be done with 
 the exhaust side beyond reconciling conflicting require- 
 ments as well as possible. In engines provided with 
 independent cut-ofi valves this condition no longer 
 holds : the exhaust can usually be arranged to suit the 
 designer's fancy; and it hence follows that in such 
 engines the leading considerations in the design of the 
 main valve are usually those pertaining to the exhaust. 
 It is essential that the exhaust have a certain lead, in 
 order that the cylinder may free itself of steam, and, 
 on the other hand, this lead should be no greater than 
 is necessary for this purpose, since that would involve 
 exhausting the steam at a point where it might still do 
 
102 ' SL/£>E VALVE GEARS. 
 
 some'usefu^l wpl-k. ' The determination of the point of 
 release is, therefore, a leading factor in the design of this 
 class of valves. ,][t|ip not to.be expected that there will 
 be any^lose dgreerrient in ^ detail of this character in 
 the work of different. designers; but, as a general rule, 
 modified sbrjoeyh^t by questions of piston-speed, etc., 
 it may be said that release should occur at from 93 to 
 95 per cent of the piston stroke.* The other event of 
 the exhaust side of the valve, the compression, is de- 
 termined, it must be owned, largely by the taste and 
 fancy of the designer. A late compression by requiring 
 a small exhaust lap conduces to a small travel of the 
 valve, which, if it is to be unbalanced, is a desirable 
 feature. The features of the exhaust side of the main 
 valve and the port opening to steam having been 
 settled, the steam side is determined by the force of 
 circumstances. To give the proper points of exhaust 
 opening and closure, the steam lap will usually be 
 small and the cut-off late. This, however, is of no 
 consequence, as the cut-off valve is introduced for the 
 express purpose of providing for it. 
 
 THE GONZENBACH VALVE GEAR. 
 
 * A description and analysis of this valve gear is here 
 given as an introduction to those which follow. It is 
 now seldom employed. It comprises two valve chests, 
 two valve seats, and two valves, as shown in Fig. 62. 
 The lower or " main valve" is driven by a fixed eccen- 
 
 * In engines of slow rotative speed — for example, Corliss engines, 
 and others of similar general character — the release will frequently be 
 found to be somewhat later than the figure given in the text. 
 
THE GONZENBACH VALVE GEAR. 
 
 103 
 
 trie, and determines the admission, release, and com- 
 pression of' steam. The upper or " cut-off valve" is 
 used solely for the purpose of the cut-off, and is usu- 
 ally of the gridiron type, in order to secure quickness 
 of cut-off with moderate travel. It is driven by an 
 eccentric of its own, which, if the expansion is to be 
 varied, must be turned forward or backward, as the case 
 
 Fig. 62 
 
 The Gonzenbach Valve. 
 
 may be, on the main shaft. This movement affects the 
 angular advance only, and, unhke the eccentric move- 
 ments of Part II, does not change the travel of the 
 valve.* 
 
 The action of this cut-off valve is different from any. 
 thing that has thus far been examined. The previous 
 
 * The following applications of the Bilgram diagram to the Gonzen- 
 bach, and also to the Buckeye and Bilgram valve gears, are substantially 
 the same as those previously published (now largely inaccessible) by 
 Mr. Bilgram. 
 
104 
 
 SLIDE VALVE GEARS. 
 
 valves open and close their ports with the same edge, i.e., 
 in opening the port the valve draws to one side, and in 
 closing it resumes the previous position. This cut-off 
 valve, however, opens and closes the port by the port 
 in the valve passing bodily across the port in the seat, 
 the opening being done by one edge, and the closing 
 by the other. Further, the same ports serve for both ' 
 ends of the cylinder ; the valve ports passing over the 
 seat ports in one direction for one end of the cylinder, 
 and in the opposite direction for the other end. 
 
 It will be seen from Fig. 62 that the cut-off valve 
 
 r? 
 
 /it \ 
 
 <- 
 
 
 Fig. 63 
 
 Fig. 64 
 
 has negative lap, since the ports are open when the 
 valve stands at its central position. The width of port 
 in the valve may equal or exceed the width of port in 
 the seat. In the former case, the negative lap is equal 
 to the width of port ; in the latter, to the distance a of 
 Fig. 63. The location of the eccentrics is shown in Fig. 
 64, d being the main and d' the cut-off; S being the ad- 
 vance angle of the former, and d' of the latter. The 
 centres of the lap circles Q and Q', Fig. 65, are found in 
 
THE GONZENBACH VALVE GEAR. 
 
 105 
 
 the usual way, by laying off the angles S and 8' up- 
 ward from the horizontal centre line. The effect of 
 the three ported valve being equivalent to a valve with 
 a single port of three times the width and travel, the 
 throw of the cut-off eccentric is in the diagram in- 
 
 Fi'g. 65 
 
 creased to three times that shown in Fig. 64, and the 
 lap circle is likewise drawn, with a radius three times 
 the actual negative lap for each port. Starting at 
 crank position A, it is clear that the main valve is 
 open by the amount of its lead. The cut-off valve is 
 at a distance Q'a from its central position, which being 
 
J05 SLIDE VALVE GEARS. 
 
 less than the negative lap, the cut-off ports are open, — 
 a fact which is also shown by the dotted (negative) lap 
 circle going below the horizontal centre line. As the 
 crank rises, the port opens more widely, up to position 
 
 B. In the original discussion of the Bilgram diagram 
 it appeared that when the crank passed through Q the 
 valve stood central upon its seat. In that position the 
 ports of the present valve stand wide open, — as is 
 apparent from the plan of the valve and the present 
 diagram alike. Passing crank position B, the valve 
 begins to close the port, not by returning toward its 
 former position as with previous valves, but by passing 
 on to the other side of its centre line, — as is indicated 
 in the present diagram, by the perpendicular from Q' 
 falling upon the opposite side of the crank. 
 
 The closure is completed and cut-off takes place at 
 
 C, which is indicated in the usual manner. From this 
 point expansion goes on in the cylinder and lower chest 
 together, until crank position D is reached, where the 
 main valve closes its port. As has been stated, the ex- 
 pansion is varied by changing the angular advance of 
 the cut-off eccentric. If S' of Fig. 64 be increased, Q' 
 of Fig. 65 will be lowered toward the centre line and 
 the cut-off position C of the crank will be shifted to an 
 earlier part of the stroke. This change in the cut-off 
 will be accompanied by an earlier and earlier admission 
 from the upper to the lower steam chest, as will be 
 shown by the large lap circle having a larger and larger 
 segment below the horizontal centre line. Crank posi- 
 tion D extended backward gives the position at which 
 the main valve cuts off the steam on the previous stroke, 
 and it is clear that the cut-off eccentric might be ad- 
 
THE G0N2.EMBACH VALVE GEAR. I07 
 
 vanced so far that the admission from the upper to the 
 lower chest would occur before the main valve had 
 closed its port in the previous stroke ; i.e., in advanc- 
 ing the eccentric to obtain an early cut-off the result 
 would be to give a second admission of steam at the 
 latter end of the expansion. This feature limits the 
 range of variation to the expansion which this gear can 
 give. The only way to provide a shorter cut-off is to 
 increase the lap of the main valve, since this carries 
 crank position D backward, and allows the cut-off lap 
 circle to be carried farther back before interfering with 
 the main valve. 
 
 The principles of this valve, and of the application 
 of the diagram to it, can be fixed in the mind by fqjy 
 lowing the solution of 
 
 Problem VII. A Gonzenbach valve gear is to be 
 constructed with a maximum cut-off of f stroke. The 
 greatest port opening to steam of the main valve is to 
 be ij". Since there is nothing to prevent liberality in 
 this respect, the cut-off ports will number three, each 
 one inch wide in valve and seat ahke. Required the 
 shortest possible cut-off, and the positions of the cut- 
 off eccentric for the earliest and latest cut-off. 
 
 In Fig. 66 the centre Q of the main valve lap 
 circle is found in the usual manner. Lead position 
 A and maximum cut-off position B are then drawn. 
 At the latest cut-off the cut-off valve lap circle must 
 be tangent to A and B, and its radius being three 
 inches (three times the port opening), it is easily drawn, 
 giving Q' the position of cut-off eccentric for latest cut- 
 off. Extending B downward and finding Q' such as 
 to make the cut-off lap circle tangent to B extended, 
 
io8 
 
 SLIDE VALVE GEARS. 
 
 determines crank position C, the earliest cut-off prac- 
 ticable with the dimensions given, and also the range 
 of movement Q! to Q' of the cut-off eccentric. 
 
 It has been shown that the range of cut-off with this 
 gear is somewhat limited. Another defect of the ar- 
 rangement is the large volume of the lower chest, which 
 increases the clearance space during expansion. The 
 
 object of a separate cut-off valve is to introduce early 
 cut-off, and it is in these early cut-offs that the effect 
 of this increased clearance is greatest, making a serious 
 discrepancy between the " real " and " apparent" ex- 
 pansion. For these reasons, together with the inac- 
 cessibility of the lower valve, the plan has largely fallen 
 into disuse. 
 
THE MEYER VALVE GEAR, 
 
 109 
 
 THE MEYER VALVE GEAR. 
 
 X 
 
 In this gear, which has been very extensively used, 
 a separate valve is used for the sole purpose of cutting 
 off, as in the last example. The general arrangement 
 of the valves is shown in Fig. 6"], from which it will be 
 seen by reference to the dotted lines that the main valve 
 is essentially a plain valve of the usual type, with the 
 addition of a bridge at each end to form a port through 
 
 (E 
 
 Fig. 67 
 
 The Meyer Valve. 
 
 it, and planed upon its back to form a seat for the cut- 
 off valves. These cut-ofi valves are driven by a sepa- 
 rate eccentric, and, as shown, the cut-off valve rod con- 
 tains a right and a left hand screw upon which the 
 valves are threaded. The valve rod has a hand wheel 
 upon it, and its connection with the eccentric rod is 
 such as to permit its being rotated at will by means of 
 the hand wheel. This rotation increases or decreases 
 the distance apart of the valves, and thereby changes 
 their lap and the point of cutting off. An index is at- 
 tached, which, moving over a graduated scale, shows at 
 a glance the position of the valves upon the stem and 
 
'10 SLIDE VALVE GEARS. 
 
 the degree of expansion. Occasionally this rotation of 
 the valve rod has been connected to the governor, but 
 the extent of the movement required and the friction 
 incident to the mechanism are so great as to render 
 such a plan a questionable success. Unlike the pre- 
 vious gear, the angular location of the cut-off eccentric 
 is not a matter requiring exactness. In the older prac- 
 tice it was customary to place that eccentric exactly 
 opposite the crank, or, since that gave the same motion, 
 to connect the valve rod to the cross-head by means of a 
 lever. This plan is still followed in marine, hoisting, and 
 other engines which are to turn in both directions, since 
 the motion of the cut-off valves is then correct for both 
 forward and backward rotation. In present practice 
 Ine cut-off eccentric of stationary engines is not usu- 
 ally placed so far in advance of the main eccentric. A 
 common location is forty five degrees in advance. The 
 effect of this is to require a smaller movement for a 
 given change of the expansion. To offset this advan- 
 tage, it reduces somewhat the width of port opening 
 given by the cut-off valve and the speed of cutting off. 
 The application of the Bilgram diagram to this gear 
 is shown in Fig. 68. The locations of the eccentrics 
 are shown at d and d' , the throw of the latter exceed- 
 ing that of the former, as is customary in practice. It 
 will be understood at the outset that since the lap of 
 the cut-off valve is changed to vary the point of cutting 
 off, a number of cut-off lap circles will appear in the 
 diagram. Some of these will represent positive and 
 some negative lap, and the determination of the proper 
 lap for different expansions is one of the leading points 
 to be determined from the diagram. Since the seat of 
 
, TH^ MEYER VALVE GEAR, ''--y^' HI 
 
 r< 
 
 the cut-off valves is upon the batk of the m'am valve, it 
 is clear that the diagram must show the 'position pf',the 
 former in relation to the latter. \' Beg|[t|i(i/ng with crank 
 
 '^^m^s'^-^' 
 
 Fig. 68 
 
 position A, it is clear that the main valve is advanced 
 to the right of its mid position by the distance Qa, and 
 the cut-off valve by the distance Q'a'. The'cut-off valve 
 
"/Cs ■ .... / 
 
 1 12 <^ -^i.'' 5Z/»^ VALVE GEARS. 
 
 is therefore removed from its mid position a distance 
 gV greater fhan the main valve. If it is desired that 
 the cut-off vshtill tkke jilace with the crank at A, there 
 must be a lap givpn to the cut-off valve equal to Qa" . 
 Hence the lap circle /'. Similarly for crank position B 
 the main V^ali'C is at a distance Qb and the cut-off Q'b' 
 from the central position. The displacement of the 
 main valve is here the greatest by Qb", and if the cut-off 
 valve had a lap of zero the main valve port would still be 
 covered by the distance Qb" . Therefore, if the cut-off 
 is to occur at this position of the crank, the cut-off valve 
 must have a negative lap equal to Q , b". Similarly the 
 value of the lap required for any cut-off may be found. 
 If the range of cut-off is to be from zero to that given 
 by the main valve, the positive lap required for the 
 former and the negative lap for the latter is easily found, 
 and the sum of the two amounts will give the total move- 
 ment of each valve on the stem to accomplish the required 
 range. The tangents drawn from point Q to the various 
 lap circles, and the perpendiculars dropped to them 
 from the point Q, form precisely the same construction 
 from as a centre that the diagram for the plain valve 
 did from O as a centre, and these lines with the lap 
 circles give the relations of the two valves to one an- 
 other precisely as though the main were a fixed seat 
 for the cut-off valve. As in Fig. 15, the distance Oc 
 represented the velocity of a plain valve at the moment 
 of cutting off, so in Fig. 68 the distances Qa" , Qb" repre- 
 sent the velocity of the cut-off valve relative to the main 
 valve at the same moment. In the figure it will be seen 
 that this velocity is somewhat less than the correspond- 
 ing velocity for the maximum cut-off by the main valve, 
 
fHk MMVER VAtfE GEAR. 113 
 
 and in fact a somewhat sluggishcut-off is a characteristic 
 of this valve gear. The only method of quickening this 
 velocity is to increase the distance between Q and Q' by 
 increasing the throw or angular advance of the cut off 
 eccentric. This, however, increases the diameters of 
 the lap circles, and the distances which the valves must 
 be moved on the stem, together with the length of steam- 
 chest to permit the increased movement. If the full 
 range of expansion is not required, the entire move 
 ment on the stem is available for the limited range, and 
 this can be put to good use by increasing the quickness 
 of the cutting off ; but generally in practice it is neces- 
 sary to adjust the conflicting requirements to one an- 
 other with a view to securing the best compromise 
 possible. 
 
 The greatest distance apart of the centres of the main 
 and cut-off valves, or in other words the half travel of 
 the cut-off relative to the main valve, is the distance 
 QQ ■ Should the cut-off plates be brought so near 
 together that the negative lap equalled this distance 
 QQ! , the cut-off valve would close the main valve port 
 for an instant and immediately reopen it. Should this 
 happen before the final cut-off by the main valve, it 
 would give a readmission of steam. To determine if 
 this is possible, strike the negative lap circle in ques- 
 tion with radius QQ' . Draw its tangent c through Q 
 and a crank line D parallel to the tangent. This crank 
 line D comes well within the main valve lap circle, indi- 
 cating that the latest possible cut-off by the cut-off valve 
 at which the momentary closure occurs takes place after 
 the closure of the port by the main valve. Had the line 
 D come tangent to the lap-circle it would have indicat- 
 
114 
 
 &Llt)£: VaLVB CEAkS. 
 
 e<J that the momentary closure of the main valve port 
 would have occurred just at the closure of the port by 
 the main valve ; and had it fallen without the lap circle, 
 as in Fig. 69, it- would have indicated that some of the 
 later grades of expansion would have been accompa- 
 
 Fig. 69 
 
 nied with readmission. This is of but little moment, 
 as, unlike the previous gear, it affects the late and not 
 the early cut-offs ; but it can be easily avoided. Thus 
 in Fig. 69, lines C and D being parallel, QQ', which is 
 perpendicular to C, is also perpendicular to D. If the 
 
THE MEYER VALVE GEAR. 
 
 115 
 
 position of Q' be altered to Q' , such that QQ' is per- 
 pendicular to E, it is clear that D and E will coincide, 
 the limiting condition will have been reached, and if 
 
 
 \ L 
 
 A 
 
 
 
 — -Vq' /i 
 
 
 \ ^-^^ 
 
 yf^^^'^ / 1 
 
 
 w 
 
 ^7-'-^^^^^^ / 
 
 
 / A \ 
 
 / i yxH /^\ \ 
 
 
 / / \ \ 
 
 
 
 / / \ \ 
 
 
 
 1 ' \ 
 / / \ 
 
 A- 
 
 1 \ 
 
 /■^ ! ^-—1—^-^1 
 
 r\ 
 
 
 a' « j 1 
 
 
 I 
 
 / 
 
 
 \ ', 
 
 / / 
 
 
 / / 
 
 
 / / 
 
 
 V\. 
 
 // 
 
 
 \ "v^ 
 
 ^'^ / 
 
 
 \ ^^ 
 
 ^^^^ / 
 
 
 s^ ^--. 
 
 
 
 v^ 
 
 ~" ''^ / 
 
 
 N» 
 
 ^ 
 
 
 ^ 
 
 ^H"'^ 
 
 
 
 .^^ 
 
 
 ^^^~ 
 
 
 Fig. 70 
 
 the centre of the cut-off lap circles be located slightly 
 to the right of Q' , no possible readmission can occur. 
 One point requiring attention remains. It is clear 
 
Il6 SLIDE VALVE GEARS. 
 
 that were the cut-off plates quite narrow, they might 
 when screwed well apart pass entirely over the main 
 valve ports and readmit steam by their back edges, and 
 the width must plainly be made great enough to pre- 
 vent this. In Fig. 70 place the crank at the dead-point 
 position A, and determine the lap necessary for cut-off 
 at that extreme position. The valves are located at dis- 
 tances Qa and Q'a' from their mid positions, and Q'a" is 
 the radius of the required lap circle. As the crank 
 mounts upward Qa lengthens and Q'a' shortens, until at 
 crank position B parallel to QQ , Qa and Q'a' are equal. 
 Beyond B, Qa exceeds Q'a', until at C, Q'a' vanishes. 
 Beyond C, Q'a' falls upon the rear side of the crank, and 
 at Z>, Qa' becomes (2V. At this point the distance 
 apart of the centres of the valves is Qd' plus Qd. In 
 other words, 'that distance has diminished from Q'a" \.o 
 zero, and increased again in the opposite direction to 
 (2df plus Q'd'. With the crank at ^ the edge of the 
 cut-off plate just closed the port, and at D it will have 
 closed the port by a distance Q'a" plus Q'd' plus Qd\ 
 and the width of the plate must equal this distance, 
 plus the width of the main valve port, plus an allow- 
 ance for tightness — say J". 
 
 THE BUCKEYE VALVE GEAR. 
 
 This exceedingly ingenious valve gear is in one 
 sense a combination of the two preceding. To the 
 small clearance and mechanical capabilities of the Me}er 
 valve it unites the turning eccentric of the Gonzenbach 
 with its convenient attachment to the shaft governor.* 
 * The Buckeye was the pioneer shaft-governor engine. 
 
THE BUCKEYE VALVE GEAR. 
 
 "7 
 
 At the same time it is not limited in range as is the 
 Gonzenbach, and it has a sharper cut-off than either 
 one. Balancing and other features of the valve dis- 
 guise its relationships somewhat, but discussion of these 
 features is beyond the scope of the present work. The 
 
 "^1 
 
 Fig. 71 
 
 The Buckeye Valve. 
 
 construction of the valve, so far as its action on the 
 ports is concerned, is shown in Fig. 71, from which it 
 will be seen that it takes steam from within its box-like 
 form, and exhausts by its ends into what with other 
 valves is commonly the steam-chest. The cut-off 
 valves are similar to those of the Meyer system, ex- 
 cept that they are secured immovably upon the rod. 
 
 c b 
 Fig. 72 
 
 Fig. 72 is an ideal view of the same valve with a diagram 
 of the eccentrics. The position of the crank being 
 at A, the main eccentric, by reason of the valve ex-' 
 hausting by its outside edges, is at d. The main 
 eccentric and valve rods are connected to a rocker 
 
Il8 SLIDE VALVE GEARS. 
 
 pivoted at b. This rocker does not change the motion 
 of the main eccentric in transmitting it to the valve. 
 The cut-off eccentric and valve rods are also connected 
 to a rocker, the former at c and the latter at e. This 
 rocker is pivoted at f, which pivot is carried by the 
 main rocker. It is clear that the motion which the 
 cut off eccentric rod imparts to the lower end of its 
 rocker is, if the eccentric be properly set, precisely the 
 same as that required for a Gonzenbach cut-off valve, 
 having its seat in line with the eccentric rod. But the 
 distance be always equals eg, or, in other words, the 
 motion of the upper end of the cut-off rocker relative 
 to the main rocker is the same as that of the lower end 
 relative to a fixed valve seat. That is, the motion of 
 the cut-off valve relative to the main valve is the same 
 as that of the Gonzenbach cut-off valve relative to its 
 fixed seat. With the Gonzenbach gear a single set of 
 ports through the cut-off valve-seat served for both ends 
 of the cylinder, and it was shown that, in consequence, 
 there was danger in the early grades of expansion of a 
 readmission of steam before final closure of the port by 
 the main valve. With the construction of the present 
 gear this is avoided, and, properly proportioned, there 
 can be no readmission in either the early or late grades. 
 The exhaust taking place at the ends of the main valve 
 locates the eccentric diametrically opposite from its 
 usual position, and the cut-off rocker does the same for 
 the cut-off eccentric. The angular position of the cut- 
 off eccentric rod also moves the cut-off eccentric from 
 the positions shown in Fig. "j}, by the same angle. 
 Since the action of the cut-off valve is essentially the 
 same as in the Gonzenbach gear, it may be represented 
 
THE BUCKEYE VALVE GEAR. 
 
 119 
 
 by essentially the same diagram as in Fig. 73. Q is as 
 usual the centre of the main valve lap circles and Q' , 
 Q", Q'" oi the cut-off (negative) lap circle for different 
 points of cut-off, Q' being the position for cut-off at 
 
 Fig. 73 
 
 zero, Q" for latest cut-off, i.e., at the main valve closure, 
 and Q'" for any desired crank position A. The open- 
 ing of the ports by the cut-off valves is in this instance 
 of little moment, since it occurs during the previous 
 stroke, when the admission port for the end of the 
 cylinder under consideration is out of action. 
 
I20 
 
 SLIDE VALVE GEARS. 
 
 THE STRAIGHT LINE INDEPENDENT CUT-OFF GEAR. 
 
 Fig. 74 is a horizontal section of a steam cylinder 
 fitted with the above valves, the bottom of the figure 
 
 showing the steam and the top the exhaust valve. The 
 two are of similar construction, both being fitted with 
 
STRAIGHT LINE INDEPENDENT CUT-OEE GEAR. 121 
 
 relief plates and multiple ports, and both acting by 
 their outside edges. They differ chiefly in that the 
 exhaust valve is driven by a fixed, and the steam valve 
 by a swinging eccentric. The Bilgram diagram as ap- 
 plied to the gear consists of the diagram already 
 
 Fig. 75 
 
 familiar for the swinging eccentric gear, but with the 
 exhaust lap circle occupying a fixed position instead of 
 the moving one of the usual swinging eccentric gear. 
 Contrary to all previous practice with independent 
 valves, this engine is arranged for positive lead in the 
 
122 SLIDE VALVE GEARS. 
 
 late and negative in the early cut-offs. The object of 
 this is as follows : It is generally understood that com- 
 pression does not begin to bring the piston to rest until 
 the pressure on the compression side exceeds that on 
 the expansion side of the piston. With an early cut- 
 off this state of affairs occurs at some distance from the 
 end of the stroke, but at later cut-off the expansion 
 curve is higher and the compression curve does not 
 rise so soon to equal it. Hence the effect of the com- 
 pression in bringing the parts to rest is lessened at late 
 cut-off, and to make up for the deficiency a prominent 
 lead is given. 
 
 The application of the Bilgram diagram is shown in 
 Fig. 75, in which Q is the centre of the steam valve lap 
 circle for greatest throw, cut-off at ^ ; Q is the fixed 
 centre of the exhaust lap circle, and Q" the centre of 
 the steam circle with the eccentric shifted for cut-off at 
 A, the path of the eccentric centre being QQ" . It will 
 be observed that for cut-off at B the lead is positive 
 and at A negative. The fixed position for compression 
 is C, and for release D. 
 
 ^ THE BILGRAM VALVE GEAR. 
 
 This gear has been designed to provide a more rapid 
 cutting off than the Gonzenbach or Meyer gear. The 
 following description is from Mr. Bilgram's book on 
 this subject (now out of print) : 
 
 Both valves are operated by one single eccentric /, 
 Fig. 76 ; the main valve directly by the eccentric rod, 
 and the cut-off valve through a peculiar mechanism, 
 consisting of four members ; viz. : the link, the rocker, 
 
THE BILGRAM VALVE GEAR. 
 
 123 
 
 Fi2- 7G 
 
124 SLIDE VALVE GEARS. 
 
 the cut-off rod, and the adjustment lever. The link 
 AB being jointed by the pin A to the eccentric rod, 
 imparts to the rocker a rocking motion on its fulcrum 
 F. The rocker is of a peculiar shape, as shown de- 
 tached in the cut, but it virtually represents a bell crank 
 (or angular lever) having an angle BFC of about 50°, 
 the arm CF of which is about twice as long as the arm 
 BF. To the extreme end C of this rocker is jointed 
 the cut-off rod, by which the cut-off valve is moved. 
 For the purpose of changing the degree of expansion 
 the fulcrum F of the rocker can be moved in a circular 
 arc, being attached to the end of the adjustment lever 
 GF, whose fulcrum G^ is a fixed point. 
 
 The study of this gear will consist in the investiga- 
 tion of the movement of the cut-off valve for several 
 positions of the adjustment lever. In every case we 
 shall proceed from the neutral position of the rocker 
 (found by transferring the eccentric rod to the centre 
 of the crank shaft), remembering that the movement of 
 the mechanism will be symmetrical to both sides of this 
 position. Besides, we shall as usual neglect all com- 
 pHcating influences resulting from the angularity of 
 the several members ; and besides, we shall assume the 
 movement of the pin A to be strictly circular and co- 
 incident with the movement of the eccentric /. 
 
 At first we move the adjustment lever until the line 
 CF of the rocker assumes a vertical position (see Fig. 
 "j"]^, the theory for this position being the least compli- 
 cated. When the mechanism is in operation, the pin 
 A will move in a circle, and hence the points B and C 
 will move in the arcs b'b" and c'c". For the latter arc 
 we shall substitute the chord to simplify the theory. 
 
THE BILGRAM VALVE GEAR. 
 
 125 
 
 When the crank is on its centre, the pin A will occupy 
 the position A° corresponding to the position of the 
 eccentric /, and since the link AB represents, as it 
 were, the eccentric rod for the cut-off gear, we can 
 measure the angle of advance 8° = VAA° by drawing 
 ^ Fat right angles to BA. The angle CFB being 50° 
 
 X 
 
 
 
 Fig. 77 
 
 and AB being at right angles with FB, or approximately 
 so, it is evident that the angle YAA° =■ S° exceeds 
 the angle of advance of the eccentric / by 50°. Owing 
 to the dimensions of the rocker, the travel of the point 
 C, and consequently also the travel of the cut-off valve, 
 equals double the travel of the main valve ; and hence 
 we can find the ideal eccentric i° of the movement of 
 the cut-off valve for the considered grade by advancing 
 the line 01 through an angle of 50° and doubling its 
 length. 
 
126 SLIDE VALVE GEARS. 
 
 Next we move the fulcrum F towards the right to 
 F' to change the grade, and denote the angular change 
 of the rocker by the Greek letter (i. The correspond- 
 ing angular change of the link AB is practically the 
 same, and the angular advance is consequently farther 
 increased by this angle. We can therefore draw the 
 line Oi' , but we have yet to find its length. The move- 
 ment d'd" of the pin C of the rocker is doubtless the 
 same as it was before ; but being inclined, it is only its 
 horizontal component d'd° that is transmitted to the 
 valve, and the throw Oi' of the ideal eccentric for this 
 grade will be less than Oi°. The necessary reduction 
 can be made by drawing the line i°i' at right angles to 
 Oi' , which will be understood when we consider the 
 similarity of the triangles Oi'i° and d'd°d" . 
 
 In moving the fulcrum F of the rocker in the oppo- 
 site direction we would have found the ideal eccentric 
 i" , and other positions of the fulcrum i^ would furnish 
 more points of the locus of ideal eccentrics. The angle 
 i°i'0 being a right one, it will easily be understood that 
 all the ideal eccentrics will be located in a circle of 
 which the line Oi° is a diameter. 
 
 These results relate to the absolute movement of the 
 valve, and to find the ideal eccentrics for the relative 
 movement we move the locus in the direction of and 
 through a distance equal to 10. Having thus deter- 
 mined the locus j'j°j" of the relative movement, we can 
 draw the valve diagram. Fig. 78, in the usual manner. 
 
 This diagram now shows that the cut-off can be ad- 
 justed to any point between the crank angles OA and 
 OE as the angular adjustment of the rocker is not lim- 
 ited. It shows, moreover, that this valve gear is distin- 
 
THE BILGRAM VALVE GEAR. 
 
 127 
 
 guished by the decided rapidity in cutting off. The 
 closure of the steam passagej is very sharp for all grades 
 cutting-off before the half stroke ; for a later cut-off 
 however, this rapidity will get less, until when cutting 
 off at OE the rapidity of the cutting off of the cut-off, 
 valve will about equal that of the main valve. 
 
 Fig. 78 
 
 The rapidity of the late cut-offs can be improved, if 
 desired, by. making the arm CFoi the rocker more than 
 double the length of the arm BF, whereby the line Oi° 
 will be lengthened, and consequently the locus circle will 
 be enlarged. This change entails an increase of the ab- 
 solute movement of the cut-off valve above twice the 
 travel of the main valve. Another measure consists 
 
128 
 
 SLIDE VALVE GEARS. 
 
 in increasing the negative lap of the cut-off valve ; but it 
 should never exceed the positive outside lap of the main 
 valve. A reduction of the angle BFC of the rocker 
 would likewise be efificient, but this reduction is at- 
 tended by an increase of certain irregularities. 
 
 The sharpness of the cut-off will in reality be slightly 
 less than indicated in the diagram, from the fact that > 
 the movement of the pin A is not circular, as was as- 
 sumed, but is more or less flattened. 
 
 The proportioning of the mechanism requires some 
 
 Fig. 79 
 
 care, for on it depends largely the proper operations 
 and regularity of the cut-off. To this end we draw the 
 rocker BFC (Fig. 79) with the line CF in a vertical 
 position and the line BF a.t an angle of 50°, and make 
 the arm BFirom three to four times the throw of the 
 eccentric, and the arm CF twice as long. (The figures 
 
TBE BILGRAM VALVE GEAR. 12g 
 
 given have been tested by a number of experiments.) 
 Then we draw the link AB at right angles to BF and 
 make it about -f- of the length of CF. The eccentric 
 rod OP ca.n next be shown in its neutral position, pass- 
 ing through the end A of the link. The cut-off rod 
 CP° can likewise be shown. 
 
 To find the length and position of the adjustment 
 lever GF, it is necessary to make a model of thin wood 
 or veneer, consisting of the eccentric rod, the link, the 
 rocker, and the cut-off rod. Next we draw the orbit of 
 the eccentric, and on it the exact position of the eccen- 
 tric, say for every one sixth of the stroke of the piston, 
 which may be done in the following way, identifying 
 the eccentric path with the path of the crank pin : 
 
 We divide the diameter of the orbit passing through 
 the initial position of the eccentric / in six equal parts, 
 and draw the projection arcs of the proper radius 
 through those points as shown. The ne!xt thing to be 
 done is to attach the model to the drawing by joining 
 the parts properly together with pins or thumb tacks, 
 and fastening the ends P and P° of the rods to two 
 slides representing the valves. The right end of the 
 eccentric rod may be provided with a needle point 
 which at first we put in the centre 0, when we set the 
 rocker directly over the position shown in the drawing, 
 and mark the relative position of the two slides repre- 
 senting the valves. Then we make two additional 
 marks on one of them, at a distance equal to the as- 
 sumed negative lap of the cut-off valve, to show the 
 relative position for the cutting off on either side. 
 Suppose now we desire to find the proper position of 
 the rocker for cutting off at the point 1. To this end 
 
130 SLIDE VALVE GEARS. 
 
 we set the needle point of the eccentric rod in the point 
 1 of the fore stroke, and fix the valves for cutting off 
 at the proper side, when we will find that the end F of 
 the rocker cannot be moved but in a certain curve. 
 This curve we mark on the drawing by setting a needle 
 point into the rocker and making a slight scratch on 
 the paper. Thereupon we attach the eccentric to the 
 point V of the return stroke, fix the cut-off valve to the 
 point of closure of the other passage of the main valve, 
 and mark another curve by the point F oi the rocker. 
 The juncture F' of the curves must of necessity be the 
 exact position of the fulcrum of the rocker when we de- 
 sire to cut off at one sixth of the stroke. In this way 
 we can find the required position of the fulcrum for all 
 the other grades, which will be found to form a curve. 
 By substituting a circular arc for this curve, osculat- 
 ing as closely as possible, we obtain the location and 
 length of the adjustment lever GF. An arc can gener- 
 ally be found to agree with the constructed curve with 
 an almost absolute precision ; and hence it will be seen 
 that this valve gear will admit of a practically perfect 
 equalization of the difference between fore and return 
 stroke. 
 
INDEX. 
 
 PAGE 
 
 Admission 13, ig, 21, 23 
 
 Advance angle 18 
 
 Allen valve, the 69 
 
 Angle, lap 15 
 
 " lead 23 
 
 Angular advance 18 
 
 Angular vibration of the connecting rod 45 
 
 " " " eccentric rod 49,85 
 
 Areas of the ports and pipes 42 
 
 Armington & Sims valve, the 73 
 
 Armstrong valve, the 72 
 
 Backward rotation 11, 26 
 
 Bilgram diagram, the 28 
 
 " valve gear, the 122 
 
 Buckeye valve gear, the 116 
 
 Cavity, influence of the exhaust , 39 
 
 " width of the exhaust 38 
 
 Centers, locating the engine on the 59 
 
 Clearance, inside 4 
 
 Compression 15,21,23 
 
 Connecting rod, angular vibration of the 45 
 
 " " irregularities due to the 5 
 
 " " of infinite length 47 
 
 Cross-head, the slotted 5 
 
 Cut-off 13,21,23 
 
 ' ' and lead equalized 95 
 
 " equalized 54 
 
 ' ' the slide valve at short 67 
 
 131 
 
13^ iNtoM. 
 
 PAGfi 
 
 Defects of the primitive engine 13 
 
 Diagram, the Bilgram 28 
 
 Eccentric, position of, for either direction of rotation 27 
 
 " rod, angular vibration of the 49, 85 
 
 " " irregularities due to the 5 
 
 the 4 
 
 " " shifting 78 
 
 " " swringing 80 
 
 " throw of the 4 
 
 Engine, the primitive 7 
 
 " " " defects of 13 
 
 Equalized cut-off 54 
 
 " exhaust 56, 57 
 
 ' ' lead 89 
 
 ' ' lead and cut-off 95 
 
 Examples, illustrative 24, 35 
 
 Exhaust cavity, influence of the 39 
 
 " " width of the 38 
 
 " equalized 50, 57 
 
 " lead 31 
 
 " lap 4,25 
 
 " port opening 26,31 
 
 Gear, the Bilgram valve 122 
 
 " " Buckeye " 116 
 
 " " Gonzenbach valve 102 
 
 " " Meyer " 109 
 
 " " Straight Line " 54, 89, 120 
 
 Giddings valve, the 74 
 
 Gonzenbach valve gear, the I02 
 
 Gridiron valve, the 103, 105 
 
 Ide valve, the 74 
 
 Influence of the exhaust cavity 39 
 
 Illustrative examples 24, 35 
 
 Lap 3, 15 
 
 " angle 15 
 
PAGE 
 
 Lap, circle 31 
 
 effects of 1 8, 35 
 
 how measured 4 
 
 inside or exhaust 4.25 
 
 negative 4. 26 
 
 outside or steam 3.15 
 
 positive and negative, how shown 31 
 
 Lead 13. 21 
 
 ' ' and cut-off equalized 95 
 
 " angle 23 
 
 ' ' equal and constant defined 77 
 
 " decreasing in early cut-off 82,93,122 
 
 " increasing " " " 81 
 
 " equalized 89 
 
 ' ' exhaust 31 
 
 ' ' negative 93 
 
 Limitations of the plain slide valve 40 
 
 " " " " " how overcome 67 
 
 Meyer valve gear, the 109 
 
 Negative lead 93 
 
 Opening, exhaust port 26, 31 
 
 " port 18, 31 
 
 " " definition of 42 
 
 " varying width of port 37 
 
 ' ' width of port to steam 43 
 
 Over-travel of the valve 42, 77 
 
 Pipes and ports, areas of the 42 
 
 " " velocity of steam through the 43 
 
 Piston, speed of, in the two strokes 47 
 
 Port opening 18, 31 
 
 " " defined 42 
 
 " " exhaust 26,31 
 
 " " varying width of 37 
 
 " " width of , to steam 43 
 
 Ports, length and breadth of 44 
 
134 lND&)i. 
 
 PAGfi 
 
 Ports, multiple 68, 69, 72 
 
 " " for the exhaust 7° 
 
 Primitive engine, the 7 
 
 " " defects of the 13 
 
 Release 13, 21, 23 
 
 " proper location of the 102 
 
 Reverse rotation 11, 26 
 
 Rice, valve, the 72 
 
 Rock shaft 7. 27, 56 
 
 Rod, angular vibration of the connecting 45 
 
 " " " " eccentric 49.85 
 
 ' ' connecting, of infinite length 47 
 
 Rotation, reverse 11, 26 
 
 " position of eccentric for either direction of 27 
 
 Scotch yoke, the S 
 
 Setting the slide valve 59 
 
 Shaft, rock 7, 27, 56 
 
 Shifting eccentric, the 78 
 
 Slide valve, laying out the 38 
 
 " " limitations of the plain 40 
 
 " " " " " how overcome 67 
 
 " " setting the 59 
 
 " " the, at short cut-off 67 
 
 " " the plain 3 
 
 Steam, velocity of, through pipes and passages 43 
 
 Straight Line valve, the 69, 120 
 
 " " " gear, the 54,89,120 
 
 Swinging eccentric, the 80 
 
 Throw of the eccentric 4 
 
 Valve, laying out the slide 38 
 
 ' ' limitations of the plain slide 40 
 
 " " " " " how overcome 67 
 
 " over-travel of the 42, 77 
 
 ' ' setting the slide 59 
 
 " the Allen 69 
 
I\DEX. 135 
 
 FACE 
 
 Valve, the Armington & Sims 73 
 
 " " Armstrong 72 
 
 " " Buckeye n6 
 
 " " G'iddings 74 
 
 " " gridiron 103,105 
 
 " " Gonzenbach 102 
 
 " Ide 74 
 
 " " Meyer 109 
 
 " " Rice 72 
 
 " " slide at short cut-off 67 
 
 " " Straight Line 6g, 120 
 
 " " plain slide 3 
 
 " " Woodbury 70 
 
 " velocity of the 39 
 
 Valve gear, the Bilgram 122 
 
 " " " Buckeye 116 
 
 " " " Gonzenbach 102 
 
 " ' "Meyer 109 
 
 " " " Straight Line 54, 89, 1 20 
 
 Velocity of steam through pipes and passages 43 
 
 ' ' of the valve 39 
 
 Vibration of the connecting rod, angular 45 
 
 " " " eccentric " " 49i 85 
 
 Width of the exhaust cavity , 38 
 
 Woodbury valve, the 70 
 
 Yoke, the Scotch 5 
 
Cutulogue of the Scientific Publications 
 
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