>i 4 V PRACTICAL INSTRUCTIONS RELATING TO THE CONSTRUCTION AND USE OF THE STEAM ENGINE INDICATOR PAET I SENERAL DESIGN AND CONSTRUCTION OF STEAM ENGINE INDICATORS SPECIAL DESIGN, CONSTRUCTION AND USE OF THE CROSBY INDICATOR PAET II APPLICATIONS OF THE INDICATOR PART III PROPERTIES OF STEAM AND OF PERFECT GASES DESIGN OF A PLAIN SLIDE VALVE VALVE SETTING ON PLAIN SLIDE VALVE ENGINES AND ON CORLISS ENGINES PARTS II AND III By EDWARD F. MILLER Pro/e.i.sor nf Stcnm Eiifiiiitfrinri Massachusetts Institute of Technology PUBLISHED BY THE CROSBY STEAM GAGE AND VALVE COMPANY Boston, Massachusetts, U.S.A. 1911 Copyright, 1911, by Crosby Steam Gage and Valve Company QKO. H. ELLIS CO. PRINTERS, BOSTON INTRODUCTION The purpose of this book is to enable any engineer, First, To understand the design, construction and use of the Crosby Steam Engine Indicator. Second, To make suitable preparation for applying it to a steam engine, and attach- ing the mechanism for operating the paper drum. Third, To take diagrams, read them intelligently, and, after some experience, to deduce from them such information concern- ing the working of an engine as a good instrument skilfully applied and handled is capable of revealing to the studious and observing mind. Crosby Steam Gage and Valve Company Boston, Sept. 1, 1911 CONTENTS PART I CHAPTER I The Steam Engine Indicator 1 Diagram Lines Explained 6 Definitions of Technical Terms 9 CILYPTER II The Crosby Steam Engine Indicator 16 The Crosby Standard Steam Engine Indicator ... 18 The Crosby New Steam Engine Indicator 24 The Crosby New Indicator No. 2 27 The Crosby Indicator with Drum for Taking Continu- ous Diagrams 29 The Lanza Continuous Diagram Appliance .... 32 CHAPTER III The Crosby Gas Engine Indicator 33 The Crosby Combined Gas and Steam Engine Indi- cator 34 The Crosby Anmaonia Indicator 34 The Crosby Ordnance Indicator 35 The Crosby Hydraulic Indicator 36 ' CHAPTER IV Indicator Attachments and Accessory Apparatus Needed in Making Tests 37 Sargent Improved Electrical Attachment 37 Cro.sby Standard Indicator with Detent 42 Planimeters 43 Tlu-ottling Calorimeter 49 V COXTEXTS CHAPTER V How to Handle and Take Care of a Crosby Indicator 55 Indicator Springs 59 Indicator Scales 60 CHAPTER VI How and Where to Attach the Indicator 62 CHAPTER VII Drum Motion 65 Reducing Lever 65 Brumho Pulley 67 Pantograph 69 Crosby Reducing Wheel 71 Crosby Reducing Wheel with Detent 73 Crosby Reducing Wheel with Recording Counter . . 74 Testing the Accuracy of Reducing Mechanism ... 77 CHAPTER VIII How to Take Diagrams 78 CHAPTER IX How to Find the Power of an Engine 81 The Piston Area 81 The Travel of the Piston 81 The Mean Effective Pressure 81 Calculating I. H. P 86 Discussion of M. E. P 86 Calculating H. P. of Gas Engine, Otto Fouy-Cycle . 88 Calculating H. P. of Gas Engine, Two-Cycle ... 93 Theoretical Efficiency of a Four-Cycle Gas Engine . 93 Actual Efficiency of a Gas Engine 93 CHAPTER X The Hyperljolic, Curve 94 CONTENTS PART II Applications 103 PART III CHAPTER I Properties of Steam and of Perfect Gases . . . . 123 Properties of Saturated Steam 124 Properties of Superheated Steam 128 Heat Consumption and Thermal Efficiency of aii Engine 132 Carnot Engine 133 Non-Conducting Engine 135 Temperature Entropy Chart . 137 Flow of vSteam through an Orifice 140 Measurement of Dry Steam by the Flow through an Orifice 141 Design of a Tiirbine Nozzle for Complete Expansion 141 Calculating the Size of a Steam Main 144 Characteristic Equation for Perfect Gases and its Ap- plication 146 Measurement of Air by the Flow through an Orifice . 148 Isothermal Lines . . , 148 Compressing Air 150 Calculation of Power Needed for a Compressor . . 150 Stage Compression 151 Probable Horse])ower of an Engine 153 CHAPTER II Method of Calculating from the Indicator Card from a Steam Engine, the Per Cent of Mixture Accounted for as Steam at CutH)f¥ and at Release . . . . 155 CONTENTS CHAPTER III Design of a Plain Slide Valve 158 Valve Setting on a Plain Slide Valve Engine and on a Corliss Engine 158 Explanation and Use of Zeuner Diagram 160 Laying Out a Plain Slide Valve 165 Setting a Plain Slide Valve Gear 166 Setting a Corliss Valve Gear 166 Explanation and Use of Logarithms 168 TABLES Logarithms 172 Areas and Circumferences of Circles 174 Weight of a Cubic Foot of Water 182 Charts Giving the Values of the Temperature, Heat of the Liquid, Total Heat, Latent Heat, and Specific Volume, Between and 10 Pounds Absolute and Between 10 Pounds and 250 Pounds Absolute . . 182a-& Temperature Entropy Chart 182c APPENDIX Crosby Revolution Counter 185 Crosby Square Counter 187 Crosby Locomotive Counter 187 Crosby Recording Counter 188 Crosby Pressure and Vacuum Gages 190 Crosby Pressure Recorder 191 Crosby Pressure Recorder and Gage 193 Thermometers 195 Lanza Continuous Diagram Appliance 196 Crosby Lidicator Awards .,.,.. 201 PRACTICAL INSTRUCTIONS KELATINO TO THE CONSTRUCTION AND USE OF THE STEAM ENGINE INDICATOR PAET I CHAPTER I THE STEAM ENGINE INDICATOR The steam engine indicator, invented by James Watt, and long kept secret, was for many years after its secret became known, strangely neglected by most makers and users of steam engines. The earlier forms of the instrmnent, which preceded that invented by Richards, were so imperfect and so ill-adapted to engines running at other than very low speeds, that their indications were often misleading, more often unintelligible, and seldom of much value beyond revealing the point of stroke at which the valves ojjened and closed : a most valu- able service, alone worth the cost of an indicator, but only a small part of the service to be obtained from a really good instrument. The general princijiles on which the best type of the steam engine indicator is designed, may be briefly stated as follows : A piston of carefully determined area is nicely fitted into a cylinder so that it will move up and down without sensible 1 Z THE STEAM ENGIXE INDICATOR friction. The cylinder is open at the bottom and fittea so that it may be attached to the cylinder of a steam engine and have free communication with its interior, by which arrangement the under side of the piston is subjected to the varying pressure of the steam acting therein. The upward movement of the piston — due to the pressure of the steam — is resisted by a spiral spring of known resilience. A piston rod projects upward through the cylinder cap and moves a lever having at its free end a pencil point, whose vertical movement bears a constant ratio to that of the piston. A drum of cylindrical form and covered with paper is attached to the cylinder in such a manner that the j^encil point may be brought in contact with its surface, and thus record any movement of either paper or pencil ; the drum is given a horizontal motion coincident Avith and bearing a constant ratio to the movement of the piston of the engine. It is moved in one direction by means of a cord attached to the crosshead and in the opposite direction by a spi'ing within itself. When this mechanism is properly adjusted and free com- munication is opened with the cylinder of a steam engine in motion, it is evident that the pencil will be moved vertically by the varying pressure of steam under the piston, and as the drum is rotated by the reciprocating motion of the en- gine, if the pencil is held in contact v\dth the moving paper during one revokition of the engine, a figure or diagram will be traced representing the pressure of steam in the cylinder ; the upper line showing the pressure urging the engine piston forward, and the lower the pressure retarding its movement on the return stroke. To enable the engineer to more correctly interpret the nature of the pressures, the line showing the atmospheric pressure is drawn in its relative position, which indicates whether the jiressvire at any part is greater or less than that of the atmosphere. WHAT IS THE OUOD OF AX INDICATOR ? 8 From such a diagram may be deduced many particulars which are of supreme miportance to engine builders, engi- neers, and the owners of steam plants. WHAT IS THE GOOD OF AN INDICATOR? This question was asked by a young engineer who had come to examine and purchase a Crosby indicator, with a view to rendering his services of greater value to his em- ployer, by a knowledge and use of that instrument. His question was overheard by the proprietor of a large estab- lishment in the city of Worcester, Mass., who took occ'asion to re])ly as follows : " I will tell you what good an indicator did at our works. Our steam engine was not giving sufficient power for our business, and we expected to be obliged to procure a larger one. A neighbor suggested that we have our engine indi- cated to see if we were getting the best service obtainable from it. This was done with a Crosby indicator, and the result was that when the valves were properly adjusted and other slight changes made we had ample power, and the improved condition of the engine made a reduction in our coal bills during the following year of $500." Another case : An expert engineer was called to indicate several locomotives just completed by one of our prominent lo- comotive builders, who had in use a large Corliss engine, which ' had been running only a few months. When the locomotives were indicated, the pi-oprietor proposed that the indicator be applied to the Corliss engnie, the engineer of which remarked, " Guess you'll find her all right, as she's running fine." The first card showed that nearlij all the ivork was being done at one end of the cyUnder. The valves were changed and a great improvement was apparent in the running of the engine, while the actual consunq)tion of coal was reduced from an average of 3,370 pounds per day, before the change was made, to 2.338 pounds afterwards. 4 INDICATOR DIAGRAMS These two instances are valuable in showing " the good of an indicator." Items of Information to be obtained by the use of the Indicator The arrangement of the valves for admission, cut-off, release and compression of steam. The adequacy of the ports and passages for admission and exhaust, and when applied to the steam chest, the adequacy of the steam pipes. The suitableness of the valve motion in point of rapidity at the right time. The quantity of power developed in the cylinder, and the qiiantity lost in various ways : by wire drawing, by back l)ressure, by premature release, by mal-adjustment of valves, l)y leakage, etc. It is useful to the designers of steam engines, as by prop- erly combining the cards the effective pressure on the piston at any point can be determined, and from this the rotative effect or the rotating force acting at right angles to the crank can be calculated. Taken in combination with measurements of feed water and the condensation and measurement of the exhaust steam, with the amount of fuel used, the indicator furnishes many other items of importance when the economical generation and use of steam are considered. For every one of these purposes it is important that the diagrams traced by the indicator should truly represent the path of the piston and the pressure exerted on both sides of the piston at every point of that path. INDICATOR DIAGRAMS The degree of excellence to which steam engines of the present time have been brought is due more to the use of the indicator than to any other cause, as a careful study of indicator diagrams taken under different conditions of load, ANALYSIS OF THE DIAGRAM 5 pressure, etc., is the only means of becoming familiar with the action of steam in an engine, and of gaining a definite knowledge of the various changes of pressure that take place in the cylinder. An indicator diagram is the result of two movements, namely : a horizontal movement of the paper in exact corre- spondence with the movement of the piston, and a vertical movement of the pencil in exact ratio to the pressure exerted in the cylinder of the engine ; consequently, it represents hy its length the stroke of the engine on a reduced scale, and hy its height at any point, the pressure on the piston at the corresponding point in the stroke. The shape of the diagram depends altogether upon the manner in which the steam is admitted to and released from the cylinder of the engine ; the variety of shapes given from different engines, and by the same engine under different circumstances, is almost endless, and it is in the intelligent and careful measurement of these that the true value of the indicator is found, and no one at the present day can claim to be a competent engineer who has not become familiar with the use of the indicator, and skilful in tui-ning to practical advantage the varied information which it furnishes. A diagram shows the pressure acting on one side of the piston only, during both the forward and return stroke, whereon all the changes of pressure may be properly located, studied, and measured. To show the corresponding pres- sures on the other side of the piston, another diagram must be taken from the other end of the cylinder. When the tlii"ee-way cock is used, the diagrams from both ends are usually taken on the same paper, as in Fig. 2. ANALYSIS OF THE DIAGRAM The names by which the various points and lines of an indicator diagram are known and designated are given on the page following. See Fig. 1. DIAGRAM LINES EXPT.AIXER The closed figure or dia- gram, C D E F G H is drawn by the indicator, and is the result of one in- dication from one side of the piston of an engine. The straight line A B is Fig. 1 also drawn by the indicator, but at a time when steam con- nection Avith the engine is closed, and both sides of the indi- cator piston are subjected to atmospheric pressure only. The straight lines O X, O Y, and J K, when required, are drawn by hand as explained below, and may be called reference lines. DIAGRAM LINES EXPLAINED The admission line C D shows the rise in pressure due to the admission of steam to the cylinder by the opening of the steam valve. If the steam is admitted quickly when the engine is about on the dead-center this line will be nearly vertical. The steam line D E is drawn when the steam valve is open and steam is being admitted to the cylinder. The point of cut-off E is the point where the admission of steam is stopped by the closing of the valve. It is some- times difficult to determine the exact point at which the cut-off takes place. It is usually located Avhere the outline of the diagram changes its curvature from convex to concave. REFERENCE LIXES EXPLAINED i The expansion curve E F shows the fall in pressure as the steam in the cylinder expands behind the moving piston of the engine. The point of release Y shows when the exhaust valve opens. The exhaust line F G represents the loss in pressure which takes place when the exhaust valve opens at or near the end of the stroke. The hack 2»'e-'isitre line G H shows the pressure against which the piston acts during its return stroke. On diagranis taken from non-condensing engines it is either coincident with or above the atmospheric line, as in Fig. 1. On cards taken from a condensing engine, however, it is found below the atmospheric line, and at a distance greater or less, according to the vacuum obtained iii the cylinder. . The j^oint of exhaust closure His the point where the exhaust valve closes. It cannot be located veiy definitely, as tlie change in pressure is at first due to the gradual closing of the valve. The compression curve H C shows the rise in pressure due to the compression of the steam remaining in the cylin- der after the exliaust valve has closed. The atmospheric line A B is a line drawn by the pencil of the indicator when its connections with the engine are closed and both sides of the piston are open to the atmos- phere. This line represents on the diagram the pressure of the atmosphere, or zero of the steam gage. REFERENCE LINES EXPLAINED The zero line of pressure, or line of absolute vacuum, O X, is a reference line, and is drawn by hand, 14 ^^ pounds by the scale, below and parallel with the atmospheric line. It represents a perfect vacuum, or absence of all ])ressure. The line of boiler pressure i K is drawn by hand parallel to the atmospheric line and at a distance from it by the scale O DERANGED VALVE MOTION equal to the boiler pressure shown hy the steam gage. The ; difference in pounds between it and the line of the diagram i D E shows the pressure which is lost after the steam has I flowed thi'ough the contracted passages of the steam pipes and the ports of the engine. The clearance line O Y is another reference line drawn at right angles to the atmospheric line and at a distance from the end of the diagram equal to the same per cent of its length as the cleai-ance bears to the piston travel or dis- placement. The distance between the clearance line and the end of the diagram represents the volume of the clear- ance and waste room of the ports and passages at that end of the cylinder. DERANGED VALVE MOTION Fig. 2 In Fig. U the lighter lines show two diagrams, one from each end of the cylinder of a single valve liigh pressure en- gine. This valve admits the steam over its ends and ex- hausts inside. The derangement is caused by the valve stem being too long ; consequently, at the l)ack end the diagram shows that the steam was admitted late, cut off early, exhausted early, and the exhaust valve closed late, so that there is little or no compression. The diagram at the crank end shows the opposite defects, viz., steam is admitted too soon and carried too far on the stroke, the exhaust valve UNITS OF MEASUREMEXT \j is opened too late ami closed too soon to get the steam well out of the cylinder, causing excessive hack pressure, even greater than the hoiler pressure, as shown hy the loop at the top. To remedy this derangement, the valve stem should be shoi'tened hy the screw threads at one end. It may then he found that the steam valve opens a little too late at hoth ends, and it will therefore he necessary to turn the eccentric ahead on the shaft until hoth diagrams resemble the figure shown l)y the hea^^est Une. UNITS OF MEASUREMENT AND TECHNICAL TERMS All substances of whatever nature are measurable, and their measurements are referable to some established units, to be properly expressed and dealt with. An intimate knowl- edge of some of these is indispensable to the engineer ; a few are here briefly defined. The unit of linear measiirement is the inch, or one- twelfth part of a foot. The unit of superficial Tneasurement is the square inch. The unit of solid measuretnent is the cubic inch. The unit of fluid ^9/*e.s.5«re is the pound avoirdupois, consisting of 7,000 gi*ains. The wilt of elasticiti/, or the pressure exerted by elastic fluids, is, for popular use, 1 pound on 1 square inch. The unit of work or potver is 1 pound lifted 12 inches, or, in other words, 1 pound of force acting through 1 foot of distance, and is caUed the foot-pound. As a foot-pomid is the amount of work done in raising 1 pound through the distance of 1 foot, an equivalent amount of work would be raising ^ pound 2 feet, or 12 pounds 1 inch. Horsepower. The standard used for measuring the power of a steam engine is the horsepower. It was origi- nally determined by James Watt from experiments made on London drayhorses. It is considerably above the power 10 TECHNICAL TERMS of an ordinary horse, and is now simply an arbitrary stand- ard. It is equal to 33,000 foot-pounds exerted during one minute of time, or 550 foot-pounds during one second. Indicated horsepo^ver is the horsepower of an engine as found by the use of a steam engine indicator, and is thus expressed : I. H. P. Net horsepoivei' is the indicated horsepower of an en- gine, less the horsepower which is consumed in overcom- ing its own friction. Wire drawing, as applied to steam, is the reducing of its presstire, due to its floA\ang through restricted or crooked pipes and passages. Absolute pressure is pressure reckoned from absolute vacumn ; in other words, it is the pressure of any fluid as shown by a pressure gage, with the weight or pressure of the atmosphere added thereto. Initial forward pressure in a cyhnder is the pressure acting on the piston at or near the beginning of the foi-ward stroke. Terminal forward pressiire is the pressure above the Une of perfect vacuum that would exist at the end of the stroke if the steam had not been released earlier. It may be found by continuing the expansion curve to the end of the diagram, as in Fig. 1 at F, or it may be taken at the point of release. This pressure is always measured from the line of perfect vacuum, hence it is the absolute terminal pressure. Mean effective pressure (written as M. E. P.) is that equivalent constant pressure which will do the same amount of work on the piston per stroke as is done by the varying pressure shown by the indicator card. This may be calcu- lated by dividing the area of the card by the length and multiplying by the scale of the spring used in the indicator, or it may be obtained by taking the average of a number of pressures measured between the top and the bottom lines of TECHNICAL TERMS 11 the card at equidistant intervals along the length of the card. This is illustrated more fully on page 85. Piston displacemeyit is the space in the cyhnder swept through by the piston in its travel. It is reckoned in cubic feet, and is found by multipljang the net area of the piston in square feet by the length of stroke in feet, allowance being made for the piston rod. Clearance is all the waste room or space at either end of the cylinder, between its head and the piston when on a dead center, including the counterbore and the ports, up to the face of the closed valves. Clearance is generally given as a percentage of the piston displacement. Many of the modern steam engines have clearances no gi'eater than 2\ per cent. The number of expansions is the nimiber of times the steam admitted up to cut-off in the first cyhnder of a mul- tiple expansion engine has increased in volume up to release in the last cylinder. If the release be considered to come at the end of the stroke the number of expansions for any engine may be cal- culated from the diameter of the cylinders and the per cent of cut-oif in the first cylinder. Thus — cylinders of a triple engine are 9" — 16" — 24" X 30" sti"oke ; cut-ofE at ^ stroke in liigh pressure cyhnder. As the strokes are the same on all the cylinders of this engine the volmnes of the cylinders Avill be as the squares of their diameters. If the high j)ressure cylinder took steam to the end of its stroke the number of expansions would be -gi'. but the steam expands tlu'ee times in the high, so the total expansion in the engine is ^^^ X 3 = 21.3. Sensible heat is the temperature of any body, as air, water, or steam, which may be measured by the thermometer. SpecifTG heat is the quantity of heat required to raise one unit of weight of the substance through one degree of tem- perature, measured in- thermal units. 12 TECHNICAL TERMS The unit of heat, or thermal unit, is the quantity of heat required to raise the temj)erature of one pound of water from 62° to 63° F. This is often called the British Thermal Unit (written B. t. u.), to distingiiish it from the German and the French standard, which is larger. Mechanical equivalent of heat. It has been found by experiment that if one pound of pure water at 62° F. be raised to 63° F., energy is exerted equivalent to lifting seven hundred and seventy-eight (778) pounds one foot high, or one pound seven hundred and seventy-eight (778) feet high. This energy is called the inechanical equivalent of one therntial unit of heat, and it is usually designated by the letter J, and its reciprocal or yi^ by A. Saturated steam. When steam is formed in a closed vessel in contact with its own liquid, it is said to be satu- rated and it will have a certain definite pressure and den- sity corresponding to each different temperature. If, at the same time, the steam contains no liquid in susjiension, it is said to be dry and saturated. Superheated steam. If, after all the liquid has been converted into steam, more heat be added, the tenq)erature will rise and the steam is said to be superheated, because its temperature will l»e greater than that corresponding to saturated steam of the same 2)>'4.5 -\ 1 . This amount is smaller than in the case 566.5 568.5 where the temperature remained constant. To get the cor- rect value of the increase in entropy for this case, we should liave a summation of a great many terms, adding, instead of one heat unit, an infinitesimal amount of heat each time, and then di\ading each infinitesimal amount of heat by the absolute temperature at which it was added. It is evident that entropy is always figured as the increase or the decrease between two conditions. In other words, there is no zero entropy. CHAPTER II THE CROSBY STEAM ENGINE INDICATOR The Crosby Steam Engine Indicator is designed and constructed to meet the exacting requirements of modern steam engineering. During the last few years, under tlie keen search and exhaustive tests of eminent engineers, the practice in this department of science has undergone impor- tant changes, tending to estabUsh more correct methods and thereby to reach more accurate results ; especially is this true in the use and scope of the indicator, so that the work done with such instruments in former times seems coarse and crude when compared with the more exact attainment of the present. Educators in the scientific schools of botli Euro])e and America have seen the importance of more exact knowledge and instruction in the technical sciences ; and the great achievements of recent years in the construction of build- ings, ships, armaments and macliines attest the thoroughness with which research in tliese departments has been pi'ose- cuted ; in none has there been greater progress made than in mechanical and steam engineering. A knowledge of these facts has kept us on the alert in the manufacture of all our steam appliances, and especially in that of the steam engine indicator. Within a recent time we have made important improvements, which, as we believe, place it far in advance of any other instrument of its kind. Radical changes in design, more perfect me- chanical construction, due to the use of improved and specialized machinery, and careful selection of metals for the different parts, have all contributed to this favorable result. 16 THE CROSBY STANDARD INDICATOR 17 Tlie movements of piston and pencil ])oint are pevtectly parallel, the movement of the pencil point is also exactly parallel with the axis of the drum. This accuracy is secured hy mathematically correct design and careful workmanship. " k—iiiiJ The rating of the springs hy our newly constructed test- ing apparatus, which emhodies all the valualde aids to exactness which have yet heen discovered, is nearer perfec- tion than could have heen attained, or even expected, until within a very recent time. 18 DESCRIPTION OF THE INDICATOR CROSBY STANDARD STEAM ENGINE INDICATOR The illustration on page 19 shows the design and arrange- ment of its parts. The cylinder, 4, in which the piston moves, is made of a special alloy, exactly suited to the varying temperatures to which it is subjected, and secures to the piston the same freedom of movement with high pressure steam as with low ; and as its bottom end is free and out of contact with all other parts, its longitudinal expansion or contraction is unimpeded, and no distortion can possibly take place. Between the cylinder, 4, and the casing, 5, is an annular chamber, which serves as a steam jacket ; and being open at the bottom, can hold no water, but will always be filled with steam of nearly the same temperature as that in the cyhnder. The ■pi^^ion-i 8, is formed from a solid piece of the finest tool steel. Its shell is made as thin as possible consistent with proper strength. It is hardened to prevent any reduc- tion of its area by wearing, then ground and lapped to fit (to the twenty-thousandth part of an inch) a cylindrical gage of standard size. Shallow channels in its outer sur- face provide a steam packing, and the moisture and oil wliich they retain act as lubricants, and prevent undue leak- age by the piston. The transverse web near its center sup- ports a central socket, which projects both upward and downward ; the upper part is threaded inside to receive the lower end of the piston-rod. The upper edge of this socket is formed to fit nicely into a circular channel in the under side of the shoulder of the piston-rod, when they are prop- erly connected. It has a longitudinal slot, Avliich permits the straight portion of wire at the bottom of the spring, vrith its bead, to drop to a concave bearing in the upper end of the piston-screw, 9, which is closely threaded into the lower part of the socket ; the head of this screw is hexag- onal, and may be turned with the hollow wTench which accompanies the indicator. DKvSCBIPTION OF TUK IKDICATOB 19 The jyiston-rod , 10, is of steel, and is made hollow for lightness. Its lower end is threaded to screw into the upper socket of the piston. Above the tlu'eaded portion is a shoulder having in its under side a circular channel formed to receive the upper edge of the socket, when these parts are connected together. When making this connec- tion be sure that the piston-rod is screwed into the socket as far as it will go, that is, until the upper edge of the socket is brought firmly against the bottom of the channel in the piston-rod, before the piston-screw, 9, is tightened against the 20 DESCRIPTION OF THE INDICATOR l)ea(l at the foot of the spring. This is very important, as it insures a correct aUgnnient of the parts and free movement of the piston within the cyhnder. The swivel head, 11, is threaded on its lower half to screw into the piston-rod more or less, according to the required height of the atmospheric line on the diagram. Its head is pivoted to tlie piston-rod link of the pencil mechanism. This adjustment of the position of the dia- gram upon the card is a valuable advantage peculiar to the Crosby indicator. The cap, 2. rests on top of the cylinder, and holds the sleeve and all connected parts in place. It has a cen- tral depression in its upper surface, also a central hole, furnished with a hardened steel bushing, which serves as a very durable and sure guide to the piston-rod. It projects downward into the cylinder in two steps, having different lengths and diameters ; both these and the hole have a com- mon center. The lower and smaller projection is screw- threaded outside to engage with the like threads in the head of the spring, and hold it Urndy in place. The upper and larger projection is screw-threaded on its lower half to engage with the light threads inside the cylinder ; the up})er half of this larger projection — being the smooth, vertical portion — is accurately fitted into a corresponding recess in the top of the cylinder, and forms thereby a guide by which all the moving paits are adjusted and kept in correct align- ment, which is very important but practically impossible to secure by the use of screw threads alone. The sleeve, 3, surrounds the upper part of the cylinder in a recess formed for that purpose, and supports the pencil mechanism ; the arm, X, is an integral part of it. It turns around freely, and is held in place by the cap. The handle for adjusting the pencil point is threaded through the arm, and being in contact with a stop-screw in the plate, 1, may be delicately adjusted to the surface of the paper on the DESCRIPTION OF THE INDICATOR 21 drum. It is made of hard wood with a lock-nut to main- tain the adjustment. The pencil mechanism is designed to afford sufficient strength and steadiness of movement, with tlie utmost liglit- ness ; tliereby eliminating as far as possible the effect of momentum, which is especially troublesome in high speed work. Its fundamental kinematic principle is that of the pantograph. The fulcrum of the mechanism as a whole, the point attached to the piston-rod, and the pencil point are always in a straight line. This gives to the pencil point a movement exactly parallel with that of the piston. The mechanism is theoretically correct as well as mechanically accurate ; the result is, therefore, mathematical precision in the pencil movement, not merely an approximation. The movement of the spring throughout its range bears a con- stant ratio to the force applied ; and the amount of the movement of the piston is multiplied six times at the pencil point. The pencil lever, links, and pins are all made of hardened steel ; the latter — slightly tapering — are ground and lapped to fit accurately, without perceptible friction or lost motion. Springs. In order to obtain a correct diagram, the height of the pencil of the indicator must exactly represent in pounds per square inch the pressure on the piston of the steam engine at every point of the stroke ; and the velocity of the surface of the drum must bear at every instant a con- stant ratio to the velocity of the piston. These two essen- tial conditions have been attained to a greater degree of exactness in the Crosby indicator than in any other make, by a very ingenious construction and nice adaptation of both its piston and drmii springs. The piston spring is of unique and ingenious design, being made of a single piece of the finest spring steel wire, wound from the middle into a double coil, the ends of which are screwed into a metal head having four radial wings 22 DESCRIPTION OF THE INDICATOR drilled helically to receive and hold the spring securely in place. Adjustment is made hy screwing the ends into the head more or less, until exactly the right strength of spring is obtained, when they are there firmly fixed. This method of adjusting and fastening removes all danger of loosening coils, and obviates all necessity for grinding the wires — a practice fatal to accuracy in indicator S2)rings. The foot of the spring — in which freedom and lightness are of great im- portance, it being the part subject to the greatest movement — ^ is a small steel bead, firmly " staked " on to the wire. This takes the place of the heavy brass foot used in other indicators, and reduces the inertia and momentum at this point to a minimum, whereby a great improve- ment is effected. This bead has its bearing in the center of the piston, and in connection with the lower end of the piston-rod and the upper end of the piston-screw, 9 (both of which are concaved to fit), it forms a ball and socket joint which allows the spring to yield to pressure from any direc- tion without causing the piston to bind in the cylinder, which occurs when the sjjring and piston are rigidly united. Designing the spring so that any lateral movement it may receive when being compressed shall not be conmmnicated to the piston and cause errors in the diagram, is of extreme importance. See also page 59. The dnirn spring, 31, in the Crosby indicator is in form a heUx, while in other indicators it is a long volute. It is obvious from the large contact surfaces of a long volute spring that its friction would be greater than that of a short, open helical form of like power ; and that in a spring of DESCRIPTION- OF THE INDICATOR 23 this kind, for a given amount of compression — as in the move- ment of an indicator drum — the recoil will be greater and exerted more quickly in the helical than in the volute form. If the conditions under which the drum spring operates be considered, it will readily be seen that at tlie beginning of the stroke, when the cord has all the resistance of the drum and spring to overcome, the spring should offer less resistance than at any other time ; and at the beginning of the stroke in the opposite direction, when the spring has to overcome the inertia and friction of the drum, its energy or recoil should be greatest. These conditions are fully met in all Crosby indicators, the drum spring being a helix having no friction, a quick recoil, and scientifically proportioned to the work it has to do. At the beginning of the forward stroke it offers to the cord only a very slight resistance, which gradually increases until at the end its maximum is reached. At the beginning of the stroke in tlie other direction, its recoil is greatest at the moment when it is most needed, and gradually de- creases as the work it has to do decreases, until at the end of the stroke it is redxiced to its minimum again. Thus, by a most ingenious balancing of opposing forces, the most nearly uniform stress on tlie cord is maintained throughout each revolution of the engine. The drum., 24, and its appurtenances, except the drum spring, are similar in design and function to like parts of any indicator, and need not be particularly described. All the moving parts are designed to secure svifficient strength with the utmost lightness, by whicli the effect of inertia and momentimi is reduced to the least possible amount. It is ordinarily 1^ inches in diameter, this being the correct size for high speed work, and answering equally well for low speeds. If, however, the indicator is to be used only for low speeds, and a longer diagram is preferred, it can be furnished with a 2 inch drum. 24 CROSBY NKW INDICATOR All Crosby indicators (except some of the Standard Steam Engine Indicators numbered below 3737) can be readily changed from right-hand to left-hand instruments as occa- sion may re(|uire. CROSBY NEW STEAM ENGINE INDICATOR Patented This instrimient is a departure from the ordinary steam engine indicator. One difference is in the location of the spring, which is of the same form and construction as the one described and illustrated on page 22. Tliis has been removed fi'om the inside of the cylindrical case near the piston to the outside and affixed above the moving parts, CROSBY XKW INDICATOR 9r, where it will remain cool under all conditions of use. Whatever error arises from heat, therefore, as affecting the spring in the ordinary indicator, is not present in this instrmnent. The other and more important difference lies in the size and shape of the piston. This piston is one s(piare inch in area, and is in form the central zone of a sphere. This increased area of the piston provides great active force with a very light pencil mechanism. It is attached hy a rod directly to the uj)per part of the spring, and moves freely 26 CROSBY NEW INDICATOR and without restraint notwithstanding there may be eccen- tricity in the action of the spring. In other words, this piston serves as a universal joint to take care of the torsional sti'ains of the spi'ing when it operates the pencil mechanism of the indicator. The pencil mechanism is connected to the piston by means of a rod having at its lower end a ball, which fits into a socket in the center of the piston. This socket is formed upon a headless slotted screw, adjustable in the piston, by which it is possible to take up all wear upon the ball joint that might develop after long service ; l»ut this adjustment should not ordinarily be disturbed, and care must always be taken to insure that the piston is firmly screwed to the piston-rod before the adjustment screw is tightened to just the amount sufiicient to prevent any possibility of lost motion, without binding. The socket at the upper end of the piston-rod, to receive the ball bear- ing of the spring, is likewise upon an adjustable headless screw, which is independent of the screw beneath it that secures the swivel head of the piston-rod in its place. The piston-rod moves freely within a sleeve attached to the base of the pencil mechanism, and, moving in a vertical line, compels the pencil to move also in a vertical line. Thus, any motion of the piston due to the movements of the spring, which causes the spring-rod to deviate, wiD not affect the pencil mechanism in its vertical course. The contact of the piston with the interior side of the cylinder is a line, and does not induce friction. Ordinarily, the piston of an indi- cator is a short cylinder fitted to shde easily within another cylinder. Such a piston is usually about one-half inch long, and in use will develop friction throughout its circumference. The piston so made must resist and overcome if possible the eccentricities of the spring in action. Yet, even then, there is always a want of freedom, notwithstanding there are devices to aid the piston in such case. This condition tending to error is recognized by engineers, and considered CROSBY NEW INDICATOR XO. 2 27 in the computations made of the diagram taken by the in- dicator. The freedom of the piston movement in this indi- cator dispenses with the necessity of this correction. When an indicator is to be used in higlily superheated steam or in gases of high temperature this type, with outside spring, will give accurate results. All parts of the indicator are constructed to give the greatest possible wear and durability with extreme lightness and freedom from all friction and the joints are upon har- dened taper bearings. Means are thus provided to prevent all error or looseness, and no proper excuse exists for per- mitting any inaccuracy to develop. Although the adjust- ment is rarely needed and at every point is slight and simple, greater satisfaction will result if this work be done by skilled mechanics whose special experience enables them to work accurately and quickly, wnthout the risk of dam- age involved in repairs undertaken by persons unfamiliar with such mechanism. This indicator is made also for gas engine work with piston 1- square inch in area and special pencil mechanism ; and may be made of steel when required, for ammonia. The Crosby New Indicator appeals to the discriminating engineer because of its acknowledged supeinority in design and workmanship, affording unapproachable accuracy in results. The linkage is a true parallel motion, and the relationship of the parts is not disturbed when changing the spring or cleaning the cylinder. The operation and adjust- ment of the indicator in use is simple and convenient. On the following page examples are shown of its free- dom of piston movement, being reproductions of the original test cards of a variety of springs. CROSBY NEW INDICATOR NO. 2 Patented This instrument has been designed to meet the demand for an accurate and trustworthy instrument of the outside- 28 TKST f'ARDS OF SPKTXriS lOcftSPrtlNtt 12. LS. 3PRIMGv lb UB. SPRING. 2:0 (_B. SPRING. 30 30 UB. SPRING, -10 T 60 1-6. SPRING I 2 -Li ^^tJ MO UB.SPRlNG» 100 LB SPRING. £00 ^^—i m 50LB.SPFi.lNa too laO LBSPRING. — s fcOLB.apaiNOi CROSHV NKW 1M)I( ATOR NO. 2 29 s])riiig t.yi)e, .smaller and less costly than the Crosby New Indicator, bnt containing its essential features of design. It is convenient to handle and gives accurate and satisfactory results. The pencil mechanism and spherical piston are similar to those which give such superiority to the Crosby New Indicator, bxit the piston has an area of ^ scpiare inch. This Crosby New Indicator No. 2 is made also for ammonia. For gas engine work the piston is ^ square inch in area. As a Combined Gas and Steam Engine Indicator it has two interchangeal)le ])istons j and ^ square inch in area. THE CROSBY INDICATOR WITH DRUM FOR TAKING CONTINUOUS DIAGRAMS I'ateuted 30 DRUM FOR CONTINUOUS DIAGRAMS The cut represents the Crosby New Steam Engine Indi- cator equipjjeil vntlx a drum for taking continuous dia- grams. Tliis drum can he ap^jlit^d to any indicator. It is designed to use a roll of paper 2 inches Avide and 12 feet long, upon wliich the operation of the indicator traces a series of diagrams which will continue until the roll is ex- hausted, unless interrupted hy the operator. The roU of ])aper is located within an opening in the shell of the drum, thence the paper passes around the outside of the drum and uaward to the central cylinder, to which it is attached. The central cylinder is concentric with the di'um, and after the })aper has been wound upon it, may be withdrawn through the toj) and the paper easily detached. Upon the top of the drum and cooperating with the central cylinder is a knurled head loosely attached to the drum spindle, wliich controls the distance between the diagi'ams so that by adjustment they will vary in number from 6 to 100 per foot of paper. Tliis advantage of taking any number of diagrams on the roll at the will of the operator is of importance, as he will be able to regulate the duration of the test to the speed of the engine in taking a less or greater mimber per foot of l^aper. Tliis feature is novel and is an improvement over devices for taking diagrams of tliis character where the number is fixed for all engine sjjeeds ; for it enables the operator by limiting the nmiiber according to his own judg- ment more easily to read and measure the diagrams taken. The demand for an indicator with a drum for continuous diagrams has been stimulated recently by its use in rolUng mills, and in other industries where there is an irregular load on the steam engine, varying rapidly and in such se- quence that knowledge of its continuous work could not be obtained except by an unbroken series of diagTams, extend- ing over a definite time of greater or less extent. But its usefulness is not confined to such conditions. Its applica- tion to any steam or gas engine will afEord abundant exam- COXTIXUOUS DIAGRAMS 31 Sections of Continuous Diagrams Taken with the Crosby Indicator from Rolling Mill Engines 32 PRUM FOR ( ONTINUOUS DIAGRAMS pies of its action, continuously or intermittently at tlie will or convenience of the engineer. It furnishes recorded proof of such operation in a form that permits one diagram to be compared with another, and the variations during a cycle of operations to he intelligently observed in the sequence of their occurrence. The examples on page ol reproduced from actual diagrams taken on steam engines are given only to illustrate the fore- going statement. Single isolated diagrams can also be taken as wdth the ordinary climn. THE LANZA CONTINUOUS DIAGRAM APPLIANCE WITH CROSBY INDICATORS Patented This apparatus for taking an uninterrupted record of the pressure changes occurring in any compression chamber or in the cylinder of any steam engine, pump, or internal com- bustion engine, is a device for accuratel}^ feeding a con- tinuous strip of paper in one direction at velocities strictly proportionate to the varying velocity of the piston or pump plunger through as many consecutive strokes of the reciprocat- ing parts as may be desired. It is the invention of Professor Gaetano Lanza, Professor of Theoretical and Applied Mechanics, Emeritus, of the Massachusetts Institute of Technology. The paper is drawn forward from a roll and wound after- ward in form for convenient removal and study. The suc- cessive diagrams or pressure records are not overlapping or deformed in any way, but each pressure cycle is separately developed in its true proportions. The horse power and pressures can be conveniently measured by scale or plani- meter and the actual location of the several events deter- mined. A full description of this instrument and its uses is given on page 196, in the Appendi.x. CHAPTER III THE CROSBY GAS ENGINE INDICATOR. THE CROSBY COMBINED GAS AND STEAM ENGINE INDICATOR. THE CROSBY AMMONIA INDICATOR. THE CROSBY ORDNANCE INDICATOR. THE CROSBY HYDRAULIC INDICATOR CROSBY STANDARD GAS ENGINE INDICATOR The increase in the use of gas and of gasohne engines has created a demand for an acciu-ate indicator capable of 33 34 CROSBY COMBINED INDICATOR withstanding the heat, the high pressure, and the shock which result from the explosions in the cyhnder. The Crosby Standard Gas Engine Indicator designed to meet these requirements has given ^)erf act satisfaction. The piston is :^ of a square inch in area and springs made for ^ inch pistons have their rating doubled when used in this instrument. Its great accuracy and durability have been fully demonstrated, and its method of construction leads to the least error in the taking of such diagrams. The Crosby New Indicator is made also for gas engine work, with piston ^ square inch in area, of the design described on page 25. CROSBY COMBINED GAS AND STEAM ENGINE INDICATOR Patented This indicator is for use either with the steam engine or with gas or oil engines, and is suppUed with two pistons, either of which can be fitted separately as desired. The piston for steam is ^ square inch in area, the same as is used with the Crosby Standard Steam Engine Indicator ; the one for gas or oil is ^ square inch in area. The cylinder is of special construction to suit the respect- ive diameters of the two pistons. CROSBY AMMONIA INDICATOR Patented The Crosby Ammonia Indicator is made like the Crosby Standard Steam Engine Indicator, except that all surfaces exposed to the action of ammonia are of steel. The Crosby New Indicator, having the outside spring, is also made of steel when required for ammonia. For ammonia indicators, both common and three-way (;ocks are made of steel. CROSBY ORDXANCE INDICATOR CROSBY ORDNANCE INDICATOR Patented 35 This instrument will give a true record of high pressures, such as ohtain in the operation of the pneumatic gun car- riage for heavy ordnance, or in hydraulic pumps. The pencil mechanism is strong, and has a post bearing lightly against the ])encil arm to keep it in contact with the drum during sudden shocks. The piston is -^^ of a square inch in area, and is fitted into a cylinder at the bottom of the instrument. There is a by-pass by wliich the pressure may be transmitted to the larger piston above, when the pressures to be recorded are not too high for the capacity of the spring. This by-pass is closed by a cock when the small piston is to be used. 36 CROSBY HYDRAULIC IXDICATOR CROSBY HYDRAULIC INDICATOR Patented The Crosby Hydraulic; Indicator (litters from the one shown in the cnt in that it has no by-pass and in })lace of the piston in the upper chamber a guide is substituted. It is a strong and efficient instrument for indicating under liigh pressure conditions in all liquids or gases. The piston is -^Q of a square inch in area. The cylinder is constructed in such a manner as to afford a uniform area of cross-section below the piston, thus preventing pockets or enlargements. The pencil mechanism is substantial and without appreciable inertia effect. CHAPTER TV INDICATOR ATTACHMENTS AND ACCESSORY APPARATUS SARGENT IMPROVED ELECTRICAL ATTACHMENT For Steam or Gas Engine Indicators Fig. 3 In making elaborate tests of power plants, it has hereto- fore been necessary to employ as many assistants as there were intlicators used, but the difficulty of securing simulta^ neous action on their part is so great that satisfactory work is rarely to be obtained, and more certain means to that end are now considered necessary. Mr. Frederick Sargent. M.E., invented and patented an electrical device applicable to an indicator, by means of which any number of instruments can be operated and dia- grams taken at the same instant of time, simply by closing an electric circuit. We are the sole owners of this patent 37 38 SARGENT IMPROVED ATTACHMENT and of the rights under it ; and are the sole makers of tliis apparatus, which has been modified and improved. Fig. 4 Fig. 3 shows a Crosby Standard Indicator fitted with this electrical attachment. Fig. 4 shows the same indicator fitted Avith a Circuit Closer. Description Fig. 5 represents the Sargent Improved Electrical Attach- ment, consisting of an electromagnet, A, which is supported by a bracket, B, wliich also secures it to the indicator plate. Binding posts, C, C, are attached to the same bracket. The armature D is opposed to the magnet by a spiral spring in the center of the coil, the tension of which is adjustable by means of the screw E, at the back of the magnet. The movement of the armature outwardly is limited by two screws, 1 and 2. To the armature is secured a small latch or hook, F, which is free to work vertically, and engage with the arm A, Fig. 3. The thumb-screw G is for fasten- ing the attachment to the plate of an indicator through a hole therein. TO ATTACH THE ELECTRICAL ATTACHMENT 39 Fig. 6 represents the Circuit Closer, and is designed to operate the electrically connected indicators, by closing the circuit through them whenever the stylus or marking point is put against the paper on the drum of the indicator to wliich it is attached. This enables the engineer making the test to control this indicator directly hy hand — a feature often desirable — and by its use one Sargent attachment is dispensed with. It consists of a bracket, H, with a tubular projection, I, fastened to it which contains the circuit closing mechanism. It is attached to the indicator plate by the thumb-screw, J, in precisely the same way that the magnets are to the other indicators, and is electrically connected in the same manner through the binding posts, K, K. To Attach the Sargent Improved Electrical Attachment To get the position of the hole in the frame of the indi- cator, take out the screw G (Fig. ;">), and place the bracket 40 TO ATTA^. 2 fortieths of an inch, which, divided l>y 40, gives 0.88 of an inch, the average height. This multijjlied hy the scale of the spring used and we have 52.8 pounds M. E. P., the same as in the last example. A simpler process is to multiply the reading hy {\\efacto7' corresponding with the scale of the spring, which for a 60 pound spring is 1.5, then we have 35.2 X 1.5 = 52.8 pounds, the same as by the other process. FoUoAving is a list of the pressures or scales to which in- dicator springs are commonly made, with their correspond- ing /"actons immediately below. Springs, I 8 j 12 | 16 20 24 I 30 40 I 50 i 60 I 80 1 100 120 150 j 180 Factors, I 0.2 1 0.3 I 0.4 I 0.5 1 O.B I 0.75 1.0 1.2511.5 I 2.0 I 2.5 3.0 1 3.751 4.5 When two diagrams are taken on the same card they may be measured conjointly and the average height divided by two to get the average height of Itoth. We, however, recom- mend that each diagram be measured separately, especially if there is a difference in their areas, which is generally the case. When there is a loop in the diagram caused by the steam expanding below the back pressure line when the engine is non-condensing, its outline should be traced in the same way as directed for a plain diagram, as the principle on which the planimeter works is such that the area of the looji will be subtracted fi-om the main pai't of the diagram, and the reading of the instrument when the measurement is com- pleted will be the correct net area sought. When one has become familiar with the use of the plani- meter it is not necessary always to set the wheels at zero, as recpiired in the foregoing directions, but their reading as they stand just before beginning to trace a diagram may be THE THR()TTLIX(t CALORIMETER 49 noted down and this quantity subtracted from the reading when the tracing is completed. The difference between the two readings is the area sought. For instance : Suppose we find that the reading of the wheels, including the counting disc, at the beginning is 47.31, and when the tracing is completed it is 49.43, then 49.43 — 47.31 = 2.12 square inches, the area measured. Then to measure a second diagi-am, note down the last read- ing, viz., 49.43, and when the tracing is completed we read 51.63. Then 51.63 — 49.43 = 2.20 square inches, the area of the second diagram. The foregoing directions for using the planimeter ai-e appli('al)le to any single diagram. The use of Amsler's Polar Planimeter in the measure- ment of indicator diagrams enables one to measure ten cards with it in the time which would be required to measure one card by any other method, and it insures the utmost accuracy in the work. The i)lanimeter is a precise and delicate instrument and should l)e handled and kept with great care, in order that it may be depended upon to give correct results. After using, it should be wiped clean with a piece of soft chamois skin. THE THROTTLING CALORIMETER In order that the test of an engine or boiler may be com- plete a determination should be made of the quality of the steam, i.e., the j)rinung or the amount of moisture carried by the steam. This determination was formerly made by methods wliich could be made to give satisfactory results in the hands of a physicist or a trained expert, but which were troublesome and unreliable when enq)loye(l by an inexpe- rienced observer. The quality of steam delivered by a boiler or su])plied to an engine can now be determined with ease and certainty l)y aid of the throttling calorimeter, invented by Prof. C. H. Peabody of the JVIassachusetts Institute of 50 THK THROTTLING CALORIMKTER Technology, and described hy him in the " Journal " * of the Franklin Institute, and in the " Proceedings of the American Society of Mechanical Engineers."! Fi(!. 10 The throttling calorimeter depends on tlie 2)rinci})le that steam which contains a moderate amount of moisture will * " Journal " Franklin Institute. June, 1888. Volume CXXVI., Page 1.34. t " Proceeding.s American Society of Mechanical Engineers," 1888-89, Volume X., Page 327, and 188'J-"J0, Volume XI., Page 193. THK THROTTLIN(i CAI.ORIMETER 51 become su])erheate(l if the pressure is reduced by tlu'ottling, without loss of heat. The form here shown is simple, sul)stantial, and inexpensive, and has been used by the inventor and others with complete satisfaction. The calorim- eter, shown in Fig. 10, is a closed cylindrical metallic chamber K, having an inlet passage at A, controlled by the valve E, an outlet ])assage at the bottom N, and a ther- mometer cup at T. The chamber is thickly wrapped with asbestos and hair felt, protected by wood lagging to reduce radiation and loss of heat. The U shaped tubes or siphons for attaching the pressure gages B and C are furnished with the calorimeter ; the gages and thermometer are extra, and may be furnished or not, as required. The nip])le A, connecting the inlet valve E with the chamber K, is made of composition, cut with pijje thread and provided with a well rounded orifice for gaging the flow of steam as shown by the full size Fig. 11. The connection with the main steam pipe from which a sam- ple of steam to be tested is taken, should be as short and direct as possible, and should be well wrapped to reduce i-adiation. The su])ply pijte should enter the main steam pi])e at least half an inch, when the con- nection is made on the up])er side of the main. If the calorimeter is attached to the bottom half of the main, the entering ])ipe should extend in beyond the center. The waste pipe N should be at least one inch in diameter for its entire length, and may be larger if longer than twenty feet. The gage C for measuring the ])ressure in the main steam i)ipe must l)e attaclied di- rectly to that pipe close to the calorimeter. To use the calorimeter, fill the thermometer cup with oil and insert the thermometer ; see that the siphons Fig. 11 52 THK THROTTLING CALORIMETER are filled with cold water and that they do not leak ; open the valve E wide, and wait ten or fifteen minutes till the whole apparatus is heated. Read the gage B and add the pressure of the atmosphere* to get the ahsolute pressure in the calorimeter ; find the corresponding temperature from a talde of the properties of saturated steam and compare with the temperature in the calorimeter given l)y the thermometer ; the excess of the latter over the former is the superheating of the steam in the calorimeter. The flow of steam through the calorimeter will he sufficient to make the loss hy radiation of no consequence and no cor- rection need be applied. When all is ready, read the pressure of the steam p in the main steam pii)e, the temperature t^ in the calorim- eter, the pressure p^ in the calorimeter, and take the ])res- sure y>„ of the atmosphere. From a table of the ])roperties of saturated steam, find the temjierature t^ corresponding to the absolute pressure P^ = p^ + Pa From the same tables find the total heat X^ corresponding to the pressure P^ ; also the heat of vaporization /• and the heat of the liquid q corresponding to the ahsolute pressure in the steam pipe Y = p -\- p^^ The weight or moisture in 1 pound of moist steam drawn from the steam pipe is to be calculated by the equation Prixning = 1 - K^^-^HU-t>-y appropriate mechanism, be reduced to the length of the diagram to be taken, and tliis reduced motion must be, in point of rapidity, in exact ratio to the motion of the piston. To obtain this reduced motion, various devices may be employed. The reducing lever in some one of its various forms can be easily made and adapted to suit almost any conditions. A common form of this device is shown in Fig. 13, and answers fairly well for lai'ge and quick running- engines. It should be made of straight grained pine, one inch oi* more in thickness, al)out tlu'ee inches wide at the top. and tapering to a width of about two iiudies at the bottom; its length sliould be at least one and a half times the length of the stroke of the piston. Tlie lever. A, is suspended by a bolt from the ceiling or from a truss or frame overhead, ju'epared for that purpose. Fig. 13 (55 66 DRUM MOTION in such a manner as to permit it to swing edgewise and parallel with the guides of the engine. Near the bottom of the lever is a steel stud, secured hy a nut on the outside shown at B. This stud has a T-head projecting inwardly from the lever, and is formed to run freely, but w^thout looseness, in a T-slot, cut in an iron plate, and firmly attached to the center of the cross-head, which, as it moves to and fro, gives to the lever the necessaiy swinging motion. Fig. 14 shows the arrangement of the T-headed stud, or, in connection with the slotted iron plate, c : one of the screws by which it is attached to the cross-head is shown at d. The head of the stud should be about one inch in diameter and the shank about one-half inch. The T-slot is milled out of a cast-iron plate of suitable size and shape to give the proper run for the stud. When the lever is j)erpendicular, or in the middle of its path, the stud should be near the bottom of the slot, wdiich should be long enough to retain the stud when the cross- head is at the exti-eme end of the stroke. By this de\ace the bottom end of the lever is moved the full distance that the cross-head travels in either direction, and for this reason it is more accurate than a lever of the same kind having its lower end slotted to work on a stud inserted in the cross-head, as is sometimes used. I) is a small pulley placed near and on a level with the pin in the lever, for the indicator cord to pass over. While this form of reducing lever is commonly made Avith a, p'u^ for attaching the indicator cord, greater constancy of motion for the di'um would lie attained by the use of a sector, such as is shown at S in Hg. 15. To find the point on the lever at which to attach the in- dicator cord, proceed as follows : Divide the length of the lever by the length of the piston stroke, and multiply the quotient by the required length of the diagram, all exju'essed in inches and decimals of an inch, and the product will be DRUM MOTION 6; the ]iroper distaiu-e from the pivot in the top of lever to the point of attac'luiient. For example : If the lever is 48 inches long and the piston stroke is 30 inches, and we wish to obtain a diagi-am 3^ inches long, we have 48 -^ 30 = 1.6 ; 1.6 X 3.5" = 5.6". tlie radius required to give a 3.^ inch diagram. If we re- (piire a diagram 4^ inches long, then : 1.6 X 4.5" = 7.2 , the radius required to give a 44- inch diagram. The object of all mechanisms for actuating the drmn of the indicator should be such that the relation of piston to drum movement will be constant. Such constancy can- not, however, be fully attained by the use of any form of reducing lever, and so should not be employed when im- portant adjustments or tests are to be made. Their simplic- ity and the small expenditure of time and money in their construction may entitle them to favorable consideration on the part of beginners in the use of the indicator, and when only ordinary work is to be done. The forms shown in Fig. 16, Fig. 17, Fig. 18, and Fig. 19 are correct in principle, and when care- fully constructed may be relied upon to give correct results. Tlif Bruvihn inilh'ii. shown in Fig. 15, is an- other form of reducing "' lever, and one often used by engineers, especially on locomotives. It can lie quickly and cheaply made and can be used on ahnost any kind of engine. The swinging lever E is a strip of straight Fig. 15 68 DRUM MOTION grained pine, one inch or more in thickness, three to four inches wide, and from one and a half to two times as long as the piston stroke. It is suspended l)y a holt or screw, serving as a pivot, from a frame or truss overhead constructed for that pur])ose, and is connected at its lower end hy the wooden link F, to the usual stud or ])in fixed in the center or other convenient part of the cross-head ; the link shoidd he from one-third to one-half the length of the ])iston stroke. In the illustration the proportions of lever and link are as (JO to 15 ; the lever being two times and the link one-half the length of stroke. The sector S may he constructed of wood or of metal, as here shown ; it has a groove in its circmlar edge for the cord to run in and is screwed to the ujjper end of the lever or pendulum, so that its center will coincide with the center of the pivot on which it swings. The radius of the sector which is necessary to give the jn'oper motion to the drum to obtain the desired length of iliagram can be found as fol- lows : Divide the length of the lever by the length of the piston stroke and multiply the quotient l)y the length of diagram desired, and the product will be the required radius, all the terms being expressed in inches and decimals of an inch. F'or example : If the lever is 30 inches long and the piston stroke is 20 inches, and we wish to obtain a diagram 3 inches long, we have 30-^ 20 = 1| ; 1| X 3" = 4^", the radius required to give a 3 inch diagram. When the (conditions are favorable, the lever should he hung so that it will swing in a vertical plane, parallel with the guides and in line with the indicator, as this arrange- ment is the most simple, and the use of guide pulleys is avoided. It is not absolutely necessary, however, that the lever shall swing in a vertical jdane, Imt it may swing in a plane at any angle thereto, where the conditions re- quire it. In such cases a man's ingenuity and inventive faculty must aid hun. A link made of a thin strip of DRUM MOTION 69 steel, that will twist a little, is in some cases found very convenient. Wlien the cross-head is at midstroke the lever must hang plumb and the pin which connects its lower end to the link nuist be as much helow the horizontal line of motion of the atiid in the cross-head as it sweeps (ihnve that line at either end of the stroke. See the dotted line for an illustration of this point, which is important. The cord must lead from tlie sector in about the same plane with its swing. Carrying pulleys should be avoided as far as possible, but whatever number is necessary should be firmly placed. The swinging arm of the gaiide-pulley on the indicator should always be fixed in the direction from which the coi'd is received. A ])iece of piano wire is often used to replace the string leading' from tlie sector to the indicator. Fig. 16 Tlie pnntor/raph, illustrated in Fig. 16, is another style of reducing motion. Although theoretically it gives a per- fect motion, owing to its many joints it niay become shaky and give erroneous results, unless it is very nicely made and carefully used. When the indicator is applied to the side of 70 DRUM MOTION Fig. 17 the cylinder the pantograph works in a horizontal plane. The pivot end B rests on a post or other support set oppo- site to the middle of the guides, and the working end A receives motion from the cross-head — to which it is attached hy a suitable iron with a dr hole drilled in it for the stud A to work in. By adjusting the support for the pivot end to the proper height and at a proper distance from the guides, the cord may he carried directly from the pin E to the indicator without the need of car- rying pulleys. The ^( ^ — ■ movable bar may be set forward or backward by the pins C, D, so as to perfectly adjust the movement of the pin E to the required length of the diagram ; this pin niust always be in a straight line with the stud A and the pivot B. The string from E should always lead off in a line parallel to the pis- ton rod. The directions here given for constructing and arranging drum motions are general ; special cases niay require modification of the forms and special adaptation of the means here described, all of which call forth the ingenuity and skill of the engineer. OROSBY REDUCING WHEP:L 71 Fig. 17 shows a pantograph device at midstroke. This is made of bar iron. The pins d, e, f, g, are nicely fitted. The indicator cord may he attached at b. The end a is at- tached to a pin on the cross-head. The fixed fidcrum is at e. a, b, and c must always lie in the same stmight line, and e d, b n, parallel and equal to f g. Also, a f: nf = stroke of piston to length of indicator diagram. Fig. 18 illustrates a device used at the Massachusetts Institute of Technology. / is a rod moving in a slide paral- lel to the piston-rod. The link b d is attached to /, and the link a e to the cross-head, a, b, and c must always lie in the same straight line, a e : b d and e c : c d, = stroke of ])iston to length of indicator diagram. The cord is hooked on a i)in at g : it is well to have a pin for each indicator used. Fig. 19 is a device hy Armand St^vart for long strokes. a and b are fixed ends of cord wrapped around a pulley D. The indicator cord is attached to a small pulley d and passes around a guide pulley e. D and d are attached to the cross-head. Dia. D -^ dia. d = stroke of the piston -^ hy the difference between stroke of piston and length of card. The redi(cing wheel is another device for giving the proper motion to the paper drum. Although old in prin- ciple, and as formerly made not highly approved by careful engineers, it is now coming into more general use, and the superior manner in which it is designed and constructed seems to warrant this change. CROSBY REDUCING WHEEL The Crosby reducing wheel is attached directly to the cylinder cock of the steam engine, and has connected to it the steam engine indicator which it is to serve ; thus it forms a base or support for the latter, and receives all the strains and shocks in the operations of the engine, to the relief of the indicator. All its parts are designed 72 CROSBY REDUCING WHEEL and constructed fov strength, accuracy, and durability. Its bearings are not only nicely adjiisted, but are made comparatively fi-ictionless by the introduction of balls run- ning in liardened tool steel bearings, affording lightness and freedom of movement. It has a helical spring v^^hich is more active in recoil than the volute spring in common use, this being a very essential feature for accurate results on high speed engines. The cord pulley is horizontal to allow the cord leading to the engine cross-head to take any direc- tion the circumstances may require without regard to the position of the indicator. Patented This Citt Shows the Crosby Standard Steam Engine Indicator Mounted upon the Crosby Reducing Wheel CKOSBY REDUCING WHEEL WITH DETENT • 73 Special tools have been provided for making it, so that like parts are interchangeable, and when worn or destroyed others can be easily siibstitnted ; in other words, everything has been done so far as possible to make the instrument in all respects as excellent for its purpose as is the Crosby indicator. It is adapted to receive any steam engine indicator or indi- cator cock by means of interchangeable bushings ; and by a series of sjieed pulleys it can he adapted to all steam engines having strokes between the limits of 14 inches and 72 inches. Whenever the reducing wheel is to be attached to a ver- tical engine an elbow nipple is provided, which will allow the cord pulley to travel in the proper plane for guiding it to the cross-head of the engine, with the indicator in an upright position as usual. CROSBY REDUCING WHEEL WITH DETENT Patented The detent applied to the Crosby Reducing Wheel does not affect the connection between it and the engine, and does not allow the cord leading from the indicator drum to the reducing wheel to slacken. When the clutch is thrown in to stop the motion, the in- dicator drum is revolved to the end of the stroke and held there by the drum cord, while the mechanism of the detent controls the cord leading from the reducing wheel to the cross-head of the engine. When the clutch is i-eleased and the motion of the engine is again communicated to the drum, the latter takes up the motion without shock from the point where it stopped, be- cause it starts from a state of rest at the end of the stroke. This is imj)ortant, for if a drum is stopped and held by a detent in midstroke where the piston is running at its high- est speed, at the release of the detent the drum will neces- sarily start again at such liighest speed with a shock. 74 CROSBY KEDUCIXG WHEEL WITH DETENT This Cut Shows the Crosby New Indicator Mounted upon THE Crosby Reducing Wheel with Detent Moreover, as such a detent must engage at the highest speed, it often fails to operate and always wears rapidly. Directions for using the Crosby Reducing Wheel, either without or with detent, are sent w^ith each instrument. CROSBY REDUCING WHEEL WITH RECORDING COUNTER Patented To determine the number of revolutions of the engine per minute an ingenious and convenient device is shown by the cut, representing the Crosby Reducing Wheel having at- tached to it the Crosby Recording Indicator Counter. CROSBY REDUCING WHEKL WITH COUNTER 75 The latter is actuated by the moving parts of the reduc- ing wheel and records on a chart every revolution of the engine ; so that during the taking of the diagrams by the indicator attached to the reducing wheel the revolutions of the engine are recorded simultaneously. Its capacity to record 5,000 revolutions permits its use during a considerable period of indicating work ; and the average number 2)er minute so determined is more accurate for such purpose than if the revolutions were merely counted intermittently l)y the ordinary speed insti-uments. Besides, tliere is thus preserved by the chart a record of the work done, to be filed with the diagrams taken by the indicator for future consideration. It has recorded upwards of 4,000 revolutions per minute without a fault. No difficulty will arise in its attaclmient and use. After the reducing wheel has been adjusted to the 76 IMPORTANT SUGGESTIONS stroke of the engine, the counter is attached according to the following dii-ections : Loosen the clamping nut on the back of the counter ; raise the lever to its vertical position, and if the operating pin does not drop, press it lightly downward. Loosen the hexa- gon nut below the guide bracket of the reducing wheel and slip the fork of the counter bracket under the nut ; adjust the height of the counter on its bracket so that the opera- ting pin of the counter when down will just clear the guide bracket ; tighten all the nuts securely. To start the coun- ter, thi'ow the finger lever down ; to stop it, raise the lever to its vertical position. Set the chart at zero. Note the time of starting and stopping on the face of the chart, where indicated. IMPORTANT SUGGESTIONS In all cases the indicator coixl should be of the right length to prevent the paper drum from recoiling against its stop ; and before attaching it to the cross-head of the en- gine it should be drawn out its full length to ascertain whether or not the cords on the indicator and reducing wheel have been properly adjusted. All the woi'king parts must be kept well oiled. The reducing wheel is adapted to be used with a steam engine indicator having either a 1|- inch or 2 inch drum. As indicators Avith 2 inch drums are now more commonly used, the reducing wheel is ordinarily provided only with stroke pulleys for such size drum. If the reducing wheel is to be used with an indicator having the 1^ inch drum, it should be so stated in order to receive the stroke pulleys of the projjer size. These stroke pulleys are provided in sets and can be so obtained. With the 2 inch drum, the pro])er stroke pulleys will give cards 4 inches long, and with the 1^ inch drum the stroke pulleys are calculated to give cards 3 inches long. TESTIXG REDUCING MECHANISM 77 Busliings may be obtained for attaching other than the Cro.s])y indicators, and elljow nipples are made for attach- ing the reducing wheel to a vertical engine. TESTING THE ACCURACY OF REDUCING MECHANISM Whatever drum motion mechanism is used, its accuracy can be easily tested in the following manner : Lay off on the engine guides points at ^, ^, and f of the stroke. Connect the indicator with the drum motion in the same manner as for taking diagi'ams. When the cross-head is on either dead center, touch the pencil to the paper and make a vertical mark, and in the same way make vertical marks when the cross-head reaches each successive quarter point on the guides. If the marks are exactly at fourths on the card, the motion of the cross-head has been accurately reduced. CHAPTER VIII HOW TO TAKE DIAGRAMS First connect the indicator to the indicator cock. Adjust the guide wheel under the drum so that the cord leads from this wheel in the right plane- All reducing motions of the pantograph type, such as the lazy tongs shown by Fig. 16 and the modifications shown hy Figs. 17 and 18, require for correct reduction of motion that the string to the indicator should run in a line parallel to the line of motion of the piston-rod. AVith reducing motions of the Brumbo pulley type, shown by Fig. 15, it makes no difference at what angle the string leads from the guide wheel to the sector. The string must, of course, be in the plane of the sector. After the guide wheels under the drum have been ad- justed and fastened, change the lo(;ation of the hook on the drum string so that when the hook is pulled away out as far as it will go, it overlaps the pin or ring or loop or what- ever is provided for a connection on the reducing motion, by about §■ of an inch. Then let the drum spi-ing pull the hook away ])ack and note how near the hook comes to the pin or loop on the reducing motion. If the hook is drawn Ijack ^ of an inch beyond the travel of the pin or loop on the reducing motion the cord is the right length. Should the distance at this end be 1 inch, and at the other f of an inch, tlie cord should l>e lengthened so as to make the distances alike at the two extremes of the travel. The paper is now put on the drum. The paper must be tight and pushed down to the bottom of the clips. There are two ways in which the jjaper may be held by the clips. The ends of the paper may be brought out in 78 HOW TO TAKE DIAGRAJMS 79 the center between the two clips, or the two clips may he used as one piece and the two ends laj)ped under them. Next, connect the drum to the reducing motion. If one understands how to do this, it makes no difference whether the engine is making 10 or 600 revolutions per minute. Oftentimes it is amusing to watch one who does not know how, try to catch the loop in the string from a Brumho pulley reducing motion on a high speed engine. With one hand pull the hook on the indicator cord out as far as it Avill go. With the other hand take hold of the sti'ing from the Brumlio pulley and let the string he pulled through your fingers till the loop is reached. Hold the loop so that each time the engine reaches the crank end of its stroke you will feel a slight pull on the loop due to the winding of the string on the sector. The hook on the indi- cator cord will reach |- of an inch heyond the end of the loop, making it easy to connect. The speed of the engine, it will be seen, does not make any difficulty about connect- ing on if this method is used. Steam is now turned on the indicator tlu'ough the indi- cator cock, and after a period of ten seconds, in which time the indicator is being heated up by the steam, a card may be taken by pressing the wooden handle moving the pencil mechanism up against its stop. After taking the card, close the cock and draw an atmospheric line. Then discon- nect the drum string from the reducing motion. Should the lines on the card be too faint, the wooden handle may be screwed back a turn or two. Formerly, graphite was used for the marking point and ordinary paper as drum paper. To-day metallic paper (a paper coated Avith a salt of lead) is almost universally used and the marking point is a piece of soft brass. This makes it possible to get very fine lines on the card and to take cards with very little pressure on the marking point. Any friction between the pencil and the paper makes an error in 80 HOW TO TAKE DIA(;RAMS the card, and cards should be taken with as faint hnes as possible on this account. Make notes on the card of as many of the following facts as possible. The day and hour of taking the diagram ; the kind of engine from which the diagram is taken, and which eiigine, if one of a pair ; which end of the cylinder, the diameter of the cyhnder, the length of the stroke, the diameter of the piston-rod, and the number of revolutions per minute ; the position of the throttle ; the atmospheric pressure ; the steam pressure at the boiler and at the engine, by the gages ; the vacuum by the gage on the condenser and the temperature of the feed at the boiler ; if the engine is compound, the pressure in the receiver ; the scale of the spring used in the indicator ; the volume of the clearance at each end of the cylinder, and what per cent of the piston displacement each of these volumes is. (Directions for ascertaining the volume of the clearance, and what per cent that volume is of the piston displacement, are given on pages 94 and 96.) It is often useful to make notes of special circumstances of importance, such as a description of the boiler, the diame- ter and length of the steam and exhaust pipes, the tempei'a- ture of the feed water, the quantity of water consumed per hour, etc. On a locomotive, note the tmie of passage between mile- posts in minutes and seconds, from which, when the diame- ter of the drivers is known, the number of revolutions per minute may be calculated. Note also the position of the throttle and the link, the size of the blast orifice, the weight of the train, and the gradient. On diagrams from marine engines note, in addition to the general facts, the speed of the ship in knots per hour, the direction and force of the wind, the direction and state of the sea, the diameter and pitch of the sia-ew, the kind of coal, the amount consumed, and the ashes made per hour. chaptp:r IX HOW TO FIND THE POWER OF AN ENGINE To find the power actually exerted witliin the cylinder of a steam engine, it is necessary to ascertain separately three factors and the product o£ their continued multiplication. These factors are : The area of the two sides of the ])iston ; the total travel of the piston in feet per minute ; and the mean effective pressure urging the piston forward, desig- nated M. E. P. The 2)'iston area. This, at the back end, is the same as the area of cross-section of the cyHnder ; at the crank end it is the same, less the area of cross-section of the piston- rod. These areas may be found from their diameters in a ta]>le of the areas of circles, or may be computed by multiply- ing the square of the diameter in inches by the approximate nmnber 0.7854. The trarel of the jji-'^ton. The total travel of the piston in feet per minute is found by nudtiplying twice the length of the stroke measured in feet, by the number of revolutions of the crank shaft per minute, which should be carefully ascer- tained by taking the mean of many countings, or the readings of a speed counter during a considerable time. The mean piston speed will be expressed in terms of feet per minute. The mean effective pressure. There are several approxi- mate methods for computing the mean effective pressure, on© of which is to divide the diagram into ten equal parts, as shown in Fig. 20. Then through the points of division draw lines, which are called ordinates, at right angles to the atmospheric line. The mean heights or pressures of the small areas thus formed are indicated by the dotted lines midway between the ordinates. 81 82 MEASURING THE DIAGRAM The mean effective pressure of the whole (of each) dia- gram may now he found, hy measuring (on the dotted lines) the mean pressure in each of the small areas with the scale corresponding to the spring used in taking the diagram. H cd 2; K h( (-) O w W bs The sum of these mean pressures, divided by 10, the number of divisions, will give the mean effective pressure sought, in pounds per square inch. If a diagram has many irregularities of outline, it may he necessary to divide it into twenty equal divisions to insux'e a correct measurement of the pressures ; in such a case we MEASURING THE DIAGRAM 83 divide the sum of the pressures by 20 instead of 10. In other cases, when irregularities occur only in a part of a diagram, it is only necessary to subdivide one or more of the ten divisions to insure greater accuracy in that part ; in such a case we must measure the pressure in each subdivision and divide their sum by 2 to get the mean pressure of that division. (See Fig. 22 for a full illustration of this method.) If the scale is not at hand, the heights of the divisions may be pricked or marked ofE on a strip of paper, one after the other continuously until all are measured ; then the distance from the end of the strip to the last mark vnll represent the sum of all the measurements, which can be measured in inches with an ordinary rule. This quantity, divided by the number of divisions in the diagram — or diagrams, if there are two — and multiplied by the scale of the spring used, will give the average or mean effective pressure, the same as by the other method. Fig. 21 When there is a loop in the diagram, as in Fig. 21, the area enclosed in the loop should be subtracted from the other part, as it represents loss of efficiency. The quickest and most accurate method for measuring the diagram and finding the mean effective pressure is by the use of Amsler's Polar Planimeter. With careful manipula- tion, the planimeter will give the exact area of a diagram in 84 MEASURIN(:t THE DIAGRAM square inches and decimal parts thereof, to hundredths of a S(^uare inch, and the tedious process of dividing the diagram into equal parts and measuring their average pressures or heights, with the liability of making ei'roi's, is avoided. Measure the diagram with the planimeter as directed in Chapter IV, at page 45. Divide the number of square inches area thus found by the length A of the diagram, expressed in inches and decimals, and the result will be the average height of the diagram. Multiply this average height by the scale corresponding to tlie spring used in taking the diagram and the result will be the mean effective pressure. It is better to multiply first and divide afterwards to avoid troublesome fractions. Fig. 22 illustrates two diagrams divided first into ten equal spaces and then each end space subdivided so as to more accurately measure those parts of each in which the greatest iriegularities occur. Observe that the pressures or heights of the subdivisions of each end space are measured, and the sum of these measurements divided by 2 to get the mean pressure or height of that one of the ten spaces. The pressures of Diagram No. 1, as measured by the scale, are set in a column on the left, while those of No. 2 are set in a column on the right. The sum of each column divided by 10 gives the M. E. P. of that diagram. The heights of Diagram No. 1, marked off on a slip of paper continuously, measure 11.91 inches, while those of No. 2 measure 11.95 inches ; these quantities, divided by 10 and multiplied by 50, give the M. E. P. of each diagram respectively, and if accurately measured, will be the same as found by the scale. These diagrams, when measured by the planuneter, give results which are substantially the same. As the error of the planimeter is less than its smallest scale graduation, this method of finding the mean effective pressure is the most accurate as well as the most convenient. measuring the diagram Fig. 22 85 Diagram No. 1 Pressurea Diagram No. 2 Pressurea 10 ) 595.5 M.E. P., 59.55 M. E. P., 59.75 Heights of Divisions Measured on a Strip of Paper Diagram No. 1 Diagram No. 2 10) 11.91 111. Divide by 10 10) 11.95 in. 1.191 1.195 ,50 Multiply by proper scale M. 50 M.E. P., 59.r.r.0 E. P., 59.750 Diagram No. 1 Square inches, 4.43 Length, 3.72 Average height, 1.191 M. E. P., 59.55 lbs Planimeter Measurements Diagram No. 2 Square inches, 4.46 Length, 3.73 Average height, 1.195 M.E. P., 59.75 lbs. 86 CALCULATING HORSE-POWER CALCULATING \. H. P. Let a = the area of the head end of the piston in square inches. Let r = the area of the piston-rod in square inches. Let s = the stroke of the engine in feet. Let n = the number of revolutions per minute. The I. H. P., or indicated horsepower, of the liead end of the cyhnder, is a X (M. E. P. of head end) X s X n 33,000 The I. H. P. of the crank end is (a — r)X (M. E. P. of crank end) Xs Xn 33,000 The I. H. P. of the cyhnder is the sum of these two. If the M. E. P. and the revolutions per minute are each made equal to 1 in the preceding expressions, then the result obtained from each is the I. H. P. per pound M. E. P. at one revolution per minute. These factors are called the engine constants. The engine constants for the two ends are respectively a X s _ (a — ?') X s and 33,000 33,000 If the valves of an engine are well adjusted and the M. E. P. for the two ends of the cylinder is nearly the same, an approximate calculation of the indicated horse- power of the cylinder may be made by multiplying the average M. E. P. of the two ends by the number of revo- lutions per minute and by the sum of the engine constants. DISCUSSION OF M.E.P. The indicator card from one end of a cylinder shows the pressures on tliat end during a revolution, or a stroke foi'ward and a stroke back. CALCULATING HORSE-POWER 87 The Mean Effective Pressure, M. E. P. (improperly named perhaps) used in figuring horsepower is calculated from the indicator cards as already explained. The effective pushing pressure or pulling pressure per square inch of piston area at any point of the stroke is evi- dently the difference hetween the total pressures on the two sides of the piston at that point divided hy the piston area. Obviously the average pressure, calculated in this way, would not be the same as the mean effective pressure. (See discussion of stroke cards given later on.) That the horsepower obtained is correct when the M. E. P. is calculated as previously explained is shown liy the illustration which follows. Let the mean pressure above the atmospheric line corre- sponding to line a b c d ^ Pj-. A B Let the mean pressiire above atmospheric line correspony H--7^ Clearance 0.04 of Stroke Fig. 24 measured in a quart or pint measure and the number of cubic inches found directly. A gallon contains 231 cubic inches, a quart 57.75, and a pint 28.875 cubic inches. The volume of the clearance will rarely be the same at the two ends of the cylinder, therefore the number of cubic 96 THE HYPERBOLIC CURVE inches in the clearance at each end nui.st he divided hy the net area of the piston at its own end : that is, the number of cubic inches in the clearance at the end nearest the crank must be divided by the number of square inches in the cross-section of the cylinder, less the number of square inches in the cross-section of the piston-rod ; and the number of cubic inches in the clearance at the end farthest from the crank must be divided by the numl)er of square inches in the cross-section of the cylinder. The quotient in each case will be the length of clearance at the resjiective ends of the cylindei-, expressed in ii>ches. In this instance (Fig. 24) it is found to be 0.16 of an inch. It is convenient to have the length of the clearance expressed as a fraction of the piston displacement or stroke of the piston. To obtain this fraction, divide the number of cubic inches in volume of clearance by the number of cubic inches in the volume swept through by the jjiston at each end separately, taking care to allow for the volume occupied at one end by the piston-rod, and the quotient will be the decimal fraction that the clearance space is of the volume swept through by the piston. Fig. 24 illustrates a good method for locating points in the hyperl>ola through which the curve may be drawn. First, draw the zero line V, at the proper distance, viz., 14^^ pounds by the scale, below and parallel with the atmospheric line ; next, draw the clearance line O, as com- puted, 0.16 of an inch from the end of the diagram ; next, locate the point of cut-ofB X, and draw the perpendicular line numbered 3 through it ; next, divide the space between this line and the clearance line into three equal parts ; then, taking one of these parts for a measure, point off, on the vacuum line, eqiad spaces toward the left hand until one or more falls beyond the end of the diagram as shown, and erect perpendicular lines from each ])oint. These lines are called ordinates and numbered consecutively 1, 2, 3, 4, etc., THE HYPERBOLIC CURVE 97 beginning with the one next to the clearance line. It is well to bear in mind the fact that vertical distance on a diagram represents pressure and horizontal distance tiolimie. In this case we have started the hyperljola from the point of cut-ofE X, and its course is indicated by the short lines drawn through the ordinates a little above the actual curve, with their calculated pressures written above ; the actual pressures of the expansion curve are written lielow it. The properties of the hyperbola are such, that if the distance of the point X from the clearance line O be multiplied by the height of X from the zero line V, the height of any other point in the curve can be found by dividing this product by its distance from the clearance line. And on this principle we proceed to locate points on the ordinates through which our hyperbola will run. We find the pressure at the point of cut-off to be 121 pounds with a volume which we call 3, because there are three spaces or volumes between it and the clearance line. Then, 121 X 3 = 363, which is our dividend for all the other volumes. Therefore, the height at which the hyper- bola will cut ordinate 4 will be determined by dividing 363 by 4, which is 90.8 (it is unnecessary to carry the division beyond one decimal) ; and at ordinate 5, 72.6 ; at ordinate 6, 60.5 ; and so on to the end. At ordinate 12 we find that the hyperbolic and the actual curves practically coincide. In like manner we may extend the curve to the right : 363 -f- 2 = 181 pounds, which would be the pressure if the steam were compressed up to 2 volumes. If desired, the hyper- bolic curve can be started just before the point of release and projected in the opposite direi^tiou by the same method. Instead of using figures which stand for pressures or volumes of steam to locate the liy])erbola, as in this instance, the distances from the base and perpendicular lines of any ])oint niay be expressed in inches and decimal parts, with the same result. 98 METHODS OF FINDING THE HYPERBOLA A quick way to draw the hyperbola is to take the whole distance between ordinate 3 and the clearance line, (Fig. 24), as a measure, and set off equal spaces to the left as be- fore directed. Then we would have but four ordinates and would niuiiber them as follows : 1 at 3d, 2 at 6th, 3 at 9th, Fig. 25 and 4 at 12th. At 1 we would have a pressure of 121 pounds ; at 2, 121 pounds -r- 2 = 60.5 ; at 3, 121 pounds 4- 3 = 40.3 ; and at 4, 121 pounds -^ 4 = 30.25. METHODS OF FIXDIXG THE HYPERBOLA 99 As a general rule, the near approximation of the expan- sion curve to the theoretical or hyperbolic curve may be taken as evidence of good conditions but should not be accepted for a certainty, unless all the known facts and conditions tend in the same direction. GEOMETRIC METHOD OF FINDING THE HYPERBOLA The hyperbola may be found by following the directions given below, in connection with Fig. 25. A is the atmos- jiheric line ; Z the zero line, or line of no pressure ; B the line of boiler pressure, and C the clearance line. Locate the first point in the hyperbola at the point of release X and draw tlie vertical line X E. Then draw diagonal line, E H ; then, from X, draw horizontal line 5 to its intersec- tion w4th E H, through which draw vertical line F O. Now mark off points between O and E as 1, 2, 3, 4 — exact spa^ cing is unnecessary — and from these points draw diagonal lines to H and vertical lines down to, or a little below, the actual curve. Now draw horizontal lines 6, 7, 8, and 9 from the points of intersection in the line F O, of the diagonal hnes H 4, H 3, H 2, and H 1 respectively ; and the points where these lines cross the vertical lines, 1, 2, 3, and 4, in connection with points X and O, are the points through which the hyperbola should be drawn, as shown by the dotted curve. ANOTHER METHOD OF FINDING THE HYPERBOLA Through the point of release h, draw any line as a B and make A B equal to (/ h, as shown in Fig. 26. Then draw any other line as c D and make c d equal to A D ; then d wall be a point in the hyperbola passing from h to A, as shown by the dotted curve. By drawing a number of lines through A and following the same method, we can find as many points in the hypei'bola. 100 MJETHODS OF KIXDING THE HYPERBOLA q f^ Fig. 26 PART II PART II APPLICATIONS The steam engine indicator may be used for a great many purposes besides those mentioned in the preceding chapters. The a2>phcations are so varied that the cases selected and illustrated in these pages show only a few of those which seem to be most useful. I. Valve Setting If the cards taken from the two ends of the cylinder re- semble Figs. 27 or 28, the eccentric has too little angular Fig. 27 advance and must be turned ahead ; in the case of an engine giving cards shown by Fig. 27, moving the eccentric ahead Fig. 28 103 104 APPLICATIOSrS 5° to 10° would probably be sufficient, while with Fig. 28, 20° to 30° would be ncLMled. If the cards from both ends resemble Figs. 29 or 30, the eccentric has too much anjrular advance and should be turned Fig. 29 back a small amount for Fig. 29, and a much larger amount for Fig. 30. Cards similar to Figs. 29 and 30 are obtained at early Fig. 30 cut-off from most single valve high speed engines with fly- wheel governors. A plain slide valve engine, or an engine with piston valve, taking steam on the outside, will give cards like Figs. 31 and 32 when the valve spindle is too long, the eccentric being in the right place. The effects of lengthening the valve spindle are (1) to APPLICATIONS 105 increase the steam lap on the head end, delaying admission and hastening cut-off on this end ; (2) to decrease the steam lap on the crank end, hastening admission and delay- ing cut-off ; (3) to decrease the exhaust lap on the head end, hastening release and delaying compression ; and (4) to increase the exhaust lap on the crank end, delaying release and hastening compression. Fig. 31 If the valve spindle is too long and at the same time the eccentric has too little angular advance, or is set too far hack, the cards from the engine will he similar to Figs. 33 and 34. Fig. 32 If the eccentric is set too far ahead and the spindle is too long, the appearance of the cards may he predicted by 106 APPLICATIONS Head End Fig. 33 combining the effects shown by Figs. 29 or 30 with Figs. 31 and 32. 2. Steam Chest Cards A steam engine indicator may be connected to the steam chest of the engine and cards taken simnltaneously with Crank End Fig. 34 cards from the cyhnder, botli indicators being attached to the same reducing motion. For comparison, it is convenient to superimpose the chest card on the cyhnder card, as has been done in Fig. 35. The steam chest card A B C D E C A, Fig. 35, is for one revolution. If the steam pipe and steam port leading from the steam chest to the cylinder are large enough, there will APPLICATIONS 107 be no appreciable drop in pressure between the boiler and tlie steam chest, or between the chest and the cylinder. If, however, a chest card similar to that shown by the full line is obtained, the steam pipe is too small. This is shown by the fact that the di'op from boiler pressure A appears in the steam chest card while the drop between the steam chest and the cylinder is slight. Fig. 35 If the clie.st card showed a slight drop in pressure, as indicated by the dotted line AG, it would mean that the steam port leading from the chest to the cylinder was too small. A chest card sliown by the line AH would mean that both the steam pl])e and the steam ports were too small. Sometimes the pressure at C is greater than boiler pres- sure, A. Tliis results from the sudden checking of the velocity of the steam in the pipe supplying the engine. 3. The Eccentric Card Near the ends of the stroke of an engine the crank turns through a considerable number of degrees without giving much motion t(» the cross-head. 108 APPLICATIONS On account of this fact the indicator card taken in the ordinary way is of httle vahie in investigating any peculi- arities which may he noticed at or near the ends of the stroke. Fig. 36 If, however, the drum motion he taken from the eccen- tric, which is ordinarily a little over 90° ahead of the crank, the compression and admission lines and the line at release will he spread out at the center of the diagram, while the expansion and exhaust lines Avill he shortened and a2)pear at the ends of the cards. Fig. 37 Fig. 37 represents a good steam card, and Fig. 38 an eccentric card. APPLICATIOXS 109 The cards are lettered at admission, cut-off, release, and compression with the letters A, B, C, D, respectively. It will be noticed on the eccentric card tliut tlie line DA is a reverse curve. Fig. 38 On the card taken from an engine with throttling governor, Fig. 36, a peculiar drop near the end of com- jiression is found. This is due partly to a leakage of steam from the cleaiance space over the bridge into the exhaust and partly to a slight amount of condensation. Tliis drop appears on the eccentric card as in the dotted line. 4, Steam Cards from a Westinghouse Air Brake Pump, or from a Wet Air Pump with Surface Condenser In the diagi'am shown by Fig. 39 the piston starts at the left and moves towards the right. As the work ojiposed to the steam piston by the air piston is but trifling during the first part of the stroke, the steam piston " runs away from the steam," causing the drop in pressure shown. Near the end of the stroke the extra work opposed to the steam piston l)y the air piston causes it to slow do^\Ti, and then steam has time to fill the cylinder at nearly boiler pressure. On the return stroke the piston, during the first part of its stroke, travels so fast that the steam cannot be freely exhausted. Dvu-ing the latter part of the stroke. 110 APPLICATIONS liowever, when the piston slows up, the jjressure drops nearly to that in the exhaust pipe, as shown hy the lower hue of Fiir. 39. Fig. 39 A casual inspection of Fig. 39 might lead to the con- clusion that the greatest effective pressure on the piston was at the left-hand end near the beginning of the stroke. This is not the case, as may he seen hy constructing what is called the stroke card, shown hy Fig. 40, and again by Fig. 46. Assvmiing that the piston has a tail-rod so that the area of the head end of the piston is the same as the area of the crank end, the effective push per square inch on the piston at any time is the difference of pressure on the two sid-es at that time. If now the steam line of the card from Fig. 40 APPLICATIONS 111 the head end he comhined with the hack pressure line from the card of the other end, we get a diagi'ani known as the Stroke Card, sometimes called the True Card, which, hy its distance between lines, gives the effective pressure per square inch on the piston at any point. Such a diagram is shown hy Fig. 40 for the Air Brake Card. It A^dll be noted that the greatest effective push on the piston comes at the riffht-hund end, not the left. If the two ends of the steam piston have not the same area, the pressures from one indicator card may be multi- plied by the ratio of the two areas, before plotting, in order to reduce to the same basis for comparison. 5. Air Compressor Cards Figs. 41 and 42 are respectively from an air compressor and from the air end of a certain type of air pump. The irregiilarities in the delivery line of Fig. 41 are due to the vibrations of the delivery valve. The slight drop at Fig. 41 the beginning of ail' intake results from resistance to open- ing offered by the suction valves. The air pumj) pumps a mixture of water and air. On account of the large clearance the curves are much less steep than in the case of the air compressors. 112 APPLICATIONS Fig. 42 6. Gas Engine Cards Figs. 43 and 44 are from an Otto Gas Engine. Fig. 44 has the firing delayed till the end of the stroke, and shows plainly the effect of not having a " lead " on the firing spark. Engines working on the Otto cycle can have only one working stroke in four, and as many of these engines work on the " hit and miss " principle, in figixring the horsepower from the cards it is necessary to note the actual mmiher of explosions per minute. Starting at exhaust on the right-hand end, the piston D Fig. 43 APPLICATIOlSrS 113 moves to the left, along AB, and drives out the burned gases through the exhaust valve ; next the exhaust valve closes, and as the piston moves to the right, gas and air are drawn in, along BA, the mixture being regulated by the opening of the gas inlet, so as to get the proper ratio of gas to air. On the third stroke this mixture is compressed, along AC, and just before the piston reaches the end of the stroke the mixture is fired ; the hot gases expand dm-ing the fourth stroke, DA. B^ Fig. 44 If the engine is up to speed and gas is not admitted by tlie governor, the cylinder is filled with air on the fiUing stroke ; this air is compressed on the third stroke and expands back again along nearly the same line on the fourth stroke. Fig. 45 114 APPLICATIONS 7. Ericsson Hot Air Engine Cards Fig. 45 is from an Ericsson hot air engine. This is taken with a 10 pound spring. As there are no valves in this engine, the same air being alternately heated and cooled, it is impossible to get sharp corners on the card. 8. Stroke Card Fig. 46 represents a stroke card from a Corliss engine. This is constructed as explained in conftection with Fig. 40. Fig. 46 Near the end of the stroke the pressure on the opposing side of the piston is greater than that on the pushing side, as shown by the part cross-hatched. During this short interval the fly wheel pulls the engine over. Fig. 47 APPLICATIONS 115 9. Rotative Effect The total pressure on the piston-rod at any point may be found by multiplying the pressure measured across the stroke card at that point by the area of the piston. Sup- pose the total pressure on the piston-rod at the position shown in Fig. 48 is 1,000 pounds. Draw the line P to represent this pressure at some assumed scale, say, for example, one inch representing 500 pounds. Then P = 2 inches long. Fig. 48 This force P produces a push along the connecting rod and a downward thrust on the guides. This push along the rod and this thrust on the guides may be found by making a triangle of forces as sho^vn. The length of the different sides of the triangle multiplied by 500 gives these forces in pounds. The tlunist in the connecting rod is seen to be greater than P. Tliis thrust at the cross-head end of the connecting rod is carried to the crank pin where it may be separated into two forces, one force R at right angles to the crank tending to produce rotation, and another force along the crank making a compression in the crank casting. If, now, values of R are calculated for a sufficient num- ber of points and plotted on a line wliich represents the development of the crank pin circle, a diagram of rotative effect hke Fig. 49 is obtained. The upper half comes from one stroke card and the other half from the other stroke card. 116 APPLICATIONS The mean rotative effect is shown by the clot and dash lines. The amount of energy stored and restored by the fly wheel during a stroke is represented by the area within the curve outside of the dash and dot line. In tliis discussion it has been assumed that the entire pressure on the piston was available for producing rotative effect. This is not the case, however. A certain amount of this pressure is used up at the beginning of the stroke in Fig. 49 accelerating the piston, piston-rod, cross-head, and a part of the connecting rod. As these are brought back to rest at the end of the stroke, as much energy is recovered as was lost at the beginning. The dotted line on Fig. 46 shows how the upper Une should be changed to make allowance for this, in the case of a low speed Corhss engine. On a high speed engine this is a much larger factor, as may be seen in Fig. 47. In this figure the effective pressure per square inch available for producing rotative effect is shown by the area cross-hatched. APPLICATIONS 117 10. Explosive Force of a Mixture of Gas and Air Fig. 50 was obtained with a gas engine indicator and a tuning fork. The mixture, which was one part Boston gas Fig. 50 to six parts air, was compressed to 25 pounds, as shown at the left of the diagram. It was then fired by a spark, and a pressure of 225 pounds above the atmosphere resulted. The tuning fork, which was marking on the paper at the same time, gave a means of estimating the time required to reach maximum pressure. Each wave denotes ^^ of a second. This explosion was /^ or ^^ of a second in reaching maximmn pressure. II. Measuring Water Hammer Fig. 51 was taken from a 4 incli drive pipe 90 feet long, supplying a Rife Hydraulic Ram. The fall of water to Fig. 51 118 APPLICATIONS tlie ram was about 8 feet. Beneath the card a wave line drawn by a tuning fork gives a means of measuring time accurately. The maximum pressure is 320 pounds. The recui'rence of figures similar to the fii'st, but with rapidly decreasing pressures, seems to indicate a wave traveUng back and forth in the pipe. The air which is carried by the water no doubt has sometliing to do with tliis. 12. Flather Dynamometer A form of dynamometer built by Mr. John J. Flather makes use of a steam engine indicator for measuring power. Figs. 52 and 53 show the indicator cards taken from a Fig. 52 Fig. 53 dynamometer attached to a power drill. Fig. 52 was taken with a sharp driU running into a cored hole in a casting. The hole was coated with rough sand and the drill lost its edge rapidly, when it gave a diagram like Fig. 53. This dynamometer consists of a hollow shaft on which are two pulleys, one tight and the other loose. On opposite Fig. 54 APPLICATIONS 119 arms of the tight pulley are two small cylinders which are open at one end. The cylinders connect through pipes, at the closed ends, with the hollow shaft. Built out from the arms of the loose pulley are two studs carrying pistons which fit into the cylinders. The cylinders are filled with oil, as is also the hollow shaft, to the end of which the indi- cator is attached. The loose pulley drives the tight pulley through its pistons, wliich press on the oil in the cylinders Fig. 55 carrie,d hy the tight pulley. The steam engine indicator records this pressure. The drmn of the indicator is driven from the shaft through a worm and wheel. 13. Pulsometer Steam Pump Figs. 54, 55, 56 are taken from the left side, the right side, and the air chamber of a pulsometer steam pump. Fig. 56 These cards were taken at the same time. The drums of the indicators were moved at the same uniform rate by means of gears driven by a line of shafting. Fig. 57 shows the combined diagram, giving the pressm-es at any part of the pump at any time. 120 APPLICATIONS The line AA represents the atmospheric line, the line W that corresponding to an absolute vacuum, and the line -1-03 seconds V ' Fig. 57 V. PP the pressure in pounds due to the hydrostatic head the pimip was delivering against. The shaded portions repre- sent deliveries of" water. PART III PART III CHAPTER I PROPERTIES OF STEAM AND OF PERFECT GASES In order to make complete calculations of an engine test, and in order to get as much information as is possible from the cards, it is necessary to understand the properties of saturated steam and to be aide to make intelligent use of tables or plots giving such properties. It is not the intention to give here any lengthy discussion of thermodynamics, and oidy such parts of that subject will be touched as bear directly on work depending upon the indicator card or the solution of practical problems such as may come to an engineer in charge of a plant. Pmssicres. The pressure of the atmosphere is usually taken as 14.7 pounds per square inch. This corresponds to a corrected reading on the barometer of 29.92 inches. Steam gages are made to read pressures above the atmos- l)here ; therefore to get what is called the absolute pressure, the pressure of the atmosphere must be added to that shown by the gage. A barometric reading in inches of mercury may be re- duced to pounds pressure on the square inch by multiplying its corresponding reduced height at 32° F. by 0.491. The reduced height for a barometer having a brass scale may be calculated from the following : [1 + 0.0000102 {t — 62)] X h 1 + 0.000101 {t — 32) where h is the observed height in inches and t is the Fahren- heit tem])erature at the barometer. 123 124 ' PROPERTIES OF STEAM AND PERFECT GASES To measure pressure below the atmosphere, a vacuum gage or a glass U tube filled with mercury may be used. It is customary to quote the vacuum in inches of mercury in- stead of in pounds. If the barometer stood 29.9 inches a vacuum of 2G inches would mean that there was an abso- lute pressure of 3.9 inches, or (3.9 X 0.491) pounds. All pressures as given in plots or in tables of the proper- ties of saturated steam are absolute pressures. Specific i^t'^^'^^fo'^ and sjiccific volume. Specific pressure is absolute pressure on the square foot. Specific volume is the volume of one pound. The specific volume of water is g-jrr^ 0.016 cubic feet, 62.4 pounds ])eing the weight of a cubic foot of water at 62°. The volume of a i)ound of dry steam, represented by the letter s, varies with the pressure. The Brtttsh thermal unit, B. t. u., is the amount of heat necessary to raise one pound of water from 62° F. to 63° F. The heat of the liquid is the amount of heat expressed in B. t. u. necessary to raise one pound of water from 32° to the temperature desired. If the specific heat of water was unity throughout the entire range of temperature, the heat of the Hquid would be 32 less than the temperature. The specific heat is slightly above unity at some temperar tiu'es, and slightly below unity at other temperatures. The heat of the htpiid is represented by the letter q. Relation, of jjressure and temperature of saturated steam: Regnault found that the temjjerature of steam depended upon the pressure ; that the temperature of the steam, if it was not su])erheated, was exactly the same as that of the water in contact with it. Particles of water may float in steam the same as fog floats in the air. This does not affect the tenqjerature of the steam. PROPERTIES OF STEAM A2fD PERFECT GASES 125 Total latent heat or heat of vaporization (represented by /•) : If a pound of water at 32° is heated up to the boihng point at atmospheric 2)ressiu'e, 180.3 lieat units (the vahie q of the lieat of the Uquid), wall he consumed in raising the tem})erature from 32° to 212°. If now heat is added, the water Avill gra(hially go off as steam. To entirely vaporize this i)oun(l 969.7 B. t. u. will he needed. This 969.7 B. t. u. is the heat of vaporization at this pressure. It is often called the total latent heat. The heat of vaporization is different at different pressures. The total heat at any jiressure (represented hy the Greek letter \ called lambda) is the amomit of heat necessary to raise a pound of water from 32° to the temperature corre- sponding to the pressure and to tlien entirely vaporize the water at this temperature and imder the constant pressure. It is evidently equal to the smn of q and r, the heat of the li(piid and the total latent heat. Until recently the values of X- as determined hy Regnault were used, although they were known to he somewhat in error ; recently, however, Mr. H. N. Da\as has deduced correct values of the total heat hy making use of the experi- mental data at hand, mainly that of Grindley, of Griess- nian, and of Knoblauch, all three of whom were at Avork on the determination of the values of the specific heat of superheated steam. Heat equivalent of external work and lieat equivalent of internal ivork : As water passes into steam at constant pressvire and at constant temperature, we have seen that the heat of vapor- ization r is re(][uired. This value r is made up of two parts. One part, the heat equivalent of the external work, can be calculated. The other part, the heat equivalent of the internal work, is obtained by subtracting the first from r. 126 PROPERTIES OF STEAM AJS'D PERFECT GASES The following examjile will illustrate the method of calcu- lating the heat equivalent of the external work. Suppose one pound of water at 32° to be placed in the bottom of a vertical cylinder of one square foot piston area. Let the piston be weighted so that together with the atmos- pheric pressure there is a load of 100 pounds per square inch on the piston. If heat is added to the water, vaporization will not begin till a temperature of 327. 8G° F. is readied. As vaporiza- tion takes place the piston rises in the cylinder. When all the water has been made into steam, the piston will stand 4.432 feet above the bottom of the cylinder. The pound of water occupied 0.016 of a cubic foot, and as tlie cylinder is one square foot in sectional area, the piston nmst have moved up a distance of 4.432 — 0.016 = 4.416 feet. The external work done is 100 X 144 X 4.416 foot-jjounds. Dividing this by 778, the mechanical equivalent of one heat unit, gives as a result 81.9 B. t. u. The heat equivalent of the external work is represented by Apu. A is the heat equivalent of one foot-pound and is equal to y^-g ; p is the absolute pressure on the square foot ; u equals the change in volmne in passing from water to steam. Subtracting the heat equivalent of the external work from the total latent heat gives the heat equivalent of the in- ternal work. This is represented l)y the Greek letter p (called rho). In tliis case, at this pressui-e, p amounts to 887.6-81.9= 805.7 B.t.u. This heat equivalent of the internal work increases as the volume of a pound of steam increases. As the vohuue occujiied by a pound of steam at very low PKUPEKTIES OF STEAM A^s'^D PERFECT GASES 127 pressures is large, it will be found that the iuterual latent heat is a large proportion of the total heat. Where tliis heat goes to, may be illustrated thus. All substances are supposed to be made up of small particles called molecules. The pound of water occupying 0.016 of a cubic foot had a certain number of these molecules. The number remained the same in the pound of steam which filled a volume of 4.432 cubic feet. The relative distance between these molecules has been increased 275 times. Each molecule exerts an attraction for its neighbor, and as tliis attraction has been overcome thi-ough space, work has been done. Tlus work has required an equivalent expenditure in heat. Tliis internal Avork is often called dlsyregatloii work. Total heat A vapor ..f 1 lijuid heat of ization 'J r heat equivalent of internal heat equivalent of external work work P Apu Volume of a 2^0 and of vuxture, of steam ami water : The volume of a pound of steam is s, the volume of a pound of water is 0.016 of a cubic foot. If the mixture is x parts steam by weight the volume o of the pound of mixtm-e is v = .r.s-+(l— a-)0.016 v = x (.s — 0.016) + 0.016 128 PROPERTIES OF STEAJVI AiiD PERFECT GASES Total heat of a pound of mixture of steam and water above S^ : Before any water can be made into steam at a given pressure, the whole of the water must first he heated to the temperature corresponding to the pressure. Then if x parts ])y weight are made into steam, the heat x r nuist he added, making the total heat to he added q + x r. Total heat of a jpound of a mixture of steam and water above any yiven temperature. First find the heat of the pound of mixture above 32° equal to 5* + j" r, then subtract the heat of the liquid at the given temperature. Superheated steam is steam of a liigher temperature than that corresponding to saturated steam of the same pressure. The difPerence of teiuperature is the number of degrees of superheating. To tell whether or not steam is superheated, a thermom- eter, a steam gage, and a table or jjlot giving the tempera- tui'es of saturated steam are needed. Knoblauch, Linde, and Klebe, from recent experiments made in Munich, have determined the followdng ecpiation for sujierheated steam : pv = 85.85 T—p (1 + 0.n0O00f)7('.y>) { ^'^^"^y^^*^^^ — 0.0S328 [ A much more simple equation giving results agreeing with the above within 0.8 of one per cent is pv = 85.85 T_ 0.256^^ where p is the absolute pressure in pounds on the square foot, and v is the volume of one pound. T is the absolute temperature of the superheated steam in degrees F. ; this is found by adding 459.5 to the temperature of the steam as given by the thermometer. Having the temperature and pressure as known terms, PROPERTIES OF STEAM AXD PERFECT GASES 129 the volume niay be found, or, with a known vokinie and a known pressure, the temperature may lie found. Specific heat of superheated steam at consta.nt piressure It was formerly assumed that this speeilic heat of super- heated steam was constant. It is now known that the specific heat increases with increase in pressure, but at any constant pressure the value decreases as the amount of superheating increases. The mean values of the sjiecific heat for different pres- sures and for different degrees of superheating, as given by the experimental work of Thomas & Short, are quoted in the accompanying table. Mean Value of Specific Heat of Superheated Steam {Thomas & Short) Degrees of Pressure, pounds per square inch, absohite Superheat JFahr. 6 15 30 50 100 200 20 50 100 150 200 250 0.536 0.522 0.503 0.486 0.471 0.456 0.547 0.532 0.512 0.496 0.480 0.466 0.558 0,542 0.524 0.508 0.494 0.481 0.571 0.555 0.537 0.522 0.509 0.496 0.593 0.575 0.557 0.544 0.533 0.522 0.621 0.600 0.581 0.567 0..556 0..546 Total heat of a pound of superheated steam : This is evidently equal to the total heat of a pound of saturated steam of the same pressure, ])his the average value of the specific heat for the range of superheating times the nmnber of degrees of superheat. Using the letters which represent the different values q -\- r -\- CpX (degrees superheat) ; or X + Cp X (degrees superheat). 130 PROPERTIES OP STEAM AND PERFECT GASES At the back of the book there are two charts, one giving the different vahies of t, q, r, X, A p u, p, and s for pres- sures from to 10 pounds absohite and the other giving vahies of the same terms from 10 pounds absohite to 250 pounds absohite. These curves, which are drawn to represent the vahies given in Peabody's Steam Tables, the tables in general use by engineers, will serve to give values with a moderate de- gree of accuracy. For accurate work such values should be taken from some reliable steam table which gives these values for each degree difference of temperature or for each pound increase in pressure. Tables which give values for intervals of 5 pounds, and where values for intermediate points must be obtained by interpolation, ai-e fairly accurate at high pressures, but unre- liable at low ])i'essures on account of the error due to inter- ])olation. Even tables reading to one pound are unreliable at low pressures for the same reason. If either Peabody's Steam Tables or the Steam Tables by Marks and Davis are used, all low jiressure values should be taken from the temperature table which gives values for each degree from 32°, The pressure correspond- ing to each temjjerature is given also. As there are seventy sets of values for })ressiires between and one pound absolute, sufficient ac-curacy can be obtained. The charts show that the total heat and the heat equiva- lent of the external work change but little ; that the tem- perature, the specific volume of steam, and the heat equivalent of the internal work (internal latent heat), change rapidly at low pressures and slowly at high pressures. In order to show the application of the discussion in the preceding images a few examples will be solved. Problem (1). How much heat will it take to make 3 pounds of water at 00° F. into wet steam at 150 pounds absolute pressure ? The steam is primed 2 j)er cent. PROPERTIES OF STEAM AXD PERFECT GASES 131 If the wet steam contains 2 per cent moisture there must be 98 per cent dry steam. In solving probleins in steam where use is made of the vakies X, q, r, s, p, A p i', etc., it must be remembered that these vahies are for one pound. It is advisable to work all problems as if the actual weight were one pound and to finally multiply the result by the actual weight. The heat which must be added to a pound of water at 32° in order to make this into wet steam at this pressure is q _|_ 0.98r where q and /• are the values of the heat of the liquid, and the total latent heat at 150 pounds absolute, respectively. The water was originally at 60°. The heat of the liquid of water at 60° must be subtracted from this to give the anu)unt to be added ])er pound. (7 150 lbs. ahs. + 0.98r 150 1,,^ ^,,^ — q goo p,) X S From tile chart and tlie table of heat of the licpiid these values are [330. + (0.98 X 863.0) — 28.1] X 3 = 3443. Problem (2). What volume will the 3 pounds of wet steam occupy ? From the chart it appears tliat the volume of one pound of dry steam at 150 ])ounds absolute pressure is 3.0 cubic feet. The volume of one jiound of mixture or of wet steam is V = 0.98 (3.0 — 0.016) + 0.016 = 2.940 The 3 pounds will occu])y a volume = 3 y = 8.820 cubi(t feet. Problem (3). An engine is supplied with steam at 144 pounds absolute pressure. The steam contains one per cent of moisture. The engine uses 2,800 pounds of steam per hour (all through the cylinders, there being no jackets). 132 THERMAL EFFICIENCY OF AN ENGINE The indicated horse-power is 200. The temj^erature of the exhaust at the condenser is 126° F. The air pump discharges the condensed steam l)ack to the boilers through a primary heater on the exhaust pi])e. The temperature of the feed-water entering the boiler is 100° F. Each pound of coal burned under the l)oilers gives up 14,500 B. t. u., 9,900 of which are taken u]) by the boiler and utilized in making steam. What is the number of pounds of coal per horse-power as indicated ? What is the thermal unit consumption of the engine per horse-power per minute ? _ 2800 \1 144 lbs. abs. + 0. J Jr j_,4 „,j, j,,,^ q jOqo fJ^TT gives the niimber of thermal units supplied l)y the boiler per 1. H. P. Substituting the values from the chart or tallies [326.7 + (0.99 X 865.6) — 68.0] X 14 = 15619. Dividing this by 9900 gives the coal per I. H. P. of the engine alone as 15619 = l.Oo pounds. 9900 ^ In calculating the thermal unit consumption of the engine it is customary to assume that the condensed steam could be returned by the air-pump to the boiler at the same tempera- ture as that of the exhaust steam. The thermal unit consumption per I. H. P. per minute is V*/ 144 His. abs. I ''•'^'''' 144 lbs. abs. 'il260F.) OOO X 60 ~ (326.7 + 857.0 — 94.0)— = 254.26 Problem (4). Suppose that the steam supplied to the engine was of 144 pounds absolute pressure and 400° F. in temperature ; that the steam consumption per hour was CAKXOT EXGIXE 133 2,600 pounds, and that the I. H. P. and other conditions were the same, what would be the B. t. u. per I. H. P. per minute ? ( ") 2600 I X :« u.. + 0.587 (400.0 - 355.29) - a ,,,. ,, j- ^^^-^^ = I 1192.3 + 26.24 — 94.0 I - = 243.65 ( f 60 • The specific, lieat of superheated steam is taken from the preceding table as 0.587. Should the engine be provided with steam jackets the weight of jacket steam per H. P. per minute times the B. t. u. given up })y the condensation of one pound is to be added to the B. t. u. per H. P. per minute through the cylinders. Problem (5). What is the thermal efficiency of the en- gines in (3) and (4) as previously explained? 33000 7(8 = 42.42 B. t. * 42.42 42.42 ^f:_ = 0.1(37 -^^^^ = 0.174 2.54.26 243. (w Carnot engine. It is found in tlie preceding problem that the thermal efficiency of the engines is low. One might be led to think that the steam engine was not as economical as it might be made to be. This is not the case, however. Many of our best engines when compared in thermal unit consumption -wath that of the theoretically perfect engine, working between the same pressures and temperatures, give 70 per cent comparative efficiency. The theoretically perfect engine, called the Carnot engine, is not necessarily one with 100 per cent thermal efficiency, but one in whidi there are no losses from friction, conduc- tion, radiation, etc. It is one in which all the heat supplied is accounted iav by the sum of the heat A^thdrawn, and the lieat transformed into work. Evidently an engine to have 100 per cent thermal effi- ciency must transform all the heat it receives into work, 134 CARXOT EXGINE and have none to throw away oi- be Avithdrawn. It can be shown that the efficiency of such a theoretically perfect en- gine is given by dividing the difference of teniperatui'e worked through in the cycle, by the absolute temperature at wliich heat was supplied to the engine. A Carnot engine working through the same temperature intervals as those given in Problem (3) would have a thermal efficiency : 355.29-126. _ ^ ^81 355.29 + 459.5 Comparing the actual with that of the Carnot : 0.281 The thermal unit consumption per H. P. per minute for this case is witli tlic Carnot engine : ^^=151. 0.281 The B. t. u. consumed per H. P. per minute liy the actual engine and by the theoretical liear the same ratio as that of the thermal efficiencies : ^l^ = o.r,9 254.2() The only correct way to quote the performance of an engine is by its thermal efficiency or by its B. t. u. consump- tion per I. H. P. per minute. The weight of steam per H. P. per hour does not mean anything unless one knows the heat in that steam as sup- plied to the engine and the temperatiu-e and pi-essure of the exhaust. One engine may develop a H. P. on 9 pounds of steam, the steam being highly superheated. Another engine with perhaps a liigher thermal efficiency than the first may use 12 povmds per H. P. NOX-COXDUCTIXG EXGINE 135 If two engines work under exactly the same conditions as to boiler pressure, steam, and vacuiun, then a compari- son may be made of the steam consmnptions per H. P. per hour. In the Carnot engine it is supposed that the same charge of working substance, air, steam, or whatever it may be, is ailternately heated and cooled in the cylinder. The actual engine has a new supply of working substance brought into the cylinder on each power stroke. It would seem better to compare the actual engine with a perfect engine which was sunilaily supplied. By a perfect engine is meant one in wliich there is no friction, no radia- tion, and no absoii)tion or conduction of heat by the cylinder walls ; one in which the expansion drops the pressure down to that of the back pressure. Such an engine is called a non-conducting engine or an engine working on the liankine cycle. Non-conducting engine. The amount of heat which must be added to a pound of feed water at the boiler to make it into a pound of steam of the condition as suppUed to the engine, assuming that the feed water enters the boiler at the temperatiu'e of the engine exliaust, is q^ + x^ i\ — q^ ; where qi is the heat of the liquid, r^ the total latent heat or heat of vaporization at boiler pressiu'e, and Xy is the quality of the steam made by the boiler. If there is one per cent pruning in the steam then Xy = 0.99. If the quaUty of the steam after an adiabatic expansion from cut-off down to the back pressure is a'g the heat to be abstracted during the ex- haust is X2 ^2 where ?*2 is the latent heat of steam at the pressure corresponding to the exhaust. The efficiency of any engine is the dilference lietween the heat supplied and the heat exhausted divided by the heat supphed. In tliis case the efficiency becomes gi+^1^1— g2 — J^2^2 _ i__ ^2 '•2 136 NON-COXDUCTING ENGINE The adiabatic line was discussed in Chapter I, page 14. It was shown that for a reversible line the entropy remained constant. This fact is made use of in calculating x^. /2.3026 1og.^ + ^^)- where T^ is the absolute temperature coi-responding to the temperature of the steam and T^ that of the feed water. The deiivation of the formula will be found under the discussion of the temperature entropy diagram. Problem (6). What would be the thermal efficiency of a non-conducting engine working as in Problem (3) with steam primed one per cent at 144 pounds absolute pressure and with exhaust at 126° F. ? What would be the number of pounds of steam per H. P. per hour ? What would be the B. t. u. consumption per H. P. per minute ? / 355.29+4.59.5 , 0.99X865.(5X^126 + 459.5 a:, = ( 2.o02d log. —-. — , ,.-, . + .,.. ,,,, , ,.,.., I X r-r^ ^ \ ^ 126. +459.5 3.d5.29 + 4o9.5/ 1021 x^ = 0.79 The efficiency =1 ^.nQX102\. _ ^^ ^^ ^ 327.6 + (0.99 X865.S)— 94 ' or 26 per cent. The foot-pounds of work done by the engine per pound of wet steam supplied is 778 {q^ + .i\ )\ — q^, — -f^^'i) '■> this being the difference between the heat supplied and the heat exhausted per pound or the heat per pound transformed into work multiplied by 778. The number of foot-pounds corresponding to a H. P. for one hour is 33,000 X 60. The steam per H. P. per hour is then 33000 X 60 — S 96 778[327.6+(0.99X865.8) — 94— (0.79X1021)] ~ 33000 The B. t. u. consmiiption per H. P. per minute is 778 0.26 = 163.2. The engine in Problem (3) showed an actual efficiency of 0.167. This is ' _ , = 0.64, or 64 per cent of TEMPERATUKE ENTROPY CHART 137 that of the non-conducting engine, and, as previously shown, 59 per cent of that of a Carnot eugme. TEMPERATURE ENTROPY CHART FOR STEAM Under the discussion of entropy it was pointed out that there was no zero of entropy. As all problems involving quantities of heat, internal energy, entropy, etc., deal vnth a change between two conditions, tables or plots of such values may be made above an assmned zero ; then by taking the difference of the readings at the two conditions, each reading being above the assumed zero, the correct change between the two conditions may be obtained. It is custom- ary to take 32° ¥. as the assumed zero. On the plots re}> resenting the })roperties of steam the values of q and \ are so reckoned. The temperatiu'e entiopy chart is similarly constructed. If heat is added to a pound of water at 32° F. the tem- perature of the water rises and the entropy increases. From what has been said. in a preceding chapter it is e\4dent that the increase in the entropy of the liquid between 32° and any high temperature must be foiuid by a sunnnation of a large number of terms. If the sjjecific heat of water be as- sumed as constant and equal to luiity, the smnmation of an infinite number of such terms, each term representing the ratio of an inhnitesimal amount of added heat to the abso- lute temperature at wliich it was added, is given by 2.3026 T log. » where T is the absolute temperature at the upper 491. .5 condition and 491.5 is the value of the absolute zero corre- sponding to 32° F. Referring to the temperature entropy chart it will be seen that entropy is measured to the right and absolute temperatures ai-e measured vertically. If now the entropy of the liquid be figm-ed for a nmnber of temperatui-esj^nd 138 TEMPERATUKE ENTROPY CHART the values so figured are plotted, a line marked liquid line will be obtained. From the plot the entropy of the liquid at any temperature may be read directly : at 697.5° absolute the entropy of the liquid is 0..S5 at 800° " " " " " " '^ 0.49 at 550° " " " " " " " 0.11 To make steam at a given pressure from water at 32° the water is first heated uj) to the temperature corresponding to the pressure by the addition of the heat of the liquid q. The entropy increases by an amount which may be read from the liquid line. Next the heat of vajjorization r is added and the water gradually passes into steam at the same temperature. The increase in entropy due to the addition of the heat of vai)orization is — . If the value of T T be figured for each pressure and laid off to the right of the li(|uid line, the dry steam line is obtained. If instead of vaporizing the entire pound of water, only 80 per cent of it had been vaporized, the heat added at constant tempera- ture would have been 0.80 r and the increase in entropy due O.SO r to vaporization ^^^ or 80 per cent of the value between the liquid line and the dry steam line. The horizontal distance between the li(piid fine and the dry steam line has been divided into 10 parts marked ./' = 0.10, x = 0.20, etc., and these parts each subdivided into 5 additional parts. Illustration. The entropy of a pound of dry steam at 800° absolute temperature is read from the chart as 1.58. The entropy of a pound of dry steam at 550° absolute is 2.02. The entropy of a pound of mixture of steam and water which is 80 per cent steam by weight at 550° absolute is 1.64. Between the liquid line and the dry steam line there are four curves which are used in finding the absolute tempera- ture corresponding to any absolute pressure. TEMPERATURE ENTROPY CHART 139 The absolute temperature of steam at 2 pounds absolute pressure appears to be 587. 5""' at 4 pounds " " " " " 613.° at 10 pounds " " " " " 654.° at 220 poimds '' " " " " 850.° The entropy of a pound of mixture of steam and water at 50 pounds absolute pressure, the mixture being 36 per cent steam by weight, is read on the chart as 0.855. Beyond the dry steam line are lines marked 250 pounds, 200 pounds, 150 pounds, etc., leading upward from the dry steam line. These lines give the entropy of superheated steam. Take for illustration 150 pounds absolute. This line starts from the dry steam line at 818°, the absolute temjiera- ture of saturated steam at this pressure ; as heat is added to the dry steam and the pressure kept constant, the temperature increases and the entropy increases. The temperature in- creases more rapidly than the entropy. As an illustration, the entropy of a pound of steam at 150 pounds absolute })ressure, superheated 100° F., is 1.632. The temperature of saturated steam at 150 pounds is 818° al)solute. The entropy of the liquid at 818° absolute is 0.513. The entropy of a pound of dry steam at 818° is 1.565. The increase in entropy due to the 100° superheat is .067. During a reversible adiabatic expansion the entropy re- mains constant. This plot is a great help in solving for the iinal condition of a mixture after an adiabatic expansion. In Problem (6) on the non-conducting engine, steam at 144 pounds absolute pressure Avith one per cent priming was expanded adiabatically to 126° F. or 585.5° absolute. It was found by a numerical calculation that x.^ = 0.79. This value may be found at once by the chart. Follow along at the temperature level corresponding to 144 pounds until .r = 140 FLOW OP STEAM THROUGH AX ORIFICE 0.99 is reached. The entropy at this point is 1.56. Follow down on enti'opy 1.56 to temperature 585.5 and note the value oi X ; x is found to he 0.79. Problem (7). Steam at 100 pounds alisolute pressure, superheated 125°, expands adiahatieally to 10 pounds pres- siire ahsolute. What per cent is steam at the end of the expansion ? At what pressure is the steam just dry ; that is with no moistui-e and with no superheat ? Follow up on the 100 ])ound superheat line till a point is reached 125° ahove the temperature at which this line starts from the dry steam line. Read the entropy at this upper point as 1.68. Follow down at constant entropy till the dry steam line is reached at a temperature of 725° ahsolute. At this tempera- ture level the pressure is found from the pressure curves to he 38 pounds ahsolute ; continue on entropy line 1.68 down to the temperature corresponding to 10 pounds and note x as 0.93. FLOW OF STEAM THROUGH AN ORIFICE The velocity of steam at lOO to 150 pounds pressure, issuing from an orifice into the air, is from 1,300 to 1,500 feet per second. The weight of steam discharged through an oritice with rounded entrance, having 150 pounds abso- lute pressure on the entrance side, will be the same in amount for any back pressure from 90 jjounds absolute down. At first sight this does not seem reasonable. The pressure drops at what is called the throat or the smallest section of the orifice or nozzle to 0.6 the absolute entrance pressure, provided the back pressure is not over 0.6 of the entrance pressvire. Under these conditions, as the throat pressure and the velocity at the throat are the same, the quantity discharged will remain constant during changes in back pi'essiire from 0.6 of the boiler pressure down to zero. The same is true also for gases. DESIGN OF A TURKIXE NOZZLE 141 Measurement of Dry Steam, by the Flo IV through an Orifice An empirical formula known as Napier's or as Rankine's gives very accurate results. The orifice should have a rounded edge at entrance. W = the weight of steam flowing per second. P^ = the absolute pressure in pounds per square inch on the entrance side. P2 = the absolute pressure in pounds per square inch on the exit side. A = area of the orifice in square inches. Where P^ is e(pial to or greater than | P^ W = A^ 70 Where P^ is less than | P., W = J J ^ —^ :: [ ^ = 0.0292 J (P P. — P.?) ^ As P2 approaches Py more steam goes through the orifice than this formula gives. This second formula is not to he recommended as accu- p., rate within 8 per cent when — - hears the ratio 0.85 or higher. Design of a Tnrhhie Nozzle for Complete Expansion By gi-adually increasing the diameter of a nozzle beyond the throat or smallest section, the velocity of the steam in the nozzle may be increased as the pressure drojxs, till at the end of the nozzle a velocity of from 3,600 to 4,000 feet per second may be realized if the back pressure is low. By complete expansion is meant a drop in pressure in the nozzle from the highest to the lowest pressure ; that is, there is no drop after leaving the nozzle. The method commonly used in calculating a nozzle is 142 DKSKiN OF A TURBINE NOZZLE given ill the following pages, but the derivation of the for- mulae used is omitted. Let the subscript / denote eonditions and values of the liigh pressure steam at entrance to the nozzle ; the subscript / similar conditions at the throat, and the subscript e at exit. H 1^ = y^. + J•^ i\ for saturated steam. Hi = ill "^ '■(• ^~ ^ ';- (degrees of superheat) for superheated steam, //j = y^ + -Pf i\ for saturated steam. Hf = qf + i\ + 6p (degrees superheat) for sui)erlieated steam. He = 'e- The values of .r^ and x^ are read from the temperature en- tropy plot, assuming adiabatic expansion from the condition .'■^.. If the steam is superheated to start with, the chart is used in the same way after locating the starting position. Call V^ the velocity at the throat in feet per second and Vg the velocity at the exit. V, = 224 ^{H-H,) The area of the throat and the exit sections are calculated lluis : The volume of one pound of steam at the throat is y;,=.r,(.sj — 0.016) + 0.016 where Sf is the volume of one pound of dry steam at the throat pressure. Should the steam be superheated at the throat, the volume of a pound would be calculated by the formula given in the earlier part of tliis chapter. Vf X weight per second = area of throat in square feet. In finding V^, 85 per cent of //^ — //^ was used l)ecause a friction loss amounting to 15 per cent of H^ — //^ was as- smued to occur in the nozzle. The friction loss up to the tlii'oat is small and is not considered in this calculation. A small allowance is sometimes ma20 X 60 The steam j^er H. P. hour is 1.4.55 X 3600 -, . nc n = 14.96 lbs. 350 The steam ])er nozzle per second is i:^ = 0.208 ll)s. 7 The vohmie of a pound of mixture at the pressure and the condition at the throat is 0.99 (3.723 - 0.016) + 0.016 = 3.686 cul)ic feet. The volume of a pound at exit is 0.845 X (173.1 - 0.016) + 0.016 = 146.2 cubic feet. The area of the tlu'oat in square feet is 3.686 X 0.20s A -^Q • 1 r * ; or O.oj inches diameter. 1390 The area of the nozzle at exit in scpiare feet is 146.2 X 0.208 -, 00 . , 1- ; or i.oo inches diameter. 3620 CALCULATING THE SIZE OF A STEAM MAIN The indicator when apjjlied to the steam chest as ex- plained in Part II, page 107, sometimes shows that the steam pipe is not large enough to supply the engine. CALCULATING THE SIZE OF A STEAM MAIX 145 If the pipe is furnishing steam to a slow speed engine, and the pipe is not much under the correct size, a drum placed in the steam pipe close to the engine may remedy the trouhle. The volume of this drum should be at least four times the volmne of the cyhnder. If the pipe supplying a high-speed engine is too small, it will have to be changed in order to remedy the trouble. In figuring the size of a steam pipe or steam main it is customary to allow 6,000 feet velocity of the steam per minute if the pipe is short, mth l)ut few elbows. If the pipe is of moderate length, 5,000 feet per minute ; 4,000 is used on long runs where there are many elbows and bends. Knomng the weight of steam to be carried thi-ough the \n\)e ])er minute, and knowing also the loicest ^;re.s.sv^re at which the plant ^^'ill ever work, the volume of the steam can l>e figured. This volume divided by the allowable velocity will give the area of the pipe needed. Example : 300 pounds of steam per minute are to be car- ried through the pipe. The highest ])ressure at which the plant runs is 125 pounds absolute. The lowest, 100 pounds absolute. From the cliart it is found that the volume of one pomid of steam at 100 pounds pressure is 4.4 cubic feet. ^•^ ^ '^^^ = 0.264 sq. ft. = 38.01 sq. in. 5000 ^ ^ This area corresponds to 6.96 inches diameter. For the higher pressure an area of — = 0.216 sq. ft. is needed 5000 ^ If the pipe has this area the velocity of steam through the pipe at the loAver pressure will be f ^ X 5000 = 6100 feet per minute. 146 PERFECT GASES PERFECT GASES The characteristic equation of a perfect gas or the equa- tion giving the relation between the absolute pressure, the volume and the absolute temperature is T T, r. This relation was determined experimentally. The volume of a pound of air at atmospheric pressure and at freezing jDoint has been determined experunentally to be 12.39 cubic feet. That of hydrogen, 178.2 cubic feet. Atmospheric pressure is 14.7 pounds on the square inch, ov 2116.3 pounds on the square foot, equivalent to 29.92 inches of mercury or 760 mm. of mercury. The tempera- ture T is absolute ; as has been stated, this is found by adding 459.5 to the reading of a Fahrenheit thermometer. A few exanqjles will best illustrate how use is to be made of this equation. (1). Wliat will be the volume of one pound of air at 100 pounds absolute pressure and at 139.3° F. ? 14.7 X 12.39 _ ioo X ;; 491. .5 459.5 + 139.3 V = 2.22 cu. ft. (2). What will be the weight of a cubic foot of air at this pressure and temperature ? -=— =0.45 lbs. V 2.22 (3). An air compressor draws in 100 cubic feet of free air per minute at 14.6 pounds pressure (absolute) and at 60° F. The air is compressed to 200 pounds absolute and leaves at 120° F. What is the volume of the air discharged ? ■ 14.6 X 100 _ 200 X U 459.5 + 60 ~ 459.5 + 120 V = 8.14 cu. ft. (4). A balloon of 10.000 cubic feet ca])acity, weighing together with car, sand bags, etc., 550 pounds, has 9,000 PERFECT GASES 147 cubic feet of hydrogen run into it at 80° F. and at 30.2 inches of mercuiy pressure, this being the temperature and the pressure of the surrounding air. Find the weight of gas run in ; the pull on the rope holding the balloon to the gi-ound, and the amount the balloon would have to be light- ened in order for it to reach a height where the barometer reads 20 inches and the temperature is 32° F. ^Hiat would be the pressure of the gas on the inside of the balloon at the upper level, assuming that no gas escapes ? The lifting force is the ditference between the weight of the air displaced by the hydrogen and the weight of hydro- gen run in. Call Vfj the volume of one pound of hydrogen at the ])ressure and temperature at the gi'ound, and J^ ^ that of a })ound of air at the same place. 29.92 X 12.39 491.5 " 30.2 X V^ 539.5 F.1 = 13.45 cu. ft, 29.92 X 17S.2 491.5 ~ 30.2 X ^H 539.5 r,j -= 193.2 cu. ft. 9000 9000 = (]{■/,) — 46 .() = 622.4 lbs. 13.45 193.2 622.4 — 550 = 72.4 pounds pull needed to bold the V)alloon to the groimd. As the balloon rises the hydrogen expands and fills the balloon ; and as the balloon continues to rise, the hydrogen if not allowed to escape would produce a jiressure tending to rupture the balloon. The weight of air displaced by the balloon at the upper level is calculated thus : 29.92 X 12.39 20 X V\ 491.5 491.5 VI 18.52 cu. ft. The 10,000 cid)ic feet of air displaced weigh 10000 roQ - 11 ■ — — = 539.;) lbs. 18.52 148 ISOTHERMAL LIXE As no hydrogen has escaped, according- to the assumption, its weight is 46.6 pounds, as found previously. 539.5 — 46.6 = 492.9 550 — 492.9 = 57.1 Ihs., the weight of sand wliich must be thrown ovit in order to reach this level. The pressure P inside of the balloon at the upper level is 30.2 X 9000 P X 10000 „ ^ . „ . , = ; P = 24.7 inches. 539.5 491.5 The outside air pressure is 20 inches, so the excess pres- sure inside the balloon is 4.7 inches of mercury or 2.35 pounds per square inch approximately. Measureriient of air hy the Jioir through an, orifice : Experiments have shown that the following empirical for- mula gives quite accurate results for orifices up to one inch in diameter. The orifice should ])e made with a rounded entrance, the radius of the cvirve being equal to the diameter of the orifice, and the length of the straight part of the orifice should be equal to the diameter. Whei-e the pressui-e on the entrance side of the orifice is greater than twice the pressure on the exit side : P w = 0.530 ^= « y/T where w is the weight of air per second. P is the absolute pressure on the square inch on the entrance side. T is the absolute temperature of the air on the entrance side, a is the area of the orifice in square inches. Isothermal line. The equation for an isothermal exjian- sion or compression of a perfect gas is Pi^ = P^ 'i;^, or the product of the absokite pressure and the volume is a constant. The work required for an isothermal conqjression, or devel- oped by an isothermal expansion of a gas is Tr= 144 Pj v^ X 2.3026 log. ^ Pi ADIABATIC LIXE 149 where W is in foot-pounds. J^j is the absohite pressure on the square inch at the beginning of compression or at the end of expansion ; i\ is the vohmie in cubic feet at this ])ressm'e. I^^ i^ tlie absolute pressure on the square inch at the end of an isothermal compression or at the beginning of an isothermal expansion. The heat which must be ab- stracted during an isothermal comjiression or added dvu'ing W an isothermal expansion is — . 778 Adlabatic Hue. The equation in terms of pressure and volmiie representing an adiabatic expansion or compression of a perfect gas is p ,. 1.405 ^ p ,, 1.405 X c -^ 1 ' 1 The temperature along an adiabatic change may be cal- culated by combining this equation with the characteristic equation for gases P V P^ v^ T ~ T^ The work done by an adiabatic expansion of a perfect gas or required for an adiabatic conqiression is 0.40.5 L Wv, / J where TT^ is in foot-pounds. -P^ is the absolute pressure on the square inch at the beginning of expansion or at the end or compression ; xi ^ is the vohune at this pressure, -v „ is the volmne after the expansion or at the beginning of compression. The volumes are measured in cubic feet. Tliis value — will always come out less th-an unity. Suppose for illustration — = 0.3. This is to be raised to the ^2 0.405 power. The logarithm of 0.3 is 9.47712 — 10. Write this 999.47712 — 1000 and multiply by 0.405 thus: (999.47712 — 1000) x 0.405 = (404.78823 — 405.) or 9.78823 - 10 The munber corresponding to this log. is 0.G141. 150 COMPRESSING AIR COMPRESSING AIR The niininmin work required to compress air and to de- liver it at the tenijierature of tlie intake would he that needed for an isothermal compression P v^ = P^ v^^ For such a compression heat nuist l)e ahstracted, as has been shown. If no heat was abstracted during compression the com- pression becomes adiabatic and P V i-«^ = P^ y/'-'O-' The ordinary compressor is water jacketed and although attempts are made to get an isothermal com])ression, the actual compression is neither isothermal nor adiabatic, but somewhere between these two lines. For the best com- pressors a line having the equation p ,.1.2 _ p^ ,,^1.2 represents the compression. The compression in the aver- age compressor is more nearly represented by a Une having the equation p ^,l.^ = p „ 1.3 J ( ^ 1 ' 1 The H. P. required at the compression cylinders of a two-stage compressor to compress a certain number of cubic feet of free air (that is, cubic feet of air as taken from the room) per minute, from the pressure at the eml of the suction stroke to the delivery pressure along a line having the equation P v^"^ = a constant, is 144 X 2 X Ps y X 1.3 { /J^a\ 'd_il (t) 33000 X 0.90 X 0.3 ; \p which reduces to 0.0422 7^, r j (^g) - 1 1 = H. COMPRESSIXG AIR 151 where P^ is the ahsolute pressure per s(piare inch at end of the suction stroke, and P^ is the ahsohite dehvery pressure ; and V is the cubic feet of free air. For a tlu'ee-stage comjjressor this fonuula becomes 0.0633 P-r\("\ - 1 = H. P. The air at entrance to a compressor is shghtly rarefied, thus making P^ less than atmospheric pressure, and the vohime displaced by the piston of the compressor has to be gi'eater than the free aii* on this account and also on account of the clearance. The ratio of the volume of free air per minute to the piston displacement is called the displacement efficiency. For the very best com])ressors with mechan- ically operated valves this is approximately 95 per cent. In the expression just given for calculating H. P.. a value of 90 has been used for the displacement efficiency as tliis is more nearly correct for the ordinary compressor. BE A Fig. 58 The water jackets of a compressor are not very efficient in a])stracting the heat of compression. By dividing the (•()m])ression up between two or more cylinders or by com- ])ressing in stages it is possible to cool the air between stages down to its original temperature l)y ])assing it through 152 COMPRESSING AIR inter-coolers placed Ijetvveen the compressor cylinders. This greatly reduces the work of compression as is shown by the illustration, Fig. 58. The vertical line represents the cylinder head. H A rep- resents the entire compression as taking place in one cylinder along a line P o ^'^ = a constant. The dotted line H B rej> resents an isothermal compression. Air compressed along the line H A would shrink in volume from A to B as it cooled to its original temperature at intake. If the com- pression had been divided into two stages with an inter- cooler between the two cylinders the air delivered by the first stage at F would shrink in the inter-cooler to the volume at G before entering the second stage. The compression in the second stage is along a line G E of equation P v ^'^ = a constant, and the air at delivery shrinks from E to B. Evi- dently there has been a saving of work equal to that repre- sented by the area F G E A. Against this saving is to be charged the extra mechanical loss due to the friction of the second cylinder. For a two-stage compression the absolute pressure on the sqiiare inch Pp is equal to \ Pg X P^ the pressures at H and A being absolute. For a three-stage compression the absolute pi'essure at the end of the first stage should be J pi x P ^^^^ ^^ the end of the second stage the pressure should be Jp x P" 5 ^^ pressures P^ and P ^ being absolute. Problem on the compressor. 1,000 cubic feet of free air per minute are compressed to 265.3 pounds gage pressure in a two-stage compressor which is steam driven. The dis- placement efficiency of the compressor is 90 per cent. The pressure in the first cylinder at the end of the suction stroke is 14.0 pounds absolute, or 0.7 pounds below the atmos- phere. The compression is along a line P v ^ ^ = a, constant. Calculate the H. P. needed at the compressor cylinders, and assuming a mechanical efficiency of 85 per cent, what is the PROBABLE HORSE-POWER OF AN ENGINE IHS I. H. P. needed at the steam cylinders ? Wliat should l>e the pressure at the end of the coiupression in the first stage ? K 265.3 + 14.7 \ -1134 ) — ) ~ r = ^^^• 244 ,— — = 287 H. P. for steam cylinders. Absolute pressure 0.85 '' ^ at end of first stage = V^280 X 14 = 62.6 ; or 47.9 pounds gage jjressure. PROBABLE HORSE-POWER OF AN ENGINE The method of finding the number of expansions was explained in Chapter I, at page 11. As far as the power de- veloped by a compound or triple expansion engine is con- cerned, the total number of expansions worked through by the steam might be made in the low pressure cyUnder. By dividing the expansion between two or three cylinders the total cylinder condensation is reduced and a better rotative effect is obtained. The expansion line of an indicator card does not vary nuich from a rectangular hyperlxda having the equation P V = a, constant, and such an equation is commonly as- sumed. The entire cycle of expansions being assumed to take place in the low pressure cylinder, the M. E. P. for the en- tire cycle is figaired for the low, and this M. E. P. multiphed by a constant between 0.7 and 0.9, Avhich makes allowance for the losses in area and in M. E. P. due to the rounding of the card at cut-off and at release, and to the loss due to compression. For a Corliss valve gear these losses are small and the multiplier 0.9 would be used. For a plain slide valve a nniltiplier as low as 0.7 would be used. The exi)ression for M. E. P. is M. E. P. = -i -1- -i X 2.3026 log. n — I\ n n ° 154 PROBABLE HORSE-POWER OF AN ENGINE where Pj is the ahsohite boiler pressure in pounds on the square inch ; P., the back pressure on the square inch in pounds absolute ; and it the number of expansions. One or two examples will show the application of this formula. (1). The steamship Nantucket has cylinders 28" — 45" — 72" X 54" ; makes 94 revolutions per minute ; works against a back pressure of 2 pounds absolute ; and is sup- plied with steam at 140 pounds gage. The cut-off in the High is at .70 stroke. " " " " Int. " " .75 " u a u u Low " " .75 " What is the probable H. P. ? The total number of expan- sions is 72X72 10 Q,,,. X — ^ = 9.440 2S X 28 7 M. E. P. = ^^ + ^-^ X 2.3026 log. 9.446 - 2 9.446 9.446 ^ = 16.377 + 36.777 - 2 = 51.15 Considering the type of valve gear it is probable that a multiplier of 0.77 would be about right. 0.77 X 51.15 = 39.38 as the probable M. E. P. TT -n 3.1416 X 72 X 72 X 39.38 X 94 X 2 X .54 on^n H. P. = ■ = 3950 4 X 33000 X 12 (2). An engine with plain slide valve gear has one high, one intermediate, and two low pressure cylinders ; 20" — 40" -2 (50") X 60" stroke; the engine runs at 80 revs. jDer min. ; boiler pressure 165.3 gage ; back pressure 2 lbs. abs.; as.sume multiplier for gear to be 0.7 ; the cut-off is at ^ stroke in high pressure cylinder. -c, . 2 X .50 X ,50 ^ 2 or Expansions = n = X - = Zo. ^ 20 X 20 1 Actual M. E. P.=0.7(-W+ W X 2.3026 log. 25-2) = 19.86 -pj p _ 3.1416 X 50 X 50 X 2 X 19.86 X 80 X 2 X 60 ^ ^gg^ 4 X 33000 X 12 CHAPTER II METHOD OF CALCULATING FROM THE INDICATOR CARD FROM A STEAM ENGINE, THE PER CENT OF MIX- TURE ACCOUNTED FOR AS STEAM AT CUT-OFF AND AT RELEASE Draw on the indicator card a line at each end of the card perpendicular to the atmospheric Hne. Draw a Una through the point of cut-off as estimated on the card ; also a line just preceding the opening of the exhaust valve as shown on the card, and a line at some point later than the closure of the exhaust valve at compression. The pressures at cut-off', release, and compression are measured above the atmospheric line and the pressure of the atmospliere added. To find the ]jer cent of the stroke at which tliese events occur, a scale having 100 divisions in a length of 4 inches is placed diagonally across the diagram with the zero on the ordinate at one end of the card and the 100 on the ordinate at the other end of the card. The percentage at cut-off, at release, and at compression can be read directly from this scale. A certain amount of steam is brought into the cylinder at each stroke, and the same amount by weight is exhausted per stroke. The weight of steam used per stroke can be found by dividing the total weight of the condensed steam by the total strokes. Call tliis weight of steam per sti'oke through the cylinder M. There is a certain amount of steam in the cylinder at compression. This steam at compression plus the amount brouglit in per stroke gives the total weight present in tlie 155 156 CALCULATING PER CEXT OF MIXTURE cylinder up to cut-off and up to release. This is called the total weight o£ mixture. The weight of steam in the cylinder at compression is found by assuming that the space between the piston and the head of the cylinder, including port passages, is filled with dry steam of the absolute pressure at compression. The weight at compression is equal to the (per cent clearance plus the per cent compression) times the piston displacement and times the weight of a cubic foot of steam at the absolute pressure at compression. (The weight of a cubic foot of steam is the reciprocal of the volume of a pound.) Call this weight at compression 71/q. The weight of mixture in the cylinder ])er stroke is The volume at cut-off is equal to the (})er cent clearance plus the per cent of cut-off) times the piston displacement. Call this Fi. This volume is filled by (M + J/y) pounds of mixture at the absolute j^ressure of steam at cut-off as obtained from the diagram. It has previously been shown (page 127) that the volume of one pound of mixture is V=x (s — 0.016) + 0.016 where x is the per cent steam by weight. Hence Fj, the volume of (M + J/p) pounds, nmst equal Fi = {31 + il/o) X (s — 0.016) + {31 + 3Q 0.016. The volume .s of one pound of steam can be found from tables or from a chart. X, the only unknown term, is obtained by solving this equation. The percentage of the mixture accounted for as steam at release is found in a similar way. The volume V^ is re- placed by Vo, the volume including clearance and the piston displacement up to release. s is taken at the absolute pressure at release. CALCULATING PER CENT OF MIXTURE 157 The percentage of mixture accounted for as steam at release fre(juently is as low as 0.6. The iiidicdtoi' Jiij itself does not show that there is anij water with the steam in the cylinder. If the steam con- sumption of an engine Is figured froTn the indicator card, assuming drij steam at release and drij steam at comjyres- sion, (I result as low as 18 jiouiuls rnaij he obtaiued when the actual consuniption, as measured hij the steam con- densed in the condenser, is as much as SO pounds. CHAPTER III DESIGN OF A PLAIN SLIDE VALVE Valve Setting on a Plain Slide Valve Engine and on a Corliss Engine Cards taken from a steam engine often show defects, which may l)e due to an improper setting of the valve, as shown in Part II, or to a poor design of the valve gear. A thorough knowledge of the plain slide valve may he hest obtained by studying some one of the graphical methods used in designing such valves. The two graphical diagrams most generally used are the Zeuner and the Bilgram. In nearly all stationary engines the cross-head is con- nected to the crank by a connecting rod. This connecting rod is about seven times the length of the crank. In some marine engines the connecting rod is only three and one- half times the length of the crank. It is evident that when the crank turns from 0° to 90° on the forward stroke, the piston moves from the head end center towards the crank end a distance greater than one- half its entire travel. On the return stroke, starting at the crank center, the piston moves through less than half its travel during the first 90° angular motion of the crank. If instead of a connecting rod, a slotted cross-head had been used to connect the cross-liead to the crank pin, then the same angular motion of the crank, from either center, Avould make the same displacement of the cross-head from either end. If the crank rotates with a uniform angular velocity the slotted cross-head is said to move in harmonic motion. The smaller the ratio of the length of the connecting rod to that of the crank the greater is the variation from liar- monic in the displacement of the cross-head. 158 DESIUX OF A PLAIN SLIJJK VALVP: 159 An eccentric and an eccentric rod are equivalent to a crank and a connecting rod ; the length of the crank being the distance f i-om the center of the shaft to the center of the eccentric, called the eccentricity. An eccentric is simply a crank with a crank pin so large that it takes in the shaft. The diameter of the eccentric has nothing to do with the travel given by it ; this depends solely on the eccentricity. The eccentric is generally set from 95° to 110° ahead of the crank. The excess over 90° is called the ungtdar advance. The eccentric rod is so long in proportion to the eccen- tricity of the eccentric that the travel of the valve is not affected ap]jreciahly by the slight angular movement of the eccentric rod and it is customaiy to assume that the valve moves in harmonic motion. Fig. 59 Tn Fiff. 59 the light lines show the crank at the center and the eccentric set ^^'ith an angular advance d. 160 ZEUNKK DIAGRAM If the displacement of the valve is measured from the middle of its travel it is evident that the valve is displaced to the left an amount a o. The maximum displacement to the left will he a b, equal to the eccentricity, and will occur when the crank is at the dotted line or an angle d hefore the 90° point. The maximum displacement of the valve to the right comes at a crank position directly opposite to this dotted line. The valve has no displacements or is in mid position when the crank is at the position shown by the dash lines A at position making an angle d before each dead point. Starting at the crank position a A the valve is in mid position and has no displacement ; as the crank moves in the direction of the arrow the valve is displaced to the left, reaching a maxunmn a h when the crank is at the dotted line ; beyond this crank position the displacements of the valve gi'ow less till at the crank position a B the valve is back in mid position. While the crank is turning from B to A the valye is displaced in a similar manner on the right- hand side of mid position. The displacement of the valve for the ])osition shown by the heavy line is a f. The following graphical solution, known as the Zcitner Diagram, will give the disjilacement of the valve for any crank angle. The actual position of the crank and eccentric when the engine is on one dead center is shown by the full lines. In this graphical solution the angle d is laid off back of the 90° Une, and on this line two circles are drawn, each circle be- ing made of a diameter equal to the eccentricity of the eccentric. The displacement of the valve from mid position for any crank angle is equal to the chord cut from either of these circles which the crank position may intersect. For example, at the crank position O 8, shown by the dotted line, the dis- ZEUNER DIAGEAIVI 161 placement of the valve is O S to the left pf the mid position. The maximum displacement comes at a crank angle Avhen the chord cut is of maximum length or at angle d before each of the 90° points. The valve has no displacement or is in mid position when there is no chord cut, or at the crank position O INI making an angle d before each of the dead points. These positions agree with those as found in the previous discussion. M, d^^d- 'U\ Fig. 60 Starting at a crank position M (360° — d) the valve moves from mid position to the left, reaching a maximmn distance to the left at a crank angle (90° — d) ; the displace- ments gradually grow less as the valve comes back to mid position, which is reached again when the crank is at O M 162 ZEUNER DIAGRAM (180° — d). From this point on, the valve is similarly displaced to the right of its mid position. A section through a plain shde valve and its seat is given below. It is seen that when the valve is in mid jjosition, or in the center of its travel, the outer edge of each end of the valve overlaps the outer edges of the ports. This overlap is called the outside lap. It may or may not he the same on the two ends of the valve. The outer edges of the valve govern the admission of steam and the cut-oif of steam. The inner edges of the valve overlap the inner edges of the port in the same way. This distance is called the inside lap. The inside edge of the valve governs the release of steam and compression of steam. Fig. 61 Considering now tlie Zeuner diagram and the valve. When the crank is at the position O M (360° — d) the valve is in mid position, as shown in Fig. 61. As the crank reaches the position O A the valve is displaced to the left a distance O E. The arc O E is drawn with a radius equal to the outside lap on the right-hand end of the valve. At this crank position the outer edge of the valve is on the outer edge of the port and admission of steam is ahout to begin ; see Part I, Chapter I, page 6. When the crank gets to the dead point, the displacement of the valve is greater than the outside lap by an amount /, which is called the lead. This lead varies from 0.01 of an inch to 0.38 of an inch in different engines. ZEUNER DIAGRAM 163 When the crank gets to an angle (90° — (/) the valve is displaced its maximum amount to the left ; the outer edge of the valve is now to the left of the outer edge of the port by a distance equal to the eccentricity minus the outside lap. The valve then begins to move back to its mid position and at a crank angle O C the outer edge of the valve is on the outer edge of the port, since the displacement is equal to O E, the outside lap, and cut-oflE occurs. It is seen that the displacement of the valve is the same at cut-off and at admission ; at admission the displacements are increasing and at cut-off decreasing. After cut-off, the steam in the cylinder expands as the valve moves to mid position at the crank angle O M = (180° — d) and then.to the right of the mid position till the crank angle O R is reached. At the crank angle O R the valve is displaced to the right of the mid position a distance O Y, which is equal to the in- side lap on the right-hand end of the valve. {Note. This is drawn out of proportion on the diagram in order to avoid confusion.) The inner edge of the valve is now on the inner edge of the port and steam is al)out to escape from the cylinder over the bridge into the exhaust port. This is re- lease. Steam is exhausted from the cylinder from the crank ])osition O R to the crank jjosition O K when the inner Lulge of the valve is again on the inner edge of the port, giving compression. The dis])lacement of the valve at release and at compres- sion is the same in amount ; the displacements at release are increasing and those at com])ression decreasing. Consider now the left-hand end of the valve, which con- trols the distribution of steam to the left-hand end of the cylinder. P>vidently the valve must be displaced to the right for ad- mission and cut-off and this dis])la('ement must be equal in amount to the outside lap. The ai-c o z is drawn with a ladius 164 ZKUXKR DIAGRAM equal to this outside lap. Admission conies at the dead point. There is then no lead. Cut-off comes at o c. Release and compression occur when the valve is dis- placed to the left o£ the mid position an amount o m (drawn out of proportion) equal to the inside lap. This brings release at o r and compression at o h. If the angular advance of the eccentric is decreased, or the angle d made less, admission, cut-off, release, and com- pression all come later in the stroke, as was shown by Figs. 27 and 28, Part II, page 103. If the angular advance is increased, or the angle d made larger, all the events come sooner, each event moving ahead through the same crank angle. The effect on the laps, both inside and outside, of a change in the length of the valve spindle, was pointed out in Part II, at page 104. The diagram makes it possible to trace out the effect of all such changes. Sujjpose it is desired to increase the power of the engine. The cut-off may be lengthened by decreasing the outside lap and the release delayed by increasing the inside lap. De- creasing the outside lap would make admission come sooner and increasing the inside lap would make compression come earher. To prevent these from coming abnormally early, the angular advance of the eccentric should be decreased. If the outside lap and the inside lap are made zero, so that the length of each foot of the valve is just equal to the width of the steam port, compression and admission will come at the crank position M and cut-off and release will come at the crank position O INI opposite. If the inside laps O M and O Y are reduced, the release comes sooner and the comjoression later. If these are made zero, release and compression come 180° apart at O M and O M. If it is desired to make the compression come still later, the inner edge of the valve niay be cut back from the inner edge of the port, making a clearance. Evidently, LAYIXG OUT A PLAIN SLIDE VALVE 165 when a valve has a clearance on its inner edge, to bring this edge to the inner edge of the port the valve must he dis- placed to the same side of the mid position that it was for cut-off. Tliis means that the arc drawn on the Zeuner dia- gram to represent the inside clearance would he on the same side as that for the outside lap. To lay oat the seat for a value : The width of the steam ports can he figured by assuming a velocity of steam as 100 feet per second, and the length of the port as about 0.8 the diameter of the cylinder. Begin at the end of the valve which has the smaller out- side lap. Starting at the outer edge of the port, measure oft' the outside lap. This outer edge of the valve will move to the right and to the left a distance in each direction equal to the eccentricity. To allow the valve to over-travel its seat, the seat is de- pressed from a point about ^ inch inside of the extreme travel out to the ends of the chest. The travel of the valve in the other direction brings the outer edge over onto the bridge. The inner edge of the bridge should be about -} inch beyond this j)oint. The inner edge of the bridge being now determined, and the width of the steam port having been figured, the width of the Inidge itself is known. To find the width of the exhaust ^jort : Lay off the greater inside lap from the inner edge of the port onto the bridge. It may happen that the greater inside lap does not come on this end of the valve. The correct lap may be put on later after the width of the exhaust port is found. Measure from this lap towards the centei- of the chest a distance equal to the eccentricity, then add the width of the steam, port ; from this point, which is the inside edge of the bridge of the other end, lay off the bridge and then the steam port. Now lay out the laps. 166 SETTING A PLAIN SLIDE VALVE SETTING A PLAIN SLIDE VALVE A plain slide valve is almost always set for equal lead. Tlie amount of lead and the direction of motion of the en- gine depend upon the position of the eccentric. The equality of the lead dej)ends solely upon the length of the valve spindle. Put the engine on a dead center. Remove steam chest cover. Loosen the set screws holding eccentric to shaft. Turn the eccentric till the steam port on one end is open its maximum amount. Caliper this distance from the outer edge of the port to outer edge of the valve. Now turn the eccentric until the maximum port opening on the other end is reached. Caliper this distance. Lengthen or shorten the valve spindle one-half the difference between these two measurements as taken hy the cali])ei'S, lengthening if the head end o])ening was the greater and shortening if the crank end was the greater. Turn the eccentric in the direction in which the engine is to, run. As the engine is on the center the valve should move so as to open the port on that end of the cylinder and when the port has opened an amount corresponding to the lead desired, the eccentric should he set. By setting a valve hy this method it makes no difference whether or not there are bell crank levers or rockers be- tween the eccentric and the valve. SETTING CORLISS VALVES The valves of a Corliss engine may be set quickest by the use of the indicator. If there is reason to suspect that the valve gear is very badly derangefl, it might be well to see that_ the eccentric has a small angular advance and that the wrist plate swings through ecjual angles either side of the vertical. Sliould these angles be unequal, the length of the eccentric rod may be changed till e(|uality is secured. SETTING A CORLISS VALVE GEAR 167 The engine is now started up and a set of cards taken. The release and conijjression are adjusted by lengthening or shortening the hnks between the wrist plate and the ex- haust valves. Lengthening the link increases the exhaust lap and delays release and hastens compression ; shortening it hastens release antl delays compression. The cut-ott' is adjusted last. This is done by varying the length of the rods from the governor to the knock-off tappets and may be done while the engine is running. After setting the cut-off the engine should be tested with the governor pushed up against the top collar to see if the tappets keep the claws from engaging, and tested also with the governor at its lowest position, not resting on the starting block, to see if the safety tappets prevent the claws from catching. EXPLANATION OF LOGARITHMS AND HOW TO USE THEM The common logarithm of a numher represents the power to wliich 10 must he raised to equal the mimher. Thus the log. 100 = 2 hecause 10 must he raised to the second jiower to equal 100. The log. 1000 = 3. The log. 10 = 1. The log. 1 = 0. Evidently the logaritlmi of a numher hetween 1 and 10 will he hetween and 1 ; lietween 10 and 100 will he hetween 1 and 2 ; hetween 100 and 1000 hetween 2 and 3. The logarithm of a numher less than 1 will he con- sidered later. It is known that (r X (c^ = a^ and that a'' -f- ((^ = (r. If log. 3 = .4771 and log. 5 = .6990 then lO-*"' = 3 and 10-6990 = 5. 5X3= 10*=^°° X 10-^'" = lO-«»''" + -'"i = lOi-i'''' 5 -=- 3 = lO''''^"'^ lO'*"^ = 10-«»^- ""1 = l0-22i9 To multiply two numliers, add their logarithms and this sum is the logarithm of the product ; to divide one numher hy another, suhtract the logarithms of the numbers, and the result is the logaritlun of the answer. Example : Multiply 5 X 4 X 20 X 3 ; log. 5 = .6990 log. 4 = .6021 log. 20 = 1.3010 log. 3 = .4771 3.0792 The numher corresponding to this logarithm is 1200. The part of the logarithm to the left of the decimal point is called the mantissa. The value of the mantissa deter- 16S EXPLANATIOJq^ OF LOGARITHMS 169 mines the location of the decimal point in the answer. Thus log. 5 = .6990 log. 50 = 1.6990 log. 500 = 2.6990 log. 5000 = 3.6990 It is seen that the mantissa is one unit less than the num- ber of figures to the left of the decimal point. The part of the logaritlun to the right of the decimal point is the same for the same figures irrespective of the location of the decimal point in the number. Logarithm of a Ninnher Less Than 1. log. 0.5 = log. Jq = log. 5 - log. 10 = .6990 — 1 = 9.6990 — 10 log. 0.05 = log. y|^ = log. 5 — log. 100 = .6990 — 2 = 8.6990 - 10 log. 0.005 = log. yJg = log- ^ - log- 1000 = .6990 — 3 = 7.6990 - 10 It is seen that the logarithm is followed by — 10 and that the mantissa is 9 if the left-hand figure of the number is in the first decimal place, 8 if in the second, 7 if in the tliird, etc. _ , 332. X 4.13 X (i9.5 X 0.95 X 0.00075 njne . 930 log. 332 = 2.5211 log- 4.13 = .6160 log. 69.5 = 1.8420 • log. 0.95 = 9.9777- -10 log. 0.00075 = 6.8751 - -10 21.8319 - -20 log. 930 = 2.9685 18.8634 - ■20 170 EXPLANATION OF LOGARITHMS The niimlier corresponding to .8634 is 730; 18 — 20 is the same as 8 — 10 ; this indicates that the left-hand figure is in the second decimal place, or 0.0730 = Ans. To raise a numher to any power, multiply the log. of the number by the exjjonent of the power and the result is the log. of the answer. Examples : (15)^ log. 15 = 1.1761 2 log. Ans. = 2.3522 Ans. = 225. (1.83)3 log. 1.83 = .2625 3 log. Ayis. = .7875 A71S. = 6.13 log. 1.83 = .2625 ; multiply by ^ or divide by 4, log. Ans. = .0656 loff. 1.16 = .0645 11 In the table of proportional parts, on page 172, at the right of this line in which .0645 is found, 11 corresponds to 3, so the next figure is 3 and the answer is 1.163. V0X)0373= (0.00373)^ log. 0.00373 = 7.5717 — 10 tliis may be written 47.5717 — 50 ; divide by 5 ; log. Ans. = 9.5143 — 10 ; A71S. = 0.3268 TABLES 172 TABLES LOGARITHMS o Proportional Parts 1 3 3 4 5 6 7 8 9 re 1 3 3 4 5 6 7 8 9 10 0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 4 8 12 17 21 25 29 33 37 11 04140453 0492] 05 31 0569 0607 (1645 0682 0719 0755 4 8 11 IS 19 23 26 30 34 13 0792,0828 0864 0899 0934!u969 1004 1038 1072 1106 3 7 10 14 17 21 24 28 31 13 1139:1173 1206! 1239 1271 1303 1335 1367 1399 1430 3 6 10 13 16 19 23 26 29 14 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 3 6 9 12 15 18 21 24 27 15 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 3 6 8 11 14 17 20 22 2S 16 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 3 5 8 11 13 16 18 21 24 17 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 2 5 7 10 12 15 17 20 22 18 2553 2577 2601 2625 2648 2672 2695 2718 2742 2765 2 5 7 9 12 14 16 19 21 19 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 2 4 7 9 11 13 16 18 20 20 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 2 4 6 8 11 13 IS 17 19 31 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 2 4 6 8 10 12 14 16 18 33 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 2 4 6 8 10 12 14 15 17 33 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 2 4 6 7 9 11 13 15 17 34 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 2 4 5 7 9 11 12 14 16 25 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 2 3 S 7 9 10 12 14 15 36 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 2 3 S 7 8 10 11 13 IS 37 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 3 5 6 8 9 11 13 14 38 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 3 5 6 8 9 11 12 14 39 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 3 4 6 7 9 10 12 13 30 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 3 4 6 7 9 10 11 13 31 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 3 4 6 7 8 10 11 12 33 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 3 4 S 7 8 9 11 12 33 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 3 4 5 6 8 9 10 12 34 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 3 4 5 6 8 9 10 11 35 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 2 4 5 6 7 9 10 11 36 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 2 4 S 6 7 8 10 11 37 5682 5694 5705 5717 5729 5740'5752|5763 5775 5786 2 3 S 6 7 8 9 10 38 5798 5809 5821 5S32 5843 5855 5866 5877 5888 5899 2 3 5 6 7 8 9 10 39 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 2 3 4 S 7 8 9 10 40 6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 2 3 4 5 6 8 9 10 41 6128 6138 6149 6160 6170 6180 6191 '6201 6212 6222 2 3 4 5 6 7 8 9 43 6232 6243 6253;6263 6274 6284 6294 '6304 6314 6325 2 3 4 5 6 7 8 9 43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 2 3 4 5 6 7 8 9 44 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 2 3 4 5 6 7 8 9 45 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 2 3 4 5 6 7 8 9 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 2 3 4 5 6 7 7 8 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 2 3 4 5 5 6 7 8 48 6812:6821 6830 6839 6848 6857 6866'6875 6884 6893 2 3 4 4 5 6 7 8 49 6902 6911 6920 6928 6937 6946 6955^6964 6972 6981 2 3 4 4 5 6 7 8 50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 2 3 3 4 S 6 7 8 51 7076 7084 7093 7101 7110 71187126 7135 7143 7152 2 3 3 4 S 6 7 8 53 7160 716S7177|71S5:7193 72027210 7218 7226 7235 2 2 3 4 5 6 7 7 53 7243 725117259 7267'7275 728417292 7300!7308:7316 2 2 ^^ 4 5 6 6 7 54 7324 7332|7340j734Sl7356:7364|7372|7380l73S8|7396 2 2 3 4 5 6 6 7 TABLES 173 LOGARITHMS o Proportional Parts 1 2 3 4 5 6 7 8 9 2; 1 3 3 4 5 6 7 8 9 55 7404 j 7412 7419 742717435 7443 7451 1 1 7459 7466 7474 2 2 3 4 5 5 6 7 66 7482 7490 7497l75057513!7520!7528'7536i7543|7S51 2 2 3 4 S 5 6 7 57 7559,7566 75747582 75897597,7604 76127619;7627 2 2 3 4 S 5 6 7 58 7634 7642,76497657 76647672 76797686,7694:7701 2 3 4 4 5 6 7 59 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 2 3 4 4 5 6 7 60 7782 7789 7796 7803 ' 7810 7818 7825 7832 7839 7846 2 3 4 4 5 6 6 61 7853 786017868 7875 7882 7889 7896 7903 79107917 2 3 4 4 5 6 6 63 ,7924 7931 7938 7945 7952 7959 7966 7973 79807987 2 3 3 4 5 6 6 63 7993 8000 8007:8014 80218028 8035 8041 S048'8055 2 3 3 4 5 S 6 64 8062,8069,8075 8082 8089 8096 8102 8109 8116 8122 2 3 3 4 5 s 6 65 8129 813618142 8149 8156'8162 8169 8176 8182 8189 2 3 3 4 5 5 6 66 8195!S202 8209 8215 S222i8228 8235 8241 8248 8254 2 3 3 4 5 5 6 67 8261; 8267 8274 8280 8287IS293 8299 8306 8312 8319 2 3 3 4 5 5 6 68 8325 S3^l!833S 8344 8351,8357 8363 8370 8376 8382 2 3 3 4 4 5 6 69 8388 8395 8401 8407 1 84 14 8420 8426 8432 8439 8445 2 2 3 4 4 5 6 70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 2 2 3 4 4 5 6 71 8513 8519 8525 8531:8537 8543 8549 8555 8561 8567 2 2 3 4 4 5 5 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 2 2 3 4 4 5 5 73 8633 '8639 8645 8651 865718663 8669 8675 8681 8686 2 2 3 4 4 5 5 74 8692 j 8698 8704 8710 8716 8722 8727 8733 8739 8745 2 2 3 4 4 5 5 75" 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 2 2 3 3 4 5 5 76 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 2 2 3 3 4 5 5 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 2 2 3 3 4 4 5 78 8921 8927 8932)8938 8943 8949 8954 8960 8965 8971 2 2 3 3 4 4 5 79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 2 2 3 3 4 4 5 80 9031 9036 9042,9047 9053 9058 9063 9069 9074 9079 2 2 3 3 4 4 5 81 908519090 9096 91019106 9112 9117 9122 9128 9133 2 2 3 3 4 4 5 83 9138|9143 9149 9154 5159 9165 9170 9175 9180 9186 2 2 3 3 4 4 5 83 919l'9196 9201 9206 9212 9217 92229227 9232 9238 2 2 3 3 4 4 5 84 9243 9248,9253 9258 9263,9269 9274;9279 9284 9289 2 2 3 3 4 4 5 85 9294 9299 93049309 9315 9320 9325 '9330 9335 9340 1 2 2 3 3 4 4 5 86 9345 9350 9355 9360:9365 9370,9375 93So'9385 9390 1 2 2 3 3 4 4 5 87 !9395i9400j9405 9410'9415i9420l942S 9430,9435 94401 2 2 3 3 4 4 88 9445 9450,9455 9460 946519469 9474 9479,9484 9489: 2 2 3 3 4 4 89 9494,949919504,9509 9513 1 1 i 1 9518 9523 9528 9533 9538 2 2 3 3 4 4 90 9542 9547 9552 9557 9562 9566 95719576 9581 9586 2 2 3 3 4 4 91 9590 9595 9600 9605 9609 9614 9619(9624 9628 9633 2 2 3 3 4 4 93 i963S 964319647 9652 9657 9661,9666 9671i9675i9680i 2 2 3 3 4 4 93 9685 9689 9694 9699 9703]9708,9713 971719722 9727 1 2 2 3 3 4 4 94 97319736|9741 9745 9750 975419759 9763,9768 9773: 2 2 3 3 4 4 95 9777 9782 9786 9791 9795 9800 9805 ]9809 9814 9818 2 2 3 3 4 4 96 9823 9827 9832 9836 9841 9845 985019854 9859 98631 2 2 3 3 4 4 97 9868; 9872 19877 988119886 9890 1 9894 98*?l<5903 9908 2 2 3 3 4 4 98 '9912i9917l9921 9926:9930 9934 9939 9943 9948 9952 2 2 3 3 4 4 99 ,9956 9961,9965 9969 9974 9978 9983,9987 9991 9996 2 2 3 3 3 4 174 TABLES AREAS AND CIRCUMFERENCES OF CIRCLES ADVANCING BY EIGHTHS Diam. Area. Circum. Diam. Area. Circum. 7.4613 Diam. Area. Circum. 1-64 .00019 .04909 a 3-8 4.4301 6. 28.274 18.850 1-32 .00077 .09818 7-16 4.6664 7.6576 1-8 29.465 19.242 3-64 .00173 .14726 1-2 4.9087 7.8540 1-4 30.680 19.635 1-16 .00307 .19635 9-16 5.1572 8.0503 3-8 31.919 20.028 3-32 .00690 .29452 5-8 5.4119 8.2467 1-2 33.183 20.420 1-8 .01227 .39270 11-16 5.6727 8.4430 5-8 34.472 20.813 5-32 .01917 .49087 3-4 5.9396 8.6394 3-4 35.785 21.206 3-16 .02761 .58905 13-16 6.2126 8.8357 7-8 37.122 21.598 7-32 .03758 .68722 7-8 6.4918 9.0321 7. 38.485 21.991 15-16 6.7771 9.2284 1-8 39.871 22.384 1-4 .04909 .78540 3. 7.0686 9.4248 1-4 41.282 22.776 9-32 .06213 .88357 .98175 1-16 7.3662 9.6211 3-8 42.718 23.169 5-16 .07670 1-8 7.6699 9.8175 1-2 44.179 23.562 11-32 .09281 .11045 1.0799 1.1781 3-16 7.9798 10.014 5-8 45.664 23.955 3-8 1-4 8.2958 10.210 3-4 47.173 24.347 13-32 7-16 15-32 1-2 17-32 .12962 .15033 .17257 .19635 .22166 1.2763 1.3744 1.4726 1.5708 1.6690 5-16 3-8 7-16 1-2 9-16 5-8 11-16 3-4 13-16 7-8 15-16 4. 8.6179 8.9462 9.2806 9.6211 9.9678 10.321 10.680 11.045 11.416 11.793 12.177 12.566 10.407 10.603 10.799 10.996 11.192 11.388 11.585 11.781 11.977 12.174 12.370 12.566 7-8 8. 1-8 1-4 3-8 48.707 50.265 51.849 53.456 55.088 24.740 25.133 25.525 25.918 26.311 9-16 19-32 .24850 .27688 1.7671 1.S653 1-2 5-8- 56.745 58.426 26.704 27.096 5-8 21-32 11-16 23-32 .30680 .33824 .37122 .40574 1.9635 2.0617 2.1598 2.2580 3-4 7-8 9. 1-8 60.132 61.862 63.617 65.397 27.489 27.882 28.274 28.667 3-4 .44179 2.3562 1-16 12.962 12.763 1-4 67.201 29.060 25-32 .47937 2.4544 1-8 13.364 12.959 3-8 69.029 29.452 13-16 .51849 2.5525 3-16 13.772 13.155 1-2 70.882 29.845 27-32 .55914 2.6507 1-4 14.186 13.352 5-8 72.760 30.2.S8 7-8 .60132 2.7489 5-16 14.607 13.548 3-4 74.662 30.631 29-32 .64504 2.8471 3-8 15.033 13.744 7-8 76.589 31.023 15-16 .69029 2.9452 7-16 15.466 13.941 10. 78.540 31.416 31-32 .73708 3.0434 1-2 15.904 14.137 1-8 80.516 31.809 9-16 16.349 14.334 1-4 82.516 32.201 1. .7854 3.1416 5-8 16.800 14.530 3-8 84.541 32.594 1-16 .8866 3.3379 11-16 17.257 14.726 1-2 86.590 32.987 1-8 .9940 3.5343 3-4 17.721 14.923 5-8 88.664 33.379 3-16 1.1075 3.7306 13-16 18.190 15.119 3-4 90.763 33.772 1-4 1.2272 • 3.9270 7-8 18.665 15.315 7-8 92.886 34-165 5-16 1.3530 4.1233 15-16 19.147 15.512 3-8 1.4849 4.3197 11. 95.033 34.558 7-16 1.6230 4.5160 5, 19.635 15.708 1-8 97.205 34.950 1-2 1.7671 4.7124 1-16 20.129 15.904 1-4 99.402 35.343 9-16 1.9175 4.9087 1-8 20.629 16.101 3-8 101.62 35.736 5-8 2.0739 5.1051 3-16 21.135 16.297 1-2 103.87 36.128 11-16 2.2365 5.3014 1-4 21.648 16.493 5-8 106.14 36.521 3-4 2.4053 5.4978 5-16 22.166 16.690 3-4 108.43 36.914 13-16 7-8 15-16 2.5802 2.7612 2.9483 5.6941 5.8905 6.0868 3-8 7-16 1-2 9-16 22.691 23.221 23.758 24.301 16.886 17.082 17.279 17.475 7-8 12. 1-8 110.75 113.10 115.47 37.306 37.699 38.092 2. 3.1416 6.2832 5-8 24.850 17.671 1-4 117.86 38.485 1-16 3.3410 6.4795 11-16 25.406 17.S68 3-8 120.28 38.877 1-8 3.5466 6.6759 3-4 25.967 18.064 1-2 122.72 39.270 3-16 3.7583 6.8722 13-16 26.535 18.261 5-8 125.19 39.663 1-4 3.9761 7.0686 7-8 27.109 18.457 3-4 127.68 40.055 5-16 4.2000 7.2649 15-16 1 27.688 18.653 7-8 130.19 40.448 •TAHLES 175 AREAS AND CIRCUMFERENCES OF CIRCLES For Diameters from ,^^ to 99, advancing by Tenths Diam. Area. Circum. Diam. Area. Circum. Diam. Area. Circum. 0.0 .1 .2 .3 .4 .007854 .031416 .070686 .12566 ■ .31416 .62832 .94248 1.2566 5.0 .1 .2 .3 .4 19.6350 20.4282 21.2372 22.0618 22.9022 15.7080 16.0221 16.3363 16.6504 16.9646 10.0 .1 .2 .3 .4 78.5398 80.1185 81.7128 83.3229 84.9487 31.4159 31.7301 32.0442 32.3584 32.6726 .5 .6 .7 .8 .9 .19635 .28274 .38485 .50266 .63617 1.5708 1.8850 2.1991 2.5133 2.8274 .5 .6 .7 .8 .9 23.7583 24.6301 25.5176 26.4208 27.3397 17.2788 17.5929 17.9071 18.2212 18.5354 .5 .6 .7 .8 .9 86.5901 88.2473 89.9202 91.6088 93.3132 32.9867 33.3009 33.6150 33.9292 34.2434 1.0 .1 .2 .3 A .7854 .9503 1.1310 1.3273 1.5394 3.1416 3.4558 3.7699 4.0841 4.3982 6.0 .1 .2 .3 .4 28.2743 29.2247 30.1907 31.1725 32.1699 18.8496 19.1637 19.4779 19.7920 20.1062 11.0 .1 .2 .3 .4 95.0332 96.7689 98.5203 100.2875 102.0703 34.5575 34.8717 35.1858 35.5000 35.8142 .5 .6 .7 .8 .9 1.7671 2.0106 2.2698 2.5447 2.8353 4.7124 5.0265 5.3407 5.6549 5.9690 .5 .6 .7 .8 .9 33.1831 34.2119 35.2565 36.3168 37.3928 20.4204 20.7345 21.0487 21.3628 21.6770 .5 .6 .7 .8 .9 103.8689 105.6832 107.5132 109.3588 111.2202 36.1283 36.4425 36.7566 37.0708 37.3850 2.0 .1 .2 !3 .4 3.1416 3.4636 3.8013 4.1548 4.5239 6.2832 6.5973 6.9115 7.2257 7.5398 7.0 .1 .2 .3 .4 38.4845 39.5919 40.7150 41.8539 43.0084 21.9911 22.3053 22.6195 22.93.% 23.2478 12.0 .1 .2 .3 .4 113.0973 114.9901 116.8987 118.8229 120.7628 37.6991 38.0133 38.3274 38.6416 38.9557 .5 .6 .7 .8 .9 4.9087 5.3093 5.7256 6.1575 6.6052 7.8540 8.1681 8.4823 8.7965 9.1106 .5 ,6 .7 .8 .9 44.1786 45.3646 46.5663 47.7836 49.0167 23.5619 23.8761 24.1903 24.5044 24.8186 .5 .6 .7 .8 .9 122.7185 124.6898 126.6769 128.6796 130.6981 39.2699 39.5841 39.8982 40.2124 40.5265 3.0 .1 .2 .3 .4 7.0686 7.5477 8.0425 8.5530 9.0792 9.4248 9.7389 10.0531 10.3673 10.6814 8.0 .1 .2 .3 .4 50.2655 51.5300 52.8102 54.1061 55.4177 25.1327 25.4469 25.7611 26.0752 26.3894 13.0 .1 .2 .3 .4 132.7323 134.7822 136.8478 138.9291 141.0261 40.8407 41.1549 41.4690 41.7832 42.0973 .5 .6 .7 .8 .9 9.6211 10.1788 10.7521 11.3411 11.9459 10.9956 11.3097 11.6239 11.9381 12.2522 .5 .6 .7 .8 .9 56.7450 58.0880 59.4468 60.8212 62.2114 26.7035 27.0177 27.3319 27.6460 27.9602 .5 .6 .7 .8 .9 143.1388 145.2672 147.4114 149.5712 151.7468 42.4115 42.7257 42.0398 43.3540 43.6681 4.0 .1 .2 .3 .4 12.5664 13.2025 13.8544 14.5220 15.2053 12.5664 12.8805 13.1947 13.5088 13.8230 9.0 .1 .2 .3 .4 63.6173 65.0388 66.4761 67.9291 69.3978 28.2743 28.5885 28.9027 29.2168 29.5310 14.0 .1 .2 .3 .4 153.9380 156.1450 158.3677 160.6061 162.8602 43.9823 44.2965 44.6106 44.9248 45.2389 .5 .6 .7 .8 .9 15.9043 16.6190 17.3494 18.0956 18.8574 14.1372 14.4513 14.7655 15.0796 15.3938 .5 .6 .7 .8 .9 70.8822 72.3823 73.8981 75.4296 76.9769 29.8451 30.1593 30.4734 30.7876 31.1018 .5 .6 .7 .8 .9 165.1.W0 167.4155 169.7167 172.0336 174.3662 45.5531 45.8673 46.1814 46.4956 46.8097 176 TABLES AREAS AND CIRCUMFERENCES OF CIRCLES For Diameters from Jg to 99, advancing by Tentlis Diam. Area. Circum. Diam. Area. Circum. Diam. Area. Circum. 15.0 .1 .2 .3 .4 176.7146 179.0786 181.4584 183.8539 186.2650 47.1239 47.4380 47.7522 48.0664 48.3805 20.0 .1 .2 .3 .4 314.1593 317.3087 320.4739 323.6547 326.8513 62.8319 63.1460 63.4602 63.7743 64.0885 25.0 .1 .2 .3 .4 490.8739 494.8087 498.7592 502.7255 506.7075 78.5398 78.8540 79.1681 79.4823 79.7965 .5 .6 .7 .8 .9 188.6919 191.1345 193.5928 196.0668 198.5565 48.6947 49.0088 49.3230 49.6372 49.9513 .5 .6 .7 .8 .9 330.0636 333.3916 336.5353 339.7947 343.0698 64.4026 64.7168 65.0310 65.3451 65.6593 .5 .6 .7 .8 .9 510.7052 514.7185 518.7476 522.7924 526.8529 80.1106 80.4248 80.7389 81.0531 81.3672 16.0 .1 .2 .3 .4 201.0619 203.5831 206.1199 208.6724 211.2407 50.2655 50.5796 50.8938 51.2080 51.5221 21.0 .1 .2 .3 .4 346.3606 349.6671 352.9894 356.3273 359.6809 65.9734 66.2876 66.6018 66.9159 67.2301 26.0 .1 .2 .3 .4 530.9292 535.0211 539.1287 543.2521 547.3911 81.6814 81.9956 82.3097 82.6239 82.9380 .5 .6 .7 .8 .9 213.8246 216.4243 219.0397 221.6708 224.3176 51.8363 52.1504 52.4646 52.7788 53.0929 .5 .6 .7 .8 .9 363.0503 366.4354 369.8361 373.2526 376.6848 67.5442 67.8584 68.1726 68.4867 68.8009 .5 .6 .7 .8 .9 551.5459 555.7163 559.9025 564.1044 568.3220 83.2522 83.5664 S3. 8805 84.1947 84.5088 17.0 .1 2 '.3 A 226.9801 229.6583 232.3522 235.0618 237.7871 53.4071 53.7212 54.0354 54.3496 54.6637 22.0 .1 .2 .3 .4 380.1327 383.5963 387.0756 390.5707 394.0814 69.1150 69.4292 69.7434 70.0575 70.3717 27.0 .1 '.3 A 572.5553 576.8043 581 .0690 585.3494 589.6455 84.8230 85.1372 85.4513 85.7655 86.0796 .5 .6 .7 .8 .9 240.5282 243.2849 246.0574 248.8456 251.6494 54.9779 55.2920 55.6062 55.9203 56.2345 .5 .6 .7 .8 .9 397.6078 401.1500 404.7078 408.2814 411.8707 70.6858 71.0000 71.3142 71.6283 71.9425 .5 .6 .7 .8 .9 593.9574 598.2849 602.6282 606.9871 611.3618 86.3938 86.7080 87.0221 87.3363 87.6504 IS.O .1 .2 .3 .4 254.4690 257.3043 260.1553 263.0220 265.9044 56.5486 56.8628 57.1770 57.4911 57.8053 23.0 .1 .2 .3 .4 415.4756 419.0963 422.7327 426.3848 430.0526 72.2566 72.5708 72.8849 73.1991 73.5133 28.0 .1 .2 .3 .4 615.7522 620.1582 624.5800 629.0175 633.4707 87.9646 88.2788 88.5929 88.9071 89.2212 .5 .6 .7 .8 .9 268.8025 271.7164 274.6459 277.5911 280.5521 58.1195 58.4336 58.7478 59.0619 59.3761 .5 .6 .7 .8 .9 433.7361 437.4354 441.1503 444.8809 448.6273 73.8274 74.1416 74.4557 74.7699 75.0841 .5 .6 .7 .8 .9 637.9397 642.4243 646.9246 651.4407 655.9724 89.5354 89.8495 90.1637 90.4779 90.7920 19.0 .1 .2 .3 .4 283.5287 286.5211 289.5292 292.5530 295.5925 59.6903 60.0044 60.3186 60.6327 60.9469 24.0 .1 .2 .3 .4 452.3893 456.1671 459.9606 463.7698 467.5947 75.3982 75.7124 76.0265 76.3407 76.6549 29.0 .1 .2 .3 .4 660.5199 665.0830 669.6619 674.2565 678.8668 91.1062 91.4203 91.7345 92.0487 92.3628 .5 .6 .7 .8 .9 293.6477 301.7186 304.8052 307.9075 311.0255 61.2611 61.5752 61.8894 62.2035 62.5177 .5 .6 .7 .8 .9 471.4352 475.2916 479.1636 483.0513 486.9547 76.9690 77.2832 77.5973 77.9115 78.2257 .5 .6 .7 .8 .9 683.4928 688.1345 692.7919 697.4650 702.1538 92.6770 92.9911 93.3053 93.6195 93.9336 177 AREAS AND CIRCUMFERENCES OF CIRCLES For Diameters from J^ to 99, advancing by Tenths Diam. Area. Circum. Diam. Area. Circum. [ 109.9557 110.2699 110.5841 110.8982 111.2124 Diam. 40.0 .1 .2 .3 .4 Area. Circum. 30.0 .1 .2 .3 .4 706.8583 711.5786 716.3145 721.0662 725.8336 94.2478 94.5619 94.8761 95.1903 95.5044 35.0 .1 .2 .3 .4 962.1128 967.6184 973.1397 978.6768 984.2296 1256.6371 1262.9281 1269.2348 1275.5573 1281.8955 125.6637 125.9779 126.2920 126.6062 126.9203 .5 .6 .7 .8 .9 730.6167 735.4154 740.2299 745.0601 749.9060 95.8186 96.1327 96.4469 96.7611 97.0752 .5 .6 .7 .8 .9 989.7980 995.3822 1000.9821 1006.5977 1012.2290 ] 11.5265 111.8407 112.1549 112.4690 112.7832 .5 .6 .7 .8 .9 1288.2493 1294.6189 1301.0042 1307.4052, 1313.8219 127.2345 127.5487 127.8628 128.1770 128.4911 31.0 .1 .2 .3 .4 754.7676 759.6450 764.5380 769.4467 774.3712 97.3894 97.7035 98.0177 98.3319 98.6460 36.0 .1 .2 .3 .4 1017.8760 1023.5387 1029.2172 1034.9113 1040.6212 113.0973 113.4115 113.7257 114.0398 114.3540 41.0 .1 .2 .3 .4 1320.2543 1326.7024 1333.1663 1339.6458! 1346.1410 128.8053 129.1195 129.4336 129.7478 130.0619 .5 .6 .7 .8 .9 779.3113 784.2672 789.2388 794.2260 799.2290 98.9602 99.2743 99.5885 99.9026 100.2168 .5 .6 .7 .8 .9 1046.3467 1052.0880 1057.8449 1063.6176 1069.4060 114.6681 114.9823 115.2965 115.6106 115.9248 .5 .6 .7 .8 .9 1352.6520 1359.1786 1365.7210 1372.2791 1378.8529 130.3761 130.6903 131.0044 131.3186 131.6327 32.0 .1 .2 .3 .4 804.2477 809.2821 814.3322 819.3980 824.4796 100.5310 100.8451 101.1593 101.4734 101.7876 37.0 .1 .2 .3 .4 1075.2101 1081.0299 1086.8654 1092.7166 1098.5835 116.2389 116.5531 116.8672 117.1814 117.4956 42.0 .1 .2 .3 .4 1385.4424 1392.0476 1398.6685 1405.3051 1411.9574 131.9469 132.2611 132.5752 132.8894 133.2035 .5 .6 .7 .8 .9 829.5768 834.6898 839.8185 844.%28 850.1229 102.1018 102.4159 102.7301 103.0442 103.3584 .5 .6 .7 .8 .9 1104.4662 1110.3645 1116.2786 1122.2083 1128.1538 117.8097 118.1239 118.4380 118.7522 119.0664 .5 .6 .7 .8 .9 1418.6254 1425.3092 1432.0086 1438.7238 1445.4546 133.5177 133.8318 134.1460 134.4602 134.7743 33.0 .1 .2 .3 .4 855.2986 860.4902 865.6973 870.9202 876.1588 103.6726 103.9867 104.3009 104.6150 104.9292 38.0 .1 .2 .3 .4 1134.1149 1140.0918 1146.0844 1152.0927 1158.1167 119.3805 119.6947 120.0088 120.3230 120.6372 43.0 .1 .2 .3 .4 1452.2012 1458.%35 1465.7415 1472.5352 1479.3446 135.0885 135.4026 135.7168 136.0310 136.3451 .5 .6 .7 .8 .9 881.4131 886.6831 891.9688 897.2703 902.5874 105.2434 105.5575 105.8717 106.1858 106.5000 .5 .6 .7 .8 .9 1164.1564 1170.2118 1176.2830 1182.3698 1188.4724 120.9513 121.2655 121.5796 121.8938 122.2080 .5 .6 .7 .8 .9 1486.1697 1493.0105 1499.8670 1506.7393 1513.6272 136.6593 136.9734 137.2876 137.6018 137.9159 34.0 .1 .2 .3 .4 907.9203 913.2688 918.6331 924.0131 929.4088 106.8142 107.1283 107.4425 107.7566 108.0708 39.0 .1 i .4 1194.5906 1200.7246 1206.8742 1213.0396 1219.2207 122.5221 122.8363 123.1504 123.4646 123.7788 44.0 .1 .2 .3 .4 1520.5308 1527.4502 1534.3853 1541.3360 1548.3025 138.2301 138.5442 138.8584 139.1726 139.4867 .5 .6 .7 .8 .9 934.8202 940.2473 945.6901 951.1486 956.6228 108.3849 108.6991 109.0133 109.3274 109.6416 .5 .6 .7 .8 .9 1225.417= 1231.630C 1237.8582 1244.1021 1250.3617 124.0929 124.4071 124.7212 125.0354 125.3495 .5 .6 .7 .8 .9 1555.2847 1562.2826 1569.2962 1576.3255 1583.3706 139.8009 140.1153 140.4292 140.7434 141.0575 178 AREAS AND CIRCUMFERENCES OF CIRCLES For Diameters from ^'^ to 99, advancing by Tentlis Diam. Area. Circum. Diam. Area. Circum. Diam. Area. Circum. 45.0 .1 .2 .3 .4 1590.4313 1597.5077 1604.5999 1611.7077 1618.8313 141.3717 141.6858 142.0000 142.3142 142.6283 50.0 .1 .2 .3 .4 1963.4954 1971.3572 1979.2348 1987.1280 1995.0370 157.0796 157.3938 157.7080 158.0221 158.3363 55.0 .1 .2 .3 .4 2375.8294 2384.4767 2393.1396 2401.8183 2410.5126 172.7876 173.1017 173.4159 173.7301 174.0442 .5 .6 .7 .8 .9 1625.9705 1633.1255 1640.2962 1647.4826 1654.6847 142.9425 143.2566 143.5708 143.8849 144.1991 .5 .6 .7 .8 .9 2002.9617 2010.9020 2018.8581 2026.8299 2034.8174 158.6504 158.9646 159.2787 159.5929 159.9071 .5 .6 .7 .8 .9 2419.2227 2427.9485 2436.6899 2445.4471 2454.2200 174.3584 174.6726 174.9867 175.3009 175.6150 46.0 .1 .2 .3 .4 1661.9025 1669.1360 1676.3853 1683.6502 1690.9308 144.5133 144.8274 145.1416 145.4557 145.7699 51.0 .1 .2 .3 .4 2042.8206 2050.8395 2058.8742 2066.9245 2074.9905 160.2212 160.5354 160.8495 161.1637 161.4779 56.0 .1 .2 .3 .4 2463.0086 2471.8130 2480.6330 2489.4687 2498.3201 175.9292 176.2433 176.5575 176.8717 177.1858 .5 .6 .7 .8 .9 1698.2272 1705.5392 1712.8670 1720.2105 1727.5697 146.0841 146.3982 146.7124 147.0265 147.3407 .5 .6 .7 .8 .9 2083.0723 2091.1697 2099.2829 2107.4118 2115.5563 161.7920 162.1062 162.4203 162.7345 163.0487 .5 .6 .7 .8 .9 2507.1873 2516.0701 2524.9687 2533.8830 2*42.8129 177.5000 177.8141 178.1283 178.4425 178.7566 47.0 .1 .2 .3 .4 1734.9445 1742.3351 1749.7414 1757.1635 1764.6012 147.6550 147.9690 148.2832 148.5973 148.9115 52.0 .1 .2 .3 .4 2123.7166 2131.8926 2140.0843 2148.2917 2156.5149 163.3628 163.6770 163.9911 164.3053 164.6195 57.0 .1 .2 .3 .4 2551.7586 2560.7200 2569.6971 2578.6899 2587.6985 179.0708 179.3849 179.6991 180.0133 180.3274 .5 .6 .7 .8 .9 1772.0546 1779.5237 1787.0086 1794.5091 1802.0254 149.2257 149.539S 149.8540 150.1681 150.4823 .5 .6 .7 .8 .9 2164.7537 2173.0082 2181.2785 2189.5644 2197.8661 164.9336 165.2479 165.5619 165.8761 166.1903 .5 .6 .7 .8 .9 2596.7227 2605.7626 2614.8183 2623.8896 2632.9767 180.6416 180.9557 181.2699 181.5841 181.8982 48.0 .1 .2 .3 .4 1809.5574 1817.1050 1824.6684 1832.2475 1839.8423 150.7964 151.1106 151.4248 151.7389 152.0531 53.0 .1 .2 .3 .4 2206.1834 2214.5165 2222.8653 2231.2298 2239.6100 166.5044 166.8186 167.1327 167.4469 167.7610 58.0 .1 .2 .3 .4 2642.0794 2651.1979 2660.3321 2669.4820 2678.6476 182.2124 182.5265 182.8407 183.1549 183.4690 .5 .6 .7 .8 .9 1847.4528 1855.0790 1862.7210 1870.3786 1878.0519 152.3672 152.6814 152.9956 153.3097 153.6239 .5 .6 .7 .8 .9 2248.0059 2256.4175 2264.8448 2273.2879 2281.7466 168.0752 168.3894 168.7035 169.0177 169.3318 .5 .6 .7 .8 .9 2687.8289 2697.0259 2706.2386 2715.4670 2724.7112 183.7832 184.0973 184.4115 i84.7256 185.0398 49.0 .1 .2 .3 .4 1885.7409 1893.4457 1901.1662 190S.9024 1916.6543 153.9380 154.2522 154.5664 154.8805 155.1947 54.0 .1 i .4 2290.2210 2298.7112 2307.2171 2315.7386 2324.2759 169.6460 169.9602 170.2743 170.5885 170.9026 59.0 .1 .2 .3 .4 2733.9710 2743.2466 2752.5378 2761.8448 2771.1675 185.3540 185.6681 185.9823 186.2964 186.6106 .5 .6 .7 .8 .9 1924.4218 1932.2051 1940.0042 1947.8189 1955.6493 155.5088 155.8230 156.1372 156.4513 156.7655 .5 .6 -.7 .8 .9 2332.8289 2341.3976 2349.9820 2358.5821 2367.1979 171.2168 171.5310 171.8451 172.1593 172.4735 .5 .6 .7 .8 .9 2780.5058 2789.8599 2799.2297 2808.6152 2818.0165 186.9248 187.2389 187.5531 187.8672 189.1814 179 AREAS AND CIRCUMFERENCES OF CIRCLES For Diameters from J^ to 99, advancing by Tenths Diam. Area. Circum. Diam. Area. Circum. Diam. Area. Circum. 60.0 .1 .2 .3 .4 2827.4334 2836.8660 2846.3144 2855.7784 2865.2582 18S.4956 188.8097 189.1239 189.4380 189.7522 65.0 .1 .2 .3 .4 3318.3072 3328.5253 3338.7590 3349.0085 3359.2736 204.2035 204.5176 204.8318 205.1460 205.4602 70.0 .1 .2 .3 .4 3848.4510 3859.4544 3870.4736 3881.5084 3892.5590 219.9115 220.2256 220.5398 220.8540 221.1681 .5 .6 .7 .8 .9 2874.7536 2884.2648 2893.7917 2903.3343 2912.8926 190.0664 190.3805 190.6947 191.0088 191.3230 .5 .6 .7 .8 .9 3369.5545 3379.8510 3390.1633 3400.4913 3410.8350 205.7743 206.0885 206.4026 206.7168 207.0310 .5 .6 .7 .8 .9 3903.6252 3914.7072 3925.8049 3936.9182 3948.0473 221.4823 221.7964 222.1106 222.4248 222.7389 61.0 .1 .2 .3 .4 2922.4666 2932.0563 2941.6617 2951.2828 2960.9197 191.6372 191.9513 192.2655 192.5796 192.8938 66.0 .1 .2 .3 .4 3421.1944 3431.5695 3441.9603 3452.3669 3462.7891 207.3451 207.6593 207.9734 208.2876 208.6017 71.0 .1 .2 .3 .4 3959.1921 3970.3526 3981.5289 3992.7208 4003.9284 223.0531 223.3672 223.6814 223.9956 224.3097 .5 .6 .7 .8 .9 2970.5722 2980.2405 2989.9244 2999.6241 3009.3395 193.2079 193.5221 193.8363 194.1504 194.4646 .5 .6 .7 .8 .9 3473.2270 3483.6807 ^494.1500 3504.6351 3515.1359 208.9159 209.2301 209.5442 209.8584 210.1725 .5 .6 .7 .8 .9 4015.1518 4026.3908 4037.6456 4048.9160 4060.2022 224.6239 224.9380 225.2522 225.5664 225.8805 62.0 .1 .2 .3 .4 3019.0705 3028.8173 3038.5798 3048.3580 305S.1520 194.7787 195.0929 195.4071 195.7212 196.0354 67.0 .1 .2 .3 .4 3525.6524 3536.1845 3546.7324 3557.2960 3567.8754 210.4867 210.8009 211.1150 211.4292 211.7433 72.0 .1 .2 .3 .4 4071.5041 4082.8217 4094.1550 4105.5040 4116.8687 226.1947 226.5088 226.8230 227.1371 227.4513 .5 .6 .7 .8 .9 3067.9616 3077.7869 3087.6279 3097.4847 3107.3571 196.3495 196.6637 196.9779 197.2920 197.6062 .5 .6 .7 .8 .9 3578.4704 3589.0811 3599.7075 3610.3497 3621.0075 212.0575 212.3717 212.6858 213.0000 213.3141 .5 .6 .7 .8 .9 4128.2491 4139.6452 4151.0571 4162.4846 4173.9279 227.7655 228.0796 228.3938 228.7079 229.0221 63.0 .1 .2 .3 .4 3117.2453 3127.1492 3137. 068S 3147.0040 3156.9550 197.9203 198.2345 19S.54S7 198.8628 199.1770 68.0 .1 .2 .3 .4 3631.6811 3642.3704 3653.0754 3663.7960 3674.5324 213.6283 213.9425 214.2566 214.5708 214.8849 73.0 .1 .2 .3 .4 4185.3868 4196.8615 4208.3519 4219.8579 4231.3797 229.3363 229.6504 229.9646 230.2787 230.5929 .5 .6 .7 .8 .9 3166.9217 3176.9043 3186.9023 3196.9161 3206.9456 199.4911 199.8053 200.1195 200.4336 200.7478 .5 .6 .7 .8 .9 3685.2845 3696.0523 3706.8359 3717.6351 3728.4500 215.1991 215.5133 215.8274 216.1416 216.4556 .5 .6 .7 .8 .9 4242.9172 4254.4704 4266.0394 4277.6240 4289.2243 230.9071 231.2212 231.5354 231.8495 232.1637 64.0 .1 .2 .3 .4 3216.9909 3227.0518 3237. 12S5 3247.2222 3257.3289 201.0620 201.3761 201.6902 202.0044 202.3186 69.0 .1 .2 .3 .4 3739.2807 3750.1270 3760.9891 3771.8668 3782.7603 216.7699 217.0841 217.3982 217.7124 218.0265 74.0 .1 .2 .3 .4 4300.8403 4312.4721 4324.1195 4335.7827 4347.4616 232.4779 232.7920 233.1062 233.4203 233.7345 .5 .6 .7 .8 .9 3267.4527 3277.5922 3287.7474 3297.9183 3308.1049 202.6327 202.9469 203.2610 203.5752 203.8894 .5 .6 .7 .8 .9 3793.6695 3804.5944 3815.5350 3826.4913 3837.4633 218.3407 218.6548 218.9690 219.2832 219.5973 .5 .6 .7 .8 .9 4359.1562 4370.8664 4382.5924 4394.3341 4406.0916 234.0487 234.3628 234.6770 234.9911 235.3053 180 AREAS AND CIRCUMFERENCES OF CIRCLES For Diameters from J^ to 99, advancing by Tenths Diam. Area. Circum. Diam. Area. Circum. Diam. Area. Circum. 75.0 .1 .2 .3 .4 4417.8647 4429.6535 4441.4580- 4453.2783 4465.1142 235.6194 235.9336 236.2478 236.5619 236.8761 80.0 .1 .2 .3 .4 5026.5482 5039.1225 5051.7124 5064.3180 5076.9394 251.3274 251.6416 251.9557 252.2699 252.5840 85.0 .1 .2 .3 .4 5674.5017 5687.8614 5701.2367 5714.6277 5728.0345 267.0354 267.3495 267.6637 267.9779 268.2920 .5 .6 .7 .8 .9 4476.9659 4488.8332 4500.7163 4512.6151 4524.5296 237.1902 237.5044 237.8186 238.1327 238.4469 .5 .6 .7 .8 .9 5089.5764 5102.2292 5114.8977 5127.5819 5140.2818 252.8982 253.2124 253.5265 253.8407 254.1548 .5 :f .8 .9 5741.4569 5754.8951 5768.3490 5781.8185 5795.3038 268.6062 268.9203 269.2345 269.5486 269.8628 76.0 .1 .2 .3 .4 4536.4598 4548.4057 4560.3673 4572.3446 4584.3377 238.7610 239.0752 239.3894 239.7035 240.0177 81.0 .1 .2 .3 .4 5152.9973 5165.7287 5178.4757 5191.2384 5204.0168 254.4690 254.7832 255.0973 255.4115 255.7256 86.0 .1 .2 .3 .4 5808.8048 5822.3215 5S35.8539 5849.4020 5862.9659 270.1770 270.4911 270.8053 271.1194 271.4336 .5 .6 .7 .8 .9 4596.3464 4608.3708 4620.4110 4632.4669 4644.5384 240.3318 240.6460 240.9602 241.2743 241.5885 .5 .6 .7 .8 .9 5216.8110 5229.6208 5242.4463 5255.2876 5268.1446 256.0398 256.3540 256.6681 256.9823 257.2966 .5 .6 .7 .8 .9 5876.5454 5890.1407 5903.7516 5917.3783 5931.0206 271.7478 272.0619 272.3761 272.6902 273.0044 77.0 .1 .2 .3 .4 4656.6257 4668.7287 4680.8474 4692.9818 4705.1319 241.9026 242.2168 242.5310 242.8451 243.1592 82.0 .1 .2 .3 .4 5281.0173 5293.9056 5306.8097 5319.7295 5332.6650 257.6106 257.9247 258.2389 258.5531 258.8672 87.0 .1 .2 .3 .4 5944.6787 5958.3525 5972.0420 5985.7472 5999.4681 273.3186 273.6327 273.9469 274.2610 274.5752 .5 .6 .7 .8 .9 4717.2977 4729.4792 4741.6765 4753.8894 4766.1181 243.4734 243.7876 244.1017 244.4159 244.7301 .5 .6 .7 .8 .9 5345.6162 5358.5832 5371.5658 5384.5641 5397.5782 259.1814 259.4956 259.8097 260.1239 260.4380 .5 .6 .7 .8 .9 6013.2047 6026.9570 6040.7250 6054.5088 6068.3082 274.8894 275.2035 275.5177 275.8318 276.1460 78.0 .1 .2 .3 .4 4778.3624 4790.6225 4802.8983 4815.1897 4827.4969 245.0442 245.3584 245.6725 245.9867 246.3009 83.0 .1 .2 .3 .4 5410.6079 5423.6534 5436.7146 5449.7915 5462.8840 260.7522 261.0663 261.3805 261.6947 262.0088 88.0 .1 .2 .3 .4 6082.1234 6095.9542 6109.8008 6123.6631 6137.5411 276.4602 276.7743 277.0885 277.4026 277.7168 .5 .6 .7 .8 .9 4839.8198 4852.1584 4864.5128 4876.8828 4889.2685 246.6150 246.9292 247.2433 247.5575 247.8717 .5 .6 .7 .8 .9 5475.9923 5489.1163 5502.2561 5515.4115 5528.5826 262.3230 262.6371 262.9513 263.2655 263.5796 .5 .6 .7 .8 .9 6151.4348 6165.3442 6179.2693 6193.2101 6207.1666 278.0309 278.3451 278.6593 278.9740 279.2876 79.0 .1 .2 .3 .4 4901.6699 4914.0871 4926.5199 4938.9685 4951.4328 248.1858 248.5000 248.8141 249.1283 249.4425 84.0 .1 .2 .3 .4 5541.7694 5554.9720 5568.1902 5581.4242 5594.6739 263.8938 264.2079 264.5221 264.8363 265.1514 89.0 .1 .2 .3 .4 6221.1389 6235.1268 6249.1304 6263.1498 6277.1849 279.6017 279.9159 280.2301 280.5442 2S0.85S4 .5 .6 .7 .8 .9 4963.9127 4976.4084 4988.9198 5001.4469 5013.9897 249.7566 250.0708 250.3850 250.6991 251.0133 .5 .6 .7 .8 .9 5607.9392 5621.2203 5634.5171 5647.8296 5661.1578 265.4646 265.7787 266.0929 266.4071 266.7212 .5 .6 .7 .8 .9 6291.2356 6305.3021 6319.3843 6333.4822 6347.5958 281.1725 281.4867 281.8009 282.1150 282.4292 TABLES 181 AREAS AND CIRCUMFERENCES OF CIRCLES For Diameters from J^ to 99, advancing by Tenths Diam. Area. , Circum. Diam. Area. Circum. Diam. %.o .1 .2 .3 .4 Area. Circum. 90.0 .1 .2 .3 .4 6361.7251! 282.7433 6375.8701 j 283.0575 6390.0309 283.3717 6404.2073 283.6858 6418.3995 284.0000 93.0 .1 .2 .3 .4 6792.9087 6807.5250 6822.1569 6836.8046 6851.4680 292.1681 292.4823 292.7964 293.1106 293.4248 7238.2295 7253.3170 7268.4202 7283.5391 7298.6737 301.5929 301.9071 302.2212 302.5354 302.8405 .5 .6 .7 .8 .9 6432.6073 284.3141 6446.8309, 284.6283 6461.0701 284.9425 6475.3251 285.2566 6489.5958j 285.5708 .5 .6 .7 .8 .9 6866.1471 6880.8419 6895.5524 6910.2786 6925.0205 293.7389 294.0531 294.3672 294.6814 294.9956 .5 .6 .7 .8 .9 7313.8240 7328.9901 7344.1718 7359.3693 7374.5824 303.1637 303.4779 303.7920 304.1062 304.4203 91.0 .1 .2 .3 .4 6503.8S22 285.8849 6518.1843 286.1991 6532.5021 286.5133 6546.8356 286.8274 6561.1848 287.1416 94.0 .1 .2 .3 .4 6939.7782 6954.5515 6969.3106 6984.1453 6998.9658 295.3097 295.6239 295.9380 296.2522 296.5663 97.0 .1 .2 .3 .4 7389.8113 7405.0559 7420.3162 7435.5922 7450.8839 304.7345 305.04S6 305.3628 305.6770 305.9911 .5 .6 .7 .8 .9 6575.5498 6589.9304 6604.3268 6618.7388 6633.1666 287.4557 287.7699 288.0840 288.3982 288.7124 .5 .6 .7 .8 .9 7013.8019 7028.6538 7043.5214 7058.4047 7073.3033 296.8805 297.1947 297.5088 297.8230 298.1371 .5 .6 .7 .8 .9 7466.1913 7481.5144 7496.8532 7512.2078 7527.5780 306.3053 306.6194 306.9336 307.2478 307.5619 92.0 .1 .2 .3 .4 6647.6101 6662.0692 6676.5441 6691.0347 6705.5410 289.0265 289.3407 289.6548 289.9690 290.2832 95.0 i .3 .4 7088.2184 7103.1488 7118.1950 7133.0568 7148.0343 298.4513 298.7655 299.0796 299.3938 299.7079 98.0 .1 .2 .3 .4 7542.9640 7558.3656 7573.7830 7589.2161 7604.6648 307.8761 308.1902 308.5044 308.8186 309.1327 .5 .6 .7 .8 .9 6720.0630 6734.6C08 6749.1542 6763.7233 6778.30S2 290.5973 290.9115 291.2256 291.5398 291.8540 .5 .6 .7 .8 .9 7163.0276 7178.0366 7193.0612 7208.1016 7223.1577 300.0221 300.3363 300.6504 300.9646 301.2787 .5 .6 .7 .8 .9 7620.1293 7635.6095 7651.1054 7666.6170 7682.1444 309.4469 309.7610 310.0752 310.3894 310.7035 DECIMAL EQUIVALENTS OF FRACTIONS OF ONE INCH 1-64 .015625 j 17-64 .265625 ' 33-64 .515625 49-64 .765625 1-32 .03125 ! 9-32 .28125 17-32 .53125 25-32 .78125 3-64 .046875 19-64 .296875 35-64 .546875 51-64 .796875 1-16 .0625 5-16 .3125 9-16 .5625 ; 13-16 .8125 5-64 .078125 21-64 .328125 37-64 .578125 53-64 .828125 3-32 .09375 11-32 .34375 19-32 .59375 i 27-32 .84375 7-64 .109375 23-64 .359375 39-64 .609375 1 55-64 .859375 1-8 .125 3-8 .375 5-8 .625 1 7-8 .875 9-64 .140625 25-64 .390625 41-64 .&t0625 57-64 .890625 5-32 .15625 13-32 .40625 21-32 .65625 29-32 .90625 11-64 .171875 27-64 .421875 43-64 .671875 59-64 .921875 3-16 .1875 ■7-16 .4375 11-16 .6875 15-16 .9375 13-64 .203125 29-64 .453125 45-64 .703125 61-64 .953125 7-32 .21875 15-32 .46875 23-32 .71875 31-32 .96875 15-64 .234375 31-^4 .484375 47-64 .734375 63-64 .984375 1-4 .25 1-2 .50 3-4 .75 1 1. 182 TABLES WEIGHT OF A CUBIC FOOT OF WATER BETWEEN 32° AND 212° F Temper- Weight, Temper- Weight, Temper- Weight, ature lbs. per ature lbs. per ature lbs. per Fahr. cubic foot Fahr. cubic foot Fahr. cubic foot 32° 62.42 123° 61.68 168° 60.81 35 62.42 124 61.67 169 60 79 40 62.42 125 61.65 170 60.77 45 62.42 126 61.63 171 60.75 50 62.41 127 61.61 172 60.73 52 62.40 128 61.60 173 60.70 54 62.40 129 61.58 174 60.68 56 62.39 130 6r.56 175 60.66 58 62.38 131 61.54 176 60.64 60 62.37 132 61.52 177 60.62 62 62.36 133 61.51 178 60.59 64 62.35 134 61.49 179 60.57 66 62.34 135 61.47 180 60.55 68 62.33 136 61.45 181 60.53 70 62.31 137 61.43 182 60.50 72 62.30 138 61.41 183 60 48 74 62.28 139 61.39 184 60.46 76 62.27 140 61.37 185 60.44 78 62.25 141 61.36 186 60.41 80 62.23 142 61.34 187 60 39 82 62.21 143 61.32 188 60.37 84 62.19 144 61.30 189 60.34 86 62.17 ,145 61.28 190 60.32 88 62.15 146 61 26 191 60.29 90 62.13 147 61.24 192 60.27 92 62.11 148 61.22 193 60.25 94 62.09 149 61.20 194 60.22 96 62 07 150 61.18 195 60.20 98 62.05 151 61.16 196 60.17 100 62.02 152 61.14 197 60.15 102 62.00 153 61.12 198 60.12 104 61.97 154 61.10 199 60.10 106 61.95 155 6108 200 60.07 108 61.92 156 61.06 201 60.05 110 61.89 157 61.04 202 60.02 112 61.86 158 61.02 203 60.00 113 61.84 159 61.00 204 59.97 114 61.83 160 60.98 205 59.95 115 61.82 161 60.96 206 59.92 116 61.80 162 60.94 207 59.89 117 61.78 163 60.92 208 59.87 118 61.77 164 60.90 209 59.84 119 61.75 165 60.87 210 59.82 120 61.74 166 60.85 211 59.79 121 61.72 167 60.83 212 59.76 122 61.70 WEIGHT OF A CUBIC FOOT OF WATER AT HIGH TEMPERATURES Tem- pera- ture Fahr. Weight of 1 cubic foot Differ- ence per 1 degree Tem- pera- ture Fahr. Weight of 1 cubic foot Differ- ence per 1 degree Tem- pera- ture Fahr. Weight of 1 cubic foot Differ- ence per 1 degree 220'^ 230 240 250 260 270 280 59.641 59.372 59.096 58.812 58.517 58.214 57.903 0.0253 0.0269 0.0276 0284 0.0295 0.0303 0.0311 290° 300 310 320 330 340 57.585 57.259 56.925 56.584 56.236 55.883 0.0318 0.0326 0.0334 0.0341 0.0348 0.0353 350" 360 370 380 390 400 55.523 55.158 54.787 54.411 54.030 53.635 0.0360 0.0365 0.0371 0.0376 0,0381 0.0395 ■980 CUAllT UF PKOi'KKTlES OF STEAM / \"-l _.. LL.. A i > V ■^ _j_ - 1^7 fen ^^ ffii ri i " ti PRESSURES ABSOLUTE Apu 8 CHART OK FUO /! n^ ' /lAI '1- ; -I---.1.-3-: I- 1 I '^ I -t- PRESSURES ABSOLUTE iPY CHAKi fe; ^ 3?*± ii^ 1 /•/ / / . / J-—t ^' ^' : / 7 f^5»| - .1 mm- y , .y fr,/ ':S. K^^^:;"^-^r^" 'TROPY E-EXTHOI'V LHAKT FVH STEAM TEMP£RATURE-£MTftOf>Y ABSOLUTE PRESSURE w« aw j ' 1 . 1 J ."■ IT-^liilllM APPENDIX APPENDIX COUNTERS, GAGES, AND OTHER ACCESSORY APPARATUS THE CROSBY REVOLUTION COUNTER OR ENGINE REGISTER Patented Engine Revolution Counters, as commonly designed and constructed, depend iipon an escapement for re- cei\ang the actuating force, and a star-toothed wheel for transmitting the movement to the figure-.wheels. The escapement principle, while well adapted to a delicate machine actuated by a constant force, like a watch or clock, is ill suited to a counter for registering the stroke of a steam engine or other ponderous macliine, where the actuating force may be out of all suitable propor- tion to the structural strength of the counter, and such as to destroy it, if from any cause, like the varying sti'oke of a piunp, the pallet fails to properly engage with the tooth of the wheel. From the same causes such counters may also fail to register. These facts are well known to all mechanics who have had experience with escapement counters. To forcibly illustrate how poorly adapted to a counter the escapement principle is, it is only necessary to state, that in a watch, by the slight force of the actuating s])ring or weight, it simply perviitii a tooth to escape, wliile in a 185 186 REVOLUTION COUXTERS counter it is required to move the irhole nieehanifim., and to do this intermittently and with the varying resistance of one or all of the figure-wheels. In a Revolution Counter which shall he rellaJile, durahLe, and free from liahility to serious injury, the actuating force must, through proper mechanism, he transmitted directly and with certamty to the figure- wheels, and this can best be done by means of a crank. It matters not in the Crosby Counter whether the movement of the crank is rotary or merely oscillatory, it will count just the same. The Crosby Improved Revolution Counter, only, employs the crank principle, applied through other simple mechanical motions, so as to record with certainty the operations of any machine, and at the same time obviate all danger of injury to the counter itself or the machine to which it is attached. This co^mter is adapted to either right or left hand rotary or reelprocatinfj motions, and is ca^pable of 500 revolutions per minute with safety to the machine and accuracy in the enumeration. The shaft through which the actuating force is applied may extend from the counter either on the right-hand or left-hand side as desired. It is made in the following sizes : 12 inch dial 8 wheels 12 " '' 7 " 12 '• " . 6 " 10 " " 8 " 10 •• " ....... 7 " 10 '• " , .• 6 " 8i '• " ■ 8 " 81 " " 7 " 81 '• - 6 " 6i - " ....... 6 " 6 " " 6 " REVOLUTIOX COUNTERS CROSBY SQUARE COUNTER 187 The actuating mechanism of this counter is positive and employs the principles just des(;rihe(:l, as used in the Croshy Revolution Counter. It is a strong and useful instrument, compact in form, durahle and accurate. It may he provided with a re-setting device and also with a padlock if desired. When recpiired for rotary motion, it should he stated U^ whether it is to he used for right-hand or left-hand rotation. This counter is made in the following sizes : 4f X 1^ in. dial 4 figures 5i X 1^ •• •• 5 " 6X1^'-" 6 " 7i X 2^ •• '^ 4 " 8i X 2]r '• •• 5 " 9i X 21 - " 6 " lOf X 2:^ " " 7 " THE CROSBY LOCOMOTIVE COUNTER For High Rotative Speeds The cut on ])age 18S shows the Locomotive CoHuter. It is designed ])articularly for use on locomotives and higli s])eed engines, and is a valuahle auxiliary to the steam engine in- dicator. The arm which moves the ratchet is connected hy a cord with some recipiocating 2)art of the engine, or with 188 CROSBY LOCOMOTIVE COUI^^TER the drum motion, so as to give it about 1^ inches swing back and forth during each revohition of the shaft. It is provided with a convenient starting and stopping device, so that it can be made to l)egin or stop counting at any instant. CROSBY RECORDING COUNTER Patented This instrument furnishes a chart record of the revolu- tions or strokes of any engine, pump, or moving part. It is designed with remarkable genius for its special purpose, CROSBY RECORDING COUXTER 189 and it w-ill record the highest speeds with mathematical accuracy. Every counter is tested to at least two thousand revolutions per minute, and will give positive results at much higher speeds without slip or error. Each regvilar chart affords a pen record up to tifty thousand consecutive strokes or revolutions, and the exact total nund)er, or the elapsed count between any two noted periods, can be read with cer- tainty. The highest working speeds found in mechanical operations are within the range of this device. The Crosby Recording Counter is not a tachometer, but a chart-recording instrument, occupying a field by itself of peculiar importance. There is no other instrument like it, or that gives similar results. Its applications are varied and universal. It will be found especially valuable in making permanent records of the performance of mat^hinery or engines either under special test or in daily service, and it is of the greatest usefidness and importance to every engineer, designer, and user of power. The chart is 8 inches in dia- meter and easily read ; the mechanism is well constructed, durable, and accurate ; it cannot get out of order or adjust- ment. All like parts are interchangeable and suitably de- 190 PRKSSURE GAGES signed to give proper wear and service. It is adapted for hoth revolutions and reciprocating motion without alteration. It is simple to attach and no skill is required to operate it. A smaller recording counter capable of registering at the highest speeds upon a chart reading to 5,000 revolutions or strokes, and adapted to he attached to the Crosby Reducing Wheel, is described on l)age 73. CROSBY PRESSURE AND VACUUM GAGES Im.poi'tant Accuracy is the essential feature in all gages, whether pressure or vacuum. The principle of construction of Crosby gages is correct and they embody important improve- ments in many essential details. In the Crosby Improved Pressure Gage the tube springs are connected at each end with their respective parts by screw threads, without tl>e use of any soldering material wliatever, thus insuring tight joints under all conditions of heat and pressure. The index mechanism and the dial are mounted upon an extension of the socket, thus rendering the entire operating EECORDIXa OAGKS 191 parts of the gage independent of the case and free from any errors arising from its distortion or from external heat. The method by which Crosby gages are tested and grad- uated will insure a truthful and reliable gage. Each one is tested under steam pressure and subjected to pressures accu- rately measui-ed by standardized weights, and the gage is graduated to such absolute pressm'es and not by comparison only with another gage. An equally accurate method is used in the testing of vacuum gages ; each one is tried, marked, and adjusted by the direct readings of a mercury column, by means of an apparatus in wliich the successive stages of vacumu ai-e actually produced. Every gage used to indicate the pressure^ of steam should have a siphon or some other device which wdll furnish water to and completely fill the tube springs to keep them cool. Be sure that the connections between the gage and the siphon are perfectly tight. CROSBY PRESSURE RECORDER Patented The Crosby Pressure Recorder records the pressure of any fluid during a cex'tain jieriod of time. 192 RECORDIXG GAGES It is designed to supply the great and constantly increas- ing demand for a compact and reliable, yet not too costly, instrmiient for recording all the variations of pressure which take place in a steam boiler or other receptacle. It gives a graphic chart showing every such variation of pressure, its extent and duration, and the time wheii it occurs. The case is circular and is uniform in appearance with the other in- struments usually set up in an engine room. The socket by which it is attached to the boiler extends upward within the case, and supports the clock and other operating parts, thus producing a unity of action which gives a record true to the axis of the chart under all condi- tions. On the same post with the pen lever and below it, is a corresponding lever carrying a small table on which rests the pen point. Between the pen and table is placed the chart, and as both bear upon it there is insured a con- tinuous contact and in operation a continuous line. The pen is charged with a supply of red ink, and is easily and delicately adjusted to the surface of the chart by an ingenious device at its base, giving records of unequaled legibility and accuracy. RECOKDIXG GAGES 193 CROSBY PRESSURE RECORDER AND GAGE Patented The Crosby Pressure Recorder and Gage, in addition to recording the pressure of any fluid during a certain period of tinie, has an index hand and an outside circle of figures to show the actual pressure recorded on the chart at the moment of observation ; in this respect it ojjerates like an ordinary steam gage. The chart rotates once in 24 hours, and by the employ- ment of a special clock movement, the rotation of the chart may be made to conform to any period of time from one hour to one week, thus adapting the instrimient to ahnost any conditions to be found, in which a record of pressures is desirable or necessary ; and the range of pressures which may be recorded is practically unlimited. The reading of the chart, as shown above, is 110 pounds })ressure at 6.30 o'clock a.m. Supposing the instru- ment to be properly connected to a steam boiler, or other receptacle, then during the next 24 hours, a red line is traced by the pen completely around the dial, showing by its deviations from a true circle, the variations of pressure which take place during the whole of that time. 194 RECORDING GAGES Special Crosby Recording Gages are made to give con- tinuous chart records of the working pressures in air-brake reservoirs and train lines, and in the cylinders and tanks of puinps and hydraulic presses. The Crosby Gas, Mine, and Draft Recorder is an instru- ment designed for making a continuous record of the pres- sure of fluids, either above or below the atmosphere, as « ordinarily measured in inches of water. It is useful for determining and recording the drafts of chimneys, or the pressure of air in the ash pit of a steam boiler, in mines when forced therein, or in buildings when introduced for heating and ventilation ; it will show the pressure of gas for illuminating or other purposes at the works or at the place of consumption, or of any fluid where the pressure is sought and its record desired. This instrmnent is similar in the character of its work or operations to the Crosby Recording Gage, but is adapted to conditions requiring one which is more sensitive and delicate. THERMOMETERS 195 Steam Pipe Thermometer Hot Water Thermometer Hot Well Thermometer 196 LANZA CONTINUOUS DIAGRAM APPLIANCE THE LANZA CONTINUOUS DIAGRAM APPLIANCE WITH CROSBY INDICATORS Patented The Lanza Continuous Diagram Appliance is not in itself an indicator, but displaces the ordinary drum as a means for supplying the paper for taking indicator cards, and any indicator may be combined or adapted for use with it. It is assembled upon a bracket, or frame, which is designed to support also the indicator and its connections so that these parts may be rigidly fixed in proper mutual relation. Upon this bracket are mounted the spindle for receiving the new roll of paper, the drum which feeds the paper forward, and upon which the pencil point bears in making the record, and the spool upon which the paper is afterward wound. The drum is rotated continuously in one direction by the alternate engagement of two series of clutches controlled by a cord passing over the pulley at the extreme end of the bracket arm and actuated by a cross-head block which is LANZA CONTINUOUS DIAGRAM APPLIANCE 197 positively connected to the cross-head of the engine or some other convenient portion of the machinery which moves in exact accordance with the piston. This connection between the cross-head block of the Continuous Diagram Appliance and the engine cross-head is not illustrated, but it may be any reducing motion which will drive the Appliance positively in both directions, on the forward and backward strokes, as a spring is not depended upon for the return stroke, as in ordinary indicator drums and reducing motions. From this peculiar and desirable mode of connection there must result accuracy and positiveness of action in making continuous records. There are other important details of the Appliance, such as a method of marking upon the paper the end of each stroke or half revolution of the engine, mechanically controlled by contacts conveniently arranged for easy adjustment at either end of the stroke of the cross-head block, and an atmospheric marker which is immediately adjustable to any required position. Moreover, Crosby indicators afford further means in themselves for readily adjusting the position of the pencil point to bring the atmospheric line at any convenient posi- tion upon the paper. Uses of Such an Instrument Whenever the diagrams corresponding to successive revolutions of an engine differ, the need for a continuous series of cards becomes apparent, whether the variation be due to a variable load, as in locomotives, rolling mills, and many stationary steam plants, or to the nature of the opera- tions within the cylinder, as in gas engines. Thus, in the case of a steam engine, single ordinary indica- tor cards taken at intervals of from three to five minutes do not exhibit the variations in consecutive revolutions and do not enable us to determine the average M. E. P. If, on the other hand, a series of diagrams is taken on the same paper, as when using the ordinary indicator drum, the lines of the different cards become so confused, overlying each other, 198 LANZA CONTINUOUS DIAGRAM APPLIANCE that (a) it is not possible to distinguish them sufficiently to obtain a record of the variations, and (b) any attempt to determine from them the average M. E. P. results in a con- siderable error. In the case of a gas engine a complete cycle of operations involves a considerable number of revolutions of the engine, and hence several successive cards must be secured to furnish complete information regarding what occurs and to enable us to determine the M. E. P. for any given cycle of operations. Thus in the case of fire 1, miss 5, twelve successive diagrams are involved, while in the case of fire 8, miss 4, twenty-four revolutions, and hence twenty-four successive diagrams, are involved. If the entire set be taken on one ordinary indi- cator card, the lines (especially those in the lower part of the diagram) are so confused with each other that it is impossible to separate them, and, if the lower part of the diagram be omitted or disregarded, the error may reach twenty per cent. Description of the Diagrams On the roll of paper will be found: (a) The line traced by the indicator pencil. (6) The atmospheric line, (c) The continuous line drawn by the stroke-marker pencil, with its short vertical lines that mark the ends of the stroke. The record obtained during twenty consecutive revolutions of a steam engine, for example, consists of twenty consec- utive cards, which are not overlapping, but clearly sepa- rated. The nature of the separate portions of the line thus drawn by the indicator pencil and the events of each stroke are plainly seen on the diagram. The diagram obtained during one complete cycle of operations of a gas engine, with a cycle of fire and miss strokes, shows what occurs during the successive complete revolutions of the engine, and the nature of the separate portions of the line traced by the indicator pencil indicates the events of the strokes. The usual result of taking such an entire series on one ordinary indicator card is a confusion of the lines in the lower part of the LANZA CONTINUOUS DIAGRAM APPLIANCE 199 diagram, but with this instrument all such unccrtaintj' and error is avoided. Determination of M. E. P. by Mearis of a Planimcter or an Integrator Having taken a diagram corresponding to a certain num- l)er of revolutions of the engine by means of the Lanza Con- tinuous Diagram Appliance, we must first draw through the points which mark the ends of the several strokes lines perpendicular to the atmospheric line. If we use an ordinary planimeter, we need only to plani- meter the positive and the negative areas separately, and then to subtract the sum of the negative areas from the sum of the positive areas, to oi:)tain the total area of the given series of cards. Having obtained the resultant area in this way, we obtain the M. E. P. for this diagram by first dividing it by the total length divided by the number of complete revo- lutions, and then multiplying this average height by the scale of the indicator spring. Time can be saved if an integrator is used. It will be convenient to set the track of the integrator approximately parallel to the atmospheric line. To obtain the area of the diagrams corresponding to the successive revolutions of the engine, we can start the pencil of the integrator anywhere on the pressure line. In the forward motion we must drag the pencil of the integrator along the line drawn by the in- dicator pencil for every forward stroke, and along the at- mospheric line for every return stroke, while in the return motion we must drag the pencil of the integrator along the line drawn by the pencil of the indicator for every return stroke and along the atmospheric line for every forward stroke. The resultant area can then be read off on the in- tegrator. Any line parallel to the atmosi)heric could bo used in this operation instead of the atmospheric, if for any reason jt were more convenient. 200 LANZA CONTINUOUS DIAGRAM APPLIANCE Convenience in Taking Diagrams The paper can be removed from the winding-spindle when the entire roll has been used or it can be torn off at any point and the portion already on the spool removed. The free end of the unused portion can then be wound upon it to com- mence the taking of a new series of diagrams. The mechanism of the instrument continues in operation so long as the connection to the cross-head or reducing motion is in place, but by means of the pressure roll, controlled by a simple lever, the taking of diagrams can be started or stopped at any time and continued at will. Diagrams can be made by means of this Appliance used with Crosby indicators as made for steam, air, gas, ammonia or any liquid, or any ordinary pressure indicator can be adapted by simply disregarding the ordinary drum and turn- ing the pencil linkage to bear upon the drum of the instru- ment. The Lanza Continuous Diagram Appliance is made only by this Company. Full directions for operating it are sent with each instrument. A detailed description with illus- trative diagrams will be forwarded on application. 201 THE CROSBY INDICATOR It may be of interest to those Avho have read tliis book to know that whatever of merit in this instrument has been described and ilhisti'ated in these pages has been recog- nized and acknowledged as follows : At the Paris Exposition of 1889, where it received the highest award, a gold medal. At the AVorld's Columbian Exjjosition, Chicago, in 1893, where it received the highest award, a medal and diploma. At the Cotton States and International Exposition at Atlanta, in 1895, where it received the highest award. At the Russian Exposition held at Nijni Novgorod, in 1896, where it received the highest award, a gold medal and diploma of honor. At the Louisiana Purchase Exposition, held at St. Louis in 1904, where it received the grand prize. The Crosby Indicator is approved and adopted by the United States Govermnent. It is the standard in nearly all the great electric light and power stations of the United States. It has been approved and adopted by the principal navies, the government shipyards, and the most eminent technical schools of the world. Full particulars for the proper care and handling of the Crosby Indicator accompany each instrument. CROSBY STEAM GAGE AND \\\LVE COMPANY 40 Central Street, Marshall Building, Boston, Mass. 44 Dey Street, Hudson Terminal, New York, N. Y. 435-437 West Lake Street, Chicago, 111. 147 Queen Victoria Street, London, E. C, Eng. THE LIBRARY UNIVERSITY OF CALIFORNIA Santa Barbara THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW. A 000 587 488 8