tj 155 till fymtll itmwwitg Jtotg BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF 3Uettrg W< Sage 1891 ^..,..,£..^.. J fcf.iUZ..3U.. ■ . Hf-J3Z..Q.f-., 3513-1 Cornell University Library TJ 755.H71 Internal combustion engines :a reference 3 1924 022 810 224 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924022810224 INTERNAL COMBUSTION ENGINES A REFERENCE BOOK FOB DESIGNERS, OPERATORS, ENGINEERS, AND STUDENTS BT WM. M. HOGLE, B.S. CONSULTING ENGINEEK NEW YORK MCGRAW PUBLISHING COMPANY 239 WEST 39th STREET 1909 1> COPTHIGHT, 1909, BY ttcGRAW PUBLISHING COMPANY NEW YORK Stanbope iPrees H. G1LSON COMPANY BOSTON. U.S.A. To all who may find its contents useful, this book is respectfully dedicated. W.M. H, iii PREFACE. That this work is placed on the market at all is due prin- cipally to the lack of satisfactory, compact reference books treating on the subject in question. There are many excellent books of reference which treat the subject from a theoretical standpoint and deal largely with the growth and development of the internal-combustion engine. Many of these books, however, have not been brought down to date and, while beyond reproach as expo- nents of theory, fall far short in the matter of present practice and modern design. It would be well to supplement the use of this book with any one of several works on the gas engine, in order that the mathematical side of the subject may not be slighted. Works by Clerk, Hutton, and Donkin are particularly available along these lines. A complete knowledge of thermodynamics is invaluable for the perfect understanding of the theory of internal-com- bustion engines, one of the best text-books on this subject being "Thermodynamics, Heat Motors and Refrigerating Machines," by De Volson Wood. However, it has been the aim of this work to eliminate, as far as practicable, the more involved mathematical formulas and to confine the matter contained to the more practical and applied phase of the subject. In the chapter on "Com- pression" several thermodynamic formulas have been used to prove the relation of the compression to the thermal efficiency; these formulas, however, have no immediate bearing, except in a general way, on the problems of actual design and operation, but the formula PV = C, by far the most impor- tant formula used in the actual designing, is found and derived in this chapter, and its discussion is taken up in the following chapter on "The Indicator Card." vi PREFACE For practical information and data contained in this work the author is indebted, to a large extent, to different manu- facturers who have placed the result of practical tests at his disposal. It has been the intention to use only that infor- mation which appeared most reliable and in keeping with actual practice. In the matter of design, average practice has been con- sidered, and while the formulas given should not by any means be taken to give results in keeping with each and every engine on the market, their use will insure results closely in keeping with the average. The tables and formulas herein contained should fill all average requirements, either for the designer or the operator, and while neither original nor compiled especially for gas- engine practice (they may be found in any standard hand- book), the fact that they may be found here assembled should be of advantage. It is the desire of the author in issuing this book that it may find a place for itself and fulfill, in part at least, his intentions. WILLIAM M. HOGLE. Toledo, Ohio, December, 1908. CONTENTS. Introductory. PAGE History of internal combustion as a motive power 1 Development of internal combustion as a motive power 2 Fundamental working conditions 4 Chapter I. — The Beau de Rochas Cycle. Sequence of cycle 6 Description of cycle 6 Relation of card to cycle 8 Discussion of card 9 Chapter II. — The Clerk Cycle. Description of Clerk principle 11 Clerk and Day theories compared 11 The Robson engine 12 The Stockport engine 12 The Day engine 12 The Day cycle 13 Description of the Day cycle 14 Discussion of the Day card : 15 Chapter III. — The Diesel Motor. Fuel admission in Diesel motors 17 Temperature of combustion 17 Period of fuel injection 18 Compression space 18 Fuel economy 18 The Diesel cycle of operations 19 Relation of card to cycle 19 vii Viu CONTENTS Chapter IV. — Comparison of the Cycles. PAGE The four-cycle principle 20 Automobile motors 20 Marine motors 21 Comparative power development of two and four cycle engines. ... 21 Comparative fuel economy 22 The Diesel motor 22 Chapter V. — Practical Operation. Starting a stationary engine 23 Stopping a stationary engine 24 Starting an automobile or marine engine 25 Stopping an automobile or marine engine 26 Care of Engine. Cooling of engine cylinder 27 Ignition point 28 The bearings 29 The valves 29 The circulating water 30 Proper care of governor 30 Proper mixture for successful operation 31 Troubles and Remedies. Failure to start 31 Cylinder flooded 32 Carburettor out of adjustment 32 Spark weak or wanting 32 Engine stops 33 Ignition tube cold 34 Mixture too rich — Back firing in exhaust 34 Back firing in compression stroke 34 Water in cylinder 35 Engine smokes 36 Valves leak 36 Engine races , . , ', 36 CONTENTS. XX Chapter VI. — Starting Devices. PAGE Methods of starting 37 Starting cams 40 Chapter VII. — Carburettors, Vaporizers, and Injectors. Methods of securing explosive mixture 42 The carburettor 42 Requirements for successful carburetting of fuel 42 Carburetting alcohol '. 43 Carburetting petroleums 43 The vaporizer 43 The injector principle 44 The Hornsby-Akroid method of fuel injection 44 The Meitz and Weiss method of fuel injection 44 The Diesel valves and method of fuel injection 44 The Daimler carburettor 45 Mechanical ebullition 45 Surface carburettor 47 Spray carburettor 48 Mixing valves 49 The Schebler carburettor 52 The Holley carburettor 53 Alcohol carburettors 56 Carburettor design 57 Chapter VIII. — Producers. Pressure producers 58 Fuels available for use in pressure producers 60 Distilling producers 61 Quantity and heating value of gas from distilling producer 61 Combustion producers 62 Quantity and heating value of gas from combustion producers 62 The suction producer 62 Fuels available for suction producers 62 Operation of the suction producer 63 Comparison of steam and gas producer power plants 64 Gas analysis from suction producer 65 X CONTENTS. Chapter IX. — Fuels and Combustion. PAGE Gaseous fuels 66 Advantages of gaseous fuels 66 Natural gas compared with producer gas 66 Blast furnace gas 67 Heating values of fuels (tabulated) 68 Volumetric analysis of Pennsylvania gases (tabulated) 68 Analysis of gases 69 Liquid fuels 71 Petroleum distillates 71 Properties of petroleum distillates (tabulated) 72 Composition of crude oils (tabulated) 72 Gas oil 73 Gasoline 73 Kerosene 74 Heat of combustion 75 Measurement of heat 75 Air necessary for combustion 76 Air required for combustion of different fuels 77 Vaporization 78 Requirements for complete vaporization 78 Laws for perfect gases 78 Vapor pressure of saturation 78 Avogadro's law as applied to vapor pressure 80 Temperature necessary for a perfect mixture 81 Acetylene 82 Alcohol 82 Relative heating values of gasoline and alcohol 82 Power derived from alcohol as compared with that derived from gasoline 83 Cost of alcohol as compared with gasoline 83 Chapter X. — Compression. Limits to which compression may be carried 84 Compression temperatures (tabulated) 85 Ignition obtained by means of high compression 86 Derivation of the formula for the ideal indicator card 86 The theoretical card 87 CONTENTS XI Chapter XI. — The Indicator Card. PAGE What constitutes a perfect cycle in any given cylinder — How com- puted 89 The cams as related to the card 89 Values in general use for 7 91 The ideal indicator card 91 Computation of values for the ideal card 92 Determination of the constant for the expansion curve 93 Design of engine as related to ideal card 94 Chart for determining compression pressure 95 Chapter XII. — General Dimensions. The mechanical efficiency 97 Mean effective pressure 97 Average values of mean effective pressures 98 Determination of bore and stroke 98 The fuel factor 98 Mechanical efficiency of multiple cylinder engine 101 Chapter XIII. — The Cam Mechanism. Location of the cams 102 Transmission of cam motion to valves 102 Cams with lever transmission 103 Shifting of lever to bring starting cams into operation 104 Cams classified 105 Method of laying out single cam 105 The double cam 107 Application of double cam to vertical engine 109 Method of laying out double cam 110 Material necessary for cams Ill The Reduction Gearing. Types of gearing in use Ill Speed ratio in skew gearing 113 Adjustable gear 113 Fiber gearing 114 xil CONTENTS Chapter XIV. — The Valves and Ports. PAGE Mushroom valves 115 Effective valve opening 117 Design of inlet and exhaust passages 117 Determination of effective valve opening 119 Minor valve dimensions 121 Methods of setting valves 121 The suction inlet valve 124 Ports in two-cycle design 125 Design and location of two-cycle ports 126 The exhaust port lead 127 The third port 128 Chapter XV. — The Cylinder. The air-cooled cylinder 129 The water-cooled cylinder 129 Thickness of cylinder wall 130 Depth of water jacket 131 Thickness of outer water jacket wall 132 Copper water jackets 132 Length of water jacket 133 Design of cylinder to facilitate boring 133 Openings for inlet and discharge 133 Grinding of cylinder 134 Bolts 135 Material for cylinder castings 136 Chapter XVI. — The Flywheel. Function of flywheel 137 Calculation of weight of wheel 138 Design of flywheel 140 Table of keys 141 Chapter XVII. — The Frame. Purpose of frame 143 Advantage of heavy frame 143 Frame for horizontal engine 143 Frame for vertical engine 144 The crank-case engine 145 The sub-base 146 CONTENTS xiii Chapter XVIII. — Engine Foundations. PAGE Drawings for foundations 147 Advantage of good foundation 147 Material for foundation 147 Design of foundation 148 Foundation bolts 149 Laying out foundation (the bolt template) 150 Chapter XIX. — The Crank Shaft and Reciprocating Parts. Style of piston 151 Strength of crank shaft 151 Design of shaft and length of bearing 152 The balance weights 153 Determination of necessary weights 155 Crank shaft bearings and brasses 156 Oil rings 156 The connecting rod 157 The Piston, Wrist Pin, and Piston Rings. The wrist-pin bearing 159 The outer diameter of piston 160 Design and construction of ring 160 The two-cycle piston head 161 Chapter XX. — Governing Devices. Methods of governing 162 The governor controlling mechanism 163 Design of centrifugal governor 164 The simple fly-ball governor 166 The loaded governor 166 Devices for throttling 167 The inertia governor 168 Chapter XXI. — Ignition. Methods of igniting charge 170 Jump-spark ignition 170 Make-and-break system of ignition 171 xiv CONTENTS PAGE Non-inductive resistance and condenser 172 Connections for single cylinder with Ruhmkorff coil 173 Wiring diagram for four-cylinder engine 173, 174 Use of commutator 174 Types of make-and-break igniters 175 The commutator — how constructed 179 Types of commutators 179 The spark plug — Insulation, etc 181 Types of spark plugs 182 Dynamo ignition 183 The Apple igniter 183 The Bosch type of dynamo 185 The Motsinger sparker 187 The Remy magneto 187 Flame igniters 189 Barnett ignition cock 189 The hot-tube igniter 190 Auto-ignition 191 Time of ignition 194 Firing order for multiple cylinders 195 Chapteh XXII. — Engine Testing. Methods of testing 196 The Prony brake 196 Derivation of brake formula 197 Factors for Prony brake (tabulated) 200 The belt dynamometer 200 Testing with Prony brake 202 Log of test 204 Testing of gasoline, alcohol, and oil engines 206 Chapter XXIII. — Report of Tests. Form of report 207 Weight and specific heat of gases 209 The planimeter 211 Determination of the mean effective pressure 212 The heat balance 212, 213 Determination of brake horsepower 214 CONTENTS xv Miscellaneous. PAGE The muffler 215 Definition of units 215 Wire and sheet metal gauges (table) 216 Tap drill sizes (table) 218 Machine screw sizes (table) 219 Wrought iron pipe sizes (table) 220 Circumferences and area of circles (table) 221 Trigonometric functions (table) 225 Common logarithms (table) 233 INTEKNAL COMBUSTION ENGINES. INTRODUCTORY. The internal-combustion engine, as we have it in use to-day, is the result of more than two hundred and twenty-five years of experiment, during the greater part of which time, however, no advance was made over the original device produced in 1678. In that year the Abb6 de Hautefeuille used the explosive force of gunpowder as a motive power, deriving his work in exactly the same way as the modern internal-combustion engine, by the expansion and subsequent cooling of a volume of heated gas. Two years later, in 1680, Huygens, a Dutch savant, pub- lished a work describing an apparatus, suitably arranged with cylinder and valves, in which the explosion of gun- powder was made to force a volume of heated air into the cylinder, after which, the valve having closed, the gas became cool and soon fell to a pressure less than that of the atmosphere, causing the piston to be forced down by the excess atmospheric pressure. The apparatus as well as the operation was exceedingly crude and no very flattering results were obtained from its use. Later, about the year 1690, Papin continued the experi- ments of Huygens, attempting to find a substitute for the gunpowder, the operation of which was very uncertain. His experiments seemed to show very conclusively that the condensation of steam was the most suitable method of producing the vacuum required for the operation of the Huygens motor, and the process was used to some extent in the operation of pumping engines. Shortly after this time the discoveries of Watt turning 1 2 INTERNAL COMBUSTION ENGINES the attention of the public to the steam engine, the develop- ment along the lines of internal combustion ceased, and it was not until about the year 1791 that any suggestions were made which were improvements on the engine of Abb6 de Hautefeuille. In this year an English inventor, by name John Barber, took out a patent on the use of a mixture of hydrocarbon gas and air in an "exploder." In 1794 this patent was followed by one covering the production of an explosive vapor by means of a liquid and air. This patent was also taken out by an English inventor named Robert Street. In the year 1799 Philip Lebon, of Brachay, France, took out a patent on the principle as well as the construction of an engine using the explosion of coal gas as motive power. This inventor also took out patents on a pump for the compression of the explosive mixture and a machine, operated by the engine, for the production of an electric spark for igniting the charge. The career of this inventor terminating abruptly shortly after this time, and before he had developed his inventions, closed what might have been an epoch-marking period in gas-engine development. From 1799 until 1860, in which year the first practically successful engine was designed and built, several different schemes were advanced. One brought out by Wright in the year 1833 was very well developed from a theoretical standpoint, a governor being used in connection to vary the mixture of gas to make it proportional to the work being done and to regulate the compression of the charge. A double-acting engine produced by Johnston, and devised for the use of hydrogen and oxygen, two parts of the former to one part of the latter, was somewhat unique in its operation, and had it not been for the cost of the fuel would doubtless have been used quite extensively. The hydrogen being exploded, formed with oxygen a water vapor which on being cooled was precipitated and a partial vacuum formed, the unbalanced force of the atmospheric pressure then acting during the return stroke of the piston. INTRODUCTORY 3 In 1838 Barnett took out a patent covering substantially the same ground as did that of Lebon, two pumps being used to compress separately the gas and air and then force them into the cylinder. The explosion was produced by means of the so-called Barnett ignition cock, later described in Chapter XXIII on "Ignition." The use of the magneto as medium for producing the sparking current was suggested by Stephard in 1850. In the year 1857 Barsanti and Matteucci devised a motor with a very long cylinder fitted with a piston to which a rack meshing with a spur gear on the fly-wheel shaft was attached. On the explosion stroke a pawl allowed the rack to run freely, but on the return stroke the pawl engaged and the rack caused the spur gear and shaft to revolve. The explosion of the charge drove the piston upwards in the cylinder, and its inertia caused it to pass the point where the internal pressure was equal to the atmosphere and in con- sequence a vacuum was formed. The cooling of the exploded charge increased this vacuum, with the result that the piston was forced down with considerable force. In 1858 an engine was devised by Degrand in which the gases were compressed in the cylinder, but because of mechanical difficulties it did not meet with any success, although the idea was a forerunner of the engine of the present day. The appearance of the Lenoir motor in 1860 marked an epoch in gas-engine construction, as it was the first engine capable of comparatively regular and efficient work. The machine was constructed along the lines of a double-acting steam engine, the ignition was obtained by means of a primary battery and Ruhmkorff coil producing a jump spark, and altogether it was a very decided advance over all existing forms of gas engines up to that time. But the Lenoir engine was uneconomical, requiring about 100 cu. ft. of gas per hp.-hr. and four times as much water for cooling as was used in a steam engine of like power. The great heat in the cylinder required that the piston be kept flooded with oil. In view of these several difficulties the Lenoir engine 4 INTERNAL COMBUSTION ENGINES disappeared in a very short time, but not before it had stirred the minds of the inventors to renewed activity along the lines of the internal-combustion engine. In the same year, 1860, Hugon introduced a motor in which he attempted to keep down the temperature of the cylinder by means of the, injection of a spray of water. This engine was more economical in the consumption of gas, requiring a trifle more than 80 cu. ft. of gas per hp.-hr., and the temperature of the exhaust gases was appreciably diminished. Several other ideas were advanced about this time, all of them being either of minor importance or repetitions of previous attempts. In the year 1862 M. Beau de Rochas took out a method patent setting forth, theoretically, the best working conditions for an internal-combustion engine. His cycle of operations was in all respects the same as that in use at the present day in the so-called Otto-cycle engines. The following propositions were embodied in his patent: 1. The largest cylinder capacity with the smallest circumferential surface. 2. Maximum piston speed. 3. Greatest possible expansion. 4. Greatest pressure at beginning of working stroke. While the honor of promulgating the theory belongs, beyond a doubt, to M. de Rochas, he did not in his patent set forth any means for producing the theoretical proposition in practice, and, owing to irregularity in the proceedings, his patent became public property soon after the application was filed, but not until 1878 was attention again called to it. In that year the Otto gas engine, substantially as it now appears, was first placed on the market. Previous to this time, about the year 1872, Otto, in connection with Langen, placed on the market the so-called Otto and Langen engine, of which, due to its comparatively economical opera- tion, they were enabled to sell quite a large number, notwith- standing the fact that it was of the free-piston type and exceedingly noisy in its operation. Its gas consumption INTRODUCTORY 5 was about 26 cu. ft. per hp.-hr., and the cost of energy produced was somewhat less than with the existing steam engines. Continuing his experiment, Otto, in 1878, produced and placed on the market the first four-cycle engine operating on the Beau de Rochas cycle but commonly known as the Otto cycle. This engine was almost immediately adopted as the standard type of internal-combustion motor, the perfection of which has been the problem of designers. In 1879 a modification of this engine was produced by Dugald Clerk and formed the basis for present-day two- cycle engine practice. In the Clerk engine the charge was compressed and exploded once every revolution, as against one explosion every two revolutions in the engines of the Otto type. Since the year 1880 several motors of greater or less value have been placed on the market, but without exception they have disappeared, and at the present time the engines of the four-cycle and two-cycle types, with greater or less modifications, hold the field. CHAPTER I. THE BEAU DE ROCHAS CYCLE. Reference to Fig. 1 will explain fully the Beau de Rochas or Otto cycle, the four strokes of which are designated as follows: 1. Suction; 2. Compression; 3. Explosion; 4. Exhaust. The four strokes as above enumerated form the basis for the term "four-cycle" as applied to gas-engine practice. Hr%W- Fig. 1. The Four-Cycle Principle. In the figure, A represents the cylinder, B the piston, C the inlet valve, and D the exhaust valve. An ideal indicator card has been placed directly above that part of the cylinder comprising the piston displacement, in order to facilitate the explanation of the cycle of operations. The projected path of the crank pin has been divided into ten equal spaces, as has also the path of the piston. From this latter set of points ordinates have been erected and the indicator card drawn. On the indicator card reference points have been G THE BEAU DE ROCHAS CYCLE 7 indicated by small letters; corresponding points on the crank circle are indicated by the same letters with the subscript c. Outside the crank circle two larger circles have been drawn on which the cycle of operations is shown. The inner circle represents the suction and compression strokes and the outer one the explosion and exhaust. On the suction stroke the port, C, opens as the piston travels from a' to b', as shown on the indicator diagram from a to b. Unless valves C and D are sufficiently large, point, a, on the suction line would tend to be slightly above atmosphere and point, b, would tend to be slightly below, due to the resistance of the ports to satisfactorily supply the charge and remove the products of combustion. Especially would this be true on high-speed engines. These results are generally present, to a greater or less extent, in most engines placed on the market. It is obvious that in the different designs of engines the proportion of the ports and valves will vary, and for this reason these defects, in the card, are quite pronounced in some, while in others the suction and exhaust lines will be found to follow very closely the atmospheric line. The carburettor may also be a factor in determining the suction line of the card, as it is apparent that one with a capacity too small for the cylinder displacement cannot supply a full charge under all conditions. It would then appear that a suction line whose initial point, a, was above and whose terminal point, b, was below the atmosphere, would indicate that either the engine valves were too small to do their work in a satisfactory manner or that the carburettor was not sufficiently large. On the compression stroke the piston moves from b' back toward a', as shown on the indicator diagram, from b back to an indefinite point i on the compression curve, be, or to i c on the crank circle, at which point the compressed charge is ignited, the pressure rising rapidly to the maximum, which should be just as the engine passes dead center at a'. As the combustion of the gases is more or less slow, the igni- tion point is, of necessity, given a positive lead in order to obtain this result. As the velocity of the piston increases 8 INTERNAL COMBUSTION ENGINES it is obvious that the igniter lead must be increased in order to give the charge sufficient time to burn and reach its maximum pressure at dead center. If a card shows a shape as at d, Fig. 2, it would indicate that the ignition was not sufficiently advanced, in consequence of which the maximum pressure is not reached until the engine has passed its dead center. The expansion line being nearly an adiabatic, a loss of energy necessarily results. The pressure at release is correspondingly higher, as shown by comparison of the dotted expansion curve of Fig. 2 with that shown in full line, but the mean ordinate is decreased, owing to the fact Card showing Late Ignition. that the maximum pressure is not developed until after the piston is in the working stroke, and as the ordinates, diminished in length by this late ignition, appear in that portion of the stroke where the pressure is highest, they affect the value of the mean ordinate most. On the expansion stroke the piston again moves from a' toward V , or, as shown on the indicator diagram, from d to e, and on the crank circle the pin moves from to e c , at which point the exhaust port opens, allowing the expansion curve, which up to that point, according to Thurston, is nearly an adiabatic, to drop off quite suddenly nearly to atmosphere. In effect, then, the exhaust takes place from e to /. The location of the release, e, varies considerably in different makes of engines, the theoretically correct point THE BEAU DE ROCHAS CYCLE 9 being so located that the cylinder pressure would fall very nearly to atmosphere just as the engine passed the forward dead center in order that there should be no great amount of back pressure at the beginning of the expulsion stroke; on the other hand, the release must not take place too early in the expansion stroke, as this would seriously impair the power as well as the heat efficiency of the engine. Fig. 3. Card showing Inertia Effect of Governor Spring. Changing the point of release may be made the basis of one type of governing device (see Chapter XXII). If the effective area of the exhaust valve is not amply large, then point, /, will not be down to atmosphere, and on the expulsion stroke, as the piston again moves from b' back to a', the line of the card, fa, may be slightly above atmos- phere all the way. In well-designed engines these effects are seldom encountered to an appreciable extent, but the possibility of their occurrence makes it necessary to guard against conditions that would tend to produce these results. This completes the theoretical cycle of operations in the four-cycle engines. In practice the gas-engine card is much distorted, owing to the sudden variations in pressure which take place. The explosion line will be found to run higher in some cases than the maximum theoretical pressure of the burning gases, due to the inertia of the indicator parts. This trouble may be in part remedied by the use of a heavier spring. When the explosion pressure as 10 INTERNAL COMBUSTION ENGINES indicated by the card is too high, the expansion line will as- sume a ragged outline, due to the harmonic motion of the spring in overcoming the effect of the inertia. This ragged appearance may continue until well into the next compression stroke. CHAPTER II. THE CLERK CYCLE. The Clerk cycle engine, more commonly known as the two-cycle engine, as previously mentioned, was first intro- duced by Dugald Clerk about the year 1879, and was the first of the compression motors built, receiving an impulse every revolution. In the Clerk motor its inventor introduced the charge into the cylinder under compression, as is done in the present types of two-cycle engines. Instead of obtain- ing his primary compression in the crank case, as is the modern practice, he used an auxiliary pump. The exhaust ports were arranged in the cylinder wall, being uncovered by the piston on its downward stroke, the inrush of the compressed charge expelling the products of combustion in practically the same manner as this is accomplished in the later two-cycle engines. This type of motor was composed of two cylinders, one the power cylinder and the other the primary compression cylinder. The primary cylinder com- municated with the explosion cylinder at the top of the compression space, and herein differed from the present type, in which the charge is introduced through a port very nearly in line with the exhaust port; it being uncovered, with the exhaust port, by the downward stroke of the piston. The theory of the Clerk engine is the same as that of the Day two-cycle (i.e. introduction of the charge under com- pression), but the added number of parts with the consequent addition of weight and complexity is a feature which made this type of engine impracticable for general use, more especially where a light motor is required; and as nothing is gained, in its construction, over the Day type, the balance is all against it. Nevertheless the honor of first describing the two-cycle principle must be accorded to Clerk and the practical improvements and application to later inventors. 11 12 INTERNAL COMBUSTION ENGINES The Robson Engine. A forerunner of the Day type of motor was the Robson engine, manufactured by Messrs. Tangye under Robson's patent. In this engine the cylinder was closed at both ends and used a piston rod. The forward end of the cylinder was used for obtaining the primary compression, the charge being drawn in on the suction stroke and compressed during the greater part of the explosion stroke, and the gas thus compressed was forced into the power cylinder through an automatic lift valve, which operated when the piston was fully out and the exhaust valve wide open. This charge was then compressed by the return stroke of the piston and exploded as in the ordinary two-cycle motors. Two valves were necessary in this engine, an automatic valve for admitting the charge to the primary compression chamber and one opening from this space into the power cylinder. The engine was of rather neat design and not nearly as cumbersome as the Clerk production. The Stockport Engine. This engine was exactly similar in principle to the Robson engine, but the forward end of the cylinder was not utilized to obtain the primary compression. The engine was similar in design to the two-cylinder opposed motors of the present day, one cylinder being used for the primary com- pression, while the other was used for the power cylinder. Several other types of engines were evolved and placed on the market about this time, but the most of them were either too cumbersome or too complicated to meet with gen- eral use, and the Day cycle proper has almost, if not quite, displaced these earlier types. The Day Engine. As the Day engine is the analogue, in two-cycle construc- tion, of the Otto engine in four-cycle design, a complete description of it will be given. In the description of the Day engine and cycle we are describing, in principle, the original Clerk idea. THE CLERK CYCLE 13 Referring to Fig. 4, A represents the cylinder, B the piston, C the inlet valve, and D the connection between the crank case, in this instance the primary compression space, and the power cylinder. An ideal indicator card has been placed directly above that part of the cylinder comprising the piston displacement, in order to facilitate the explanation of the cycle of operations. The projected path of the crank Fig. 4. The Two-Cycle Principle. pin has been divided into equal spaces, as has also the path of the piston. From the latter set of points ordinates have been erected and the indicator card drawn. On the indicator card reference points are indicated by small letters; corresponding points on the crank circle are referred to by the same letter with the subscript c. Outside the crank circle another larger circle is drawn, on which the cycle of operations in the cylinder is shown; on a still larger circle the cycle of operations in the crank case is shown. Directly above the projected path of the crank pin the crank-case indicator card has been constructed, the points of reference being indicated by the letters x and y with suitable subscripts. 14 INTERNAL COMBUSTION ENGINES On the suction stroke the piston travels from b' toward a', or, as shown on the crank-case indicator card, from x toward y. Just as the forward end of the piston passes point P, the inlet valve, C, starts to open. A vacuum has been produced in the crank case up to this point, by the piston traveling upwards in the cylinder, and in consequence when this port commences to open a charge of gas rushes in from the carburettor, F, and continues to flow until the vacuum in the crank case is entirely balanced or until the piston on the return stroke completely covers the port, C. At x on the crank-case indicator card the suction line would tend to be slightly above atmosphere, due to the fact that the opening D between the crank case and the cylinder, when uncovered by the piston head on its forward stroke, will not, in all probability, allow the passage of enough of the compressed charge in the crank case to the cylinder to bring its pressure down to atmosphere. Then on the back stroke of the piston, the crank-case space being enlarged, the pressure falls, until, when the forward end of the piston uncovers port, C, at y on the crank-case card, a considerable vacuum has been produced. The charge rushing in through port, C, causes the line of the card to rise as the pressure in the case is increased, and when, on the forward stroke, the port, C, is again completely covered, the card should show a pressure of about atmosphere as at y 2 . If port, C, is too small, this will not be the case, but the point y 2 will still show a slight vacuum, which will necessarily affect the maximum crank-case compression at x 1 when the piston head uncovers port, D. From y 2 to x t on the card the pressure should rise regularly until at x l the pressure should be maximum, which should be from 6 to 10 lb. per sq. in., in no case less than 5 lb. per sq. in. At this point, port D being opened by the piston, the pressure line com- mences to fall, and continues to do so until the pressure is equalized on both sides of the piston, or until the piston on its return stroke again closes valve, D (shown at point, or,, on the indicator card). Since the displacement of the piston is the same on the THE CLERK CYCLE 15 cylinder end as on the crank-case end, the charge taken into the crank case on the suction stroke should exactly fill the cylinder space, and the pressure at ,t, should be equal, in pounds, to the vacuum at y x . But it is practically impos- sible to so proportion the ports that they will produce these results at all speeds, unless they are made abnormally large. This is especially true in the three-port type of engine here described. The charge introduced into the crank case on the suction stroke does not vary with the speed at which the engine is running, as the vacuum produced will not vary to any considerable extent except as the increased speed of the piston gives less time for leakage of air into the crank case before the inlet valve opens, consequently on slow speeds the port being open longer allows a larger charge to rush in. This accounts for the inability of some two-cycle motors to run at high speeds and deliver power in proportion. As noted, these conditions are more noticeable in the valve- less engine than in the engines using a poppet valve for the inlet port, as indicated at G, Fig. 4, in which case inlet port, C, is not used. In this construction it is always possible to get a full crank-case charge with a correspond- ingly higher pressure at x u but we are still confronted with the difficulty of making port D large enough to give a full charge at all speeds, but, as pressure x is greater, the flow will be somewhat more rapid. It is probable, however, that this advantage is sufficient to make the balance favor the engine with the valve over the more simple three-port engine; in fact many manufacturers have tried and dis- carded the three-port type. The crank-case card for the two-port type is shown in Fig. 4 below the crank case. Having followed through the cycle of operations in the crank case, let us look at the operations taking place in the cylinder. On the cylinder indicator card let a represent the point of opening of the exhaust port, E, b the opening point of inlet port, D, c the point of closing for inlet port, D, and d the point of closing for exhaust port, E. On the forward stroke of the piston B, the charge having 16 INTERNAL COMBUSTION ENGINES been exploded, at point a on the card the piston head commences to uncover exhaust port, E. At this point, then, the pressure of the expansion line falls off rapidly, forming some such a break in the card as is indicated. At point, B, on the indicator card the port from the crank case into the cylinder commences to open; at this point, b, it is obvious that the pressure of the exhaust gases in the cylinder should have fallen to such an extent as to make the cylinder pressure less than that of the crank case, otherwise the cylinder will exhaust back into the crank case and cause what is known as back firing, with consequent loss of power. For this very reason the exhaust port is given a lead over the inlet port, varying to some extent in different two-cycle designs (see Chapter XVI). From b to c on the indicator card the crank-case charge rushes through port, D, to fill the cylinder space. A baffle plate, G, is placed on the piston head to deflect the incoming charge to the top of the cylinder, so that it may more effectively force out the burned gases without being exhausted itself. At point, d, the exhaust port closes and the cylinder compression commences. The charge is compressed from point, d, up to the point of ignition, which of course is varied for different speeds by the spark-timing device. From e to / the explosion takes place and the expansion follows from /back to a. In two-cycle work the following points should be striven for: 1. Quick exhaust, with consequent large exhaust port. 2. Unrestricted exhaust port. 3. Crank-case compression high enough to make the primary pressure greater than the cylinder pressure when the inlet port opens. 4. As large inlet ports as possible. 5. As long a compression and expansion line as possible. A little study of the card will serve to show that some of these points must necessarily be sacrificed, to a greater or less extent, in order to attain the others. The expansion line must be shortened in order to give sufficient exhaust period, and a shortening of the expan- sion line produces a corresponding shortening of the com- pression line. The most satisfactory arrangement of these several points will be taken up later in the design. CHAPTER III. THE DIESEL MOTOR. While the cycles of Beau de Rochas and Clerk cover, in the broadest sense, all modern practice along the line of internal-combustion engines, at least one other engine has been produced and placed on the market which, while it utilizes the four-cycle principle as a basis for its construction, has made use of a different method for obtaining its fuel charge. This engine was the invention of Rudolph Diesel, a German scientist and inventor. The cycle requires two revolutions of the crank shaft for its completion; the first outward stroke of the piston draws into the cylinder a charge of pure air instead of combustible mixture, and on the following return stroke of the piston this charge is compressed to a pressure of about 500 lb. per sq. in., at which pressure its temperature is sufficient to ignite any form of crude or refined petroleum. When the piston has reached the top of the compression stroke the fuel valve opens and a charge of vaporized fuel is injected into the incandescent cylinder by means of air compressed to about 800 lb. per sq. in., but cooled before it reaches the fuel valve. It is the intention to maintain the temperature of combustion constant at the temperature of compression, thus allowing the pressure to fall in accordance with the laws for expansion at constant temperature, or, in other words, to make the combustion curve as nearly as possible an isothermal, this being the curve of maximum economy for an internal-combustion engine. It is obviously impossible to obtain this result except when the engine is running under very nearly normal conditions. When the engine is overloaded and the amount of fuel is increased by means of the governor, the tempera- ture will rise above that of compression, in order that the 17 18 INTERNAL COMBUSTION ENGINES mean effective pressure may be higher, while with a light load the temperature and pressure will fall, due to the quantity of fuel being less. After the period of fuel injection, which comprises about 10 per cent of the working stroke, is completed, the fuel valve closes and the ignited charge expands until 90 per cent of the working stroke has been completed, at which point the exhaust valve opens in order to relieve the pressure before the expulsion stroke commences. The manufacturers claim their pressure at exhaust to be about 35 lb. per sq. in. for normal load, which pressure would necessarily be in- creased or diminished as the engine was operated at over- load or running light. The fourth stroke in the cycle is the expulsion stroke during which the piston, traveling upwards with the exhaust valve open, ejects the burned charge. In the Diesel cycle there is no opportunity whatsoever for premature explosion, since the fuel is not injected until the beginning of the working stroke. The high compression and correspondingly small compression space, about 7 per cent of the cylinder volume, make it possible to eject nearly all of the burned. gases and to secure a charge of almost pure air to support the combustion during the working stroke. The fuel economy, with the theoretical conditions attained, would necessarily be high, and actual results seem to prove this to be the case. There is some question, however, as to the wear and tear resulting from the heavy parts made necessary by the long-sustained high compression. This high compression causes the temperature in the cylinder to approximate for a much longer period the temperature of combustion, but as this temperature of combustion is much lower than in most internal-combustion engines, it is probably true that the parts subjected to this heat are not damaged to any appreciable extent, and it is doubtful if the long-sustained compression would be more harmful than the suddenly applied pressure induced in engines operating on the Otto principle. Fig. 5 will explain fully the cycle of operations taking THE DIESEL MOTOR 19 place in the Diesel engine. The same arrangement of diagram has been followed in this as in the previously described cycles. xa represents the clearance. ab represents the stroke. The stroke is divided into ten parts by the ordinates 0-10, as shown. In the engine diagram v u v.,, and r 3 are respec- tively the inlet, exhaust and fuel valves. On the first for- Fig. 5. The Diesel Principle. ward stroke of the piston, from a to b, occurs the suction of pure air, valve, v lt being open. On the backward stroke of the piston the air is compressed, following the curve be on the card, all the valves being closed. On the second forward stroke of the piston, from cd on the card, the fuel valve, v 3 opening, the fuel is injected. The curve cd, as previously described, h an approximate isothermal; at d a break occurs, as the fuel valve is closed ; and from d to e, or during about 80 per cent of the working stroke, expansion takes place. At e, the exhaust valve, v 2 , being opened, the pressure falls and reaches atmosphere at 6; and from 6 to o during the expulsion stroke, on the second backward stroke of the piston, the products of combustion are discharged. CHAPTER IV. COMPARISON OF THE CYCLES. The four-cycle engine has found most favor with the general public, and in consequence has been most widely manufactured. In stationary engine practice this design is in almost universal use, although there are some two-cycle engines in use for this class of work, and it seems that they are gaining some headway. There are several good reasons for the two-cycle engine not gaining general popularity as readily as the four-cycle. For stationary engines, the question of lightness of parts, or of the complete engine, plays no important part, the design tending more strongly toward stability and weight, within reasonable bounds. As the weight is no inducement, the engine which can be most readily controlled, which is most certain in operation, and most economical in fuel consumption, gains precedence. These three important points are found in the four-cycle type of engine with all valves mechanically controlled and all working parts reduced to a scientific and mechanical basis, when, with the quality of fuel known, the cycle of operations, with the resulting power delivered, may be depended on as unvarying, pro- vided, of course, that ignition is insured by means of a perfect sparking device. In automobile engines the four-cycle type, while not universally adopted, is used in the very large majority of cases, but in a somewhat modified form. Here the different manufacturers have striven to create a machine with the greatest power and the least weight; in other words, they try to make the weight of the engine per horsepower as low as possible. To accomplish this many manufacturers use the suction inlet valve, but not to as large an extent as 20 COMPARISON OF THE CYCLES 21 formerly, the mechanically controlled inlet and exhaust being looked upon with more favor at the present time, due to the fact that the suction inlet has not, in all cases, given universal satisfaction, and in fact was quite unsatis- factory in many instances. In marine-engine practice probably about an equal number of two and four cycle engines are manufactured and sold. The two-cycle type is more satisfactory for marine use than for any other purpose, as the necessary amount of cooling water is more readily available. Since in the two-cycle type of motor, an impulse or explosion occurs at every revolu- tion, it naturally follows that the cylinder heats up more rapidly than in the four-cycle type, in which the impulse, occurring only once every other revolution, gives the cylinder more chance to cool. While the two-cycle engine grows hotter, due to the more frequent explosions, it should produce more work and steadier power for the same reason. This will be found to be the case, if the ports are properly proportioned; but no two-cycle engine ever built could produce twice as much work for the same number of revolutions, at all speeds, stroke and bore being the same, as a four-cycle engine. The reason for this is found when one tries to proportion the ports for a gas speed of 100 ft. per sec. for the inlet and 90 ft. per sec. for the exhaust and finds that the ports must necessarily be quite large to admit a full charge at 800 rev. per min. and under the most favorable conditions, that is, with the cylinder completely scavenged of the previous charge and the carburettor sufficiently large and properly adjusted to allow a full charge to enter the crank case on the suction stroke. In the majority of two-cycle engines the ports are made much smaller than they should be, even for their nominal speed, with the result that when the speed is increased the charge is very greatly diminished. At speeds where the four-cycle engine would obtain a full charge of gas it is probable that a two-cycle motor does not obtain much more than half a charge, and as the speed is further increased, even less than that amount. It is doubtful 22 INTERNAL COMBUSTION ENGINES if the average two-cycle motor does more than 30 per cent more work than a four-cycle motor of the same size, both operating under most favorable conditions. The two-cycle motor is more wasteful of fuel than the four- cycle type, and trouble with crank-case explosions is frequent, due to the explosion following back into the crank case when the crank-case compression is lower than the cylinder pres- sure as the inlet port opens. This may be obviated, in a large measure, by placing a screen baffle plate in the inlet passage; the screening acts on the principle of a Davy miner's lamp. The baffle plate must be a close fit, however, to be effective, and must be inclined in the passage, so that the meshes, through which the gas passes, may be equal in area to that of the port itself. The Diesel motor is gaining some favor as a prime mover in power plants. Its performances, as far as known, are excellent, its manufacturers claiming the exceptionally high efficiency of 38 per cent. The engines are accompanied by a guarantee, as to fuel consumption per horsepower-hour, good for one year from the date of installation. The question of first cost and the necessarily heavy parts possibly inducing an extraordinary amount of wear, are, as a general rule, the most serious obstacles to prospective purchasers. However, reports from plants in actual operation tend to show that the manufacturer's guarantee is none too high. In fact, some operators claim their fuel consumption to be below the manu- facturer's guarantee. The municipal lighting and waterworks plant of Bryan, Ohio, report that their motors have given not the slightest trouble from regulation or wear, and that they have made runs of a month at a time without stopping.* *The author is indebted to Mr. S. L. Folk of Bryan, Ohio,- for the information in regard to the practical operation of the Diesel motor. CHAPTER V. PRACTICAL OPERATION. Starting a Stationary Engine. — Starting a gas engine is in most cases a simple operation, if a few rules are remembered. A gas engine will not start without it obtains enough initial power from some outside source to enable it to com- mence its cycle of operations. The mixture of fuel and air must be neither too rich nor too poor in fuel, for if either of these conditions obtain, an explosive mixture will not result. In starting a stationary engine by hand, or in fact any other way, the ignition should be given a negative lead, or, in other words, the sparking point should be past the upper dead center in the direction in which the engine is running. Failure to note this important point will result in back firing, with more or less disastrous results. Compression should be relieved and the load thrown off, unless a powerful starting device is used, as, for instance, the compressed-air system. Always be sure that the engine is well oiled, and the oil cups are filled. See that the ignition apparatus is in good order and the sparking points clean, if electrical ignition be used. If the fuel used is clean and burns without producing a large amount of soot and crust, the sparking points will remain clean much longer than if a dirty fuel is used. Use a cylinder oil with a high flashing point, in order to obtain the best results, as an oil which flashes at a low temperature will assist, very materially, in fouling a cylinder. A foul spark- ing device cannot be made to yield good results. Be sure that all wiring connections are close and clean and that the batteries and coils are in good working order. 23 24 INTERNAL COMBUSTION ENGINES If a hot tube igniter is used, bring the tube to a cherry- red heat and adjust the flame to maintain this temperature. If the engine has a starting cam (a double cam acting on the exhaust valve and serving the same purpose as a relief cock), it should be thrown into starting position. If the engine is provided with a relief cock, instead of the cam, open the cock. Set the igniter to the proper starting position and open the valve in the gas supply pipe about one-quarter full, or possibly a little more. Now give the engine an impulse, and, as soon as it begins its cycle of operations, commence slowly to open the gas valve and continue until the engine is getting its maximum supply and is running at its regular speed. Do not open the valve too rapidly, or the engine will get too much gas, and in consequence too rich a mixture; it will soon slow down and stop. While the valve is being opened, the relief valve mechanism may be thrown out of gear, or the relief cock closed, and the spark or ignition device advanced to running position, unless a governor acting on the igniter mechanism is used. When the engine is well started, the load may be thrown on and the water turned into the water jacket until the discharge water is at a temperature of from 160 deg. fahr. to 180 deg. fahr., for stationary engines of low compression. For high-compression engines, a somewhat lower temperature is necessary. If the engine is provided with a starting device, allow it to make several revolutions before opening the gas valve. (See later chapter on "Starters.") As soon as the engine is running well, inspect all oil cups and make sure that they are feeding properly. Stopping. — To stop a gas engine turn off the gas valve, and if it is desirable to stop the momentum of the flywheel, a friction brake, in the shape of a plank, may be made to press against its rim, by placing the stick against the floor or other available fulcrum, and prying against the rim. Turn off the oil and water supply and turn off the flame in the hot tube igniter, if one be used, or if electrical ignition PRACTICAL OPERATION 25 is used, turn off the switch. If there is the slightest danger of the jacket water freezing, or if the engine is to be left any length of time, drain the jacket. A little care in this direc- tion will often prevent a crack in the water jacket. Starting an Automobile or Marine Engine. — The same general rules apply in the starting of these machines as in the starting of a stationary engine. However, they are, in nearly all cases, turned over by hand until the cycle of operations is established, and they are always found to be far more erratic in their action than the stationary engine, due largely to the varying mixtures obtained from the carburettor. This mixture, under different atmospheric conditions, varies to such an extent that, where one day a machine may be started with a single cranking, on another day, or even a few minutes later, with the same adjustment of the carburettor, it will not start at all. Of course trouble in starting may not always be due to the carburettor: the wiring connections may be poor, a battery connection may be broken, the sparking coil may be out of adjustment or the points corroded, or the batteries may be weak. The gasoline, not infrequently, is of poor grade; personally the author has encountered gasoline containing more than 50 per cent of water, although this condition was, of course, extreme. By filling the gasoline tank through a funnel, chamois skin lined, this latter difficulty may be obviated, as gasoline passes through and the water does not. In starting, the following mode of procedure should be carried out. Retard the spark advancing lever to a point beyond dead center, in the direction which the engine runs, open the gasoline supply valve, if such an arrangement is provided, or, if the machine is supplied with a pump, give it three or four strokes. See that the clutch or transmission lever is in neutral position, or, if a foot clutch mechanism is used, see that it is thrown out of gear. Close the sparking circuit, either by inserting the plug or by throwing the switch. 26 INTERNAL COMBUSTION ENGINES Open the oil supply valves. Now give the engine a few turns with the starting crank, and, if it fails to start at once, try priming the carburettor; this will usually solve the difficulty; but if it still fails to start, prime the cylinder, through the priming cup usually provided, using care not to use too much gasoline; a few drops is sufficient. Failure to start at once, after these attempts, shows that the cylinder either is getting too rich gas, or is flooded, or that some other part is out of order. (Troubles and remedies are more fully discussed later in this chapter.) There are two ways of starting a two-cycle marine engine. One way, the engine is turned over the same as a four-cycle until it takes up its operation. The other way, and the one most frequently employed in small engines, is to work the flywheel back and forth to get a charge into the cylinder, then with the sjDark retarded in the direction in which the engine is to run (a two-cycle engine is reversible), turn the flywheel sharply back against the compression, until it sparks, instead of turning it over dead center. The same difficulties in starting are found in the two-cycle engine as in the four-cycle type. When the engine, either automobile or marine, is well started, gradually advance the spark, and open the throttle to running position; as this is a variable quantity in these types of engines, no fixed rule can be given, but do not open out too quickly; give the engine time to "catch up." Always be sure that the engine circulation is good and that the oil supply is working properly; too much oil is bad, but too little oil is worse. Stopping. — To stop an automobile engine, throw off the spark or close the gas supply, shift the transmission into neutral and apply the transmission brake. After stopping the engine, close the oil supply valves, if a force lubricator is not used, and, if the machine is to be left any length of time, remove the plug from the coil or throw off the switch. In stopping a marine engine, the propeller acts as a brake, PRACTICAL OPERATION 27 and it is only necessary to throw off the spark or close the gas supply. The same general rules apply to closing the oil valves and leaving everything about the engine ready to start again. Care of Engine. As a matter of fact, a gas-engine plant requires less atten- tion, by far, than a steam plant of the same size. However, the gas-engine owner or operator should not confuse this statement, or similar statements, into meaning that a gas engine requires no attention and will "run itself" after starting. A stationary gas engine should have its regular attendant, who, while he need not give his entire attention to the engine, should be depended on to see that it is always in good running condition. A gas engine should always be as clean and as well oiled as a steam engine, and it should always have a sufficient supply of jacket water to maintain a uniform temperature of from 170 deg. fahr. to 180 deg. fahr. It is of importance that the temperature of the cylinder be kept uniform, especially in the case of an engine running electrical machinery, as variations in temperature may be readily detected in the operation of the engine. In order to main- tain a uniform temperature, the pressure of the water at the jacket must be kept constant. One of the best ways to accomplish this is to depend on the water pressure of a uniform head of water instead of direct pressure from the circulating pump. This may be accomplished by pumping the water first to an elevated tank and allowing it to circulate from there to the engine and then to the pump, from which it is again pumped to the tank. Suitable means for cooling should be provided, either in the shape of a cooling tower or other device by which the temperature of the water may be lowered as rapidly as possible. It is always advisable to use the cooling water over and over, since, after two or three circulations through the jacket, it will be "broken, " that is, the lime or other impurity contained will have been precipitated; frequent renewal of the jacket water will 28 INTERNAL COMBUSTION ENGINES quickly cause a crust to form in the jacket or sediment to lodge at some point, at which place a "hot-spot" will be produced. If, as is sometimes the case, the exhaust valve is provided with means for circulating the water through it, the water passages should be drilled out as often as once a week in order to insure their remaining open to circulation. The exact point of ignition should be known, so that, in starting, the engineer may know when to expect the explo- sion; also the sparking device may, for some reason, become out of adjustment, or it may be necessary to remove it for repairs. With a make-and-break electrical ignition system, this point may be determined as follows: slowly turn the engine over until the igniter snaps, at which point the spark is produced. Now, without moving any part, make corre- sponding points on the flywheel and frame or on the piston and cylinder, the latter way being most desirable if possible. It is obvious, then, that the engine may, at any time, be turned to its sparking point, even though the igniter is removed; that is, it may be turned to the exact distance from dead center where the ignition occurs; but here, in the four- cycle engine, a difficulty confronts us: we must be sure we are in the explosion stroke and not in the suction stroke. This may be most readily determined by inspecting the cams. If both cams are down, then both valves are closed, and we are all right ; but if the inlet cam is just commencing to raise the valve, we are in the suction stroke and must turn the engine over one complete revolution until the reference marks again correspond, at which point the sparker may be set to snap. All first-class engines, when they leave the shop, should have their valve and spark positions marked; and these marks, together with printed instructions, should enable any average mechanic to reset the valve or igniter mechanism. The care of the ignition mechanism is an all-important part in the operation of a gas engine. Electrical devices, if properly cared for, give excellent satisfaction, while if PRACTICAL OPERATION 29 allowed to become dirty or out of adjustment they will give very poor satisfaction. Be sure that the connections are clean and close and that the battery, if one be used, is not allowed to run down. It is good practice to have two sets of cells connected up with a switch, by means of which either set may be thrown into circuit. If a tube igniter is used, the best material that can be purchased is none too good. Nickel alloy or porcelain with- stands the action of the heat and gases best, and, with ordinary care, a tube of either of these substances will last a comparatively long time, while an iron tube needs to be replaced every few days. Several tubes should always be kept readily available so that, in case of accident to one, another may be quickly substituted. The tube should be kept at the very lowest temperature at which the gas will ignite and should never be hotter than a cherry-red. In practice, some gases will be found to inflame more readily than others as the quality is richer or poorer. The bearings and running parts of a gas engine should be well lubricated with a good grade of machine oil, but the cylinder should be lubricated with a gas-engine cylinder oil of high flashing point, or otherwise the carbonized oil produced will soon choke the passages, prevent the valves from seating, and, becoming incandescent, cause premature ignition and back firing. In any event the exhaust passages should be cleaned occasionally to prevent any possible accumulation from reducing their effective area, thus producing a back pressure and reduction of power. The valves should be frequently examined and ground in with flour, emery and oil, if they leak ever so little. The valve- stem springs should be stiff and strong; if they become weakened it is not always necessary to replace them, but they may be removed and stretched to increase their strength. The few engines that use the suction inlet observe the reverse of this rule, and in their case the valve spring should only be strong enough to properly seat the valve, so that a small vacuum, in the cylinder, will open it quickly. The seat for a suction-inlet valve must always be perfect, 30 INTERNAL COMBUSTION ENGINES since the pressure of the spring is not sufficient to exert any appreciable grinding effect. Never turn the circulating water into a hot cylinder too rapidly, or the sudden cooling of the walls may cause them to contract, while the piston is still hot and expanded, with the result that the piston sticks and cuts the inner surface of the cylinder. A ring cut, once started in the cylinder, will grow until the compression of the engine is ruined and its power gone. When a cylinder is cut badly it can be repaired only by reboring and providing a new piston and rings. The governing device should receive frequent attention to prevent its becoming clogged or gummed up with grease and losing its sensitiveness. This is especially true in the case of governors contained in the crank case, where they are in a position to accumulate a great amount of dirty grease. For this reason it would be much better design to place the governor in an apartment by itself, or even to leave it exposed where it may be easily attended to. The hit-and- miss governors act on the gas supply by opening and closing a gas valve; as the engine increases speed beyond a certain limit, the governor catches and closes the valve, or releases it and allows it to close, and it will remain closed until the engine slows down enough to allow the valve mechanism to connect again. If the gas supply valve is not open enough, the engine will not get a charge and impulse the first time the governor connects, and the engine will slow down until the aperture opens wide enough or long enough to allow a charge to enter the cylinder. A hit-and-miss governor, properly adjusted, and with proper opening of the gas valve, should govern the engine very closely. There are a number of the so called hit-and-miss governors of different design on the market, all acting on the same general principle of closing off the gas supply. With the hit-and-miss governor, the first impulse received, after the governor connects, is always stronger than the nor- mal, due to the fact that all the hot exhaust gases have PRACTICAL OPERATION 31 been expelled, and the cylinder, in consequence, gets a full charge and a cooler one than usual. The quality of the mixture should be watched, and may be determined by inspecting the exhaust, which should be almost colorless, what color there is being imparted by the cylinder oil, which will always burn more or less. The nature of the combustion may also be determined by opening the relief cock, if one be provided, and watching the color of the flame, which, for perfect combustion, should be deep blue, bordering on a violet. The cylinder and piston and the valve stems should be cleaned occasionally with kerosene, and no oil that will gum or carbonize should ever be used on the valve stems. The crank-pin bearings and the main bearings should be inspected from time to time, and adjusted at the first sign of wear or looseness. The method of impulse, in a gas engine, will loosen and wear the bearings much more rapidly than in a steam engine, and once they start to loosen and the engine commences to pound, the trouble will grow very rapidly. Troubles and Remedies. Trouble in the operation of a gas engine is due more frequently to ignorance in handling than from any fault of the engine itself. Ignorance in handling may also be understood to include careless handling and inattention to small details, which, if given their proper consideration, will assist very materially in the successful operation of an engine. In the enumeration of the troubles connected with gas or gasoline engine operation, the subject will be treated as a whole, it being understood that the carburettor difficulties apply only to that class of engine in which liquid fuel is used in connection with a carburettor. Nearly all other sources of trouble are common to both engines using liquid and gaseous fuel. Engine Fails to Start. — If the engine will not start, examine the gas valve to see if it has been open too long and allowed 32 INTERNAL COMBUSTION ENGINES too much gas to leak into the cylinder, or if it is open too wide, allowing too full a charge to be taken. If either of these conditions is found to be true, close the valve entirely and turn the engine over once or twice, to clear the cylinder, or until an explosion occurs; then open the valve to starting position and try starting the engine. If this fails, go over the ignition system thoroughly, as described under heading "Spark Weak or Wanting," or, if the hot tube igniter is used, see that the tube is hot enough to ignite the charge. Cylinder Flooded. — Partially close the gasoline supply and turn the engine over enough times to satisfy yourself that all surplus gas has been worked out of the cylinder. Carburettor out of Adjustment. — As every carburettor is different, the engine operator must familiarize himself with his special one and find in what adjustment it produces, on the average, the best results. It is useless to attempt any fine adjustment of the carburettor while the engine is not running, but it may be set to its approximate adjustment, once that is known. Spark Weak or Wanting. — If the spark grows weak, the batteries are probably poor or old. This trouble may be remedied, to a certain extent, by adjusting the points of the coil; for weak batteries the points should be set much closer than when the batteries are strong. The spark may be tested by removing the spark plug and holding it, by means of the insulated wire, against the cylinder; then turn the engine over to see if there is a good fat spark between the points. If the spark is weak and uncertain when exposed to the open air, it will be very much weaker when under cylinder compression, with the probability that there will be no spark at all between the points under these condi- tions. When the spark plug is taken out, see that the points are set the proper distance apart; the size of this spark gap will vary, to some extent, with the age or strength of the batteries, but 1/32 in. is about right. Be sure that the points are clean and free from soot; to insure this condition, they should be cleaned, from time to time, with gasoline. If an extra set of cells is carried, throw them into the PRACTICAL OPERATION 33 circuit and see if the spark is improved. If a good spark is not produced after these trials, look over the wiring connec- tions, through the batteries, and complete the circuit, to make sure that no wire is grounded or contact broken. A well-insulated wire will often ground if covered with oil and grease, and for this reason the wiring should always be kept as clean as possible. If the wiring connections are all found to be in good con- dition and neither set of batteries gives a good spark, they are, in all probability, both in need of renewal. There is a possibility, of course, that the coil is poor or that the insula- tion of the high-tension wire has broken down, but this trouble is not of common occurrence. Open-circuit cells, or cells that polarize rapidly, are not suitable for the rapid work required of a sparking battery. Engine Stops. — If suddenly, in all probability a wiring connection is broken. If it slows down and stops, the cylinder is either overheated, the gasoline low or of poor quality, the mixture is not right, or the spark is too weak to explode the charge every revolution. The engine may be overloaded, or there may be an abnormal amount of friction at some point, due to an overheated bearing or to lack of sufficient or suitable cylinder oil. The inlet or exhaust valve may be obstructed and unable, in consequence, to seat itself properly, thus spoiling the compression and power of the engine. The valve stems may be sticking, with the same result. The relief cock may be partially or wholly open, or the starting cam may be in gear. If the engine is found to be running hot, ascertain if the circulation is good; there may be an obstruction in the suction line to the pump. If the water seems to be circu- lating, see if any part of the cylinder seems hotter than the rest; if the engine is vertical, that part of the jacket opposite the water inlet usually heats up first, due to the poor circu- lation at that point, and the resulting deposit of impurities from the water. If the engine is horizontal, the hot part of the cylinder will usually be found at the bottom, for the same reason. If a " hot-spot" is located, it is usually due to 34 INTERNAL COMBUSTION ENGINES the presence of a deposit; and to improve the circulation, this deposit must be removed. Many engines provide an open- ing into the jacket at these points and fit the opening with a pipe plug, which may be removed, when necessary, to flush out the jacket. If the engine is so equipped, remove the plug, and, using a bent wire, break up the deposit and then, with the water outlet closed, force water through the jacket until it is clear. If no such plug is provided, and the engine continues to give trouble from overheating, it may be found necessary to drill and tap a hole for a 1-in. pipe plug. Ignition Tube Cold. — If the ignition tube is too cold to fire every charge, then some unburned gas will be discharged into the exhaust passages and explode there. If the tube does not fire the charge frequently enough to keep up the cycle of operations, the engine will stop. Mixture too Rich. — This condition usually results in explo- sions in the exhaust passages, or in stopping of the engine. Back Firing. — When this condition exists, the charge fires back, in the compression stroke, against the direction in which the engine is running. Back firing may be due to any one of a number of causes; the compression may be too high, but this should not result in back firing, except at low speeds, as on high speed the charge should be ignited con- siderably ahead of dead center in order to allow the gas to expand to its maximum pressure by the time dead center is reached; it is doubtful if, unless the pressure were abnor- mally high, the charge would ignite before this critical point was reached. There would be more likelihood of the con- dition being encountered in gases of low ignition temperature, as gasoline vapor. Back firing may also be caused by the cylinder becoming overheated, or by projections, or fins, on the inside of the cylinder becoming incandescent and holding their heat, derived from one explosion, long enough to ignite the next partially compressed charge. A particle of car- bonized oil may become incandescent with the same result. The spark may be too far advanced for the speed at which the engine is running. PRACTICAL OPERATION 35 In the two-cycle type of motor, premature explosions may occur in the crank case, due to its compression being poor, as has been previously explained. Premature explosions are accompanied by pounding of the engine bearings, although a bearing pounding does not necessarily indicate that premature explosions are taking place, as a bolt or nut may be loose and produce the same result. Water in the Cylinder. — This may result from water being introduced in the mixture, or, as is sometimes the case when the engine is made with a detachable cylinder head, from the gasket blowing from the cylinder into the water space. The condition is accompanied by loss of power, or, as is usually the case, by stopping of the engine. The igniter mechanism, if electrical, becomes grounded. The only remedy is to repack the head, an operation often done the wrong way by those inexperienced. The packing, which should be a good grade of wire-woven asbestos, should be carefully cut and fitted to the cylinder head, being sure to provide the openings for the water spaces and any others that may occur. Carefully cut all bolt holes, making them large enough to permit the bolt to pass through freely, without drawing the gasket out of place when they are screwed up. Cut all openings as nearly to the exact size as possible. Now place the gasket carefully in place on the head or cylinder, as is most convenient; place the head in position and insert the screws or bolts. With the engine cold, draw up the bolts as tight as they will go, of course using a reasonable amount of judgment and not twisting the heads off. Now, with the jacket dry, run the engine for 3 or 4 min., or until it is good and warm; this will soften the rubber, or other cementing material in the gasket, and allow the bolts or screws to be tightened up to their final position. Failure to perform this last tightening opera- tion will mean that the gasket will blow again, as, when the engine is hot, it sometimes takes three-quarters of a turn on the screw, to take up the gasket and squeeze the cement into all the cracks so as to produce an absolutely tight joint. 36 INTERNAL COMBUSTION ENGINES Engine Smokes. — Smoke, issuing from the exhaust, indicates too rich a mixture or too much oil. Smoke, issuing from the front of the cylinder, indicates that the piston is leaking, due to the rings being worn or the cylinder out of round, or the engine may be running hot. The remedy for these con- ditions has already been mentioned. Valves Leak. — See if the stems are sticking, or if the seat is crusted or cut, or if a spring is weak. The remedy has been previously suggested. Engine Races. — If the engine, running light, races, or runs faster than it can be supplied with gas, it is an indication that the spark is too far advanced for the amount of mixture being fed to the cylinder. The remedy is to retard the spark or give the engine more mixture. CHAPTER VI. STARTING DEVICES. There are a number of different methods in use for starting gas engines, all of which are used, more or less extensively, as requirements demand. They may be enumerated about as follows: 1. Hand starting, which is' used most extensively in the starting of engines of moderate size, and requires that the engine be provided with compression relief cocks or starting cams. In using this method of starting, care must be taken that the ignition is so set that the charge will not be pre- maturely exploded, causing back firing, with accompanying dangerous results to the operator. Engines which are to be started by this method are generally provided with an automatic throw-out collar which enables the operator to clutch the shaft with the starting crank, but which, when the engine starts, automatically throws the crank out of connection. Several devices, of greater or less efficiency, have been placed on the market, the object of which is to cause the starting crank to disengage as the engine starts or back fires, thus insuring immunity to the operator. 2. It is sometimes possible in multi-cylinder engines, and even at times in engines of but one cylinder, to start, after a moderately short stop, by retarding the sparking apparatus and igniting a cylinder containing part of a charge drawn in before the engine was stopped. To do this successfully demands that the engine be stopped with the spark and that the piston rings be a tight fit, insuring a tight cylinder. 3. The engine may be turned over until it takes up its cycle of operations by some external source of energy. Electric motors are often used to advantage for this purpose, or the large engine may be provided with a starting engine 37 38 INTERNAL COMBUSTION ENGINES small enough to be turned over by hand and of sufficient power, when running, to start the large engine. 4. An explosive mixture of gas and air may be stored in an auxiliary air-tight chamber. This may be accomplished by the engine itself charging this receptacle before it is stopped. On starting the engine, it is turned over dead center into the explosion stroke, and a charge of the explosive mix- ture is admitted to the cylinder by opening a valve in the supply pipe. The explosion of this charge will generally be sufficient to give the engine enough impulse to make it take up its cycle of operations. 5. The last-named method may be varied by using an air pump, operated by hand, to compress a charge of explo- sive mixture into the cylinder. In either of these last two methods named, the charge may be exploded by an electrical spark, if the electrical system of ignition be used, or by means of a match starter; see Fig. 6. 6. The method of inserting an explosive cartridge in a tube, opening into the cylinder, and exploding it by mechanical means, has been used to some extent. 7. A charge may be exploded in an auxiliary chamber and the resulting pressure conveyed to the engine cylinder. Hutton, in his treatise on " The Gas Engine," illustrates such a starter, the operation of which is shown in Fig. 7. Gas enters the auxiliary chamber, A, through the supply pipe, B, and, the poppet valve, C, on the engine being closed, passes out through the cock, D, where it is ignited. As long as the gas valve in the supply pipe is kept open, the pressure in the explosion chamber is maintained suffi- ciently high to prevent the flame at the jet, D, from running back into it; but as soon as the supply is cut off, the gas in the chamber is gradually consumed at the jet until the Fig. 6. Match Igniter. STARTING DEVICES 39 mixture is such that the flame runs back and ignites the entire charge, and the resulting pressure is admitted to the cylinder through the poppet valve, C. 8. By far the most widely used method of starting is by means of compressed air, compressed and stored by the engine itself or by means of a smaller auxiliary air compressor. Fig. 7. Auxiliary Chamber Starter. In order to operate the compressed-air starter, it is neces- sary that the cam movement in a four-cycle engine be so arranged that one or more of the cylinders may be converted, for starting purposes, into a compressed-air engine. To accomplish this it is necessary that the cylinder exhaust once every revolution and that the inlet valve remain continu- ally closed while the starting operation is proceeding. The air may then be turned into the cylinder, either by means of an air cock actuated by hand or by automatic means. Where a single cylinder, in a multiple-cylinder engine, is thus arranged, it is necessary that the engine be turned over by hand until the piston of the air cylinder is at the begin- ning of the working stroke, when the starting mechanism may be thrown into gear and the air admitted. As mentioned in Chapter XIV, if the cams are made to 40 INTERNAL COMBUSTION ENGINES operate an intermediate lever mounted on a shaft, which mechanism, in turn, operates the valve rod, it is an easy matter to make the shaft, on which the levers are mounted, to shift in such a way as to bring the starting mechanism into gear. Such an arrangement is shown in Figs. 8 and 9, which figures show the arrangement of the cams for a three- «toite=^ Fig. 8. Compressed Air Starting Cams. cylinder, four-cycle engine. In the illustrations A, B and C are the three exhaust cams, and D, E and F are the inlet cams, all mounted on the one cam shaft, G. The trans- mission levers, H, are shown mounted on the shifter shaft, 7. On the transmission levers are the hardened steel contacts, Section X-X Fig. 9. Detail of Starting Cam shown in Fig. 8. J, on which the valve stems impinge. Cams A and D are the double starting cams. Cam A is provided with two eccentric portions, as shown, so that the exhaust valve is made to open once every revolution, while cam D is made with one-half of it with the outline of the regular inlet cam, while the other half is concentric to the shaft at all points, STARTING DEVICES 41 so that when the lever, H, acts on the concentric portion it will not raise, and, in consequence, the inlet valve will remain closed. In starting, the engine is turned over until the cylinder, which the cams, A and D, control, is in the explosion stroke; then, by means of the lever, K, the shifter shaft carrying the levers, H, is moved in the direction of the arrow to the starting position and the air cock opened. A double cam, mounted on the cam shaft, is provided by some manufacturers to open and close an air poppet valve. This, however, is not an absolute necessity, although more economical of air, as it shuts off the air supply during the exhaust stroke of the piston, when the exhaust valve is open to the atmosphere. With the air-starting system a pressure of from 200-300 lb. is maintained in the storage tank. CHAPTER VII. CARBURETTORS, VAPORIZERS AND INJECTORS. The gas, gasoline, alcohol, and oil engines operate on the same general principle, as far as the generation of power is concerned, but the methods pursued for obtaining the requisite fuel in gaseous form vary with the several different types. Thus, in the gas engine, that is, the engines which operate on some form of gas as a fuel, no intermediate steps are necessary for the transformation of the fuel from a liquid to a vaporous or gaseous form, although, in the engines operating on producer gas, an apparatus, known as a producer, is necessary to distill from the fuel, as it appears in a solid state, a gas, available for use in internal-combustion engines. The different devices used for the production of the com- bustible gasoline, alcohol, or oil mixture will first be dis- cussed, after which the operation of a suction gas producer will be taken up. There are three general methods in use for securing an explosive mixture from liquid fuels: (1) Carburetting, (2) Vaporizing, (3) Injecting. The carburettor, in any one of its many forms, is a device by which the liquid fuel is transformed into a vapor by passing air either over, through, or across a portion of the supply and taking up particles of the liquid in a vapor form. To facilitate the operation, when carburetting gasoline, it is much better, although not absolutely necessary, that the air, as well as the gasoline, be warm, especially in cold weather; and for this reason we find the engine manu- facturers leading their suction from a "hot-box," located either on the exhaust manifold or on the cylinder base, or 42 CARBURETTORS, VAPORIZERS AND INJECTORS 43 where the warm water, from the jacket, may be made to circulate around it. When carburetting alcohol it is necessary, under all circumstances, that the fuel be warmed; the reason for this is fully explained in Chapter IX. In carburetting petroleums it is necessary, especially with the heavier grades, that the air under pressure be forced through the liquid in order that it may break up or pulverize the fuel and carry a portion of it, in suspension, to the engine cylinder. In many engines, after the oil is thus broken up, the mixture is carried to a heated chamber or through heated coils where it is vaporized and mixed with air to form the proper explosive mixture. In other types, the vaporized fuel is carried direct to the cylinder, and the residual heat of previous explosions produces the same general results, although in a less satisfactory manner. Still another method consists in heating the fuel oil, by passing it through coils exposed to the action of the exhaust gases, and thereby driving off an oily vapor which, due to its heat, has sufficient pressure to carry it past an air nozzle where sufficient air is mixed with it to produce the proper explosive mixture. The same result is also obtained by causing the oil to fall, a drop at a time, on a hot plate, thus causing it to vaporize. The vaporizer (and it may here be said that they are only applicable, as ordinarily designed, to the use of gasoline or naphtha) differs from the carburettor in that the latter always has a supply of gas on hand, while the vaporizer, or mixing valve, makes only enough gas for each revolution or charge, as required. Many, so-called, carburettors are, in reality, improved types of mixing valves, and in fact, it may be said that the majority of them are. The vaporizer consists, essentially, of a gasoline valve, of needle design, capable of being adjusted to deliver the necessary amount of the fuel to produce the requisite vapor for the mixture required, and an adjustable air valve, by means of which the air supply may be regulated so as to vary the quality of the mixture, as requirements demand. 44 INTERNAL COMBUSTION ENGINES The gasoline is dropped in the path of the entering air and carried along in the form of a finely divided spray, or it is made to rise in a nozzle, placed in the path of the entering air, which carries enough of the fuel with it to produce the necessary mixture. Vaporizers are made supplied with a throttling device and in all respects similar to the majority of the, so-called, carburettors on the market with the exception that they are not supplied with an automatic float feed device. Injecting, as the name implies, consists in injecting into the cylinder, or a chamber adjacent thereto, a quantity of the fuel mixed with the requisite amount of air. This method of introducing the fuel into the cylinder is practiced quite largely by the different oil-engine manufacturers. The Hornsby-Akroid and the Meitz and Weiss, the injection and ignition of whose charges are later described under "Igni- tion," make use of this principle, as does also the Diesel motor. The Diesel method is as follows. Referring to Fig. 10, the air valve, the exhaust valve, and the fuel valve are plainly marked. The air valve allows the air charge, as previously described, to enter the cylinder on the suction stroke. At the beginning of the working stroke the fuel valve is opened and the charge of oil is forced into the cylin- der by means of compressed air under a pressure of 800 lb. per sq. in. The construction of the fuel valve is somewhat unique; the fuel enters the valve through the pipe, A, and the auxiliary compressed air, through the pipe, B. The valve, proper, consists of concentric washers, C, drilled with small holes, as shown, parallel to the spindle, D, which, by means of the governor acting through the bell crank, E, opens and closes the valve at F. The capillary attraction of the oil, as it falls on the washers, causes it to fill the holes above mentioned, and when, on the working stroke, the valve, F, is opened, the oil is carried with the air in a finely divided spray to the cylinder where, as described in the chapter on "Ignition," the heated air contained in the cylinder completely vaporizes and ignites it. The valve stem is made of nickel steel, as it has been found by experi- CARBURETTORS, VAPORIZERS AND INJECTORS 45 ence that where the packing abrades the spindle, as it is moved back and forth, it soon becomes worn and requires to be replaced. This method, as used on the Diesel motors, is very econom- ical of fuel and could be applied to engines of lower com- pression with probably as satisfactory results. Fig. 10. Diesel Valves. Returning to the subject of carburettors and referring to Fig. 11, we have an example in which the carburetted air is obtained by passing it through the fuel and thence to the engine. This method is sometimes spoken of as mechanical ebullition. In the illustration in question, A represents the suction pipe to the engine; B, the screened openings, through which the auxiliary air supply is drawn; C, the tube, termina- ting in the float, E, through which the carburetted air is drawn ; 4G INTERNAL COMBUSTION ENGINES D, a shield acting on the principle of a separator and causing the surplus particles of gasoline to separate from the vapor when they impinge against its surface; F, an indicator and gauge by which the height of gasoline in the carburettor may be determined. The end of tube, C, terminates in such a position as always to be just below the surface of the liquid; the float, E, causing it to move up or down, as the elevation of the surface of the liquid is changed. On the suction stroke of the engine, air is drawn through the tube, C, and mixes with the auxiliary air supply drawn in at B, and the mixture thus obtained is carried to the cylinder of the engine. This carburettor was used in the earlier Daimler engines and was first devised by Gottlieb Daimler. There were, however, two very marked disadvantages in its use. In the vaporization of any liquid a certain amount of heat, known as the latent heat of vaporization, is lost; now unless heat be supplied to the liquid, from outside sources, as this vaporization continues, the temperature of the liquid continues to fall until it may become so cold that it will have lost nearly all of its volatility. (See Chapter IX for detailed description of this condition in different fluids.) This was the great difficulty encountered in the operation of this type of car- burettor. Added to this, trouble was also experienced from fractional distillation; that is, the lighter portions of the liquid naturally rose to the top and, in the process of vapori- zation, passed off first, leaving in the carburettor the heavier part of the fuel. As a result of this condition the last part of the liquid to be vaporized, or distilled, was of poor quality, naturally affecting the operation of the engine. Fig. 11. Daimler Carburettor. CARBURETTORS, VAPORIZERS AND INJECTORS 47 Several carburettors of this general type were designed and used to some extent, but the same difficulties were experienced in all. Fig. 12 represents one of the earlier carburettors, in which the carburetted charge was obtained by passing air across CH _ -i i— "i i —"•I i- --i i i _ I 1 i ^J Fig. 12. Surface Carburettor. a large surface on which the fuel to be vaporized was maintained. In the illustration, A is the inlet valve, through which the air to be carburetted is drawn; Bis the suction pipe to the engine; C is the auxiliary air supply valve, by means of which the mixture may be regulated; E is a light metal casing, containing the spiral F, which is fastened, to the top of the casing and allowed to project nearly to the bottom, as shown. On either side of the spiral partition is basted light flannel or felt. When the carburettor is partially filled with fuel, as shown it is apparent that the air, entering at A, must pass com- pletely through the spiral to reach the outlet at B. The 48 INTERNAL COMBUSTION ENGINES flannel or felt, reaching down into the liquid, serves in the capacity of a wick, and, by capillary attraction, the part above the liquid is kept saturated with the fuel. The passage of the air currents across this large expanse of wick surface evaporates the fuel and saturates the air. Experience has shown that, in carburettors of this type, the best results are obtained when the carburettor, if about 8 in. deep, is half full of the liquid to be evaporated. The principal objection to the wick carburettor is that the wick gradually becomes clogged with foreign matter, taken in with the air supply or contained in the fuel, and ceases to perform its functions properly. To overcome the difficulty connected with the use of wicking, carburettors are designed in which the liquid fuel is made to drop on very fine wire gauze, and, forming a thin film over the wires and open spaces of the fabric, is easily evaporated by the entering air. Of the carburettors, in which the air is carburetted by passing it over the gasoline, we have many examples; in fact, the large majority of the modern designs use this method. These carburettors are commonly spoken of as the "spray type," and the name is aptly chosen, the fuel being injected into the entering air, through a nozzle, in the form of a finely divided spray or mist. The operation of the carburettor is as follows: a nozzle, fitted with a needle valve, is so situated in the air passage that the entering air must pass over it on the way to the engine. On the suction stroke, a partial vacuum is formed in the carburettor, and the air, rushing over the spraying nozzle, is attempting to fill this vacuum. In consequence its pressure is less than that of the atmosphere, and the fuel, supported in the nozzle, is thrown off into it by the unbalanced pressure. As has been previously noted, these carburettors have a capacity of but little more than one complete charge for the cylinder, and are really improved types of mixing valves, their one distinctive feature being the float feed, with which they are almost universally equipped. If not equipped with CARBURETTORS, VAPORIZERS AND INJECTORS 49 a float feed, an aspirating valve is necessary to automatically open and close the spraying nozzle. Their greatest difficulty arises from the tendency of small particles of foreign matter to lodge in the spraying nozzle, and this fact necessitates great care in the filling of the fuel supply tank. In the carburettors in which an automatic aspirating valve is used in place of the float feed, some difficulty is encountered, especially on high speeds, from the inertia of Fig. 13a. James-Lunkenheimer Mixing Valve. the valve spring not allowing sufficient time, on every suction stroke, for the entering air to secure its requisite amount of vaporous fuel. As commonly spoken of, the carburettor is not flexible enough, and, on high speeds, the power of the engine is not proportional to the increased number of impulses 'received. For this reason the ordinary mixing valve gives, as a rule, a good deal of difficulty when used on a two-cycle engine of the three-port type. The generic patent, under which nearly all the modern carburettors are manufactured, is shown in Fig. 13, and is known as the James-Lunkenheimer design. It consists essentially of a poppet valve, A, the movement of which may be restricted by means of the screw, B, and which is held to its seat by the spring, C. The air supply enters through the port, D, and the gasoline through the nozzle 50 INTERNAL COMBUSTION ENGINES in the valve seat at E. The gasoline supply is regulated by means of the needle valve, the handle of which is shown at f — T^S Mixing Valve. F, and the amount of opening of the needle valve is indicated by the pointer, G, and the dial, H. The gasoline connection is shown at / and the engine connection at J. Fig. 14. Plain Pattern Generator Valve. Figs. 14, 15 and 16 represent three different types of mixing valves manufactured by the Lunkenheimer Company, of Cincinnati, Ohio. Fig. 14 is the plain pattern generator CARBURETTORS, VAPORIZERS AND INJECTORS 51 valve, Fig. 15 shows a valve with screws for varying the opening of the poppet and the tension of the spring, and Fig. 15. Generator Valve with Adjustable Air Poppet. Fig. 16. Generator Valve with Throttle. Fig. 16 is a valve having throttle connections, means for varying the air and gasoline supply and for changing the tension of the valve spring. 52 INTERNAL COMBUSTION ENGINES These valves, especially the one with throttle connection, give excellent satisfaction, and the operator is able to con- trol the motor very closely. With nearly all types of mixing valves the best results are obtained when they are operated on ordinary stove gasoline. This is due to the fact that the lack of the float feed allows the fuel to run into the valve more freely than is necessary, and, in consequence, the mixture is liable to become too rich with the more highly volatile gasoline. Fig. 17. The Schebler Carburettor. Fig. 17 is a cut of the Schebler carburettor, manufactured by Wheeler & Schebler, Indianapolis, Indiana. It is of the spray-float feed type, and the working parts are shown quite dearly in the cut. Reference figures and letters are as follows: 9 is the constant air opening, through which the air, to be carburetted, passes. The air, entering at 9, passes upwards past the spraying nozzle P, to the mixing chamber of the carburettor, where the auxiliary air supply, entering through the poppet valve, A, is mixed with it, and the explosive mixture, thus formed, is drawn into the CARBURETTORS, VAPORIZERS AND INJECTORS 53 engine cylinder. The 'float feed mechanism is shown at F, J, H, and consists of a float, F, surrounding the constant air supply tube, as shown, which operates the needle valve, H, through the lever, J, maintaining the level of the fluid such that it will just overflow the nozzle, P. Gasoline enters the carburettor, from the supply tank, through the supply pipe, G. The nozzle, P, is fitted with a needle valve, E, which is adjusted permanently for low throttle by means of the knurled button, /; then for open throttle, the needle valve mechanism is raised or lowered, by the operator, by means of the lever, P, which actuates the cam mechanism, Y, and causes the lever, Q, to revolve about the point, T, thus raising or lowering the needle point. The auxiliary air supply is provided with two valves, a damper valve Z\, by means of which the opening may be increased or dimin- ished; and the poppet valve A, held to its seat by the tension of spring 0, which tension may be increased or diminished by means of the knurled screw M. Push pin U is used for priming the carburettor when starting the engine. Pushing the pin down lowers the float and opens the needle valve, H, causing the nozzle, P, to overflow and producing, momentarily, a very rich mixture, suitable for starting. The float chamber is usually provided with a pet-cock, at its lowest point, for draining off the poorer grade of gasoline, which usually accumulates there. If the gasoline contains water it also accumulates in the bottom of the float chamber, and may be removed from time to time. Fig. 18 shows two sectional views of the Holley carburet- tor, manufactured by the Holley Brothers Company, Detroit, Michigan. It is also of the spray type, and its operation is as follows: the incoming air enters through port A, which is pro- vided with a fiber valve BC; situated around the valve are the constant openings a, through which air is constantly passed. The valve proper is held to its seat by means of the spring, b, as shown, the tension of the spring being capable of adjustment by means of the adjusting screw c. The spraying nozzle, D, situated in the path of the incoming air, 54 INTERNAL COMBUSTION ENGINES may be opened or closed by means of the needle valve, d. The mixture passes to the engine past the butterfly throttle, E, which may be opened or closed, to suit requirements, by means of the lever, F. Gasoline enters the carburettor through the gasoline connection, H, which is opened or closed by means of the needle valve, /, being raised or Fig. 18. Old Type Holley Carburettor. lowered by the float, G, acting through the lever, J. The mechanism is set to maintain the height of the liquid such that it will just overflow the spraying nozzle. On low speeds the air enters entirely through the constant air openings, a, but, as the speed increases, these openings not being large enough to supply the requisite amount of air to overcome the partial vacuum formed, the auxiliary valve BC raises and allows an extra supply to enter the carburettor. A pet-cock at K is used to drain the carburet- tor, as already described. Fig. 19 is a later design of the Holley carburettor in which an entirely new principle has been made use of to produce the varying mixtures necessary for the changing speeds. More or less trouble is encountered with carburettors, in which this variation is accomplished by means of an auxiliary air supply, owing to derangements of the spring device, which closes the auxiliary valve. Frequent adjustments of this CARBURETTORS, VAPORIZERS AND INJECTORS 55 Fv G P Fig. 19. Holley Carburettor. 56 INTERNAL COMBUSTION ENGINES spring are necessary, and even then trouble is often encoun- tered at different speeds. The Holley claims to have overcome this difficulty by varying the amount of evaporating surface of the gasoline, thus changing the quality of the mixture. The method of operation is as follows: in the illustration, the air enters at A and passes downward and then up through a U-shaped tube. At the lowest point of this tube the area is gradually constricted and the gasoline orifice, B, is located there, the size of this orifice being adjusted, as in most carburettors, by means of the needle valve, E. The mixture passes through the butterfly throttle and to the engine through the outlet, C. The float chamber surrounds the U, and has an annular cork float, J, which controls the needle valve, L, through the lever, N, pivoted at K. The lower constricted part of the U is, in principle, a venturi tube, and makes it possible to maintain a very high air velocity over the gasoline orifice B. The gasoline level, in the float chamber, is maintained so that it will overflow B about $ in., and when the engine is not operating, this condition will maintain. When the engine is started, the suction does not have to lift the gaso- line but merely evaporates it off the top of the puddle, and is carburetted by surface evaporation. As the engine speed increases and the throttle is opened, the increased velocity of the air sweeps the puddle away, and on high speeds the mixture is carburetted by the spray from the orifice. Drain pipe D is provided to prevent the puddle from growing deeper than £ in. The engine is throttled by means of the lever, F, operating the butterfly valve, as shown. The principle of operation of this carburettor is good, and results seem to justify it. Alcohol Carburettors. As already mentioned, the only requirement for the car- buretting of alcohol in an ordinary carburettor is that the air shall be of sufficient warmth to vaporize the alcohol in sufficient quantities to produce a properly saturated mixture. CARBURETTORS, VAPORIZERS AND INJECTORS 57 However, it has been found in many cases to be the fact that the suction should be increased when carburetting alcohol, owing to the increased amount of fuel used to produce the same power. In Germany and France double carburettors are in use to some extent. The engine is started on gasoline and, when sufficient heat has been generated to insure the perfect operation of the alcohol, a valve cuts out the gasoline supply and cuts in the alcohol. Other carburettors for use with alcohol utilize the exhaust gases to heat and vaporize the fuel and when in a vaporous state it is mixed with the air and passes to the engine. It is apparent that carburettors, through which the exhaust gases must pass, are more or less cumbersome and it is doubtful if they would be as efficient, as producers of power at the engine cylinder, as those in which the fuel is not heated to as high a temperature. It was proven conclusively, by tests made on gasoline engines, that this was so in their case, and there is no good reason why the same rule should not hold true in the use of alcohol, for the hotter the entering charge, the less the range of temperature in the cylinder and the less the power developed. Moreover, since government tests have seemed to show that most gasoline carburettors are, with slight alterations, adaptable to the use of alcohol there is no valid reason for making them more complicated. Carburettor Design. A jet carburettor, in order to give satisfaction, should have an air velocity at the jet sufficient to secure a good spraying effect. The vacuum in a carburettor operating on alcohol, should be, according to best authority, equal to between f in. and -J- in. of mercury, and for starting, this value should be about doubled. In a carburettor operating on gasoline, a vacuum of 0.1 in. of mercury is generally sufficient. The speed of the gases passing the spraying nozzle should be, in the use of gasoline, about 80 ft. per sec, while to satisfactorily spray alcohol into the passing air the velocity should be about 220 ft. per sec. CHAPTER VIII. PRODUCERS. Producer gas fuel, for gas engines, may be generated with apparatus operating under pressure, or by suction. The first producers to be made and marketed were intro- duced by a Londoner, named Dowson, and they were used to such an extent that the name Dowson gas came to be almost synonymous with producer gas. They were of the pressure type and required for their operation a hard grade of anthracite. The producer plants were quite complicated, due to the necessity of scrubbers, cooling apparatus, and a gasometer, in which the gas, since it was under somewhat varying pressure, had to be stored before being fed to the engine. There are many cases, however, in which it is necessary that a pressure system be used ; in fact for any other purpose than for use in connection with a gas engine, where the suction of the piston produces the necessary flow of air through the producer, pressure of air is necessary in order to operate the apparatus and to convey the gas to the required point. Nearly all pressure generators are copies of the original Dowson idea and include a generator or retort, in which the gas is driven off from the fuel; an air-compressor fan or other apparatus for blowing a mixture of steam and air through the generator; a scrubber, a gas purifier, and a gasometer. Fig. 20 represents, diagrammatically, such a plant. The retort or producer consists of a metal shell, lined with fire brick or clay, vertically mounted. A charging hopper, so arranged that the producer is never opened to the air, is provided at the top. The bottom of the producer rests on a grate through which the ashes fall, the air and steam being 58 PRODUCERS 59 passed through these ashes to the producer, or a water seal is provided, in which the generator sits, and the mixture of air and steam is introduced under a conical hood which protects the open end of the pipe from becoming clogged drijtj^ Fig. 20. Pressure Producer. with ashes and coal. The mixture should be superheated if possible, in order that no more heat energy than is necessary be lost in heating the entering air. The entering fuel should be carefully distributed, and means provided for breaking the clinker formation on the walls of the retort; some manufacturers provide tuyere openings to accomplish this; the apparatus must be tight and, if not provided with a water seal, suitable means must be had for cleaning the grate. Distribution of the fuel charge is accomplished by making the drop grate of the hopper conical in form, which spreads the coal over a large surface. (See Fig. 21.) The air blast may be supplied to the producer in any one of several different ways. The pressure may be obtained direct from a steam boiler maintained, as nearly as possible, at 80 lb. per sq. in. pressure; a blower, operating on the principle of a draft inducer or injector; by means of a mechanical fan or centrifugal blower; or by the use of compressed air. 60 INTERNAL COMBUSTION ENGINES Fig. 21. Charging Hopper for Producer. When blowing with steam, trouble is more than likely to be encountered from the varying steam pressure produc- ing different qualities of gas. Mechanical blowers may be driven directly from the engine, if used in connection with a producer for a gas engine. The use of compressed air results in a good even quality of gas, but the cost of production is, necessarily, high. The gas leaving the producer passes to the scrubber, where it is cleaned of any dust which it may contain by passing through sprays of water and being filtered through beds of coke, calcium hydrate, moss, or sawdust, placed on removable trays so arranged that the filtering or purifying material may be cleansed or renewed. From the scrubber and purifier the gas passes on to the gasometer, where it is stored ready for use. The gasometer acts in the capacity of a pressure regulator and should have sufficient capacity to take care of any possible stopping of the production of gas for a brief time. In producers operating on the pressure system, any combustible or volatile material may be used to produce the gaseous fuel, and in nearly all cases the economy over the combustion of the same material under a steam boiler is very marked. This gas may be produced from sawdust, sawmill refuse, street sweepings, garbage, lignite, peat, etc. The methods used for producing the gas vary to some extent — the gas being obtained either by distillation or combustion. Since these waste products and the cheaper grades of coal or peat in burning form a rather closely compacted mass, considerable . pressure is required to drive the air through the producer; hence, without exception, these materials are not available for suction producers. In the production of gas from wood or wood refuse, by the distillation process, the material is placed in a cast-iron PRODUCERS 61 crucible which is subjected to the heat of a furnace and the volatile part of the fuel distilled off, leaving charcoal in the crucible. The walls of the crucible should be heated to a cherry-red heat, between 1600 degrees and 1700 degrees fahr., and its diameter should not exceed 12 in. Fig. 22 is a cut of the Riche distilling producer as illus- trated by Mathot in his "Modern Gas Engines and Producer Gas Plants." The heated gases from the furnace pass through the flue opening, A, into the flue space, B, which surrounds the retort, as shown; the gases then circulate around the retort and pass up and out to the stack through port, C. The crucible is charged with the fuel to be distilled, in this case pieces of wood, and the top closed to make an air-tight joint. From the bottom of the crucible the gas generated is led to the scrubber and purifier and then to the gasometer. The heat generated in the crucible raises the pressure of the products being distilled and, since there is no outlet at the top, the gases must pass from the cooler part past the hot part of the apparatus on the way to the scrubber. This has a tendency to burn out the impurities contained. Producers operating on the distillation principle burn about 1 lb. of coal to every 2.5 to 3 lb. of material distilled, and produce from 2S to 35 cu. ft. of gas having a heating value of about 340 B.t.u. per cu. ft. or 9860 B.t.u. per pound of coal, whereas 1 lb. of good coal will produce of itself about 10,000 B.t.u. Fig. 22. The Riche Distilling Producer. 62 INTERNAL COMBUSTION ENGINES The gas produced from the wood, however, is of permanent composition and can be transported long distances. The residual charcoal, if wood be used, also has some value. The residual weight of charcoal is approximately one-fifth the original weight of the wood — depending, however, to quite an extent on the amount of water in the wood, a wood like elm containing a very large percentage. Combustion producers produce the gas by the combustion of the fuel in the presence of water. The products of combustion are then passed on to a reducer, which disso- ciates the hydrogen and oxygen contained in the steam, reduces the carbonic acid gas to carbon monoxide, and produces the hydrocarbons. The reducer contains coke, which, when incandescent, produces the necessary reactions. One pound of wood waste, in a combustion reducer, will produce about 10 cu. ft. of gas having a heating value of approximately 115 B.t.u. per cu. ft. Inverted producers operate by forcing the air down from the top, through the fuel. The distilled volatile products, when they reach the incandescent part of the fuel, are reduced and a permanent gas, free from tar, is obtained. The Suction Producer. As has already been mentioned, the suction producer draws the air charge through the fuel by means of the suction of the engine piston and, in consequence of this fact, only certain fuels are available for use in these plants. The pressure type, it is readily seen, has greater elasticity in meeting the different fuel conditions, but the suction plant takes up much less floor space and the cost of installa- tion is much less than for a pressure plant of the same size. The suction producer can use only anthracite coal, or carbonized fuels, as charcoal or coke. The anthracite must not be too small — not less than pea size — and it must be clean and carry as small a percentage of ash as possible, not more than 15 per cent. Undue resistance in the producer will produce an over amount of back suction on the engine piston, with consequent loss of power. PRODUCERS 63 If anthracite coal is used, one pound of good quality will produce about 1 b. hp.-hr., and it will require about 1.3 lb. of coke to produce the same result. For small units the amount of fuel is somewhat increased and may be as high as 1.5 lb. per b. hp.-hr. tg Fig- 2o. Suction Producer. In operating the suction producer, a fire is kindled on the grate and a bed is built upon it in the ordinary manner, the necessary air being supplied, for the time being, with a hand or belt-driven fan. Beyond the vaporizer, the prod- ucts of combustion escape through a waste pipe. When the test cock shows that a good quality of gas is being pro- duced, the scrubber and purifier is thrown into the circuit, and when good gas appears at the engine cock, the engine is started and the fan stopped. 64 INTERNAL COMBUSTION ENGINES Fig. 23 illustrates a suction producer manufactured by R. D. Wood & Co., of Philadelphia. It is very compact, an area of 15 by 35 ft. being sufficient for a plant of several hundred horsepower, a smaller plant, of course, requiring less space. Fig. 24 shows very clearly the comparative efficiencies of a gas producer and steam plant.* Fig. 24. Comparative Efficiencies of Steam and Producer Plants. The first cost of a producer plant is approximately the same as for first-class steam engines and boilers of the same horsepower, but the resultant economies in fuel and atten- tion are very marked, one man being able to care for a large plant. The cost of attention is from 50 to 75 per cent that of a steam plant. No time is required, as with the steam * The author is indebted to R. D. Wood & Co. for the cuts on suction producers, and the results shown in their diagram are very closely in keeping with the results of modern practice where the steam engine used is of non-expansion, non-condensing type. PRODUCERS 65 plant, to get up a head of steam, and when the engine is stopped for any length of time the producer may also be shut down. The gas obtained from a suction plant operating with good fuel has a heat value of about 145 B.t.u. per cu. ft. The following analysis gives the approximate composition: Carbon dioxide, CO;, 0.7 to 0.9 Carbon monoxide, CO 0.24 to 0.28 Hydrogen, H 0.16 to 0.20 Marsh gas, CH 4 0.04 to 0.06 Nitrogen, N 0.45 to 0.49 For large plants or plants operating several engines the pressure producer is advisable, but for use in connection with a single unit of moderate size the suction plant is cheaper, occupies less floor space, and serves the purpose equally as well. CHAPTER IX. FUELS AND COMBUSTION. For the motive power in an internal-combustion engine any gaseous fuel is available, as well as any other fuel which may be vaporized or transformed into a gas. By vaporized fuel we mean any fuel, such as gasoline, petroleum, oil, or alcohol, which may be used in the cylinder of a gas engine without the intermediate step of transforming it into a gas. There is absolutely no combustible substance which may not be transformed into a gas, or rather have its gaseous products driven off, by the action of heat. Any one of these gases may be used, with greater or less efficiency, as their calorific efficiency is greater or less, in the cylinder of a gas engine. It is furthermore true that in all cases the power obtained from any fuel first converted into a gas and then burned in the cylinder of an internal-combustion engine, is always greater than if the same amount of fuel were burned under a boiler and the steam used to drive a steam engine. This is true because the heat efficiency of a gas engine is about 25 per cent, while that of the steam engine is from 10 to 12 per cent. As nearly all of the combustible part of the fuel becomes gas — especially is this true in the case of vapo- rized fuels — it is obvious that the fuel so used must be much more economical than when fired under a boiler. The manufacturers' guarantee accompanying stationary gas engines usually insures that their engine will produce 1 hp.-hr. on from 11 to 12 cu. ft. of natural gas. The heat units contained in natural gas range from 900 to 1100 per cu. ft., according to the nature of the gas, and in producer gas there are .about 160 heat units per cu. ft. ' Running on producer gas, then, the same engine would require 66 FUELS AND COMBUSTION 67 11 X = 75 cu. ft. approximately. Now one pound of bituminous coal will produce 75 cu. ft. of gas and, in consequence, to produce 1 hp.-hr. would require that 1 lb. of coal be used in the producer. The very best steam engines yield but 1 hp.-hr. on 1.5 lb. of coal. If we could use the relative heat efficiencies of a gas and a steam engine as a basis of comparison, we would expect to find that where 1 lb. of coal, as gas, in a gas-engine cylinder, would produce 1 hp.-hr., it would require 2 lb. of coal, or a trifle more, when used under a steam boiler. This comparison may not be used in the comparison of producer gas, as a certain amount of the available heat is used in the producer in distilling off the gas and in vaporizing the water contained in the fuel. As regards plant construction and operation, the gas producer is much cheaper and simpler an apparatus than the steam boiler and requires less atten- tion. A surplus of gas may always be kept on hand, in a gasometer or storage tank, and the engine started on a moment's notice, while with a steam boiler time must be consumed in getting up a head of steam. Gas too lean to be used under a boiler is found to ignite rapidly when under compression in a gas-engine cylinder. Blast-furnace gas is an example of the above, large two- cycle engines operating on this gas being in use at the shops of the Lackawanna Steel Company, in Buffalo, New York. The value of a gas as used in a gas-engine cylinder is largely dependent on the number of British thermal units it contains, although the richness of the gas must also be considered. A lean gas may be burned completely in a cylinder with less air, and a consequent larger amount of gas, than a gas of high thermal value. The following table gives the heat units per pound and per cubic foot for the different fuels. Natural gas v is seen to have the greatest heat value, but, notwithstanding this, gasoline vapor, with its lower heat value, is credited with about 11 per cent more power. This fact is due to the rate of flame propagation being more rapid in the gasoline vapor than in the use of (>S INTERNAL COMBUSTION ENGINES natural gas, with the result that the combustion assumes more the aspect of an explosion. A corresponding increase in the mean effective pressure results. TABLE I. HEATING VALUES OF DIFFERENT FUELS. Fuel. Molecular Weight. Heat Units per Lb. Heat Units per Cu. Ft. 1 12 142 78 86 46 60 26 38 61,560 14,540 22,000 18,448-22,000 18,000-21,000 12,950 20,000 21,492 18,000 18,350 293.5 Carbon, C Alcohol, ethyl, C 2 H 6 OH.... Alcohol, methyl, C,H 4 2 . . . Acetylene, C 2 H 2 Gasoline vapor, CH 14 868 900-1,050 800 665 620 300 100-160 135 1,051 1,677 " 16 " ... " 15 " ... Marsh gas (methane), CH 4 . defiant gas, ethylene, 13 28 23,594 21,430 The constituent parts of natural gases vary in different localities. Table II gives some of the different volumetric analyses of Pennsylvania gases. TABLE II. VOLUMETRIC ANALYSIS OF PENNSYLVANIA GASES. Constituents. Hydrogen, H Ethylene, THE FLYWHEEL 139 In which W = weight of rim, a =24,000,000 for engines firing charge every revolution and 48,000,000 for engines of the four-cycle type, A = area of piston in sq. in. S = stroke in ft. R = rev. per min. D = outside diameter of wheel in ft. The revolutions per minute or speed for which engines are designed being known, the above formula, with the constant a as given, is good for average purposes, but, as we have AS observed, the value of ^p- may vary, for different purposes, from 1.5 per cent to 3 per cent; hence it is obvious that for varying conditions we should introduce a factor to take care of this allowable variation. As a matter of fact the constants a = 24,000,000 and a = 48,000,000 are average figures, and the value of a should be taken from 20,000,000 to 30,000,000 and from 40,000,000 to 60,000,000. We are then able to modify the formula to suit different conditions as follows: W= 2AiL. x (27) R 2 D 2 In which we consider a as 20,000,000 in all cases for a two-cycle engine, and as 40,000,000 in all cases for a four- cycle engine, and x is a constant, for different conditions, as shown in the following table: Portable engines 1.0 Pumping and ordinary use 1.1 Driving machine tools 1.2 Driving looms or textile machinery, etc 1.3 Driving electric machinery, etc 1.4 Driving cotton spinning, etc 1.5 Automobile and motor-boat engines permit, and their usage demands, a lighter flywheel than for stationary pur- poses, and in these engines we may safely use a value of x as low as 0.60 for automobiles and 0.75 for motor boats. Having determined the weight of rim necessary, its content in cubic inches is determined by dividing the weight by 140 INTERNAL COMBUSTION ENGINES E ^ 0.27, which is the approximate weight, per cubic inch, for cast iron. Now assume some thickness for the rim ■ — the thickness should, wherever possible, be its minor dimension, so that its center of gravity may be as far from its center of rotation as possible. The mean diameter of the rim will, then, be equal to its outside diameter plus its inside diameter, divided by two. The mean diameter and circum- ference and thickness of rim being known, its width must be such that it may contain the number of cubic inches, above determined, necessary to produce the required weight. Use the nearest -J- in. above the calculated width. Most flywheels used on stationary engines are made with six spokes, while the majority of automobile and marine engines use the webbed pattern. Fig. 51 is a spoked wheel showing the average dimensions in good use. In the equations, s = crank-shaft diameter. Then Flywheel. h = 2 s. i d b = 3s. = s (approximately). = 0.4 s (approximately) The dimension d may be computed from Unwin's flywheel formula, in which D = diameter of pulley in in. B = breadth of rim in in. n = number of arms,* thus: rf = 0.6337 V n (Single belt) d= 0.798 J— (Double belt) V n (28) (29) For a flywheel transmitting no power a smaller value may be used. THE FLYWHEEL 141 D = 6000 = 1910 : tzR R (30) iiMiiiiiiiiiiiiiiiiiiiiiiiiiiiiiniim T Some manufacturers design their flywheels in two parts, and provide notches, in the rims, in which a bar may be inserted for turning the engine over. Fig. 52 represents such a wheel; the outer rings a and b are shrunk on, leaving the space in which the notches have been cut, as shown. The rings and bolts bind the wheel firmly together. The maximum velocity of the rim is generally taken at 6000 ft. per min. Then 6000 = nRD. Whence Fig. 52. Flywheel. The size of key necessary may be found in Tables X to XIII and should be of as strong cross-section as possible and a tight drive fit in order to lessen the tendency to work loose. TABLE X. DIMENSIONS OF FLAT KEYS, IN INCHES. Diam. of shaft. . . 1 H i* if 2 2* 3 3* 4 5 6 7 8 Breadth of keys . ■ i A if A .\ i * i 1 n 1* 1* 1* Depth of keys . . . • A A i & A i A i 1 « « i 1 TABLE XI. DIMENSIONS OF SQUARE KEYS, IN INCHES. Diam. of shaft. . Breadth of keys Depth of keys . . 1 H i* i* 2 2* 3 3* 4 A A A M M 4» H A H A i A a A i A * i TABLE XII. DIMENSION OF SLIDING FEATHER-KEYS, IN INCHES. Diam. of shaft. . Breadth of keys Depth of keys . . . H n if 2 21 2i 3 3* 4 4+ i i A A * * * A A • I i A A i 1 s 1 i 1 * Kent's " Mechanical Engineer's Pocket Book," pages 821-822. 142 INTERNAL COMBUSTION ENGINES I— MM— I Table X should be used for all fixed work wherein the key not only drives, but also holds the parts against endwise motion. These keys are tapered and "bear all over." * A webbed flywheel, Fig. 53, should use a comparatively small thickness for its web. This thickness varies, in auto- mobile and marine engines, from 0.5 to 0.75 in., and need not be computed, as, in small wheels, a web as thin as could safely be poured would probably be as strong as six spokes. In most cases the thickness of the web will be found to be approximately one-fourth the shaft diameter. In a spoked wheel, always fillet the spokes well where they join the rim, as the large mass of metal may, otherwise, cause a crack to form at the joint. The flywheel must be accurately turned and balanced. If, after finishing, one side is found to be heavier than the other, holes are drilled in the heavy side in order to overcome this difficulty. Some manufacturers go so far as to finish the face of the web in a webbed wheel, but except for finest machines this will be found unnecessary. Fig. 53. Flywheel. * John Richards, in Cassier's Magazine. CHAPTER XVII. THE FRAME. The gas-engine frame serves a twofold purpose; it rigidly supports the crank shaft and cylinder and resists their tendency to separate from the force of the explosion, and, by its inertia, absorbs a part of the unbalanced forces in the engine and transmits to the foundation proper the remainder of these forces. The advantage of having a comparatively heavy foundation on which to rest the engine frame is due to the fact that it is undesirable as well as impractical to make the frame heavy enough in itself to effectively absorb the vibrations, as such a large mass of metal would be exceedingly cumber- some to handle. In view of this fact it is customary and good practice to make the engine frame of cast iron and as heavy as may be, at the same time preserving its mechanical appearance and limiting its weight to such a degree as to permit of its being handled in the machining process. For these reasons it is not customary for the engine designer to compute any part of the frame, with the exception of the bolts, as it is assumed that it will be amply strong to resist any shock to which it may be subjected. The formula to be used for computing the bolts that fasten the cylinder to the frame is given in Chapter XV, page 135, and needs no further discussion. Horizontal Engines. — Fig. 54 will serve to show the general character of design of frame as used in gas engines. Nearly every manufacturer will be found to modify his frame to some extent, and it would be useless to go more fully into their special characteristics. In the frame shown in Fig. 54, the bearings are set at a 45° angle, in order that most of the thrust of the crank 143 144 INTERNAL COMBUSTION ENGINES shaft may be against the frame instead of against the bearing studs. While an angle of 45° will not be such that the maximum forward thrust will be received by the frame, a greater angle would not be desirable, as it would bring the joint in the brasses too near the bottom of the bearing. In Fig. 54. Frame for Horizontal Engine. the design shown brass liners, a, are used to take up the play in the shaft. Four or five of these liners, made of light-gage brass, should be used. They are cut to conform to the shape of the cap and to clear the shaft ^ in. Two or three may be made of 30-gage B. & S. and a like number of about 40-gage. A good rule to follow for the size of the bearing studs is to make their diameter, at the base of thread, 0.25 the diameter of the shaft- Some manufacturers carry a projection of the frame out under the cylinder, on which lugs are cast, and bolts are passed through corresponding lugs on the cylinder. It is doubtful if this is good design, as the unequal expansion of the cylinder and frame will either loosen these bolts or cause a distortion of the cylinder alignment. The air supply for this type of engine is generally drawn from the hollow base, in order to make the operation as quiet as possible and to secure a warm dry suction. The Vertical Engine. — In this type of engine, the frame usually becomes a crank case, completely housing the shaft and cam gearing. There are exceptions, of course, in cheaply constructed single-cylinder engines for general purposes, but the modern high-class vertical engine as a THE FRAME 145 rule has a closed crank chamber. The same general rules apply to proportioning and designing as in the horizontal type, whether the frame consists of a closed case or is of similar construction to that used in the horizontal engine. In the crank-case type of engine the case is generally made in two halves, the lower half carrying the bearings, which are independent of the upper half. The cylinders are Squared fa vtrenchp Fig. 65. Frame for Vertical Engine. fastened to the upper half, and the two halves are fastened securely together. Fig. 55 gives a good general idea of this class of design. The formula for the cylinder studs, a, has already been given and needs no further discussion. The two halves of the case are shown fastened together by means of the bolts or cap screws, b. The bearing pedestal, as shown, is integral with the lower half. The play in the bearings is taken up by means of the wedge, c, which acts on the screw, d, as shown. As the bearings in this case are more or less, in- accessible, it is desirable that this method of taking up the play be used instead of placing liners between the bearings, as described in the horizontal type. Some of the best horizontal engines also use the wedge and screw to secure their adjustments. 146 INTERNAL COMBUSTION ENGINES Access is had to the interior of the case by means of plates e and /. Plate /, as shown, covers the cam and valve, as well as the starting mechanism, if used; the push-rod bushing being inserted at g, above the cam shaft, shown at h. The bearing studs i, as shown, require that the side plate / be removed in order to reach them. A better design would be to use a long cap screw C, with a shoulder to act on the bearing cap, and continue it through the top of the crank case, where it would be easily accessible. Manufacturers of both vertical and horizontal engines often make a sub-base or bed plate. Especially is this true in the manufacture of direct-connected units, the sub-base forming an accurately machined bed, onto which the engine and dynamo are fastened, and their perfect alignment assured. CHAPTER XVIII. ENGINE FOUNDATIONS. The engine foundations are almost always built by the owner or contractor from drawings furnished by the engine builder. The drawings consist of accurately dimensioned plates showing location of the foundation bolts, and also a drawing of a template to be made for locating these bolts in the foundation. Without a good foundation an engine is bound to give trouble, sooner or later, from settling or from the engine working loose from the foundation and getting out of line. The foundation of the engine may be considered as a part of the bed plate or frame, in that it should be given sufficient mass to absorb, by its inertia, the effect of the suddenly applied cylinder or crank-pin forces not absorbed by the bed plate and frame. It should get a good bearing on solid ground, the quality of the soil governing, to a large extent, the depth of foundation necessary. Under no condi- tions should an engine be fastened directly to the floor of the engine room, except for a temporary job, and furthermore, the floor of the building should be absolutely independent of the foundation, in order to prevent the transmission of vibrations to other parts of the building, except as may be transmitted by the concussion of the air or the vibration of the ground. When it becomes necessary to reduce the vibration still further, a layer of some insulating material, 2 or 3 in. thick, should be placed between the foundation and the surrounding soil. A substance such as deadening felt, horsehair felt, or cork may be used and a layer 8 or 10 in. thick placed next to the foundation. Cork, however, should not be used below the foundation owing to its tend- ency to absorb water and swell. A bed of dry sand as a bottom has been used with good results. 147 148 INTERNAL COMBUSTION ENGINES If it becomes necessary to install an engine on an upper floor where a bearing on the ground cannot be obtained, a crib of heavy timbers should be built below the floor to support a foundation of concrete. This foundation will absorb, by its inertia, a great deal of the vibration. An engine foundation may be made of concrete, brick laid in cement, or stone. If of concrete, the mixture should be one part good Portland cement, two parts sharp clean sand, and four parts broken stone small enough to pass through a 2-in. ring. The concrete should be laid in layers of not more than 6 in., each layer being thoroughly tamped before the next layer is put in. Foundations made of brick should be laid in cement mortar composed of one part Portland cement to two parts clean sharp sand. The brick used should be hard- burned foundation brick. A very good foundation, up to the floor line, may be made of brickbats laid in the above- mentioned mortar, care being taken to fill all voids. This foundation may then be built up of concrete or brick, in the ordinary way, to receive the engine. A brick foundation should have a cap of limestone or granite, or a cement cap 1 ft. in thickness may be put on. Stone foundations should be laid up in cement mortar, and in regular steps, being sure that the stones have a good level bearing, so as to prevent any tendency to slide. A concrete foundation should be given a batter of about 2 or 3 in. to the foot, and a brick or stone foundation should follow, in general, the same outline. A concrete foundation of standard design is shown in Fig. 56. If, as frequently is the case, the engine is a direct-con- nected unit, that is, an engine directly connected to a dynamo, then the foundation should be so designed as to take in the dynamo and outboard bearings. The weight of an engine foundation is seldom computed, as differently designed engines are subject to different degrees of shock, from their unbalanced forces, and the weight of their frame and bed plate may vary to such an extent that any formula would be applicable to but few cases were the surrounding conditions the same. With the condition of the soil varying, it would be impossible to ENGINE FOUNDATIONS 149 derive a universal formula that could be used in all cases with even a reasonable degree of accuracy. When the engine and building foundation both rest on rock, it is often found that this rock carries the vibration of the engine to the building. It is good practice to make the foundation Fig. 56. Standard Engine Foundation. amply heavy; go well below the frost line and give the foundation a good broad base and its weight will in most cases be ample. If brick is used in the foundation, it is well to remember that 1.25 cu. ft. of brick is about equal to 1 cu. ft. of concrete. (See table of weights.) The number of foundation bolts used varies with the size of the engine, in no case being less than four and usually not more than eight. The approximate number may be found by the formula P N- (31) Where P is the horsepower of the engine always use the nearest even number of bolts. The size of the bolts used varies from 0.75 in. for small engines to 1.5 in. or 1.75 in. for large machines. It is not advisable to make the bolts smaller than 0.75 in., as there is a good chance of their being twisted off in tightening. The engine frame should be, to all intents and purposes, a part of the foundation, so that their combined inertia may act together to absorb the shocks. For this reason the founda- 150 INTERNAL COMBUSTION ENGINES tion bolts should be ample in size and of sufficient number to accomplish this result. In laying out a foundation proceed as follows: Dig down to good firm ground, or hard pan, and level this bottom off carefully; in case the ground is marshy it may be necessary to use piling, but this is unusual except in some localities. If it is found to be necessary, piles may be driven on 30-in. centers and cut off at ground-water level. The concrete should then be filled in between the piles and the foundation proper started up from that point. Having secured a good bed, locate accurately the position of the engine, and place the bolt template in such a position over the excavation that the foundation bolts may be suspended, by their nuts, through the holes in the template, in the position which they will assume when the engine is set. The bolts, before being suspended from the template, should have a piece of iron pipe slipped over them, Fig. 56, A. This pipe should be large enough to allow a slight movement of the bolt in setting the engine. The pipe is supported at its lower end by the bolt anchor, and its upper end should come just below the top of the finished foundation. The foundation may now be built up around these pipes. When the top course, either brick or concrete, is laid, be sure that the surface which is to receive the bed plate is perfectly level. This leveling should be done with a Y level and must be accurate. After the engine has been set the pipes should be filled with cement mortar. A good size of pipe to use is a 2-in. standard gas pipe. Foundations after being built should be allowed to set for at least a month, unless circumstances demand them to be used sooner, in which case the concrete should be made as dry as possible to secure a good mixture. It should not be assumed that it is common practice to insulate the foundation with a shock absorbent, as above described. This is done only when the location of the engine is such as to make it desirable that every precaution be used to prevent a nuisance. CHAPTER XIX. THE CRANK SHAFT AND RECIPROCATING PARTS. The crank shaft, connecting rod, and piston, together with their respective parts, constitute the rotative and recipro- cating parts of a gas engine. The crank shaft, as previously described, carries the flywheel, and balance weights, if used. With but few exceptions, gas-engine pistons are of the trunk variety. The reason for this very general use of the trunk piston is that if the engines were provided with a piston rod and made double-acting, as is the practice in steam engines, the rod end of the piston would be subjected to as much heat as the head end, and the rod, becoming heated, would expand and cut into the stuffing-box. Except in the case of two-cycle engines, in which the crank case is used as a primary compression chamber, there is no necessity of closing the forward end of the cylinder, the piston itself being made long enough to act as a guide without the use of a piston rod and cross-head. A few engines have been designed which were double-acting, the rod and packing box being cooled by means of water made to circulate about them, but as these types may be considered in the "freak" class no special discussion will be given them. The crank shaft of a gas engine, while it serves in the same capacity as the shaft of a steam engine, must be made very much stronger, since it is subjected not only to the strain due to the conversion and transmission of the power received but, at the beginning of the working stroke, it is subjected to six times the average power of the engine. In determining the size of crank shaft necessary, the diameter of the piston and the maximum cylinder pressure are taken as the basic conditions for the computation. 151 152 INTERNAL COMBUSTION ENGINES Let D B — the diameter of the shaft in in. D c = the diameter of the cylinder in in. P m = the maximum cylinder pressure. For a drop-forged steel shaft the average practice is to make D, = 0.05 D e VPm ■ ■ ■ (32a) For malleable or wrought iron, D s = 0.06 D c VK (32b) These values will be found to produce results closely in keeping with average practice when the stroke is equal to 1.5 D c . E. W. Roberts gives the following formulas for crank shafts where the ratios of the stroke L to the cylinder bore is other than 1.5 : 1. For wrought iron, D, = 0.056 VPJL.Dc 2 .... (33a) For steel, D a = 0.052 VPJL.Dc 2 .... (33b) As he remarks, the formulas will be found to give results larger than the average practice, but for stationary engines this is a good fault. For marine and automobile engines the values will be found to be much larger than average practice requires. The length of the crank-shaft bearing necessary is readily determined, once the diameter is known, from the following formula : T) 2 P I = Uc r (34) 1018 D s K ' In which I = length of the bearing. D c = cylinder diameter, as above. D s = Shaft diameter, as determined. P = Mean effective pressure. In practice, however, the crank-shaft bearings are usually made much longer than the value which would be obtained by the use of this formula. A good rule to follow is to make I = 2.5 D a . THE CRANK SHAFT AND RECIPROCATING PARTS 153 The crank-pin diameter is usually made from 1.1 to 1.3 the diameter of the crank shaft, and its length would then be determined from the following formula: D C 2 P lp — ■ (35) 508 Z) p In which D p = diameter of the crank pin. I = length of the crank pin. D c and P as in the above formula. The crank arms should be sufficiently large to withstand the suddenly applied forces to which they are subjected. Fig. 57 illustrates a good design of crank for a stationary slow-speed engine. The relative dimensions of the crank Fig. 57. Crank with Oil Ring. arms are given in terms of the crank-shaft diameter, and will be found to produce values closely in keeping with stationary- engine practice, although slightly heavy for automobile or marine engines. It is customary to leave ^V m - finish for the ends of the crank-pin brasses as indicated at a. In larger shafts this finish is sometimes increased to ~fa in. A like finish is allowed at b. This allows the fillets for the brasses to be finished, as shown, without facing both surfaces of the crank throws. Single-throw cranks for high-speed engines are provided with balance weights in order to neutralize the weight of the crank arms and that part of the connecting rod regarded as rotative. It is customary to assume two-thirds of the weight of the connecting rod to be centered in the crank pin 154 INTERNAL COMBUSTION ENGINES and hence to be added to the weight of the pin when comput- ing the balance weights necessary. The usual location for the balance weights is to place them one on either crank throw and on the side of the shaft opposite to the pin. When located in this manner they should be securely fastened in place with pins, and a perfect bearing secured by babbitting the joint or by machining both the weights and crank arms to a perfect and tight fit. The slightest play in these weights will increase very rapidly as the engine is run and will cause no end of trouble. When the weights are babbitted a groove in the weight and crank arm, as indicated in Fig. 58, retains the babbitt and secures the weight firmly, and when the rivet and cap screw are in place, as shown, a good job is secured. When the joint is machined the rivet and cap screw are used in the same manner. Some engines carry the balance weights on the flywheel and on the side opposite the crank pin. When located in this latter position they may be much smaller, owing to their increased radius of rotation, but their increased distance from the center of force introduces a greater amount of wear on the engine bearings. In balancing a single-throw crank the first thing to deter- mine is the weight, considered centered in the crank pin, to be balanced by the counter weight. As previously men- tioned, two-thirds of the connecting rod is considered as rotative. Then the weight to be balanced would be equal to § Wr+W p + x. In which W r = Weight of connecting rod, brasses, and bolts, etc. W p = Weight of crank pin and that part of the arms concen- tric to the pin. x = Weight of the remainder of the crank arms considered centered in the crank pin. The values W r and W v are easily determined, but the value of x, accurately computed, would possibly require a rather complicated equation. Hence it is customary to determine the moment of W r and W P and then to balance THE CRANK SHAFT AND RECIPROCATING PARTS 155 them with a weight 10 per cent in excess of the calculated value. Then 1.1 (W r + W p ) I = moment of balance weights necessary (I being the distance from center of shaft to center of pin). Now taking the distance of the center of gravity from the crank-shaft center to be l u the weight necessary to balance the crank and rod would be W _ 1.1 (W r +W p )l h (36) Half of this amount in each weight with their centers of gravity l t distant from the shaft would nearly produce a balance. To determine the value of l t it is customary to "cut and try." Lay out the crank and balance weights, as shown in Fig. 58. Then cut out a template of cardboard Machine ffr/sjornf or babbit en indicated aotteet /mea o Fig. 58. Balanced Crank. the exact shape of the weight as drawn; find the center of gravity of this template by balancing it on a pencil point and then determine the distance of this point from the center of the shaft when the weight is in place. Using this value in equation (36) gives the total amount of balance necessary, and half of this amount is to be placed in each weight. If the value of l u as determined, is found to be so small that, in order to make the two weights equal to W, it is necessary to make them thicker than the crank arms, then a larger template should be laid out and a larger value for l x deter- 156 INTERNAL COMBUSTION ENGINES mined, from which a smaller value for W will be found. Crank shafts with more than one throw are not balanced, since the different rods and arms balance each other; neither is it customary to balance the crank of the cheaper industrial engines. The more expensive engines have their shafts turned and then ground in order to insure a smooth bearing. The shaft and connecting-rod bushings are made of some good bearing metal, turned and finished to the proper size, after which they should be "scraped in" and the oil grooves cut to carry the lubricant. Fig. 59 illustrates such a bushing ^j_ ■oceO c Fig. 63. Piston Ring. amount of metal, expands much more rapidly than the crank end and is liable to stick and cut the cylinder. Obviously this taper should increase with the piston diameter. A good average rule is to make the head diameter equal to 0.998 D c and the crank end equal to 0.999 D c . The length of the piston should approximate 1.5 the stroke with the wrist pin located practically at its center. The best pistons are usually provided with four eccentric rings, although some of the cheaper ones are made with three or even two rings. The ring at the crank end serves in the capacity of an oil ring and also provides a bearing for that end of the piston. The piston ring is shown in Fig. 63 and its dimensions are given in terms of the cylinder diameter. The rings should be made of the best grade of gray cast iron THE CRANK SHAFT AND RECIPROCATING PARTS 161 and cast in a so-called "piston pot." A "piston pot" is generally made large enough to turn out eight or more rings; it is finished to the size required on the outside, and the inside turned to the proper eccentricity, after which the rings are cut off and slotted. The rings may then be chucked in an electric chuck and ground to the exact cylinder bore, or they may be used with the machine finish. The best engines have the rings ground, as this insures a ring perfectly round Two-Cycle Piston Head. when compressed into the cylinder. To maintain the rings in their fixed positions and with their joints properly staggered, a dowel pin is placed in the piston groove to correspond with the pin hole in the ring slot as shown. The rings are then fitted to their respective grooves, making them just small enough to contract and expand without binding. Pistons for use in two-cycle engines are cast with suitable means for deflecting the incoming gases to the top of the cylinder. This may be accomplished by means of a web cast on the top of the piston, see Fig. 64, A, or in a more satis- factory manner by casting the piston as shown at Fig. 64, B. The general dimensions of the piston and rings remain the same as in four-cycle engines. The method of obtaining the exhaust-port lead in type B has already been discussed in the chapter on cylinders. CHAPTER XX. GOVERNING DEVICES. There are four principal methods used for governing the speed of an internal-combustion engine, viz. : (1) By throttling the charge; (2) By cutting off the supply during one or more complete cycles, commonly known as hit or miss; (3) By keeping the exhaust valve open or closed during one or more strokes; (4) By interrupting the spark if electrical ignition is used. Greatest regularity of operation but poorest economy is obtained by throttling the charge, but it is undoubtedly the most satisfactory when, owing to the nature of work per- formed by the engine, the speed variation must be slight as in the driving of electrical machinery. A combination of the two methods has been used in which the charge is throttled up to certain limits and then cut off. See Fig. 65, the Otto electric-light governor. The properties of explosive mixtures of gas and air will show the reason for the throttling method being uneconomical. "The limits of change allow- able in the proportions of gaseous explosive mixtures are very narrow, the gas present ranging from \ to -jV of the total volume. A mixture containing \ of its volume of coal gas in air has just sufficient oxygen to burn it and no more; any further increase of gas will pass away unburned, there being insufficient oxygen present for its combustion." — Clerk, "The Gas and Oil Engine," page 226. A mixture of air and gas containing less than -fa of its volume of gas loses its inflammability altogether. It follows that governors acting on the gas supply should be set to govern between these limits only. The mixture itself may be throttled without altering the 162 GOVERNING DEVICES 163 ratio of gas to air, thus producing instead of an inferior mixture a greater or less amount of the same quality of mixture. This method reduces the force of explosion and at the same time maintains a uniformly explosive charge. Keeping the exhaust valve open is of course wasteful of fuel and less economical, as is also stopping the spark. Keep- ing the exhaust valve closed produces a mixture of unburned products in the cylinder which must be completely exhausted before the cycle of operations can again be taken up. The "hit or miss" type in which the fuel supply is entirely cut off for one or more complete cycles is of course the most Fig. 65. The Otto Electric Light Governor. economical method in use, as the charge is never varied and there is either an explosion of full force or none at all. It is apparent, however, that "hit or miss" governing admits of a greater range of speed variation, although it is possible with a properly adjusted governor to obtain regulation within four or five per cent as against two per cent with the throttling governor. The mechanisms used to control the different governing devices are of two general designs, viz : (1) The centrifugal 164 INTERNAL COMBUSTION ENGINES governor, which may be used for any one of the above-men- tioned methods of governing; (2) The inertia governor which is applicable only to "hit or miss" governing. A modification of one of these two methods, more or less involved, is the principle of every governing device. The centrifugal governor is essentially a revolving pen- dulum with inclined arms, advantage being taken of the tendency of these arms to revolve in the same plane as their points of support. Figs. 66, A and B, illustrate the principle of the centrifugal governor. At A the two fly balls a and b are connected, as shown, to collars c and d. Collar c is fastened to shaft e, while collar d, carrying the swivel / to which bell crank h is fastened, is free to move. As shaft e is revolved the balls a and b separate as indicated by the arrows and in doing so lift the collar d. This movement is resisted by spring s, the tension of which may be adjusted by collar i. When the speed reaches a certain limit collar d will be raised until bell crank h throws the push rod / away from the valve stem as shown. Valve k then remains closed until the speed decreases and j returns to its place below the valve stem. This device is of the "hit or miss" variety. To determine the lift of the governor balls for any given speed — their weight and the resistance of the spring s being known — we have, for a simple pendulum, the ratio h __ weight _ _w_ _qr r centrifugal force wv 2 v 2 9 r or h = 8? Substituting for v its value 2 nrn, , 9.788- h = — — in. 35.237 • /00 . or " -JfT m (88) GOVERNING DEVICES 165 I? 166 INTERNAL COMBUSTION ENGINES In which h = distance from plane of center line of balls to the plane of their points of suspension. r = radius of circle described by balls in ft. g = 32.2. v = velocity of center of balls in ft. per sec. = 2 nrn. n = number of rev. per sec. N = number of rev. per min. The simple fly-ball governor is not isochronous; that is, it does not revolve at a uniform speed, since the speed changes with the angle of the arms. To remedy this defect the governor is loaded by means of a spring or weight. For the loaded governor we have the value of the centrif- ugal force, due to the weight of the balls, unchanged, but the value of the weight now becomes equal to the combined weight of the balls and the value of the spring load con- sidered directly below the center of gravity of the balls. Let I = length of arm y from the point of suspension to the center of gravity of the ball, and let the length of the suspending link l x = x be the length of the arm y from its point of suspension to its point of attachment to the ball; v) = weight of one ball; w s = half the value of the spring load in pounds; h= the height from plane of revolution of balls to point of suspension of y; then h =W[ 1 + 2 $j)] ■ ■ ■ ■ ^ the ratio of half the spring load to the weight of one ball being — and the relation of its suspension point to the center w of gravity of the ball being as -j. Unless the links y and x are equal in length, this relation will not hold true. The lift being determined, the bell crank or other mechanism con- necting the governor to the valves is easily laid out. Since a governor is designed and set for a certain speed it must- be run at this normal speed regardless of that of the engine. If the engine speed is increased or diminished, the governor must be geared down or up as the case may be. GOVERNING DEVICES 167 At B is shown another application of the centrifugal ball type of governor. The lift of the balls, a and b, may be determined by means of another application of the ratio h _,_ Weight r Cent. Force I W - Ws h _ £, sin a (Considering the spring load to be r Wv 2 combined with the weight of the balls.) gr Simplifying, h = 5^1 /(I + — ^M . . . (40) n 2 \ Wl ! sin a) In which n = The rev. per sec. Ws = Half the spring load. W = The weight of one ball. a = The angle of the arm I. If we allow N to represent the rev. per min., then the formula will be h - ™L (i - -&-.). N 2 \ TfZjSina/ This formula for small movements of the balls is suffi- ciently accurate for all purposes. In this style of governor, referring to the figure, we have two levers acting on / as a fulcrum and exerting their lifting force at c and d. The bell crank g rides the cam roller h off or onto the cam i as the speed varies, and valve /, actuated by lever k, opens or remains closed as the case may be. It would be possible, by making the lift of the cam variable as shown at /, to produce a throttling effect at the valve. Throttling with a poppet valve, however, produces an abnormal amount of wire drawing of the charge. A better arrangement is to use an independent throttle valve in the gas main. Fig. 67 represents such a throttling valve with governor connection. As the balls a and b move outward the bell crank c moves with the collar d and the valve V is shoved in the direction of the arrow e. The openings / in the valve gradually move across the openings g in the shell h, reducing the 168 INTERNAL COMBUSTION ENGINES effective port openings into the annular space i, and throt- tling the mixture. The principle of the inertia governor is illustrated in Fig. 68. The weight a is connected to bell crank b and pivoted to the push rod c. The tendency of the weight to turn the bell crank in the direction of the arrow is Fig. 67. Centrifugal Governor and Throttle. resisted by the spring d, but as the push rod is moved rapidly the inertia of the weight partially overcomes this resistance and the engaging parts of the valve gear are separated when the speed reaches a certain limit. The strength of the spring required is determined by means of the following formula: W = WV, 9 h (41) In which W = Capacity of the spring in lb. Wa = Weight of a in lb. l l = Lever arm of a about c. V = Velocity attained by push rod b in ft. per sec. g = 32.2 ft. per sec. In the above formula the weight of the rod carrying the pendulum is neglected. To be accurate the resultant moment of it and the weight should be used, but by thread- ing the weight onto the rod, as shown, adjustment may be GOVERNING DEVICES 169 secured by moving it in or out as required. Inertia governors are used, as a rule, on industrial engines where regularity of operation is a secondary consideration to the cost. Electrical governing is accomplished by switching off the current for the ignition system by adapting some one of the above-mentioned governing devices to the requirements. When the engine attains a certain speed the current is cut off, and for one or more cycles the engine runs without an impulse. Electrical governing is of the "hit or miss" type. In order to operate well a governor mechanism must be as sensitive to the variations of speed as it is possible to make it. For this reason the practice of placing the mechan- ism in the crank case is unfortunate. The device, when in this location, is constantly subjected to the splash from the crank shaft, and the dirty oil soon gums and causes the parts to stick. The engine will then be found to be governing poorly, and the result in electrical installations is a fluctuation in the e.m.f. If it is deemed advisable to inclose the governing mechanism, a separate chamber should be used for this purpose and the governor inspected and cleaned from time to time. t>8. Inertia Governor. CHAPTER XXI. IGNITION. There are three general methods employed for securing the ignition of the compressed charge in a gas-engine cylinder : (1) By means of an electrical spark; (2) By means of a mechanically operated flame or heated surface; (3) By auto-ignition, in which heat sufficient to ignite the charge is produced either by means of the compression alone or by means of the combined effect of compression and residual heat. Electrical ignition devices are most extensively used, and these may be subdivided into two classes: (1) The jump- spark system; (2) The make-and-break system. Jump-spark ignition, as the name implies, consists in causing an induced current of high potential to spark between two metallic points conveniently placed in the compression space of the cylinder, the spark thus produced igniting the compressed charge. To produce the spark at the proper instant in the cylinder a make-and-break contact must be placed somewhere in the electrical circuit, this contact being so operated by means of the crank or cam shaft that at some point in every operating cycle the circuit will be closed and an e.m.f. generated sufficient in value to cause a spark to jump across the gap. This make-and-break device is generally known as the commutator or spark advancer, the latter name having its origin from the fact that the com- mutator is so arranged that the engine operator, by means of a suitable lever, is able to change the point at which the charge is ignited so that it may correspond to the speed at which the engine is running. This statement may be some- what confusing inasmuch as the speed regulation is obtained, to a very large extent, by advancing or retarding the time 170 IGNITION 171 of ignition. Nevertheless the point in the cycle must correspond to the speed at which the engine is operating, at any particular instant, in order to secure smooth running. In starting the engine the spark is set at a point slightly beyond dead center and in the expansion stroke. As soon as the explosions commence to occur regularly the spark is gradually advanced past dead center and into the compression stroke, thus giving the engine time to gather speed. If the spark is rapidly thrown over dead center into the compression stroke the engine will either stop or pound badly until it attains sufficient speed to carry itself from the point of ignition up to dead center before the burning gases reach their maximum pressure. The make-and-break system of electrical ignition consists in causing, by mechanical means, two points or electrodes located in the compression space to close and then open the electrical circuit. This may be accomplished by causing the points to rub together and then separate, producing what is known as the "wipe spark," or by forcing the points together and causing them to separate by means of a spring, some- times called the "hammer break." When the points break contact an intensely hot spark or arc is produced, due to the inertia of the electric circuit producing, momentarily, a very high potential. The make-and-break spark is much hotter than the jump spark and on reasonably slow speed engines is the most satisfactory form of electrical ignition, it being almost certain that, if the points are in good condition, a spark hot enough to ignite the charge will be produced at every contact. On the other hand, the points are subject to much wear, especially with the wipe spark, and conse- quently deteriorate quite rapidly. If platinum alloy is used for the points they are usually quite expensive, and the necessity of replacing them is troublesome as well. Within the past few years other alloys, which it is claimed by their manufacturers give better satisfaction, have been placed on the market. "Casalloy" or " meteor- wire" is one of these substitutes. 172 INTERNAL COMBUSTION ENGINES The points of a make-and-break ignition may, with proper care and a current of proper strength, be made to last a long time. If the electric pressure is too low, unsatisfactory ignition will result, while, on the other hand, should the pressure be too high the plugs will require adjustment or renewal in a very short time. With a battery of low internal resistance, as a storage cell, the difference of potential at the terminals should be much less than with cells of high internal resistance. In order that a sufficiently large number of prim- ary cells may be carried for all emergencies and to allow for nil B -cna Fig. 69. The Non-inductive Resistance and the Condenser. depletion, the destructive action at the points may be reduced by placing a condenser in parallel with the points or by introduction into the circuit of a non-inductive resistance. Fig. 69 illustrates clearly these two methods. A non- inductive resistance thrown into the circuit in series causes a fall in potential without producing any unbalanced electromagnetic action which would affect the sparking coil. Such a resistance coil is made by doubling a wire, placing the closed end on a bobbin of wood or other non-magnetiz- able substance, and winding the wire about the bobbin as indicated at A, Fig. 69. The electromagnetic action in one wire is thus neutralized by an exactly similar and equal action in the other. It is apparent that if this method is used a suitable resistance box with varying resistances to accommodate itself to varying conditions must be provided. If the condenser method is used and a condenser large enough to meet all requirements is provided, no further adjustment or attention will be necessary. IGNITION 178 The ordinary commercial condenser consists of sheets of tin foil as shown in B, Fig. 69, insulated from one another with the alternate sheets connected to terminals. The current for the ignition is obtained by means of primary cells, storage batteries, or a small dynamo inducing high potential secondary current in an induction coil. For the primary-secondary jump-spark ignition system a secondary current of momentarily extremely high potential Ground' Fig. 70. The Ruhmkorff Coil and Connections for Single Cylinder. is required; this is obtained by means of the so-called Ruhmkorff induction coil or vibrator. Fig. 70 shows the construction of this coil as applied to a single cylinder. T l and T 2 are the battery terminals of coil of which T is the ground terminal; B the battery; C the contact screw with platinum point p; D the commutator, one terminal being grounded by means of its own shaft closing the primary circuit with T when the commutator points are in contact; E the vibrator of soft iron which opens and closes the circuit at point p; F the condenser, which momentarily arrests the primary current and minimizes the break spark 174 INTERNAL COMBUSTION ENGINES at p (the condenser is not essential and many coils are made and operate successfully without it); G the primary coil of heavy wire carrying battery current; H the secondary coil of heavily insulated fine wire; / the spark plug, to one terminal of which the secondary coil is connected, the other terminal being connected through the ground to the opposite end of the secondary coil, and / the iron core of very soft annealed wire. Fig. 71 shows, diagrammatically, the wiring connections for a four-cylinder engine with jump-spark ignition. The Fig. 71. Wiring Connections for Four Cylinders. coil consists of four unit coils identical with the single coil previously described and all using the same ground connec- tion. By means of the commutator the primary current is made to pass alternately through the units 1, 2, 3, and 4, producing in each, in turn, a high-potential current which fires the charge in the cylinder to which it is connected. The system as shown is wired for two sets of batteries, B and B t . By means of the three-point switch A either set of coils may be thrown into the primary circuit, so that if one is found to produce an insufficient spark the other set may be used. The coil is a very important element in the successful operation of a jump-spark ignition system. Numerous makes of coils are marketed, many of which are apparently very reasonable in cost, but it is doubtful if it is advisable, in any case, to purchase a coil and consider its low cost as IGNITION 175 a recommendation. The coils which give best satisfaction are rather expensive, but it will be found in the long run that they are most economical. To give good results, especially on high-speed engines, a coil must be fast, that is, it must charge and discharge very rapidly. In order to accomplish this result the core must be of best annealed iron wire and the coils well insulated, especially the high-tension windings. With a sluggish hungry coil the best of engines will give poor results. Every coil is rated to give a certain length of spark, but the points of the spark plug must be set very much closer than this maximum, since it requires much greater pressure to spark across a gap under high compression than in a vacuum or at atmospheric pressure. The strength of current must also govern the spark gap. For average practice tV in. is about right for this gap. The vibrator coil is not suitable for a make-and-break ignition system. The vibrating high-potential current will cause the ignition points to spark as they come together, or a spark may be produced at some equally undesirable point in the cycle. The ordinary single induction coil, or "booster," produces the best results, unless a sparking dynamo is used, in which case no coil is necessary, the current from the dynamo being sufficient to produce a good spark. In using the make-and-break system of ignition no commutator is used, as the current is interrupted at the ignition points and the timing of the ignition is secured by changing the point in the cycle at which they separate. In the jump-spark ignition system the spark is produced when the circuit is closed, this result being accomplished by the vibrator interrupting the current and producing the necessary high potential many times a second, while in the make-and-break system, this high potential being produced only once, as the points separate, it is at that point that the spark occurs. Fig. 72 illustrates a make-and-break system in which the points p and p t are forced apart suddenly without the wiping effect. In the figure, A is a quick- return cam which in the position shown is about to trip 176 INTERNAL COMBUSTION ENGINES push rod B. On this push rod is located the stop and adjustment collar C which impinges against the fiber washer D when the circuit is broken. The flat compen- sating spring E takes up the motion of the push rod B after the points p and p, are in contact. Coil spring F, acting ,6V Fig. 72. Hammer-Break Igniter. on lever G, as shown, throws the sparking points sharply apart as the point of the cam A leaves the push rod. The plug H, which carries the battery terminal p u must be con- structed of porcelain, or other insulating material equally as good, and brass. In the plug as shown the parts marked b are brass and those marked i are insulation. The entire sparking device is set into the cylinder head on the plate I and held in place with cap screws. The wiring connections are exceedingly simple, the coil J and battery K being connected up in series. The free terminal of the coil is grounded on the engine frame and the free terminal of the battery connected to the plug H as shown. It is apparent that the time of ignition may be varied by causing cam A to trip early or late, thus advancing or retarding the spark. IGNITION 177 This may be accomplished by making the edge c of the cam as shown at L, Fig. 72. Then by moving the shaft in the direction of X the spark may be advanced, the push rod tripping sooner than if the shaft were shifted toward Y, in which position the spark would be re- tarded. Fig. 73 shows a water-cooled hammer-break igniter, similar to that in use on the Rathbun gas engines. Fig. 74 shows a common type of wipe-spark ignition mechanism. The point p mounted on the oscillating device A makes and breaks contact with the spring point p. This oscillating move- ment is produced by means of the cam and push rod as shown, the re- turn movement being obtained by means of spring B. Timing may be accomplished by changing the tripping point of the cam as described. The ignition points should be located as nearly in the path of the incoming gases as possible in order to secure the greatest cooling effect. The electrode points in this igniter are not made of platinum alloy, and for that reason this form is inexpensive and, if properly designed, efficient. Ignition mechanisms attached to the piston head are used to some extent. The Pennington igniter is one of these and its principle is illustrated in Fig. 75. The circuit- breaking device A is tapped into the piston head, as shown, the insulated terminal being tapped into the cylinder and consisting of a coiled spring carried on the forked end of plunger C, as shown. As the piston P nears the end of its stroke the stirrup-shaped end of A, which has an inclined surface as shown, strikes B. If plunger C has been pulled out, as indicated by the arrow, only the point of B will be Fig. 73. Water-Cooled Igniter. 178 INTERNAL COMBUSTION ENGINES engaged by A and only a slight movement of the piston will be required to cause it to slip off of A and produce a spark. Under these conditions the ignition will be advanced. If, however, plunger C is pushed farther in, the contact break can be made to occur in the explosion stroke, the spring B being too long to slip past the inclined position of A which is merely pulled away from B as the piston recedes. With the Fig. 74. Wipe-Spark Igniter. ignition advanced it is apparent that this mechanism will produce two sparks, one as the finger B slips off A into the stirrup and another as it snaps out on the return stroke of the piston. The commutator or spark advancer, as used in connection with the jump-spark ignition system, is made in a variety of different forms and a description of one typical form should be sufficient for all purposes. For four-cycle engines it is either mounted on the cam shaft or geared to it with 1 : 1 gearing, it being apparent that, since but one explosion occurs in each complete cycle, the spark as well as the valve mechanism must be operated by a half-time shaft. In 10N1TI0N 179 two-cycle engines the commutator is either mounted on the crank shaft or geared directly to it without any reduc- tion in time. A commutator consists essentially of a piece of fiber, or other tough insulating material, carrying one terminal, and another terminal, connected to the ground, which once in every cycle comes in contact with the , J ; - insulated terminal, thus momen- tarily closing the electrical circuit. ri^fce;-) ! VSTf* ! T C m ?- 33 Fig. 75. The Pennington Igniter. Fig. 76. Commutator for Two- Cylinder Engine. Fig. 76 shows a common form of commutator for a two- cylinder engine. In the drawing, A is a fiber ring mounted as shown on a flanged sleeve B, which may be rotated about shaft C by means of the lever D. Shaft C, which may be the cam shaft or an auxiliary timing shaft, carries the ground con- tact mechanism E. As the shaft C revolves, and the con- tact E engages the shoe F, the circuit is closed through the primary coil, and the current from the battery causes an electromotive force to be generated in the secondary wind- ing, producing a spark. It is apparent that by shifting the 180 INTERNAL COMBUSTION ENGINES sleeve B around the shaft C the ignition may be advanced or retarded by varying the point where the ground contact E meets the shoe F. A commutator similar to the one described may be made for any number of cylinders by increasing the number of contacts accordingly. For two-cycle engines a simple and inexpensive commuta- tor may be made of a flat fiber disk mounted on the end of the bearing next the flywheel, the ground contact point being a spring pin in the wheel. Fig. 77 represents this form of Fig. 77. Crank Shaft Commutator for Two-Cycle Engine. commutator. Means for advancing or retarding the spark is provided by lever A, by which the fiber may be moved about the shaft C. Fig. 78 represents a form of commutator, of cheap con- struction, which may be used to advantage in single-cylinder four-cycle construction. The make and break is secured by means of the cam C, mounted on the cam shaft, acting on the spring S which is carried on the fiber F as shown. Timing is secured by moving the fiber around the shaft by means of the rod R. Fig. 79 illustrates a more complicated and expensive commutator. IGNITION 181 "mr&— Commutators are on the market which distribute to the secondary while timing the primary current, thus making it possible to use a single coil to spark multiple cylinders. While this method reduces the number of unit coils and vibrators necessary, the system is not as good as one using the multiple units in which the com- mutator current is low tension and much more easily insulated. Spark plugs for use with jump- spark ignition systems consist of a porcelain or lava insulated point projecting into the explosion chamber and in close proximity with another similar point con- nected to the ground through the cylinder. Many forms are offered for sale. By far the most important point in a spark plug is to make sure that there is perfect insula- tion, otherwise under the high compression the spark will jump across at some point in the circuit where the resistance is less than at the spark gap. While this may not be apparent with the plug withdrawn from the cylinder, it is often the cause of serious ignition trouble. Fig. 80 shows a spark plug of French make which is an efficient but expensive plug. In the illustration, A is the grounded and B the insulated point between which the spark jumps across the gap C. The porcelain insulation is in three pieces, as shown, with suitable packing, where the brass parts bear upon it, to prevent breaking. The plug must necessarily have its joints gas tight in order to prevent leakage of the compression, and the several joints make this style of plug particularly efficient in this respect. Cheaper plugs are made that give excellent satisfaction. The author has had the best results with the so-called Fig. 78. Cam Shaft Timer for Pour-Cycle Engine. 182 INTERNAL COMBUSTION ENGINES Fig. 79. Commutator with Hammer Break Contacts. J? Fig. 80. The Pognon Spark Plug. Fig. 81. Spark Plug of Ordinary Construction. IGNITION 183 "Rajah" plugs, although the porcelains being light they are subject to breakage. Figs. 81, 82, 83, and 84 represent several well-known makes of plugs. Dynamo ignition has become quite popular in the past few years, and were it not for its rather high first cost it would undoubtedly be the universal electrical ignition. It is absolute in its operation, and used in connection with a Fig. 82. Plug with Spring Clip Con- nection. Fig. 83. Sta-Rite Plus. Fig 84. Sta-Rite Plug. storage cell, the operator need give no attention to the matter of batteries. Without the storage cell it becomes necessary to use two or three cells for starting, if the engine is too large to turn over quite rapidly by hand, after which, by means of the dynamo, it generates its own sparking current. 184 INTERNAL COMBUSTION ENGINES Of the dynamo igniters probably the one most commonly in use is the Apple made by the Dayton Electrical Manu- facturing Company, Dayton, Ohio. It is a neat and compact device, the reasonable first cost of which, as well as its efficiency, recommends it. The parts are entirely enclosed in a water and dust proof case. It is provided with a centrifugal friction clutch governor, as shown in Fig. 85, the shoes of which release as the engine speed increases, thus causing it to run steadily. The brushes are so placed as to enable the dynamo to run in either direction, the field magnets being permanent. These igniters are made either for jump-spark or make-and-break ignition, and generate a constant e.m.f. of Fig. 85. The Apple Igniter. from 4 to 5 volts at from 1000 to 1200 rev. per min. Storage batteries may be connected up to these dynamos and the surplus energy not used for sparking stored up for starting. Fig. 86 shows the wiring diagram for a single cylinder with jump-spark ignition. For a multiple cylinder the system is identical except that there are extra spark plugs and com- mutator connections to be made. See Fig. 87. The storage battery, Fig. 88, always furnishes the current to the primary, and by means of the four-point automatic cut-out switch S, see Fig. 89, it is possible to read on the volt-ammeter the IGNITION 185 «— o Commutator sis < O 0J E p to . HO. S« S Before commencing the actual test two or three assistants should be secured in order that the different readings may be taken as nearly at the same time as possible. One reading of the barometer and the room thermometer is generally sufficient for an hour's run. The engineer in charge of the test should handle the speed indicator while an assistant takes the brake scale readings, keeping the scale beam constantly floating as the power fluctuates. Another assistant will be able to handle the indicator and to take the temperature of the inlet and discharge water, while a fourth assistant will be able to take care of the weighing tank and to take whatever other readings are necessary. Readings should be taken at five-minute intervals while the test lasts, and an hour's test is generally sufficient for any one adjustment of the engine. One run should be made at maximum power, one at the rated horsepower, and a third at no load with the brake removed, the latter being merely an indicator test. Runs may also be made at quarter, half, and three-quarter load if desired. In order that the readings may be taken as nearly as possible at the same time the engineer in charge should be provided with a ENGINE TESTING 205 whistle, and signal ten seconds before a reading is taken and again as it is to be started. A stop watch is valuable, although not absolutely necessary, to the person handling the speed indicator. After completing the test, the clearance of the engine, its stroke and piston diameter should be carefully measured and recorded. To measure the clearance, place the. engine on its upper dead center, being sure that the valves are carefully seated. Now weigh a quantity of water, more than sufficient to fill the compression space; then fill the compression space from this measured quantity, being careful not to spill any part of the water, and weigh the remaining water. The difference between the two weights W and W t is the weight of the water contained in the compression space of the engine. Now a cubic inch of water at 39.1 deg. fahr. weighs 0.036 lb., hence the weight of the water contained in the compression space divided by 0.036 will give accurately the number of cubic inches in that space. If the temperature of the water is much higher than 39.1 deg. and extreme accuracy is required, its weight per cu. in. may be determined by means of the following thermodynamic formula: w .036 X 2 .... W= t + 4Bl. 500 - (45) 500 t + 461 Wherein t = temperature of the water. In taking a series of tests with a transmission dynamometer the same general method as to readings is adhered to. .There are so very many different forms of transmission dynamometers that the author, since the scope of this work is necessarily limited, would refer the reader to standard engineering works embracing the subject.* It is sufficient to say that the transmission dynamometer is placed between the prime mover and the driven machinery — the power transmitted being measured by the tendency to rotate gears, which tendency is resisted by springs of known resistance, * See Carpenter's "Experimental Engineering," pages 219-234, Thurston's "Engine and Boiler Trials," page 264, or Weisbach's " Mechanics, " Vol. II, pages 39-73. 206 INTERNAL COMBUSTION ENGINES or by weights, suitable recording arrangements, either auto- matic or dial, being provided. The method of engine testing as described applies to the making of a complete test of a gas engine, in every detail. Such a complete test is not usually run except in cases where a record of the actual performance of an engine is required in every such detail as a basis for a guarantee or to detect faulty design. A description of a complete test naturally takes into consideration all the smaller details, but it is an easy matter to perform any part of the test required. The most common tests performed are the brake and indicator tests to determine the horsepower and the mechanical efficiency of the engine. Gasoline, Alcohol, and Oil Engines. — In the testing of engines operating on liquid fuel, while the indicator and brake tests, as well as a majority of the other tests, will be run in the same way, the tests for fuel consumption will be differ- ent. In place of the column " cu. ft. of gas, " a column read- ing "gal. of fuel" should be substituted. The column "press, of gas in in. of water" is omitted, and the column reading the "temperature of the gas" should be replaced by one reading the "temperature of the fuel"; in all other respects the log sheet may be used as it stands. The tem- perature of the fuel, if a carburettor is used, should be taken at the carburettor; if a jet or mixing valve is used the tem- perature should be taken just before the fuel reaches the valve. In a gasoline automobile motor, while many manufacturers make talking points of their low fuel consumption, the question of the amount consumed is secondary to the power derived, flexibility of control, and weight, and, as a matter of fact, with the varying loads and speeds to which such an engine is constantly subjected it is impossible to obtain any very great fuel economy, and as a consequence a brake and indicator test is all that is usually required for such an engine. CHAPTER XXIII. REPORT OF TESTS. The data having been obtained by the method discussed in the last chapter, a report of the conditions found must be made. When a number of tests are being conducted a printed form of report blank should be made as follows: Place . Date Engineer in charge Assistants Name of engine Manufacturer Rated hp Rev. per min Dimensions. Stroke ft. Diam. piston in. Area piston sq. in. Piston displacement cu. in. Compression space cu. in . Compression space per cent Theoretical compression lb. Data. Length of test Average Rev. per min Rev. per hr Explosions per min Explosions per hr Gas per hr Air per hr Ratio gas to air As 1 : x Water consumption lb. Temperature inlet water deg. fahr. Temperature dis. water " Range water temperature Av. " " Temperature room " " " Temperature exhaust " " " Pressure inlet water Av. lb. 207 208 INTERNAL COMBUSTION ENGINES Prony Brake. Length lever arm (R) ft. Constant brake (Correction) lb. Brake load average (Gross) lb. Brake load average (Net) lb. Weight of gas per cu. ft lb. Weight of air per cu. ft lb. Average mixture Ratio gas to air Weight of mixture per cu. ft lb. Sp. heat gas Sp. heat air Sp. heat mixture Heat value cu. ft B.t.u. Results. Work Av. ft.-lb. per min. Work Av. ft.-lb. per hr. d.hp Average Indicated m.e.p Av. lb. Indicated hp Average Gas per i.hp cu. ft. Gas per d.hp cu. ft. Mech. efficiency Av. d.hp. -t- Av. i.hp. Friction loss i.hp. — d.hp. Heat per Hour. Supplied by fuel B.t.u. Absorbed by water B.t.u. In exhaust gases B.t.u. Absorbed in work B.t.u. Radiation and friction B.t.u. Thermal efficiency Per cent B.t.u. per i.hp As there will probably be some items in the report not readily understood by the reader, an explanation of these will be given. The ratio of gas to air is the quantity of gas consumed per hour divided by the air consumed. In the engines which take a charge of air into the cylinder, whether gas is taken or not, as in the type governed by means of the "hit or miss" cut-off type of governor, the exact ratio cannot be obtained, except as the engine takes an impulse at every cycle. An approximate result may be obtained, however, REPORT OF TESTS 209 by taking the difference between the actual average cycles performed per hour and the average number of explosions per hour and subtracting from the air meter reading the computed amount of air used in these idle cycles, which would be the product of the cylinder volume times the idle cycles, and using this corrected value of air in the ratio. This ratio would not be absolutely accurate, owing to the probability of the cylinder not always obtaining a complete fresh charge of air on the suction stroke. The weight of the gas fuel may be obtained from the records of the gas com- pany or it may be computed from the quantitative analysis of the gas — this analysis should be performed by a com- petent chemist. When the constituent parts of the gas, together with their weight, are known the weight may be determined by multiplying the weight per cubic foot of the constituents by their percentages as they appear in the gas analysis, and adding the results. Table XIV will give the weights and specific heats of the constituent parts of the gases most commonly encountered as gas-engine fuels. TABLE XIV. WEIGHT AND SPECIFIC HEAT OF GASES. Constituent. Air Hydrogen Oxygen Nitrogen Marsh gas, CH 4 Carbonic oxide, CO Carbonic acid, C0 2 . , Olefines Lb. per Cu. Ft. 0.08082 0.00559 0.0894 0.0779 0.0445 Sp. Ht. Const, Pr. 0.237 3.409 0.217 0.244 0.593 0.245 0.216 0.404 Sp. Ht. Const. Vol. 0.168 2.406 0.155 0.173 0.467 0.173 0.171 0.332 The weights and specific heats given are for an atmospheric pressure of 14.7 lb. per sq. in. and a temperature of 32 deg. fahr. The specific heat of the gas and of the mixture may be found by the same method as for finding the weight, the percentage of the constituent parts being known and their specific heat is found in the above table. The weight 210 INTERNAL COMBUSTION ENGINES of the mixture is found by taking the weight of air to be 0.08082 lb. at 32 deg. fahr. and atmosphere 14.7. The weight of the gas being known, or having been determined, the weight of mixture per cubic foot is found by the follow- ing formula: W m = (0.08082) x + ay . . . (46) In which x is the percentage of air, a the weight of the gas per cubic foot, and y the percentage of gas. The heating value of the gas should always be determined at a laboratory by an expert chemist. While Table I, Chapter IX, gives the heating values of various gases, their composition in different localities or under different conditions is subject to variation and for accurate results should not be depended on, but only used as a basis for computing probable results. Samples of the gas should be obtained at different times and then mixed; a sample of the mixture should then be sent to the laboratory. The volumes of gas and air as obtained in the test and recorded in the log sheet must be reduced to standard temperature and atmospheric pressure in order to form a basis of comparison. The standards in use are the tempera- ture of water at the freezing point, 32 deg. fahr., and the atmospheric pressure at sea level, which is equivalent to 30 in. of mercury. The following formula may be used in the reduction : V = p P x 49L2 (47 ) 14.7 X (2, + 459.2) ■■•<>> In which t t = temperature at time of test. ■p = atmospheric pressure at time of test. v = volume at this pressure and temperature. V = corrected volume at 32 deg. fahr. and pressure of 14.7 lb. This formula, while derived on the basis of the air ther- mometer, will give an approximately correct value when used for the gas. The gas pressure, as measured in the test, in inches of water may be reduced to inches of mercury by REPORT OF TESTS 211 dividing by 13.62, or if the pressure of the gas has been taken in pounds per sq. in. it may be reduced to inches of mercury by multiplying by 2.033. These ratios are for temperatures of 32 deg. fahr. but will be found to give sufficiently accu- rate results if used at any average temperature. The indicated work is to be computed from the indicator cards taken during the test and is the product of the mean effective pressure, the area of the piston in inches, the stroke in feet, and the number of explosions per minute. The mean ordinate of the cards is obtained best by means of a planimeter.* If a planimeter is not available it may be obtained by the ordinate method, see Fig. 106. From the atmospheric line AB erect ordinates equal distances apart, the first and last ordinates being half a space Fig. 106. Engine Card. from the ends of the diagram. Add the lengths of the lines contained in the diagram, in this case ten, from AB to the expansion curve ex, and add the lengths of the same lines from AB to the compression curve ay, subtract the second sum from the first and divide by the number of lines. The result will be the approximate value of the * A planimeter, as the name implies, is an instrument for computing areas. It may be so adjusted as to record, without further calculation, the mean ordinate of any irregular figure of given length. See Car- penter's "Experimental Engineering," page 31. 212 INTERNAL COMBUSTION ENGINES mean ordinate in inches. If the expansion curve should be irregular, due to the vibration of the indicator spring, a mean curve may be drawn as shown to right of Fig. 106. While the ordinate method will give fairly close results, its use in computations requiring extreme accuracy is not advisable. The mean effective pressure is the result obtained by multiplying together the mean ordinate in inches and the scale of the spring in lb. per sq. in., which is known. The mean effective pressure being known, the indicated horse- power is calculated by means of the following formula : H Plan (48) 33,000 In which P = Mean effective pressure. I = Length of stroke in ft. a = Area of piston in sq. in. n = Number of explosions per min. Note. — The difference between n in the above formula and n in the same formula as applied to the steam engine should be noted. In steam- engine work n = number of rev. per min. but in gas-engine work n = the number of impulses given per min. If the engine "hits" regularly every cycle there would only be half as many impulses as revolutions in a four-cycle engine. For a two-cycle engine, however, the value of n would be the same as for a steam engine. The quantity of heat supplied by the gas per hour is the product of the heating value per cu. ft. times the cu. ft. con- sumed. The heat absorbed in the water is the product of the water consumed, as determined in the test, and the range of temperature: H i = (t 2 -t l )W (49) In which t l = The temperature of the discharge. t 2 = Temperature of the inlet. W = Weight of the cooling water. REPORT OF TESTS 213 The result obtained is in B.t.u (British thermal units). The B.t.u. is the heat required to raise 1 lb. of water through 1 deg. fahr. The heat absorbed in work is the ft.-lb. per hr. divided by the foot-pound equivalent of the B.t.u., which is 778: rr 2 nrWn X 60 ,, m Hw = 778 (50) The heat carried off in the exhaust is found as follows: the specific heat of the mixture having been determined, as previously described, gives us, in terms of a decimal, the B.t.u. required to raise one pound through one degree fahrenheit. Then knowing the weight of a cu. ft. of mixture in pounds, the quantity exhausted in cu. ft. and the range of temperature (obtained by means of the pyrometer and thermometer), the formula resolves itself into one of the same class as that derived for water: H e = S (t 2 - *,) W (51) In which S = Specific heat of mixture. t 2 = Temperature as obtained by pyrometer. t t = Temperature of entering mixture or gas. W = Total weight of mixture per hour. To be absolutely accurate the amount of unburned mixture passing out with the exhaust should be considered, and its heating value subtracted from that of the fuel entering the engine, but in practice it is considered as part of the heat lost by radiation. The heat lost by radiation is determined by subtracting the sum of the three computed losses from the heat supplied by the gas. The thermal efficiency of the engine is the quotient of the heat absorbed in work divided by the heat supplied the engine in fuel: T= 778 CH (52) 214 INTERNAL COMBUSTION ENGINES In which the numerator is recognized as the numerator of the formula (50) C = Cu. ft. of gas per hr. H = Heat value per cu. ft. The b. hp. of the engine is found by means of the formula derived for the prony brake, H = . F J 33,000 In which the constants for different lengths of r are given in the table, page 200. MISCELLANEOUS. The Muffler. — The volume of muffler necessary, for any given size of engine, can be only approximately determined by formulas. As a general proposition, however, the volume of the muffler is from four to six times the total cylinder volume. While it is true that some engines, especially those in use on motorcycles, employ a muffler with a much less comparative volume, their use does not produce as good results from the standpoint of quietness of operation although the back pressure is less. A muffler, in its simplest form, consists of an iron box or drum into which the exhaust gases are discharged before passing to the atmosphere. While such a muffler deadens, to a certain extent, the noise of the explosion, the develop- ment of the automobile industry has demanded a more efficient sound deadener. To produce this result the gases are made to pass through orifices or past baffle plates in order to give them more time to approach the pressure of the atmosphere before discharging into it. One simple method is to enclose an iron pipe, bored full of small holes, in an iron shell and discharge the exhaust gases into the pipe from which they pass through the holes to the shell of the muffler and finally to the open air. It should be remembered that the more efficient a muffler is the greater is the back pressure and loss of power; hence the use of the simple drum type on industrial engines and other engines where quietness of operation is a secondary consideration. DEFINITIONS OF UNITS. Work. — The sustained exertion of pressure through space. Unit of Work. — One foot pound, i.e., a pressure of one pound exerted through a space of one foot. 216 216 INTERNAL COMBUSTION ENGINES Horse-power. — The rate of work. Unit of horse-power = 33,000 ft. lb. per minute, or 550 ft. lb. per second = 1,980,000 ft. lb. per hour. Heat Unit. — Heat required to raise 1 lb. of water 1 deg. Fahr. (from 39 deg. to 40 deg.). 33 000 Horse-power expressed in heat units = ' = 42.416 heat units per minute = 0.707 heat units per second = 2545 heat units per hour. , „ , , , , , ( 1,980,000 ft. lb. per lb. of fuel. 1 lb. of fuel per hp.-hr. = <„-,., r r ( 2545 heat units. 1,000,000 ft. lb. per lb. of fuel = 1.98 lb. of fuel per hp.-hr. 5280 22 Velocity. — Feet per second = — X miles per hour. y ^ 3600 15 TABLE XV. WIRE AND SHEET-METAL GAUGES COMPARED. oi bo a (A o o gham or ' Iron Wire. Metal.) an or Browne ,rpe. (Sheet Copper ) j5 ■a S m a "a g 0J Steel Wire. Std. Sheet — •° s 03 ■ a 2 2 CO .153 .0281 .024 .61 051 24 .022 .0201 .02; 1 .151 .025 .022 .56 055 25 .02 .0179 .02( ) .148 .0219 .02 .51 059 26 .018 .01594 .on ! .146 .0188 .018 .46 063 27 .016 .01419 .01' ' .143 .0172 .0164 .42 067 28 .014 .01264 .OK > .139 .0156 .0148 .38 071 29 .013 .01126 .01! .134 .0141 .0136 .35 074 30 .012 .01002 .01' t .127 .0125 .0124 .31 078 31 .01 .00893 .OK 5 .120 .0109 .0116 .29 082 32 .009 .00795 .OK .115 .0101 .0108 .27 086 33 . 008 .00708 .011 .112 .0094 .01 .25 090 34 .007 .0063 .01 .110 .0086 .0092 .23 094 35 .005 .00561 .00£ 5 .108 .0078 .0084 .21 098 36 .004 .005 .005 .106 .007 .0076 .19 . 37 .00445 .00* 5 .103 .0066 .0068 .17 . 38 .00396 .00* .101 .0063 .006 .15 . 39 .00353 .00; 5 .099 .0052 .13 . 40 .00314 .OCi .097 .0048 .12 . 41 . .095 .0044 .11 . 42 . .092 .004 .10 . 43 . .088 .0036 .09 . 44 . .085 .0032 .08 . 45 . .081 .0028 .07 . 46 . .079 .0024 .06 . 47 . .077 .002 .05 . 48 . .075 .0016 .04 . 49 . .072 .0012 .03 . 50 . .069 .001 .025 . 218 INTERNAL COMBUSTION ENGINES TABLE XVI. TAP DRILL TABLE. Diameter of Taps. Number of Threads per Inch. Diameter of Tap Drill. V. Thread. U. S. Std. Thread. V. Thread. U. S. Std. Thread. i A i A * A i A 1 tt 1 t tt l J } t i f * 2 32 24 20 18 16 14 12 12 11 11 10 10 9 9 8 7 7 6 6 5 5 4* 4} 20 18 18 14 13 12 11 11 10 10 9 9 8 7 7 6 6 51 5 5 4* #44 #29 #14 tt L& R H 29 ST i A tl 48 S4" 23 T2 II II 59 6? iA ij HI 1 21 's* 129 !?? 1 35 L SZ 143 !?* A c N S If H 33 6"¥ 37 S4" tt H 51 ^¥ 27 3 "2 61 S¥ 1A 1*4 lit ill i* if 1 2 3 i 3 2" MISCELLANEOUS 219 TABLE XVII. MACHINE SCREW TABLE. Bcrew Gauge. Diam. Deci- mals. Approx. Diam. No. Thread per 1 Inch. Size Tap Dr. 2 . .0842 A 56 49 3 .0973 A 48 45 4 .1105 & 36 42 5 .1236 i 36 38 6 .1368 & 32 35 7 .1500 A 32 30 8 .1631 h 32 29 9 .1763 tt 30 27 10 .1894 ft 24 25 11 .2026 a 24 21 12 .2156 h 24 17 13 .2289 u 22 15 14 .2421 « 20 13 15 .2552 i 20 8 16 .2634 17 ST 18 5 17 .2816 A 18 2 18 .2947 1 9 18 1 19 .3079 ft 18 C 20 .3210 II 16 D 22 .3474 §4 16 J 24 .3737 1 16 N 26 .4000 M 16 P 28 .4263 H 14 R 30 .4526 ft 14 U •220 INTERNAL COMBUSTION ENGINES TABLE XVIII. WROUGHT IRON PIPE. Diameter. Thread per Inch. Size of Tap Drill. Nominal. Actual Ex- ternal. Actual In- ternal. I .405 .27 27 H i .540 .364 18 29 i .675 .494 18 3 9 i .840 .623 14 23 f 2 i 1.050 .824 14 tt i 1.315 1.048 n| 1A i 1.660 1.38 111 itf i 1.900 1.611 111 123 1 '5 2" 2 2.375 2.067 111 2A i 2.875 2.468 8 21 3 3.500 3.067 8 31 i 4.0 3.548 8 31 4 4.500 4.026 8 41 1 5.0 4.508 8 4f 5 5.563 5.045 8 5& 6 6.625 6.065 8 6A 7 7.625 7.023 8 n 8 8.625 7.982 8 8* 9 10 9.625 10.75 8.937 10.019 8 8 MISCELLANEOUS 221 TABLE XIX.— CIRCUMFERENCES AND AREAS OF CIRCLES ADVANCING BY EIGHTS. Diam. Circ. Area. Diam. Circ. Area. Diam. Circ. Area. o A .04909 .00019 2 6.2832 3.1416 5 15.708 19.635 A .09818 .00077 A 6.4795 3.3410 A 15.904 20.129 A .14726 .00173 i 6.6759 3.5466 i 16.101 20.629 A .19635 .00307 A 6.8722 3.7583 A 16.297 21.135 & .29452 .00690 i 7.0686 3.9761 i 16.493 21 .648 i .39270 .01227 A 7.2649 4.2000 A 16.690 22.166 A .49087 .01917 I 7.4613 4.4301 1 16.886 22.691 A .58905 .02761 A 7.6576 4.6664 A 17.082 23.221 A .68722 .03758 i .78540 .04909 i 7.8540 4.9087 i 17.279 23.758 A .88357 .06213 A 8.0503 5.1572 A 17.475 24.301 A .98175 .07670 f 8.2467 5.4119 1 17.671 24.850 ti 1.0799 .09281 H 8.4430 5.6727 H 17.868 25.406 1 1.1781 .11045 a 4 8.6394 5.9396 1 18.064 25.967 H 1 .2763 . 12962 H 8.8357 6.2126 H 18.261 26.535 A 1.3744 . 15033 1 9.0321 6.4918 i 18.457 27.109 J§ 1.4726 .17257 a 9.2284 6.7771 if 18.653 27.688 4 1.5708 .19635 3 9.4248 7.0686 6 18.850 28.274 tt 1 .6690 .22166 A 9.6211 7.3662 i 19.242 29.465 A 1.7671 .24850 i 9.8175 7.6999 i 19.635 30.680 if 1.8653 .27688 A 10.014 7.9798 t 20.028 31.919 1 1.9635 .30680 i 10.210 8.2958 4 20.420 33.183 tt 2.0617 .33824 A 10.407 8.6179 * 20.813 34.472 « 2.1598 .37122 i 10.603 8.9462 I 21.206 35.785 23 f2" 2.2580 .40574 A 10.799 9.2806 I 21.598 37.122 } 2.3562 .44179 i 10.996 9.6211 i 21.991 38.485 II 2.4544 .47937 A 11.192 9.967B i 22.384 39.871 if 2.5525 .51849 i 11.388 10.321 i 22.776 41.282 27 2.6507 .55914 « 11.585 10.680 1 23.169 42.718 J 2.7489 .60132 if 11.781 11.045 i 23.562 44.179 29 72 2.8471 .64504 it 11.977 11.416 f 23.955 45.664 « 2.9452 .69029 1 12.174 11.793 1 24.347 47.173 81 3.0434 .73708 « 12.370 12.177 i 24.740 48.707 1 3.1416 .7854 4 12.566 12 566 8 25.133 50.265 A 3.3379 .8866 A 12.763 12.962 i 25.525 51.849 i 3.5343 .9940 4 12.959 13.364 i 25.918 53.456 A 3.7306 1 . 1075 A 13.155 13.772 1 26.311 55.088 i 3.9270 1.2272 i 13.352 14.186 f 26.704 56.745 A 4.1233 1 .3530 A 13.548 14.607 1 27.096 58.426 i 4.3197 1.4849 1 13.744 15.033 i 27.489 60.132 A 4.5160 1 .6230 A 13.941 15.466 I 27.882 61.862 J 4.7124 1.7671 i 14.137 15.904 9 28.274 63.617 A 4.9087 1.9175 A 14.334 16.349 i 28.667 65.397 * 5.1051 2.0739 i 14.530 16.800 i 29.060 67.201 tt 5.3014 2.2365 * « 14.726 17.257 i 29.452 69.029 J 5.4978 2.4053 I 14.923 17.728 i 29.845 70.882 H 5.6941 2.5802 « 15.119 18.190 i 30.238 72.760 J 5.8905 2.7612 * 15.315 18.665 2 4 30.631 74.662 « 6.0868 2.9483 if 15.512 19.147 1 31.023 76.589 222 INTERNAL COMBUSTION ENGINES CIRCUMFERENCES AND AREAS OF CIRCLES. — Continued. Diam. Circ. Area. Diam. Circ. Area. Diam. Circ. Area. 10 31.416 78.540 16 50.265 201. 22 69.115 380.13 i 31.809 80.516 i 50.658 204. i 69.508 384.46 1 32.201 82.516 i 51.051 207. i 69.900 388.82 f 32.594 84.541 i 51.444 210. i 70.293 393.20 i 32.987 86.590 i 51.836 213. i 70.686 397.61 I 33.379 88.664 f 52.229 217. i 71.079 402.04 I 33.772 90.763 i 52.622 220. a 4 71.471 406.49 i 34.165 92.886 1. 53.014 223. 1 71.864 410.97 11 34.558 95.033 17 53.407 226.98 23 72.257 415.48 i 34.950 97.205 I 53.800 230.33 i 72.649 420.00 i 35.343 99.402 i 54.192 233.71 1 4 73.042 424.56 f 35.736 101.62 i 54.585 237.10 i 73.435 429.13 i 36.128 103.87 i 54.978 240.53 i 73.827 433.74 f). 8 36.521 106.14 § 55.371 243.98 « 74.220 438.36 I 36.914 108.43 i 55.763 247.45 a 4 74.613 443.01 I 37.306 110.75 I 56.156 250.95 I 75.006 447.69 12 37.699 113.10 18 56.549 254.47 24 75.398 452.39 i 38.092 115.47 i 56.941 258.02 i 75.791 457.11 1 4 38.485 117.86 { 57.334 261.59 i 76.184 461.86 t 38.877 120.28 $ 57.727 265.18 3 76.576 466.64 * 39.270 122.72 i 58.119 268.80 * 76.696 471.44 I 39.663 125.19 f 58.512 272.45 A 8 77.362 476.26 ! 40.055 127.68 i 58.905 276.12 i 77.754 481 . 1 1 7 8 40.448 130.19 i 59.298 279.81 i 78.147 485.98 13 40.841 132.73 19 59.690 283.53 25 78.540 490.87 i 41.233 135.30 i 60.083 287.27 i 78.933 495.79 i 41.626 137.89 i 60.476 291.04 i 79.325 500.74 a. 8 42.019 140.50 * 60.866 294.83 1 79.718 505.71 i 42.412 143.14 i 61.261 298.65 J 80.111 510.71 1 42.804 145.80 i 61.654 302.49 8 80.503 515.72 1 43.197 148.49 a 4 62.046 306.35 3. 4 80.896 520.77 8 43.590 151.20 i 62.439 310.24 i 81.289 525.84 14 43.982 153.94 20 62.832 314.16 26 81.681 530.93 i "s 44.375 156.70 i 63.225 318.10 i 82.074 536.05 } 44.768 159.48 4 63.617 322.06 i 82.467 541.19 f 45.160 162.30 £ 64.010 326.05 i 82.860 546.35 i 45.553 165.13 i 64.403 330.06 i 83.252 551.55 f 45.946 167.99 § 64.795 334.10 f 83.645 556.76 J 46.338 170.87 i 65.188 338.16 I 84.038 562.00 i 46.731 173.78 1 65.581 342.25 i 84.430 567.27 16 47.124 176.71 21 65.973 346.36 27 84.823 572.56 i 47.517 179.67 i 66.366 350.50 J 85.216 577.87 i 47.909 182.65 i 66.759 354.66 i 85.608 583.21 f 48.302 185.66 i 67.152 356.84 i 86.001 588.57 i 48.695 188.69 * 67.544 363.05 i 86.394 593.96 I 49.087 191.75 1 67.937 367.28 t 86.786 599.37 i 49.480 194.83 ! 68.330 371.54 3 4 87.179 604.81 I 49.873 197.93 1 68.722 375.83 i 87 572 610.27 MISCELLANEOUS 223 CIRCUMFERENCES AND AREAS OF CIRCLES. — Continued. Diam. Circ. Area. Diam. Circ. Area. Diam. Circ. Area. 28 87.965 615.75 34 106.814 907.92 40 125.664 1256.6 i 88.357 621.26 i 107.207 914.61 i 126.056 1264.5 i 88.750 626 80 i 107.600 921.32 i 126.449 1272.4 i 89.143 632.36 I 107.992 928.06 i 126.842 1280.3 i 89.535 637.94 i 108.385 934.82 i 127.235 1288.2 f 89.928 643.55 f 108.778 941.61 i 127.627 1296.2 1 90.321 649.18 2 109.170 948.42 1 128.020 1304.2 1 90.713 654.84 i 109.563 955.25 I 128.413 1312.2 29 91.106 660.52 35 109.956 962.11 41 128.805 1320.3 * 91.499 666.23 i 110.348 969.00 i 129. 198 1328.3 i 91.892 671.96 i 110.741 975.91 i 129.591 1336.4 i .92.284 677.71 i 111.134 982.84 i 129.983 1344.5 i 92.677 683.49 i 111.527 989.80 i 130.376 1352.7 S 93.070 689.30 t 111.919 996.78 i 130.769 1360.8 i 93.462 695.13 I 112.312 1003.8 i 131.161 1369.0 I 93.855 700.98 i 112.705 1010.8 I 131.554 1377.2 30 94.248 706.86 36 113.097 1017.9 42 131.947 1385.4 * 94.640 712.76 i 113.490 1025.0 i 132.340 1393.7 i 95.033 718.69 i 113.883 1032.1 i 132.732 1402.0 I 95.426 724.64 i 114.275 1039.2 1 133.125 1410.3 i 95.819 730.62 i 114.668 1046.3 i 133.518 1418.6 i 96.211 736.62 1 115.061 1053.5 f 133.910 1427.0 i 96.604 742.64 i 115.454 1060.7 I 134.303 1435.4 i 96.997 748.69 i 115.846 1068.0 i 134.696 1443.8 31 97.389 754.77 37 116.239 1075.2 43 135.088 1452.2 i s 97.782 760.87 i 116.632 1082.5 i 135.481 1460.7 i 98.175 766.99 i 117.024 1089.8 i 135.874 1469.1 f 98.567 773.14 i 117.417 1097.1 i 136.267 1477.6 i 98.960 779.31 i 117.810 1104.5 i 136.659 1486.2 i 99.353 785.51 ■1 118.202 llll. 8 i 137.052 1494.7 J 99.746 791.73 i 118.596 1119. 2 i 137.445 1503.3 i 100.138 797.98 i 118.988 1126.7 I 137.837 1511.9 32 100.531 804.25 38 119.381 1134.1 44 138.230 1520.5 i 100.924 810.54 i 119.773 1141. i 138.623 1529.2 i 101.316 816.86 i 120.166 1149.1 1 4 139.015 1537.9 i 101.709 823.21 f 120.559 1156.6 f 139.408 1546.6 i 102.102 829.58 i 120.951 1164.2 i 139.801 1555.3 f 102.494 835.97 f 121.344 1171. 7 1 140.194 1564.0 1 102.887 842.39 1 121.737 1179.3 1 140.586 1572.8 i 103.260 848.83 I 122.129 1186.9 i 140.979 1581.6 33 103.673 855.30 39 122.522 1194.6 45 141.372 1590.4 i 104.065 861.79 i 122.915 1202.3 1 141.764 1599.3 i 104.458 868.31 i 123.308 1210.0 i 142.157 1608.2 | 104.851 874.85 1 123.700 1217.7 i 142.550 1617.0 i 105.243 881.41 i 124.093 1225.4 i 142.942 1626.0 f 105.636 888.00 I 124.486 1233.2 i 143.335 1634.9 f 106.029 894.62 4 124.878 1241.0 i 143.728 1643.9 J 106.421 901.26 i 125.271 1248.8 i 144.121 1652 9 224 INTERNAL COMBUSTION ENGINES CIRCUMFERENCES AND AREAS OF CIRCLES. — Continued. Diam. Circ. Area. Diam. Circ. Area. Diam. Circ. Area. 46 144.513 1661. 9 * 148.833 1762.7 f 153.153 1866.5 X 144.906 1670.9 i 149.226 1772.1 * 153.545 1876.1 I 145.299 1680.0 f 149.618 1781.4 1 145.691 1689.1 i 150.011 1790.8 49 153.938 1885.7 l 146.084 1698.2 i 150.404 1800.1 i 154.331 1895.4 f 146.477 1707.4 i 154.723 1905.0 a 146.869 1716.5 48 150.796 1809.6 f 155.116 1914.7 i 147.262 1725.7 I 151.189 1819.0 h 155.509 1924.4 i 151.582 1828.5 155.902 1934.2 47 147.655 1734.9 A 151.975 1837.9 3: 156.294 1943.9 i 148.048 1744.2 _J. 152.367 1847.5 1 156.687 1953.7 i 148.440 1753 5 "s 152.760 1857 MISCELLANEOUS 225 TABLE XX. TRIGONOMETRIC TABLES. To find the function of any angle between the values given in the table the following example will illustrate the method: To find sin - 81° - Ay sin - 81° - 40" = 0.9894 sin - 81° - 50" = 0.9899 Dif . last unit = 5 From table of proportionate parts, marked P. P., we have 5 x .3 = 1.5 Adding 0.9894 we have sin 81° - 43' = 0.98955 Where the difference, in last unit place, for 10 minutes is less than 4 the pro- portionate parts have not been tabulated, but are readily determined. For angles more than 90° sin, cos, tan, cotan, sec, or cosec of 90° + x° = sin, cos, tan, cotan, sec, or cosec of 180° - (90° + a;). sin, cosin, tan, cotan, sec, or cosec of 180° + x° (but leas than 270°) = sin, cosin, tan, cotan, sec, or cosec of x°. sin, cosin, tan, cotan, sec, or cosec of 270° + x° — sin, cosin, tan, cotan, sec, or cosec of 360° - (270° + x"). The sec and cosec, versed sin and co-versed sin are not contained in the follow- ing table, but their values may be determined as follows: sec = versed sin =1 — cosin. cosin cosec = oo-versed sin = 1 — sio. sine 226 INTERNAL COMBUSTION ENGINES TABLE XX. — TRIGONOMETRIC FUNCTIONS. / Sin. d. Tan. d. Cot. d. Cos. d. P. P. O.0000 29 0.0000 29 infinit. 1.0000 90 10 0.0029 0.0029 343.7737 1 .0000 50 20 0.0058 29 0.0058 29 171.8854 1.0000 40 30 30 40 0.0087 0.0116 29 29 0.0087 0.0116 29 29 114.5887 85.9398 1 .0000 0.9999 30 20 2 3 6.0 9.0 50 0.0145 29 30 29 29 0.0145 29 30 29 29 68.7501 0.9999 10 4 5 6 7 8 9 12.0 15.0 18.0 21.0 24.0 27.0 1 0.0175 0.0175 57.2900 81861 61398 47756 38207 31262 26053 22047 18898 16380 14334 12648 11245 10061 9057 8194 7451 6804 6237 0.9998 1 89 10 20 0.0204 0.0233 0.0204 0.0233 49.1039 42.9641 0.9998 0.9997 50 40 30 0.0262 29 0.0262 29 38. 1885 0.9997 30 40 0.0291 29 0.0291 29 34.3678 0.9996 1 20 50 0.0320 29 29 29 0.0320 29 29 29 31.2416 0.9995 1 10 1 2 29 2.9 5.8 2 0.0349 0.0349 28.6363 0.9994 ' 88 10 0.0378 0.0378 26.4316 0.9993 50 3 4 S 6 8.7 11.6 14.5 17.4 20 30 0.0407 0.0436 29 29 0.0407 0.0437 29 30 24.5418 22.9038 0.9992 0.9990 1 2 40 30 40 0.0465 29 0.0466 29 21.4704 0.9989 1 20 7 8 9 20.3 23.2 26.1 50 0.0494 29 29 29 0.0495 29 29 29 20.2056 0.9988 1 2 10 3 10 0.0523 0.0524 19.0811 0.9986 87 50 0.0552 0.0553 18.0750 0.9985 20 0.0581 29 0.0582 29 17.1693 0.9983 2 40 1 2 28 2.8 5.6 30 0.0610 29 0.0612 30 16.3499 0.9981 2 30 40 0.0640 30 0.0641 29 15.6048 0.9980 1 20 3 8.4 50 4 0.0669 29 29 0.0670 29 29 14.9244 0.9978 2 2 10 86 4 6 6 11.2 14.0 16.8 0.0698 0.0699 14.3007 0.9976 29 30 5740 5298 4907 4557 4243 2 7 8 19.6 22.4 10 0.0727 0.0729 13.7267 0.9974 50 20 0.0756 29 0.0758 29 13.1969 0.9971 i 40 9 25.2 30 0.0785 29 0.0787 29 12.7062 0.9969 2 30 40 0.0814 29 0.0816 29 12.2505 0.9967 2 20 50 0.0843 29 0.0846 30 11.8262 0.9964 3 10 5 29 29 28 29 29 30 3961 3707 3475 3265 3074 2898 2738 2591 2455 2329 2214 2105 2007 1913 2 3 2 1 2 0.5 1.0 5 0.0872 0.0875 11.4301 0.9962 85 10 20 0.0901 0.0929 0.0904 0.0934 11.0594 10.7119 0.9959 0.9957 50 40 3 4 S 1.5 2.0 2.5 30 0.0958 29 0.0963 29 10.3854 0.9954 3 30 6 7 8 9 3.0 3 5 4.0 4.5 40 50 0.0987 0.1016 29 29 29 29 0.0992 0.1022 29 30 29 29 10.0780 9.7882 0.9951 0.9948 3 3 3 20 10 6 0.1045 0.1051 9.5144 0.9945 84 10 0.1074 0.1080 9.2553 0.9942 50 20 30 0.1103 0.1132 29 29 0.1110 0.1139 30 29 9.0098 8.7769 0.9939 0.9936 3 3 40 30 1 2 0.4 0.8 40 0. 1 161 29 0.1169 30 8.5555 0.9932 4 20 3 4 5 1.2 1.6 2.0 50 0.1190 29 29 79 0.1198 29 30 79 8.3450 0.9929 3 10 7 0.1219 0.1228 8.1443 0.9925 4 83 6 7 2.4 2 8 10 0.1248 28 29 29 29 ?9 0.1257 30 30 29 30 ?9 7.9530 1826 1746 1671 1600 1533 0.9922 4 4 3 4 4 50 8 3.2 20 0.1276 0.1287 7.7704 0.9918 40 9 3.6 30 0.1305 0.1317 7.5958 0.9914 30 40 0.1334 0.1346 7.4287 0.9911 20 50 0.1363 0.1376 7.2687 0.9907 10 8 0.1392 0.1405 7.1154 0.9903 82 Cos. d. Cot. H. Tnn. d. Sin. d. ' ° P. P. MISCELLANEOUS TRIGONOMETRIC FUNCTIONS. — Continued. 227 o / Sin. d. Tan. d. Cot. d. Cos. d. p. p. 8 0.1392 29 0.1405 30 7.1154 1472 0.9903 4 82 10 0.1421 0.1435 6.9682 0.9899 50 n 20 0.1449 28 0.1465 30 6.8269 1413 0.9894 5 40 30 0.1478 29 0.1495 30 6.6912 1357 0.9890 4 30 1 2 32 3.2 n 4 31 3.1 fi 2 30 3.0 6.0 40 0.1507 29 0.1524 29 6.5606 1306 0.9886 4 20 50 0.1536 29 0.1554 30 6.4348 1258 0.9881 5 10 3 9.6 9.3 9.0 30 30 30 1210 1168 1126 4 5 4 4 5 12.8 16.0 12.4 15.5 12.0 15.0 9 0.1564 29 29 0.1584 6.3138 0.9877 81 10 20 0.1593 0.1622 0.1614 0.1644 6.1970 6.0844 0.9872 0.9868 50 40 b 7 8 19.2 22.4 25 6 18.6 21.7 '4 8 18.0 21.0 24.0 30 0.1650 28 0.1673 29 5.9758 1086 0.9863 5 30 9 28.8 27.9 27.0 40 0.1679 29 0.1703 30 5.8708 1050 0.9858 5 20 50 10 0.1708 29 28 29 0.1733 30 30 30 5.7694 1014 981 949 0.9853 5 5 5 10 80 0.1736 0.1763 5.6713 0.9848 10 0.1765 0.1793 5.5764 0.9843 50 20 30 0.1794 0.1822 29 28 0.1823 0.1853 30 30 5.4845 5.3955 919 890 0.9838 0.9833 5 5 40 30 1 29 2 9 28 ?, 8 27 2-7 40 0.1851 29 0.1883 30 5.3093 862 0.9827 6 20 2 5.8 5.6 54 50 11 0.1880 29 28 0.1914 31 30 5.2257 836 811 0.9822 5 6 10 79 3 4 5 8.V 11.8 14.5 8.4 1.2 4.0 8.1 10.8 13.5 0.1908 0.1944 5.1446 0.9816 29 30 788 5 6.8 9 6 16.2 18.9 10 0.1937 0.1974 5.0658 0.9811 50 7 20.3 20 0.1965 28 0.2004 30 4.9894 764 0.9805 6 40 8 9 23.2 22.4 26.1 25.2 21.6 24.3 30 0.1994 29 0.2035 31 4.9152 742 0.9799 6 30 40 0.2022 28 0.2065 30 4.8430 0.9793 20 50 0.2051 29 28 0.2095 30 31 4.7729 683 0.9787 6 10 12 0.2079 0.2126 4.7046 0.9781 78 29 30 664 6 10 0.2108 0.2156 4.6382 0.9775 50 20 0.2136 28 0.2186 30 4.5736 0.9769 40 9 8 30 0.2164 28 0.2217 31 4.5107 629 0.9763 6 30 1 2 3 4 0. 1. 2. 3. 9 0.8 5 1.6 7 2.4 5 3.2 40 50 0.2193 0.2221 29 28 0.2247 0.2278 30 31 4.4494 4.3897 597 0.9757 0.9750 7 20 10 29 28 31 30 582 568 554 540 527 515 6 7 7 6 7 7 5 6 4 5. 5 4.0 1 4.8 13 0.2250 0.2309 4.3315 0.9744 77 10 0.2278 0.2339 4.2747 0.9737 50 7 8 9 6. 7. 8 3 5.6 2 6.4 17.2 20 0.2306 28 0.2370 31 4.2193 0.9730 40 30 0.2334 28 0.2401 31 4.1653 0.9724 30 40 0.2363 29 0.2432 31 4.1126 0.9717 20 50 0.2391 28 0.2462 30 4.0611 0.9710 10 28 31 503 14 0.2419 0.2493 4.0108 0.9703 76 28 31 491 481 469 459 448 10 0.2447 0.2524 3.9617 0.9696 7 8 7 7 8 50 20 0.2476 29 0.2555 31 3.9136 0.9689 40 1 2 V 0. 1 6 7 0.6 1 1.2 30 0.2504 28 0.2586 31 3.8667 0.9681 30 40 0.2532 28 0.2617 31 3.8208 0.9674 20 3 2. 1.8 50 0.2560 28 28 0.2648 31 31 3.7760 0.9667 10 5 2. 3 i 2.4 53 15 0.2588 0.2679 3.7321 0.9659 75 6 4. 2 3.6 28 28 28 28 28 28 32 31 31 32 31 31 7 8 4 5. J4.2 3 4.8 10 0.2616 0.2711 3.6891 421 411 403 395 387 0.9652 8 8 8 7 8 50 20 0.2644 0.2742 3.6470 0.9644 40 9 6. 3 5.4 30 0.2672 0.2773 3.6059 0.9636 30 40 0.2700 2805 3.5656 0.9628 20 50 16 0.2728 0.2836 3.5261 0.9621 10 0.2756 0.2867 3.4874 0.9613 74 Cos. d. Cot. d. Tan. d. Sin. d. / o P. P. 228 INTERNAL COMBUSTION ENGINES TRIGONOMETRIC FUNCTIONS. — Continued. . Sin. d. Tan. d. Cot. d. Cos. d. p. p. 16 0.2756 0.2867 3.4874 0.9613 74 10 28 32 379 371 365 357 350 8 50 0.2784 0.2899 3.4495 0.9605 5 1 20 0.2812 28 0.2931 32 3.4124 0.9596 9 40 1 0.5 0.4 30 0.2840 28 0.2962 31 3.3759 0.9588 8 30 3 s l 2 40 0.2868 28 0.2994 32 3.3402 0.9580 8 20 4 2.01.6 50 2896 28 0.3026 32 3.3052 0.9572 8 10 5 2.5 2.0 28 31 32 9 8 17 0.2924 0.3057 3.2709 338 0.9563 73 7 3.5 2.8 8 4.0 3.2 9 4.5 3.6 10 0.2952 0.3089 3 2371 330 325 319 313 0.9555 50 20 0.2979 27 0.3121 il 3.2041 0.9546 9 40 30 0.3007 28 0.3153 32 3.1716 0.9537 9 30 40 0.3035 28 0.3185 32 3.1397 0.9528 9 20 50 0.3062 27 0.3217 32 3.1084 0.9520 8 10 37 36 35 9 9 18 0.3090 28 0.3249 32 3.0777 302 0.9511 72 2 3 4 7.4 11.1 14 S 7.2 10. i 14 4 7.0 10.5 14.0 10 0.3118 0.3281 3.0475 297 0.9502 50 20 0.3145 27 0.3314 33 3.0178 291 287 0.9492 40 5 18. 5 18. ( 17.5 30 40 0.3173 0.3201 28 28 0.3346 0.3378 32 32 2.9887 2.9600 0.9483 0.9474 9 9 30 20 6 7 8 22.2 25.9 29 fi 21. b 25.2 28. 8 21.0 24.5 28.0 50 0.3228 11 28 27 0.3411 ii 32 33 2.9319 277 0.9465 10 9 10 9 33.3 32.4 31.5 19 0.3256 0.3443 2.9042 272 0.9455 71 10 0.3283 0.3476 2.8770 268 263 259 255 250 0.9446 50 2C 0.3311 28 0.3508 32 2.8502 0.9436 IU 40 34 33 32 30 0.3338 27 0.3541 33 2.8239 0.9426 10 30 1 3.4 3.3 3.2 40 0.3365 27 0.3574 33 2 79E0 0.9417 9 :o 2 3 4 6.8 10.2 13 6 6.6 9.9 13 2 6.4 9.6 12.8 50 0.3393 28 27 28 0.3607 ii 33 33 2 7725 0.9407 10 10 10 10 20 0.3420 0.3640 2.7475 247 0.9397 70 b 6 17.0 m 4 16. b 19 8 16.0 19.2 10 0.3448 0.3673 2.7228 243 239 0.9387 30 7 23.8 23.1 22.4 20 0.3475 27 27 0.3706 33 2.6985 0.9377 10 10 10 8 9 21 . 2 30 ft 26.4 S9 7 25.6 28.8 30 0.3502 0.3739 2 6746 235 0.9367 30 40 0.3529 27 0.3772 33 2.6511 0.9356 II 20 50 0.3557 28 27 0.3805 33 34 2.6279 228 0.9346 10 10 10 21 0.3584 0.3839 2.6051 225 0.9336 69 28 27 26 27 33 II 2.V S.4 2.6 5.2 10 0.3611 0.3872 2.5826 221 219 214 0.9325 30 2 fi.fi 20 0.3638 11 0.3906 34 2.5605 0.9315 10 40 3 8.4 8.1 7.8 30 0.3665 27 0.3939 33 2.5386 0.9304 II II 30 4 6 11.2 14 10.8 13 S 10.4 13.0 40 0.3692 0.3973 34 2.5172 212 209 0.9293 20 6 16.8 16.2 15.6 50 0.3719 27 27 27 0.4006 33 34 34 2.4960 0.9283 IU II II 10 7 8 19.fi » 4 18.9 '1 6 18.2 20 8 22 0.3746 0.4340 2.4751 206 0.9272 68 9 25.2 24.3 23.4 10 0.3773 0.4074 2.4545 0.9261 50 20 0.3800 11 0.4108 34 2.4342 0.9250 40 30 40 0.3827 0.3854 11 27 0.4142 0.4176 34 34 2.4142 2.3945 197 195 0.9239 0.9228 11 11 30 20 1 13 1 3 12 1.2 50 0.3881 11 26 27 0.4210 34 35 34 2.3750 191 0.9216 10 2 3 4 2.6 3 9 5.2 2.4 3.6 4.8 23 0.3907 0.4245 2.3559 190 0.9205 67 10 0.3934 0.4279 2.3369 186 0.9194 12 50 6 6 b.h 7 S 6.0 7 2 20 0.3961 11 0.4314 35 2.3183 185 0.9182 40 7 9.1 8.4 30 0.3987 26 0.4348 34 2.2998 181 180 0.9171 30 8 0.4 9.6 40 0.4014 27 0.4383 35 2.2817 0.9159 12 12 12 20 9 1.7 0.8 50 0.4041 11 26 d. 0.4417 34 35 d. 2.2637 177 0.9147 10 21 0.4067 0.4452 2.2460 174 0.9135 d. 66 Cos. Cot. Tan. d. Sin. P. P. MISCELLANEOUS TRIGONOMETRIC FUNCTIONS. — Continued. 229 24 I "0 20 30 40 50 25 10 20 30 40 50 2!i 10 20 30 40 50 27 10 20 30 40 50 29 10 20 30 40 50 1 10 20 30 40 50 30 10 20 30 40 50 .1 10 20 30 40 50 32 Sin. 0.4067 0.4094 0.4120 0.4147 0.4173 0.4200 0.4226 0.4253 0.4279 0.4305 0.4331 0.4358 0.4384 0.4410 0.4436 0.4462 0.4488 0.4514 0.4540 0.456O 0.4592 0.4617 0.4643 0.46)9 0.4o95 0.4720 0.4746 0.4772 0.4797 0.4823 0.4848 0.4874 0.4899 0.4924 0.4950 0.4975 0.5000 0.5025 0.5050 0.5075 0.5100 0.5125 0.5150 0.5175 0.5200 0.5225 0.5250 0.5275 5299 Cos. Tan. d. Cot 0.4452 0.4487 0.4522 0.4557 0.4592 0.4628 0.4663 0.46W 0.4734 0.4770 0.4806 0.4841 0.4877 0.4913 0.4950 0.4986 0.5022 0.5059 0.50M 0.5132 0.5169 0.5206 0.5243 0.5280 0.531/ 0.5354 0.5392 0.5430 0.5467 0.5505 0.5543 0.5581 0.5619 0.5658 0.5696 0.5735 0.5774 0.5812 0.5851 0.5890 0.5930 0.5969 0.6009 0.6048 0.6088 0.6128 0.6168 0.6208 6249 Cot. 2.2460 2.2286 2.2113 2.1943 2.1775 2. 1609 2.1445 2.1283 2.1123 2.0965 2.0809 2.0655 2.0503 2.0353 2.0204 2.0057 1.9912 1.9768 1.9626 1.9486 1 .9347 1.9210 1 .9074 1.8940 1 . 8607 1.8676 1.8546 1.8418 1 .8291 1.8165 1.8040 1.7917 1.7796 1.7675 1.7556 1.7437 1.7321 1.7205 1.7090 1.6977 1.6864 1.6753 1.6643 1.6534 1 .6426 1.6319 1.6212 1.6107 1.6003 Tan. 174 173 170 168 166 164 162 160 158 156 154 152 150 149 147 145 144 142 140 139 137 136 134 133 131 130 128 127 126 125 123 121 121 119 119 116 116 115 113 113 111 110 109 108 107 107 105 104 1~ Cos. d. 0.9135 0.9124 0.9112 0.9100 0.9088 0.9075 0.9063 0.9051 0.9038 0.9026 0.9013 0.9001 0.8988 0.8975 0.8962 0.8949 0.8936 0.8923 0.8910 0.8897 0.8884 0.8870 0.8857 0.8843 0.8.29 0.8816 0.8802 0.8788 0.8774 0.8760 0.8746 0.8732 0.8718 0.8704 0.8689 0.8675 8560 0.8646 0.8631 0.8616 0.8601 0.8587 0.8572 0.8557 0.8542 0.8526 0.8511 0.8496 0.8480 Sin. d. 65 61 63 62 61 60 59 58 P. P. 11 10 9 1 1.1 1.0 0.9 2 2.2 2.0 1.8 3 3.33.02.7 4 4.4 4.0 3.6 5 5.55.04.5 6 6.68.05.4 7 7.77.06.3 8 8.8 8.0 7.2 9 9.9 9.0 8.0 44 43 42 1 4.4 4.3 4.2 2 8 8 i .6 8.4 3 3.2 12.9 12.6 4 7.6 17.2 16.8 5 !2.0 21.5 21.0 6 •6 4 25.8 25.2 7 0.8 30.1 29.4 8 5.2 '4.4 23.6 9 39.6 38.7 37.8 41 4 39 1 4.1 4 .0 3.9 2 8.2 * .0 7.8 3 2.3 12 .0 11.7 4 6.4 ie .0 15.6 5 '0.5 2C .0 19.5 6 !4.6 24 .0 23.4 7 8.7 2! .0 27.3 8 2.KS2 .0 31.2 9 6.9 36 .0 35.1 38 37 . 3.8 3.7 1 7.6 7.4 1 11.4 11. 1 i , 15.2 14.8 5 19.0 18.5 122.8 22.2 ' 26.6 25.9 1 30.4 29.6 134.2 33.3 26 25 2.6 2.5 5.2 5.(1 7.8 7.5 10.4 10.0 13.0 12.5 15.6 15.0 18.2 17.5 20.8 211.(1 23.4 22.5 24 2.4 4.8 7.2 9.6 12.0 14.4 16.8 19.2 21.6 P. P. 230 INTERNAL COMBUSTION ENGINES TRIGONOMETRIC FUNCTIONS. — Continued. o , Sin. d. Tan. d. Cot. d. Cos. d. p.p. 32 10 0.5299 25 0.6249 40 1.6003 103 0.8480 15 58 50 0.5324 0,6289 1.5900 0.8465 20 0.5348 24 0.6330 41 1.5798 102 0.8450 15 40 30 0.5373 25 0.6371 41 1.5697 101 0.8434 16 30 23 17 16 1 2.3 1.7 1.6 2 4.6 3.4 3.2 40 0.5398 25 0.6412 41 1.5597 100 0.8418 16 20 50 0.5422 24 0.6453 41 1.5497 100 0.8403 lb 10 3 6.9 5.1 4.8 24 25 24 41 42 41 98 98 97 16 16 16 33 0.5446 0.6494 1.5399 0.8387 57 5 11.5 8.5 8.0 10 20 0.5471 0.5495 0.6536 0.6577 1.5301 1.5204 0.8371 0.8355 50 40 6 13.8 10.2 9.6 7 16.1 11.9 11.2 8 18.4 13.6 12.8 30 0.5519 24 0.6619 42 1.5108 96 0.8339 16 30 9 20.7 15.3 14.4 40 0.5544 25 0.6661 42 1.5013 95 0.8323 16 20 50 0.5568 24 24 24 0.6703 42 42 42 1.4919 94 93 93 0.8307 16 17 16 10 34 0.5592 0.6745 1.4826 0.8290 56 15 14 13 1 1.5 1.4 1.3 10 0.5616 0.6787 1.4733 0.8274 50 2 3.C 2.8 2.6 20 0.5640 24 0.6830 43 1.4641 92 0.8258 16 40 3 4.i 4 6.( 5 7.E 4.5 5.( 7 f 3.9 5.2 6.5 30 0.5664 24 0.6873 4i 1.4550 91 0.8241 17 30 40 0.5688 24 0.6916 41 1.4460 90 0.8225 16 20 6 9.G 8.4 7.8 50 35 10 0.5712 24 24 24 0.6959 43 43 44 1.4370 90 89 88 0.8208 0.8192 17 16 17 10 55 50 7 10.5 8 12.0 9 13.5 9.t 11.2 12.6 9.1 10.4 11.7 0.5736 0.7002 1.4281 0.5760 0.7046 1.4193 0.8175 20 0.5783 Li 0.7089 43 1.4106 87 0.8158 17 40 30 0.5807 24 0.7133 44 1.4019 87 0.814*1 17 30 58 I 5.8 ! 11.6 1 67 57 1 4 1 56 5.6 1 ? 5 5 11.0 40 0.5831 24 0.7177 44 1 3934 85 0.8124 17 20 ; 50 0.5854 li 7221 44 1.3848 86 0.8107 i; 10 i 17.4 : 7.1 : B.S 16.5 ?4 44 84 17 ' 23.2 5 •/, H'< •>.>> 22.0 36 0.5878 23 24 0.7265 45 45 1 .3764 84 83 0.8090 17 17 54 { 29.0 2 8.5 5 8.0 27.5 10 0.5901 0.7310 1.3680 0.8073 50 \ 34.8 3 40.6 3 4.2 3 9 9 3 3.6 9 ? 33.0 38.5 20 0.5925 0.7355 1.3597 0.8056 40 £ 46.4 4 5 64 4 R 44.0 30 0.5948 li 0.7400 45 1.3514 83 0.8039 17 30 S 52.2 5 1.3 5 0.4 49.5 40 0.5972 24 0.7445 45 1.3432 82 0.8021 18 20 50 0.5995 23 23 23 0.7490 45 46 45 1.3351 81 81' 80 0.8004 17 10 37 10 0.6018 0.7536 1.3270 0.7986 53 j 50 2 54 5.4 10.8 1 S3 5.3 0.6 1 t>'4 5.2 0.4 ai 5.1 10.2 0.6041 0.7581 1.3190 0.7969 20 0.6065 24 23 0.7627 46 46 1.3111 79 79 0.7951 40 \ 16.2 1 21.6 2 b.9 1 1 ?, ? 5.6 n s 15.3 20.4 30 0.6088 0.7673 1.3032 0.7934 30 5 27.0 2 i 5? sn MS 40 0.6111 23 0.7720 47 1 .2954 78 0.7916 20 6 32.4 i 1.8 S 1.2 30.6 50 38 10 0.6134 23 23 23 0.7766 46 47 47 1.2876 78 77 76 0.7898 7 10 l t 52 9 50 37.8 3 43.2 4 48.6 4 /.I 3 2.4 4 7.7 4 5.4 1.6 6.8 35.7 40.8 45.9 0.6157 0.7813 1.2799 0.7880 O.6180 0.7860 1.2723 0.7862 20 0.6202 22 0.7907 Al 1.2647 76 0.7844 40 50 1 5.0 49 4 q 48 4.8 30 0.6225 23 0.7954 47 1.2572 75 0.7826 30 40 0.6248 23 0.8002 48 1 .2497 75 0.7808 20 2 10.0 9 P 9.6 50 0.6271 23 22 0.8050 48 48 1 .2423 74 74 0.7790 10 3 15.0 4 20 14.7 19 6 14.4 19.2 24.0 39 0.6293 0.8098 1.2349 0.7771 51 5 25.0 24.5 73 48 73 6 30. ( W ' 28.8 10 0.6316 0.8146 1.2276 0.7753 50 7 35.0 34 a 33.6 20 0.6338 11 0.8195 49 1.2203 73 0.7735 40 8 40( 39 ? 38.4 30 0.6361 li 0.8243 48 1.2131 72 0.7716 30 9 45.0 44.1 43.2 40 0.6383 11 0.8292 49 1.2059 72 0.7698 20 50 0.6406 23 22 8342 50 49 1.1988 71 70 0.7679 10 50 40 0.6428 0.8391 1.1918 0.7660 Cos. d. Cot. d. Tan. d. Sin. d. / o P. I > MISCELLANEOUS 231 TRIGONOMETRIC FUNCTIONS. — Continued. ' Sin. d. Tan. d. Cot. d. Cos. d 40 10 20 30 40 50 41 10 20 30 40 50 42 10 20 30 40 50 43 10 20 30 40 50 44 10 20 30 40 50 45 0.6428 0.6450 0.6472 0.6494 0.6517 0.6539 0.6561 0.6583 0.6604 0.6626 0.6648 0.6670 0.6691 0.6713 0.6734 0.6756 0.6777 0.6799 0.6820 0.6841 0.6862 0.6884 0.6905 0.6926 0.6947 0.6967 0.6988 0.7009 0.7030 0.7050 0.7071 Cos. 0.8391 0.8441 0.8491 0.8541 0.8591 0.8642 0.8693 0.8744 0.8796 0.8847 0.8899 0.8952 0.9004 0.9057 0.9110 0.9163 0.9217 0.9271 0.9325 0.9380 0.9435 0.9490 0.9545 0.9601 0.9657 0.9713 0.9770 0.9827 0.9884 0.9942 1.0000 Cot. .1918 1.1847 1.1778 1.1708 1.1640 1.1571 1.1504 1.1436 1.1369 1.1303 1.1237 1.1171 1.1106 1. 1041 1.0977 1.0913 1 .0850 1.0786 1 .0724 1.0661 1 .0599 1.0538 1.0477 1.0416 1 .0355 1.0295 1.0235 1.0176 1.0117 1 .0058 1.0000 Tan. 0.7660 0.7642 0.7623 0.7604 0.7585 0.7566 0.7547 0.7528 0.7509 0.7490 0.7470 0.7451 0.7431 0.7412 0.7392 0.7373 0.7353 0.7333 0.7314 0.7294 0.7274 0.7254 0.7234 0.7214 0.7193 0.7173 0.7153 0.7133 0.7112 0.7092 0.7071 Sin. 50 50 40 30 20 10 49 50 40 30 20 10 4S 50 40 30 20 10 47 50 40 30 20 10 46 50 40 30 20 10 45 P.P. 47 4.7 9.4 14.1 18.8 23.5 28.2 32.9 37.6 42.3 46 4.6 9.2 13.8 18.4 23.0 27.6 32.2 36.8 41.4 45 4.5 9.0 13.5 18 22.5 27.0 31.5 40.5 24 23 22 2.4 2.3 2.2 4.8 4.6 4.4 7.2 6.9 6.6 9.6 9 2 8.8 12.0 11.5 11.0 14.4 13.X 13.2 16.8 16.1 15.4 19.2 18.4 17.6 21.6 20.7 19.8 20 19 18 2.0 1.9 1.8 4.(1 3.8 3.6 6.0 5.7 5.4 8,(1 7.6 7.2 10.0 9.5 9.6 12.(1 11.4 10. K 14 (1 13.3 VI, 6 16.0 15.2 14.4 18.0 17.1 16.2 21 2.1 4.2 6.3 8.4 10.5 12.6 14.7 16.8 18.9 17 1.7 3.4 5.1 6.1 8.5 10.2 11.9 13.1 15.; p. p. TABLE XXI. TABLE OF COMMON LOGARITHMS OF NUMBERS From 1000 to 10000 A minus sign (— ) before or after any tabular log. indicates that its true value is less than the tabulated value by less than half of the unit in the last place. 233 MISCELLANEOUS LOGARITHMS OF NUMBERS. 235 No. 1000 Log. Dif. No. 1050 Log. Dif. No. Log. Dif. No. 1150 Log. Dif. P.P. 00000 43 02119 41 1100 04139 40 06070 38 44 43 01 043 44 51 160 42 01 -179 39 51 -108 37 1 4 4 02 -087 43 52 -202 41 02 218 40 52 145 38 2 9 9 03 130 43 53 -243 41 03 -258 39 53 -183 38 3 13 13 04 173 44 54 284 41 04 -297 39 54 -221 37 4 6 18 22 17 22 05 -217 43 55 325 41 05 336 40 55 258 38 6 26 26 06 -260 43 56 366 41 06 -376 39 56 -296 37 7 31 30 07 -303 43 57 407 42 07 -415 39 57 333 38 8 35 34 08 346 43 58 -449 41 08 -454 39 58 -371 37 9 40 39 09 389 43 59 -490 41 09 493 39 59 408 38 1010 432 43 1060 -531 41 1110 532 39 1160 -446 37 42 41 11 475 43 61 -572 40 11 571 39 61 483 38 1 4 4 12 518 43 62 612 41 12 610 40 62 -521 37 2 8 8 13 -561 43 63 653 41 13 -650 39 63 -558 37 3 13 12 14 -604 43 64 694 41 14 -689 38 64 595 38 4 5 17 21 16 21 15 -647 42 65 -735 41 15 727 39 65 -633 37 6 25 25 16 689 43 66 -776 40 16 766 39 66 -670 37 7 29 29 17 732 43 67 816 41 17 805 39 67 707 37 8 34 33 18 -775 42 68 857 41 18 844 39 68 744 37 9 38 37 19 817 43 69 -898 41 19 883 39 69 781 38 1020 860 43 1070 938 41 1120 -922 39 1170 -819 37 40 39 21 -903 42 71 -979 40 21 -961 38 71 -856 37 1 4 4 22 945 43 72 03019 41 22 999 39 72 -893 37 2 8 8 23 -988 42 73 -060 40 23 05038 39 73 -930 37 3 12 12 24 01030 42 74 100 41 24 -077 38 74 -967 37 4 6 16 20 16 20 25 072 43 75 -141 40 25 115 39 75 07004 37 6 24 23 26 -115 42 76 181 41 26 -154 38 76 -041 37 7 28 27 27 157 42 77 -222 40 27 192 39 77 -078 37 8 32 31 28 199 43 78 -262 40 28 -231 38 78 -115 36 9 36 35 29 -242 42 79 302 40 29 269 39 79 151 37 1030 -284 42 1080 342 41 1130 -308 38 1180 188 37 38 37 31 -326 42 81 -383 40 31 346 39 81 -225 37 1 4 4 32 -368 42 82 -423 40 32 -385 38 82 -262 36 2 8 7 33 4IC 42 83 -463 40 33 -423 38 83 298 37 3 11 11 34 452 42 84 -503 40 34 461 39 84 335 37 4 6 15 19 15 19 35 494 42 85 -543 40 35 -500 38 85 -372 36 6 23 22 36 -536 42 86 -583 40 36 -538 38 86 408 37 7 27 26 37 -576 42 87 -623 40 37 576 38 87 445 37 8 30 30 38 -620 42 88 -663 40 38 614 38 88 -482 36 9 34 33 39 -662 41 89 -703 40 39 652 38 89 518 37 1040 703 42 1090 -743 39 1140 690 39 1190 -555 36 36 41 745 42 91 782 40 41 -729 38 91 591 37 1 4 42 -787 41 92 822 40 42 -767 38 92 -628 36 2 7 43 828 42 93 862 40 43 -805 38 93 664 36 3 11 44 870 42 94 -902 39 44 -843 38 94 700 37 4 5 14 18 45 -912 41 95 941 40 45 -881 37 95 -737 36 6 22 46 953 42 96 981 40 46 918 38 96 773 36 7 25 47 -995 41 97 04021 39 47 956 38 97 809 37 8 29 48 02036 42 98 060 40 48 994 38 98 -846 36 9 32 - -078 41 99 -100 39 49 06032 38 99 -882 36 236 INTERNAL COMBUSTION ENGINES LOGARITHMS OF NUMBERS. —Continued. No. Log. Dif. No. 1250 Log. Dif No. Log. Dif. No. Log. Dif. P. P. 1200 07918 36 09691 35 1300 11394 34 1350 13033 33 36 35 01 954 36 51 -726 34 01 -428 33 51 -066 32 1 4 4 02 990 37 52 760 35 02 461 33 52 -098 32 2 7 7 03 08027 36 63 795 35 03 494 34 63 -130 32 3 11 11 01 -063 36 54 -830 34 04 -528 33 54 -162 32 4 14 14 5 18 18 05 -099 36 55 864 35 05 561 33 55 -194 32 6 22 21 06 -135 36 56 -899 35 06 594 34 56 -226 32 7 25 25 07 -171 36 57 -934 34 07 -628 33 57 -258 32 8 29 28 08 -207 36 58 -968 35 08 -661 33 58 -290 32 9 32 32 09 -243 36 59 10003 34 09 -694 33 59 -322 32 1210 -279 35 1260 037 35 1310 727 33 1360 -354 32 34 11 314 36 61 -072 34 11 760 33 61 -386 32 1 3 12 350 36 62 -106 34 12 793 33 62 -418 32 2 7 13 386 36 63 140 35 13 826 34 63 -450 31 3 10 14 -422 36 64 -175 34 14 -860 33 64 481 32 4 6 14 17 15 -458 35 65 209 34 15 -893 33 65 513 32 6 20 16 493 36 66 243 35 16 -926 33 66 545 32 7 24 17 529 36 67 -278 34 17 -959 33 67 -577 32 8 27 18 -565 35 68 -312 34 18 -992 32 68 -609 31 9 31 19 600 36 69 346 34 19 12024 33 69 640 32 1220 -636 36 1270 380 35 1320 057 33 1370 672 32 33 21 -672 35 71 -415 34 21 090 33 71 -704 31 1 3 22 707 36 72 -449 34 22 123 33 72 735 32 2 7 23 -743 35 73 -483 34 23 -156 33 73 767 32 3 10 24 778 36 74 -517 34 24 -189 33 74 -799 31 4 5 13 17 25 -814 35 75 551 34 25 -222 32 75 830 32 6 20 26 849 35 76 585 34 26 254 33 76 -862 31 7 23 27 884 36 77 619 34 27 287 33 77 893 32 8 26 28 -920 35 78 653 34 28 -320 32 78 -925 31 9 30 29 955 36 79 687 34 29 -352 33 79 956 32 1230 -991 35 1280 -721 34 1330 385 33 1380 -988 31 32 31 09026 35 81 -755 34 31 -418 32 81 14019 32 1 3 32 061 35 82 -789 34 32 450 33 82 -051 31 2 6 33 096 36 83 -823 34 33 483 33 83 082 32 3 10 34 -132 35 84 -857 33 34 -516 32 84 -114 31 4 6 13 18 35 -167 35 85 890 34 35 548 33 85 -145 31 6 19 36 -202 35 86 924 34 36 -581 32 86 176 32 7 22 37 -237 35 87 -958 34 37 613 33 87 -208 31 8 26 38 272 35 88 -992 33 38 -646 32 88 -239 31 9 29 39 307 35 89 11025 34 39 678 32 89 270 31 1240 342 35 1290 -059 34 1340 710 33 1390 301 32 31 41 377 35 91 -093 33 41 -743 32 91 333 31 1 3 42 412 35 92 126 34 42 775 33 92 -364 31 2 6 43 447 35 93 -160 33 43 -808 32 93 395 31 3 9 44 482 35 94 193 34 44 -840 32 94 426 31 4 5 12 16 45 -517 35 95 -227 34 45 872 33 95 457 32 6 19 46 -552 35 96 -261 33 46 -905 32 96 -489 31 7 22 47 -587 34 97 -294 33 47 -937 32 97 -520 31 8 25 48 621 35 98 327 34 48 -969 32 98 -551 31 9 28 49 656 35 99 -361 33 49 13001 32 99 -582 31 MISCELLANEOUS LOGARITHMS OF NUMBERS. — Continued. 237 No. Log. Dif. No. 1450 Log. Dif. No. Log. Dif. No. 1550 Log. Dif. P.P. 1400 14613 31 16137 30 1500 17609 29 19033 28 31 01 -644 31 51 -167 30 01 638 29 51 061 28 1 3 02 -675 31 52 -197 30 02 -667 29 52 089 28 2 6 03 -706 31 53 -227 29 03 -696 29 53 117 28 3 9 04 -737 31 54 256 30 04 -725 29 54 145 28 4 5 12 16 05 -768 31 55 286 30 05 -754 28 55 173 28 6 19 06 -799 30 56 316 30 06 782 29 56 -201 28 7 22 07 829 31 57 -346 30 07 811 29 57 -229 28 8 25 08 860 31 58 -376 30 08 840 29 58 -257 28 9 28 09 191 31 59 -406 29 09 -869 29 69 -285 27 1410 -922 31 1460 435 30 1510 -898 28 1560 312 28 30 11 -953 30 61 465 30 11 926 29 61 340 28 1 3 12 983 31 62 -495 29 12 955 29 62 368 28 2 6 13 15014 31 63 524 30 13 -984 29 63 -396 28 3 9 14 -045 31 64 554 30 14 18013 28 64 -424 27 4 5 12 15 15 -076 30 65 -584 29 15 041 29 65 451 28 6 18 16 106 31 66 613 30 16 -070 29 66 479 28 7 21 17 -137 31 67 643 30 17 -099 28 67 -507 28 8 24 18 -168 30 68 -673 29 18 127 29 68 -535 27 9 27 19 198 31 69 702 30 19 -156 28 69 -562 28 1420 -229 30 1470 -732 29 1520 184 29 1570 -590 28 29 21 259 31 71 761 30 21 -213 28 71 -618 27 1 3 22 -290 30 72 -791 29 22 241 29 72 645 28 2 6 23 320 31 73 820 30 23 -270 28 73 -673 27 3 9 24 -351 30 74 -850 29 24 298 29 74 700 28 4 5 12 15 25 381 31 75 879 30 25 -327 28 75 728 28 6 17 26 -412 30 76 -909 29 26 355 29 76 -756 27 7 20 27 442 31 77 938 29 27 -384 28 77 783 28 8 23 28 -473 30 78 967 30 28 412 29 78 -811 27 9 26 29 503 31 79 -997 29 29 -441 28 79 838 28 1430 -534 30 1480 17026 30 1530 469 29 1580 -866 27 28 31 -564 30 81 -056 29 31 -498 28 81 893 28 1 3 32 594 31 82 -085 29 32 -526 28 82 -921 27 2 6 33 625 30 83 114 29 33 554 29 83 948 28 3 8 34 -655 30 84 143 30 34 -583 28 84 -976 27 4 6 11 14 35 685 30 85 -173 29 35 -611 28 85 20003 27 6 17 36 715 31 86 -202 29 36 639 28 86 030 28 7 20 37 -746 30 87 231 29 37 667 29 87 -058 27 8 22 38 -776 30 88 260 29 38 -696 28 88 085 27 9 25 39 806 30 89 289 30 39 -724 28 89 112 28 1449 836 30 1490 -319 29 1540 752 28 1590 -140 27 27 41 866 31 91 -348 29 41 780 28 91 167 27 1 3 42 -897 30 92 -377 29 42 808 29 92 194 28 2 5 43 -927 30 93 -406 29 43 -837 28 93 -222 27 3 8 44 -957 30 94 435 29 44 -865 28 94 -249 27 4 6 11 14 45 -987 30 95 464 29 45 -893 28 95 276 27 6 16 46 16017 30 96 493 29 46 -921 28 96 303 27 7 19 47 -047 30 97 522 29 47 949 28 97 330 28 8 22 48 -077 30 98 551 29 48 977 28 98 -358 27 9 24 49 -107 31 99 580 29 49 19005 28 99 -385 27 238 INTERNAL COMBUSTION ENGINES LOGARITHMS OF NUMBERS. — Continued. No. Log. Dif. No. Log. Dif. No. Log. Dif. No. Log. Dif P.P. 1600 20412 27 1650 21748 27 1700 23045 25 1750 24304 49 50 49 01 439 27 51 -775 26 01 070 26 52 353 50 1 3 2 02 466 27 52 801 26 02 -096 25 54 -403 49 2 5 5 03 493 27 53 827 27 03 121 26 56 452 50 3 8 7 04 520 28 54 -854 26 04 -147 25 58 -502 49 4 5 10 13 10 12 OS -548 27 55 -880 26 05 172 26 1760 551 50 6 15 15 06 -575 27 56 906 26 06 -198 25 62 -601 49 7 18 17 07 -602 27 57 932 26 07 223 26 64 -650 49 8 20 20 08 -629 27 58 95S 27 08 -249 25 66 699 49 9 23 22 09 -656 27 59 -985 26 09 274 26 68 748 49 10 25 25 1610 -683 27 1660 22011 26 1710 -300 25 1770 797 49 48 47 11 -710 27 61 -03/ 26 11 325 25 72 846 49 1 2 2 12 -737 26 62 063 26 12 350 26 74 895 49 2 5 5 13 763 27 63 08S 26 13 -376 25 76 944 49 3 7 7 14 790 27 64 115 26 14 401 25 78 993 49 4 5 10 12 9 12 15 817 27 65 141 26 15 426 26 1780 25042 49 6 14 14 16 844 27 66 167 27 16 -452 25 82 -091 48 7 17 16 17 871 27 67 -194 26 17 477 25 84 139 49 8 19 19 18 -898 27 68 -22C 26 18 502 26 86 188 49 9 22 21 19 -925 27 69 -246 26 19 -528 25 88 237 48 10 24 24 1620 -952 26 1670 -272 26 1720 -553 25 1790 285 49 27 26 21 978 27 71 -29f 26 21 578 25 92 -334 48 1 3 3 22 21005 27 72 -321 26 22 603 26 94 382 49 2 5 5 23 -032 27 73 -35C 26 23 -629 25 93 -431 48 3 8 8 24 -059 26 74 -376 25 24 -654 25 98 -479 48 4 5 11 14 10 13 25 085 27 75 401 26 25 -679 25 1800 527 48 6 16 16 23 112 27 76 427 26 26 704 25 02 575 49 7 19 18 27 -139 26 77 453 26 27 729 25 04 -624 48 8 22 21 28 165 27 78 479 26 28 754 25 06 -672 48 9 24 23 29 192 27 79 505 26 29 779 26 OS -720 48 1630 -219 26 1680 -531 26 1730 -805 25 181C -768 48 25 31 245 27 81 -557 26 31 -830 25 12 -816 48 1 3 32 272 27 82 -583 25 32 -855 25 14 -864 48 2 5 33 -299 26 83 608 26 33 -880 25 16 -912 47 3 8 34 325 27 84 634 26 34 -905 25 13 959 48 4 5 10 13 35 -352 26 85 -660 26 35 -930 25 1820 26007 48 6 15 36 378 27 86 -686 26 36 -955 25 22 -055 47 7 18 37 -405 26 87 -712 25 37 -980 25 24 102 48 8 20 38 431 27 88 737 26 38 24005 25 26 150 48 9 23 39 -458 26 89 -763 26 39 -030 25 28 -198 47 1640 484 27 1690 789 25 1740 -055 25 1830 245 48 24 41 -511 26 91 814 26 41 -080 25 32 -293 47 1 2 42 537 27 92 840 26 42 -105 25 34 -340 47 2 5 43 -564 26 93 -866 25 43 -130 25 36 387 48 3 7 44 590 27 94 891 26 44 -155 25 38 -435 47 4 5 10 12 45 -617 26 95 -917 26 45 -180 24 1840 -482 47 6 14 46 -643 26 96 -943 25 46 204 25 42 -529 47 7 17 47 669 27 97 968 26 47 229 25 44 576 47 8 19 48 -696 26 98 -994 25 48 254 25 46 623 47 9 22 49 722 26 99 23019 26 1 49 -279 25 48 670 47 MISCELLANEOUS LOGARITHMS OF NUMBERS.— Continued. 239 No. 1850 Log. Dif. No. 1950 Log. Dif. No. 2050 Log. Dif. No. 2150 Log. Dif. P.P. 26717 47 29003 45 31175 43 33244 40 47 46 62 764 47 62 -048 44 62 -218 42 62 284 41 1 2 2 64 -811 47 54 092 45 64 260 42 54 -325 40 2 5 5 56 -858 47 66 -137 44 66 302 43 56 -365 40 3 7 7 58 -905 46 68 181 45 58 -345 42 68 405 40 4 6 9 12 9 12 I860 95 47 1960 -226 44 2060 -387 42 216C 445 41 6 14 11 62 -996 47 62 -270 44 62 -429 42 6! -486 40 7 16 16 64 27045 46 64 314 44 64 -471 42 64 -526 40 8 19 18 66 09 47 66 358 45 66 513 42 66 -566 40 9 21 21 68 -I3£ 46 68 -403 44 68 555 42 68 -606 40 10 24 23 187(1 184 47 1970 -447 44 2070 597 42 217C -646 40 45 44 72 -23 46 72 -491 44 72 -639 42 72 -686 40 1 2 2 74 -27/ 46 74 -535 44 74 -681 42 74 -726 40 2 5 5 76 323 47 76 -579 44 76 -723 42 76 -766 40 3 7 7 78 -37C 46 78 -623 44 78 -765 41 78 -806 40 4 5 9 11 9 11 1880 — 4ie 46 1980 -667 43 2080 806 42 2180 -846 39 6 14 13 82 -462 46 82 710 44 82 848 42 82 885 40 7 16 15 84 505 46 84 754 44 84 -890 41 84 925 40 8 18 18 86 554 46 86 -798 44 86 932 42 86 965 40 9 20 20 88 601 46 88 -842 43 88 973 42 88 34005 39 10 23 22 1890 646 46 1990 885 44 2090 32015 41 2190 044 40 43 42 92 692 46 92 -929 44 92 056 42 92 084 40 1 2 2 94 -738 46 94 -973 43 94 -098 41 94 -124 39 2 4 4 96 -784 46 96 30016 44 96 139 42 96 163 40 3 6 6 98 -83C 45 98 -060 43 98 -181 41 98 -203 39 4 6 9 11 8 11 1900 875 46 2000 -103 43 2100 -222 41 2200 242 40 6 13 13 02 921 46 02 146 44 02 263 42 02 -282 39 7 15 15 04 -967 45 04 -190 43 04 -305 41 04 321 40 8 17 17 06 28012 46 06 233 43 06 -346 41 06 -361 39 9 19 19 08 -058 45 08 276 44 08 387 41 08 -400 39 10 22 21 1910 103 46 2010 -320 43 2110 428 41 2210 439 40 41 40 12 -149 45 12 -363 43 12 469 41 12 -479 39 1 2 2 14 194 46 14 -406 43 14 510 42 14 -518 39 2 4 4 16 -240 45 16 449 43 16 -552 41 16 -557 39 3 6 6 18 -285 45 18 292 43 18 -593 41 18 596 39 4 5 8 10 8 10 1920 -330 45 2020 535 43 2120 -634 41 2220 635 39 6 12 12 22 375 46 22 578 43 22 -675 40 22 674 39 7 14 14 24 -421 45 24 621 43 24 715 41 24 713 40 8 16 16 26 -466 45 26 -664 43 26 756 41 26 -753 39 9 18 18 28 -511 45 28 -707 43 28 797 41 28 -792 38 10 21 20 1930 -556 45 2030 -750 42 2130 -838 41 2230 830 39 39 38 32 -601 45 32 792 42 32 -879 40 32 869 39 1 2 2 34 -646 45 34 835 43 34 919 41 34 908 39 2 4 i 36 -691 44 36 -878 43 36 960 41 36 947 39 3 6 6 38 735 45 38 920 42 38 33001 40 38 > 986 39 4 5 8 10 8 10 1940 780 45 2040 963 43 2140 041 41 2240 35025 39 6 12 11 42 -825 45 42 31006 42 42 -082 40 42 -064 38 7 14 13 44 -870 44 44 048 43 44 122 41 44 102 39 8 16 15 46 941 45 46 -091 42 46 -163 40 46 -141 39 9 18 16 48 -959 44 48 -,33 42 48 203 41 48 -180 38 10 20 17 240 INTERNAL COMBUSTION ENGINES LOGARITHMS OF NUMBERS. — Continued. No. 22S0 Log. Dif. No. 2350 Log. Dif. No. Log. Dif. No. 2550 Log. Dif P.P. 33218 39 37107 37 2150 38917 35 40654 34 39 38 62 -257 38 52 -144 37 62 952 35 52 68E 34 1 2 2 54 295 39 54 -181 37 54 987 36 51 722 34 2 4 4 66 -334 38 56 -218 36 56 39023 35 56 756 34 3 6 6 68 372 39 58 254 37 68 058 36 58 790 34 4 8 8 5 10 10 2260 -411 38 2360 291 37 2160 -094 35 2560 -824 34 6 12 11 62 449 39 62 -328 37 62 -129 35 62 -858 34 7 14 13 64 -488 38 64 -365 36 61 164 35 64 -892 34 8 16 15 66 -526 38 66 401 37 66 199 35 66 -926 34 9 18 17 68 564 39 68 438 37 68 -235 35 68 -960 33 10 20 19 2270 -603 38 2370 -475 36 2170 -270 35 2570 993 34 37 36 72 -641 38 72 511 37 72 -305 35 72 41027 34 1 2 2 74 679 38 74 546 37 71 -340 35 74 -061 34 2 1 4 76 717 38 76 -585 36 76 375 35 76 -095 33 3 3 5 78 755 38 78 621 37 78 410 35 78 128 34 4 5 7 7 ) 9 2280 793 39 2380 -658 36 2180 455 35 2580 -162 34 6 11 11 82 -832 38 82 694 37 82 480 35 82 -196 33 7 13 13 84 -870 38 84 -731 36 84 515 35 81 229 34 8 15 14 8E -90E 38 86 76/ 36 86 550 35 85 -263 33 9 17 16 88 -946 38 88 803 37 88 585 35 88 296 34 10 19 18 2290 -984 37 2390 -840 36 2490 -620 35 2590 -330 33 3 5 34 92 36021 38 92 876 36 92 -655 35 92 363 34 1 . ! 2 94 055 38 91 912 37 94 -690 34 94 -397 33 2 ' I 3 9£ 09; 38 93 -949 36 93 724 35 98 430 34 3 . > 5 98 135 38 98 -985 36 98 759 35 98 -464 33 4 ' 5 < 7 9 2300 -173 38 2400 38021 36 2500 794 35 2600 497 34 6 1 10 02 -211 37 02 05/ 36 02 -829 34 02 -531 33 7 11 12 04 246 38 04 093 37 04 863 35 04 564 33 8 V 14 06 -28t 38 06 -130 36 06 898 35 06 597 34 9 If 15 08 -324 37 08 -165 36 08 -933 34 08 -631 33 10 1! 17 2310 361 38 2110 -202 36 2510 967 35 2810 664 33 33 12 -399 37 12 -238 36 12 40002 35 12 697 34 1 2 , 14 436 38 11 -274 36 14 -037 34 14 -731 33 2 3 16 -474 37 16 -310 36 16 071 35 16 -764 33 3 5 18 511 38 18 -346 36 18 -106 34 18 -797 33 4 6 6 7 8 10 2320 -549 37 2120 -382 35 2520 140 35 2620 830 33 22 586 38 22 417 36 22 -175 34 22 863 33 7 12 21 -624 37 24 453 36 21 -209 34 21 896 33 8 13 23 -661 37 26 489 36 26 243 35 26 929 34 S 15 28 698 38 28 -525 36 28 -278 34 28 -963 33 10 17 2330 -736 37 2130 -561 35 2530 312 34 2630 -996 33 32 32 -773 37 32 596 36 32 346 35 32 42029 33 1 2 34 810 37 31 632 36 34 -3S1 34 34 -062 33 : 3 36 847 37 36 -668 35 36 -4l5 34 36 -095 32 s 5 38 884 38 38 703 36 38 449 34 38 127 33 4 t i 6 8 10 2310 -922 37 2410 -739 36 2540 483 35 2610 160 33 42 -959 37 12 -775 35 42 -518 34 12 193 33 ' 11 14 -996 37 11 810 36 41 -552 34 11 226 33 f (13 46 37033 37 16 -846 35 46 -586 34 46 -259 33 ( 114 48 -070 37 IS 881 36 18 -620 34 48 -292 33 1( 116 MISCELLANEOUS LOGARITHMS OF NUMBERS.— Continued. 241 No. Log. Dif. No. 2750 Log. Dif. No. 2850 Log. Dif. 31 No. Log. Dif. P.P. 2650 42325 32 43933 32 45484 2950 46962 30 33 32 52 357 33 52 -965 31 52 -515 30 62 47012 29 1 2 2 54 390 33 54 996 32 54 545 31 54 041 29 2 3 3 56 -423 ■32 56 44028 31 66 -576 30 56 070 30 3 5 5 58 455 33 58 059 32 58 606 31 58 -100 29 4 6 7 6 3 8 2660 488 33 2760 -091 31 2860 -637 30 2960 129 30 6 10 10 62 -521 32 62 122 32 62 -667 30 62 -159 29 712 11 64 553 33 64 -154 31 64 697 31 64 -188 29 8 13 13 66 586 33 66 185 32 66 -728 30 66 217 29 9 15 14 68 -619 32 68 -217 31 68 -758 30 68 246 30 10 17 16 2670 651 33 2770 -248 31 2870 788 30 2970 -276 29 31 72 -684 32 72 279 32 72 818 31 72 -305 29 1 2 74 716 33 74 -311 31 74 -849 30 74 334 29 2 3 76 -749 32 76 -342 31 76 -879 30 76 363 29 3 5 78 781 32 78 373 31 78 909 30 78 392 30 4 5 6 6 8 9 2680 813 33 2780 404 32 2880 939 30 2980 -422 29 82 -846 32 82 -436 31 82 969 31 82 -451 29 7 11 84 87 33 84 -46/ 31 84 46000 30 84 -480 29 8 12 86 -911 32 86 49£ 31 88 -030 30 86 -509 29 9 14 88 -943 32 88 529 31 88 -060 30 88 538 29 10 16 2690 975 33 2790 560 32 2890 -090 30 2990 567 29 30 92 43008 32 92 -592 31 92 -120 30 92 596 29 1 2 94 -040 32 94 -623 31 94 -150 30 94 625 29 2 3 96 -072 32 96 -654 31 98 -180 30 96 654 29 3 5 98 104 32 98 -685 31 98 -210 30 98 683 29 4 5 6 6 8 9 2700 136 33 2800 -716 31 2900 -240 30 3000 712 29 02 -169 32 02 -747 31 02 -270 30 02 741 29 7 11 04 -201 32 04 -778 31 04 -300 30 04 -770 29 8 12 06 -233 32 06 -809 31 06 -330 29 06 -799 29 9 11 08 -265 32 08 -840 31 08 359 30 08 -828 29 10 15 2710 -297 32 2810 -871 31 2910 389 30 3010 -857 28 29 12 -329 32 12 -902 30 12 419 30 12 885 29 1 1 14 -361 32 14 932 31 14 -449 30 14 914 29 2 3 16 -393 32 16 963 31 16 -479 30 16 943 29 3 i 18 -425 32 18 994 31 18 -509 29 18 -972 29 4 5 6 6 7 9 2720 -457 32 2820 45025 31 2920 538 30 3020 48001 28 22 -489 32 22 -056 30 22 568 30 22 029 29 7 10 24 -521 32 24 086 31 24 -598 29 24 058 29 8 12 26 -553 31 26 117 31 26 627 30 26 -087 29 9 13 28 584 32 28 -148 31 28 657 30 28 -116 28 10 15 2730 616 32 2830 -179 30 2930 -687 29 3030 144 29 28 32 648 32 32 209 31 32 716 30 32 -173 29 1 1 34 -680 32 34 -240 31 34 746 30 34 -202 28 2 3 36 -712 31 36 -271 30 36 -776 29 36 230 29 3 i 38 743 32 38 301 31 38 805 30 38 -259 28 4 6 6 6 7 8 2740 775 32 2840 -332 30 2940 -835 29 3040 287 29 42 -807 31 42 362 31 42 864 30 42 -316 28 7 10 44 838 32 44 -393 30 44 -894 29 44 344 29 8 11 46 870 32 46 423 31 46 923 30 46 -373 28 9 13 48 -902 31 48 -454 30 48 -953 29 48 401 29 10 14 242 INTERNAL COMBUSTION ENGINES LOGARITHMS OF NUMBERS. — Continued. No. Log. Dif. No. Log. Dif. No. Log. Dif. No. Log. Dif. P.P. 3060 48430 28 3150 49831 28 3250 51188 27 3350 52504 26 29 52 458 29 52 -859 27 52 215 27 52 530 26 1 1 54 -487 28 54 886 28 54 -242 26 54 556 26 2 3 56 515 29 56 -914 27 56 268 27 56 582 26 3 4 58 -544 28 58 941 28 58 295 27 58 608 26 4 5 6 6 7 9 3060 572 29 3160 -969 27 3260 -322 26 3360 -634 26 62 -601 28 62 996 28 62 348 27 62 -660 26 7 10 64 -629 28 64 50024 27 64 375 27 64 -686 25 8 12 66 657 29 66 051 28 66 -402 26 66 711 26 9 13 68 -686 28 68 -079 27 68 428 27 68 737 26 10 15 3070 -714 28 3170 -106 27 3270 -455 26 3370 -763 26 28 72 742 28 72 133 28 72 481 27 72 -789 26 1 1 74 770 29 74 -161 27 74 -508 26 74 -815 25 2 3 76 -799 28 76 188 27 76 534 27 76 840 26 3 4 78 -827 28 78 215 28 78 -561 26 78 -866 26 4 5 6 6 7 8 3080 855 28 3180 -243 27 3280 587 27 3380 -892 25 82 833 28 82 270 27 82 -614 26 82 917 26 7 10 84 911 29 84 297 28 84 640 27 84 943 26 8 11 86 -940 28 86 -325 27 86 -667 26 86 -969 25 9 13 88 -968 28 88 -352 27 88 693 27 88 994 26 10 14 3090 -996 28 3190 379 27 3290 -720 26 3390 53020 26 27 92 49024 28 92 406 27 92 -746 26 92 -046 25 1 1 94 052 28 94 433 28 94 772 27 94 071 26 2 3 96 080 28 96 -461 27 96 -799 26 96 -097 25 3 i 98 108 28 98 -488 27 98 825 26 98 122 26 4 6 6 5 7 8 3100 136 28 3200 -515 27 3300 851 27 3400 -148 25 02 164 28 02 542 27 02 -878 26 02 173 26 7 9 04 192 28 04 569 27 04 904 26 04 -199 25 8 11 06 220 28 06 596 27 06 930 27 06 224 26 9 12 08 248 28 08 623 28 08 -957 26 08 -250 25 10 14 3110 276 28 3210 -651 27 3310 -983 26 3410 275 26 26 12 -304 26 12 -678 27 12 52009 26 12 -301 25 1 1 14 -332 28 14 -705 27 14 035 26 14 326 26 2 3 16 -360 28 16 -732 27 16 061 27 16 -352 25 3 4 18 -388 27 18 -759 27 18 -088 26 18 377 26 4 5 6 5 7 8 3120 415 28 3220 -786 27 3320 -114 26 3420 -403 25 22 443 28 22 -813 27 22 -140 26 22 428 25 7 9 24 471 28 24 -840 26 24 166 26 24 453 26 8 10 26 -499 28 26 866 27 26 192 26 26 -479 25 9 12 28 -527 27 28 893 27 28 218 26 28 504 25 10 13 3130 554 28 3230 920 27 3330 244 26 3430 529 26 25 32 582 28 32 947 27 32 270 27 32 -555 25 1 1 34 -610 28 34 974 27 34 -297 26 34 580 25 2 3 36 -638 27 36 51001 27 36 -323 26 36 605 26 3 4 38 665 28 38 -028 27 38 -349 26 38 -631 25 4 5 6 5 6 8 3140 -693 28 3240 -055 26 3340 -375 26 3440 -656 25 42 -721 27 42 081 27 42 -401 26 42 681 25 7 9 44 748 28 44 108 27 44 -427 26 44 706 26 8 10 46 -776 27 46 -135 ■27 46 -453 26 46 -732 25 9 11 48 803 28 48 -162 26 48 -479 25 48 -757 25 10 13 MISCELLANEOUS LOGARITHMS OF NUMBERS.— Continued. 243 No. Log. Dif. No. Log. Dif. 24 No. Log. Dif. 24 No. Log. Dif. P.P. 3450 53782 25 3550 55023 3350 56229 3750 57403 58 26 25 62 807 25 52 047 25 52 253 24 55 -461 58 1 1 1 54 832 25 54 —072 24 54 —277 24 60 -519 57 2 3 3 56 857 25 56 096 25 56 —301 23 65 576 58 3 4 4 58 882 26 58 —121 24 58 324 24 70 634 58 4 5 5 7 5 6 3460 —908 24 3560 —145 24 3660 348 24 3775 -692 57 6 8 8 62 —933 25 62 169 25 62 —372 24 80 749 58 7 9 9 64 —958 24 64 —194 24 64 —396 23 85 -807 57 8 10 10 66 —983 24 66 216 24 66 419 24 90 -864 57 9 12 11 68 54008 25 68 242 25 68 —443 24 95 921 57 10 13 13 3470 —033 25 3570 —267 24 3670 -467 23 3800 978 57 24 23 72 —058 25 72 291 24 72 490 24 05 58035 57 1 1 1 74 —083 25 74 315 25 74 —514 24 10 092 57 2 2 2 76 —108 25 76 —340 24 76 —538 23 15 149 57 3 4 3 78 —133 25 78 364 24 78 561 24 20 206 57 4 5 5 6 5 6 3480 —158 25 3580 388 25 3680 —585 23 3825 263 57 6 7 7 82 —183 25 82 -413 24 82 608 24 30 -320 57 7 8 8 84 —208 25 84 —437 24 84 —632 24 35 -377 56 8 10 9 86 —233 25 86 461 24 86 —656 23 40 433 57 9 11 10 88 —258 25 88 485 24 88 679 , 24 45 -490 56 10 12 12 3490 —283 24 3590 509 25 3690 —703 23 3850 546 56 58 57 92 307 25 92 —534 24 92 726 24 55 602 57 1 1.2 1.1 94 332 25 94 -558 24 94 —750 23 60 -659 56 2 2.3 2.3 96 357 25 96 —582 24 96 773 24 65 -715 56 3 3.5 3.4 98 —382 25 98 606 24 98 —797 23 70 771 56 4 5 4.6 5.8 4.6 5.7 3500 —407 25 3600 630 24 3700 820 24 3875 827 56 6 7.0 6.8 02 —432 24 02 654 24 02 —844 23 80 883 56 7 8.1 8.0 04 456 25 04 678 25 04 867 24 85 939 56 8 9.3 9.1 06 481 25 06 —703 24 06 —891 23 90 -995 56 9 10.4 10.3 08 —506 25 08 —727 24 08 -914 23 95 59051 55 10 11.6 11.4 3510 —531 24 3610 —751 24 3710 937 24 3900 106 56 56 55 12 555 25 12 —775 24 12 -961 23 05 162 56 1 1.1 1.1 14 580 25 14 —799 24 14 984 24 10 -218 55 2 2.2 2.2 16 -605 25 16 —823 24 16 57008 23 15 273 56 3 3.4 3.3 18 —630 24 18 —847 24 18 -031 23 20 -329 55 4 5 4.5 5.6 4.4 5.5 3520 654 25 3620 —871 24 3720 054 24 3925 -384 55 6 6.7 6.6 22 —679 25 22 —895 24 22 -•078 23 30 439 55 7 7.8 7.7 24 —704 24 24 —919 24 24 -101 23 35 494 56 8 9.0 8.8 26 728 25 26 —943 24 26 124 24 40 -550 55 9 10.1 9.9 28 —753 24 28 —967 24 28 -148 23 45 -605 55 10 11.2 11.0 3530 777 25 3630 —991 24 3730 -171 23 3950 -660 55 54 32 802 25 32 56015 23 32 194 23 55 -715 55 1 1.1 34 —827 24 34 038 24 34 217 24 60 -770 54 2 2.2 36 851 25 36 062 24 36 -241 23 65 824 55 3 3.2 38 —876 24 38 086 24 38 -264 23 70 879 55 4 5 4.3 5.4 3540 900 25 3640 110 24 3740 287 23 3975 -934 54 6 6.5 42 —925 24 42 —134 24 42 310 24 80 988 55 7 7.6 44 949 25 44 —158 24 44 -334 23 85 60043 54 8 8.6 46 —974 24 46 — 182 23 46 -357 23 90 097 55 9 9.7 48 998 25 48 205 24 48 -380 23 95 -152 54 10 10.8 244 INTERNAL COMBUSTION ENGINES LOGARITHMS OF NUMBERS. — Continued. No. Log Dif. No. Log. Dif. No. Log. Dif. No. Log. Dif. P. P. 4000 60206 54 4250 62839 51 4500 65321 48 4750 67669 46 54 53 52 05 260 54 55 -890 51 05 369 49 55 715 46 1 1.1 1.1 1.0 10 314 55 60 -941 51 10 -418 48 60 -761 45 2 2.2 2.1 2.1 15 -369 54 65 -992 51 15 -466 48 65 806 46 3 3.2 3.2 3.1 20 -423 54 70 63043 51 20 -514 48 70 -852 45 4 5 4.3 5.4 4.2 5.3 4.2 5.2 25 -477 54 75 -094 50 25 -562 48 75 897 46 6 6.5 6.4 6.2 30 -531 53 80 144 51 30 -610 48 80 -943 45 7 7.6 7.4 7.3 35 584 54 85 195 51 35 -658 48 85 968 46 8 8.6 8.5 8.3 40 638 54 90 -246 50 40 -706 47 90 68034 45 9 9.7 9.5 9.4 45 -692 54 95 296 51 45 753 48 95 -079 45 10 10.8 10.6 10.4 4050 -746 53 4300 -347 50 4550 801 48 4800 124 45 51 50 49 55 799 54 05 397 51 55 -849 47 05 169 46 1 1.0 1.0 1.0 60 -853 53 10 -448 50 60 896 48 10 -215 45 2 2.0 2.0 2.0 65 906 53 15 498 50 65 944 48 15 -260 45 3 3.1 3.0 2.9 70 959 54 20 548 51 70 -992 47 20 -305 45 4 5 4.1 5.1 4.0 5.0 3.9 4.9 75 61013 53 25 -599 50 75 66039 48 25 -350 45 6 6.1 6.0 5.9 80 066 53 30 -649 50 80 -087 47 30 -395 45 7 7.1 7.0 6.9 85 199 53 35 -699 50 85 -134 47 35 -440 45 8 8.2 8.0 7.8 90 172 53 40 -749 50 90 181 48 40 -485 44 9 9.2 9.0 8.8 95 225 53 45 -799 50 95 -229 47 45 529 45 10 10.2 10.0 9.8 4100 278 53 4350 -849 50 4600 -276 47 4850 574 45 4 8 47 05 331 53 55 -899 50 05 -323 47 55 -619 45 1 1 0.9 10 384 53 60 -949 49 10 370 47 60 -664 44 21 9 1.9 15 -437 53 65 998 50 15 417 47 65 708 45 32 9 2.8 20 -490 52 70 64048 50 20 464 47 70 -753 44 43 64 8 3.8 8 4.7 25 542 53 75 -098 49 25 511 47 75 797 45 65 8 5.6 30 595 53 80 147 50 30 558 47 80 -842 44 76 76.6 35 -648 52 85 -197 49 35 -605 47 85 886 45 87 7 7.5 40 700 52 90 245 50 40 -652 47 90 -931 44 98 6 8.5 45 752 53 95 -296 49 45 -699 46 95 975 45 10 9 6 9.4 4150 -805 52 4400 345 50 4650 745 47 4900 69020 44 ' 16 45 55 857 52 05 -395 49 55 -792 47 05 -064 44 10 .9 0.9 60 909 53 10 -444 49 60 -839 46 10 108 44 21 .81.8 65 -962 52 15 493 49 65 885 47 15 152 45 32 .8 2.7 70 62014 52 20 542 49 70 -932 46 20 -197 44 43 54 .73.6 .64.5 75 -066 52 25 591 49 75 978 47 25 -241 44 65 .55.4 80 -118 52 30 640 49 80 67025 46 30 -285 44 76 .46.3 85 -170 51 35 689 49 85 -071 46 35 -329 44 87 .47.2 90 221 52 40 738 49 90 117 47 40 -373 44 98 .38.1 95 273 52 45 787 49 95 -164 46 45 -417 44 10 9 .29.0 4200 -325 52 4450 836 49 4700 -210 46 4950 -461 43 14 43 05 -377 51 55 -855 48 05 -256 46 55 504 44 10 .90.9 10 428 52 60 933 49 10 302 46 60 548 44 21 .8 1.7 15 -480 51 65 982 49 15 348 46 65 -592 44 32 .62.6 20 531 52 70 65031 48 20 394 46 70 -636 43 43 64 .53.4 .44.3 25 -583 51 75 079 49 25 440 46 75 679 44 65 .3 5.2 30 634 51 80 -128 48 30 486 46 80 -723 44 78 .26.0 35 685 52 85 176 49 35 -532 46 85 -767 43 8; .06.9 40 -737 51 90 -225 48 40 -578 46 90 810 44 9; .9 7.7 45 -788 51 95 -273 48 45 -624 45 95 -854 43 10 £ .88.6 MISCELLANEOUS LOGARITHMS OF NUMBERS. — Continued. 245 No. 5000 Log. Dif. No. Log. Dif. 41 No. Log. Dif. 40 No. Log. Dif. P. P. 69897 43 5250 72016 5500 74036 5750 75967 38 44 43 OS 940 44 55 057 42 05 -076 39 65 76005 37 1 0.9 0.9 10 -984 43 60 -099 41 10 115 40 60 042 38 2 1.8 1.7 16 70027 43 65 -140 41 15 -155 39 65 -080 38 3 2.6 2.6 20 070 44 70 181 41 20 -194 39 70 -118 37 4 5 3.5 4.4 3.4 4.3 25 -114 43 75 222 41 25 233 40 75 155 38 6 5.3 5.2 30 -157 43 80 263 41 30 -273 39 80 -193 37 7 6.2 6.0 35 -200 43 85 304 42 35 -312 39 85 230 38 8 7.0 6.9 40 243 43 90 -346 41 40 -351 39 90 -268 37 9 7.9 7.7 45 286 43 96 -387 41 45 390 39 95 305 38 10 8.8 8.6 5050 329 43 5300 -428 41 5550 429 39 5800 -343 37 42 41 65 372 43 05 -469 40 55 468 39 05 380 38 1 0.8 0.8 60 415 43 10 509 41 60 507 40 10 -418 37 2 1.7 1.6 65 -458 43 15 550 41 65 -547 39 15 -455 37 3 2.5 2.5 70 -501 43 20 591 41 70 -586 38 20 492 38 4 6 3.4 4.2 3.3 4.1 75 -544 42 25 -632 41 75 624 39 25 -530 37 6 50 4.9 SO 586 43 30 -673 40 80 663 39 30 -567 37 7 59 5.7 85 629 43 35 713 41 85 702 39 35 604 37 8 6.7 6.6 90 -672 42 40 754 41 90 741 39 40 641 37 9 7.6 7.4 95 714 43 45 -795 40 95 780 39 45 678 38 10 8.4 8.2 5100 757 43 6350 835 41 5600 -819 39 5850 -716 37 40 39 05 -800 42 56 -876 40 05 -858 38 55 -753 37 1 0.8 0.8 10 842 43 60 916 41 10 896 39 60 -790 37 2 1.6 1.6 15 -885 42 65 -957 40 IS -935 39 65 -827 37 3 2.4 2.3 20 -927 42 70 997 41 20 -974 38 70 -864 37 4 6 3.2 4.0 3.1 3.9 25 969 43 75 73038 40 25 75012 39 76 -901 37 6 4.8 4.7 30 71012 42 80 078 41 30 -051 38 80 -938 37 7 5.6 5.5 35 054 42 85 -119 40 35 089 39 85 -975 37 8 6.4 6.2 40 096 43 90 -159 40 40 -128 38 90 77012 36 9 7.2 7.0 45 -139 42 95 199 40 45 166 39 95 048 37 10 8 7.8 6150 -181 42 5400 239 41 5650 -205 38 5900 085 37 38 37 65 -223 42 05 -280 40 55 243 39 05 -122 37 1 0.8 07 60 -265 42 10 -320 40 60 -282 38 10 -159 36 2 15 1.5 65 307 42 15 -360 40 65 -320 38 15 195 37 3 2.3 2.2 70 349 42 20 -400 40 70 358 39 20 232 37 4 5 3.0 3.8 3.0 3.7 75 391 42 25 -440 40 75 -397 38 25 -269 36 6 4.6 4.4 80 -433 42 30 -480 40 80 -435 38 30 305 37 7 5 3 5.2 85 -475 42 35 -520 40 85 473 38 35 342 37 8 6.1 5.9 90 -517 42 40 -560 40 90 511 38 40 -379 36 9 6.8 6.7 95 -559 41 45 -600 40 95 549 38 45 415 37 10 7.6 7.4 6200 600 42 5450 -640 39 5700 587 39 5950 -452 36 36 05 642 42 55 679 40 05 -626 38 56 488 37 1 0.7 10 -684 41 60 719 40 10 -664 38 60 -525 36 2 1.4 15 725 42 65 759 40 15 -702 38 65 561 36 3 2.2 20 767 42 70 -799 39 20 -740 38 70 597 37 4 6 2.9 3.6 25 -809 41 75 838 40 25 -778 37 75 -634 36 6 4.3 30 850 42 80 878 40 30 815 38 80 670 36 7 5.0 35 -892 41 85 -918 39 35 853 38 C5 706 37 8 5.8 40 933 42 90 957 40 40 891 38 90 -743 36 9 6.5 45 -975 41 95 -997 39 46 929 38 95 -779 36 10 7.2 246 INTERNAL COMBUSTION ENGINES LOGARITHMS OF NUMBERS. — Continued. No. Log. Dif. No. Log. Dif. No. Log. Dif. 34 No. Log. Dif. P.P. 6000 77815 36 6250 79588 35 6500 81291 6750 82930 33 37 36 05 851 36 55 -623 34 05 -325 33 55 -963 32 1 ).7 0.7 10 887 37 60 657 35 10 358 33 60 -995 32 2 .5 1.4 15 -924 36 65 692 35 15 391 34 65 83027 32 3 2.2 2.2 20 -960 36 70 -727 34 20 -425 33 70 -059 32 4 5 i.O S.7 2.9 3.6 25 -996 36 75 761 35 25 458 33 75 -091 32 64 4 4.3 30 78032 36 80 -796 35 30 491 34 80 -123 32 7 5.2 5.0 35 -068 36 85 -831 34 35 -525 33 85 -155 32 8 5.9 5.8 40 -104 36 90 865 35 40 -558 33 90 -187 32 9 6.7 6.5 45 -140 36 95 -900 34 45 -591 33 95 -219 32 10 7.4 7.2 6050 -176 35 6300 934 35 6550 624 33 6800 -251 32 35 34 55 211 36 05 -969 34 55 657 33 05 -283 32 10.7 0.7 60 247 36 10 80003 34 60 690 33 10 -315 32 2 1.4 1.4 65 283 36 15 037 35 65 723 34 15 -347 31 32.1 2.0 70 -319 36 20 -072 34 70 -757 33 20 378 32 4 2.8 5 3.5 2.7 3.4 75 -355 35 25 106 34 75 -790 33 25 410 32 6 4.2 4.1 SO 390 36 30 140 35 80 -823 33 30 442 32 7 4.9 4.8 85 426 36 35 -175 34 85 -856 33 35 -474 32 85.6 5.4 90 -462 35 40 -209 34 90 -889 32 40 -506 31 9e .3 6.1 95 497 36 45 243 34 95 921 33 45 537 32 10 7.0 6.8 6100 -533 36 6350 277 35 6600 954 33 6850 569 32 33 05 -569 35 55 -312 34 05 987 33 55 -601 31 10.7 10 604 36 60 -346 34 10 82020 33 60 632 32 21.3 15 -640 35 65 -380 34 15 -053 33 65 664 32 32 20 675 36 70 -414 34 20 -086 33 70 -696 31 42.6 53.3 25 -711 35 75 448 34 25 -119 32 75 727 32 6 4 30 746 35 80 482 34 30 151 33 80 -759 31 74 6 35 781 36 85 516 34 35 184 33 85 790 32 85.3 40 -817 35 90 550 34 40 -217 32 90 -822 31 9 5.9 45 852 36 95 584 34 45 249 33 95 853 32 10 6.6 6150 -888 35 6400 -618 34 6650 282 33 6900 -885 31 32 55 -923 35 05 -652 34 55 -315 32 05 916 32 1 0.6 60 958 35 10 -686 34 60 347 33 10 -948 31 i 1.3 65 993 36 15 -720 34 65 380 33 15 979 32 i 1.9 70 79029 35 20 -754 33 70 -413 32 20 84011 31 4 2.6 3.2 75 -064 35 25 787 34 75 445 33 25 -042 31 t 3.8 80 -099 35 30 821 34 80 -478 32 30 073 32 ' 4.5 85 -134 35 35 -855 34 85 510 33 35 -105 31 i 5.1 90 169 35 40 -889 33 90 -543 32 40 -136 31 I 5.8 95 204 35 45 922 34 95 575 32 45 167 31 1C 6.4 6200 239 35 6450 -956 34 6700 607 33 6950 198 32 31 05 274 35 55 -990 33 05 -640 32 55 -230 31 1 0.6 10 309 35 60 81023 34 10 672 33 60 -261 31 2 1.2 15 344 35 65 -057 33 15 -705 32 65 292 31 3 1.9 20 379 35 70 090 34 20 -737 32 70 323 31 4 S 2.5 3.1 25 -414 35 75 -124 34 25 769 33 75 354 32 6 3.7 30 -449 35 80 -156 33 30 -802 32 80 -386 31 7 4.3 35 -484 34 85 -191 33 35 -834 32 85 -417 V 8 SO 40 518 35 90 224 34 40. -866 32 90 -448 31 9 5.6 45 553 35 95 -258 33 45 i 898 32 95 -479 31 10 6.2 MISCELLANEOUS LOGARITHMS OF NUMBERS. — Continued. 247 No. Log. Dif. No. Log. Dif No. Log. Dif No. Log. Dif P.P. 7000 845IC 31 725C 86034 30 7500 8750t 29 775( 8893( 28 31 OS -541 31 55 -064 30 OS 53! 29 55 95! 28 1 0.6 10 -572 31 6C -094 30 10 -56< 29 60 98« 28 s 1.2 IS -603 31 65 -124 29 IE -593 29 65 89014 28 3 1.9 20 -634 31 70 153 30 20 -622 29 70 042 28 4 I 2.S 3.1 25 -665 31 75 183 30 25 -651 28 75 070 28 6 3.7 30 -696 30 80 213 30 30 679 29 80 -098 28 7 4.3 35 726 31 85 -243 30 35 708 29 85 -126 28 8 5.0 40 757 31 90 -273 30 40 737 29 90 -154 28 9 5.6 45 788 31 95 -303 29 45 -766 29 95 -182 27 10 6.2 7050 -819 31 7300 332 30 7550 -795 28 7800 209 28 30 55 -850 30 05 362 30 55 823 29 05 237 28 1 0.6 60 8S0 31 10 -392 29 60 852 29 10 265 28 2 1.2 65 •III 31 15 421 30 65 -881 29 15 -293 28 3 1.8 70 -942 31 20 451 30 70 -910 28 20 -321 27 4 S 2.4 3.0 75 -973 30 25 -481 29 75 938 29 25 348 28 6 3.6 80 85003 31 30 510 30 80 -967 29 30 376 28 7 4.2 85 -034 31 35 540 30 85 -996 28 35 -404 28 8 4.8 90 -065 30 40 -570 29 90 88024 29 40 -432 27 9 5.4 95 095 31 45 599 30 95 -053 28 45 459 28 10 6.0 7100 -126 30 7350 -629 29 7600 081 29 7850 -487 28 29 05 156 31 55 658 30 OS -110 28 55 -515 27 1 0.6 10 -187 30 60 -688 29 10 138 29 60 542 28 2 1.2 IS 217 31 65 717 30 15 -167 28 65 -570 27 3 1.7 20 -248 30 70 -747 29 20 195 29 70 597 28 4 5 2.3 2.9 25 278 31 75 776 30 25 -224 28 75 625 28 6 3.5 30 -309 30 80 -806 29 30 252 29 80 -653 27 7 4.1 36 339 31 85 835 29 35 -281 28 85 680 28 8 4.6 40 -370 30 90 864 30 40 309 29 90 -708 27 9 5.2 45 400 31 93 -894 29 45 -338 28 95 735 28 10 5.8 7150 -431 30 7400 923 30 7650 366 29 7900 -763 27 28 SS -461 30 05 -953 29 55 -395 28 05 790 28 1 0.6 60 491 31 10 -982 29 60 -423 28 10 -818 27 2 1.1 65 -522 30 15 87011 29 65 451 29 15 845 28 3 1.7 70 -552 30 20 040 30 70 -480 28 20 -873 27 4 S 2.2 2.8 75 582 30 25 -070 29 75 -508 28 25 -900 27 6 3.4 80 612 31 30 -099 29 80 536 28 30 927 28 7 3.9 85 -643 30 35 128 29 85 564 29 35 -955 27 8 4.5 90 -673 30 40 157 29 90 -593 28 40 982 27 9 5.0 95 703 30 45 186 30 95 -621 28 45 90009 28 10 5.6 7200 733 30 7450 -216 29 7700 649 28 7950 -037 27 27 05 763 31 56 -245 29 05 677 28 55 064 27 1 0.5 10 -794 30 60 -274 29 10 705 29 60 091 28 2 1.1 15 -824 30 65 -303 29 15 -734 28 65 -119 27 3 1.6 20 -854 30 70 332 29 20 -762 28 70 -146 27 4 S 2.2 2.7 25 -884 30 75 361 29 25 -790 28 75 173 27 6 3.2 30 -914 30 ' 80 390 29 30 -818 28 80 200 27 7 3.8 35 -944 30 85 419 29 35 646 28 85 227 28 8 4.3 40 -974 30 90 448 29 40 874 28 90 -255 27 9 4.9 45 86004 30 95 477 29 15 902 28 95 -282 27 10 5.4 248 INTERNAL COMBUSTION ENGINES LOGARITHMS OF NUMBERS.— Continued. No. Log. Dif. 27 No. Log. Dif. 27 No. Log. Dif. 25 No. Log. Dif 25 PP 3000 90309 8250 9164! 850C 92942 875C 94201 28 OS 336 27 55 -672 26 OS 96/ 26 55 -226 24 1 0.6 10 363 27 60 69f 26 1C -993 25 60 250 25 2 1.1 IS 39C 27 65 721 27 15 930 IS 26 65 275 25 3 1.7 20 417 28 70 -751 26 20 -044 25 70 -300 25 4 5 2.2 2.8 25 -445 27 75 -777 26 25 069 26 75 -325 24 6 3.4 30 -472 27 80 803 26 30 -095 25 80 349 25 7 3.9 35 -499 27 85 829 26 35 120 26 85 374 25 8 4.5 . 40 -526 27 90 855 27 40 -146 25 90 -399 25 9 5.0 45 -553 27 95 -882 26 45 171 26 95 -424 24 10 5.6 8050 -580 27 8300 -908 26 8550 -197 25 8800 448 25 27 55 -607 27 05 -934 26 55 222 25 05 -473 25 1 0.5 60 -634 26 10 960 26 60 247 26 10 -498 24 2 1.1 65 660 27 15 986 26 65 -273 25 15 522 25 3 1.6 70 687 27 20 92012 26 70 298 25 20 -547 24 4 5 2.2 2.7 75 714 27 25 038 27 75 323 26 25 571 25 6 3.2 80 741 27 30 -065 26 80 -349 25 30 596 25 7 3.8 85 768 27 35 -091 26 85 374 25 35 -621 24 8 4.3 90 -795 27 40 -117 26 90 399 26 40 645 25 9 4.9 95 -822 27 45 -143 26 95 -425 25 45 -670 24 10 5.4 8100 -849 26 8350 -169 26 8600 -450 25 8850 694 25 26 05 875 27 55 -195 26 05 475 25 55 -719 24 1 0.5 10 902 27 60 -221 26 10 500 26 60 743 25 2 1.0 15 -929 27 65 -247 26 15 -526 25 65 -768 24 3 1.6 20 -956 26 70 -273 25 20 -551 25 70 792 23 4 5 2.1 2.6 25 982 27 75 298 26 25 -576 25 75 -817 24 6 3.1 30 91009 27 80 324 26 30 601 25 80 841 25 7 3.6 35 -036 26 85 350 26 35 626 25 85 -866 24 8 4.2 40 062 27 90 376 26 40 651 25 90 890 25 9 4.7 45 089 27 95 402 26 45 676 26 95 -915 24 10 5.2 8150 -116 26 8400 -428 26 8650 -702 25 8900 939 24 25 55 142 27 05 -454 26 55 -727 25 05 963 25 1 0.5 60 169 27 10 -480 25 60 -752 25 10 -988 24 2 1.0 65 -196 26 15 505 26 65 -777 25 15 95012 24 3 1.5 70 222 27 20 531 26 70 -802 25 20 036 25 4 5 2.0 2.5 75 -249 26 25 -557 26 75 -827 25 25 -061 24 6 3.0 80 275 27 30 -583 26 80 -852 25 30 085 24 7 3.5 85 -302 26 35 -609 25 85 -877 25 35 109 25 8 4.0 90 328 27 40 634 26 90 -902 25 40 -134 24 9 4.5 95 -355 26 45 -660 26 95 -927 25 45 158 24 10 50 8200 381 27 8450 -686 25 8700 -952 25 8950 182 25 24 OS -408 26 55 711 26 05 -977 25 55 -207 24 1 0.5 10 434 27 60 737 26 10 94002 25 60 -231 24 2 1.0 15 -461 26 65 -763 25 15 -027 25 65 255 24 3 1.4 20 487 27 70 788 26 20 -052 25 70 279 24 4 5 1.9 2.4 25 -514 26 75 -814 26 25 -077 24 75 303 25 6 2.9 30 -540 26 80 -840 25 30 101 25 80 -328 24 7 3.4 35 566 27 85 865 26 35 126 25 85 -352 24 8 3.8 40 -593 26 90 -891 25 40 151 25 90 -376 24 9 1.3 45 619 26 95 916 26 45 -176 25 95 400 24 10 1.8 MISCELLANEOUS LOGARITHMS OF NUMBERS. — Continued. 249 No. Log. Dif. No. Log. Dif. 24 No. Log. Dif. 23 No. Log. Dif. P. P. 9000 95424 24 9250 96614 9500 97772 9750 98900 23 25 05 448 24 55 -638 23 05 795 23 56 -923 22 1 0.5 10 472 25 60 661 24 10 818 23 60 -945 22 2 1.0 15 -497 24 65 -685 23 15 -841 23 65 967 22 3 1.5 20 -521 24 70 -708 23 20 -864 22 70 989 23 4 5 2.0 2.5 25 -545 24 75 731 24 25 886 23 75 99012 22 6 3.0 30 -569 24 80 -755 23 30 909 23 80 -034 22 7 3.5 35 -593 24 85 778 24 35 932 23 85 056 22 8 4.0 40 -617 24 90 -802 23 40 -955 23 90 078 22 9 4.5 45 -641 24 95 -825 23 45 -978 22 95 100 23 10 5.0 9050 -665 24 9300 848 24 9550 98000 23 9800 -123 22 24 55 -689 24 05 -872 23 55 023 23 05 -145 22 1 0.5 60 -713 24 10 -895 23 60 -046 22 10 -167 22 2 1.0 65 -737 24 15 918 24 65 068 23 15 189 22 3 1.4 70 -761 24 20 -942 23 70 091 23 20 211 22 4 6 1.9 2.4 75 -785 24 25 -965 23 75 -114 23 25 233 22 6 2.9 80 -809 23 30 988 23 80 -137 22 30 255 22 7 3.4 85 832 24 35 97011 24 85 159 23 35 277 23 8 3.8 90 856 24 40 -035 23 90 -182 22 40 -300 22 9 4.3 95 880 24 45 -058 23 95 204 23 45 -322 22 10 4.8 9100 904 24 9350 081 23 9600 227 23 9850 -344 22 23 05 -928 24 55 104 24 05 -250 22 55 -366 22 1 0.5 10 -952 24 60 -128 23 10 272 23 60 -388 22 2 0.9 15 -976 23 65 -151 23 15 -295 23 65 -410 22 3 1.4 20 999 24 70 -174 23 20 -318 22 70 -432 22 4 6 1.8 2.3 25 96023 24 75 197 23 25 340 23 75 -454 22 6 2.8 30 047 24 80 220 23 30 -363 22 80 -476 22 7 3.2 35 -071 24 85 243 24 35 385 23 85 -498 22 8 3.7 40 -095 23 90 -267 23 40 -408 22 90 -520 22 9 4.1 45 118 24 95 -290 23 46 430 23 95 -542 22 10 4.6 9150 142 24 9400 -313 23 9650 -453 22 9900 -564 21 22 55 -166 24 05 -336 23 56 475 23 05 585 22 1 0.4 60 -190 23 10 -359 23 60 -498 22 10 607 22 2 0.9 65 213 24 15 382 23 66 520 23 15 629 22 3 1.3 70 -237 24 20 405 23 70 -543 22 20 651 22 4 6 1.8 2.2 75 -261 23 25 428 23 75 565 23 25 673 22 6 2.6 80 284 24 30 451 23 80 -588 22 30 -695 22 7 3.1 85 -308 24 35 474 23 85 -610 22 35 -717 22 8 3.5 90 -332 23 40 497 23 90 632 23 40 -739 21 9 4.0 95 355 24 45 520 23 95 -655 22 45 760 22 10 4.4 9200 -379 23 9450 "543 23 9700 677 23 9950 782 22 21 05 402 24 55 566 23 05 -700 22 55 804 22 1 0.4 10 -426 24 60 589 23 10 -722 22 60 -826 22 2 0.8 15 -450 23 65 <>\2 23 15 744 23 65 -848 22 3 1.3 20 473 24 70 -635 23 20 -767 22 70 -870 21 4 6 1.7 2.1 25 -497 23 75 -658 23 25 -789 22 75 891 22 6 2.5 30 520 24 80 -681 23 30 811 23 80 913 22 7 2.9 35 -544 23 85 -704 23 35 -834 22 86 -935 22 8 3.4 40 567 24 90 -727 22 40 -856 22 90 -957 22 9 3.8 45 -591 23 96 749 23 45 878 22 95 978 22 10 4.2 INDEX Pagb Abb6 de Hautefeuille 1 Acetylene, combustion, rate of. 82 generation of 81 heating value of 82 pressure of liquefication . . 82 yield per pound of calcium carbide 82 Air supply for horizontal en- gine 144 Alcohol, combustion, air re- quired for 76, 80 heat of 75 rate of 71 composition 76 heat value of, computed . . 82 temperature for mixture, 56, 71, 79, 80 thermal efficiency 83 vaporization, heat re- quired 78, 80 Aspirating valve 49 Automatic engines 25 Avogadro's law 80 Back firing. 16, 23, 34, 35, 38, 127 Baffle plate 16, 22, 134 Balance weights 154 Barber, John 1 Barnett engine 3 Barsanti and Matteucci .... 3 Battery cells 32, 33, 173 storage 187 Bearings, adjustment of, in closed case 145 connecting rod 157 crank shaft 156 length of, for crank shaft. 152 liners 144 lubrication 29 pounding 35 setting, in horizontal en- gines 143 setting, in vertical engines, 144 studs 144 Beau de Rochas principle, 4, 6, 17 Page Calorie 75 Calorimeter, the 75 Cams, classification 105 double 107 operation 109 layout 110 effect of, on card 89 exhaust 105 inlet 107 material Ill offsetting 103 single, layout 105 sparking 177 starting 24, 39, 40, 103 Cam mechanism, double cam shaft 124 gearing 102, 111 lost motion in 107 timing of shaft 102, 111 transmission of motion to valves 102, 103 Carburrettor, adjustment . 25, 32 air supply 42 alcohol 56,83 auxiliary air supply ... 53, 54 design 57 effect on card 7 flexibility 49 float feed 43, 48, 53 Holley 53, 54 mechanical ebullition type 46 primer 53 Schebler 52 spray type 48 surface type 47 two-cycle engine 21 Carburetting, alcohol .... 43, 56 petroleums 43 temperature of fuel as af- fected by continued vaporization 46 Care of engine 27 Circulation 27, 30, 33, 129 Clearance of engine, deter- mination of 205 Clerk, Dugald 5,11,12 251 252 INDEX Page Coal gas, see Gas. Coil 3,173 requisites of 175 Combustion 31 air required 76, 77 heat 75, 82 rate 67, 71, 82, 194 Commutator 174, 178 single cylinder 180 timing 178, 179 two cylinders 179 two-cycle 180 Compression, chart 95 Clerk engine 5, 1 1 curve 92 Degrand engine 3 Diesel engine 17, 18 effect of valve 33, 36 efficiency, relation to . . 86, 88 limits 84 mean effective pressure, relation to 97 premature explosion pro- duced by 34 pump 2, 11 relation to fuel 85 relation to speed 84 relief cock '37 relieved for starting .... 23 Robson engine 12 space, ratio to stroke, 91, 94, 99 table 85 temperature 84 two-cycle engine (crank case) 14, 16 two-cycle engine (cylin- der) 16 Condenser, electrical. . . 172, 174 Condensation, latent heat . 75 Connecting rod 157 adjustment of bearings. . 157 formula 158 Cooling, Hugon spray 4 tower 27, 133 water, effect of, in hot cyl- inder 30 heat lost in 213 inlet and outlet, location 132 inlet and outlet, size. . 133 pressure 27, 96 regulation 131 temperature 24, 27 Cost of fuel, acetylene ... 82 alcohol 83 oxygen and hydrogen. ... 2 producer gas 64 Crank case explosions 22 Page Crank pin 153 Crank shaft, arms 153 balance weights 154 bushings 156 capacity 151 finish 156 pin 153 size 151 Crude oil, composition .... 72 Cylinder, air cooled 129 automobile 131, 134 bolts 135 bore 98 bore, ratio to stroke 100 boring 133, 134 care 31 casting, cost of 136 effect of overheating 34 equation for 99, 101 flooded 32 gasket for 35 "hot-spot" in 33 material 136 oil 23, 33 proportionate equation for 100 thickness of walls 130 water cooled 129 water in 35 water jacket 131, 132 Day engine 12 Degrand engine 3 Diesel engine 17 cycle 19 economy of 22 efficiency 22 Drawings for foundations . . 147 Dynamometer, absorption. . 196 belt 200 transmission 196, 205 Economy of operation . . . 66, 67 automobile engines 206 Diesel engine 18, 22 four and two cycle engines 18 Hugon engine 4 Lenoir engine 3 Otto and Langen engine . 4 Efficiency of engine, 86, 88, 96, 97, 101; 213 Electric ignition, 2, 3, 28, 170, 171, 172, 175 Engines, Abb6 de Haute- feuille 1 Barber patent 2 Barnett 3 Barsanti and Matteucci . . 3 INDEX 253 Page Engines (continued) blast furnace gas 67 clearance, determination of 205 Clerk 5, 11 Day 12 Degrand 3 Diesel 17, 22, 192 horsepower of. . 197, 212, 214 Hornsby-Akroid . . . 44, 86, 192 Hugon 4 Huygens 1 Johnston double acting . . 2 Lebon patents 2 Lenoir 3 Mietz and Weiss. . 44, 86, 192 Otto 4, 5 Otto and Langen 4 Otto slide valve 125, 189 Papin 2 Rathbun 122, 177 Robson 12 Stockport 12 Street, patents of 2 sub-base 146 Wright 2 Exhaust, heat lost 213 pressure 18 time of 8, 19 Expansion 16, 18, 19 curve 93 Explosion 21, 31 force 90, 97 ideal chamber for 121 in crank case 22 order of, in multiple cylin- ders 195 premature 35 Flywheel, automobile 139 calculation of weight 138 coefficient of fluctuation 137 formula 139 finish 142 function 137 rim 140 speed regulation effected by 137 spokes 140 webbed 142 Foundations, bolts. . . . 149, 150 drawings 147 material 148 on upper floors 148 purpose 147 Four-cycle engine, 5, 6, 17, 20, 44, 86, 192 Page Four-cycle engine, advan- tage 20 Fractional distillation 46 table 74 Frame, bolts 143 purpose of 143 weight 143 Fuel factor 98 Fuel, high heat value 75 low heat value 75 mixture necessary, 23, 24, 25, 26, 31 period of injection, Diesel engine 18, 19 Fuels (see fuel in question) . acetylene 81 air required for combus- tion (Table) 77 alcohol, 56, 71, 75, 76, 78, 79, 80, 82 crude oil 72 economy 66, 67, 206 for internal combustion . . 66 for producers 58, 60 fuel oil 73 gas oil 73 gasoline, 25, 33, 71, 74, 76, 78, 79, 81 kerosene 74 oxygen and hydrogen. ... 2 petroleum distillates, 71, 72, 75 Gas, amount required per horsepower hour . . 66, 67 analysis 209 blast furnace 67 coal gas as motive power. 2 economy 66 heating value 210 natural, composition 68 heating value 66 Table 68 oil 69 perfect, definition of 86 pressure uniform 201 producer, composition, 62, 65, 69, 71 heating value. ... 61, 62, 66 production 61, 62, 63 ratio to air 208 speed of 117 water, composition 70 production 70 weight and specific heat (Table) 209 Gas oil, composition 73 254 INDEX Page Gasoline (see Fuels, Frac- tional distillation, and Combustion), air required for combus- tion 77,81 combustion, rate of. 67, 71, 194 fractional distillation .... 74 lighting gas from 74 low heat value of, com- puted 76 mean effective pressure produced 71, 98 quality 25, 33 straining 25 vaporization, heat re- quired 78, 79, 81 weight 74 Gasometer 58, 60, 67 Gearing, pitch 113 reduction for cam-shaft, 102, 111 skew ratio 113 Governing, closeness of regu- lation 163 methods of 162 Governors, care of 30, 169 centrifugal 164 electrical governing 169 exhaust 9 hit or miss 30, 208 inertia 164, 168 lift of balls 164,167 location 169 magneto for 184 throttle valve for 167 uniformity of speed re- quired 166 Wright 2 Gunpowder as motive power 1 Heat balance 212 Heat losses 212 Heating of cylinder wall. ... 21 Horsepower, computation of, 197. 212, 214 definition of 216 friction 97 ratio of i.hp. to b.hp.. . . 96, 97 theoretical 97 Hugon engine 4 economy 4 Huygens 1 Igniter, care of 23,25,28 hammer break. . . 171, 176, 177 hot tube 190 material 29, 191 Page Igniter, Pennington 177 porcelain tube for 191 setting 28 wipe spark 171, 177 Ignition, effect on card 7 auto-ignition, Hornsby- Akroid 191 Mietz and Weiss. . 191, 193 Diesel ignition 17, 191 electric ignition, jump spark 170, 175 Lebon patent 2 Lenoir ignition 3 make-and-break igni- tion 28, 171, 175 sparking points, mate- rial for 171 prevention of destruc-. tive action 172 flame ignition, Barnett ig- nition cock 2, 189 hot-tube 24, 29, 34, 189 lead of 194 magneto ignition 183 apple 183-185 Bosch 185 Motsinger 187 Remy 187 Stephard 3 time of, 7, 23, 24, 25, 2S, 34, 170, 194 Indicator, computation of card 211 Diesel card 19 for gas engine 201 formula for card 86, 90 four-cycle card 6 ideal card 91, 94 purpose of card 89 spring effects on card, 9, 10, 212 two-cycle crank case card, 13, 15 two-cycle cylinder card, 13,15 Indicated work 211 Injectors, Diesel method . 17, 44 Hornsby-Akroid 44 Mietz and Weiss 44 Insulation of engine founda- tion 147 James-Lunkenheimer mix- ing valve 49 Johnston engine 2 Kerosene 74 ignition temperature 74 Keys, table of 141 INDEX 255 Page Lebon-Philip 2 Lenoir engine 3 economy 3 Liquid and air explosive mixture 2 Lubrication. . 23, 24, 26, 29, 156 Marine engine 25 Mean effective pressure . 94, 212 Mechanical ebullition 45 efficiency 96, 97 multiple cylinder en- gines 101 Mixing valve, difficulty for two-cycle engines. ... 49 fuel most desirable 52 James-Lunkenheimer de- sign 49 throttle connection 51 Mixture, effect on explosion. 97 explosive, 23, 24, 25, 26, 31, 34 lack of 36 limits of explosive 162 weight 210 Muffler 215 Natural gas, see Gas. Non-inductive resistance . . . 172 Oil gas, see Gas. Oil rings 156 Otto cycle 4 Otto and Langen engine. ... 4 economy 4 Pantograph 202 Papin 1 Permanent gas 62 Petroleum distillates (Table) 72 combustion, heat 75 rate 71 Piling for foundation 150 Piston, design 159 double acting 151 expansion 160 pin 159 rings 160 speed 99, 118 taper 160 two-cycle 16,128,161 Planimeter 211 Ports, effective opening .... 126 lead of exhaust, for two- cycle 127 location of, in two-cycle . . 11 operation of , in two-cycle, 14, 15, 16, 21 Page Ports, period of opening in two-cycle engine .... 126 proportion 125 third, in Day engine 128 Power, comparative produc- tion in two and four cycle engines 21 Premature explosion, 18, 34, 170 Pressure required for air starting. : 41 Priming of carburettor. . . 26, 53 cylinder 26 Producer, air pressure re- quired 59 charging hopper for 58 cost of operation 64, 67 distilling, temperature ... 61 efficiency of plant as com- pared with steam. ... 64 fuel available 60, 61, 62 suction, operation of 63 Producer gas, see Gas. Producers, distilling (Riche) 60 Dowson 58 inverted 62 pressure 58 suction 62 Prony brake, constant of . . . 202 cooling 198 design 197, 199 formula, derived .... 196, 197 discussed 199 hydraulic brake 200 length of brake arm 199 (Table) 200 wheel, design 197, 198 pv y = k, formula 90, 92 Radiation, loss by 213 Reducer for producer gas. . . 62 Reducing motions, panto- graph 202 reducing pulley 202 Report of test, form of 207 Ring cuts 30 Robson engine 12 Ruhmkorff coil 3, 173 Schebler carburettor 52 Scrubber 58, 60 Sediment in jacket 28 Smoke from cylinder 36 exhaust 36 Spark, cause of failure 32 length of gap 32, 175 weak, cause of 32, 33 256 INDEX Page Spark plug. ... 32, 174, 181, 1S3 tap for 135 Spraying nozzle 52, 53 Starting devices, air starters, 23, 39 auxiliary explosion cham- ber 38 auxiliary storage cham- ber 38 cartridge starter 38 compression of first charge by means of hand pump 38 externally applied energy . 37 hand starting 37 match igniter 38 retarding spark 37 Starting of automobile or marine engine 25 stationary engine 23 Starting troubles 31 Steam, condensation of, to produce vacuum .... 1 Stockport engine 12 Stopping of automobile or marine engine 26 stationary engine 24 Street, Robert 1 Stroke of engine 98 ratio of, to bore : 100 Tables, circumferences and areas of circles 221 compression temperatures 85 cylinder dimensions 101 flywheel coefficients 139 keys 141 logarithms 233 machine screw 219 Prony brake factors 200 tap drill 218 trigonometric functions . . 225 valve dimensions. . . . 119, 120 weight and specific heat of gases 209 wire and sheet metal gauges 216 wrought iron pipe 220 Temperature, cylinder 27 Diesel combustion 19 compression 17 Tests, apparatus 201 arrangement 202 assistants 204 methods 196 liquid fuel engines 206 loads for 204 Page Tests, log of 204 readings, interval of 204 report 207 Thermal efficiency 213 Throttle 26 Two-cycle engine, 5, 11, 12, 20, 67 per cent increase of power over four-cycle 22 ports for 125 Units, definition of 215 Valves, air, for vaporizer. . . 43 angle seated, advantage . . 115 arrangement 121-125 aspirating, for carburettor 49 care of 29 cooling 28, 122, 130 design and proportion . . 7, 116 diameter 120 Diesel 44 dimensions (Table) 119 effective opening. . . . 117, 119 (Table) 120 flat seated, advantage of. 115 gas 24 material 116 mechanically controlled, 20, 21 mixing 43, 48, 49 needle, for vaporizers .... 43 Robson engine 12 size 7, 9 stems 121 timing 105 timing, for hot tube ig- niter 191 two-cycle, see Ports. Vapor, pressure of gas ... 78, 80 saturation pressure 78 (Table) 79 Vaporization 78 Venturi tube in carburettor design 56 Volatility as affected by vaporization 46 Water gas, see Gas. Water jacket, copper 132 depth 131 draining 25 length 133 Watt i Wiring connections 23 for four-cylinder 174 Wright engine 2 Wrist pin 159