5 Liferwond Hm'stintf Quar GIFT OF DEAN FRANK H PROBERT mump DEPT. (Established 1X70.) HELLER & BRIGHTLY, Surveying Instruments, Spring Garden St. and Ridge Ave., PHILADELPHIA. ....MINE SURVEYING INSTRUMENTS Transits, Levels, Etc., a Specialty. Descriptive and Illustrated Price L,ists sent postpaid on application. PERFORATED SCREEN PLATES IN STEEL OR BRONZE, For Coke, Goal, j/fa, Ore, and Rock. THE tfENDRICK MANUFACTURING CO., Ltd., CAR BON DALE, PA. 1 WE MANUFACTURE COMPLETE ? $ 4 + * | Haulage Plants for Mines f i ALS -- i Hoisting Engines, Fans, and $ All Sorts of Mining Machinery. f * 4* ^ ^. Your job can't be too big for us, and a small one 4. ^ will have prompt attention and the benefit of our long J * experience. Robinson Machine Co. MONONGAHELA, PENNA. $ GOOD MATERIAL. PROMPT DELIVERY. REASONABLE PRICE. Mine-Car Hitchings WM. HARRIS & SON, 1 1 1 Ferry Street, Pittsburg. Prompt shipments of Strictly First-Class Materials jit Satisfactory prices for the installation and operation of Electric Mine Haulage Plants. ViVA/ I We manufacture a complete line of the following : TROLLEY WIRE HANGERS, TROLLEY WIRE EARS AND CLAMPS, TROLLEY AND FEEDER WIRE SPLICERS, GLOBE AND BROOKLYN STRAIN INSULATORS, FEEDER WIRE INSULATORS AND PINS, STEEL AND COPPER BONDING CAPS, LIGHTNING ARRESTERS, ETC., ETC. T Illustrated descriptive catalogue furnished on application. THE OHIO BRASS COMPANY, MANSFIELD, OHIO, U. S. A. Diamond Drills FOR PROSPECTING. American Diamond Rock Drill Co. 120 Liberty St., New York. P. 0. Box 1442. SCIENCE INDUSTRY IS THE NAME OF AN Instructive and Inter- esting Illustrated Monthly Magazine, Which explains in a simple and concise way the applica- tion of the sciences in indus- trial operations. Subscription, $1.00 per Year. Send for FREE Sample Copy. Science and Industry, Scranton, Pa. Rubber Goods of the Highest Grade for MINE AND COLLIERY USE. Belting, Hose of all Kinds, Packings, Valves, Gaskets, Springs. 4 When it's anything about RUBBER ask us. t WRITE FOR CATALOGUE. This Trade Mark assures the Quality. MANUFACTURED BY JAMES BENNETT FORSYTH, Mfg. Agt. and Gen. Mgr. BOSTON, 256 Devonshire St. NEW YORK, PHILADELPHIA, PITTSBURU, loo Reade St. 14 V. 4th St. 186 Sixth St. YU t.> operate a STEAM PLANT without a ROBERTSON- THOMPSON INDICATOR. Your ENGINE will work more ECONOMICALLY. The HINE ELIMINATOR will give DRY steam and prevent accidents from water. EUREKA PACKING will reduce PACKING hills in a year's run ONE-THIRD and keep rods in fine condition. JAS. L. ROBERTSON & SONS, New York. AIR AND GAS COMPRESSORS, For all Pressures and Volumes. THE NORWALK IRON WORKS CO., Send for Circulars. SOUTH NORWALK, CONN. ESTABLISHED 1857. The Everhart Brass Works, 426 Penn Ave., Scranton, Pa. MANUFACTURERS OF Brass Goods for Water, Steam, and Gas Also Manufacturers and Dealers in All Kinds of Safety Lamps, Gauzes, and Glasses, Water Gauges, Steam Gauges, Anemometers, Aneroid Barometers, and Pneumatic Signal Gongs for Speaking Tubes. The signal does not interfere with the speaking and can be attached to any tubes you may now have. Write for Circulars and Prices. Mining Drills. We manufacture Hand and Air Drills of every known description for boring Coal, Rock, Slate, Fire Clay, Gypsum, Salt, Etc. HOWELLS MINING DRILL CO., P.O. Box 1097, Plymouth, Pcnna. Union Labor Employed. Catalogs for the asking. Pipe Cutting ^Threading Machinery. WE MAKE HAND MACHINES, POWER MACHINES, AND COMBINED HAND AND POWER MACHINES. ower Pipe Cutting and Threading Machine for heaviest service. POINTS OF EXCELLENCE. Portable Hand Pipe Cutting and Threading Machine. They will cut many different sizes of pipe with one set of chasers. They have convenient means of chang- ing chasers to different sizes ; and in adjusting, the chasers can be quickly opened and positively closed. The combined arrangement for cutting and threading is convenient and saves time. We make the only hand- operated machine on the mar- ket which works satisfacto- rily to the operator in cutting 8- and 12-inch pipe. Finely Illustrated Catalogue Sent on Request. MERRELL MANUFACTURING COMPANY, 3 Curtis Street, Toledo, Ohio. 1 THE WESTON STANDARD FOR ARC AND INCANDESCENT LIGHT s I Voltmeters and Ammeters I ! CIRCUITS. These instruments are the most accurate, reliable, and sensitive portable instruments ever offered. A large variety of ranges to meet the require- ments of all kinds of work. rw . Send for Illustrated Catalogue. | WESTON ELECTRICAL INSTRUMENT CO., Office and Factory : 114-120 William St., NEWARK, N. J. * fill S.^ ss~ ^!- & iltf f ES| ? _- *< t* S** & ^*~^ _ ^J oo ? ^ ^? USED KVERYWHERK IN Coal and Rock Blasting WITH PROFIT TO MINER AND OPERATOR: Beware of Imitation. None Genuine Without Our Trade Mark. MINERS' SUPPLY COMPANY, ERICSSON SWEDISH CB TELEPHONES Ifffflra $eem 1o possess almost human Intelligence. ijntfeL The/ respond lo every requirement in a smooth, |MyJ positive fashion that shows what ,a perfect telephone JIJI W' can do. Besides this they have unequalled strength ({i \ and durability. Their reputation as [V^ "JTAA/DA/?D OF THE WOffLD" is built on merit. Is the best too ^ood for you? u ' ERICSSON TELEPHONE co.^^1?^ BALTIMORE.MD.- ' MANUFACTURERS AND DESIGNERS OF AIL KINDS OF HEAVY MACHINERY, REQUIRING FIRSTGIASSWORKMANSHIPANDMATERIALS. POOLE-LEFFEL TURBINE WAT ER-WH E E L S ^ : . LITCHFIELO FOUNDRY & MACHINE COMPANY, (INCORPORATED.) Sueoessors to LITCHFIELD CAR AND MACHINE CO., HOISTING, TAIL ROPE, ENDLESS ROPE, HAULAGE AND STATIONARY ENGINES, MANUFACTURERS OF Iron and Brass Castings, Boilers Screens, Fans, Cages, Mine Cars, Car Wheels, and . . ALL KINDS OF Mining Equipments and Supplies, Office and Shops, L.ITCHFIELD, ILLINOIS. BALDWIN V LOCOMOTIVE WORKS. MINE LOCOMOTIVES. Operating by STEAM, COMPRESSED AIR, and ELECTRICITY. ELECTRIC LOCOMOTIVES. Built in connection with the WESTINGHOUSE ELECTRIC & MFG. Co. and using WESTINGHOUSE MOTORS. BURNHAM, WILLIAMS & CO., PHILADELPHIA, PA. BULLOCK DIAMOND DRILLS For Prospecting The Standard for the World. BULLOCK MINING MACH'RY Ventilators, Rope Haulage, Cars, Skips, Cages. BULLOCK HOISTING MACH'RY We can fill any requirement. BULLOCK STEAM ENGINES Bullock-Corliss &, Willans High Speed. M. C. BULLOCK MFG. CO., Chicago, U.S. A. ,Jk^ Sltjl^ W ft 'ij>- g&t iyl &4FJ4 //^!&to % ;v/ r ^\^ <3fMI I PUMPS and PUMPING ENGINES. HIGHEST RECORDED EFFICIENCY. We will take back and replace or refund the money for any machine not as represented. BARR PUMPING ENGINE COMPANY, PHILADELPHIA, U. S. A. THE STIRLING ..... WATER TUBE SAFETY BOILER. Efficient, Durable. 1,000,000 H. P. IN USE. Especially Adapted to the Use of Low Grades of Fuel. Or JAMES MEILY, Bctz BIdg., Phila., Pa. All Wrought Metal. No Flat Surfaces or Stay Bolts. No Multitudinous Hand Hole Plates and Gaskets to Remove and Replace with Every Cleaning. Four Manholes Give Access to Every Tube. THE IDEAL BOILER FOR MINING PLANTS. Write for new Catalogue, Prices, and Plans. THE STIRLING COMPANY, General Offices, Pullman BIdg., Chicago, HI. I Kerosene Rngine. BURNS KEROSENE. SELF-IGNITION. Automatic, simple, and reliable. No electric battery or flame used. Belted or directly coupled to dynamo for electric . ^^ lighting, charging stor- A ^^ age batteries, pumping, /\LL I URPOSES. send for catalogue. A. MIETZ, 128-138 Mott St., New York City. CONTRACTORS FOR PROSPECTING WITH AND SALE OF SPRAGUE & HENWOOD, CONTRACTORS FOR PROSPEC SALE OF Sullivan Diamond Drills. BIT SETTING A SPECIALTY. Board of Trade Bldg. SRANTON, PA. AUI 'MAN 1 Elevators and Conveyors, SCREENS, SHUTES, AND WEIGH BASKETS, CAR HAULS, GRAVITY AND STEAM DUMPS, ROCK AND COAL CRUSHERS, PORTABLE ENGINES AND BOILERS, Are illustrated, listed, and described in our annual catalogue. If interested, send for it. THE AULTMAN COMPANY, CANTON. OHIO CABLE ADDRESS: "BRIQUETTE," PHILADELPHIA. CODES : "ABC " AND " LIBBERS." TELEGRAM ADDRESS PHILA. STEIN & BOERIGKE, LTD.. Metallurgical Engineers. OffJCC and Works: PRIMOS, DEL. CO., PA. Coal Washing and Separating Works. f "Greatest Economy," The advantages of our plants are: -> "Best Possible Results," ( "Lowest Repairs." We treat coals successf ullv DITTVMXr r*f\1ZT? where others fail. KLIUKI UUKt, IW.&LE.GURLEYJ TROY, N. Y., I LARGEST MANUFACTURERS IN AMERICA <$ OF ^ vr ^ I Civil and Mine Engineers* and 1 Surveyors' Instruments, 1 INCLUDING ENGINEERS', SURVEYORS', AND MINERS' TRANSITS; f ft Y-LEVELS; COMPASSES; CLINOMETERS AND $ SLOPE-LEVELS ; DIP-NEEDLE COMPASSES ; * ft GEOLOGISTS' COMPASSES; ALIDADES AND Jf PLANE-TABLES; CURRENT-METERS; HAND- LEVELS; PLUMMETS AND PLUMMET-LAMPS; $ LEVELING-RODS ; CHAINS AND TAPE-LINES. fr a ALSO DEALERS IN graphs, Slide-Rules, Drawing-Instruments and Mate- ^ rials, Stencil-Alphabets and Figures, Planimeters, ^ Scientific Books, Etc., Etc. OUR ILLUSTRATED CATALOGUE AND PRICE-LIST ^ MAILED ON APPLICATION. COALED METAL MINERS' POCKETBOOK COMPLIMENTS OF MINES AND MINERALS SCRANTON, PA. ORIGINAL MATTER. "Though index learning turns no student pale. It grasps the Eel of Science by the tail." Pope. SCRANTON, PA.: THE COLLIERY ENGINEER COMPANY. 1900. THE COALMMETAL MINERS' POCKETBOOK OF PRINCIPLES, RULES, FORMULAS, AND TABLES. SPECIALLY COMPILED AND PREPARED FOR THE CONVENIENT USE OF MINE OFFICIALS, MINING ENGINEERS, AND STUDENTS PREPAR- ING THEMSELVES FOJ* CERTIFICATES OF COMPETENCY AS MINE INSPECTORS OR MINE ^ SIXTH EDITION: REVISED AND ENLARGED, WITH ORIGINAL MATTER. "Though index learning turns no student pale, It grasps the Eel of Science by the tail." Pope. SCRANTON. PA.: THE COLLIERY ENGINEER COMPANY. 1900. TA 0! mm sin, DEAKFRANKH PROBERT COPYRIGHT, 1890, 1893, 1900, BY THE COLLIERY ENGINEER COMPANY. PINING DEFT. >:>-IE,{ EIJ & STATIONERS' HALJ-, LONDON. All Rights Reserved. PHINTKU BY THE COLLIEKY ENGINEER COMPANY, SCRANTOH, PA., U. S. A. PREFACE. The fifth edition of The Coal and Metal Miners' Pocketbook was very kindly received, and the criticisms of it were most friendly and flattering. The sixth edition has been compiled under particularly favorable circumstances and is much more complete than any previous edition. tf Prominent engineers and manufacturers of mining machinery throughout the world have kindly criticized the previous edition, have suggested wherein it could be improved, and have sent to us information from their private note books that has never before been r published. The staff of MINES AND MINERALS, the large force of Mining, Mechanical, and Electrical Engineers connected with The International Correspondence Schools, and many other engi- neers and mine managers have contributed to it. All this material has been carefully sifted, verified wherever possible, and combined with the data in the former edition. By careful selection and rewriting, or by different methods of presentation, it has been possible to include essentially all that was in the fifth edition, and at the same time to add from one- third to one-half again as much entirely new matter, without materially increasing the size of the book. Every portion of the fifth edition has been either entirely rewritten, or revised, enlarged, and brought up to date. New illustrations have been drawn, and the entire book has been printed from new plates. The sections on Mathematics and Surveying have been amplified by the addition of new tables and by text treating of the Solar Transit and Rocky Mountain methods of sur- veying. The sections on Hydraulics; the Application of Electricity to Mining; Timbering, Haulage, Blasting, Ore Dressing, and Coal Washing are entirely new. IV , PREFACE. The sections on Prospecting, Ventilation, and Methods of Working have been entirely rewritten, enlarged, and greatly improved. The tables of Logarithms, Trigonometric Functions, etc. have been reset from the latest corrected editions of standard tables. The Traverse Table has been greatly reduced in length, but without affecting its efficiency, while the table of Squares, Cubes, etc. has been added to by the addition of Circumfer- ences and Areas of Circles. The Glossary, which contains about 2,500 words, is believed to be the most complete mining glossary ever published, as it is a combination of all the mining glossaries extant of which the compilers could hear. Wherever possible, credit has been given the authorities from whom data have been taken, but in such a work it is mani- festly impossible to give full credit for everything that has been extracted, quoted, and compiled, and we can only in this very general way acknowledge our indebtedness to the large number of authors and engineers whom we have failed to mention by name in the text. No ono appreciates as fully as does the editor of such a pub- lication the value of the suggestions and data that have been so generously furnished to assist us in the compilation. We shall be greatly obliged to all readers of this volume who may call our attention to any errors that they may discover, or to the omission of any data that they may feel the lack of, so that attention may be given to these matters in future editions. TABLE OF CONTENTS. (For detailed Index, see back of volume. Sec also Glossary of Mining Terms, page 565.) WEIGHTS AND MEASURES. THE METRIC SYSTEM. I- WEIGHTS. Troy, 1; Apothecaries', 1; Avoirdupois, 2; Metric, 2. M EASURES OF LENGTH. American and British, 2; Reduction of Inches to Decimals of a Foot, 2; Decimals of a Foot for Each ^ of an Inch, 3; Metric, 3; Russian, 3; Prussian, Danish, and Norwegian, 3; Austrian, 3; Swedish, 4; Chinese, 4. MEASURES OF AREA. American and British, 4; Table for Reducing Square Feet to Acres, 4; Metric, 4. MEASURES OF VOLUME American and British, 5; Metric, 5; Liquid (U. S.). 5; Dry (U. S.), 5; British Imperial (Liquid and Dry), 5; Contents of Cylinders or Pipes for 1 Foot in Length, 6; Mexican, Central American, and South American Weights and Measures, 7. CONVERSION TABLES. Customary to Metric, 7; Metric to Customary, 9. MONEY. United States, 10; British, 10; Standard U. S. Coins, Weights and Fineness, Space Required to Store, 10; Conversion of English and American Money Values, 11; Value of Foreign Coins, U. S. Treasury Department, 11; Carat Measures, 12. TIMBER AND BOARD MEASURE. Rule for Measuring, 12; Timber Measure, 12; Round Timber, Table of i Girths, 13; Board Measure, 13. MATHEMATICS. General Principles, 14; Signs and Abbreviations, 14. ARITH M ETIC. To Cast the Nines Out of a Number, 15; To Prove Addition, Subtraction, Multiplication, and Division, 15; Common Fractions, 15; Decimals, 16; Simple and Compound Proportion, 18; Involution, 19; Evolution, 19; Percentage, 20; Arithmetical Progression, 20; Geomet- rical Progression, 21; Logarithms, 22. GEOMETRY. Principles, 24; Practical Problems in Geometrical Construc- tion, 25. MENSURATION. Surfaces, 28; Solids, 33; Prismoidal Formula, 34. PLANE TR IGO NO METRY. Principles of Trigonometry, 34; Practical Examples in the Solution of Triangles, 35. SURVEYING. The Compass, 38; Adjustments, 38; Use of Compass, 39; Magnetic Variation, 39; Isogonic Chart, 39; The Vernier, 39; The Transit, 40; Adjustments, 41; The Chain, or Steel Tape and Pins, 42; Plumb-Bob, 44; The Clinometer or Slope Level, 44; Field Notes for an Outside Compass Survey, 44; Transit Surveying, 45; Determination of Meridian by Polaris, 46; Determination of Meridian With Solar Attach- ment, 47: Use of Solar Attachment, 47; General Remarks, 49; Plotting, 49; Coordinates, 51; Contents of Coal Seam, 52; Leveling, 53; Adjust- ments, 53; Use of Level, 54; Field Work 54; Notes, 55; Trigonometric Leveling, 56; Underground Surveying, 56; Establishment and Marking of Stations, 57; Centers, 59; Notes, 60; Stope Books, 62; Mine Corps, 66; Surveying Methods, 67; Outside Surveys, 67; Inside Surveys, 67; Closing Surveys, 68; Connecting Outside and Inside Works Through Shafts and Slopes, 68; Notes on Mapping, 74; Locating Errors, 76; Locating Special Work, 77; Calculation of Areas, 77; Railroad Curves, 78; Hints to Beginners, 80; Theory of Stadia Measurements, 81; Tables, 88. VI TABLE OF CONTENTS, ELEMENTS OF MECHANICS. Levers, 91; Wheel and Axle, 92; Inclined Plane, 93; Screw, 93; Wedge, 93; Pulleys, 94; Composition of Forces, 95. FRICTION. Coefficients, 95; Shafting, 96; Friction of Mine Cars, 96. LUBRICATION. Best Lubricants for Different Purposes, 102. APPLIED MECHANICS. STRENGTH AND WEIGHT OF MATERIALS. Wooden Beams, 102; Iron and Steel Beams, 103; Structural-Steel I Beams, 104; Pillars or Props, 105; Cast-Iron Columns, 106; Specific Gravity, Weight, and Properties of Materials, 107; Line Shafting, 110; Weight of Castings, Sheets, and Plates, 111; Weight of Cast-Iron Pipe per Foot in Pounds, 113; Wood Screws, 113; Weight of Wrought Iron, 114; Iron Required for 1 Mile of Track, 117; Rails, Splices, and Bolts for 1 Mile of Track, 117. WIRE ROPES. General Remarks, 118; Flat Ropes, 119; Standard Hoisting Ropes, 120; Transmission or Haulage Rope, 122; Stress in Hoisting Ropes, 123; Relative Effects of Various Sheaves on Wire Rope, 123; Working Load for Hoisting Ropes, 125; Starting Strain, 126; Horse- power of Manila Ropes, 126; Rapid Method of Splicing a Wire Rope, 127; Ordinary Long Splice, 129; Chains, 129. HYDROSTATICS. General Principles, 130; Equilibrium of Liquids, 130; Pressures of Liquids on Surfaces, 130; Pressure Exerted by Quiet Water Against the Side of a Gangway or Heading, 130; Total Pressure of Quiet Water Against and Perpendicular to Any Surface Whatever, 131; Trans- mission of Pressure Through Water, 132; Pressure at Any Given Depth, 132; Pressure of Water in Pipes, 132; Construction of Mine Dams, 133. HYDRAULICS. General Principles, 135; Theoretical Velocity of a Jet of Water, 135: Theoretical Quantity of Water Discharged in a Given Time, 135; Flow of Water Through Orifices, 135; Coefficients of Con- traction, Velocity, Discharge, 135; Suppression of the Contraction, 136; Gauging Water, 136; Miners' Inch, 136; Duty of a Miners' Inch of Water, 137; Right- Angled V Notch, 137; Discharge of Water Through a Right-Angled V Notch, 138; Gauging by Weirs, 138; Coefficient of Discharge for Weirs With and Without End Contractions, 140; Weir Table Giving Cubic Feet Discharged per Minute, 141; Conversion Factors, lit; Flow of Water in Open Channels, 142; Ditches, 142; Safe Bottom Velocity, 142; Resistance of Soils to Erosion by Water, 143; Carrying Capacity of Ditches, 143; Grade, 143; Ditch Banks, 143; Influence of Depths on Ditch, 144; Measuring the Flow of Water in Channels, 144; Flow in Brooks and Rivers, 145; Flumes, 145; Grade and Form, 145; Timber Flumes, 145; Connection With Ditches, 146; Trestles, 146; Curves, 146; Waste Gates, 146; Flow of Water Through Flumes, 146; Tunnels, 147; Flow Through Tunnels, 147; Hydraulic Gradient, 147; Flow in Pipes, 147; Siphons, 149; Table Showing Actual Flow in Pipes From f" to 30" Diameter. 150; Loss of Head in Pipe by Friction, 151; Friction of Knees and Bends, 153; Reservoir Site, 154; Dams, 154; Foundations, 154; Wooden Dams, 154; Abutments and Dis- charge Gates, 154; Spillways or Wasteways, 155; Stone Dams, 155; Earth Dams, 156; Wing Dams, 156; Masonry Dams, 156; Theoretical Efficiency of a Water-Power, 156; Horsepower of a Running Stream, 157; Current Motors, 157; Breast and Undershot Wheels, 157"; Overshot Wheels, 158; Impulse Wheels, 158; Turbines^ 158. PUMP MACHINERY. Cornish Pumps, 158; Simple and Duplex Pumps, 158; Packing, 159; Speed of Water Through Valves, Pipes, and Pump Passages, 160; Ratio of Steam and Water Cylinders in the Direct-Acting Pump, 160; Piston Speed of Pumps, 161; Boiler Feed- Pumps, 161; Theoretical Capacity of Pumps and the Horsepower Required to Raise Water, 161; Depth of Suction, 162; Amount of Water liaised by a Single-Acting Lift Pump, 162; Pump Valves, 162; Power Pumps, 162; Electrically Driven Pumps, 162; Table Giving Water Delivered per Minute for Various Sized Pumps, 163; Miscellaneous Forms of Water Elevators, 164; Air-Lift Pumps, 164: Vacuum Pumps, 164; Water Buckets, 164; Sinking Pumps. 165; Pumps for Acid Water, 165. TABLE OF CONTENTS. Vll FORMS OF POWER. FUELS. Table of Combustibles, 166; Analyses and Heating Values of American Coals, 168; Thermal Unit, 168; Composition of Fuels, 169; Classification, Composition, and Properties of Coals, 169; Weights and Measurements of Coal, 170; Coke, 172; Analysis of Coal, 173. STEAM. High-Pressure Steam, 175; Expansion of Steam, 176: Condens- ers, 176. BOILERS. Lancashire Boiler, 177; Horsepower of Boilers, 177; Heating Surface, 177; Choice of a Boiler, 179; Explosions, 179; Questions to Be Asked Concerning New Boilers, 180; Incrustation and Scale, 182; Covering for Boilers, Steam Pipes, Etc., 183; Data for Proportioning an Economizer, 185; Care of Boilers, 185; Thickness of Boiler Iron, 187; Pressure of Steam at Different Temperatures, 188; Maximum Economy of Plain Cylinder Boilers, 188; Scheme for Boiler Test, 188; Chim- neys, 189. STEAM ENGINES. What Is a Good Engine? 190; Determination of M. E. P., 190; Rules for Engine Drivers, 191; Belting and Velocity of Pulleys, 193. COMPRESSED AIR. Classification of Compressors, 194; Construction of Compressors, 194; Theory of Air Compression, 194; Rating of Com- pressors, 195; Cooling, 195; Dry Versus Wet Compressors, 196; Trans- mission of Air in Pipes, 196; Losses in the Transmission of Compressed Air, 198; Friction of Air in Pipes, 201; Loss of Pressure in Pounds per Square Inch, by Flow of Air in Pipes, 202; Loss by Friction in Elbows, 203. ELECTRICITY. Practical Units, 203; Strength of Current, 203; Electric Pressure or Electromotive Force, 203; Resistance, 203; Power, 204; Cir- cuits, 205; Series Circuits, 205; Parallel Circuits, 206; Resistance in Series and Multiple, 206; Shunt, 207; Electric Wiring, 207; Materials, 207; Forms of Conductors, 207; Wire Gauge, 207; Estimation of Cross- Section of Wires, 207; Properties of Copper Wire, 208; Properties of Aluminum and Copper, 209; Estimation of Resistance, 209; Calculation of Wires for Electric Transmission, 210; Current Estimates, 212; Incan- descent Lamps, 213; Arc Lamps, 214; Motors, 214; Conductors for Electric- Haulage Plants, 214; Dynamos and Motors, 215; Direct-Current Dynamos, 215; Factors Determining E. M. F. Generated, 218; Field Excitation of Dynamos, 218; Series-Wound Dynamos, 219, Shunt- Wound Dynamos, 219; Compound-Wound Dynamos, 219; Direct-Current Motors, 220; Principles of Operation, 220; Speed Regulation of Motors, 222; Connec- tions for Continuous-Current Motors, 223: Alternating-Current Dyna- mos, 224; Single-Phase Alternators, 225; Multiphase Alternators, 225; Uses of Multiphase Alternators, 226; Alternating-Current Motors, 226; Synchronous Motors, 226; Induction Motors, 227, Transformers, 228; Electric Signaling, 229; Batteries, 229; Bell Wiring, 230; Special Mine Applications, 233; Telephones, 233. MINING. PROSPECTING. Outfit Necessary, 235; Plan of Operations, 236; Geological Table, 237; Coal or Bedded Materials, 238; Formations Likely to Con- tain Coal, 238; Ore Deposits, 238; Position of Veins and Ore Deposits, 239: Underground Prospecting, 239; Prospecting for Placer Deposits, 240; Value of Free Gold per Ton of Quartz, 241; Gems and Precious Stones, 241; Exploration by Drilling or Bore Holes, 242; Earth Augers, 242; Percussion or Churn Drills, 242; The Diamond Drill, 243; Selecting the Machine, 243; Size of Tools, 243; Drift of Diamond-Drill Holes, 243; The Surveying of Diamond-Drill Holes, 243; The Value of the Record Furnished by the Diamond Drill, 244; The Arrangement of Holes, 244; The Cost and Speed of Drilling, 244; Records of Cost per Foot in Diamond Drilling, 246; Cost of Operation per Month of Bed-Rock Exploration, 247; Magnetic Prospecting, 248; Prospecting for Petro- leum, Natural Gas, and Bitumen, 249; Construction of Geological Maps and Cross-Sections, 249; To Obtain Dip and Strike From Bore-Hole Records, 250; Sampling and Estimating the Amount of Mineral Avail- able, 251; Diagram for Reporting on Mineral Lands, 252. Vlll TABLE OF CONTENTS. OPENING A MINE. Opening a Gold Mine, 258; Form of Shafts, 259; Com- partments, 259; Shaft Sinking, 259; Size of Shaft, 259; Forepoling, 260; Metal Linings Forced Down, 260; Pneumatic Method of Shaft Sinking, J60: Freezing Process, 260; Table of Weil-Known Shafts, 261; Kind- Chaudron Method, 262; Long-Hole Process, 262; Comparison of Methods of Shaft Sinking, 262; Sinking Head-Frames, 262; Sinking Engines, 263; Tools, 263; Speed and Cost of Sinking, 263; Slope Sinking, 263; The Sump, 264; Driving the Gangway, 264; Levels in Metal Mines, 264; Mining Tunnels, 265. MINE TIMBER AND TIMBERING. Choice of Timber, 265; Preserva- tion of Timber, 265; Placing of Timber, 266; Size of Timber, 267; Joints in Mine Timbering, 267; Undersetting of Props, 267; Forms of Mine Timbering and Underground Supports, 267; Gangway or Level Tim- bers, 268; Shaft Timbering, 270; Square Sets, 270; Landing, Plats, or Stations, 272; Special Forms of Supports, 272; Iron and Steel Supports, 272; Trestles, 274; Timber Head-Frames or Head-Gears, 275; Steel Shaft Bottoms, 276. METHODS OF WORKING. Open Work, 277; Steam-Shovel Mines, 278; Milling, 278; Cableways, 278; Placers, 278: Hydraulicking, 278; Dredg- ing, 279; Closed Work, 279; Bedded Deposits, 279; Coal Mining, 279; Roof Pressure, 280; Character of Floor, 280; Systems of Working Coal, 280; Room-and-Pillar System, 280; Longwall Method, 281; Panel System, 283; Control of Roof Pressure, 284; Number of Entries, 284; Direction of Face, 284: Size of Pillars, 285; Room Pillars, 286; Barrier Pillars, 287; Weight on Pillars in Pounds per Square Inch, 287; Drawing Pillars, 289; Compressive Strength of Anthracite, 290; Gob Fires, 291; Spontaneous 'Combustion, 291; Coal Storage, 291: Modifications of Room-and-Pillar Methods, 291; Buggy Breasts, 291; Chute Breasts, 292; Pillar-and-Stall, 292; Connellsville Region, 293; Pittsburg Region, 295; Clearfield Region, 295; Reynoldsville Region, 295; West Virginia, 296; Alabama Methods, 297; George's Creek, 297; Blossburg Region, Pa., 298; Indiana Mining, 298; Iowa Mining, 299; Tesla, California, Method, 300; New Castle, Colorado, Method, 302; Modifications of Longwall Methods, 302; ' Overhand Stoping, 304; Methods of Mining Anthracite, 305; Brown's Method, 306; Battery Working, 307; Single-Chute Battery, 309; Double-Chute Battery, 309; Rook-Chute Mining, 310; Williams' Method, 312; Running of Coal, 312; Hints for Working Thin Seams, 313; Flushing of Culm, 314; Methods of Mining Mineral Deposits, 316; Winzes, 316; Raises, 316; Stoping, 316; Flat Deposits, 318; Large Deposits, Over 8 Feet Thick, 318; Square Work, 318; Filling, 319; Slicing, 319; Transverse Rooming With Filling, 319; Caving, 320; Square-Set System, 321; Irregular Deposits, 321; Coyoting, 321; Special Methods, 322; Frozen Ground, 322; Leaching, 322; Costs of Mining Anthracite, 323; Lehigh Region (Pa.), 323; Wyoming Region (Pa. ), 325; Prices of Coal, 326; Cost of Coking Coal, 328. EXPLOSIVES. Low Explosives, 329; High Explosives, 329; Thawing Dynamite, 329; Common Blasting Explosives, 330; Drilling, 330; Diam- eter of Hole, 330; Amount of Charge, 331; Tamping, 331; Firing, 331; Detonators; 332; Electric Firing, 332; Power of an Explosive, 334; Arrangement of Drill Holes, 3&5. MACHINE MINING. Pick Machines, 336; Chain-Cutter Machines, 337; Shearing, 337; Capacity, 337. VENTILATION OF MINES. Atmosphere, 337; Atmospheric Pressure, 339; Barometric Variations, 339; Barometers, 339; Water Column Corre- sponding to Any Mercury Column, 340; Barometric Elevations, 340; Chemistry of Gases, 341; Absolute Temperature, 344; Absolute Pressure, 345; Diffusion and Transpiration, 346; Gases Found in Mines, 348; Con- stants for Mine Gases, 349; Gas Feeders, 352; Pressure of Occluded Gases, 352; Amount of Gas, 352; Outbursts of Gas, 352; Testing for Gas by Lamp Flame, 354; Safety Lamps, 355; Lamps for Testing, 355; Detec- tion of Small Percentages of Gas, 356; Oils for Safety Lamps, 356; Types of Safety Lamps, 356; Locking Lamps, 358; Cleaning Safety Lamps, 358; Relighting Stations, 359; Illuminating Power of Safety Lamps, 359; Explosive Conditions in Mines, 359; Derangement of Ventilating Cur- rent, 359; Sudden Increase of Gas, 360; Effect of Coal Dust in Mine TABLE OF CONTENTS. sion,361; Quantity of Air Required for Ventilation, 362; Elements in Ven- tilation, 363; Power of the Current, 363; Mine Resistance, 364; Velocity of the Air-Current, 364; Measurement of Ventilating Currents, 364; Water Gauge, 365; Thermometers, 366; Calculation of Mine Resistance, 366; Calculation of Power or Units of Work per Minute, 367; Equivalent Orifice, 367; Potential Factor of a Mine, 367; Formulas, 370; Variation of the Elements, 372; Practical Splitting of the Air-Current, 373; Primary Splits, 374; Secondary Splits, 374; Tertiary Splits, 374; Equal Splits of Air, 374; Unequal Splits of Air, 374; Natural Division of the Air-Current, 374; Calculation of Natural Splitting, 374; Proportional Division of the Air-Current, 375; Box Regulator, 375; Door Regulator, 375; Splitting Formulas, 378; Methods and Appliances in the Ventila- tion of Mines, 381; Ascensional Ventilation, 381; General Arrangement of Mine Plan, 381; Natural Ventilation, 381; Ventilation of Rise and Dip Workings, 382: Influence of Seasons, 382; Construction of a Mine Furnace, 383; Air Columns in Furnace Ventilation, 384; Inclined Air Columns, 384; Calculation of Ventilating Pressure in Furnace Ventila- tion, 384; Calculation of Motive Column or Air Column, 384; Influence of Furnace Stack, 385: Mechanical Ventilators, 385; Vacuum System of Ventilation, 386; Plenum System of Ventilation, 386; Comparison of Vacuum and Plenum Systems, 386; Types of Centrifugal Fans, 387; Manometrical Efficiency, 390; Mechanical Efficiency, 390; Fan Con- struction, 391; High-Speed and Low-Speed Motors, 392; Fan Tests, 392; Conducting Air-Currents, 393; Doors, 393; Stoppings, 393; Bridges, 393; Air Brattice, 394; Curtains, 394. HOISTING. Double Cylindrical Drums, 394; Single Cylindrical Drums, 394; Koepe System, 395; Whiting System, 395; Problems in Hoisting, 396; Balancing a Conical Drum, 396; Horsepower of an Engine for Hoisting, 396; Load That a Given Pair of Engines Will Start, 396; Approximate Period of Winding on a Cylindrical Drum, 397; Head-Frames, 397; Head-Sheaves, 397; Guides and Conductors, 398; Safety Catches, 398; Detaching Hooks, 398. H AU LAG E. Gravity Planes, 398; Number of Cars in a Trip on a Self- Acting Incline, 399; Engine Planes, 399; Size of Engines Required for Engine- Plane Haulage, 399; Horsepower of an Engine to Hoist a Given Load Up an Incline, 400; Rope Haulage, 400; Tail-Rope System, 400; Tension of Hauling Rope, 401; Endless-Rope System, 401; Friction Pull on an Endless-Rope Haulage, 402; Inclined Roads, 402; Motor Haulage, 402; Locomotive Haulage, 402; Compressed-Air Haulage, 403; Tractive Efforts of Compressed-Air Locomotives, 404; Electric Haulage, 406; Speed of Haulage, 408; Cost of Haulage, 409; Mine Roads and Tracks, 410; Grade, 410; Rails, 411; Gauge, 411; Curves, 411; To Bend Rails to Proper Arc for Any Radius, 412; Rail Elevation, 412; Rollers, 412; Switches, 413; Turnouts, 413; Slope Bottoms, 413; Tracks for Bottom of Shafts, 416; Surface Tracks for Slopes and Shafts, 417. ORE DRESSING AND THE PREPARATION OF COAL. Crushing Machinery, 418; Object of Crushing, 418; Selection of a Crusher, 418; Jaw Crushers, 419; Blake Crusher, 419; Dodge Crusher, 419; Roll-Jaw Crushers, 420; Gyratory Crushers, 420; Rolls, 421; Cracking Rolls, 421; Corrugated Rolls, 422; Disintegrating Rolls and Pulverizers, 423; Ham- mers, 423; Crushing Rolls, 423; Amount Crushed, 424; Speeds, 424; Speed of Rolls, 425; Crushing Mills, 426; Roller Mills, 426; Ball Mills, 427; Gravity Stamps, 427; Order of Drop, 428; Speed of Stamps, 429; Shoes and Dies, 429; Life of the Shoes and Dies, 429; Cams, Stamp Heads, and Stems, 429; Tappets, 429; Battery Water, 430; Duty of Stamps, 430; Horsepower of Stamps, 430; Cost of Stamping, 4:30; Pneumatic Stamps, 430; Power Stamps, 431; Steam Stamp, 431; Miscellaneous Forms of Crushers, 431. SIZING AND CLASSIFYING APPARATUS. Stationary, Screens, Griz- zlies, Head-Bars, or Platform Bars, 431; Adjustable Bars, 432; Shaking Screens, 432; Revolving Screens, or Trommels, 433; Speed, 434; Duty of Anthracite Screens, 434; Revolving Screen Mesh for Anthracite, 434; Hydraulic Classifiers, 434; Spitzkasten, 435; Spitzlutten, 435; Calumet X TABLE OF CONTENTS. Classifier, 435; Settling Boxes, 435; Jeffrey-Robinson Coal Washer, 436; Log Washer, 436; Scaife Trough Washer, 437; Jigs, 437; Stationary Screen Jigs, 437; Theory of Jigging, 439; Equal Settling Particles, 439; Interstitial Currents, 439; Acceleration, 440; Suction, 440; Removal of Sulphur From Coal, 441; Preparation of Anthracite, 442. HANDLING OF MATERIAL. Anthracite Coal, 443; Bituminous Coal, 443; Ore, Rock, Etc., 443; Flumes and Launders, 443; Horizontal Pressure Exerted Against Vertical Retaining Walls, 444; Horsepowers for Coal Conveyers, 445; Weights and Capacities of Standard Steel Buckets, 446; Elevating Capacities of Malleable Iron Buckets, 446; Conveying Capaci- ties of Flight at 100 Feet per Minute, 446; Cost of Unloading Coal, 447; Briqueting, 448; Volume of a Ton of Different Sizes of Coal, 449. TREATMENT OF INJURED PERSONS. Loss of Blood, 449; To Trans- port a Wounded Person Comfortably, 450; Bleeding From Scalp Wounds, 451; Treatment of Persons Overcome by Gas, 451. TABLES. Coal Dealers' Table, Giving Cost of Any Number of Pounds at Given Price Per Ton, 452; Natural Sines and Cosines, 453; Natural Tan- gents and Cotangents, 464; Logarithms of Numbers, 473; Logarithms of Trigonometric Functions, Sines, Cosines, Tangents, Cotangents, 492; Latitudes and Departures (Traverse Table), 537; Squares. Cubes, Square and Cube Roots, Circumferences, Areas, and Reciprocals, From 1 to 1,000, 545; Diameters, Circumferences, and Areas, A- to 100, 561. GLOSSARY OF MINING TERMS. 565. COAL AND METAL MINERS' POCKETBOOK. WEIGHTS AND MEASURES. THE METRIC SYSTEM. Since the metric system is the adopted system in many countries, and as it is almost universally used in connection with scientific work, a brief description of it is here given as preliminary to the following tables of weights and measures. The metric system has three principal units: 1. The meter, or unit of length, supposed to be the one ten-millionth part of the distance from the equator to the pole on the meridian of longitude passing through the city of Paris. Its actual value is 39.370432 in., the stand- ard authorized by the United States Government being 39.37 in. According to this standard, 1 yd. = |^ me ter. o,9o/ 2. The gram, or unit of weight, is the weight of a cubic centimeter of dis- tilled water at 4 centigrade and 776 millimeters of atmospheric measure. The kilogram (Kg. V = 1,000 grams = 2.2046 lb., is the ordinary unit of weight corresponding to the English pound. According to the United States Gov- ernment regulations, 1 lb. avoirdupois = TnjnSfi kilogram. 3. The liter, or unit of liquid volume, is the volume of 1,000 cubic centi- meters of distilled water at 4 6 centigrade and 776 millimeters pressure. Multiples of these units are obtained by prefixing to the names of the printed units the Greek words deka (10), hektp (100), kilo (1,000). The sub- . iultiplesor divisions are obtained by prefixing the Latin words deci (j^), centi ( T $ w ), and milli ( TO W). The abbreviations of these several units as given in the following tables are those commonly used. The kilogram-meter is the work done in raising 1 kg. through a height of 1 m., and equals 7.233 ft.-lb. One metric horsepower (force de cheval or cheval vapeur) equals .98633 English horsepower. TROY WEIGHT. 24 grains = 1 pennyweight. 20 pennyweights = 1 ounce = 480 grains. 12 ounces = 1 pound = 5,760 grains == 240 pennyweights. In troy, apothecaries', and avoirdupois weights, the grains are the same. APOTHECARIES' WEIGHT. 20 grains = 1 scruple. 3 scruples = 1 dram = 60 grains. 8 drams = 1 ounce = 480 grains = 24 scruples. 12 ounces = 1 pound = 5,760 grains = 288 scruples = 96 drams. WEIGHTS AND MEASURES. . AVOIR DUPOlSi WEIGHT. :airi3 . , ',= 1 dram, 1 . ^ 16 drams = 1 ounce = 437 grains. 16 ounces = 1 pound = 7,000 grains = 256 drams. 28 pounds = 1 quarter = 448 ounces. 4 quarters = 1 hundredweight = 112 pounds. 20 hundredweight = 1 ton = 2,240 pounds. 1 stone = 14 pounds. 1 quintal = 100 pounds. 1 " short ton " =2,000 pounds. 1 " long ton " = 2,240 pounds. 1 ounce troy or apothecaries' = 1.09714 avoirdupois ounces. 1 pound troy or apothecaries' = .82286 avoirdupois pound. 1 ounce avoirdupois = .911458 troy or apothecaries' ounce. 1 pound avoirdupois = 1.21528 troy or apothecaries' pounds. METRIC WEIGHT. 10 milligrams (mg.) = 1 centigram (eg.) = .15432 grain. 10 centigrams = 1 decigram (dg.) = 1.5432 grains. 10 decigrams = 1 gram (g.) = 15.432 grains. 10 grams = 1 decagram (Dg. ) = .02204615. avoir. 10 decagrams = 1 hectogram ( Hg. ) = .22046 Ib. avoir. 10 hectograms = 1 kilogram (Kg.) = 2.2046 Ib. avoir. 10 kilograms = 1 myriagram (Mg.) = 22.046 Ib. avoir. 10 mynagrains = 1 quintal (Q.) = 220.46 Ib. avoir. 10 quintals = 1 tonneau, millier, or tonne = 2,204 Ib. avoir. MEASURES OF LENGTH. AMERICAN AND BRITISH. 12 inches = 1 foot. 3 feet = 1 yard = 36 in. 6 feet = 1 fathom = 2 yd. = 72 in. 66 feet = 1 chain * = 11 fath. = 22 yd. = 792 in. 10 chains = 1 furlong = 110 fath. = 220 yd. = 660 ft. = 7,620 in. 8 furlongs = 1 mile = 80 chains = 880 fath. = 1,760 yd. = 5,280 ft. = A nautical mile, or knot = 1.15136 statute miles. [63,360 in. A league = 3 nautical miles. *The chain of 66 ft. is practically obsolete. Chains of 50 or 100 ft, are now used exclusively by American surveyors. To Reduce Inches to Decimals of a Foot. Divide the number of inches by 12. Thus, 7 in. = 7 -f- 12, or .58333 ft. To reduce fractions of inches to deci- mals of a foot, divide the fraction by 12, and then divide the numerator of the quotient by the denominator. Thus, f in. = f -f- 12 = &. ^ = .0313 ft. The annexed scale shows on one side, proportionately reduced, a scale of tenths. On the other, a scale of twelfths, corresponding to inches. To reduce inches to decimal parts of a foot, find the number of inches and TENTHS OF A FOOT ? m .l r .,f. f. 9 4 567 ! , ( I ( j . , i , , . , 1 i , , . i , , , , J , 1 1 ! 1 ,,,? ?...,, 10 A ]"" "1"'" "r'^T'"''"''^"" iMu 'I'mM'j'y'f JO It jl fractional parts thereof on the side marked "inches." Opposite, on the scale of tenths, will be found the decimal part of a foot. Thus, if we want to find the decimal part of a foot represented by 7? inches, we find the mark corresponding to 7i inches on the side marked "inches." Opposite this mark we read 6 tenths, 2 hundredths, and 5 thousandths; or, expressed decimally, .625. MEASURES OF LENGTH. 3 DECIMALS OF A FOOT FOR EACH 1-32 OF AN INCH. Inch. , | ... .,, I ... 5" 6" 7" 8" 9" 10" 11" 1 o .0833 .1667 .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167 A .0026 .0859 .1693 .2526 .3359 .4193 .5026 .5859 .6693 .7526 .8359 .9193 .0052 .0885 .1719 .2552 .3385 .4219 .5052 .5885 .6719 .7552 .8385 .9219 3 .0078 .0911 .1745 .2578 .3411 .4245 .5078 .5911 .6745 .7578 .8411 .9245 1 .0104 .0937 .1771 .2604 .3437 .4271 .5104 .5937 .6771 .7604 .8437 .9271 & \ -0130 .0964 .1797 .2630 .3464 .4297 .5130 .5964 .6797 .7630 .8464 .9297 T 3 ff .0156 .0990 .1823 .2656 .3490 .4323 .5156 .5990 .6823 .7656 .8490 .9323 3 7 2 1 .0182 .1016 .1849 .2682 .3516 .4349 .5182 .6016 .6849 .7682 .8516 .9349 i .0208 .1042 .1875 .2708 .3542 .4375 .5208 .6042 .6875 .7708 .8542 .9375 3 \ 0234 1068 1901 2734 3568 4401 5234 6068 6901 7734 8568 9401 T 6 g .0260 .1094 .1927 .2760 .3594 .4427 .5260 .6094 .6927 .7760 .8594 .9427 4* .0236 .1120 .1953 .2786 .3620 .4453 .5286 .6120 .6953 .7786 .8620 .9453 if .0312 .1146" .1979 .2812 .3646 .4479 .5312 .6146 .6979 .7812 .8646 .9479 3 g .0339 .1172 .2005 .2839 .3672 .4505 .5339 .6172 .7005 .7839 8672 9505 T 7 5 .0365 .1198 .2031 .2865 .3698 .4531 .5365 .6198 .7031 .7865 .8698 .9531 .0391 .1224 .2057 .2891 .3724 .4557 .5391 .6224 .7057 .7891 .8724 .9557 / .0417 .1250 .2083 .2917 .3750 .4583 .5417 .6250 .7083 .7917 8750 9583 H -0443 .1276 .2109 .2943 .3776 .4609 .5443 .6276 .7109 .7943 .8776 .9609 T 9 .0469 .1302 .2135 .2969 .3802 .4635 .5469 .6302 .7135 .7969 .8802 .9635 4S i .0495 .1328 .2161 .2995 .3828 .4661 .5495 .6328 .7161 .7995 .8828 .9661 .0521 .1354 .2188 .3021 .3854 .4688 .5521 .6354 .7188 .8021 .8854 .9688 3} i .0547 .1380 .2214 .3047 .3880 .4714 .5547 .6380 .7214 .8047 .8880 .9714 II .0573 .1406 .2240 .3073 .3906 .4740 .5573 .6406 .7240 .8073 .8906 .9740 .0599 .1432 .2266 .3099 .3932 .4766 .5599 .6432 .7266 .8099 .8932 .9766 .0625 .1458 .2292 .3125 .3958 .4792 .5625 .6458 .7292 .8125 .8958 .9792 Si .0651 .1484 .2318 .3151 .3984 .4818 .5651 .6484 .7318 .8151 .8984 .9818 43 .0677 .1510 .2344 .3177 .4010 .4844 .5677 .6510 .7344 .8177 .9010 .9844 3i .0703 .1536 .2370 .3203 .4036 .4870 .5703 .6536 .7370 .8203 .9036 .9870 .0729 .1562 .2396 .3229 .4062 .4896 .5729 .6562 .7396 .8229 .9062 .9896 | .0755 .1589 .2422 .3255 .4089 .4922 .5755 .6589 .7422 .8255 .9089 .9922 is .0781 .1615 .2448 .3281 .4115 .4948 .5781 .6615 .7448 .8281 .9115 .9948 & .0807 .1641 .2474 .3307 .4141 .4974 .5807 .6641 .7474 .8307 .9141 .9974 METRIC SYSTEM. 10 millimeters (mm.) = 1 centimeter (cm.) 10 centimeters = 1 decimeter (dm.) 10 decimeters = 1 meter (m.) 10 meters = 1 decameter (Dm.) 10 decameters = 1 hectometer (Hm.) 10 hectometers = 1 kilometer (Km.) 10 kilometers = 1 myriameter(Mm.) .3937079 inch. 3.937079 inches. 3.2808992 feet. 10.9363 yards. 109.363 yards. .6213824 mile. 6.213824 miles. RUSSIAN. 12 inches = 1 foot = 1 American foot. 7 feet = 1 sachine, or sagene. 500 sachine = 1 verst = 3,500 feet. PRUSSIAN, DANISH, AND NORWEGIAN. 12 inches = 1 foot = 1.02972 American feet. 12 feet = 1 ruth = 12.35664 American feet. 2,000 ruths = 1 mile = 4.68+ American miles. AUSTRIAN. 12 inches = 1 foot = 1.03713 American feet. 6 feet == 1 klafter. 4,000 klafters = 1 mile = 4.71+ American miles, WEIGHTS AND MEASURES. SWEDISH. 12 inches = 1 foot = .97410 American foot. 6 feet i= 1 fathom. 6,000 fathoms = 1 mile = 6.64+ American miles. CHINESE. 1 chih = 1.054 American feet. 10 chih = 1 chang = 10.54 American feet. 180 chang 1 li = 1,897 American feet. MEASURES OF AREA. AMERICAN AND BRITISH. 144 sq. inches = 1 square foot. 9 sq. feet = 1 square yard = 1,296 sq. in. 30i sq. yards = 1 perch = 272i sq. ft. 40 perches = 1 rood = 1,210 sq. yd. = 10,890 sq. ft. 4 roods = 1 acre = 160 perches = 4,840 sq. yd. = 43,560 sq. ft. 640 acres = 1 square mile. TABLE FOR REDUCING SQUARE FEET TO ACRES. Square Feet. Acres. Square Feet. Acres. Square Feet. 100,000,000 2,295.684 90,000,000 2,066.116 900,000 20.661 9,000 80,000,000 1,836.547 800,000 18.365 8,000 70,000,000 1,606.979 700,000 16.070 7,000 60,000,000 1,377.410 600,000 13.774 6,000 50,000,000 1,147.842 500,000 11.478 5,000 40,000,000 918.274 400,000 9.183 4,000 30,000,000 688.705 '300,000 6.887 3,000 20,000,000 459.137 200,000 4.591 2,000 10,000,000 229.568 100,000 2.296 1,000 9,000,000 206.612 90,000 2.066 900 8,000,000 183.655 80,000 1.836 800 7,000,000 160.698 70,000 1.607 700 6,000,000 137.741 60,000 1.377 600 5,000,000 114.784 50,000 1.148 500 4,000,000 91.827 40,000 .918 400 3,000,000 68.870 30,000 .689 300 2,000,000 45.914 20,000 .459 200 1,000,000 22.957 10,000 .230 100 Acres. Square Feet. Acres. .207 90 .0021 .184 80 .0018 .161 70 .0016 .138 60 .0014 .115 50 .0011 .092 40 .0009 .069 30 .0007 .046 20 .0005 .023 10 .0002 .021 9 .00021 .018 8 .00018 .016 7 .00016 .014 6 .00014 .011 5 .00011 .009 4 .00009 .007 3 .00007 .005 2 .00005 .0023 1 .00002 METRIC SYSTEM. 1 square millimeter (sq. mm.) = .001550 sq. in. 1 square centimeter (sq. cm.) = .155003 sq. in. 1 square decimeter (sq. dm.) = 15.5003 sq. in. 1 square meter, or centare (m. 2 or sq. m.) = 10.764101 sq. ft. 1 square decameter, or are (sq. Dm.) = .024711 acre. 1 hectare (ha.) = 2.47110 acres. 1 square kilometer (sq. Km.) = 247.110 acres. 1 square myriameter (sq. Mm.) = 38.61090 sq. mi. MEASURES OF VOLUME. MEASURES OF VOLUME. AMERICAN AND BRITISH. 1,728 cubic inches = 1 cubic foot. 27 cubic feet = 1 cubic yard. A cord of wood = 128 cu. ft., or a pile of wood 8 ft. long, 4 ft. wide, and 4 ft. high = 1 cord. A perch of masonry contains 24 cu. ft.; but in practice it is taken as 25 cu. ft. A ton (2,240 Ib.) of Pennsylvania anthracite, when broken for domestic use, occupies about 42 cu. ft. of space; bituminous coal, about 46 cu. ft.; and coke, about 88 cu. ft. A bushel of coal is 80 Ib. in Kentucky, Illinois, and Missouri, 76 Ib. in Pennsylvania, and 70 Ib. in Indiana. METRIC SYSTEM. 1 milliliter, or cu. centimeter (cc. or cm. 3 ) 1 centiliter (cl.) 1 deciliter (dl. or dl. 8 ) 1 liter, or cu. decimeter (1.) 1 decaliter, or centistere (Dl. or dal.) 1 hectoliter, or decistere (HI.) 1 kiloliter, or cu. meter, or stere (Kl. or cm. 3 ) 1 myrialiter, or decastere (Ml.) .0610254 cu. in. .610254 cu. in. 6.10254 cu. in. 61.0254 cu. in. .353156 cu. ft. 3.53156 cu. ft. 35.3156 cu. ft. 353.156 cu. ft. LIQUID MEASURE (u. S.). 4 gills 2 pints 4 quarts 3H gallons 63 gallons = 1 pint = 1 quart = 1 gallon = 1 barrel .o gcmwuo = 1 hogshead. 2 hogsheads = 1 pipe. 2 pipes = 1 tun. A box 19f in. on each side contains 1 barrel. = 16 liquid oz. = 28.876 cu. in. = 8 gills = 57.75 cu. in. = 32 gills = 8 pints = 231 cu. in. 7,276i cu. in. = 4.21 cu. ft. DRY MEASURE (u. S.). 2 pints = 1 quart = 67.2006 cu. in. = 1.16365 liquid qt. 4 quarts = 1 gallon = 268.8025 cu. in. = 1.16365 liquid gal. 2 gallons = 1 peck = 8 quarts 4 pecks = 1 bushel = 64 pints = 537.6050 cu. in. = 32 quarts = 8 gal. = 2,150.42 cu. in. BRITISH IMPERIAL MEASURE, BOTH LIQUID AND DRY. 4 gills = 1 pint = 34.6592 cu. in. 2 pints = 1 quart = 69.3185 cu. in. 4 quarts = 1 gallon = 277.274 cu. in. 8 quarts = 1 peck = 554.548 cu. in. 4 pecks = 1 bushel = 2,218.192 cu. in. The standard U. S. bushel is the Winchester bushel, which is in cylinder form, I8i inches diameter and 8 inches deep, and contains 2,150.42 cubic inches. The British Imperial bushel is based on the Imperial gallon and con- tains 8 such gallons, or 2,218.192 cubic inches = 1.2837 cubic feet. Capacity of a cylinder in U. S. gallons = square of diameter in inches X height in inches X .0034 (accurate within 1 part in 100,000). Capacity of a cylinder in U. S. bushels = square of diameter in inches X height in inches X .0003652. WEIGHTS AND MEASURES. CONTENTS OF CYLINDERS OR PIPES FOR 1 FOOT IN LENGTH, The contents of pipes or cylinders in gallons or pounds are to each other as the squares of their diameters. Thus, a pipe 9 ft. in diameter will contain 9 times as much as a 3' pipe, or 4 times as much as a 4' pipe. DIAMETERS IN INCHES. Diam. in Inches. Diameter in Decimals of a Foot. Gallons of 231 Cu. In. (U. S. Stand- ard.) Weight of Water in Lb. in 1 Ft. of Length. Diain. Inches. Diameter in Decimals of a Foot. Gallons of 231 Cu. In. (U. S. Stand- ard.) Weight of Water in Lb. in 1 Ft. of , Length. i .0208 .0025 .02122 5 .4167 1.020 8.488 1 .0417 .0102 .08488 5 .4583 1.234 10.270 $ .0625 .0230 .19098 6 .5000 1.469 12.223 1 .0833 .0408 .33952 6k .5417 1.724 14.345 H .1042 .0638 .53050 7 .5833 1.999 16.636 H .1250 .0918 .76392 7i .6250 2.295 19.098 1* .1458 .1249 1.0398 8 .6667 2.611 21.729 2 .1667 .1632 1.3581 81 .7083 2.948 24.530 2i .1875 .2066 1.7188 9 .7500 3.305 27.501 2* .2083 .2550 2.1220 9 .7917 3.682 30.641 2* .2292 .3085 2.5676 10 .8333 4.080 33.952 3 .2500 .3672 3.0557 m .8750 4.498 37.432 3i .2917 .4998 4.1591 11 .9167 4.937 41.082 4 .3333 .6528 5.4323 11* .9583 5.396 44.901 4 .3750 .8263 6.8750 12 1.0000 5.875 48.891 DIAMETERS IN FEET. H 1.25 9.18 76.392 10 10.00 587.6 4,889.12 l* 1.50 13.22 110.00 10i 10.50 647.7 5,404.24 11 1.75 17.99 149.73 11 11.00 710.9 5,915.84 2 2.00 23.50 195.56 11* 11.50 777.0 6,485.72 2i 2.25 29.74 247.51 12 846.1 7,040.00 2* 2.50 36.72 305.57 13 992.8 8,710.00 2* 2.75 44.43 369.74 14 1,152.0 10,096.00 3 3.00 52.88 440.00 15 1,322.0 11,000.50 3i 3.25 65.28 544.37 16 1,504.0 12,516.00 31 3.50 71.97 631.00 17 1,698.0 14,166.00 3* 3.75 82.62 687.53 18 1,904.0 15,841.00 4 4.00 94.0 782.24 19 2,121.0 17,691.00 4i 4.25 106.1 885.40 20 2,350.0 19,556.50 4* 4.50 119.0 990.04 21 2,591.0 21,617.00 4* 4.75 132.5 1,105.71 22 2,844.0 23,663.00 5 5.00 . 146.9 1,222.28 23 3,108.0 25,943.00 5* 5.25 161.9 1,351.06 24 3,384.0 28,160.00 5* 5.50 177.7 1,478.96 25 3,672.0 30,557.00 5* 5.75 194.3 1,621.43 26 3,971.0 34,840.00 6, 6.00 211.5 1,760.00 27 4,283.0 35,641.00 ft 6.25 229.5 1,915.18 28 4,606.0 40,384.00 6> 6.50 248.2 2,177.48 29 4,941.0 41,117.00 6* 6.75 267.7 2,233.96 30- 5,288.0 ~v 44,002.00 7 7.00 287.9 2,524.00 31 5,646:0 46,984.00 ft 7.50 330.5 2,750.12 32 6,017.0 50,064.00 8 8.00 376.0 3,128.96 33 6,398.0 53,242.00 8* 8.50 424.5 3,541.60 34 6,792.0 56,664.00 9 9.00 475.9 3,960.16 35 7,197.0 59,891.50 n 9.50 530.2 4,422.84 36 7,614.0 63,364.00 1 WEIGHTS AND MEASURES. MEXICAN, CENTRAL AMERICAN, AND SOUTH AMERICAN WEIGHTS AND MEASURES. The following table gives weights and measures in commercial use in Mex- ico and the republics of Central and South America, and their equivalents in the United States. Published by the Bureau of the American Republics. Denomination. Where Used. U. S. Equivalents. Arobe Paraguay 25 pounds Arroba (dry) Argentine Republic 25 3175 pounds Arroba (dry) Brazil 32 38 pounds Cuba 25 3664 pounds Vrroba (dry) Venezuela 25 4024 pounds Arroba (liquid) ... Barril Cuba and Venezuela Argentine Republic and Mexico 4.263 gallons. 20.0787 gallons. Carga Mexico and Salvador 300 pounds Centavo Central America 4 2631 gallons Cuadra Argentine Republic 4 2 acres Cuadra Paraguay --- 78 9 yards Cuadra (square) Paraguav -- 8 077 square feet Cuadra Uruguay 2 acres (nearly) Fanega (dry) Central America 1 5745 bushels Fanega (dry) Chile 2 575 bushels Fanega (dry) Cuba 1 599 bushels Fanega (dry) Fanega (dry) Mexico Uruguay (double) 1.54728 bushels. 7 776 bushels Fanega (dry) Fanega (dry) Uruguay (single) Venezuela 3.888 bushels. 1 599 bushels Frasco Argentine Republic 2 5096 quarts Franco Mexico 2 5 quarts League (land) Paraguay 4 633 acres Libra Argentine Republic 1 0127 pounds Libra Central America 1 043 pounds Libra Chile 1 014 pounds Libra Cuba 1 0161 pounds Libra Mexico 1 01465 pounds. Libra Peru 1 0143 pounds Libra Uruguay 1 0143 pounds Libra Livre Venezuela Guiana 1.0161 pounds. 1 0791 pounds Manzana Costa Rica If acres Marc Bolivia . 507 pound Pie Argentine Republic 9478 foot Quintal Argentine* Republic 101 42 pounds Quintal Brazil 130 06 pounds. Quintal Chile Mexico and Peru 101 61 pounds Quintal Suerte Paraguay Uruguay 100 pounds. 2 700 cuadras. Vara Argentine Republic 34 1208 inches. Vara Central America 38.874 inches. Vara Chile and Peru .*. 33 367 inches. Vara Cuba 33 384 inches Vara . Mexico 33 inches. Vara Paraguay . 34 inches Vara Venezuela 33 384 inches CONVERSION TABLES. ( United States Coast and Geodetic Survey. ) The method of using the following tables for converting United States weights and measures into metric weights and measures will be understood by the following example: Find the number of kilometers in 125 miles. From column " Miles to Kilometers," 1 mile = 1.60935 kilometers, or 100 miles = 160.935 kilometers; 2 miles = 3.21869 kilometers, or 20 miles = 32.1869 kilometers; and 5 miles = 8.04674 kilometers. Hence, 125 miles = 160.935 + 32.1869 + 8.04674 = 201.16864 kilometers. WEIGHTS AND MEASURES. CUSTOMARY TO METRIC. LINEAR. CAPACITY. g i l - o "*"" of m Cfl "S3 II | o 02 CD 12 If cs !' Sl5| |I| S 02 CC II cS +J ^ O ^,2 S3c sS ^t-^ "SH JSi 1 3 3 uJ O 1^ S o 25.4 0.304801 0.914402 1.60935 1 3.70 29.57 0.94636 3.78543 50.8 0.609601 1.828804 3.21869 _> 7.39 59.15 1.89272 7.57087 76.2 0.914402 2.743205 4.82804 8 11.09 88.72 2.83908 11.35630 101.6 1.219202 3.657607 6.43739 4 14.79 118.29 3.78543 15.14174 127.0 1.524003 4.572009 8.04674 5 18.48 147.87 4.73179 18.92717 152.4 1.828804 5.486411 9.65608 6 22.18 177.44 5.67815 22.71261 177.8 2.133604 6.400813 11.26543 7 25.88 207.02 6.62451 26.49804 203.2 2.438405 7.315215 12.87478 8 29.57 236.59 7.57087 30.28348 228.6 2.743205 8.229616 14.48412 9 33.27 266.16 8.51723 34.06891 SQUARE. WEIGHT. 0) GO If! leg So *l S| o 5 S so ifi |i, M p d 85*1 |1 ^ 3 CD SI || la III IcM y 2 I 2 I |s %& 5| ! 2 pi K 22 6.452 9.290 0.836 0.4047 1 64.7989 28.3495 0.45359 31.10348 12.903 18.581 1.672 0.8094 2 129.5978 56.6991 0.90719 62.20696 19.355 27.871 2.508 1.2141 3 194.3968 85.0486 1.36078 93.31044 25.807 37.161 3.344 1.6187 1 259.1957 113.3981 1.81437 124.41392 32.258 46.452 4.181 2.0234 5 323.9946 141.7476 2.26796 155.51740 38.710 55.742 5.017 2.4281 i 388.7935 170.0972 2.72156 186.62088 45.161 65.032 5.853 2.8328 7 453.5924 198.4467 3.17515 217.72437 51.613 74.323 6.689 3.2375 8 518.3914 226.7962 3.62874 248.82785 58.065 83.613 7.525 3.6422 ) 583.1903 255.1457 4.08233 279.93133 CUBIC. $ rf 1 *3 - r/ MISCELLANEOUS. gol !l! 42 .In > 20 C |jo|j 'Jog f 1 5** E O O 0^ S~ WW 1 Gunter's chain = 20. 1168 meters. 16.387 32.774 .02832 .05663 0.765 1.529 0.35239 0.70479 1 sq. statute mile = 259.000 hectares. 1 fathom 1.829 meters. 49.161 .08495 2.294 1.05718 1 nautical mile = 1,853.25 meters. 65.549 81.936 .11327 .14158 3.058 3.823 1.40957 1.76196 1 ft. = .304801 meter 9.4840158 log. 98.323 114.710 .16990 .19822 4.587 5.352 2.11436 2.46675 1 avoir, pound 453.5924277 gram. 131.097 .22654 6.116 2.81914 15,432.35639 grains == 1 kilogram. 147.484 .25485 6.881 3.17154 CONVERSION TABLES. The method of using the following tables for converting metric weights and measures into United States weights and measures may be understood by the following example: Find the number of yards in 86 meters. From column " Meters to Yards," 8 meters = 8.748889 yards, or == 87.48889 yards; and 6 meter? = 6.561667 yards. Hence, 86 87.48889 + 6.561667 = 94.050557 yards. . j , meters Hence, 86 meters = METRIC TO CUSTOMARY. LINEAR. CAPACITY. Meters to Inches. Meters to Feet. Meters to Yards. Kilometers to Miles. T 2 3 4 5 6 7 8 9 Millimeters, or Cubic Centi- meters to Fluid Drams. Centiliters to Fluid Ounces. Liters to Quarts. Decaliters to Gallons. Hectoliters to Bushels. 39.37 78.74 118.11 157.48 196.85 236.22 275.59 314.96 354.33 3.28083 6.56167 9.84250 13.12333 16.40417 19.68500 22.96583 26.24667 29.52750 1.093611 2.187222 3.280833 4.374444 5.468056 6.561667 7.655278 8.748889 9.842500 0.62137 1.24274 1.86411 2.48548 3.10685 3.72822 4.34959 4.97096 5.59233 0.27, 0.54 0.81 1.08 1.35 1.62 1.89 2.16 2.43 0.338 0.676 1.014 1.353 1.691 2.029 2.367 2.705 3.043 1.0567 2.1134 3.1700 4.2267 5.2834 6.3401 7.3968 8.4535 9.5101 2.6417 5.2834 7.9251 10.5668 13.2085 15.8502 18.4919 21.1336 23.7753 2.8377 5.6755 8.5132 11.3510 14.1887 17.0265 19.8642 22.7019 25.5397 SQUARE. WEIGHT. Square Centi- meters to Square Inches. Square Meters to Square Feet. Square Meters to Square Yards. Hectares to Acres. Milligrams to Grains. Kilograms to Grains. Hectograms to Ounces Avoir. 05 03 SI* PI WS 0.155 0.310 0.465 0.620 0.775 0.930 1.085 1.240 1.395 10.764 21.528 32.292 43.055 53.819 64.583 75.347 86.111 96.875 1.196 2.392 3.588 4.784 5.980 7.176 8.372 9.568 10.764 2.471 4.942 7.413 9.884 12.355 14.826 17.297 19.768 22.239 1 2 3 4 5 6 7 8 9 .01543 .03086 .04630 .06173 .07716 .09259 .10803 .12346 .13889 15,432.36 30,864.71 46,297.07 61,729.43 77,161.78 92,594.14 108,026.49 123,458.85 138,891.21 3.5274 7.0548 10.5822 14.1096 17.6370 21.1644 24.6918 28.2192 31.7466 2.20462 4.40924 6.61387 8.81849 11.02311 13.22773 15.43236 17.63698 19.84160 CUBIC. WEIGHT ( Continued). Cubic Centi- meters to Cubic Inches. Cubic Deci- meters to Cubic Inches. Cubic Meters to Cubic Feet. Cubic Meters to Cubic Yards. Quintals to Pounds Avoir. Milliers, or Tonnes to Pounds Avoir. Kilograms to Ounces Troy. .0610 .1220 1 .1831 .2441 .3051 .3661 .4272 .4882 .5492 61.023 122.047 ] 83.070 244.094 305.117 366.140 427.164 488.187 549.210 35.314 70.629 105.943 141.258 176.572 211.887 247.201 282.516 317.830 1.308 2.616 3.924 5.232 6.540 7.848 9.156 10.464 11.771 1 2 3 1 5 6 7 H 9 220.46 440.92 661.39 881.85 1,102.31 1,322.77 1,543.24 1,763.70 1,984.16 2,204.6 4,409.2 6,613.9 8,818.5 Jl, 023.1 13,227.7 15,432.4 17,637.0 19,841.6 32.1507 64.3015 96.4522 128.6030 160.7537 192.9044 225.0552 257.2059 289.3567 10 WEIGHTS AND MEASURES. METRIC CONVERSION TABLE. (Arranged by C. W. Hunt, New York.) Millimeters X .03937 =* in. Millimeters -f- 25.4 = in. Centimeters X .3937 in. Centimeters -^ 2.54 = in. Meters X 39.37 = in. (Act Congress). Meters X 3.281 = ft. Meters X 1.094 = yd. Kilometers X .621 = miles. Kilometers -j- 1.6093 = miles. Kilometers X 3,280.7 = ft. Square millimeters X .0155 = sq. in. Square millimeters -t- 645.1 = sq. in. Square centimeters X .155 = sq. in. Square centimeters -r- 6.451 = sq. in. Square meters X 10.764 = sq. ft. Square kilometers X 247.1 = acres. Hectare X 2.471 = acres. > Cubic centimeters -j- 16.383 = cu. in. Cubic centimeters -=- 3.69 = fluid drams (U. S. P.). Cubic centimeters -r- 29.57 = fluid oz. (U. S. P.). Cubic meters X 35.315 = cu. ft. Cubic meters X 1.308 = cu. yd. Cubic meters X 264.2 = gal. (231 cu. in.). Liters X 61.022 = cu. in. (Act Con- gress). Liters X 33.84 = fluid oz. (U. S. Phar.). Liters X .2642 = gal. (231 cu. in.). Liters -=- 3.78 = gal. (231 cu. in.). Liters -f- 28.316 = cu. ft. Tonnes X 1.102 = short tons. Tonnes X .9839 = long tons. Hectoliters X 3.531 = cu. ft. Hectoliters X 2.84 = bu. (2,150.42 cu. in.). Hectoliters X .131 = cu. yd. Hectoliters -4- 26.42 = gal. (231 cu. in:). Grams X 15.432 = gr. (Act Con- gress). Grams -5- 981 = dynes. Grams (water) -5- 29.57 = fluid oz. Grams -s- 28.35 = oz. avoir. Grams per cu. cent. -~ 27.7 = Ib. per cu. in. Joule X .7373 = ft.-lb. Kilograms X 2.2040 = Ib. Kilograms X 35.3 = oz. avoir. Kilograms -~ 1,102.3 = ton ( 2,000 Ib.). Kilogr. per sq. cent. X 14.223 = Ib. per sq. in. Kilogram-meters X 7.233 = ft.-lb. Kilo per meter X .672 Ib. per ft. Kilo per cu. meter X .026 = Ib. per cu. ft. Kilo per cheval X 2.235 = Ib. per H. P. Kilowatts X 1.34 = H. P. Watts ~ 746 = H. P. Watts -=- .7373 = ft.-lb. per sec. Calorie X 3.968 = B. T. U. Cheval vapeur X .9863 = H. P. (Centigrade X 1.8) f 32 = degree F. Franc X .193 = dollars. Gravity Paris = 980.94 centimeters per sec. UNITED STATES CURRENCY. 10 mills = 1 cent. 10 cents = 1 dime. 10 dimes = 1 dollar. 10 dollars = 1 eagle. MONEY. BRITISH MONEY. 4 farthings = 1 penny. 12 pence = 1 shilling. 20 shillings = 1 pound sterling. 21 shillings = 1 guinea. STANDARD UNITED STATES COINS. Gold. Silver. Denomination. Value. Weight. Denomination. Value. Weight. * Dollar $1.00 2.50 3.00 5.00 10.00 20.00 25.8 gr. 64.5 gr. 77.4 gr. 129.0 gr. 258.0 gr. 516.0 gr. * Trade dollar- Standard -silver dollar 81.00 1.00 .50 .25 .10 420.0 gr. 412.5 gr. 192.9 gr. 96.45 gr. 38.58 gr. Quarter eagle * Three-dollar piece Half eagle Eagle Half dollar Quarter dollar... Dime Double eagle " Fineness" expresses the proportion of pure metal in 1,000 parts; thus, ' 900 fine " means that 900 of every 1,000 parts are pure metal. Fineness of # No longer coined. MONETARY VALUES. 11 U. S. coins = 900 pure metal, 100 alloy; alloy of gold coin is copper or copper and silver, but in no case shall silver exceed Jg of total alloy. Alloy of silver coin is copper. Piece. Weight. Contents. 5-cent( nickel) 77.16 grains 75$ copper, 25$ nickel. *3-cent 80 grains 75$ cppper, 25$ nickel. *2-cent 66 grains 95$ copper, 5$tin and zinc. 1-cent (copper) 48 grains 95$ copper, 5$ tin and zinc. *No longer coined. SPACE REQUIRED TO STORE U. S. COINS. Description. Amount. How Put Up. Space. Gold coins Silver dollars Subsidiary silver $1,000,000 1,000,000 1,000,000 $5,000 in 8-oz. duck bags 1,000 in 8-oz. duck bags 1,000 in 8-oz. duck bags Nearlv 17 cu. ft. 250 cu. ft. 150 cu. ft. A bag of standard silver dollars occupies a space 12 in. X 9 in. X 4 in. To CONVERT VALUE OF U. S. COINS INTO ENGLISH VALUES AND VICE VERSA. Rule. Cents ( U. S.) -=- 2.0277:7, or X .J&312 4 English pence. EXAMPLE. 100 cents X .49312 = 49.312 pence = 4s. 1.312d. Rule. English pence X 2.02771 = cents (U. S.). EXAMPLE. lOOd. X 2.02771 = 202.771 cents = $2.0277. Dollars Rule. - -= pounds sterling. 4.0000 EXAMPLE. -^^ - 20.548. .548 X 240 = 131.5d. = 10s. 11.5d. Rule. Pounds X&.8665 = dollars (U.S.). Shillings X ^.332+ = cents ( U.S.). VALUES OF FOREIGN COINS, U. S. TREASURY DEPT., JAN. 1, 1899. Argentine, Argentine Re- public Bolivar Venezuela $ 4.824 .193 .439 5.017 .465 7.300 9.647 .0075 .203 .268 1.06 1.13 .96 1.95 .96 1.000 .93 .983 .477 1.014 .935 Doubloon, Central America Doubloon Chile $14.50 3.650 15.34 15.65 .193 2.28 1.11 2.20 1.825 1.929 1.66 .56 .38 .402 .55 .48 .193 .965 .024 5.11 .40 7.92 .081 .0067 Doubloon, New Granada Doubloon, Spain and Mexico Drachma Greece Boliviano Bolivia Centen, Cuba Colon, Costa Rica Ducat, Austria, Bohemia, Hamburg, Hanover Ducat Denmark Condor Chile Condor, U. S.of Colombia and Ecuador Ducat Sweden Copeck Russia Escudo, Chile Florin, Austria-Hungary Florin, Hanover ( gold ) Florin, Hanover (silver) Florin, Holland, South Ger- many Crown, Austria-Hungary Crown, Denmark, Norway, and Sweden Crown, Germany Crown, Great Britain Crown Sicily Florin Netherlands Crown, Spain (half pistole) Dollar, Bolivia Florin, Prussia Florin Silesia f Dollar, British Honduras, British Possessions, N. A. (except Newfoundland), and Liberia Franc, Belgium, Bulgaria, France, Italy, Roumania, Switzerland Gourde, Hayti Groschen, Prussian Poland Guinea, Great Britain Gulden, Baden Dollar, Chile, Peru, and Ecuador Dollar, Mexican (gold) Dollar, Mexican (silver) Dollar, Newfoundland Dollar, U. S. of Colombia Imperial. Russia Kran Persia Kreutzer, Bavaria tThe British dollar has the same legal value as the Mexican dollar in Hongkong, the Straits Settlements, and Labuan. 12 WEIGHTS AND MEASURES. VALUES OF FOREIGN CO I NS. ( Continued.) Lira, Italy ' Mark, Finland Mark, German Empire * .193 .MB .238 3.30 .546 1.080 7.105 3.84 .193 .965 .365 .439 .926 .365 1.034 .049 .044 1.04 3.37 3.90 4.943 4.8665 .515 Rupee, India Shilling, Great Britain Sol Peru $ .208 .243 .439 .01 4.8665 .439 .710 .708 .679 .693 .656 .722 .664 .665 .682 .648 .655 .714 .688 3.409 .498 Maximilian, Bavaria Milreis, Brazil Sou, France Sovereign, G Sucre, Ecuac Tael, China - Toman, Pers Yen, Japan. reat Britain.... lor Milreis, Portugal Mohur India r Amoy Napoleon, France Peseta Spain Canton Chefoo ChinKiang Fuehau Haikwan (Cus- toms) Hankow Hongkong Niuchwang Ningpo Shanghai Swatow Peso, Argentine Republic ... Peso Chile Peso, U. S. of Colombia Peso Cuba Peso, Guatemala, Honduras, Nicaragua, Salvador Peso, Uruguay Piaster, Egypt . Piaster, Turkey Piastre Spain Pistole, Rome Takau , Tientsin da Pistole, Spain Pound, Egvpt Pound Sterling, Great Britain Ruble Russia t The British dollar has the same legal value as the Mexican dollar in Hongkong, the Straits Settlements, and Labuan. The carat (a 24th part) is used to express the proportion of gold in an alloy; thus, gold 18 carats fine is f pure. The carat is also a unit of weight for precious stones. Its value vanes according to different authorities, but the international carat is 3.168 grains, or 206 milligrams. DIAMOND WEIGHT (NYSTROM). Carats. 1 Grains. Parts. Grains, Troy. = 4 = 64 = 3.2 .25 =1 = 16 = .8 .015625 = .0625 = 1 = .05 .3125 = 12.5 = 20 = 1 15.5 1 ounce TIMBER AND BOARD MEASURE. TIMBER MEASURE. Volume of Round Timber. The volume in cubic feet equals the length multiplied by one-fourth the product of mean girth and diameter, all dimen- sions being in feet. If length is given in feet and girth and diameter in inches, divide by 144; if all dimensions are in inches, divide by 1,728. Volume of Square Timber. When all dimensions are in feet: Rule. Multiply the breadth by the depth and that product by the length, and the product will give the volume in cubic feet. When either of the dimensions is in inches: Rule. Multiply as above and divide by 12. When any two of the dimensions are in inches: Rule. Multiply as before and divide by 1UU. TIMBER AND BOARD MEASURE. ROUND TIMBER. TABLE OF i GIRTHS. 13 i Girths. Inches. Area in Feet. Girths. Inches. Area in Feet. i Girths. Inches. Area in Feet. 6 .250 m 1.04 19 2.50 6? .272 w 1.08 m 2.64 6? .294 1.12 20 2.77 6* .317 13 1.17 20? 2.91 7 .340 18t 1.21 21 3.06 71 .364 13i 1.26 2H 3.20 n .390 13* 1.31 22 3.36 7* .417 14 1.36 22i 3.51 & .444 14i 1.41 23 3.67 .472 14i 1.46 23^ 3.83 8j .501 14* 1.51 24 4.00 8* .531 15 1.56 24i 4.16 9 .562 15^- 1.61 25 4.34 9i .594 15i 1.66 25i 4.51 H .626 15* 1.72 26 4.69 9* .659 16 1.77 26^ 4.87 10 .694 16 1 1.83 27 5.06 10i .730 164 1.89 27 5.25 lOj .766 1.94 28 5.44 10* .803 17 2.00 28? 5.64 11 .840 17i 2.09 29 5.84 lit .878 17* 2.12 29^ 6.04 Hi .918 17* 2.18 30 6.25 H* .959 18 2.25 * 12 1.000 18* 2.37 Area corresponding to % girth (mean) in inches multiplied by length in feet equal solidity in feet and decimal parts. BOARD MEASURE. In measuring boards, they are assumed to be 1 inch in thickness. The number of feet, board measure (B. M.), in a given board or stick of timber, equals the length in feet multiplied by the breadth in feet multiplied by the thickness in inches. Breadth. Inches. Area of a Lineal Foot. Breadth. Inches. Area of a Lineal Foot. Breadth. Inches. Area of a Lineal Foot. i .021 4i .354 81 .688 .042 4* .375 8^ .708 1 .063 4* .396 8* .729 1 .083 5 .417 9 .750 it .104 5i .438 9i .771 H .125 1 .458 9* .792 If .146 5* .479 9* .813 2 .167 6 .500 10 .833 2t .188 6| .521 iej .854 2 .208 8| .542 10* .875 2* .229 6* .563 10* .896 3 250 7 .583 11 .917 8t .271 7i .604 1H .938 3i .292 7i .625 111 .958 3* .313 7* .646 11* .979 4 .333 8 .667 12 1.000 ! Area of a lineal foot multiplied by length in feet will give superficial con- tents in square feet. 14 MATHEMATICS. MATHEMATICS. BY EDWARD H. WILLIAMS, JR., E. M. Professor of Mining Engineering and Geology at the Lehigh University. GENERAL PRINCIPLES. Quantity or magnitude is anything that can be increased or decreased, or that is capable of any sort of measurement or calculation, such as numbers, lines, space, time, motion, weight, force, power, heat, light, electricity, etc. \Ve can measure a quantity by applying to it a portion of the same quantity, called a unit. If the quantities are of different kinds, we cannot measure them by one another, but we can compare them or institute a calculation between them. Mathematics treats of all kinds of quantity that can be numbered or meas- ured. Arithmetic is that part that treats of numbering, and is called the science of numbers. Geometry is the science of measuring. These two are the foundation of all other parts of mathematics, and are called pure mathe- matics. We can also reason about numbers by substituting letters for num- bers, and represent their relations by signs. This is called algebra, and it may be likened to a shorthand arithmetic. An extension of arithmetic to geometry, by which angles and triangles are subjected to numerical compu- tation, is called trigonometry, and plane trigonometry treats of methods of computing plane angles and triangles, and embraces the investigations of the relations of angles in general, which is called angular analysis. Another extension of arithmetic to geometry, by which lines, areas, and volumes are computed, is called mensuration. Mensuration of large portions of the earth's surface, where the curvature of the same is taken into calculation, is called geodesy. If the portions are smaller and curvature is neglected, the science is called surveying, and mine surveying if confined to underground work. COMMONLY USED MATHEMATICAL SIGNS AND ABBREVIATIONS. + means plus, or addition. D" square inches. means minus, or subtraction. round. X means multiplication. means plus or minus. [] \ , vincula, denoting that T means minus or plus. the numbers enclosed are * means division. means ratio. to be taken together; as, means proportion. 2 : 3 : : 4 : 6 shows that 2 is to 3 (a + b) c = 4~Tl5 x 5 = 35. degrees, arc or thermometer. as U is to 6. 1 minutes OTfeet. ? 1/3 means equality. means equivalency. means square root. means cube root, etc. square root of 3. n seconds or inches. 30 40' 4" is 30 degrees UO minutes k seconds. is it-feet 6 inches, accents to distinguish letters, as a', a", a'" . cube root of 5. a\ , Oo, i i b ,a c ,rea,dasubl, asubb, etc. 72 7 squared. a 2 , a :i a squared, a cubed. 83 8 cubed. al 1*K(T2 (J 1 /j! a = a/b a -r- b. 15 -r- 16 = sin a = the sine of a. 6 16 log t= logarithm. therefore. L angle. ^> greater than. right angle. <- less than. I perpendicular to. D square. sin sine. D' square feet. cos cosine. ARITHMETIC. 15 MATHEMATICAL SIGNS AND ABBREVIATIONS (Continued}. tan, or tang, tangent. sec secant. I. H. P. B. H. P. indicated horsepower, brake horsepower. versin versed sine. A. W. G. American wire gauge cot cosec cotangent, cosecant. B. W. G. (Brown & Sharpe). Birmingham wire gauge.. covers coversed sine. r. p. m.,o r rev. per min., revolutions 7T pi, ratio of circumference of fer minute. circle to diameter 3.14159. A decima point is a period (.) pre- g acceleration due to gravity fixed to a number to show = (32.16ft. per sec.). that the number is less than R, r radius. unity (1); thus, .2 = ^ rt ; \V, w weight. .35 = ^fa 5.75 = 5/o 5 c> or 5J. II. P. horsepower. ARITHMETIC. To Cast the Nines Out of a Number. Add together the digits, and find how many nines are contained in their sum. Reject these nines and set down the remainder to the right of the number. EXAMPLE. Cast the nines out of 18,304. 18,304. 7. Ans. To Prove Addition. Cast the nines out of each row of figures added, and out of their sum. Add together the remainder and cast the nines from its sum. If the remainder from this last process is equal to the remainder obtained from the sum of the numbers, the addition is correct. EXAMPLE. Prove this addition: 2,1 4 3,5 6 8 2 8,5 6 0,3 9 1 5 10,703,959 7. Ans. To Prove Subtraction. Add the remainder to the lesser number; their sum should equal the larger number. To Prove Multiplication. Cast the nines out of multiplicand and multi- plier, and multiply the remainders together. Cast the nines out of the product, and the remainder should equal the remainder obtained by cast- ing the nines from the original product. EXAMPLE. Prove this multiplication: 3,542 X 6,196 = 21,946,232. 3,5 4 2 5 6,196 4 2 1,9 4 6,2 3 2 2. Ans. To Prove Division. Subtract the remainder, if there be any, from the dividend, and divide what remains by the quotient. If the new quotient equals the old divisor, the work is right. EXAMPLE. Divide 31,046,835 by 56. 554,407|. Ans. PROOF. Take 43 from 31,046,835, and divide the remainder, 31,046,792, by 554,407. 56. Ans. Rule. To square any number containing the fraction i, multiply the whole number by the next higher whole number, and add . EXAMPLE. (8i) 3 = 8 X 9 + i = 72*. COMMON -FRACTIONS. A fraction is a part of a whole, as J, , etc. The numerator of a fraction is the number that tells how many parts of a whole are taken. Thus, 2 is the numerator of , as it shows that two of the three parts into which the whole is divided are taken. The denominator of a fraction is the number that shows into how many parts the whole is divided. Thus, in the fraction , the 3 is the denominator. A common denominator is a denominator common to two or more fractions. Thus, i and - have common denominators; and again, 12 is a common de- nominator for 4, , $, and , as they each are respectively equal to A* T 4 5 iV and T V To Add Common Fractions. If of the same denominator, add together the numerators only. Thus ^ -f T 3 S + ^ = T 9 ? , 16 FRACTIONS. If they have different denominators, change them to fractions with com- mon denominators, and proceed as before. EXAMPLE. What is the sum of +-J + ? * = IS, i = IS, and * = ft. 88 + *3 + *8 = BO- Ans. To Multiply Common Frac^ns. Multiply the numerators together for the numerator, and the denominators for the denominator. Thus, $ X i^ X = 9B, r TB- To Divide Common Fractions. Invert the divisor, and multiply. EXAMPLE. Divide B 9 by . B^ X $ = &V Ans. To Reduce Compound Fractions to Simple Fractions. Multiply the integer by the denominator of the fraction, add the numerator for the new numera- tor, and place it over the denominator. EXAMPLE. Reduce 5 to a simple fraction. 5X3 + 2 = 17, or the numerator, and the fraction is therefore ^. To Reduce Simple Fractions to Compound Fractions. Divide the numerator by the denominator, and use the remainder as the numerator of the remain- ing fraction. EXAMPLE. Reduce - 6 5 * to a compound fraction. 9)64(7 6 3 Compound fraction = 7. Ans. 1 To Reduce Common Fractions to Dec'tnal Fractions. Annex ciphers to the numerator, and divide by the denominator, and point off as many decimal places in the quotient as there are ciphers annexed. EXAMPLE. Reduce T 9 5 to a decimal fraction. 16)9.0000 (.5625 Ans. NOTE. Ciphers annexed to a deci- mal do not increase its value. 1.13 is the same as 1.1300. Every cipher placed between the first figure of a decimal and the decimal point divides the decimal by 10. Thus, .13 -=- 10 - .013. 80 100 96 40 32 80 80 TABLE OF FRACTIONS REDUCED TO DECIMALS. , .015625 it .265625 $? .515625 M .765625 1 .03125 a .28125 .53125 2 5 .78125 JL .046875 -65 .296875 i! .546875 H .796875 1 .0625 .078125 5 TB .3125 .328125 T% i! .5625 .578125 .8125 .828125 .09375 i.* .34375 S .59375 31 .84375 VI .109375 Il .359375 if .609375 if .859375 A .125 i .375 r .625 I .875 B\ .140625 B? .390625 8 .640625 i| .890625 35 .15625 *f .40625 .65625 .90625 I! .171875 .421875 43 .671875 i^ .921875 .1875 T ? B .4375 T | .6875 i-j .9375 .203125 29 .453125 .703125 6. .953125 .21875 35 .46875 II .71875 i .96875 .234375 ii .484375 i! .734375 1! .984375 i .25 ft .5 1 .75 1 1.0000 DECIMALS. Decimal fractions have for their denominators 10 or a power of 10, but the denominator is usually omitted. Thus, .1 = ^; .01 = T & ; .001 = iota, etc. To Add Decimals. Place whole numbers under .0075 whole numbers, tenths under tenths, hundredth* under hundredths, etc., and add, placing the deci- J-J 6 mal point in the sum directly under the points above. Thus, 19.6317 DECIMALS. 17 To Subtract Decimals. Arrange the figures as in 5.96978 addition, and proceed as in simple subtraction. 3.2 8 6 9 4 Thus, " To Multiply Decimals-Proceed as in 4 - 6 7 53 1 (5 decimal places.! simple multiplication, pointing off as __ - 5 3 ( 3 Decimal places.) many decimal places in the result as 1402593 there are decimal places in both mul- 2337 655 tiplicand and multiplier. Thus, 0.2 4 7 7 9 1 4 3 (8 decimal places.) To Divide Decimals. Proceed as in simple division, and point off as many decimal places in the quotient as the number of decimal places in the divi- dend exceeds those in the divisor. EXAMPLE 1. Divide 4.756 by 3.3. 3.3 ) 4.7 5 6 ( 1.4 4 1 2 Ans. EXAMPLE 2. Divide .006 by 20. 20 ).0060(.0003 Ans. 40 33 70 6J> 4 NOTE. It has been said before that algebra is a shorthand arithmetic. Before proceeding further with the various methods of arithmetic, the principles of algebra will be stated, and, after the subsequent examples are worked out by arithmetical rules, an example will be given of the algebraic method of doing the same. In every example, we have known quantities from which we seek to find certain unknown ones. While there is no way of indicating these in arithmetic, we can readily do so in algebra, by placing the first letters of the alphabet as representatives of the known quantities (as a, 6, c), and the last letters (x, y, z) of the unknown ones. The signs in algebra are those just given for arithmetic. In addition to them, we can indicate multiplication by placing a period (.) between the quantities, as a.b (read a multiplied byb),or simply by placing the two letters together, as a b. We can indicate division as in common fractions, -j- being read a divided by b. To illustrate algebraic symbols, let I denote the length, b the breadth, and h the height of a mine car. If it be desired to divide the height into the product of the length and breadth, it is expressed as follows: Ib Wh them, be multiplied . , an are multiplied together; thus, 4 X 8 = 32. If it be desired to divide the height into the sum of the length and breadth, it is expressed thus: t + b h ' The square of the length multiplied by the cube of the breadth, thus: Pb s . The square root of the length divided by the cube root of the breadth, thus: T/T #T' The square root of the difference of the length and breadth divided by the height, thus: 18 PROPORTION. SIMPLE PROPORTION, OR SINGLE RULE OF THREE. A proportion is an expression of equality between equal ratios; thus, the ratio of 10 to 5 = the ratio of 4 to 2, and is expressed thus: 10 : 5 : : 4 : 2. There are four terms in proportion. The first and last are the extremes, and the second and third are the means. Quantities are in proportion by alternation when antecedent is compared with antecedent and consequent with consequent. Thus, if 10 : 5 : : 4 : 2, then 10 : 4 : : 5 : 2. Quantities are in proportion by inversion when the antecedents are made consequents and the consequents antecedents. Thus, if 10 : 5 : : 4 : 2, then 5 : 10 : : 2 : 4. In any proportion, the product of the means will equal the product of the extremes. Thus, if 10 : 5 : : 4 : 2, then 5X4 = 10X2. A mean proportional between two quantities equals the square root of their product. Thus, a mean proportional between 12 and 3 = the square root of 12 X 3, or 6. If the two means and one extreme of a proportion are given, we find the other extreme by dividing the product of the means by the given extreme. Thus, 10 : 5 : : 4 : ( ), then (4 X 5) -^ 10 = 2, and the proportion is 10 : 5 : : 4 : 2. If the two extremes and one mean are given, we find the other mean by dividing the product of the extremes by the given mean. Thus, 10 : ( ) : : 4 : 2, then (10 X 2) -f- 4 = 5, and the proportion is 10 : 5 : : 4 : 2. EXAMPLE. If 6 men loa'd 30 wagons of coal in a day, how many wagons will 10 men load ? (They will evidently load more, so the second term of the proportion must be greater than the first. ) 6 : 10 : : 30 : ( ); then, (10 X 30) -f- 6 = 50. Ans. COMPOUND PROPORTION, OR DOUBLE RULE OF THREE. PRINCIPLES. 1. The product of the simple ratios of the first couplet equals the product of the simple ratios of the second couplet. Thus, J4 : 12) J5 : 10) _ _! v 1 _ j>_ v _6 \7 : 14/ " \6 : 18 / ~ 12 X 14 ~ 10 A 18' 2. The product of all the terms in the extremes equals the product of all the terms in the means. Thus, in (4 : 12) .. (5 : 10) I7:14j ' t6:18/ we have 4 X 7 X 10 X 18 =-- 12 X 14 X 5 X 6. 3. Any term in either extreme equals the product of the means divided by the product of the other terms in the extremes. Thus, in the same proportion, we have 5X6X12X14 7X10X18 ' 4. Any term in either mean equals the product of the extremes divided by the product of the other terms in the means. Thus, in (4 : 12) .. (5 : 10) 17 : 14 / ' |6: 18 / we have 5 - (4 X 7 X 10 X 18) -5- (6 X 12 X 14). Rule. I. Put the required quantity for the first term and the similar known quantity for the second term, and form ratios with each pair of similar quantities for the second couplet, as if the result depended on each pair and the second term. II. Find the required term by dividing the product of the means by the product of the fourth terms. EXAMPLE 1. If 4 men can earn $24 in 7 days, how much can 14 men earn in 12 days ? The sum : $24 : : j ^ : 4 j . or> the gum = 24XUXJ2 = $M4 Ang EXAMPLE 2. If 12 men in 35 days build a wall 140 rd. long, 6 ft. high, how EVOLUTION. 19 many men can, in 40 days, build a wall of the same thickness 144 rd. long, 5ft. high? INVOLUTION. To Square a Number. Multiply the number by itself. Thus, the square of 4 = 4 X 4, or 16. To Cube a Number. Multiply the square of the number by the number. Thus, the cube of 4 = 16 X 4 = 64. To Find the Fourth Power of a Number. Multiply the cube by the number. Thus, the fourth power of 4 = 64 X 4 = 256. To Raise a Number to the Sixth Power. Square its cube. To Raise a Number to the Twelfth Power. Square its sixth power. (See logarithms for shorter method.) EVOLUTION. To Find the Square Root of a Number: Rule. I. Separate the given number into periods of two figures each, beginning at the units place. II. Find the greatest number whose square is contained in the period on the left; this will be the first figure in the root. Subtract the square of this figure from the period on the left, and to the remainder annex the next period to form a dividend. III. Divide this dividend, omitting the figure on the right, by double tlie part of the root already found, and annex the quotient to that part, and also to the divisor; then, multiply the divisor thus completed by the figure of the root last obtained, and subtract the product from the dividend. IV. If there are more periods to be brought down, continue the operation as before. EXAMPLE. Find the square root of 8 7'4 2'2 5 ( 9 3 5 Ans. 874,225. 8 1 OPERATION. 18 3j~642 9 v 2 = 18. 18 into 64 goes 3 times, hence new divisor = 183. 93 X 2 = 186. 186 into 18C 5 i If* 5 932 goes 5 times, hence new divisor = 1,865. (See logarithms for shorter method.) The square root of a fraction is found by extracting the square root of the numerator and denominator separately. Thus, the square root of B \ = g. When decimals occur, the number is pointed off into periods both right and left from the decimal point, and there will be as many decimal places in the root as there are periods to the right of the decimal point in the number. EXAMPLE 1. Find the square root of 874.225. 8'7 4.2 2'5 ( 2 9.5 6+ 4|-47* .00'87'42'25(.C935 58 5|"3322 2925 r rv n 17] - > i> >7 c A' o v> u /I o y / o U 35442 4308+ To Find the Cube Root of a Number: Rule. I. Separate the given number into periods of three figures each, beginning at the units place. II. Find the greatest number whose cube is contained in the period on the left; this will be the first figure in the root. Subtract the cube of this figure from the period on the left, and to the remainder annex the next period to form a dividend, 20 PERCENTAGE. III. Divide this dividend by the partial divisor, which is 3 times the square oj the root already found, considered as tens; the quotient is the second figure of the root. IV. To the partial divisor add 3 times the product of the second, figure of the root by the first considered as tens, also the square of the second figure; the result will be the complete divisor. V. Multiply the complete divisor by the second figure of the root, and subtract the product from the dividend. VI. If there are more periods to be brought down, proceed as before, using the part of the root already found, the same as the first figure in the previous process. EXAMPLE. Find the cube root of 12,812,904. OPERATION. 1 2,8 1 2,9 4 ( 2 3 4 Ans. 2' = 8 1st partial divisor, 3 X 20 2 = 1,2 3X20X3= 180 32 - -. 9 1st complete divisor, 1,3 8 9" 2d partial divisor, 3 X 230 2 = 1 5 8,7 3X230X4 = 2,760 42 = 16 4,812 4,176 645,904 645,904 2d complete divisor, 1 6 1,4 7 6 The cube root of a fraction is found by extracting the cube root of the numerator and denominator separately. Thus, the cube root of || = |. (See logarithms for shorter method.) PERCENTAGE. Percentage means by or on the hundred. Thus, 1# = T ^ = .01, 3$ = T = .03. To Find the Percentage. Having the Rate and the Base. Multiply the base by the rate expressed in hundredths. Thus 6^ of 1,930 is found as follows: 1,930 X .06 = 115.80. To Find the Amount, Having the Base and the Rate. Multiply the base by 1 plus the rate. Thus, the amount of $1,930 for one year at 6$ is $1,930 X 1.06 = $2,045.80. To Find the Base, Having the Rate and the Percentage. Divide the percent- age by the rate. Thus, if the rate is 6# and the percentage is 115.80, the base = 115.80 -f- .06 = 1,930. To Find the Rate, Having the Percentage and the Base. Divide the percent- age by the base. Thus, if the percentage is 115.80 and the base 1,930, the rate equals 115.80 -5- 1,930 = .06, or 6#. ARITHMETICAL PROGRESSION. Quantities are said to be in arithmetical progression when they increase or decrease by a common difference. The following is an increasing series in arithmetical progression: 1, 3, 5, 7, 9, 11, 13. If the figures be read backward, 13, 11, 9, etc., it becomes a decreasing series. In the first series, the first term is 1; the last term 13; the number of terms 7; the common difference 2; and the sum of the terms 49. In any arithmetical progression, Let / = first term; I = last, or nth term; d = common difference; n = number of terms; and s = their sum. The second term =/ + (2 l)d =f -f d] the fourth term = / + (4 l)d; and the nth term = /+(-l)d. (1) From equation (1) we obtain f=l(n-I)d. (2) d= LlL m (4) GEOMETRICAL PROGRESSION. 21 Substituting the value of I from (1), = |[2/+(n-l)d]. (6) EXAMPLE 1. A company contracts to put down a bore hole at one dollar (SI) per foot for the first 100 ft.; three dollars ($3) per foot for the second 100 ft.; and two dollars ($2) per foot additional for each successive 100 ft. The hole was 800 ft. deep. What was the cost ? n = 8; / = 100; and d = 2. Substitute these values in formula (6). 8 = f [2 X 100 + (8 1) 200] = $6,400. Ans. EXAMPLE 2. If water flowing 10.12 gal. per min. be struck in a shaft 30 ft. below the surface, and the increase in flow be .02 gal. per ft. till the depth be 200 ft., and thence the flow decreases .02 gal. per ft. till the rock be dry, how deep was the shaft at the last point, and what was the total amount of water flowing into it per minute ? During the increase of flow, n = 170; / = 10.12; and d = .02. I [by formula (1)] = 10.12 + (170 - 1).02 = 13.50, or 13.50 gal. flow at a depth of 200 ft., and s = W [2X10.12 + (170 1). 02] = 2,007.7 gal. flowing in along the first 200 ft. in depth. During the decrease in flow/ = 13.50; d = .02, and I = .02. n [formula (3)] = ~^ + 1, for a decreasing progression __/=<+, I q KA Art Then, - ~^^ + 1 = 675, the depth at which the rock will run dry, and s = fi p [2 X .02 + (675 1) .02], or 4,563 gal., the amount of water that will flow in per minute along the last 675 ft. The total amount of water flowing in along the total depth of 875 ft. is 2,007.7 -f 4,563, or 6,570.7 gal. Ans. GEOMETRICAL PROGRESSION. A series of quantities, in which each is derived from that which precedes it, by multiplication by a constant quantity, is called a geometrical progression. If the multiplier be a whole number, the progression is styled increasing; if it be a fraction, the progression is styled decreasing. The series 1, 2, 4, 8, 16, 32 has 2 for a multiplier, and is an increasing progression. The series 32, 16, 8, 4, 2, 1, 1, i i i A. A have for a multiplier, and are decreasing progressions. The common multiplier in a geometrical progression is called the common ratio; or, briefly, the ratio. Let / = first term; I = last term, whose number from /is n; n = number of terms; r = ratio; s = sum of terms. I = /r-i. (1) f=~i' (4) * -f E~i--- ( 2 ) f=s-r(s- I). (5) -T^T W r = ^. (6) EXAMPLE. If a man should contract to sink a shaft to the base of the coal measures at the rate of ^ cent for the first 50 ft.; cent for the second 50 ft.; i cent for the third 50 ft.; and so on at the same rate, how much would be due if the shaft were 1,500 ft. deep? / = ^; n = 30; and r = 2. ula (1), Substituting in form I = ^ x (2*>) =x 33,554,432, and s [formula (3)] = = S671,088.63H. Ans. 22 LOGARITHMS. LOGARITHMS. USE OF LOGARITHMS. Logarithms are designed to diminish the labor of multiplication and divi- sion, by substituting in their stead addition and subtraction. A logarithm is the exponent of the power to which a fixed number, called the base, must be raised to produce a given number. The base of the common system is 10, and, as a logarithm is the exponent of the power to which the base must be raised in order to be equal to a given number, all numbers are to be regarded as powers of 10; hence, 10 = 1, we have logarithm of 1 = 0. 10 1 = 10, we have logarithm of 10 = 1. 10 s = 100, we have logarithm of 100 = 2. 10' J = 1,000, we have logarithm of 1,000 = 3. 10 4 = 10,000, we have logarithm of 10,000 = 4. The logarithms of numbers between 1 and 10 are less than unity, and are expressed as decimals. The logarithm of any number between 10 and 100 is more than 1 and less than 2, hence it is equal to 1 plus a decimal. Between 100 and 1,000, it is equal to 2 plus a decimal, etc. The integral part of a logarithm is its characteristic, the decimal part is its mantissa. EXAMPLE. The log of 67.7 is 1.830589, the characteristic of this logarithm is 1 and the mantissa is .830589. The characteristic of a logarithm is always 1 less than the number of whole figures expressing that number, and may be either negative or positive. The characteristic of the logarithm of 7 is 0; of 17 is 1; of 717 is 2; etc. The mantissa is the decimal portion of a logarithm, and is always considered positive. To Find the Logarithm of Any Number Between I and 100. Look on the first page of the table, along the column marked "No.," for the given number; opposite it will be found the logarithm with its characteristic. To Find the Logarithm of Any Number Consisting of Three Figures. Proceed in the same manner and find the decimal in the first column to the right of the number; prefix to this the characteristic 2. Thus, the logarithm of 327 is 2.514548. As the first two figures of the decimal are the same for several successive figures, they are only given where they change. Thus, the decimal part of the logarithm of 302 is .480007. The first two figures remain the same up to 310, and are therefore to be supplied. To Find the Logarithm of Any Number of Four Figures. Look in the column headed " No." for the first three figures, and then along the top of 'the page for the fourth figure. Down the column headed by the fourth figure, and opposite the first three, will be found the decimal part. To this prefix the characteristic 3. To Find the Logarithm of Any Number Containing More Than Four Figures. Place a decimal point after the fourth figure from the left, thus changing the number into an integer and a decimal. If the decimal part contains more than two figures, and its second figure is 5 or greater, add 1 to the first figure in the decimal. Find the mantissa of the first four figures and subtract it from the next greater mantissa in the table. Under the heading "P. P." find a column headed by the difference first found; find in this column the number opposite the number corresponding to the first figure of the decimal, or the first figure increased by one, and add it to the mantissa already found for the first four figures of the given number. EXAMPLE. What is the logarithm of 234,567? Placing a decimal point after the fourth figure from the left, we have 2,345.67. The mantissa of 2,345 is .37014; the difference between .37014 and the next higher logarithm .37033 is 19. Add 1 to the first figure of the decimal 6, and in the column headed 19, under " P. P.," opposite 7, we find 13.3, which, added to the portion of the mantissa already found, .37014, gives .37027. The characteristic is 5, hence the logarithm is 5.37027. To Find the Logarithm of a Decimal Fraction. Proceed according to previous rules, except in regard to the characteristic. Where the number consists LOGARITHMS. 23 of a whole number and a decimal, the characteristic is 1 less than the whole number. Where it is a simple decimal, or when there are no ciphers between the decimal point and the first numerator, the characteristic is negative, and is expressed by 1, with a minus sign over it. Where there is one cipher between the decimal point and first numerator, the characteristic is 2, with a minus sign over it. Where there are 2 ciphers, the characteristic is 3, with a minus sign over it. Thus: The logarithm of 67.7 is 1.830589. The logarithm of 6.77 is 0.830589. The logarithm of .677 isT.830589. The logarithm of .0677 is 2.830589. The logarithm of .00677 is 3.830589. The characteristic only is negative. The decimal part is positive. To Find the Logarithm of a Vulgar Fraction. Subtract the logarithm of the denominator from the logarithm of the numerator. The difference is the . logarithm of the fraction. EXAMPLE. Find logarithm of T V Log 4 = 0.60206 Log 10 = L 1.60206 1.60206 is the logarithm of .4. To Find the Natural Number Corresponding to Any Logarithm. Look in the column headed " " for the first two figures of the decimal part; the other four figures are to be looked for in the same or in one of the nine following col- umns. If they are exactly found, the number must be made to correspond with the characteristic by pointing off decimals or annexing ciphers. If the decimal portion cannot be found exactly, find the next lower loga- rithm, subtract it from the given logarithm, divide the difference by the difference between the next lower and the next higher logarithm, and annex the quotient to the natural number found opposite the lower logarithm. To Multiply by the Use of Logarithms. Add the logarithms of the factors together; the sum will be the logarithm of their product. EXAMPLE. 67.7 X .677. Log 67.7 = 1.830589 Log .677 = 1.830589 1.661178 1.661178 is the logarithm of 45.833. To Divide by the Use of Logarithms. Subtract the logarithm of the divisor from the logarithm of the dividend; the difference will be the logarithm of the quotient. EXAMPLE. Divide 67.7 by .0677. Log 67.7 = 1.830589 Log .0677 = 2.830589 3.000000 3 is the logarithm of 1,000. To Square a Number by the Use of Logarithms. Multiply the logarithm of the number by 2. The product will be the logarithm of the square of the number. EXAMPLE. Square .677. Log .677 = 1.830589 _2 1.661178 1.661178 is the logarithm of .45833. To Cube a Number. Multiply the logarithm of the number by 3. The product will be the logarithm of the cube of the number. To Raise a Number to Any Power, as 4th, 5th, 6th, or 7th, multiply the loga- rithm of the number by 4, 5, 6, or 7, and the results will be the logarithms of the 4th, 5th, 6th, or 7th powers, respectively. Thus, a number can readily be raised to any power required. 24 GEOMETRY. To Extract the Square, Cube, Fourth, Fifth, or Any Root of a Number. Divide the logarithm of the number by the index of the root required, and the quotient will be the logarithm of the required root. Thus, to find the square root of 625: Logarithm of 625 = 2.795880. 2.795880 -r- 2 = 1.397940. 1.397940 = logarithm of 25. Therefore, the square root of 625 is 25. To Find the Cube, Fourth, or Any Root. Proceed in the same way, using the index of the required root as a divisor. To Divide a Logarithm Having a Negative Characteristic. If the characteristic is evenly divisible by the divisor, divide in the usual manner and retain the negative sign for the characteristic in the quotient. But if the negative characteristic is less than, or not evenly divisible by, the divisor, add such a negative number to it as will make it evenly divisible, and prefix an equal positive number to the decimal part of the logarithm; then divide the increased negative characteristic by the divisor, to obtain the characteristic of the quotient desired. To obtain the decimal part of the quotient, divide the decimal part of the logarithm, with the positive number prefixed, in the usual manner. To this quotient prefix the negative characteristic already found, and this will be the quotient desired. EXAMPLE 1.- 6.3246846 = 2.i 08 2282. o EXAMPLE 2. = (14 +4 = 18) + (4 + .3268472)+i = 2.4807608. EXAMPLE 3. 1.9661178 = .9249+. GEOMETRY. PRINCIPLES OF GEOMETRY. 1. The sum of all the angles formed on one side of a straight'line equals two right angles, or 180. 2. The sum of all the angles formed around a point equals four right angles, or 360. 3. When two straight lines intersect each other, the opposite or vertical angles are equal. 4. If two angles have their sides parallel, they are equal. 5. If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, they are equal in all their parts. 6. If two triangles have two angles, and the included side of the one equal to two angles and the included side of the other, they are equal in all their parts. 7. In any triangle, the greater side is opposite the greater angle, and the greater angle is opposite the greater side. 8. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. 9. In an isosceles triangle, the angles opposite the equal sides are equal. 10. In any triangle, the sum of the three angles is equal to two right angles, or 180. 11. If two angles of a triangle are given, the third may be found by subtracting their sum from two right angles, or 180. 12. A triangle must have at least two acute angles, and can have but one obtuse or one right angle. 13. In any triangle, a perpendicular let fall from the apex to the base is shorter than either of the two other sides. GEOMETRY. 25 14. In any parallelogram, the opposite sides and angles are equal each to each. 15. The diagonals divide any paralellogram into two equal triangles. 16. The diagonals of a parallelogram bisect each other; that is, they divide each other into equal parts. 17. If the sides of a polygon be produced in the same direction, the sum of the exterior angles will equal four right angles. 18. The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles. EXAMPLE. The sum of the interior angles of a quadrilateral = (2X4) 4 = 4 right angles. The sum of the interior angles of a pentagon = (2 X 5) 4 = 6 right angles. The sum of the interior angles of a hexagon = (2 X 6) 4 : = 8 right angles. 19. In equiangular polygons, each interior angle equals the sum divided by the number of sides. 20. The square described on the hypotenuse of a right-angled triangle is equal to the sum of the squares described on the other two sides. Thus, in a right-angled triangle whose base is 20 ft. and altitude 10 ft., the square of the hypotenuse equals the square of 20 + the square of 10 , or 500. Then the hypotenuse equals the square root of 500, or 22.3607 ft. 21. Having the hypotenuse and one side of a right-angled triangle, the other side may be found by subtracting from the square of the hypotenuse the square of the other known side. The remainder will be the square of the required side. 22. Triangles that have an angle in each equal, are to each other as the product of the sides including those equal angles. 23. Similar triangles are to each other as the squares of their correspond- ing sides. 24. The perimeters of similar polygons are to each other as any two corresponding sides, and their areas are to each other as the squares of those sides. 25. The diameter of a circle is greater than any chord. 26. Any radius that is perpendicular to a chord, bisects the chord and the arc subtended by the chord. 27. Through three points not in the same line, a circumference may be made to pass. DIRECTIONS. Draw two lines connecting the three points. Erect perpen- diculars from the centers of each of these two lines, and the point of inter- section of the perpendiculars will be the center of the circle. 28. The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. EXAMPLE 1. If the circumference of a circle is 62.83 in. and its radius is 10 in., what is the circumference of a circle whose radius is 15 in. ? 10 : 15 : : 62.83 : 94.245 in. Ans. EXAMPLE 2. If a circle 6 in. in diameter has an area of 28.274 sq. in., what is the area of a circle 12 in. in diameter? 3 2 : e 2 : : 28.274 : 113.096 sq. in. Ans. PRACTICAL PROBLEMS IN GEOMETRICAL CONSTRUCTION. VK To Bisect a Given Straight Line A B. From A and B as centers, with a radius greater than I one-half of A B, describe arcs intersecting at E j j and F. Draw E F. It will bisect A B. C will f be the middle point, and E F will be perpendic- ular to A B. The points E and F will be equi- 'jlf distant from A, B, or C. From a Given Point C, Without a Straight Line AB, to Draw a Perpendicular to the Line. From C as a center, with a radius sufficiently great, describe an arc cutting A B in points A and B\ then from A and B as centers, with a radius greater than one-half of A B, describe two arcs cutting each other at D, and draw CD. C E 26 GEOMETRY. At a Given Point C in a Straight Line A B, to Erect a Perpendicular to That Line. Take the points A and B equally distant from C, and, with A and B as centers, and a radius greater than one-half of A B, describe two arcs cutting each other at Z>, and draw the line D C. At a Point A on a Given Straight Line A B, to Make an Angle Equal to a Given Angle EFG. From F as a center, with any radius F G, describe the arc EG. From A as a center, with the same radius, describe the arc CB; then with a radius equal to the chord EG, describe an arc from .B as a center, cutting CB at Z>, and draw A D To Bisect a Given Arc ACS. With the same radii and the extremities A B as centers, describe arcs intersecting at D and E. The line DE bisects the arc at C. To Bisect an Angle A B C. With any radius and B as a center, describe an arc cutting the sides at A and C. With these points as centers, describe arcs of equal radius intersecting at D. The line B D is the bisector, and the /_ A B D = L D B C. To Bisect an Open Atigle (Method by L. L. LOGAN). Let A B and CD be the sides of an open angle. With any point as a cen- ter, describe a circle cutting the sides at e, /, <7, and h, and with e and/, and g and h as centers and any radius, describe arcs intersecting at k and Z, respectively. Draw Ok and Ol and ran. With p and q as cen- ters, and any radius, describe arcs intersect- ing at R and S. The line drawn through R S is the required bisector. Through a Given Point A, to Draw a Straight Line Parallel to a Given Straight Line CD. From A as a center, with a radius greater than the shortest distance from A to CD, describe an indefinite arc D E. From D as a center, with the same radius, describe the arc AF. Take D E equal to A F, and draw A B. \ B To Find the Center of a Given Circumference or Arc. Take any three points A, B, and C on the circumfer- ence, and unite them by the lines A B and B C. Bisect these chords by the perpendiculars D and E 0; their intersection is the center of the circle. GEOMETRY. 27 Through a Given Point P, to Draw a Tangent to a Given Circle. 1. If P be in the circumference: Find 6' the center of the circle, draw the radius C P, and draw D E perpendicular to C P. 2. If P be without the circle: Join P and the center of the circle. Bisect P C in D\ with D as a center, and a radius D (7, describe the cir- cumference intersecting the given circumference at A and B. From the intersections A and JB, draw B P and A P. An acute angle having its vertex in the circumference and subtended by an arc is equal to one-half the central angle subtended by the same arc. Thus, the [_ A B C = i L AOC. An acute angle included between a chord and a tangent is equal to one-half the central angle subtended by the chord. Thus, [_ ABC = % i__ COB. If, from a point, two tangents be drawn to a circle, they will be equal, and their angle of intersection will be equal to the central angle subtended by the chord joining the two points of tangency. Thus, A B - and/. DAC = L B O C. AC, To Divide a Straight Line Into Any Number of Equal Parts. To divide the line AB into, say, 6 parts, draw the line A C from A, making any angle with A B; measure off 6 equal spaces on A C; draw 6 B, and from 1, 2, 3, U, 5 on A C draw parallels to 6 B. These divide A B as required into 6 equal parts. By a similar process a line may be divided into a number of unequal parts. Set off on A C divisions proportional to the required divisions, and draw the parallel lines as explained above. MENSURATION. MENSURATION. MENSURATION OF SURFACES. PARALLELOGRAMS. A parallelogram is a four-sided figure whose opposite sides are parallel. / B A B- A/ Rhombus. (F<,ur equal sides and oblique angles.) Rl omboid. (Four oblique angles and opposite sides equal.) Square. Rectangle. (Four equal sides (Four right angles and four right an- and opposite sides gles.) equal.) HJy To Find the Area of Any Parallelogram. Multiply the length of any side by the length of a perpendicular line from that side to the opposite one. Thus, in the- foregoing figures, the areas of the square and rectangle are found by multiplying the length A B by the height B C. The areas of the rhombus and rhomboid are found by multiplying the length A B by the heighten. To Find the Diagonal of a Square. Multiply the length of a side by 1.41421. Having the Diagonal, to Find the Side of a Square. Divide the diagonal by 1.41421, or multiply it by .707107. To Find a Square Equal in Area to a Given Circle. Multiply the diameter of the circle by .886227, and the result will be the side of the required square. To Find the Area of the Largest Square That May be Inscribed in a Circle. Square the radius of the circle, and multiply by 2. To Find the Side of the Largest Square That May be Inscribed in a Circle. Divide the diameter of the circle by 1.41421, or multiply it by .707107. TRIANGLES. A triangle is a figure having three straight sides. C C To Find the Area of a Triangle. Multiply its base by one-half the perpen- dicular height, or altitude. To Find the Perpendicular Height of an Equilateral Triangle. Multiply the length of one of its sides by .866025. To Find the Length of Each Side of an Equilateral Triangle. Divide the per- pendicular height by .866025, or multiply the perpendicular height by 1.1547. Or, take the square root of the area and multiply it by 1.51967. To Find the Side of a Square of Same Area as an Equilateral Triangle. Mul- tiply the length of one of its sides by .658037. TRIANGLES. 29 To Find the Diameter of a Circle of Same Area as an Equilateral Triangle. Divide the length of one of its sides by 1.34677. The following rules apply to any triangle: Having Two Sides and the Included Angle, to Find the Area. Multiply together the two sides and the natural sine of the included angle, and divide the product by 2. Or, by logarithms, add together the logarithms of the two Acute. (Three acute angles.) Obtuse. (An obtuse angle.) sides and the logarithmic sine of the included angle, and from the sum subtract the logarithm of 2, and the result will be the logarithm of the area. Having Three Sides of a Triangle, to Find the Area. Add the three sides together, divide the sum by 2; from the half sum, subtract each side sep- arately; multiply the half sum and the three remainders continuously together, and extract the square root of the product. Thus, if the triangle has three sides wh6se lengths- are 30, 40, and 50 ft., then -- = 60. Then, subtracting from this 60 each side separately, we have: 60 30 = 30; 60 40 = 20; 60 50 = 10. Then, 60 X 30 X 20 X 10 = 360,000. The square root of 360,000 = 600 sq. ft., or area. Having the Three Sides of a Triangle, to Find Its Angles. In the triangle A B C, let A B = 21 ft., B C = 17.25 ft., and A C = 32 ft. Draw BD per- pendicular to A (7; then, 32 : 21 + 17.25 = 21 17.25 :AD DC; or, AD- DC = 4.48 But A D + D C = 32 Adding, Subtracting, 2 A D = 36.48 A D = 18.24 2 D C = 27.52 D C = 13.76 cos^l = = .86857, or A = 29 42' 25.7". cos C = ~ = .79768, or C = 37 5' 26.7". B = 180 (A+C)=i8Q (29 42' 25.7" -4- 37 5' 26.7") = 113 12' 7.6". Having Two Sides and Included Angle, to Find Third Side and the Other Angles. In the triangle A B C, let A B = 19 ft., A C = 2? ft., and A = 36 3' 29". Draw B D perpendicular to A. C. B D = 19 X sin A = 19 X .58861 = 11.18ft. A D = 19 X cos A = 19 X .80842 = 15.36 ft. D C = 23 15.36 = 7.64 ft. Tan C = = 1.46335, or C = 55 39' 10". B = 180 (A + C) = 180 - (36 3' 29" + 55 39' 10") = 88 17' 21" BC = Sin C - .82562 . Having One Side and the Two Adjacent Angles, to Find the Other Two Sides. The third angle equals 180 minus the sum of the other two angles. This third angle will be the one opposite the given side. Then the sine of the angle opposite the given side is to the given side as the sine of either of the other angles is to its opposite side. Thus, in the triangle A B (7, let A = 60, B = 70, and the side A B = 200 ft. Then the angle C = 180 (60 + 70) = 50. Then, sin 50 : 200 : : sin 60 : B C, and sin 50 : 200 : : sin 70 : A C. To Find the Area. Either find the three sides as above, and follow rule already given, or multiply the natural sines of the two given angles together. 30 MENSURATION. Then, as the natural sine of the single angle is to the product of the sines of tne given angles, so is the square of the given side to twice the required area. Thus, sin C : sin A X sin B : : A B~ : to twice the area of the triangle. The area of any triangle is equal to half the area of a parallelogram having the same base and perpendicular height. TRAPEZOIDS. A trapezoid has four straight sides, only two of which are parallel. To Find the Area of a Trapezoid. Add together the two parallel sides, and divide by 2. Multiply the quotient by the perpendicular height. Thus, ' *+CJ> XEF= area. TRAPEZIUMS. A trapezium has four sides, no two of which are parallel. To Find the Area of a Trapezium. Divide the trape- zium into two triangles, and find the area of each according to the rules given under the head of " Triangles." Add together the areas of the two triangles, and the sum will equal the area of the trapezium. The sides and angles can be found in the same manner. If the diagonals and the perpendiculars from them to the opposite angles are given, add together the two perpendiculars, multiply the sum by the diagonal, and divide by 2. The sum of the four angles included in a trapezium always equals four right angles. POLYGONS. All figures bounded by more than four straight lines are called polygons. Pentagon. Hexagon. Heptagon. If all the sides and angles are equal, .it is a regular polygon. If not, it is an irregular polygon. The sum of the interior angles of any polygon is equal to twice as many right angles as the polygon has sides, less four right angles. To Find the Area of Any Regular Polygon. Square one of its sides and multiply by the number given in the column of areas in the following table. Or, multiply the. length of one of the sides by one-half the length of a perpendicular drawn to the center of the figure, and this product by the number of sides. Having the Side of a Regular Polygon, to Find the Radius of a Circumscribing Circle. Multiply the side by the corresponding number in following column of outer radii. If the radius of the circumscribing circle be given. CIRCLES. 31 divide it by the number in column of outer radii, and the quotient will be the side of the polygon. To Find the Area of an Irregular Polygon. Divide it into triangles, find the TABLE OF REGULAR POLYGONS WHOSE SIDES ARE UNITY. Number Sides. Name of Polygon. Areas. Outer Radii. Angles Contained Between Two Sides. Angle at Center of Circle. 3 4 5 Equilateral triangle Square Pentagon .4330 1.0000 1 7205 .5774 .7071 .8507 60 90 108 120 90 72 6 7 8 Hexagon Heptagon Octagon 2.5981 3.6339 48284 1.0000 1.1524 1.3066 120 128 34' 17" + 135 60 51 25' 43" 45 9 Nonagon 6.1818 1.4619 140 40 10 11 12 Decagon Undecagon Dodecagon 7.6942 9.3656 11.1962 1.6180 1.7747 1.9319 144 147 16' 22" 150 36 32 43' 38" + 30 area of each triangle, and add them together. The sum will be the area of the polygon. To Find the Area of a Figure Whose Outlines Are Very Irregular. Draw straight lines around it that will enclose within them (as nearly as can be judged) as much space not belonging to the figure as they exclude space belong- ing to it. The area of the figure thus formed may be easily found by dividing into triangles. CIRCLES. (See Table of Areas of Circles, Etc.) A circle is a figure bounded by a curved line, every point of which is equi- distant from the center. Or, a circle is a regular poly- gon of an infinite number ol sides. The circumference of a circle equals the diameter multiplied by 3.1416, or the square root of the product of the area multiplied by 12.566. To Find the Diameter. Divide the circumference by 3.1416, or multiply it by .31831. To Find the Area of a Circle. Multiply the circumfer- ence by one-fourth of the diameter, or the square of the radius by 3.1416. Multiply the square of the diameter by .7854, or the square of the circumference by .07958. To Find the Diameter of a Circle Equal in Area to a Given Square. Multiply one side of the square by 1.12838. To Find the Radius of a Circle to Circumscribe a Given Square. Multiply one side by .7071; or take one-half the diagonal. To Find the Side of a Square Equal in Area to a Given Circle. Multiply the diameter by .88623. To Find the Side of the Greatest Square in a Given Circle. Multiply the diameter by .7071. To Find the Area of the Greatest Square in a Given Circle. Square the radius and multiply by 2. To Find the Side of an Equilateral Triangle Equal in Area to a Given Circle. Multiply the diameter by 1.3468. Having the Chord and Rise of an Arc, to Find the Radius. Square half the chord, and divide by the rise. To the quotient add the rise, and divide by 2. Or, radius = the square of the chord of half the arc divided by twice the rise of the whole arc. Having the Chord and Radius, to Find the Rise. Square the radius, also square half the chord. Take the last square from the first. Extract square root of the remainder, and subtract it from the radius if the radius is greater; if not, add it to the radius. Having the Radius and Rise, to Find the Chord. From the radius subtract the rise (or from the rise subtract the radius, if rise is the greater), square 32 MENSURATION. the remainder, and subtract it from the square of the radius. Extract the square root of the remainder, and multiply by 2. Having the Rise of the Arc and Diameter of Circle, to Find the Chord. Sub- tract the rise from the diameter, and multiply the remainder by the rise. Extract the square root of the product, and multiply by 2. To Find the Breadth of a Circular Ring, Having Its Area and the Diameter of the Outer Circle. Find the area of the whole circle, and from it take the area of the ring. Multiply the remainder by 1.2732, and the square root of the product will be the diam- eter of the inner circle. Take it from the diameter of the outer one, and the remainder will be twice the breadth. To Find the Area of a Circular Ring. Take the difference of the squares of the radii, and multiply it by 3.1416. To Find the Length of an Arc When Its Degrees and Radius Are Given. Multiply the number of degrees by .01745, and the product by the radius. To Find the Area of a Sector. Multiply the arc by one-half the radius. The area of the sector is to the area of the circle as the number of degrees in the sector is to 360. To Find the Area of a Segment. Find the area of the sector having the same arc, and also the area of the triangle formed by the chord of the segment and the radii of the sector. If the segment is greater than a semicircle, add the two areas; if less, subtract them. THE ELLIPSE. ? and To Find the Area of an Ellipse. Multiply one-half of the two axes AB i CD together, and multiply the product by 3.1416. To Find the Perimeter of an Ellipse. Multiply one-half the sum of the two axes by 3.1416. To Draw an Approximate Ellipse (Methodby Three Squares). Let a be the center, b c the major, and a e half the minor axis of an ellipse. Draw the rectangle bfg c, and the diagonal line be', at a right angle to b e, draw line/ A cut- ting B B at i. With radius a e, and from a as a center, draw the dotted arc ej, giving the point j on the line B B. From k, which is central between 6 and .7, draw the semicircle b mj, cutting A A at I. Draw the radius of the semicircle b mj, cutting fg at n. With radius m n, mark on A A, at and from a as a center, the point o. With radius h o, and from center A, draw the arc p o q. With radius a I, and from b and c as centers, draw arcs cut- ting poq at the points p and q. Draw the lines h p r and h q s, and also the lines p i t and qvw. From h as a center, draw that part of the ellipse lying between r and s with radius h r. From p as a center draw that part of the ellipse lying between r and t with the radius p r. From q, draw the ellipse from s to w. With radius i t, from i as a center, draw the ellipse from t to b with radius i t, and from v as a center, draw the ellipse from w to c, and one-half the ellipse will be drawn. It will be seen that the whole construction has been performed to find the centers h, p, q, i, and v, and that while v and i may be used to carry the curve around the other side or half of the ellipse, new centers must be provided for /?, p, and q; these new centers correspond in position to h,p, q. Straightedge Method. On a straightedge, lay off A B equal to one-half the short diameter and A C equal to one-half the long diameter. Determine points on the circumference of the ellipse by marking positions of A, as the point B is moved along the major axis and, at the same time, the point C along the minor axis. MENSURATION OF SOLIDS. MENSURATION OF SOLIDS. 33 THE CUBE AND THE PARALLELO PI FED. To Find the Surface of a Cube. Multiply the area of one side by 6. To Find the Surface of a Parallelepiped. Add together twice the area of the base, twice the area of the side, and twice the area of the end. To Find the Cubical Contents of a Cube or Parallelepiped. Multiply the area of the base by the perpendicular height. THE PRISM. To Find the Convex Surface of a Right Prism. Multiply the perimeter of the base by the altitude. To find the entire surface, add the areas of the bases. To Find the Contents of a Prism. Multiply the area of the base by the altitude of the prism. THE CYLINDER. To Find the Convex Surface of a Cylinder. Multiply the circum- ference of the base by the altitude. To find the entire surface, add the areas of the ends. To Find the Contents of a Cylinder. Multiply the area of the base by the altitude. THE SPHERE. To Find the Surface of a Sphere. Multiply the diameter by the circum- ference; or, square the radius and multiply it by 4 and 3.1416. To Find the Contents of a Sphere. Multiply the surface by one-third of the radius; or, multiply the cube of the diam- eter by .5286. To Find the Surface of a Zone. Multiply the height of the zone by the circumference of a great circle of the sphere. To Find the Contents of a Spherical Segment of One Base. Add the square of the height to three times the square of the radius of the base; multiply this sum by the height, and the product by .5236. The curved surface on a hemisphere is equal to twice its plane surface, and the curved surface on a quarter of a sphere is equal to its plane surface. THE PYRAMID. To Find the Convex Surface of a Pyramid. Multiply the per- imeter of the base by one-half the slant height. To find the entire surface, add the area of the base. To Find the Contents of a Pyramid. Multiply the area of the base by one-third of the altitude. THE CONE. To Find the Convex Surface of a Cone. Multiply the circumference of the base by one-half the slant height. To find the entire surface, add the area of the base. To Find the Contents of a Cone. Multiply the area of the base by one-third of the altitude. 34 MENSURATION. THE FRUSTUM OF A PYRAMID OR CONE. To Find the Convex Surface. Multiply one-half of the sum of the perim- f ^ . / v. eters or circumferences of the two bases r^F~^k $/h==^k ~* <* b y one-half the slant height. ill Am\ j//Ill 1^5 The entire surface is found by adding the areas of the two bases. To Find the Contents of a Frustum. Add together the sum of the two bases and the square root of their product, and mul- tiply the sum by one-third of the altitude of the frustum. CYLINDRICAL RINGS. A cylindrical ring is formed by bending a cylinder or pipe until its two ends meet. To Find the Surface of a Cylindrical Ring. To the thickness of the ring, add the inner diameter, multiply this sum by the thickness of the ring, and the product by 9.8696. To Find the Contents of a Cylindrical Ring. To the thickness of the ring add the inner diameter, multiply this sum by the square of one-half the thickness. To Find the Volume of an Irregular Body. Fill a vessel of known dimensions with water, and immerse the body. The contents will equal the volume of water displaced. THE PRISMOIDAL FORMULA. This formula is the invention of Mr. El wood Morris, C. E., of Philadelphia, and is extensively used in calculating the cubical contents of cuttings, embankments, etc. It embraces all parallelepipeds, prisms, pyramids, cones, wedges, etc., whether regular or irregular, right or oblique, with their frustums when cut parallel to their bases. In fact, it embraces all solids having two parallel faces or sides, provided these two faces are united by surfaces, whether plane or curved, on which, and through every point of which, a straight line may be drawn from one of the parallel faces to the other. To Find the Contents of Any Prismoid. Add together the areas of the two parallel surfaces, and four times the area of the section taken half way between them, and parallel to them; multiply the sum by the perpendicular distance between the two parallel sides, and divide the product by 6. PLANE TRIGONOMETRY. P.ane trigonometry treats of the solution of plane triangles. In every triangle, there are six parts three sides and three angles. These parts are so related that when three of the parts are given, one being a side, the other parts may be found. An angle is measured by the arc included between its sides, the center of the circumference being at the vertex of the angle. For measuring angles, the circumference is divided into 360 equal parts, called degrees; each degree into 60 equal parts called minutes. A quadrant is one-fourth the circumference of a cir- cle, or 90. The complement of an arc is 90 minus the arc; D C is the complement of B C, and the angle D C is the complement of B C. The supplement of an arc is 180 minus the arc; A E is the supplement of the arc B D E, and the angle BO E. In trigonometry, instead of comparing the angles of triangles or the arcs that measure them, we compare the trigonometric functions known as the sine, cosine, tangent, cotangent, secant, and cosecant. The sine of an arc is the perpendicular let fall from one extremity of the PLANE TRIGONOMETRY. 35 arc on the diameter that passes through the other extremity. Thus, CD is the sine of the arc A C. The cosine of an arc is the sine of its complement; or it is the distance from the foot of the sine to the center of the circle. B COTANGENT T ' Thus, C E or D equals the cosine of arc A C. The tangent of an arc is a line that is perpendicular to the radius at one extremity of an arc and limited by a line passing through the cen- ter of the circle and the other extremity. Thus, A T is the tangent of A C. The cotangent of an arc is equal to the tangent of the complement of the arc. Thus, B T' is the cotangent of AC. The secant of an arc is a line drawn from the center of the circle through one extremity of the arc, and limited by a tangent at the other extremity. Thus, T is the secant of A C. The cosecant of an arc is the secant of the complement of the arc. Thus, T' is the cosecant of A C. The versed sine of an arc is that part of the diameter included between the extremity of the arc and the foot of the sine. D A is the versed sine of A C. The coversed sine is the versed sine of the complement of the arc. Thus, B E is the coversed sine of A C. From the above definitions, we derive the following simple principles: 1. The sine of an arc equals the sine of its supplement, and the cosine of an arc equals the cosine of its supplement. 2. The tangent of an arc equals the tangent of its supplement, and the cotan- gent of an arc equals the cotangent of its supplement. 3. The secant of an arc equals the secant of its supplement, and the cosecant equals the cosecant of its supplement. Thus, sine of 70 = sine of 110. cosine of 70 = cosine of 110. cotangent of 70 = cotangent of 110. cosecant of 70 = cosecant of 110. . tangent of 70 = tangent of 110. secant of 70 = secant of 110. Thus, if you want to find the sine of an angle of 120 30', look for the sine of 180 - 120 30', or 59 30', etc. In the rt. /\ xy z, the following relations hold: sin c =-, h tan c = a h sec c = . cose = . Functions of the sum and difference of two angles: sin (A + B) = sin A cos B + cos A sin B. cos (4 + B) = cos A cos B sin A sin B. sin (A B) = sin A cos B cos A sin B. cos (A B) = cos A cos B + sin A sin B. Natural sines, tangents, etc. are calculated for a circle whose radius is unity, and logarithmic sines, tangents, etc. are calculated for a circle whose radius is 10,000,000,000. PRACTICAL EXAMPLES IN THE SOLUTION OF TRIANGLES. CASE 1. To Determine the Height of a Vertical Object Standing on a Horizon- tal Plane. Measure from the foot of the object any convenient horizontal 36 PLANE TRIGONOMETRY. distance A B\ at the point A, take the angle of elevation BAG. Then, as B is known to be a right angle, we have two angles and the included side of a triangle. Assuming that the line A B is 300 ft. and the angle B A C = 40, the angle C = 180 - (90 + 40) = 50. Then, sin C : A B : : sin A : B C, or .766044 : 300 : : .642788 : ( ), or 251.73+ ft. Or, by logarithms: Log 300 = 2.477121 Log sin 40 == 9.808067 12.285188 Log sin 50 = 9.884254 "27400934 or log of 251.73+ ft. Hence, B C = 251.73+ ft. CASE 2. To Find the Distance of a Vertical Object Whose Height is Known. At a point A, take the angle of elevation to the top of the object. Knowing that the angle I? is a right angle, we have the angles B and A and the side B C Assuming that the side B C = 200 ft. and the angle A = 30, we have a triangle as follows: Angle A = 30, B = 90, C = 60, and the side B C = 200 ft. Then, sin A : B C : : sin C : A B, or .5 : 200 : : .866025 : ( ), or 346.41 ft. By logarithms: Log 200 = 2.301030 Log sin 60 = 9.937531 12.238561 Log sin 30 = 9.698970 2.539591 or log of 346.41 ft. CASE 3. To Find the Distance of an Inaccessible Object. Measure a hori- zontal base line A B, and take the angles formed by the lines B A C and ABC. We then have two angles and the included side. Assuming the angle A to be 60, the angle B 50, and the side A B == 500 ft., we have the angle C = 180 (60 + 50) = 70. Then, sin 70 : A B : : sin A : B (7, and sin 70 : A B : : sin B : A C; or, .939693 : 500 : : .866025 : B C, or 460.8 +, and .939693 : 500 : : .766044 : A C, or 407.6+. By logarithms: Log 500-= 2.698970 Log sin 60= 9.937531 12.636501 = 9.972986 2.663515= log of 460.8+ . Log sin 70: Log500= 2.698970 Log sin 50= 9.884254 12.583224 Log sin 70 = 9.972986 2.610238 = log of 407.6+ . CASE 4. To Find the Distance Between Two Objects Separated by an Impassa- ble Barrier. Select any convenient station, as C, measure the lines CA and C B, and the angle . included between these sides. Then we have two sides and the included angle. Assuming the angle Cto be 60, the side CA, 600 ft,, and the side CB, 500 ft., we have the following formula: CA + CB : CA - CB : : tan A ^ B : tan B ~ A . Then, A + B 180 - 60 2 ^~ t or 60. B- A Then, 1,100 : 100 : : tan 60 : tan - PLANE TRIGONOMETRY. 37 or, 1,100 : 100 : : 1.732050 : .157459, or tangent of - , or 8 57'. Then, 60 + 8 57' = 68 57', or angle B, and 60 - 8 57' = 51 03', or angle A. Having found the angles, find the third side by the same method as Case 1. The above formula, worked out by logarithms, is as follows: Log 100 = 2.000000 Log tan 60 = 10.238561 12^238561 Log 1,100 = 3.041393 9.197168 = log tan of ^yA or 8 57'. Then, 60 + 8 57' - 68 57', or angle S, and 60 8 57' = 51 03', or angle A. NOTE. The greater angle is always oppo- site the greater side. CASE 5. To Find the Height of a Vertical Object Standing Upon an Inclined Plane. Meas- ure any convenient distance D C on a line from the foot of the object, and, at the point D, measure the angles of elevation EDA and EDB to foot and top of tower. We then have two triangles, both of which may be solved by Case 1, and the height above D of both the foot and top will be known. The difference between them is the height of the tower. CASE 6. To Find the Height of an Inaccessible Object Above a Horizontal Plane. Measure any convenient horizontal line A B directly toward the object, and take the angles of elevation at A and B. We will then have sufficient data to work with. Assuming the line A B to be 1,200 ft. long, the angle A, 25, and the angle DEC, 40, we have the following: As the angle D B C is 40, the angle ABC = 90 40, or 50. Then, having the side B C, and the angle DBC = 40, and the angle B D C = 90, we find the side CD by the same method as in Case 1. Second Method. If it is not convenient to measure a horizontal base line toward the object, measure any line A B, Fig. (6a), and also measure the horizontal angles BAD, A B D, and the angle of elevation DBC. Then, by means of the two triangles A B D and CBD, the height CD can be found. Then, with the line AB and the angles BAD and ABD known, we have two angles and the included side known. The third angle is readily found, and the side BD can be found. Then, in the triangle B D C, we have the angle B; by measure- ment, D = 90, and we have the side B D. Then, the side CD, or the vertical height, can be found by Case 1. CASE 7. To Find the Distance Between Two Inaccessible Objects When Points Can Be Found From Which Both Objects Can Be Seen. Wish- ing to know the horizontal distance between a tree and a house on the opposite side of a river, measure the line A B, and, at point A, take the angles DA C, and DAB, and, at the point B, take the angles CBA and CBD. Assume the length of A B = 400 ft. Angle DAC = 56 30'. Angle DA B = 42 24'. Angle C BA = 44 36'. Angle CBD = 68 SO*. 38 SURVEYING. In the triangle A B D, we have A B = 400 ft., the angle D A B = 42 24', the angle ABD = (44 36' + 68 50') = 113 26', and the angle A D B = 180 (42 24' + 113 26') = 24 10'. Then, according to Case 1, tind the side D B. We then have three angles and two sides of the triangle A D B. We find the third side A D by Case 1. Then in the triangle A B (7, we have the angles ABC and B A C, and the distance A B. From these we find the side A C. Then, in the triangle A D C, we have the sides A D and A (7, and the angle D A C, and we then find the side CD by Case 4. SURVEYING. Surveying is an extension of mensuration, and, as ordinarily practiced, may be divided into surface work, or ordinary surveying, and underground work, or mine surveying. With slight modifications, the instruments employed in both are the same, and consist of a compass if the work is of little importance, and accuracy is not required a transit, level, transit and level rods, steel tape or chain, and measuring pins, and sometimes certain acces- sory instruments, as clinometers or slope levels, dipping needles, etc., as will be described later. As the instrumental work is generally the same in both kinds of survey- ing, a description of the instruments and the usual practice on the surface will be first given, and afterwards an account of the methods of mine survey- ing as practiced in the anthracite regions of Pennsylvania, with the deviations from the practice of the former. THE COMPASS. The compass may be either a pocket compass, or a surveyor's compass, and may be used by holding in the hand, or with a tripod. The Jacob's staff, convenient for use on the surface, is frequently useless in the mine. The compass is not accurate enough for the construction of a general map of the mine. It is useful inasmuch as it enables the mine foreman to readily secure an approximate idea of the shape of the workings, and, from a plan constructed by its use, he can get an approximate course on which to drive an opening designed to connect two or more given points. If the opening is one that will be expensive to drive, and should be straight, the compass survey should never be relied on. TO ADJUST THE COMPASS. The Levels. First bring the bubbles into the center by the pressure of the hand on different parts of the plate, and then turn the compass half way around; should the bubbles run to the ends of the tubes, it would indicate that those ends were the higher; lower them by tightening the screws immediately under, and loosening those under the lower ends until, by estimation, the error is half removed; level the plate again, and repeat the first operation until the bubbles will remain in the center during an entire revolution of the compass. The sights may next be tested by observing through the slits a fine hair or thread, made exactly vertical by a plumb. Should the hair appear on one side of the slit, the sight must be adjusted by filing off its under surface on the side that seems the higher. The needle is adjusted in the following manner: Having the eye nearly in the same plane with the graduated rim of the compass circle, with a small splinter of wood, or a slender iron wire, bring one end of the needle in line with any prominent division of the circle, as the zero or 90 mark, and notice if the other end corresponds with the degree on the opposite side; if it does, the needle is said to cut opposite degrees; if not, bend the center pin by applying a small brass wrench, furnished with most compasses, about one- eighth of an inch below the point of the pin, until the ends of the needle are brought into line with the opposite degrees. Then, holding the needle in the same position, turn the compass halfway around, and note whether it now cuts opposite degrees; if not, correct half the error by bending the needle, and the remainder by bending the center pin. The operation must be repeated until perfect reversion is secured in the first position. This being obtained, it may be tried on another quarter of the MA ONE TIC t 'A It I A TION. 39 circle; if any error is there manifested, the correction must be made in ihe center pin only, the needle being already straightened by the previous operation. When again made to cut, it should be tried on the other quarters of the circle, and corrections made in the same manner until the error is entirely removed, and the needle will reverse in every point of the divided circle. TO USE THE COMPASS. In using the compass, the surveyor should keep the south end toward his person, and read the bearings from the north end of the needle. In the sur- veyor's compass, he will observe that the position of the E and W letters on the face of the compass are reversed from their natural position, in order that the direction of the sight may be correctly read. The compass circle being graduated to half degrees, a little practice will enable the surveyor to read the bearings to quarters estimating with his eye the space bisected by the point of the needle. The compass is usually divided into quadrants, and zero is placed at the north and south ends. 90 is placed at the E and W marks, and the gradua- tions run right and left from the zero marks to 90. In reading the bearing, the surveyor will notice that if the sights are pointed in a N W direction, the north end of the needle, which always points approximately north, is to the right of the front sight or front end of the telescope, and, as the number of degrees is read from it, the letters marking the cardinal points of the compass read correctly. If the E, or east, mark were on the right side of the circle, a N W course would read N E. This same remark applies to all four quadrants. The compass should always be in a level position. MAGNETIC VARIATION. Magnetic declination or variation of the needle is the angle made "by the magnetic meridian with the true meridian or true north and south line. It is east or west according as the north end of the needle lies east or west of the true meridian. It is not constant, but changes from year to year, and, for this reason, in rerunning the lines of a tract of land, from field notes of some years' standing, the surveyor makes an allowance in the bearing of every line by means of a ver- nier that is so graduated that 30 spaces on it equal 31 on the limb of the instrument, as shown in the figure. To Read the Vernier. As the compass vernier is usually so made that there are but 15 spaces on each side of the zero mark, it is read as follows: Note the degrees and half degrees on the limb of the instrument. If the space passed beyond the degree or half-degree mark by the zero mark on the vernier is less than one-half the space of half a degree on the limb, the number of minutes is, of course, less than 15, and must be read from the lower row of figures. If the space passed is greater than one-half the spacing on the limb, read the upper row of figures. The line on the vernier that exactly coincides with a line on the limb is the mark that denotes the number of minutes. If the index is moved to the right, read the minutes from the left half of the vernier; if moved to the left, read the right side of the vernier. To Turn Off the Variation. Moving the vernier to either side, and with it, of course, the compass circle attached, set the compass to any variation by placing the instrument on some well-defined line of the old survey, and by- turning the tangent screw (slow-motion screw) until the needle of the com- pass indicates the same bearing as that given in the old field notes of the original survey. Then screw up the clamping nut underneath the vernier and run all the other lines from the old field notes without further alteration. The reading of the vernier on the limb gives the amount of variation since the original survey was made. The accompanying map shows the general course and direction of isogonic lines (those passing through points where the magnetic needle has the same 40 SURVEYING. declination), in all parts of the United States and Mexico for the year 1000. These lines are drawn full when compiled from reliable records, but dotted in other places. The declination is marked in degrees at each end of every alternate line, the sign + indicating a west declination, and the sign an east declination. The yearly variation, or change of declination, for the period 1895-1900 is marked in numerous places on the map. Th'e annual change in declination is given in minutes; a -f sign signifies increasing west or decreasing east declination, a sign the reverse motion. Stations to the right of the agonic curve, or curve of no declination, have west declination, and those to the left, east declination. The large black circles or dots indicate the capitals of the several states. The use of this chart is quite simple. The declination for any place within its borders is either found by inspection or by simple interpolation between the two adjacent curves; the value found is for 1900. For any other year (and fraction), a reduction for secular change between the epoch and given date must be applied. The annual change of the declination during the period 1895-1900, expressed in minutes of arc, is indicated in the chart ( + for increasing west or decreasing east declination and for the reverse motion). The amount varies in time, but not sufficiently during a brief interval of years to cause any serious inaccuracy, and the values given on the chart can be used for a number of years to come for all practical purposes; its variation with geographical position must be estimated from the map. THE TRANSIT. The transit is the only instrument that should be used for measuring angles in any survey where great accuracy is desired. The advantages of a transit over a vernier compass are mainly due to the use of a telescope. By its use angles can be measured either vertically or horizontally, and, as the vernier is used throughout, extreme accuracy is secured. The illustration shows the interior construction of the sockets of a transit having two verniers to the limb, the manner in which it is detached from its spindle, and how it can be taken apart when desired. The limb b is attached to the main socket c, which is carefully fitted to the conical spindle h, and held in place by the spring catch s. The upper plate a, carrying the compass circle, standards, etc., is fastened to the flanges of the socket fc, which is fitted to the upper conical surface of the main socket c. The weight of all the parts is sup- ported on the small bearings of the end of the socket, as shown, so as to make as little friction as possible where such parts are being turned as a whole. A small conical center, in which a strong screw is inserted from below, is brought down firmly on the upper end of the main socket c, thus holding the two plates of the instrument securely together, and, at the same time, allow- ing them to move freely around each other. The steel center pin on which the needle rests is held by the small disk fastened to the upper plate by two small screws above the conical center. The clamp to limb dj, with clamp screw, is attached to the main socket. The instrument is leveled by means of the leveling screws I and placed exactly over a point by means of the shifting center. The plummet is attached to the loop p. The verniers on a transit differ from those on a compass in detail only. tec* //o* 100 110" I DO 13 CHART SHOWING THE ISOGONIC AND AGONIC LINES IN THE UNITED STATE 70 YEAR lyoi), AND THE MI-:AX ANNTAL CHANGE FOR THE PERIOD 1885-190D. ADJUSTING THE TRANSIT. 41 The principle is the same. The transit vernier is so divided that 30 spaces on it equal in length 29 on the limb of the instrument. The method of reading it is practically the same as reading a compass vernier, except that on the transit the vernier is made with all of the 30 divisions on one side of the zero mark. Each division of the vernier is therefore J^, or, in other words, 1 minute shorter than the half-degree graduations on the limb. In the figure the reading is 20 10'. If the zero on the vernier should be beyond 20 on the limb of the transit, and the line marked 10 should coincide with a line on the limb, the - -ading would be 20 40 7 . case the 12th line from xero should coincide with a line on the limb, the read- ing would be 20 42', etc. In some transits, the graduated limb has two sets of concentric gradua- tions, the zero in both being the same, and, while the outside set is marked from each way to 90, and thence to on the opposite side of the circle, the other set is marked from to 360 to the right, as a clock face. The inside set has the N, S, E, and W points marked, the of the inside set being taken as north. The interior of the telescope is fitted up with a diaphragm or cross- wire ring to which cross-wires are attached. These cross-wires are either of platinum or are strands of spider web. For inside work, platinum should be used, as spider web is translucent and cannot readily be seen. They are set at right angles to each other and are so arranged that one can be adjusted so as to be vertical and the other horizontal. This diaphragm is suspended in the telescope by four capstan-headed screws, and can be moved in either direction by working the screws with an ordinary adjusting pin. The transit should not be subjected to sudden changes in temperature that may break the cross-hairs. In case of a break, remove the cross-hair diaphragm and replace the broken wire. The intersection of the wires forms a very minute point, which, when they are adjusted, determines the optical axis of the telescope, and enables the surveyor to fix it upon an object with the greatest precision. The imaginary line passing through the optical axis of the telescope is termed the line of collimation, and the operation of bringing the intersection of the wires into the optical axis is called the adjustment ofthelineofcottimation. All screws and movable parts should be covered, so as to keep out acid water or dust. If this is not done, the mine work will soon use up a transit. The vertical circle on the transit may be a full circle or a segment. The former is to be preferred, as it is always ready without intermediate clamp screws. If the dip of a sight is to be taken, the tape must be held at the transit head, and stretched in the line of sight. If the pitch of the ground is to be taken, the point of foresight must be at the same height as the axis of the transit, and the sight will then be parallel to the surface. The angle of dip is read " plus" or "minus," as it is above or below the horizontal plane. If we have the dip of a sight, and the distance between the transit head and the point of sight, we can get the vertical and horizontal components of that distance from the table of sines and cosines. ADJUSTMENTS OF THE TRANSIT. The use of a transit tends to disarrange some of its parts, which detracts from the accuracy of its work, but in no way injures the instrument itself. Correcting this disarrangement of parts is called adjusting the transit. First Adjustment. To make the level tubes parallel to the vernier plate. Plant the feet of the tripod firmly in the ground. Turn the instrument until one of the levels is parallel to a pair of opposite leveling screws; the other level will be parallel to the other pair. Bring the bubble in each tube to the middle with the pair of leveling screws to which the tube is parallel. Next turn the vernier plate halfway around; that is, revolve it through an angle of 180. If the bubbles have remained in the middle of the tubes, the levels are in proper adjustment. If they have not remained so, but have 42 SURVEYING. moved toward either end, bring them half way back to the middle of the tubes by means of the capstan-headed screws attached to the tubes, and the rest of the way back by the leveling screws. Again turn the vernier plate through 180, and if the bubbles do not remain at the middle of the tubes repeat the correction. Sometimes the adjustment is made by one trial but usually it is necessary to repeat the operation. Each level must be adjusted separately. Second Adjustment. To make the line of collimation perpendicular to the horizontal axis that supports the telescope. With the instrument firmly set at A, and carefully leveled, sight to a pin or tack set at a point B, about 400 ft. distant, and on level or nearly level ground. Reverse the tele- scope; that is, turn it over on its axis until it points in the opposite direction, and set a point at about the same dis- tance, which will be at Z>, for example, if this adjustment needs correction. Unclamp the vernier plate, and, without touching the telescope, revolve the instrument about its vertical axis sufficiently far to take another sight upon the point B. Then turn the telescope on its axis and locate a third point, as at C. Measure the distance CD, and at E, one-fourth of the distance from Cto D, set the pin or tack. Move the cross-hairs, by means of the capstan -headed screws, until the vertical hair exactly covers the pin at E, being careful to move it in the opposite direction from that in which it appears it should be moved. Haying done this, and then having reversed the telescope, the line of sight will not be at the point B, but at G, a distance from B equal to CE. Again sight to J5, then reverse, and the pin will be at F in the same straight line with A B. It may be necessary to repeat the operation to secure an exact adjustment. Third Adjustment. To make the horizontal axis of the telescope parallel to the vernier plate, so that the line of collimation will revolve in a vertical plane. Sight to some point A at the top of a building, so that the tele- scope will be elevated at a large angle. Depress the telescope, and set a pin on the ground below at a point B. Loosen the clamp, turn over the telescope, and turn the plate around suffi- ciently far to take an approximately accurate sight upon the point A. Then clamp the instrument and again take an exact sight to the point A. Next depress the telescope, and set another pin on the ground, which will come at (7. The distance B C is double the error of adjustment. Correct the error by raising or lowering one end of the telescope axis by means of a small screw placed in the standard for that purpose. The amount the screw must be turned is determined only by repeated trials. Fourth Adjustment. To make the axis of the attached level of the telescope parallel to the line of collimation. Drive two stakes at equal distances from the instrument and in exactly opposite directions. Level the plate carefully, and clamp the telescope in a horizontal position, or as nearly so as possible. Sight to a rod placed alternately upon each stake, and have the stakes driven down until the rod reading is the same on both stakes. When this condition is reached, the heads of the stakes are at the same level. Then move the instrument beyond one stake and set it up so that it will be in line with both stakes. Level the plate again and elevate or depress the telescope so that, when a sight is taken to the rod held on first one stake and then on the other, the reading will be alike on both. In this position, the line of collimation is level, and the bubble in the level attached to the telescope should stand in the center of the bubble tube. If it does not, bring it to the center by turning the nuts at the ends of the tube, being careful at the same time to keep the telescope in the position that gives equal rod readings on both stakes. THE CHAIN OR STEEL TAPE AND PINS. The chain, which is generally 50 or 100 ft. long, should be made of annealed steel wire, each link exactly 1 ft. in length. The links should be so made as to reduce the liability to kink to a minimum. All joints should be brazed, and handles at each end of D shape, or modifications of D shape, should be CHAIN AND PINS. 43 provided. These handles should be attached to short links at each end, and the combined length of each of these short links and one handle should be exactly 1 ft. The handles should be attached to the short link in such a manner that the chain may be slightly lengthened or shortened by screwing up a nut at the handle. It should be divided every 10 ft. with a brass tag, on which either the number of points represents the number of tens from the front end, or the number of tens may be designated by figures stamped on the tags. When a chain is purchased, one that has been warranted as " Correct, U. S. Standard," should be selected, and, before using it, it should be stretched on a level surface, care being taken that it is straight, and no kinks in it, and the extremities marked by some permanent mark. These marks can be used in the future to test the chain. It should be tested frequently, and the length kept to the standard as marked when it was new. In chaining, the chainmen should always remember the axiom that a straight line is the shortest distance between two points. Ordinarily, the chain should be held horizontally, and if either end is held above the ground, a plumb-bob and line should be used to mark the end of the chain on the ground. If used on a regular incline, the chain may be stretched along the incline, and, by having the amount of declination, the horizontal and vertical distances may either be calculated or found in the Traverse Table. For accuracy, steel tapes are now almost exclusively used by the leading mining engineers, on account of their greater accuracy as compared with chains. The steel tape is simply a ribbon of steel, on which are marked, by etching, or other means, the different graduations, which may be down to inches or tenths of a foot, or may be only every foot. It is wound on a reel, and may be any desired length up to 500 ft. A well-made tape should not vary T ^ ft. in 100 ft., at any given standard of temperature. The steel of the tape should not be too high in carbon, or it will be brittle and liable to snap on a short bend, nor should it be of too soft steel, or it will stretch when strongly pulled. Careful gunsmiths can make and repair steel tapes with a high degree of accuracy, and fully as reasonably as the instrument makers. For outside work, tapes 1,000 ft. long have been made, but 500 ft. will be found as long as can well be used in a mine, owing to the lack of long sights, and to the increased weight of so long a tape. The average length is 300 ft. The 300 ft. are divided into 10-ft., 5-ft., 2-ft., or 1-ft. lengths, as desired, and the tenths and hundredths of a foot are read by means of a pocket tape or measuring pin. Sometimes there is an extra division before the zero mark, which is divided into feet and the first foot into tenths. With such a tape, a distance can be accurately measured to tenths, or even quite approximately to hundredths of a foot. The ends are fitted with eyes on swivel-joints, to prevent straining by twisting. Handles of various forms have been devised to enable the tape to be stretched, or to clamp a broken end. Some parties use ordinary springs to prevent overstraining, and, in certain cases, spring scales are used, and the same degree of tension can be readily produced, and, in this way, the exact amount of sag can be calculated for any length, and the necessary correction made. To keep a mark on the tape for frequent reference, a clip (made by bending sharply on itself a piece of steel in. X 3 in.) is slipped upon the tape, where it will remain unless subjected to considerable force. Reels for winding the tape are made of iron or wood, and vary greatly in size and shape. When distances do not come at even feet, the fractional part of the foot should always be noted in tenths. Thus, 53 ft. and 6 in. should always be noted as 53.5 ft. Pins. Pins should be from 15 to 18 in. long, made of tempered-steel wire, and should be pointed at one end, and turned with a ring for a handle. When using a 50-ft. chain, a set of pins should consist of eleven, one of which should be distinguished by some peculiar mark. This should be the last pin stuck by the front chainman. When all eleven pins have been stuck, the front chainman calls "Out!" and the back chainman comes forward and delivers him the ten pins that he has picked up, and he notes the "out;" W 7 hen giving the distance to the transitman, he counts his "outs," each of which consists of 500 ft., and adds to their sum the number of fifties as denoted by the pins in his possession, and the odd number of feet and fractional parts of a foot from the last pin to the front end of the chain. 44 SURVEYING. The accuracy and value of a survey depend as much on the careful work of the chainmen as on anything else, and no one should be allowed to either drag or read the chain that is not intelligent enough to appreciate the importance of extreme accuracy. Pins are generally used in outside work, where they can be easily stuck into the ground, readily seen, and avoided, and the chances of their being disturbed are slight. Inside work generally contains so many chances of error in their use that they are usually abandoned in favor of other methods. If the sight be longer than the length of the tape, it is usual to drive a tack in a sill or a collar at a point intermediate between the stations, and take a measurement to the tack from each station, with the dip of the sights; or a tripod is set up in the line of sight, and the horizontal distance is measured from each station to the string of the plumb-bob under the tripod. The first method is the more accurate. Plumb-Bob. The plumb-bob takes the place of the transit rod in under- ground work, as the stations are usually in the roof, and strings are hung from them to furnish foresights and backsights. Plumb-bobs vary in weight and shape. At various times and in various countries where mine surveys have been made, the idea of sighting at a flame has been considered, and, from rough methods of setting a lamp on the floor on foresight and backsight, there have arisen various forms of plummet lamps. The idea is to continue the practice of sighting to a flame, but to make that flame exactly under the station, and to avoid the difficulty in sighting to the string of the plummet. The idea is good, but there has never been devised a plummet lamp that would be as free from error under all circumstances as the old-fashioned plummet, so that the majority of the best engineers have gone back to the plummet. The best plummet is the one that combines the least surface with the greatest weight, and the ordinary shapes used for outside work are the best for inside also. In a " windy " place, a hole can be dug in the ballast of the track and the " bob " let into this shelter where it will be unaffected by the air. The cord is best illuminated by placing a white paper or card- board behind it and holding the lamp in front and to one side. The string shows as a dark line against a white ground, and there is less difficulty in finding it than when the light is placed exactly behind it, and in this way a careless man cannot burn the string by poking the flame against it. The white background will also illuminate the cross-hairs of the transit. The backsight "bob " can be made of lead, as there are no " centers " to be set by this man. A number of varieties have been made for the foresight, to aid him in " center setting "; but all get out of order easily. A quick man will do as good work with the old-style bob, and have none of the accidents common to the others. In general, it may be said that the instruments used for outside work will be sufficient for mine work also. The clinometer, or slope level, is a valuable instrument for side-note work; but it is not accurate enough for a survey, and its place is taken by the vertical circle on the transit. There are two styles of clinometer, with a bubble and with a pendulum. The latter is the old-fashioned and more accurate German ' ' Gradbogen ' ' that is found on some old corps. The bubble variety is much more easily rendered worthless by the breaking of the bubble tube, and in general is not so accurate as the other style, which consists of a semicircular protractor cut out of thin brass and furnished with hooks at each end, that it can be hung on a stretched string so that the string will pass through the and 180 points. The dip is read by a pendulum swung from the center of the circle. If made sufficiently large it will readily read to quarter degrees. By inclining the string parallel to the surface and hanging the clinometer, the dip will be obtained. A pocket instrument combining a compass and clinometer can be obtained from any dealer in surveying instruments. FIELD NOTES FOR AN OUTSIDE COMPASS SURVEY. Call place of beginning Station 1. Stations. Searings. Distances. 1-2 N 35 E 270.0 At 1 + 37 ft. crossed small stream 3 ft. wide. At 1 -f 116 ft. = first side of road. At 1 + 131 ft. = second side of road. At I + 137 ft. = blazed and painted pine tree, 3 ft. left, marked for a "go by." TRANSIT S UR VE YING. 45 Station 2 is a stake at foot of white-oak tree, blazed and painted on four sides for corner. 2-3 N 831 E 129.0 Station 3 is a stake-and-stones corner. 3-4 S 57 E 222.0 3+64 ft. = center of small stream 2 ft. wide. 3 + 196 ft. = white oak " go by," 2 ft. right. Station 4 = cut stone corner. 4-5 S 34i W 355.0 4 -1- 174 ft. = ledge of sandstone 10 ft. thick, dipping 27 south. 5-1 N 56i W 323.0 5 + 274 ft. = ledge of sandstone 10 ft. thick, dipping 25 south (evidently continuation of same ledge as at 4 -f- 174). Station 1 = place of beginning. TRANSIT SURVEYING. To Read an Angle. The angle read may be included or deflected. If we set up at with backsight at B and foresight at C, we shall find that there are two angles made by the line C with the line BOA, namely the included angle B C\ and the deflected angle CO A. To Read the Included Angle. Set the zeros of vernier and graduated limb together accurately, and clamp the plates. Turn the telescope on the backsight, with the level bubble down, and, when set, fasten lower clamp so as to fix both clamped plates to the tripod head. Loosen the upper clamp and turn the telescope to C and set accurately. The vernier will read, for example, "45 left angle." To Read the Deflected Angle. Arrange verniers as above, and be sure and turn the telescope over on its axis till the bubble tube is up, and then take the backsight and fix lower clamp. Turn the telescope back (this is called " plunging" the telescope) and sight to foresight and fix as before. The vernier will read a "right angle of 135." The sum of included and deflected angles must always be 180. NOTE. In making a survey by included angles, we must add or subtract 180 at each reading to have the vernier and compass agree; by deflected angles, they will agree without the above addition or subtraction, and the latter method is generally used. TO MAKE A SURVEY WITH A TRANSIT. By Individual Angles. Set vernier at zero of limb, plunge telescope, and, when set on backsight, loosen needle and read bearing of the line from back- sight to set-up. Plunge telescope back and set on foresight and read both needle and vernier. The difference in needle readings should agree with the vernier reading within 15', as local attraction will affect the needle equally on both sights. NOTE. Any mass of iron or steel that may and will be moved during the readings of the needle, will affect the same and destroy the value of the needle as a check. The tape and other iron materials should not be moved during the taking of angles. By Continuous Vernier. Set vernier at zero, unclamp compass needle, and, when stationary, turn the north point of compass limb so as to coincide with the north point of the needle. Fix lower clamp, plunge telescope, and take backsight by loosening upper clamp. The vernier and needle should agree in giving the magnetic bearing of the line from backsight to set-up. Record this in note book; plunge telescope, and take foresight. Needle and vernier should agree as before. After making record, set up over foresight and take sight to station just left with telescope plunged,- having first seen that the vernier reads exactly as it did on the last foresight, as a slip in carrying the transit from one station to another, which is not detected at the time, can never be checked afterwards when the final work is found to be in error. The foresight is taken as before. On every sight the needle and vernier should agree if there is no local attraction of the needle. If we can see all the corners of a field that is to be surveyed from a central point, we can make the survey by setting up at that point, and, with one 46 TRANSIT S UR VE YING. corner as a backsight, take all the other corners as foresights with but one set-up, and by measuring from this point to all of the corners; or we can set up at any corner and run a line of survey around the field. This latter method is called meandering. Both methods will give the same result when plotted; but the former is much quicker, as the boundaries of a tract are frequently overgrown with bushes that must be cleared to allow a sight; while a central point can frequently be found that will allow a free sight to all the corners, and the distance can be measured by tape, or stadia. As the central point is nearer the corners than they are to one another, it follows that a shorter distance must be chained or cut in the case of a central set-up. Outside surveys may be made for many purposes. It matters not what the purpose is, the work should be fully and accurately done, and the map should contain everything that will throw light upon the subject. If 'the outside work is to be connected with inside surveys, there are a number of points to be observed, and they will be given under the head of underground work. Meridians, or Base Lines. The surveys must be based on some meridian, and started from some fixed point. There are four kinds of meridians, or "base lines." first. A line already on the ground, as one of the sides of the tract, is taken as a base. The subsequent work is referred to one or both ends of this line, and all angles measured are taken as deviations from it. Second. A stone post is sunk in the ground, or, better, an iron plug is put into rock "in place' 1 that is, not loose rock, even if a large b9ulder at such a distance from the works as to be beyond the influence of moving machinery, and a line of sight is taken to some permanent natural object, as far distant as can be clearly seen under adverse circumstances, as cloudy or dark weather. This line of sight is the base line, and the plug is the origin. No measurements of distance are needed. If no natural objects exist, a station is set up at a distance, so as to be as permanent as possible, and angles are turned from this to other points, so as to check any movement in it. Generally there are a number of tall chimneys, church spires, etc. to be found. While this is preferable to the first, it gives no method of check in underground work, and is seldom used. Third. The magnetic meridian is taken as the base line. The transit is set up over a plug, as just noted, and the subsequent work is as described under running continuous vernier. As the needle is subject to constant variation, this base line will afford a check underground only for a short time after the meridian is established, and all subsequent work can be checked only by applying the difference between the variation at the time of establishment, and at the time of making the survey. If the time of establishing the survey should be lost, the base line would become no better than that noted in Case 2. fourth. The true meridian is taken as a base. The true north and south line may be determined by observing the North Star, Polaris, or by observing the sun. The North Star does not lie exactly at the North Pole, but revolves about it in a small circle. There are two times in a day when it is exactly above or below the pole, and we take our sight at one of these times, when our transits do not have their graduated limbs made accurately enough to apply the proper angle for a sight at any other time. If we do not know the time when the star is crossing the meridian, we can find it by remembering that the fourth star in the handle of the "dipper" is in the same vertical plane with the north star 17 minutes before the latter f olaris ^ crosses the meridian. " The true meridian will give us an invariable base line. At any date after the establishment of the same, we can check the work above or below ground by applying the variation of the needle. To Find the True North by an Observation of the North Star, Polaris, at Etongation. This star has a motion around a small circle, the azimuth angle of which from the north is known for different latitudes. The star may be readily found by following the line of the so-called pointers in the Big Bear, or Dipper. The time of the greatest eastern or western elongation is found from a table. Some 10 minutes before this time .. the transit is carefully set up and leveled over a peg. ^Observer The cross- wires are made to bisect the star; they are THE SOLAR ATTACHMENT. 47 illuminated by a light held under the reflector fastened on the object end of the telescope. The star is followed with the cross-wires until its motion toward the point of its greatest elongation ceases. The telescope is lowered vertically, care being taken, of course, not to move it horizontally, and a peg is set up on the line, say 300 ft. or 400 ft. distant. The next morn- ing the correction is made for the star's azimuth. These corrections are different for different latitudes and different years. They are to be found in the nautical almanac. The method "by equal shadows" may be used with considerable accu- racy, if we take a sufficiently long staff, or can obtain the shadows of a tall spire on a level surface. A vertical staff casts equal shadows at the same time before and after noon. If we drive a stake at any time before noon, in the extremity of the shadow cast by such a staff, and measure its distance from the staff, we have one leg of an angle. After noon we wait till the shadow becomes exactly as long as the distance measured, and drive a stake at the extremity of the shadow.. Aline bisecting the angle made by lines drawn from these two stakes to the staff will be in the meridian. Establishing a Meridian Line With the Solar Attachment. The angle from the equator to the horizon of a place is its latitude; consequently, from the zenith to the pole is the colatitude, or 90 _ latitude. The angular dis- tance from the equator to the sun is the declination; consequently, from the sun to the pole is the polar dis- tance. The angular distance from the horizon to the sun is the sun's altitude; consequently, the zenith distance is the angular distance between the sun and the zenith. Adjustments of Burt's Solar Attachment. After the instrument has been carefully leveled, the zero of the vernier of the solar is placed opposite the zero of the arc. The horizontal plates of the instrument are clamped, and the sun's image brought between the horizontal lines of either silver plate by any manipulation of the instrument and attachment possible, keeping the plates horizontal and the zero of the vernier opposite the zero on the arc. When the image is accurately between the horizontal lines, the arc is revolved so that the image falls on the other plate; this must be done rapidly, as the sun's image moves. If it does not fall between the lines, half the error is corrected by the tangent screw of the solar and half by the tangent screw of the telescope. The operation is repeated until the sun's image falls between the lines of the second plate, after a revolution of the arc, it having been made to fall between the lines of the first, as described. Near noon is a good time to make this adjustment, as the sun's apparent motion is not so rapid. The zero of the vernier is now brought opposite to the zero of the arc by loosening the screws that fasten the vernier, and sliding it as may be necessary. It is often difficult to make the zeros come exactly opposite each other, as the vernier plate is apt to move slightly when the screws are tightened again. The second adjustment is to make the tops of the rectangular blocks of the solar attachment level, when the telescope is level and the arc of the solar is set at zero. Level the transit carefully, as before described, set the solar at zero and place the level, furnisheVl with the solar, across the tops of the blocks. If the bubble comes to the center of the tube, no correction is needed; if it does not, correct the error by turning the screws under the hour circle, care being taken in this as in all other movements of these adjusting screws, to leave them tight after the correction. Revolve 180 and correct again if necessary. Placing the blocks ( .0 horizontally from their first position, go through the same operation as described until in all positions the bubble remains centered. To Use the Solar. Before this instrument can be used at any given place, it is necessary to set off upon its arcs both the declination of the sun, as affected by its refraction for the given day and hour, and the latitude of the place where the observation is made. 48 TRANSIT S UK VE YING. The declination of the sun as given in the ephemeris of the nautical almanac from year to year, is calculated for apparent noon at Greenwich, England. To determine it for any other hour at a place in the United States, reference must be had, not only to the difference of time arising from the difference of longitude, but also to the change of declination during that time. The longitude of the place, and therefore its difference in time, if net given directly in the tables of the almanac, can be ascertained very nearly by reference to that of other places given which are situated on, or very nearly on, the same meridian. It is the practice of surveyors in states east of the Mississippi to allow a difference of 6 hours for the difference in longitude, calling the declination given in the almanac for 12 M. that of 6 A.M. at the place of observation. Beyond the meridian of Santa Fe, the allowance would be about 7 hours; and in California, Oregon, and Washington, about 8 hours. Having thus the difference of time, we very readily obtain the declination for a certain hour in the morning, which would be earlier or later as the longitude was greater or less, and the same as that of apparent noon at Greenwich on the given day. Thus, suppose the observation made at a place 5 hours later than Greenwich, then the declination, given in the almanac for the given day at noon, affected by the refraction, would be the declination at the place of observation for 7 A.M. This give us the starting point. To obtain the declination for the other hours of the day, take from the almanac the declination for apparent noon of the given day, and, as the declination is increasing or decreasing, add to, or subtract from, the decli- nation of the first hour the difference of one hour as given in the ephemeris, that will give, when affected by the refraction, the declination of the succeeding hour. Proceed in like manner to make a table of the declinations for every hour of the day. To Find the True North With the Burt Solar. Find from an ephemeris or nautical almanac the sun declination for noon of the day of observation at Greenwich. Find the declination for the hour of observation at the place of observation by first figuring what time it is at the place of observation when it is noon at Greenwich. If the place of observation is west of Green- wich, it will be earlier there; if east, later, and in either case the difference will be one hour for every 15 of longitude. If the place is west, subtract the hour just found as described from the hour of the observation, and multiply the hourly difference, also taken from the ephemeris, by the remainder. If the declination is increasing from the equator either north or south, add this product to it; if decreasing, subtract it. A table of refractions is given in the ephemeris for the different latitudes and the different hours of the day. This refraction is to be added if the declination is north, and subtracted if the declination is south. Having thus ascertained the declina- tion, lay it off on the declination arc. Set the colatitude of the place off on the vertical arc after having leveled the instrument carefully with clamped horizontal plates at zero. Always in solar observations it is well to level by means of the upper telescope bubble. Now, revolve the horizontal plates still clamped, and also the declination arc, around its polar axis until the sun's image is exactly between the horizontal lines of the silver plates. When the sun's image is between these lines, the object end of the telescope will be pointing north. To Take the Latitude With Burt's Solar. A few minutes before apparent noon clamp the plates at zero, level the instrument carefully, and set the zero of the vernier opposite the zero of the vertical arc. Lay off the declina- tion, corrected for noon at the place of observation and for refraction, on the declination arc, and set the time mark on the declination arc opposite XII on the hour dial. Bring the sun's image between the horizontal lines of the silver plate by moving the plates horizontally and the telescope vertically, clamp both plates and telescope and follow with the tangent movements the rising sun. Be careful to stop when the sun ceases to mount. For a moment before apparent noon there is no perceptible motion of the image. The reading on the vertical arc is the colatitude of the place. The colatitude should never be taken this way for direct-sight calcula- tions, for while it satisfies the automatic solution of the true north, it may not be accurate, and the latitude needed for direct-sight calculation should be true to within a minute. With the Burt solar there is at times what is called a false image to guard against, an image that comes between the lines of the silver plates when the object end of the telescope is not pointing TRANSIT S UR VE YING. 49 north. If the time be observed on the hour dial, or the magnetic north be noticed, no error need ever occur on this score, for with the false image the time will be out considerably and also the magnetic variation. General Remarks. With the base line located and the survey made, we see, by coming back to the point from which we started or " closing" the work, whether it be correct in distance or angle. If it be in error, see if the error can be located (as will be shown under plotting), and if it can be found, run those parts over again; if not, repeat the whole survey. Shoving the work, as it is called, or " doctoring " it so that it will close, is the poorest practice that an engineer can engage in, as all subsequent work that depends on a doctored survey must be doctored to fit the faulty work even if it be right in itself. Every engineer should be able to swear not that he "thinks the survey is accurate," but " that he knows it to be so," if he should be called as a witness in court. One of the causes of inaccuracy is haste. To make a complete map, the engineer should first make a survey around the tract to be worked, locating all the prominent physical features and improvements. If he can do so, he should make a topographical map of the tract at once; but, if time is limited, by running the vertical as well as the horizontal angle, he can carry the tidal elevation or the elevation above some assumed datum, to every station, and mark it on the map at that point. Then as he makes subsequent surveys, he can gradually get data enough to make a fairly complete topographical map in course of time. Every ledge of rock in place should be located, and the amount and direction of 'its dip, as well as the character of the rock, should be marked neatly on the map. The streams of water on the tract should be regarded as of primary impor- tance, and should be located with exactness. With a true meridian base" line w r e can connect maps made at different places with little trouble. This is especially useful with adjoining mines connected at but one point. Having made the survey and come home, we must examine all the apparatus and see if the instruments are out of adjust- ment, as such a fact will prevent our bothering over work that will not close. It will assure us, also, that we can start out at a moment's notice with no thought of the adjustment of our tools. A famous wit said that the proper time to strop a razor was just after you had used it, as you then knew how much it needed it. The same will apply to surveying instruments and tools especially for underground work. Here the lamp smoke, powder gases, mine dust, paint smears, acid water from "droppers," and the other abominations incident to underground surveying, especially in a coal mine, will so cover the tools that they would be useless if left uncleaned half a dozen times. As soon as the corps comes back from the mine, and before the clothes are changed, the tape must be stretched, tested, wiped, and oiled. It can be inspected to see if marks are too much worn, or it stands in need of mending, the marking pot is cleared of "muck," and fresh white paint is mixed, if the corps is going out in 24 hours; the plummets will have their strings overhauled and freed from knots; hatchets will be sharpened, and axes ground, pouches overhauled, and a supply of tacks or " spads " taken. Then the transitman changes his clothes and sets up the transit, wipes it with a cloth wet with alcohol, so as to remove dirt, oil, and paint. If water has gotten between the graduated limb and compass box, the verniers must be uncovered and the whole wiped dry. If the sulphureted hydrogen from the powder smoke has tarnished the silver surfaces of any of the graduated circles, it must be removed with whiting. Alcohol should be always used instead of water, as it will quickly evaporate and leave the parts dry. The telescope glasses are then wiped with soft chamois leather, and the instru- ment is tested for want of adjustment before putting it away in its box. When going to and from work, the transit should not be carried on the transit head, or the spindle will become sprung. Nor should it be carried with the arm crooked under the telescope, as the weight comes on the axis, and that soon gets sprung so that all the adjusting in the world will not make it work right. When carried in the hand, it should be reversed and the hand slipped under the compass plate and brought over so as to clamp both plates. In this way there will be no strain on any part. In case of a "fall" in the mine, remember that the transit is the baby to be protected, and stand a few bumps to save a strained or broken instrument, that will end the work for some time. Plotting. A "plot" is not only a piece of ground with bodies of water, roads, vegetation, etc. upon it, but refers also to the map of the same drawn to a given scale, and showing all of the above natural features. Plotting is 50 TRANSIT S UR VE YING. the making of such a map from notes of a survey, and may or may not require the permanent placing of the stations on the map, by which the survey is made. In underground work, the exact location and the retention of those stations is a matter of the first importance, and is secondary only to the exact plotting of the side notes. The scale of the plot is generally as large as will show the points of interest in the property; but in Pennsylvania, the maps for coal mines must be drawn to a scale of 100 ft. to an inch. There are two methods of plotting: by protractor, and by coordinates. When the scale is sufficiently large, it is a matter of little choice which method is used, if the work be carefully done with exact instruments; but with small scales 100 ft. or above, to the inch we should use the method by coordinates. With the latter scale, the prick of a pin on the paper will represent a foot square, or a circle slightly larger than a foot in diameter. If the next station is to be located from the pin prick of the first, and that is exactly located, we may not hit the exact center of that small indentation. In fact, the chances are greatly against our doing so, and the location of the second station will probably be in error. If we have a bad habit of placing the protractor or the straightedge against one side of the pin pricks, or pencil marks, when the scale is large, we shall constantly be introducing a "personal error," as it is called, and the sum of all the errors made at each of 100 stations will bring our final point very much out of the way. On this account, and from the fact that no protractor that is movable can be used without the chances of slipping while the angle is read or marked, has led all careful engineers to abandon its use in favor of the method by coordinates. When the scale is from 1 to 25 ft. to an inch, the errors are small enough to make little chances of variation in a close of ten or twelve stations; when the survey is of short sights from a main line to points where no further work is to be done, the protractor will afford a quick method of plotting. There is a chance of error in both methods that must be noted here, where the survey is not completed at one time. If the map be made in a day or two, and will never be extended by subsequent work, there will be no chance of error from a change in the paper on which it is made, due to moisture or dryness; but if the map be made on a series of very damp days, or a series of very dry ones, a change in the weather to the other extreme will swell or shrink the map. The general tendency in a large mine map that is frequently used, and is rolled and unrolled every day for five or six years, is to stretching, so that there will be a variation of from 1 to 5 ft. in 1,000. If we extend a recent survey on such a map, we are plotting it to a different scale to that assumed by the map under the conditions above noted. The paper on which the map is to be drawn should be tacked down to the table or board, and should be covered with squares each exactly 10 in. square. The sides of these squares should be the meridians, or north or south lines, and the tops and bottoms should run due east and west. Mark the first station on the paper, set your parallel ruler or T square on the meridian nearest it, and with the protractor produce the course to the next station. Measure the distance with a scale, and proceed in this manner to plot all the courses, using each time the meridian nearest the station the course is taken from. After all the stations have been plotted, fill in the side notes, marking everything on the map with great care and neatness. Always use the horizontal distances. All surveys should be traversed, and all plotting should be either checked by the traversing, or the principal stations should be plotted by use of the traverse. For a large mine map that will be in use many years, muslin- backed egg-shell paper must be used. It comes in a long roll, and any reasonable length, and a width up to 6 ft. can be obtained. To Calculate the Vertical Distances. When making the survey, read the vertical angles to all stations. If the angle is one of depression, note it with a minus sign ( ) preceding it. If it is an angle of elevation, precede it with a plus sign ( + ). These will show whether the vertical distance is to be added to, or subtracted from, the height of the preceding station. Having the horizontal distance and the vertical angle: Distance X tangent of vertical angle = vertical distance. Having the pitch distance and vertical angle: Distance X sine of vertical angle = vertical distance. To Calculate the Horizontal Distance, or Latitude. Pitch distance X cosine of vertical angle = horizontal distance. Vertical height, or departure -r sine of vertical angle = horizontal distance. TRANSIT S UR VE YING. 51 To Calculate the Pitch Distance. Horizontal distance -r- cosine of bearing, or multiplied by secant of bearing = pitch distance. Vertical distance ~ sine of vertical angle, or multiplied by cosecant of bearing = pitch distance. To Calculate the Vertical Angle. The horizontal distance -f- the pitch distance = cosine of vertical angle. Vertical distance -r- pitch distance = sine of vertical angle. Vertical distance -* horizontal distance = tangent of vertical angle. NOTE. Whenever sines, cosines, tangents, etc. are here named, they mean the natural sines, etc. of the angle. Plotting by Coordinates. In describing the establishment of a meridian and a fixed point, we made the latter a stone post, or iron plug sunk in solid rock. This point is called the origin of coordinates. We have the principal meridian passing through this point in an exact north and south direction, and a secondary meridian or base line passing through this point at right angles to the first, or in an exact east and west line. Any point we may select on the map will be a certain distance north or south, and east or west of the origin. The lines drawn from this point at right angles to the two base lines just given are called the coordinates of that point, and we can plot the point when they are given. For example, the coordinates of Station 24 are North 345.67, and East 890.12. We measure 890.12 ft. east of the origin on the secondary meridian and, from this point, measure 345. 67 ft. north to the point desired; or we can measure first on the primary meridian to the north and then turn off a right angle to the east and reach the same point. In any event we plot the position of each station independently of all the others, and any error in locating one is not carried to the next. When two stations are plotted, the distance between them on the map should be exactly what we found for their horizontal distance on the ground. This check shows whether our plotting is correct. This is also called traversing a survey if the meridian be north and south, and in books on surveying there are printed traverse tables, which are accurate within certain limits, but not so accurate as the tables of coordinates published separately, as the latter are carried to a greater number of decimals. Gurdon's Traverse Tables will enable you to find, without calculation, the coordinates for a distance of 12 miles with a chance of error of only half an inch, which is much more accurate than the graduation of the instruments with which the work was done. With a north and south meridian, the point from which we begin to measure angles the zero point is the north point, and the angles are read for continuous vernier in the direction of the hands of a watch. The sines of angles are eastings and westings, and the cosines are northings and southings. To Traverse a Survey. To traverse a survey, means to determine by calcu- lation how far north or south and east or west any station may be from another, the location of which is fixed. To do this, all distances must be either measured horizontally, or calculated to horizontal distances. The horizontal angles, or courses, must be either read as quadrant courses, or reduced from azimuth to quadrant courses. An azimuth course is one that is read on the transit which is graduated from to 360. A quadrant course is one read in the quadrant of the circle, as S 67 W, N 43 E, etc. Latitude means distance north or south, and is determined by the first initial of the recorded course. Thus, if a course is S 67 W, the latitude is south; if N 43 E, the latitude is north. Departure means distance east or west, and is determined by the last initial of the recorded course. Thus, if a course is S 67 W, the departure is west; if N 43 E, the departure is east. The latitude = distance X cosine of bearing. The departure = distance X sine of bearing. If the survey is a continuous one around a tract, and ending at the place of beginning, the sum of the northings should equal the sum of the southings, and the sum of the eastings should equal the sum of the westings. Or, in other words, the sum of all the latitudes north, should equal the sum of all the latitudes south; and the sum of all the departures east, should equal the sum of all the departures west., It is evident that by coming back to the place of beginning the surveyor has traveled the same distance north as he has south, and the same distance east as he has west. The most accurate way to construct a map is to traverse the survey and place all stations on it by the traversed distances, or to at least put a number of the principal stations on the map by the traversed distances, and 52 TRANSIT S UR VE YINQ. use the protractor to plot only the intermediate stations. As the origin of the survey is at the fixed point just mentioned, we must make a rough pencil sketch to find the approximate location of this point from the boundaries of the property, and the general trend of the property itself. This will show us the place to put the origin upon the paper so that all of the property can be placed on the map, and leave about the same amount of margin on all sides. It will also show us the direction the north and south line must take on the paper. When this is settled, mark the origin by a needle point, and lay the straightedge across it in the direction to be taken by the principal meridian, and draw the meridian with a quite hard pencil brought to a very fine point. Then lay off on both sides of the origin distances of 5 in., and mark them with needle points. These must be so accurately located that there will not be an error of one hundredth of an inch in them, or one foot in five hundred. At the point where we can get the longest line on the paper at right angles to the principal meridian, lay off points for a right angle accurately on each side of the meridian, and draw through the three points, by means of the straightedge, a line parallel to the secondary meridian and divide this accurately into 5" distances as before. Through each of the points thus marked, draw lines at right angles to the lines already drawn, until the paper is accurately divided into squares 5 in. on a side, and none of them with an error of one five-hundredth. Beginning with the origin, mark the extremities of the lines passing through it zero. All distances to the east or upon the right side of the north and south zero line are marked + with respect to that line; those to the left are marked . All distances above the east and west zero line are marked 4- with respect to that line, and all distances below it . If the coordinates of a point are N 234, and E 2,468.78, we need not nieasure the whole east distance from the origin, but start from the north and south line marked + 20. With 5" squares, a 6" scale will be sufficiently long for plotting. To illustrate plotting by use of the traversed distances,we will use the following example: Stations. Quadrant Courses. Distances. Latitudes. Departures. Totals. N S E W N S E W 1-2 2-3 . 3-4 4-5 N35E N 83 30' E S57E S 34 15' W 270 129 222 355 221 15 121 293 155 128 186 200 221 236 115 178 155 283 469 269 236 414 469 200 The foregoing table, calculated according to formula for latitudes and departures, shows that Station 2 is 221 ft. north and 155 ft. east of Station 1 ; and that Station 5 is 178 ft. south and 269 ft. east of Station 1. These stations, or Stations 3 and 4, or all, may be placed on the map by simply making the two measurements for each station. To Find the Area of a Tract of Land. If a regular polygon, find the area by the rule given under the head of "Mensuration" for polygons of the same number of sides. If an irregular polygon, divide it into triangles and calculate the area of each triangle; the sum of these areas will be the area of the tract. If the tract is an irregular polygon in shape, the map should be made on as large a scale as possible, and the distances should be measured with the greatest care, owing to liability to error through very slight inac- curacies of measurement. To Find the Contents of a Seam of Coal Under a Tract. If the seam lies flat, multiply the area of the tract in square feet by the thickness of the seam in feet. The product will be the cubical contents of the seam in feet. If the seam is an inclined one, find its area by measuring the width of the tract on its line of pitch, and find the distance on the pitch of the seam by dividing the horizontal distance measured by the cosine of the angle of inclination. This will give you the pitch distance. Multiply the pitch distance by the length of the tract, and you will have the area of the seam. This multiplied by its thickness will give the contents. _ cubic contents in feet X Sp. Gr. X 62.5 LEVELING. 53 LEVELING. Instruments. But two instruments are used the level and a leveling rod. The level consists of a telescope to which is fitted, on the under side, a long level tube. The telescope rests in a Y at each end of a revolving bar, which is attached to a tripod head very similar to that used for a transit. The telescope is similar to the telescope of a transit. The leveling rod is merely a straight bar of wood, 6 ft. or more in length, divided into feet and tenths of a foot. A target divided into four equal parts by two lines, one parallel with the staff, and the other at right angles to it, and painted red and white, so as to make it prominent at a distance, slides on the rod and is provided with a clamp screw. The center of the target is cut out and a vernier, graduated decimally, is set in, which enables the rodman to read as close as ^5 of a foot. If a long rod is required, it is made of two sliding bars, which, when closed, are similar to a single rod, as described above. When used at points where it is necessary to shove the target to a greater height than 6 or 6 ft., the target is clamped at the highest graduation on the front of the rod, and the rod is extended by pushing up the back part, which carries the target with it. The readings, in this case, are made either from the vernier on a graduated side, or a vernier on the back. The rodman must always hold his rod perfectly plumb or perpendicular. to Adjust the Level. The proper care and adjustment of the level is of great importance. A very slight error in adjustment will completely destroy the utility of any work done. To Adjust the Line of Collimation. Set the tripod firmly, remove the Y pins from the clips, so as to allow the telescope to turn freely, clamp the instru- ment to the tripod head, and, by the leveling and tangent screws, bring either of the wires upon a clearly marked edge of some object, distant from 100 ft. to 500 ft. Then with the hand, carefully turn the telescope half way around, so that the same wire is compared with the object assumed. Should it be found above or below, bring it half way back by moving the capstan-headed screws at right angles to it, remembering always the invert- ing property of the eyepiece; now bring the wire again upon the object, and repeat the first operation until it will reverse correctly. Proceed in the same manner with the other wire until the adjustment is completed. Should both wires be much out. it will be well to bring them nearly correct before either is entirely adjusted. To Adjust the Level Bubble. Clamp the instrument over either pair of leveling screws, and bring the bubble into the center of the tube. Now turn the telescope in the wyes, so as to bring the level tube on either side of the center of the bar. Should the bubble run to the end, it would show that the vertical plane, passing through the center of the bubble, was not parallel to that drawn through the axis of the telescope rings. To rectify the error, bring it by estimation half way back, with the capstan- headed screws, which are set in either side of the level holder, placed usually at the object end of the tube. Again bring the level tube over the center of the bar, and adjust the bubble in the center, turn the level to either side, and, if necessary, repeat the correction until the bubble will keep its position, when the tube is turned half an inch or more to either side of the center of the bar. The necessity for this operation arises from the fact that when the telescope is reversed, end for end, in the wyes in the other and principal adjustment of the bubble, we are not certain of placing the level tube in the same vertical plane, and, therefore, it would be almost impossible to effect the adjustment without a lateral correction. Having now, in a great measure, removed the preparatory difficulties, we Sroceed to make the level tube parallel with the bearings of the Y rings. To q this, bring the bubble into the center with the leveling screws, and then, without jarring the instrument, take the telescope out of the wyes and reverse it end for end. Should the bubble run to either end, lower that end, or, what is equivalent, raise the other by turning the small adjusting nuts, on one end of the level, until, by estimation, half the correction is made; again bring the bubble into the center and repeat the whole operation, until the reversion can be made without causing any change in the bubble. It would be well to test the lateral adjustment, and make such correction as may be necessary in that, before the horizontal adjustment is entirely completed. 54 TRANSIT SUJEt VEYING. To Adjust the Wyes. Having effected the previous adjustments, it remains now to describe that of the wyes, or, more precisely, that which brings the level into a position at right angles to the vertical axis, so that the bubble will remain in the center during an entire revolution of the instrument. To do this, bring the level tube directly over the center of the bar, and clamp the telescope firmly in the wyes, placing it as before, over two of the leveling screws, unclamp the socket, level the bubble, and turn the instrument half way around, so that the level bar may occupy the same position with respect to the leveling screws beneath. Should the bubble run to either end, bring it half way back by the Y nuts on either end of the bar; now move the telescope over the other set of leveling screws, bring the bubble again into the center, and proceed precisely as above described, changing to each pair of screws, successively, until the adjustment is very nearly perfected, when it may be completed over a single pair. The object of this approximate adjustment is to bring the upper parallel plate of the tripod head into a position as nearly horizontal as possible, in order that no essential error may arise, in case the level, when reversed, is not brought precisely to its former situation. When the level has been thus completely adjusted, if the instrument is properly made, and the sockets well fitted to each other and the tripod head, the bubble will reverse over each pair of screws in any position. Should the engineer be unable to make it perform correctly, he should examine the outside socket carefully to see that it sets securely in the main socket, and also notice that the clamp does not bear upon the ring that it encircles. When these are correct, and the error is still manifested, it will probably be in the imperfection of the interior spindle. After the adjustments of the level have been effected, and the bubble remains in the center in any position of the socket, the engineer should carefully turn the telescope in the wyes, and sighting upon the end of the level, which has the horizontal adjustments along each side of the wye, make the tube as nearly vertical as possible. When this has been secured, he may observe, through the telescope, the vertical edge of a building, noticing if the vertical hair is parallel to it; if not, he should loosen two of the cross- wire screws at right angles to each other, and with the hand on these, turn the ring inside, until the hair is made vertical; the line of colli- mation must then be corrected again, and the adjustments of the level will be complete. To Use the Level. When using the instrument, the legs must be set firmly into the ground, and neither the hands nor person of the operator be allowed to touch them; the bubble should then be brought over each pair of leveling screws successively, and leveled in each position, any correction being made in the adjustments that may appear necessary. Care should be taken to bring the wires precisely in focus, and the object distinctly in view, so that all errors of parallax may be avoided. This error is seen when the eye of an observer is moved to either side of the center of the eyepiece of a telescope, in which the foci of the object and eyeglasses are not brought precisely upon the cross-wires and object; in such a case the wires will appear to move over the surface, and the observation will be liable to inaccuracy. In all instances the wires and object should be brought into view so perfectly that the spider lines will appear to be fastened to the surface, and will remain in that position however the eye is moved. If the socket of the instrument becomes so firmly set in the tripod head as to be difficult of removal in the ordinary way, the engineer should place the palm of his hand under the wye nuts at each end of the bar, and give a sudden upward shock to the bar, taking care also to hold his hands so as to grasp it the moment it is free. Field Work. If the survey has been carefully made and vertical angles taken at every sight, leveling will be necessary only in cases where extreme accuracy in regard to vertical heights is necessary. In most cases of practical work at collieries, particularly in determining thickness of strata, general rise or fall of an inside road, etc., the elevations calculated by the use of the vertical angle will be close enough, but there are frequently instances when leveling must be done to insure success in certain work. In this connection it is well to state that if the transit telescope is supplied with a long level tube, and it is, as a whole, in first-class adjustment, levels can be successfully run with it, if the transitman uses due care. Having his instrument in proper adjustment and his note book ruled, the levelman is ready to proceed with the work. FIELD WORK. 55 The rodman holds the rod on the starting point, the elevation of which is either known or assumed. The levelman sets up his instrument somewhere in the direction in which he is going, but not necessarily, or usually, in the precise line. He then sights to the rod and notes the reading as a backsight or + (plus) sight, entering it in the proper column of his note book, and adding it to the elevation of the starting point as the "height of instrument." The rodman then goes ahead about the same distance, sets his rod on some well denned and solid point, and the levelman sights again to the target, which the rodman moves up or down the rod till it is exactly bisected by the horizontal cross-hair in the telescope, as he did when giving the backsight. This reading is noted as a foresight or (minus) sight. The foresight subtracted from the height of instrument gives the elevation of the second station. The rodman holds this latter point, and the levelman goes ahead any convenient distance, backsights to the rod, and proceeds as before. In this case we have assumed that levels are only being taken between regular stations or two extreme points. If a number of points in close proximity to each other are to be taken, the rodman, after giving the backsight, holds his rod at each point desired. The readings of any number in convenient sighting distance are taken and recorded as foresights, and any descriptive notes are made in the column of remarks. These are each subtracted from the height of instrument, and the elevation found is noted in column headed elevation. After all the inter- mediate points are taken, the rodman goes ahead to some well-defined point, which is called a "turning point" (T. P.) in the notes. The elevation of this is found and recorded. The rodman remains at this point until the levelman goes ahead, sets up and takes a backsight. This backsight reading, added to the elevation of the turning point, gives a new height of instrument from which to subtract new foresights, and thus obtain the elevation of the next set of points sighted to. When running levels over a long line, the levelman should set frequent "bench marks." These are any permanent well-defined marks that can be readily found and identified at any future time. By leveling to'.them he has secured the elevation of points from which to start any subsequent levels that may be necessary. A good bench mark can always be made on the side or root of a large tree or stump by chopping it away so as to leave a wedge- shaped projection with the point up. Drive a nail in the highest point of this, to mark where the rod was held, and blaze the tree or stump above the bench mark. In this blaze, either cut or paint the number of the bench mark, which should, of course, correspond with the number in the note book. In the mines, prominent frogs or castings in the main roads, if permanent, make good bench marks. LEVEL NOTES. Station. B. S. F. S. H. Inst. Elev. Remarks. 1 100. Assumed elevation of Station 1. 3.412 103.412 2 4.082 99.33 Station 2 of survey. See page Vol 6.791 96.621 Sight taken to ground at N. E. cor. John Smith's house. 3 = T. P. 4.862 98.55 Station 3 of survey noted above. 11.698 110.248 4 B. M. 1 9.817 6.311 100.431 103.937 Station 4 of survey noted above. B. M. 1 is on north side of large white oak. 5 6.427 103.821 Station 5 of survey noted above. In underground leveling, extreme care must be observed to record the algebraic signs of the readings, which show whether the level rod was held in its usual position, indicated by a + sign or the absence of any sign, or upside down, indicated by the sign. PROOF OF CALCULATIONS. The calculations are proven by adding together the backsights and also the foresights taken to turning points and last UNDERGROUND SURVEYING. station. Their difference equals the difference of level between the starting point and last station. Thus: Foresights. Backsights. 4.862 3.412 6.427 11.698 11.289 15.110 11.289 3.821 = 103.821 100.0 or 3.821. TRIGONOMETRIC LEVELING. This method determines the difference in elevation between two points from the measurement of the distance between the points, and from the vertical angle between them. Although generally less accurate than level- ing with a Y level, it is much more rapid and is especially adapted for pre- liminary work in a hilly country, or for the leveling of mine slopes and pitching rooms where the Y level can- not be used with any advantage or accuracy. By reading the angles and by checking the measurements a very high degree of accuracy can be ob- tained in trigonometric leveling. CASE 1. Assume the elevation of A to be 100 ft. A. T. With the transit set up over A and properly leveled, sight to a point C on a rod so that B C equals AD. Measure the vertical angle Z and the inclined distance D C, then the difference in the elevation between A and B equals B C = CD X sin Z, and the elevation of B equals 100 + B C. CASE 2. Assume the elevation of station A in the roof of a mine to be 100 ft. A.T. Then with the transit set up directly under A and properly leveled sight to a point C upon the S'umb-line suspended from the station , measure the vertical angle X, in- clined distance D C, and roof distance B C. From this, the distance C Y = D C X sin X. The elevation of B is then found as follows: The elevation of B = the elevation of A A D + (D C X sin X] + B C. There are many modifications of this simple method, but from the above diagrams the most complex modifi- cations can be worked out. TRIGONOMETRIC LEVEL NOTES. Station. Vertical Angle. Inclined Distance. Vertical Distance. Height of Instrument. Roof Distance. Eleva- tion. A +100 A B +5 100 +8.72 2' 3' 109.72 B- C +2 100 +3.49 3' 2' 114.21 C D -3 100 -5.23 A' 3' 107.99 D- E -4 100 6.98 2' V 100.01 UNDERGROUND SURVEYING. There are a number of variations in the foregoing practice that are caused by the entirely different set of conditions in underground work. These have been grouped together for convenience of reference. STATIONS. 57 The Establishment of Stations. As this is the most important duty of an engineer in surface work, so it takes the first place in work underground, as the accuracy of the work depends on the location of the stations, while its rapidity depends on using the fewest number consistent with completeness. It also stands to reason that the fewer the number.of stations, the fewer the chances of error. In underground work, stations should be located under the conditions of permanence, freedom from destroying agencies, and ease of access Temrx ~~ -*--*-? ^ ~- 1~ ~;~u*. ^ ~~- n n *u^^ ,....,,: ments. We esi in the floor. I. __,,_ set-up of the transit, and thus underground differs from surface work. The first surveys were made with lamps set on the floor, sighted to, and then set over. Permanence wsft secured by driving iron nails or tacks in the sills of the track or sets of timber. As acid water soon destroyed these, they were followed by copper tacks or brads, and all were witnessed by notches cut on both sides of the sill, as in outside work, and by a vertical paint mark on the solid wall, with the number of the station. This method is faulty, as the tracks in crooked gangways are seldom placed where one can get the longest sight, and, as they are the traveling ways, the stations run the chance of being knocked out by passing men or mules, and the whole track, on a curved incline, is generally sprung by every loaded trip. As the sights must be as long as carefulness of work will allow, we put them generally in the roof, as that offers the greatest area for a choice, and is not under foot. Any settling of the roof so as to affect the accuracy of the station would be equally effect- ive in destroying the accuracy of a station in the floor. We therefore choose places that will be least affected by subsequent work, and put the stations in collars, lids or wedges of props, in the props themselves, when they have incline sufficient to allow the transit to be set under them, or in the roof itself. Wherever set, they should not project far from the surface, and thus be liable to be brushed away in a low gangway by cars with topping higher than usual, or knocked away by flying fragments from a shot, if near the working faces. Top stations have a mark about them to call attention to their location. It is generally a circle, unless there are other corps at work in the same mine that use the circle, and the stations of the two surveys would be confused if marked alike. In this case a corps selects some easily made figure, as a triangle, square, etc. If two surveys use the same station, the mark of the second survey is placed around that of the first, and the 44 Remarks " give " Station No. 234 of L. & S. corps," etc. Kinds of Stations. The simplest top station is a shallow conical hole, made with the point of the foresight man's hatchet, which is dug into the top rock and rotated, and is called by some a jigger station. Corps using these entirely have a jigger consisting of a steel-pointed extension rod, with an offset hold- ing a paint brush. The rod is long enough to allow the point to be driven into the roof at any height, and its rotation marks a circle with the brush, which is also used to mark the number beside it. Centers are set under such stations and sights are given by another tool also called a jigger. This is an extension rod, beyond the upper end of which projects a piece of sheet iron shaped like an isosceles triangle, with the upper and smaller angle cut off so as to form an end one-quarter of an inch broad, and in this end is cut a U-shaped groove. The sights are given and the " centers " set by putting the plummet cord in this groove, and placing the end in the "jigger hole" in the roof. The cord must be more than twice the length of the section of the place, as it must be held in the hand, run over the jigger notch, and hang vertically to the plummet, which must come to the floor when the stations are set. The rod and cord are held in the left hand, and the right is free to steady the " bob," give sight, or set the center. The advantage of this method lies in the quickness with which the centers are set and the sights given, and the ease with which the highest stations are reached. The disadvantages are the impossibility of making the jigger hole perfectly conical, so that the jig- ger can be set in the same place on two successive sights, and the plummet cord will hang exactly in the same place. Second. Common shingle nails are driven into collars, or cracks in the roof. The end of the plummet line is noosed and put over the head. This causes an eccentric hanging of the plummet that may cause an error in back- sight and foresight of the width of the nail head, which will be quite appreci- able in a short sight. To dp away with this error, a variety of nails ( called spads, spuds, etc.) are made of iron or copper. Iron will not corrode in dry mines, 58 UNDERGROUND SURVEYING. and is much cheaper. The simplest is made by hammering out the head of a horseshoe or mule-shoe nail, punching a hole in the flattened head for insert- ing the cord, and cutting off the point, so as to make the finished spad an inch long. This will bring the head near the surface without having to drill too deep a hole, and will^make them unfit for lamp picks, as they are very- handy for such purposes, and thousands have been pulled out to this end. Any blacksmith can furnish them for less than 1 cent each. They are driven broadside to the line of sight, or they will be liable to the same objec- tion as the shingle nail. To remove all chance of eccentricity, a form is made with a shoulder in which a hole is drilled parallel to the length of the nail. The practice of using staples for stations is antiquated though given in the last editions of some modern textbooks and should never be used where accuracy is required. Third. All these varieties of spads are driven into a crack of the roof; but such stations cannot be called permanent, as the same force that made the crack will tend to open it and let the nail drop. Even if this does not hap- pen, we shall have the water in a wet mine coming in by these cracks, and rotting the nails, or the rock at the sides of the crack, and in a month after the placing of the station, it will be unfit for use. Fourth. Into a hole drilled in the roof, a wooden plug is driven, and into this w r e drive the spad. The swelling wood clamps the same and prevents its coming out as readily as it was put in. The plugs are made of well-dried wood outside, and are carried by the man that sets the stations. The first holes were made by a jumper, and the plugs were 2 in. square and 6 in. long. The modern holes are usually made by a twist drill of as small a diameter as will do the work without bending at the shank. Such drills can be used in slates or clays; but an ordinary drill and hammer must be used in harder rocks. The average modern holes are | in. to ^ in. in diameter, while the plugs are i in. to 1 in. long at the maximum. The smaller the hole, the quicker the work. All stations should be put in the roof in preference to the under side of a collar, or in any ordinary timbering. The only exception is where the roof is too poor to hold them. Such stations should be checked in extending a survey before they are used, if we wish to swear to the accuracy of our work. The engineer that believes in using collars may find himself in the quandary of the man whose company worked across their line because he started from a collar station. Since its location, the place was working and the collar was taken down and shifted end for end when replaced. Good side notes, if consulted, would have shown him the change. Fifth, A. twist drill & in. in diameter is used to make a hole in the roof; a piece of cord or, better, a copper wire is placed across this, and a hard- wood shoe peg is driven into the hole and binds the cord tight. The plummet is tied to the lower end. A cord will soon rot, and, if in the gangway, is pulled out by the drivers for whip lashes, while the wire is more permanent; but even this will be pulled out by catching in the topping of a car in a low place. Lastly. The use of spads is dispensed with, and all the stations put in rock roof where possible. A " twist drill makes a vertical hole 1 in. deep. Into this, when a sight is to be taken, the foresight man puts a steel clip with serrated edges. This is made by bending upon itself a thin piece of steel ft in. wide. When the ends are pressed together it will go into the hole, and the spring of the sides and the serrated edges hold the clip in the hole so that it is hard to pull out. The cord passes through a hole in the center of the bend and is, therefore, in the center of the hole no matter how the clip is inserted. It is removed by pressing together the ends of the clip. This is the easiest and quickest way of working, as there is no eyehole to be freed from dirt and no knot to be tied and untied. The hanging of the plummet takes a fraction of a second, and the station will remain as long as the roof keeps up. The disadvantages are the putting of the holes inclined to the vertical by a careless man, and the many roofs that are unfit for piercing with a twist drill. Marking Stations. We should have some regular way of witnessing our stations. In general, a vertical line on the rib calls attention to a station in the floor near the side marked. A roof station has the mark around it, as has been described, and it is some geometric figure. If three regular corps are engaged in the same field and meet in the same mines, as the company corps the corps of the individual operator, and the private corps that is looking after the interest of one or more of the land owners, they must use different signs for stations. The most common are the circle, square, and STATIONS. 59 triangle. If the " circle " corps puts in the station, it has a circle about it. The next corps uses it and puts a square about it and notes " Sta. 472 = to Sta. 742 of ( ) Corps." The third corps uses it and puts a triangle about the square, and notes " Sta. 617 = to Sta. 472 of ( ) Corps, and Sta. 742 of ( ) Corps'." If the first corps uses the station again, it notes the numbers given by the two other corps, and these three numbers will aid in identifying it if one or two of the numbers are lost. Distinguishing Stations. Each station must be lettered or numbered so that it can be readily recognized when the subsequent surveys are made. When set it may have been at the end of a gangway, while six months later the gangway has been driven hundreds of feet from that place, chambers have been turned off in what was solid, and the place be so utterly unlike its former state that nothing but a fixed mark belonging to that station alone will enable us to recognize it. The methods of distinguishing stations vary widely. In one place the writer found that each gangway and room had a Station 1 at its beginning, and the various stations numbered 1 were designated " Grog Run 1, 2, 3, etc."; " Pat James Gangway 1, 2, etc."; and so on through the map, that showed between fifty and one hundred stations numbered 1, so that a new engineer Would have had to learn the mine thoroughly before he could extend a survey. Another way is to use Al, A2, etc., up to A100, and so through the alphabet to avoid running up too high in numbers. A third was lettering the various sections of the mine A, B, C, etc., and the numbers begin with 1 in each and run up indefinitely. All of the above have disadvantages, as powder or lamp smoke, mud, mold, or the misplaced ingenuity of small boys may so obliterate or obscure a mark that it will be recognized only by association with its immediate neighbors, and these may have shared the same fate. You may have only a part of the mine map with you, and because the system of marking strives to get along with as few symbols as possible, you have to go to the office, when there would have been a chance of deciphering the mark if there had been a number of figures to it. The best practice, therefore, courts large numbers, begins with Station at the mouth of the slope or drift, or the foot of the shaft, and numbers consecutively in each bed. In a short time three figures are reached, while in old mines the 'numbers require four digits. The chances of obscuring such a mark are lessened, while the chances of our deciphering it are increased. Centers. When the station is in the roof, there must be something for the transit to set over, as it is easier to do so than to set under a station, and much more accurate as instruments are now made. The set-up is made over a " center." At first, a cross scratched on the floor or on a loose piece of slate, a daub of white lead on the same with a small piece of coal placed under the point of the plummet when that had been steadied or finally, a nail driven into a block and afterwards pointed, were used. All of these, except where the mark was on the solid floor if they were large enough to be stable were in the way of the observer's feet, while, if small, they were so light as to be readily displaced. It must be noted here that it is not so much the errors that we can foresee and detect that influence the accuracy of the work in our own eyes, but the chances of error from accidents that we cannot control and that cannot be readily detected. To avoid the above chances, we make the centers as small and as heavy as we can in other words, we make them of lead. A hole H in. in diameter and i in. deep is bored in a thick plank, a brad is set in its center with the head down; the hole is filled with melted lead and the brad is slightly raised to surround the head with lead, and held with pincers in a vertical position till the lead has set. The brad is cut off i in. above the lead and pointed. This "center" combines weight and small size, and is generally used. Paint. White lead, or Dutch white, thinned with linseed oil, is ordinarily used. It is carried in a covered tin pail holding a pint. The cover has a hole large enough to admit the brush. The pail generally has to be cleaned out after each day's work, as the brush gathers dirt every time it is used. In case the paint is to be kept for a number of days, it must be covered with water, which can be poured off before using. If the ordinary paint brush has too long bristles, it can be shortened and kept from wearing by winding with fine wire to the proper length. The top should be wiped clean and dry with a piece of cotton waste before the paint is applied, or the white will be so discolored as to be scarcely visible, or if the top is dirty it will flake off, and the numbers be lost. 60 SURVEY NOTES. KEEPING NOTES. Taking Notes. Complete notes should be taken and recorded neatly and systematically, so that a stranger can easily follow them. Every physical characteristic, and all surface improvements should be noted and located. Every ledge of rock should be noted, its character, dip, and course of strike should be taken. In a large company there should be a separate book for transit notes and for side notes, and where many collieries are operated, a separate set of books should be used for each colliery. However the notes are kept, we must note the following things: The numbers of the stations; the needle readings to check the vernier; the vernier reading; the dip of the sight: the distance measured, either flat or on the dip; the height of the axis of the transit from the ground; the height of the point sighted at from the ground; and all other necessary remarks to make the work plain. It is customary to have series of vertical columns headed (to suit the above) Sta., Needle F. S., Needle B. S., Vernier, Pitch, Dist., H. I. (height of instrument), H. R. (height of rod, or point to which sight was taken), and Remarks. At the top of the page in starting a survey, there should be entered the name of the mine and of the bed where the work is to be done; the names of the regular corps employed for the W9rk, and those that were taken from the mine to point out work or assist; the instruments used; the date of the work, and, in case it be the continuation of a previous survey, tile pages where such work was noted must be set down. Such books are complete records, and can be used as time books in paying the men, or as proofs of the kind of work done in case a lawsuit requires such testimony, by showing the number of men, the instruments used, and the time employed. Transit and Side Notes. There are about as many methods of keeping these notes as there are engineers. These methods arrange themselves into groups, and specimens of four groups will be shown, as the most common in use in the mines: First . The side notes of each sight follow the transit notes of that sight, and on the same page. Second. They are entered in the same book on opposite pages. Third. The transit notes of the whole survey come first, and are followed by the side notes in the same book. Fourth. Each set of notes has a separate book. The last method is the best even if the same man takes both sets of notes, and where two men do the work at the same time, such a method is imperative. Each mine should have a separate set of books for ordinary work and special work, and such a practice gives the engineer reference notes in a portable form. Unless this is done, and if the party makes surveys in twenty different mines, the notes of two succeeding surveys in any locality are generally in separate books, and both must be carried. This applies to side notes, and four books must be carried. With a special book for each mine, no index is needed to find a certain survey, and no set of books must be overhauled. The book for that mine is taken, the date looked up, and the notes found. The taking of side notes in an ordinary outside survey is secondary to the instrumental work; while in underground work, of ordinary character, the lines of the survey are skeletons upon which are built the side notes. The side notes are therefore of the highest value, and the forms for taking them should embrace the salient features of the underground work, so that the mapper can reproduce them faithfully even if he may never have been inside. Forms for Transit Notes. Suppose we are setting up at b; with backsight at a; foresight to c; deflected angle abc = 85 27' left; and that the distance be is 421.76 ft. measured on a pitch of + 4 35'. First Form: Sta. Needle. B. S. Vernier. Needle. F. S. Pitch. Dist. Sta. A B a b S 25 30' W L 85 27' L 85 26' S 60 0' E + 4 35' 421.76 c FORMS FOR NOTES. 61 This is read: "Set-up at 6; backsight at a; foresight to c; first reading of vernier under A; second (check) reading under B; check reading by needle computed from foresight and backsight needle, etc." Some note the readings of one vernier at A, and the opposite one at B, and take only one sight. The last column for stations is sometimes omitted, and the first widened, so that the three can be entered as fol- lows: "a-6-c." x Second Form. This differs from the first in having but one column for the venier reading, 6 238 which is not noted until two readings agree, and also in omitting the last column for sta- tions, as noted above. In some cases the line is indicated by but two stations, the one set up at, and the foresight, as in the angle given above, b-c. To note the backsight, the previous ays taken, and under "Sta." we put line is alway " a-6," and the needle reading. Third Form. In this case a continuous ver- nier is carried and the readings are put in the second column, with the needle course on foresights as a check in the third. In the column for stations only the station at which the set-up is made is noted on the line with the readings for that set-up the backsight going on the pre- vious, and the foresight on the following, lines. ] 1 5 -755 -5 4-/40-S 3 HO 6 4- -9/ -6 s 4- JO -VL -r FIG. l. Fourth Form. This is also a form for record- ing a continuous vernier, as well as the deflected angle. The right-hand page is for noting differences of level as measured by level or transit. Certain columns are filled in at the office, to make the book complete as a reference in mapping, or in the mine. This form is advocated "for its compactness": but there is such a thing as too much of that article, as there is no room on either page for remarks, while in all the other systems, the right-hand page is set aside for this purpose. Fifth FormWhere the leveling is performed by the transit, and each sight is taken with that end in view, the level notes are added to any form of transit notes chosen and they are recorded as shown in table on page 56. These figures are used to calculate the differences in elevation, as shown by the pitch of the sight. The minus signs show that the points noted are below the stations. If the station were in the floor, the sight would have a plus sign. A contin- uous vernier can be used with this form. Forms for Side Notes. In every case the notes should convey to the man that plots some idea of the form of the place surveyed. An accurate sketch cannot be made unless the whole locality can be seen at a glance which is seldom, if ever, the case and yet we must not go to the other extreme and write down the notes without a sketch; yet that is what is frequently done, and may be simply noted as the first form, and put aside as a faulty method with no good points. Second Form. In this, see Fig. 1, as in a sketch made as a person advances with no definite idea of the arrangement of the work, there is too frequently a running of the sketch off the page on one side or the other, and a cramping of certain parts. Insert- ing the figures on the line of survey confuses the one that plots if the sketch is distorted or cramped. As the hands of the note man are dirty from rub- bing along the tape, to find the numbers,it generally happens that the sketches are smeared and blurred so that they are hard to decipher when the notes are most clearly kept, and a method that encourages cramping, confusion, or obscurity must be rejected. FIG. 2. Third Form. There is no attempt made at sketching in this form, Fig. 2, but the red line in the center of the page of the note book is taken as the Tine of survey, and the next parallel lines on either side are taken as the boundaries of the solid on either side. The only figures on each side of the red line are 62 SURVEY NOTES. the distances from the line to the' solid, while the " pluses" at which they were taken are noted at the side of the page, and the exact distance between the two stations is enclosed in the parallelogram. This method at the pluses 155 and 157 calls attention to a point where practice varies greatly; namely, How shall we note the " corner of pillar " ? and Where is the corner? One method calls the corner that point where the pillar begins to diverge from the gangway line, as noted in Fig. 2, at a, where a chamber, cross- cut, or counter starts from the gangway; a second method designates the corner as the first or last solid part met with in the line of survey, as at b, j pilla line at right angles to the line of survey is tangent to the ends, no matter whether that end be 10 or 100 ft. distant. Any one can plot side notes if accurately taken, and two persons accurately plotting such notes will reach the same result. level Notes. These are kept as in outside work, as has been before stated, with the exception that, as the rod is reversed in getting the elevation of a station in the roof, the record of the reading is prefixed with a minus sign. A record of such a reversed rod, when the target is 3.78 ft. below the station, is recorded 3.78. The shaft is measured (if deep) by a fine steel wire running about an accurately graduated wheel (a sufficient number of turns being laid to prevent slipping) and noting the number of turns before the bottom is reached. The wire may be measured before and after the operation, to insure against stretching. An aneroid mining barometer, if in good condi- tion, will give quite accurate results if a number of trips are made between top and bottom, to give an average. In this case the barometer must be left quiet 10 or 15 minutes, to be sure that it has expanded or contracted to the proper degree. For rough measurements, the length of the winding rope between top and bottom is taken. By one of these methods we locate a bench mark below, that is connected with the outside work and referred to tide water. As has been stated, the rod must be reversed to get the elevation of all stations in the roof, and all such readings are noted with the minus sign, as 4.32' (read 4.32 ft. below station). We must bear in mind that roof stations are almost certain to settle, from the pressure of the superincumbent rocks. To check such settling, we must measure the distance from roof to floor accurately. Some measure from floor to rail of track. This is inaccurate, as the track may be shifted or the grade changed in making repairs, or to take out a " sag." A noted expert once swore that the roof had settled in a mine, as his measure- ments were from roof to track, and the latter had been raised without his knowledge. Whenever we begin a level survey, we must measure the distance between roof and floor and see if it agrees with the notes. If it differs, we must note the fact under the original notes, as a check for future work. STOPE BOOKS. BY JOSEPH BARRELL.* In large metal mines, where the veins are more or less vertical and great volumes of ore are extracted from between the levels, it becomes important to adopt such a system for recording the shape and location of the stopes that at any future time the engineers may be able to give precise information concerning them, without entering the mine for the purpose. Preparation of the Slope Book. Although the timbering furnishes means for sketching and locating the stopes, some regular system must be followed or inextricable confusion will result. The book must connect the stope sketches with the transit work of the drifts and also the various floors with one another. Fig. 1 is a hypothetical map of a portion of two levels. Figs. 2, 3, and 4 follow from it, Fig. 2 being one leaf from the stope book. The paper should be of the quality of that used in field books, ruled by the printer vertically and horizontally, with waterproof lines in a colored ink preferably green. A convenient scale has been found to be 4 lines to the inch, every fourth or #See "Mines and Minerals," October, 1899, page 97. STOPE BOOKS. 63 fifth line to be heavier. Each square will represent a square set, giving an actual scale of about 20 ft. to the inch. A smaller scale does not show enough detail, and a larger one is not necessary for this class of work. The most convenient size for the bound books is 11 in. long by 5i in. wide. Only the right-hand leaves are numbered, so that when open a page extends entirely across the book, 20 in., showing 400 ft. of the length of the vein and wide enough for two floors on one page. The floors imme- diately above each other must follow on consecutive pages; thus, on the first double page will be 400 ft. of the sill floor and first floor, on the second page the second and third floors, and on the seventh page the twelfth and thirteenth floors. The eighth page is reserved for cross-sections of the vein, and the ninth for the long upright section, these two Second '/ere/- , being shown by Figs. 3 and 4. The next 400 ft. of the same FIG. 1. drift will be shown on page 10, so that it joins on to page 1 on one side and to page 19 on the other, and in this way the work of one level is kept together. For convenience, the book should be indexed by placing a projecting tag with the number of the level on each page of the drift floor. Having now a general idea of the arrangement of the work in the book, it remains for us to determine, precisely, how to place it and how to show the relation to the transit surveys. First, it is necessary to have some reference line on the vein. For this purpose draw on the map, through the center of the shaft, a line perpendicular to the strike of the vein, as shown in Fig. 1. Scale off from the map the distance at which it cuts the transit course from the nearest station. Then, by adding the known distances between sta- tions to this, we obtain the surveyed distance of any point on the drift from our reference line. Select the middle or end of a page in the stope book for the zero or reference line, such that the drift will go most conveniently in the bo9k, and on the upper line locate the survey points at their proper distances from it, as in Fig. 2. The vertical location of any part can be told when the dimensions of the tim- bering are known. In this instance the drift is 7 ft. 10 in. high, and each of the following 12 floors are 7 ft. 2 in. If the levels are exactly 100 ft. apart, the thirteenth floor will conse- quently be 6 ft. 2 in. in height. The Stope Book in the Mine. Having indi- cated in the office, by a regular system, the place for everything that will be found in the mine, the next step is to proceed to the details of sketching. The location of the stations on the top line of the drift-floor pages shows on what vertical line they should lie in the sketch; but the fact that each square mus" be kept as representing a square set, and that any or all of them may not be exactly to our scale, will cause the location made in the mine to vary slightly from that made in the office. Any such discrepancy must be taken upon the edge of the page. Therefore, proceed to the station nearest the center of the page FIG. 2. G4 UNDER GR UND S UR VE YING. and locate it as nearly as possible under its position at the top, remembering that the sets of timber, no matter how irregular, must be represented as squares. Now walk along the drift, watching the character of one side at the line of the floor, sketching while walking, counting the sets, and indicating the posts by dots of the pencil. Check up the number of sets on each station and continue to the end of the drift. Sketch the other side in coming back, and by counting the sets a second time, from station to station, a further check is placed upon the work. On the correctness of the sketches of the drift floor that of the overlying stopes depends. Having finished the drift, climb to the first floor and locate the set climbed through the same distance east or west of the reference line as on the drift below, see Fig. 2. Since the chutes and man ways will ordinarily not step off sideways, but only along the dip, a chute will be represented the same distance from the side edge of a page on all those floors where it occurs. In this way each floor is located in longitude. To do the same in latitude it will be necessary to give an arbitrary number to that row of timbers on the ground floor against the hanging wall. It is well to start with 10, since then, on a wider working of the hanging wall, there will be no danger of running down into negative numbers. The rows are numbered consecutively as they step off toward the foot-wall. Thus, in Fig. 2, on the drift floor, the man way to chute No. 102 is in row 14, and that determines the numbering on the first floor. On the thirteenth floor, in this instance, as shown in Fig. 3, the man- way is in row 19. In such a manner each floor is completely located with reference to the drift below and ultimately with the transit survey. The ease and rapidity of the work will depend on the character of the mine. Much is gained by practice, the work not being sketched set by set, but a pause for sketching being made every fifth or tenth set, or wherever there is a change in the character of the wall. In drifts such as are usually found, from 3,000 to 8,000 ft. of sketching is a good day's work. The sketch should be taken at some definite horizon, and that of the floor level is best. Features of constant recurrence must be represented by conventional signs. Thus, in Fig. 2, c enclosed by a square indicates a chute passing through the floor; up means a ladder up; M, a manway down. A full line indicates a rock wall, a broken line, lagging; cross-hatching represents filling: a dashed-and-dotted line, the presumed limit of filled workings, etc. It is of importance to indicate irregularities in the tim- bers. If it is a short set, write S within the square; if a long set, L, giving the length if necessary. If there should be an angle in the timbering so that there may be a set more on one side of the drift than on the other, represent it by a wedge-shaped opening, as shown, being the appearance of the drift if it were straightened out. In sketching, it is essential to accuracy that the attention be held to a few things at a- time. On reaching the top of the raise the plan views are completed, each floor having been sketched on the way up. On descend- ing, turn to page 8 and sketch the cross-section of the manway, as shown in Fig. 3. Each set is still represented by a square, although the sets are higher than wide, but since that fact is known it can lead to no error. The stope book is taken through the mine and brought up to date at the first of each month, and it is necessary for the foreman or shift boss to accompany the engineer and point out each place where work has been done. To pick up the work readily, and identify the last set of the previous month, the last cap should have a notch cut in it and the same indicated in the book. The Long Section. The view of the vein that will be of most general use, and show at a glance the progress of the work of ore extraction, is the long section. It is a modified vertical projection of the vein, such as would be obtained if the rock on the hanging-wall side should be removed and the vein viewed from a distant standpoint at the same level. Fig. 4 shows the final section made in the office to the same scale as the map, but each part of it for the corresponding 400 ft. of a level will be placed on pages 10, 19, etc. of the stope book, and is compiled from the sketches of each floor, The long sections can be drawn from the plan views of the floors either in the FIG. 3. THE LONG SECTION. 65 mine or the office, but it is a little better to determine the limiting points in the mine. The transit stations, chutes, and raises should, of course, be located upon it as common points with the map, connecting the two. The final long section is drawn by merely piecing together the several parts from the stope book and drawing them horizontally and vertically to the same scale. Since a vein is quite an irregular surface, the question arises as to what modification of a vertical projection will give the most accurate and con- venient representation of it. That devised by Mr. A. A. Abbott, of which the essential feature is the horizontal adjustment space left between the levels is shown in Fig. 4. At our reference line, in this case the projection of the shaft upon the vein, the zero points of the levels are placed over each other. But owing to the warpings in the vein, a raise, such as No. 201, started, in this case, 40 ft. east, will not break through on the similar point of the level above. The simplest way in which to allow for these discrep- ancies is to draw the levels more than their true distance apart by the width of an adjust- ment space, lay out each level at its true length, and draw the raises perpendicular to them, provided, of course, that the raises only step off along the dip and not along the strike. All these fea- tures can be appreci- ated by studying Figs. 1, 2, 3, and 4 in con- nection with each other. Lines corre- sponding to the height are ruled on the sides of the drawing, and the floor on which the work is being done is ascertained by means of a parallel ruler. Such a view approxi- mates to a development of the vein horizon- tally, but vertically to FIG. 4. Adj. Space a projection, since the vein is projected on a series of vertical planes passing through the transit courses. The drifts are shown at their true lengths, but the heights are the vertical distances and not the lengths up the dip. The long section will be brought up to date every 3 or 6 months, and the portions of the veins extracted during the interval indicated by cross- hatching or tinting. In the illustration, the ore bodies are cross-hatched to bring them out more clearly, but to do this on the regular map would involve erasures with every extension in the workings. In the mine, a hard and sharp drafting pencil will be used, -but pencil markings in a book constantly in use soon become faint and blurred. It is necessary to go through the book at intervals and ink in everything with waterproof draw- ing ink. Two colors can be used with advantage, red for all transit lines arid survey figures, and black for the stopes and those symbols relating to them. If there are several splits to a vein, sometimes worked together and sometimes not, the work on the different splits can be readily distinguished on the long section by using red for the hanging-wall split, and blue for that of the foot-wall. If old filling is taken out, such as ore, as frequently hap- pens, the parts extracted can be cross-hatched in red, and thus a record of both the first and second extractions preserved. The value of these methods over mere sketches made without system lies in their accuracy. Where the timbering is irregular, the accuracy of the results depends largely upon the time and care taken in the work. 66 UNDERGROUND SURVEYING. MINE CORPS. The method of dividing the work in an underground survey depends on the size of the corps. We will therefore consider the work of each man, in order to get the right number for the corps. The chief of the party should be where he can do the most good, and where he can plan the work for his subordinates. The principal point of the survey is the setting of the stations so as to do the work thoroughly with the fewest set-ups, and thus diminish the chances of error in instrumental work. The chief should locate the stations and add all the necessary signs to show how the work is to be done. The transitman should not have his attention distracted from his particular work by questions as to procedure. He should work untrameled. The chief, therefore, should not run transit. Upon this basis the ideal mine corps works, and such a corps consists of at least four, and better five, men from the office, and three from the mine. It is divided into two sections. The chief takes the men supplied by the mine one or more of whom are acquainted with the work done since the last survey and locates the stations; the transitman follows with the second section, to measure angles and distances. By this time the stations are set and'the chief takes his men after the transit party and gets the side notes, with a check measurement of the distances between stations. Such a corps goes to the end of the former survey 'and identifies the last two stations. The transitman prepares to set up at the last, while the chief and party goes as far as he can see the light from the last station, or to some intermediate point from which one or more sights are to be taken. He then stops and sends a man along each place where a sight must be taken, as long as their lights are plainly seen from top to bottom where he is standing, and over this place he marks a point for a station to be inserted, and generally inserts it himself unless he be pushed by work, and must leave it for another to do, when he places a circle about the dot, places the number at the side, and as many arrows as there are new stations, the longer arrow generally pointing to the sight to be last taken and where the transit is to be set up next. Leaving a backsight at the point just set, he sets, successively, stations at the points where the I foresight men have stood, in the manner just described, until he has covered the new work the mine boss or some N. I . intelligent miner going with him to give him an idea of x *s ' / the "lay of the ground," so that the work can be covered with the fewest number of stations. Sometimes the chief takes the side notes and measures the distances between stations as fast as they are set. In a pitching place, a circu- lar brass protractor with small plummet is hung at the center of a stretched tape, to give the angle at which the tape is held; this serves as a check to the measurements of the transit party, which are taken as the basis of the work, and the other measurements are solely as checks. In flat work, both measurements should coincide. In a small corps, and where time is of little importance, the foresight man puts in the stations ahead of the transit, and while he is so doing the transitman takes the side notes. Sometimes the side notes are taken by the same man, while one of the party is taking the transit to the next station and setting it up for the next sight. There are about as many variations from these two methods as there are corps. The foresight man should be intelligent and active, as the amount of work done in a day depends on his ability to keep ahead of the transitman. Some of the latter are fast enough to keep two foresight men on the jump. His duty is to set the center for the next set-up under the station, and also place the tripod if three are used in the work, to give the sight, and, in some corps, to carry the front end of the tape and assist in taking the distance. In some corps he also carries the bag with tools for setting stations, so that he gen- erally has a load that makes rapidity of movement difficult, and anything that will diminish the weight carried will tend to quicken the work. The rapidity with which good work is done varies considerably, but it depends on -the activity of transitman and foresightman, and a. good corps should have no trouble in making twelve set-ups an hour, and taking two or three sights from each set-up. It varies also with the distances between stations. The saving of time should never be sought at the expense of accuracy in the work; it is to be gained by rapidity of moving about, in SURVEYING METHODS. 67 setting transit, center, etc., and in hanging plummets to give sight. The foresight man and backsight man should be in position to give sight before the transitman is ready, so that he can turn his instrument on one or the other and find them in position. The slowest parties were those that carried empty powder kegs (in the days when loose powder was allowed inside) for seats, and spent the greater part of the time sitting on them. The backsight man has little to do inside, and to compensate for this, he is the one that cleans and oils the tape, gets out new plummet strings, and sees that the tools are ready for the next work, as soon as the corps gets to the office. The transitman cleans the transit, unless the corps has subordinates that can be trusted with so delicate an instrument. The blackening from sulphureted hydrogen is rubbed from the silvered surfaces with whiting, and the oil or paint smears are removed with alcohol. Alcohol should be used instead of water for cleaning the instruments, and especially the lenses, which are wiped with jewelers' cotton or soft chamois skin. SURVEYING METHODS. Outside Surveys. We have spoken of the points necessary to include in the survey outside, and how the base line is established. It remains to call attention to several points that must be known before the surface plant can be protected from settling, from the removal of the deposit below. The exact location of all buildings, lakes, ponds, rivers, railroads, etc. is not only necessary for the making of a correct map; it is necessary for the determination of the amounts and location of the beds that must be left untouched by the subsequent mining. Here must be mentioned an error that generally governs the location of the retaining pillars to support the above and prevent damages to themselves or to the mine. The settling of the ground would make all bodies of water leak into the mine, and also destroy to a greater or less degree all surface plant, as well as throw out of plumb all shafts or other openings for hoisting, if it did not close them entirely. The usual custom is to extend vertical planes through the bound- ary lines of such objects, and leave untouched all parts of the superincum- bent beds embraced by those planes. This is accurate only when the strata are horizontal or vertical, as beds settle normally to the planes of the strata and not in a vertical line in case the open spaces are stowed. If the spaces are left open, they are first filled by falls, and then the settling goes on according to the above rule. No cut is necessary to show the method of settling, and the place where the bed is to be left untouched may be found as follows: Draw a vertical section through the point to be supported, and also the underlying bed on the line of the dip of the bed the section being acmirately drawn to any scale. Draw through the extremities of the object to be supported, lines to the bed, which will make right angles with it. The space included will give the dimension of the pillar measured along the dip of the bed, and the dimensions of the object taken at right angles to the first plane will give the other dimension of the pillar. Inside Surveys. As the beds of anthracite lie at all angles with the hori- zontal plane, the methods of surveying them vary accordingly, and can be divided into flat and pitching work. Flat work is where the beds have so slight a dip that the cars can be drawn to the face of the room, and where there is nothing to prevent a sight to that face from the gangway. The variations in the methods of work in this case depend on the accuracy with which the work must be performed, as, in some cases, the workings are approaching the boundary line of the property, and the sides of the rooms must be located accurately. In general, the rooms are driven at right angles to the gangway, unless the dip is too great to haul a car to the face on that line, when they are inclined to the gangway at an acute angle. The width of the rooms in flat work is generally uniform where the roof is good, but where the roof is poor the entrance is narrowed for a short distance (to better support the gangway) and then widened to the full width, or the whole is driven to the limit narrow, and the side is robbed when the top is drawn, and the whole room caves in. This last must be surveyed before the robbing begins. The most accurate method of survey is to run a line along the gangway and put a station at the entrance of each room, whence a sight is taken to the face. This may be varied by putting the stations at alternate rooms 68 SURVEYING. and measuring through the cross-cuts to get the thickness of the pillars of the intermediate rooms, or placing stations at every third room and measur- ing the thickness of pillars and width of rooms that intervene; or, finally, by running out the gangway with as few sights as possible and paying no atten- tion to the positions of the rooms in setting stations, thence up to the last room to the face, and back through the cross-cuts nearest the face to the former work, where a tie is made. When opportunity offers, sights are made from the face of the rooms to the stations in the gangway for immediate ties. In case a gangway and airway have been driven considerably ahead of the rooms, it is always necessary to run lines out each and tie at the last cross- cut. This must be done in every case where the gangway is approaching the boundary line, or old workings that have been abandoned and are full of water. In addition to this check the miners must keep bore holes 20 ft. ahead in the line of the gangway, and every 20 ft. must drive others from the corners of the heading at an angle of 30 with the line of the gangway. In this way there will be no danger of running into " a house of water," as the Cornish miners call it, if the survey be inaccurate. Pitching Work. When the bed pitches so that a car cannot be run to the face, and when there is a good deal of firedamp in the mine, it is generally difficult to see from the gangway to the face, where the roof is good and the room straight, as a baggy track or chute, or both when the pitch is slight- fill up the room, and, where the pitch is great, the gangway pillars generally run across the face, or there is a " battery" shutting off the bottom of the room, so that the face can be reached only by several sights. Where the roof is poor, the obstructions are increased, as the rooms are driven narrower, or, if wide, have center props and stowing in the center. If the coal is full of slate, or if the partings are thick, a large part of the room is taken up with piles of " gob," and with a very poor roof the body of the room that has been worked out is filled with the fallen roof, and the coal is sent out through the triangular manways, where it is almost impossible to take a sight. Work of this kind is surveyed by lines out gangway and back through the faces of the rooms, which are generally clear, even if the bodies of the rooms are filled with the fallen top. Where chance favors, sights are taken to the gangway; but this very seldom happens, as the two lines are as effectually separated as if in different mines. From the stations in the faces, lines are run down the rooms as far as possible to get their direction, and to locate the cross-cuts. The very worst case of all is where two beds are separated by a thin parting of rock and the gangway is driven in the lower one alone, the rooms in the upper one being worked by rock chutes into the rooms below, or into the chutes from those rooms. This class of work is hard to ventilate, and to survey where the rooms above are ventilated by the air system of the lower beds; but is readily mapped where there is an air system for each bed. Closfhg Surveys. To diminish the chance of error and to furnish a ready check, the survey must be closed upon itself or some part of a former survey with every twelve new stations. With good work the error in arc in a close should not exceed 1', and the error in position should be less than 6 in. Errors must not be "balanced"; they must be detected and rectified by running the line again, if they are not readily seen from the methods to be given. If an incorrect survey be balanced, each subsequent one must be altered to fit this incorrect work, though it may be correct in itself, and we never know where our work really stands. It is well, therefore, to check the work in arc as soon as we make a close and before the party leaves the place, as it is easy to rerun the work then. CONNECTING OUTSIDE AND I NSI DE WORK TH ROUGH SHAFTS AND SLOPES. As the dip of the bed increases, it is less easy to make a connection, and the chances of accuracy diminish. In a survey, R. Cos. Vert. Angle is what locates the station with regard to former work. The greatest angular - *I _- ___ **--* , _7 O SHAFTS AND SLOPES. 69 than does the pitch, and as R. Cos. Vert. Ang. diminishes, though R be fixed, the chances of error increase. When the slope reaches 60 there is an impracticability in running a line down a slope, as the line of collimation of the telescope strikes the graduated limb of the instrument. We can use a prismatic eyepiece and see up the slope; but cannot look down. As we have assumed that it is unnecessary to use an additional telescope, we shall have to run the line by intermediates. Set up at the bottom of the slope where the longest sight up the same can be secured and backsight on a station of the underground work; or set a backsight for the occasion (both stations will afterward be connected with the work below). With the prismatic eyepiece, sight up the slope on a line that will give the longest sight and, at the same time, afford a good intermediate place to set up the transit, as, on a pitch of 60 or more, it is absolutely necessary that the legs of the transit should be set solidly (in holes in the floor, or between the sills of the track) so that they will not be moved by subsequent walking about it. By this method, all the sights will be taken from one side alone, and the tripod legs can be shortened to make the sight possible without building a standing place if the man be short-legged. Call this station A; at the foot of the slope locate B, where the transit can be readily set up, and as far up the slope as we can see (this distance must be at least 100 ft.), and in a continuation of A B, locate C. Set up at B and take foresight to C; locate D under the same conditions that governed the placing of B, and, in a continuation of the line B Z>, place E. Set up at D with foresight at E, and locate F and G as before. The survey is carried by the intermediates B, D, F, etc., to the top, by a series of foresights to (7, E, G, etc. Shafts. The term shaft in American coal-mining practice is applied only to vertical openings, though in metal mining, both in this country and abroad, it is also applied to highly inclined slopes. For such shafts, most of erecti9n of a temporary (and therefore more or less unsteady) support for the tripod of the transit, and the chances of variation in its position as we stand on different sides of it are so great that we cannot feel sure that a movement has not taken place that will vitiate the work. In sighting up a shaft of greater depth than 100 ft., there is annoyance if not danger from dripping water or the fall of more solid substances. In a wet shaft the object glass is instantly covered with water, and a sight is impossible. We must also have a platform to stand upon, and we cannot feel sure that this will be perfectly rigid. From all these considerations the methods with a transit are never used by engineers in the anthracite regions, and the connections are made as follows: When the bottom of the shaft can be reached by an adit or slope in a roundabout route of such length as to render errors in measurement of dis- tance of great importance, the angles are carried by a transit with as long sights as possible, and no distances are measured, from a point on the surface in the shaft to a point vertically below it in the mine. Sometimes the guide of the cage is taken when it has been recently set, as the guides are plumbed into position; but the better way is to suspend an iron plummet by a copper wire: sink the former in a barrel of water so as to lessen the tendency to swing on account of the pull upon the "bob" and wires from the air-cur- rents, or falling drops in a wet shaft. The top of the barrel is covered with two pieces of plank with a semicircular groove of 3 in. radius cut out of the middle for the passage of the wire, to catch the substances whose fall upon the water would cause waves. The heavier the plummet and the lighter the wire, the less the tendency to swing. This wire can be sighted at by parties above and below at the same time, and the swing can be bisected to get the position of the wire. A number of sights that agree can be taken as accurate. When the shaft is the only way to get below from above, it must be plumbed with two or more wires suspended as just described. With two wires, they are so hung that an instrument can be set up below in a line passing through them produced, and at a sufficient distance from them to insure an accurate sight; with more wires, the station below can be located at any point whence all the wires can be seen. CASE 1. Two wires are used, which are located as far apart as possible. Two pieces of scantling c d and ef, Fig. 1, are spiked across the opposite corners of two compartments of a shaft to allow the cages to pass up and down 70 SURVEYING. without interference. The station X is (roughly) located in a line through the corners x, x and is connected with the outside survey. From this station locate in the line Xxx two spads for holding the wires of the plumb-bobs. These are driven up to the head in the scantlings in such a way that the line of sight passes through the center of the holes in their heads. Measure the distances Xa and a b. This completes the work of the survey above ground. The light copper wire is rolled upon a reel, and one end is fastened to a light plumb-bob to keep it free from coils or kinks in descending. It can thus be readily lowered without accident. When at the bottom, the upper end is fastened in the spad and the heavy "bob" applied to the bottom and placed in the empty barrel. The cages are then run slowly up and down, with an observer on each, to see that the wires hang free from top to bot- tom. By this time the wire will have stretched so that it will be straight, and if there be any slack, it is taken up, the barrel is filled with water, and the top boards put in place. As a last check, measure the distance between the wires below and see if it agrees with the distance above. Lining in below a point Y on the line a b, make a hole in the roof two inches in diameter, and drive in a broad plug. Setting up the transit under Y, we sight at the wires a and b alternately. A number of methods for illumi- nating the wires have been used, and are given in textbooks. The writer has always found those depending on a sight of the wire across the flame of a lamp the hardest to obtain, and concludes from experience that the method of illuminating the wires for mine surveying is the best for this also. A large white target is placed behind both wires and illuminated by a large lamp with a reflector behind it. The wire stands out black against it and can be followed across the target. As there is considerable distance between the wires, and as the transit is comparatively near them, there will be small chance of getting a sight of one, when the telescope is focused upon the other, and so the focus has to be set between them. This gives a hazy sight at each; but both are shown against the white background in strong relief. After the transit head is shifted so that the line of sight coincides approxi- mately with both, focus upon them alternately and see if the line bisects the swing of each. If so, the work is done; if not, the shifting of the transit head must follow till the end is attained. It frequently requires two or more hours of steady observation to complete the work, and, when it seems as if the proper point were secured, one of the wires will show by its swaying that it has been deflected from the vertical by a peculiar slant of wind, and the result obtained must be checked again. When you are through, there is no absolute certainty that the point you have marked is in the accurate extension of the line a b at the surface. Having decided on the proper place, you drive a spad into the plug overhead; hang a plumb-bob to it, and see if it be over the axis of the transit, as shown by the screw on the telescope. If not, drive the spad so that the point of the bob does so hang, and the station Y is said to be in the line a b. pleasure Ya and the angles to any station of the underground survey; the line ab is connected with the surveys at day- light and below, and the plumb-bobs may be removed. Criticism of the Above Method. 1. As has been stated, there is no absolute certainty that the point Y is in the line a b prolonged, and this want of certainty should not exist in so important a measurement. 2. The work must be performed by daylight, and the length of time necessary to complete it makes it impossible to work the shaft for at least half a day, and may cause annoyance to the operators, or, if you are working for a lessee, lead them to refuse to let you have the use of the shaft at the time most suitable for your purpose. 3. It may be hard to obtain a long sight below on any line running through the larger axis of the shaft. Any shorter line would give too short a base line and would increase the chances of error. To avoid these, another method is sometimes used. CASE 2. Fig. 2 shows the top set of timbers in a shaft of two hoisting compartments, down which it is desired to carry a known course or merid- ian on the surface to the entry below. First find out which side of the shaft is best adapted for setting up the transit, as the point to be marked in the mines will be vertically under the point on the surface; consequently, SHAFTS AND SLOPES. 71 the side with the widest opening leading from the foot of the shaft should be selected. Having carried the meridian to a convenient point near the top of the shaft, and having found that the south side of the shaft is the most accessi- ble, determine, with an ordinary string, the location of the point A, from which the hangers for the plumb-lines will be exactly located by means of the transit. Now mark with chalk on the timbers where the strings cross. These marks, though not accurate, serve as guides in setting the hangers. Make a permanent station at the point A and carry the meridian to it. The hangers can be made of strap iron, in. thick by 2 in. wide, and at least "16 in. long. In one end of the iron, have a jaw with a fine cut at the apex, or a drill hole just large enough to contain the wire to be used for plumbing. There should be two or three countersunk holes in the hanger, through which to fasten it to the tim- bers by means of heavy wire nails. A top view of the hanger is shown in Fig. 2. In most shafts there is a space from 2 to 4 in. wide between the ends of the cage and the sides of the timbers; \ r 1 \ 4 , / , \ / \ / 4 i FIG. 2. and in order to hoist and lower the cage to see that the wires are hanging freely, it is best to set the hangers in such a position on the timbers that the wires will hang in the middle of the space. Fasten the hangers permanently over the chalk marks previously made on the north side of the shaft, with the jaws pointing toward J., and on the south side of the shaft the outer end of the hanger may be fastened temporarily. Now set the transit over the station at A, take the backsight, foresight on the wire hole of the hanger C and set the wire hole of the hanger B on the same line. Record this course and foresight on the wire hole of the hanger E, fixing as before the wire hole of the hanger D in the same line. Record this course, and then the meridian to be carried into the workings below is established. Measure carefully and record the distances A to B, A to C, and B to C, the distances A to D, A to E, and D to E, and finally the dis- tances Bio D and C to E. The necessity of taking all these measurements is for the purpose of establishing a point at the bottom of the shaft vertically below A, and checking the work in the office. The transit party can now descend to the bottom of the shaft, taking with them four buckets of oil, the weights or plumb-bobs to be attached to the wire, and all the surveying instruments, leaving a responsible party on the surface to handle the wires. Having arrived at the bottom of the shaft, have the cage hoisted 3 ft. above the landing, throw several planks across the timbers on which to set the buckets of oil, signal to the man on top to lower a wire and to fasten it securely, passing it through the wire hole of the hanger; now attach the plumb-bob and adjust the wire to such length that, when sustaining the full weight of the plumb-bob, the latter will not touch the bottom of the bucket. Insert the weight in the oil, using care not to leave the full weight on the wire with a jerk, but let the weight down slowly, so that the wire receives the full strain gradually. Set the three remaining wires in a similar way. After the wires have been hanging a few minutes with the weights attached, the latter may move from one side to the other of the buckets. Watch this carefully and keep moving the buckets until all the weights hang perfectly free, then leave everything alone until the wires become steady. The cages can now be hoisted and lowered for the purpose of examining the wires to see that they hang free and plumb, care being taken that the cages are not brought so close to the landings as to disturb the hangers at the top, or the buckets at the bottom. To find a point vertically below A, stretch a string along the wires B, C, being careful not to touch them; stretch another along the wires Z>, E\ then, with a plumb-line, determine a point on the bottom vertically below 72 SURVEYING. the intersection of the strings. Measure the distances A B, A D, B D, and C E and compare them with the corresponding distances at the top of the shaft. If these distances compare favorably, the wires are, in all probability, steady, and the work of determining the desired course with the transit may now be begun. Set the transit up over the point of intersection just found; backsight on the wires B, C ; foresight on the wires D, E, and compare the included angle and the distances with the corresponding angle and distances at the surface. If these do not correspond, move the transit in the direction necessary to increase or decrease the angle or distances, as the case may be. Repeat this operation until the exact point verti- cally below A is determined. A simple device that is of great advan- tage is to have three links from an ordinary trace chain placed in the wires on the side toward the transit, and a few feet above the buckets. This not only enables the wires to turn freely, but also enables the transitman to sight through one of the links to the wire beyond, whereby he can place IfflHB the transit in exact line with the wires more >. : easily than if the links were not there. \ ~ v CASE 3. Two, three, or four wires are /ll\ ' employed. They are secured and hung as / 1\\ : ' before, and are located in the angles of the / \\ I - Wt compartments x, x, x, x, Fig. 3. These are / 1\ \ I connected with four stations A, B, (7, D, the I 1 \ i^^^ lines A B and C D being at right angles to \ D7 \1 one another for convenience in the subse- \ fw *yl quent calculation, and are connected with \ Jf / the outside survey. From A and B, taking \ I / I AB as a base line, the points x, x, x, x are \// ' located. The same is repeated from C and W/ - . * D, taking CD as a base line. We thus have L four locations of each wire. These are tab- ulated, and any variations in a reading must be followed by a repetition of the same. The mean of the readings gives the location. (Subsequently, the subject of cal- culating work will be taken up.) It can be briefly stated here that the bearings of each wire to each of the others, as referred to the base line of the survey, are then calculated and the distance between the wires accu- rately measured. This finishes the work at daylight. There may be two general types of arrangements of the bottom of the shaft, and both arrangements have been sketched and lettered similarly. The first is a case when the shaft is arranged across the dip of the bed, and the second is parallel to the same. In both cases and 7 are taken as far apart as possible, and all the wires x, x, x, x located from each station with reference to the other. The distances between the wires above and below are also accurately measured as a check. There will be four locations of and 7 from the four wires, and the mean of these is taken as the correct one. In every case of angle measurement mentioned, a series of readings of each angle is taken upon different parts of the graduated limb, to avoid instru- mental errors, and the mean of these taken as the true reading. From the locations of O and 7, the course between them, as referred to the mean base line, is calculated, and 07 is the base line for the underground work. The angle readings above and below can be made at the same time with differ- ent instruments, and, in taking the readings below, it is not necessary to wait for absolute quiet in the wires, as that is seldom found. A small swing can be bisected by the cross-hair, and the readings are duplicated until a FIG. i SHAFTS AND SLOPES. 73 FIG. 4. constant result is secured. By this method a greater -accuracy and speed is obtained, and the angles below can be accurately measured, no matter how the shaft may be arranged. The T-Square Method.* This ingenious method of taking the line under- ground is especially valuable in shafts with several small compartments or in cramped places where one cannot line in with the wires. The wires are placed in separate com- partments and as far apart as possible. The apparatus is made by the carpenter, and consists of a straightedge and T squares. The former is merely a planed pine board about 8 in. X $ in. and a foot longer than the distance between the wires. It rests approximately horizontally on slats tacked across the shaft for supports. It is brought to about an j or ^s in. from each wire and then nailed to the slats sufficiently to prevent slipping. One man should be at each wire. The T squares are most serviceable if made with a mov- able head clamped by a thumbscrew, and of planed pine, about 2i in. X i in. Except in cramped quarters, the T squares will be set at right angles, and should be placed together in clamping to insure that each is set at precisely the same angle. Fig. 4 shows a cramped position such as sometimes arises and in which the movable head gives more latitude in working. After clamping, the T squares are slid along the straightedge until close to the wire, but not touching it, and are there clamped by a " G " clamp, both men working at one T square. The ends of the T squares, C and D, must be supported on blocks so that the T squares lie approximately in the same horizontal plane. Everything up to the next step need be only approximately and quickly placed, but now the greatest care must be exercised in measuring out equal distances, A C and B D, from the wires. If the wire vibrates, determine the middle of its swing by a pencil or pin. Hold a footmark (not the end of the tape) opposite the wire on the T square, measure out an even number of feet, and mark the point with a sharp pencil, and insert a pin. This done for both wires gives us the parallelogram A B D C, in which the only essential is that CD should be exactly parallel to A B, the line of the wires. Now set the transit over the most convenient of the two points, as D. To get the azimuth of D (7, and, consequently, the line of the wires, sight on a known point E for a backsight, and measure the angle EDO. Establish another point as F, on the line of the backsight, in order that its course may be preserved after the instrument and T square are removed. By this means the closing angle at E may be read after the wires are removed from the shaft. Underground, the method is the same, except that D C is the known course, and is used as the backsight. To give the coordinates of the instrument at D with the greatest precision, the angle ADC and the distance A D should be measured. Surveying Slopes or Inclined Shafts. Where a single sight reaches from top to bottom of the shaft, the problem is simple enough. A station can be estab- lished on the inside of the foot-wall plate at the collar and others in similar positions at each level. The instrument set up over any station can command the whole shaft and the level opposite. Where the shaft is sunk on several dips, the survey is a much more difficult matter. Fig. 5 illustrates cases of common occurrence. The shaft may be divided into sections like A DEB, which are convex downwards, and others such as EEC, which are concave downwards. As a rule a set-up can be avoided at the convex knuckles if desired, and need only be made at those that are concave. Bent Plumb-Line Method. A may be invisible from B, but the survey may be FIG. 5. * See " Mines and Minerals," January, 1899, page 242. 74 SURVEYING. carried from one point to the other by the ingenious method of the bent plumb-line. The most complicated example which can arise is shown in Fig. 5. Establish a station at A, the foot-wall side of the collar, the center point being a small nail head projecting horizontally. Attach a long plumb-line to this and carry the other end to B. Here it will probably be necessary to use a small screw-eye, with its head turned into the vertical plane of the shaft, for the center point. Pass the plumb-line through this and draw it fairly tight. Now attach a plumb-bob at an intermediate point and regulate the tautness so that the line is clear at all points. The curves in the shaft may be such that two plumb-bobs may have to be hung, as at D and E, and even a third may become necessary. The plumb-line, perhaps 100 ft. long, is apt to be disturbed by the air- currents, and it is often better to mark a point on a convenient timber near D, and another near E, so close to the string that there is no doubt of the points lying in exactly the same vertical plane as the plumb-line. If these points be once established, the string and weights can be taken out of the shaft, leaving us four points in the same vertical plane, and whose horizontal projections lie in the same course. Now set up at A and measure the azimuth angle from the backsight to D, thereby giving the bearing from A to B. If D should be invisible from B, depress the telescope after sighting on D and locate the point N in the same vertical plane, and so situated that it is visible from both A and B. Measure the vertical angle and distance to N. Now set up at B, use the course B E for a backsight, and foresight to C. Measure the vertical angle and distance B N. It is seen that B jy might have been used as a backsight, and E only serves as an additional check. N is really an intermediate station, but since it lies in the course A B, a set-up there is unnecessary. In simple cases, it is a very convenient method of carrying a survey from the surface to the first level, and a longer horizontal projection of the sight A D can be secured than if a set-up were made in the shaft at D; but in complicated cases, such as the one shown, it may often be quicker to make the extra set-up than to use the plumb-line. In all sights for determining azimuth, keep the vertical angles as low as possible, and the horizontal projection of the course long. Method by a Single Wire in the Shaft Stretch a rather fine wire, free from kinks, down -the shaft, as shown in Fig. 6, being careful that it touches nowhere in the shaft. Take two plumb-bobs provided with fine round strings. Suspend one from A and the other from B so that they nearly touch the same side of the wire MN. In order to have the plumb-lines as far apart as possible, the line at B must be quite long and a can of water should be provided to keep the bob from swinging. The plumb-line is fastened to a nail B nearly in the proper position. Have a bar of wood with a block fastened to it placed to one side of B and a little below it. The block must have a hole so that a small screw bolt can easily screw through it. A spool is run on the bolt having a small groove turned in it and being sandpapered and greased so that the string will slip easily as the bolt is turned. Now, place the transit in line with the two plumb-bobs as in an ordinary case of shaft plumbing. Repeat this operation below. The plumb-bobs in both cases hang in the same vertical plane and thus the true bearings are found underground. Even the plumb-lines could be dispensed with, but the method would not then be so accurate. The instrument would be set nearly in the vertical plane passing through the wire, leveled and sighted at M. Dip the telescope until the lowest point on the FIG. 6. wire is visible, note the amount by which the cross-hair and wire fail to coincide and shift the instrument accordingly. But if this method were tried, the two points sighted at would not be nearly so far apart horizontally as the plumb-lines, and any error in leveling would also vitiate the result. This method of the single wire, however, provides no way of obtaining the coordinates. NOTES ON MAPPING. There are no general rules governing the minutiae of map making, so that it may be well to note some of the variations in practice. In some offices the area excavated is shown by a light wash of India ink in addition NOTES ON MAPPING. 75 to the ink line bounding the solid area. This makes a striking map, and the workings stand out prominently. If the survey were never to be extended and the map were simply made to show a particular state of the workings, there would be no objection to the practice; but as such exten- sions have to be made, and old pillars removed or cut up, it requires con- siderable skill to tint the extensions, and especially the surfaces when erasures have been made, so as to produce an effect uniform with the old tinted surface, especially as that tint has been deepened by frequent han- dling. For these reason's many offices omit the tint on the map, but some tint the back of the tracing used by the corps, or sent to the mine inspector. It is an open q'uestion whether the ends of the chambers (breasts, rooms) and gangways (entries, levels) should be closed with ink. It is well to be able to show on your map where the faces of the workings were at any given time. Some place the date of each survey at the ends of the gangways at each posting, and of every fourth or fifth chamber, and thus note the rapid- ity with which the mine is worked. Others use various colors to denote the successive postings of the survey, and place across the ends of gangways and chambers the color appropriate to the survey that located them. Where there are a number of beds worked from the same shaft, slope, or adit, the workings are frequently vertically above one another, and their location on the same map causes confusion unless care be taken. One of the methods used to distinguish between each bed is to line in the areas worked with a color appropriate to that bed. In this way, three or four beds have been plotted on the same map. A better way is to make a map for each bed and to combine the various beds on the tracings for the officers and the mine inspector. Each bed on this is lined with its color, and tinted with a wash of the same color on the back of the tracing on the parts excavated. The lines of survey are lightly drawn between stations with red ink, and the stations denoted by minute circles of the same color as that used for that particular seam. The survey lines should never cut the circumference of the circle, as such a procedure might cause doubt as to the exact location of the station in case measurements were made on the map. Stations are numbered as in the mine, and beneath each is placed the elevation above or below tide of the roof of the mine. If the stations are numerous and the elevations fre- quently taken, such a map would furnish the means of ascertaining the shape of the bed by running contours through points of equal elevation. This plan was used by a number of engineers and was adopted by the Second Geological Survey of Pennsylvania in making their mine sheets. The adop- tion of the scale of 100 ft. to the inch, under the ventilation law, also fur- nished that survey with a means of tracing and connecting adjoining properties and their workings, as had been frequently done by large com- panies having adjacent collieries, and the maps of the anthracite regions of the Second Geological Survey of Pennsylvania have been thus compiled from tracings of office maps, with little or no inside work by the corps of the survey. The ground areas of all buildings are tinted a uniform red. All railroad tracks are represented by red lines. All bridges, etc., and, in fact, any improvements built by man, are to be colored red. In the mine, the stations are represented by a small circle (o) with the number in black beside it. The lines of survey are drawn between the circumferences of the circles marking the station o o, so as to leave the centers uncolored. The elevations above tide are marked. All small bodies of water are tinted with Prussian blue; all large bodies with indigo as Prussian blue is too vivid for large areas of tint. It is the custom to allot a color to each bed, and make each bed on the general tracing in its color. In this way all the beds may be mapped on the same tracing, and can be distinguished though the workings may all under- lie the same area. Various colors are sometimes used to denote the extent of the workings at the given postings. The paper on which the map is made should be of the best quality, as frequent changes in the workings, and the removal of portions of old pillars, necessitate many erasures. Ordinary paper will not work well after erasure and subsequent handling, and the best practice is to use cloth-backed egg- shell paper. It remains to note that the temperature and humidity of the office, and of the place where the maps are stored, should vary as little as possible. As the scale is small, any variation in the paper by contraction or expansion will 76 SURVEYING. affect the scale on which the map was originally laid out, and will affect it unequally, as the paper is not homogeneous. This can be seen by making measurements on old maps to check work done in former times. In almost every case the 500' squares are slightly in error. This must be guarded against in case -measurements are taken from the map. It is best to calculate the distances wanted from the coordinates of the ends of the lines, and insure absolute accuracy. A good map is the sign of a good draftsman. The title should be subordi- nate to the map. It is common to see the fifty-cent map of a small area smothered under a gorgeous ten-dollar title. The lettering should be neat and appropriate, and a style should be adopted that can b'e readily thrown off as time is quite an item in the money made by mapping. A neat title, the judicious use of tints over the area excavated, and good lettering of minor objects will add dollars to the value of a map. A small outlay of taste and care will make a beautiful tracing out of a ragged one, and double its value. Locating Errors. Errors in arc or distance are easily located by the method of coordinates. The transitman, at the completion of a closed survey, should Fum the angles and see if it be 360. Thus, before leaving the mine, a check will be established on the transit work. In case of a variation from 360, the notes are examined to see if the needle readings show a similar variation with the vernier. In case the notes are incomplete, or, if a continuous vernier has been carried, we table the work before leaving the mine and locate the error as follows: Fig. 7 represents a close of four stations and an angular error at c. Starting from a we table as follows: Sums. Sta Course Dist N s E W N S E W a N 100 100 100 b E 100 100 100 100 c S30E 100 86.58 50 13.42 150 d (d'} S60 W 100 50 86.58 36.58 63.42 a (a") N30 W b There is an error in close of 30, as the course a"b differs from the course a 6 by 30. Reversing the order of tabling, and correcting each course by 30, we have: Sums. Sta. Course Dist. N g E W N S E i W a E 100 100 100 d N 100 100 100 100 c N60W 100 50 86.58 150 13.42 b (b') S30 W 100 86.58 50 63.42 36.58 a (a') d S70E Upon comparing the sums of the northings and southings and eastings and westings in both, we find that c is the only station for which they agree. Here the error occurred. The location of c from either direction was cor- rect, and what followed incorrect. From this we can deduce the rule: To Find an Error in Arc. Table the close from any station in both directions back to the initial station. The station which has a similar sum of eastings NOTES ON MAPPING. 77 and westings and northings and southings in both tablings is the one at which the error was made. With two or more errors nothing can be done. Errors in Distance. These maybe found in a close by tabling. Suppose we have a square abed so placed that the magnetic meridian passes through b d. Let the distance c d be incorrect. Sums. Qfo Dist \r g E W N S E W a N45E 100 1 70.71 70.71 70.71 70.71 b S 45 E 100 1 70.71 70.71 141.42 c S 45 W 150 106.06 106.06 106.06 35.36 d N45W 100 70.71 70.71 35.35 35.35 a The first location of a is southings 0, westings 0; the second location is southings 35.35, westings 35.35. The westings are sines and the southings cosines, as stated before. As sin -f- cos = tang of course referred to the base line, we divide 35.35 by 35.35 and obtain 1 as the natural tangent for 45, and, as the error was in southings and westings, the course on which the error was made is S 45 W. The amount of the error is found by dividing the error in eastings or westings as tabled by the sine of the course just found, or the error in northings or southings by the cosine of the same. Both results will agree, 35.35 -r- 70.71 = .50. Reducing the measured distance by this amount, we find the tabulation shows an accurate close. From this we deduce the rule: To Find an Error in Measurement. Divide the difference between the east- ings or westings of the two locations by the difference between the northings or southings of the same. The quotient will be the tangent of the course on which the error was made. The extent of the error is found by dividing the error in eastings or westings (as tabled) by the sine of the above course, or the error in northings or southings by the cosine of the same. Locating Special Work. This last principle may be used for finding the proper course and distance to drive a tunnel between two stations connected by a survey. In outside tunneling, the survey is generally carried over the surface in a straight line. In underground work this is impossible, so that it is a much more difficult task to ascertain the distance and direction to drive, from the number of measurements to be made in connection with the two stations, but if the work is accurately done it is much more a feat than in outside work. To include all the elements that enter into such a calculation, we will suppose that an underground slope is to be run between two beds of coal. The distance between the two ends must be accurately obtained, as well as the relation of the two stations found. Having tabled the work, we get the difference between the sums of sines and cosines, as just described, for the two points; the quotient from dividing the first by the second gives us the course, and from the last rule the horizontal distance is found. The levels give us the difference in elevation, and from these data we get the slope per hundred, and the distance measured on that slope. All of the work is done in the mine and while the transit is setting up at one of the end stations, so that before leaving the mine, we can give the course, pitch, and distance of the tunnel and set the first station for lining in the center. The more important the work, the greater need of accuracy. In one case a 1.000' chain was constructed to measure the distance between two shafts that were to be connected by work driven from both ends, and much of the outside work was done on the ice of the Susquehanna River, and a transit reading to 5" was used. The work closed vertically and laterally within an inch. Calculation of Areas. In connection with the mapping of the part newly worked, the engineer of the company sometimes calculates the area excavated since the last posting, and estimates the royalties accruing to the various parties whose lands are leased. This method, at best, is liable to grave errors, and requires a number of accurate cross-sections of the bed to determine its composition, as well as 78 SURVEYING. numerous determinations of the specific gravity to determine its weight. The old method of estimating workable coal in a property allowed 1,000 tons per acre per foot of thickness of the bed. To obtain this amount, the roof must be good, the pillars of medium size, and the bed near the surface; or the surface must be so valueless that the pillars can be "drawn" or "robbed." As beds increase in depth, if the surface be valuable, the ratio of pillars to stall must increase or the greater pressure will cause the mine to cave in. It has been found that, when the surface is to be kept up and the workings are to be carefully driven, but 850 tons per acre per foot of thick- ness can be used in calculation, under the present system of mining. Efforts are constantly being made to increase this amount, with a possible chance of success. To estimate the amount of coal excavated from any property, the best method is to institute an account of all cars of coal taken out from the work- ings under that property. As soon as the measurements on the mine tracing show that a gangway or room has crossed the property line, the office is notified, and all cars coming from those places are credited to that property. This is the only absolutely accurate method of computation. The total number of cars of coal run through the breaker is known, with the total weight of prepared coal. The ratio of the cars coming from a given property to the total number of cars is taken as the ratio between the total prepared coal and the coal sold from that property. RAILROAD CURVES. These are generally circular, and divided into simple, compound, and reverse curves. A simple curve has but one radius, a compound one is con- tinuous and has two or more radii, and a reverse one is also continuous but com- posed of arcs described in opposite direc- tions. Curves are designated by the number of degrees in the central angle, which is subtended by an arc whose chord is 100 ft. long. Thus,' if the angle BOG, Fig. 1, is 10 and B G is 100 ft. long, B G H C is a 10 curve. The angle FE C, formed by the pro- longation of two adjacent straight por- tions of a railroad, or tangents, as they are technically called, is termed an intersec- tion angle. The deflection angle of a curve is the angle formed at any point of the curve between a tangent and a chord of 100 ft., and is therefore one-half the size of the degree of the curve. If the chord B G is 100 ft., the angle EB G is .the deflection angle of the curve B G H C, and is one-half the angle BOG. When the deflection angle D is given, the radius of the curve, R, is found by the formula --- ~ sin D' The curve used to connect two tangents is determined mainly by the form of the country. When this is decided; the point of beginning, called the P. C. (point of curve) , and the point where the curve ends, called the P. T. (point of tangent), must be located. Both these points are the same distance from the point of intersection of the tangents, called the P. I. (point of inter- section). This distance is called the tangent distance of a curve, and is found by the formula T= tftani J, in which T= tangent distance; R radius of curve; / = intersection angle. Having set the tangent points B and C, Fig. 1, in order to locate points on the curve, set up the transit at B, the P. C. Set the vernier at zero, and sight to E, the P. I. Suppose B to be a full station on the tangent, and that it has RAILROAD CURVES. 79 been decided to set stakes at each 100 ft. Let the central angle BOG, meas- ured by the 100-ft. chord B G, be 10; then, the deflection angle E B G, having its vertex B in the circumference, and being subtended by the chord B G, will equal i B G, or 5. Turn an angle of 5 from B, which in this case will be to the right, measure 100 ft. from B, and drive a stake at G. Turn off an additional angle of 5, making 10 from zero, and at another 100 ft. measured from G, and drive a stake at H. Continue this process until 20, or one-half the intersection angle, has been turned off. This last deflection will bring the forechainmaii to the point of tangency C, or the P. T. >Yheii the P. C. comes between two stations it is called a substation, and the chord between it and the next station on the curve is called a subchord. Had the P. C. been a substation, say 32 ft. beyond a regular station, the deflection angle for the measuring distance of 100 32 = 68 ft. would be found in this manner: The deflection for 100 ft. is 5 = 300'; hence, for 1 ft. Qfvy it is YO^- = 3', and for 68 ft. it is 3 X 68 = 204' = 3 24'. This is turned off and a stake set in line 68 ft. from the transit. Other stations are then located as above, by turning off an additional 5 each time. Rules for Measuring the Radius of a Curve. Stretch a string, say 20 ft. long, or longer if the curve is not a sharp one, across the curve corresponding to the line from A to C, in Fig. 2. Then measure from B the center of the line A C, and at right angles with it, to the rail at D. Multiply the distance A to B, or one-half the length of the string, in inches, by itself; measure the distance D to B in inches, and multiply it by FIG. 2. itself. Add these two products, and divide the sum by twice the distance from B to D, measured exactly in inches and fractional parts of inches. This will give the radius of the curve in inches. It may be more convenient to use a straightedge instead of a string. Care ' must be taken to have the ends of the string or straightedge touch the same part of the rail as is taken in measuring the distance from the center. If the string touches the bottom of the rail flange at each end, and the center measurement is made to the rail head, the result will not be correct. In practice, it will be found best to make trials on different parts of the curve, to allow for irregularities. EXAMPLE. Let A C be a 20-ft. string; half the distance, or A B, is then 10 ft., or 120 in. Suppose B D is found on measurement to be 3 in. Then 120 multiplied by 120 is 14,400, and 3 multiplied by 3 is 9; 14,400 added to 9 is 14,409, which, divided by twice 3, or 6, equals 2,40H in., or 200 ft. H in., which is the radius of the curve. The formula is thus stated, * _ 2BD Or, applied to the above example, in - - 20 ft - H in - z ,\ o To Find the Radius of a Circular Railroad Curve, the Straight Portions of a Road Being Given. If Q I and PD, Fig. 3, are the straight portions that are to be connected, the radius of the curve ID may be found as follows: Produce Q / and PD until they meet and form the angle T. Bisect the angle Q TPby the line TC. From the pojnt on either line from which the curve is to begin, in this instance making the point /the point of curve, erect the line I C perpendicular to Q T, and the point where this joins the line T C, or C, is the center of the curve, and the line I C is the radius. To find the end of the curve, or point of tangent, as Z>, draw a line from (7, perpendicular to TP. The line CD will also be a radius of the circle of which ID is the arc, and the point D will be the point of tangent. To Find the Radii of Compound Curves to Join Two Straight Portions of Road. This kind of curve is adopted where the railroad is required to pass through given points, as C, D, E, F, Fig. 3 (6), or to avoid obstructions. Compound railroad curves are composed of straight lines and circular arcs, and have common normals, OH, OP, PI, QJ, KR, and therefore com- mon tangents where the arcs are joined. The normals are perpendicular to the straight portions of the road also; OH is perpendicular to A B, EFis perpendicular to Q J"and KR. 80 SURVEYING. To find the radii B, C Q, Fig. 3 (c), to connect two straight lines of rail- road, A B, D E, the road has to pass from the point B, through the point (7, and to touch the straight road EF&t any point D. Join B and (7, make the angle B C = B C, which is supposed to be given, equal 90 TB (7. Draw BO perpendicular to AB, then OB = CO, and is the radius of the arc B C. With B as radius, describe the arc B C; draw C F perpendicular to CQ, and produce DEto meet it in F; make DF = CF, and draw D Q perpen- dicular to E F, to meet CQin Q. Then C Q = QJ), and the radii B and Q D are determined. Practical Method of Laying Out Sharp Curves in a Mine. Curves in a mine are usually so sharp that they are designated as curves of so many feet radius, instead of as curves of so many degrees. Suppose that it is required to connect the two headings A and J5, Fig. 4 (a), which are perpendicular to each other, with a curve of 60 ft. radius. Pre- pare the device shown in Fig. 4 (&), by taking three small wires or inelastic strings / g, g h, and g k, each 10 ft. long, and connecting one end of each to a small ring, and the other end of two to the ends of a piece of wood If ft. long. Form a neat loop at the end / of the string gf. To use this device, lay off on the center line of the heading B, c d and d e equal to 60 ft. and 10 ft., respectively. Place the loop / of the device described over a small wire peg driven in at e, and the ring g over a similar peg at d. Take hold of the stick h k, pull the strings g h and g k taut, and place the center mark on h k on the center line of the heading B. Drive a small peg in at m, located by the point k, which is on the curve. Move the device forward, . place the loop / over the peg at d, the ring g over the peg at m, and take hold of the stick h k and pull until the strings g h and g k are FIG. 4. taut, and the strings fg and g h are in a straight line. The point k will fall on the curve at n, which mark by driving in a peg. To locate other points, proceed exactly as in the last step. The distance c d in any case is found by the formula c d = R tan I, in which R is the radius of the curve, and I the intersection angle of the center lines of the headings. HINTS TO BEGINNERS. Abuse of Instruments. Surveying instruments of value and precision are not made of cast iron, as one would think from the way they are frequently handled. Underground work is transacted in places dark, dirty, and con- fined, so that extra care must be observed to prevent accidental knocks that damage the instrument even if they do not destroy its accuracy. STADIA MEASUREMENTS. 81 As it frequently happens that long distances must be traversed under- ground in going between the shaft or slope and the workings to be surveyed, the transit and level should be carried so as to obviate all accidents. They should never be attached to the tripod and carried on the shoulder, and, if the route to be passed over is up or down a slope or working place, the person carrying the instrument should be the last to descend and the first to ascend, so that loose stones or dirt that may be dislodged will not affect or endanger the instrument or trip the carrier. Be sure that the tripod head is tightly screwed on to the tripod. The writer remembers a case where the transitman and himself, when new to the work, spent over an hour in endeavoring to obtain two readings of an angle that would agree. The variations from 8' to 2 were caused by the slight movement of an old instrument with too much " lost motion," and a loose tripod head. A great many engineers prefer kerosene to fish oil for their lamps. Kero- sene never drops upon your book to make an unsightly smear, and perhaps obliterate part of your notes. A kerosene lamp is hotter and, with the glazed mine hat, is more apt to produce headaches. The writer, during the latter part of his underground ^vork, wore a straw hat, had a piece of thin sheet brass riveted to its front with a hole in the top for the lamp hook. To the lamp was brazed a narrow cross-strip of the same metal, and the strip ends, bent back upon themselves, were slid down the sides of the plate on the hat and kept the lamp from swaying. With such an arrangement it is not necessary to remove the lamp to read the vernier, and when the lamp is used for other purposes, the hat can be removed with the lamp fastened to it. This arrangement keeps the hands free from lamp smoke or oil, and a cleaner note book is the result. When there is an antipathy to a lamp upon the head, and when, with a long, wooden handle, one or both hands are free in going about the work, a larger lamp is used of "torch" pattern, employed by wheel testers or engineers in railroad practice. Kerosene can be burned in this. The handle can be tucked under the left arm while taking side notes. Such a lamp is convenient in finding old stations in a high place, when there is no firedamp. For plumbing wet shafts, kerosene resists the extinguishing power of water better than fish oil, and is less readily blown out by a strong ventilating current. It makes more smoke, and, in tight headings, or mines with poor ventilation, with a large party, fouls the air much more readily than fish oil. Sometimes a mixture of the two is burnt in very drafty places, where it is hard to maintain a light. Kerosene is burned in the plummet lamp unless it is used with the " safety " attachment. Sweet oil, or any oil burning without smoke, must then be used. Smoke clogs the openings in the gauze, restricts the entry and escape of gases, and, especially if the gauze be damp with oil, may ignite and communicate the flame from within to the outside body of gas. White lead or Dutch white (white lead and sulphate of baryta in equal parts) is best for painting stations. Zinc white has been tried with less success. The mixture should not contain too much linseed oil especially in wet places or it will run and destroy the witness. THEORY OF STADIA MEASUREMENTS. BY ARTHUR WINSLOW.* Late Assistant Geologist, Second Geological Survey of Pennsylvania, State Geologist of Missouri. , The fundamental principle on which stadia measurements are based is the geometrical one that the lengths of parallel lines subtending an angle are proportional to their distancesfrom its apex. Thus if, in Fig. 1 (a), a represents the length of a line subtending an angle at a distance d from its apex, and a' the length of a line, parallel to, and twice the length of, a subtending the same angle at a distance d' from its apex, then d' will equal 2d. *Mr. Winslow's calculations and tables have been proved practically correct by the several corps of the Second Geological Survey of Pennsylvania. . The corps in the anthracite regions, under directions of Mr. Frank A. Hill, geologist in charge, took over 30,000 stadia sights, and better results were obtained when tie surveys were made than in previous work in which distances were chained. 82 SURVEYING. This is, in a general way, the underlying principle of stadia work; the nature of the instruments used, however, introduces several modifications, and these will be. best understood by a consideration of the conditions under which such measurements are generally made. There are placed in the telescopes of most instruments fitted for stadia work, either two horizontal wires (usually adjustable), or a glass with two etched horizontal lines at the position of the cross-wires and equidistant from the center wire. A self-reading stadia rod is further provided, gradu- ated according to the units of measurements used. In a horizontal sight with such a telescope and rod, the positions of the stadia wires are projected upon the rod, and intercept a distance which, in Fig. 1 (6), is represented by a. In point of fact, there is formed, at the position of the stadia wires, a small conjugate image of the rod that the wires intersect at points 6 and c, which are, respectively, the foci of the points B and C on the rod. If, for the sake of simplicity, the object glass be considered a simple biconvex lens, then, by a principle of optics, the rays from any point FIG. l. of an object converge to a focus at such a position that a straight line, called a secondary axis, connecting the point with its image, passes through the center of the lens. This point of intersection of the secondary axes is called the optical center. Hence, it follows that lines such as c C and b B, in Fig. 1 (6), drawn from the stadia wires through the center of the object glass, will intersect the rod at points corresponding to those that the wires cut on the image of the rod. From this follows the proportion: P r ^-P (1) where d = distance of rod from center of objective; p = distance of stadia wires from center of objective; a = distance intercepted on rod by stadia wires; / = distance of stadia wires apart. If p remained the same for all lengths of sight, then y- could be made a desirable constant and d would be directly proportional to a. Unfortunately, however, for the simplicity of such measurements, p (the focal length) varies with the length of the sight, increasing as the distance diminishes and vice versa. Thus, the proportionality between d and a is variable. The object, then, is to determine exactly what function a is of d and to express the rela- tion in some convenient formula. The following is the general formula for biconvex lenses: / is the principal focal length of the lens, and p and p' are the focal distances of image and object, and are, approximately, the same as p and d, respectively, in equation (1): h -j = y, approximately, d d Therefore, and From (1), d Whence, _ 7 d = 4-( (3) STADIA MEASUREMENTS. 83 In this formula, it will be noticed that as / and I remain constant for sights of all lengths, the factor by which a is to be multiplied is a constant, and that d is thus equal to a constant times the length of a, plus/. This for- mula would seem, then, to express the relation desired, and it is generally considered as the fundamental one for stadia measurements. As above stated, however, the equation f- -=- = -j is only approximately true, and the conjunction of this formula with (2) being, therefore, not rigidly admissi- ble, equation (3) does not express the exact relation.* The equation express- ing the true relation, though differing from (3) in value, agrees with it in form, and also in that the expression corresponding to y- is a constant, and that the amount to be added remains, practically, /. The constant corre- sponding to -y may be called &f, and thus the distance of the rod from the objective of the telescope is seen to be equal to a constant times the reading on the rod, plus the principal focal length of the objective. To obtain the exact distance to the center of the instrument, it is further necessary to add the distance of the objective from that center to/; which sum may be called c. The final expression for the distance, with a horizontal sight, is then d = k a + c. (4) The necessity of adding c is somewhat of an encumbrance. In the stadia work of the U. S. Government surveys, an approximate method is adopted in which the total distance is read directly from the rod. For this method the rod is arbitrarily graduated, so that, at the distance of an average sight, the same number of units of the graduation are intercepted, between the stadia wires on the rod, as units of length are contained in the distance. For any other distance, however, this proportionality does not remain the same; for, according to the preceding demonstration, the reading on the rod is propor- tional to its distance, not from the center of the in- strument, but from a point at a distance " c " in front of that center, so that, when the rod is moved from the position where the reading expresses the exact distance, to a point say half that distance from the instrument center, the reading expresses a dis- tance less than half; and, at a point double that dis- tance from instrument cen- ter, the distance expressed by the reading is more than twice the distance. The error for all distances less than the average is minus, and for greater dis- tances, plus. The method is, however, a close approx- imation, and excellent re- sults are obtained by its use. Another method of get- ting rid of the necessity of adding the constant was devised by Mr. Porro, a Piedmontese, who constructed an instrument in which there was such a combination of lenses in the objective that the readings on the rod, for all lengths of sight, were exactly proportional to the distances. \ The instrument * This is demonstrated later on. t k is dependent on /, and can therefore be made a convenient value in any instrument fitted with adjustable stadia wires. It is generally made equal to 100, so that a reading on the rod of 1' corresponds to a distance of 100' + / J A notice of this instrument will be found in an article by Mr. Benjamin Smith Lyman, entitled " Telescopic Measurements in Surveying," in "Journal Franklin Institute," May and June, 1868, aud a fuller description is contained in " Annales des Mines," Vol. XVI, fourth series. 84 SURVEYING. was, however, bulky and difficult to construct, and never came into extensive use. For stadia measurements with inclined sights, there are two modes of procedure. One is to hold the rod at right angles to the line of sight; the other, to hold it vertical. With the first method, it will be seen, by reference to Fig. 2 (a), that the distance read is not to the foot of the rod E, but to a point /, vertically under the point F, cut by the center wire. A correction has, therefore, to be made for this. An objection to this method is the difficulty of holding the rod at the same time in a vertical plane and inclined at a definite angle. Further, as the rod changes its inclination with each new position of the transit, the vertical angles of backsight and foresight are not measured from the same point. The method usually adopted is the second one, where the rod is always held vertical. Here, owing to the oblique view of the rod, it is evident that the space intercepted by the wires on the rod varies, not only with the dis- tance, but also with the angle of inclination of the sight. Hence, in order to obtain the true distance from station to station, and also its vertical and horizontal components, a correction must be made for this oblique view of the rod. In Fig. 2(6), AB = a = reading on rod; MF = d = inclined distance = c+ GF = c + k. CH; MP = D = horizontal distance = d cos n; FP = Q = vertical distance = D tan n; n vertical angle; A G B = 2 TO. It is first required to express d in terms of a, n, and TO. From the proportionality existing between the sides of a triangle and the sines of the opposite angles, AF _ sin TO ^GF ~ sin [90 -HW TO)]' i or, AF = GFsinm and or, B F = G F sin TO r or A F + B F = cos (n TO ) ' BF _ sin TO GF ~ sin [90 (n + m)] ' __1 cos (n + m)' 1 AF+ BF = a, and GF= -_ = -_ 2 tan TO 2 sin m By substituting and reducing to a common denominator, C H cos m[cos (n + m) + cos (n m)] 2 cos (n + TO) i cos (n TO) Reducing this according to trigonometrical formulas, _ TT cos 2 n cos 2 m sin 2 n sin 2 m C Jd = a - , cos n cos 2 m as d = MF = c + k. CH. , cos 2 n cos 2 TO sin 2 n sin 2 m /. d c -|- ka . cos n cos 2 TO The horizontal distance, D d cos n. .. D = c cos n -f- ka cos 2 n ka sin 2 w tan 2 TO. The third member of this equation may safely be neglected, as it is very small even for long distances and large angles 01 elevation (for 1,500' n = 45 and k = 100, it is but 0.07'). Therefore, the final formula for distances with a stadia rod held vertically, and with wires equidistant from the center wire, is the following: D = c cos n + ak cos-n. (5) STADIA MEASUREMENTS. 85 or, The vertical distance Q is easily obtained from the relation: Q = Dt&nn. .-. Q = c sin ?i + a k cos n sin n; , sin2w = c sin n - a k - (6)* With the aid of formulas (5) and (6), the horizontal and vertical distances can be immediately calculated when the reading from a vertical rod and the angle of elevation of any sight are given. From these formulas, the stadia reduction tables following have been calculated. The values of a A; cos- n and a k Sm were separately calculated for each 2 minutes up to 30 of elevation; but, as the value of c sin n and c cos n has quite an inappre- ciable variation for 1, it was thought sufficient to determine these values only for each degree. As c varies with different instruments, these last two expressions were calculated for three different values of c, thus furnishing a ratio from which values of c sin n and c cos n can be easily determined for an instrument having any constant (c). Similar tables have been computed by J. A. Ockerson and Jared Teeple, of the United States Lake Survey. Their use is, however, limited, from the fact that the meter is the unit of horizontal measurement, while the eleva- tions are in feet. The bulk of the tables furnishes differences of level for stadia readings up to 400 meters, but only up to 10 of elevation. Supple- mentary tables give the elevations up to 30 for a distance of 1 meter. For obtaining horizontal distances, reference has to be made to another table, which is somewhat an objectionable feature, and a multiplication and a subtraction has to be made in order to obtain the result. Last, but not least, these tables are apparently only accurate when used with an instrument whose constant is .43 meter. The many advantages of stadia measurements in surveying need not be dwelt on here, both because attention has been repeatedly called to them, and because they are self-evident to every engineer. Neither will it be within the compass of this article to describe the various forms of rods and instruments, or the conventionalities of stadia work. It is seen that, in the deduced formula, the factor by which the reading on the rod is multiplied is a constant for each instrument. The question now arises, Does this remain the case with a compound objective? In view of the difficulty of demonstrating this mathematically, it was decided to make a practical test of this point with a carefully adjusted instrument. The readings were taken from two targets set so that the sight should be horizontal, thus preventing any personal error or prejudice from affecting the reading. A distance of 500 ft. was first measured off on a level stretch of ground, and each 50-ft. point accurately located. From one end of this line, three successive series of stadia readings were then taken from the first 50-ft. and each succeeding 100-ft. mark. The following table con- tains the results: Spaces Intercepted on the Rod. Feet. 1st Series. Feet. 2d Series. Feet. 3d Series. Feet. Mean. Feet. 50 .485 .4860 .4855 .4855 100 .985 .9870 .9830 .9850 200 1.985 1.9860 1.9840 1.9850 300 2.989 2.9875 2.9870 2.9878 400 3.983 3.9800 3.9890 3.9840 500 4.985 4.9850 4.9900 4.9867 Multiplying the mean of these readings by 100, and subtracting the result from the corresponding distance, we obtain the following table: *The above demonstration is substantially that given by Mr. George J. Specht in an article on Topographical Surveying in "Van Nostrand's Engineering Maga/ine," February, 1880, though enlarged and corrected. . 86 SURVEYING. Distances. Feet. Mean of Stadia Readings Times 100. Feet. Differences. Feet. Variations From Mean. Feet. 50 48.55 1.45 + .02 100 98.50 1.50 + .07 200 198.50 1.50 + .07 300 298.78 1.22 .21 400 398.40 1.60 + .17 500 498.67 1.33 .10 Sum of differences = 8.60; mean of difference = 1.43. The variations between the numbers of the column of differences are slight, the maximum from a mean value of 1.43 ft. being only .21 ft. A study of the tables will show that these variations have no apparent rela- tion to the length of the sight, and as, in the maximum case, the variation corresponds to a reading on the rod of only .0021 ft. (an amount much within the limits of accuracy of any ordinary sight), we are perfectly justified in concluding that these variations are accidental, and that the "difference" is a constant value. We thus see that with a telescope having a compound, plano-convex objective, the horizontal distance is equal to a constant times the reading on the rod, plus a constant, and may, as in other cases, be expressed by the equation d = a k + c. A few precautions, necessary for accurate work, should, however, be emphasized. First, as regards the special adjustments: Care should be taken that in setting the stadia wires* allowance be made for the instru- ment constant, and that the wires are so set that the reading, at any dis- tance, is less than the true distance by the amount of this constant.f For accurate stadia work, it is better to take both distances and elevations only at alternate stations, and then to take them from both backsight and foresight in such a manner that the vertical angle is always read from the same position on each rod, which should be the average height of the telescope at the different stations. Cases will, of course, occur where this method will be impracticable, and then the mode of procedure must be left to the judgment of the surveyor. If it be desired to have the absolute elevation of the ground under the instru- . ment, the height of telescope at each station will have to be measured by the rod, and the difference between this measurement and the average height used in sighting to the rod either added or subtracted, as the case may be. This difference will ordinarily be so small that in a great deal of stadia work no reduction will be necessary. In sighting to the rod for the angle of depression or elevation, the center horizontal wire must always be used. By this -means an exactly continuous line is measured. For theoretical exact- ness it is necessary that the stadia wires should be equidistant from the horizontal center wire, for, if this is not the case, the distance read is for an angle of elevation differing from the true one by an amount proportional to the displacement of the wires. With reasonable care a high degree of accuracy can be attained in stadia measurements. The common errors of stadia reading are unlike the common errors of chaining, the gross ones (such as making a difference of a whole hundred feet) being, in general, the only important . ones, and these are readily checked by double readings. To facilitate the subtraction of the reading of one cross-hair from that of another, one should be put upon an *This applies to an instrument with movable stadia wires, and not to one with etched lines on glass. In the latter case, the graduation of the rod is the adjustable portion. It has been claimed as an advantage for etched lines on glass, that they are not affected by variations of temperature, while the distance between stadia wires is. A series of tests made with one of Heller & Brightly' s transits, to determine this point, showed no appreciable alteration in the space between the wires, as measured on a rod 500 ft. distant, with a range of temperature between that produced in the instrument by the sun of a hot summer's day and that produced by enveloping the telescope in a bag of ice. tAs the difference is evidently proportional to the length of sight, with a 1,000' sight it would amount to 22.5', etc. STADIA MEASUREMENTS. 87 even footmark, and in the check, reading the other one. This is assuming the measurements to be made by the ordinary method, and not by the approximate one of the United States Engineers. HORIZONTAL DISTANCES AND DIFFERENCES OF LEVEL FOR STADIA MEASUREMENTS. The formulas used in the computation of the following tables were those given by Mr. George J. Specht in an article on Topographical Surveying, published in " Van Nostrand's Engineering Magazine" for February, *1880. These formulas furnish expressions for horizontal distances and differences of level for stadia measurements, with the conditions that the stadia rod be held vertical, and the stadia wires be equidistant from the center wire. They are as follows: D = c cos n + a k cos 2 n\ ak sin 2?i Q = D tan n = c sin n - - D = horizontal distance; Q difference of level; = distance from center of instrument to center of object glass, plus focal length of object glass; = focal length of obj( . >bject glass divided by distance of stadia wires apart; a = reading on stadia rod; n = vertical angle; a k = reading on rod multiplied by fc, which is a constant for each instrument (generally 100). In the tables, the vertical columns consist of two series of numbers for each degree, which series represent, respectively, the different values of a k cos 2 n and for every 2 minutes, when a k = 100. To obtain the horizontal distance or the difference of level in any case, the corresponding value of c cos n or c sin n must further be added; and the mean of each of these expressions, for each degree, with three of the most common values of c, is given under each column. As an example, let it be required to find the horizontal distance and the difference of level when n = + 6 18', a k = 570, and the instrument constant c = .75. In the column headed 6, opposite 18' in the series for " Hor. Dist.," we find 98.80 as the expression for ak cos 2 w when ak = 100; therefore, when ak = 570, a k cos 2 n = 98.80 X 5.70 = 563.16. To this must be added c cos n, which, in this case, is found in the subjoined column to be .75. In a similar manner, the required difference of level is + 10.91 X 5.70 X .08 = + 62.27. One multiplication and one addition must be made in each case. It is to be noticed that, with the smaller angles, cos n in the expressions c cos n and c sin n may be entirely neglected without appreciable error. For values of c, which differ from those given, an approximate correction, proportional to the amount of difference, may very easily be made in these two expressions. STADIA MEASUREMENTS. 15 *~i T-I =1 ^ M . M . ^ T jl^l^^WOiOSOOrHrHC^COCO-^TfliOiOO'iOt^ rH rH (. , !>!>' t^QOQOodcOCOOOOOCOOOCCCOGOOOod |WQ CJ Ci cs c^ Oi ci cJs o crs as o Ci a> cs os cs C3 cr. ~. ~. ~- cr. ~. ~. ~. C5 o ~ cr. Ci o O O -O CM t Ci iO O -O 1-1 I CO 00 QS WQ COCOOOCOCOCOCOQOOOOOOOCOCOCOGOOOOOCOOOGOOOCOaOOOQOOOOOCOCOGOQO OoioOOJO5gg OS OS gs g OS OS os' os' gs os' Os' OS* OS* Os' OS* CO 00 OO OO QO OO 0(5 CO co co co co' co* co* co* o S3 WQ CO* CO* CO* CO' CO* CO CO* CO STADIA MEASUREMENTS. 89 00000(8 GOOD 00 CO 00 ODOOOOOOOOOOOOOO OOOO GO QOOO OOOO OOOO OO O S I cowc^rocococococococococococococococococococococoM c ^ 5 fa >- OK I .|g s K 5 ' ^^^^^^^rr.rftr-r.rr,^ - . ---- - - ^ 5S ll j S S & 5g " II fa * SM s* fa H2 S'| _____________ .. s " Me i C1C^C^C^^^1C^1C^1?4C^O1O1O1Ci>i>^t^i>^^^^^^i>^o^oooooojpocp oddood c^O5aJaJdaJaia5dG6< I ' J (load is raised (in ft. )j 337000 X time of hoisting (in minutes) EXAMPLE. Find the horsepower required to raise, in 3 minutes, a car weighing 1 ton and containing 1 ton of material up an inclined plane 1,000 ft. long and pitching 30, if the rope weighs 1,500 Ib. The total load equals car + contents + rope = 2,000 + 2,000 + 1,500 = 5,500 Ib. The vertical height through which the load is hoisted equals 1,000 X sin 30 = 1,000 X ;5 = 500 ft. _ 5,500 X 500 33,000 X 3 CASE 2. When the power acts parallel to the base, use the formula W X height of inclined plane = P X length of base. These rules are theoretically correct, but in practice an allowance of about 30$ must be made for friction and contingencies. The screw consists of an inclined plane wound around a cylinder. The inclined plane forms the thread, and the cylinder, the body. It works in a nut that is fitted with reverse threads to move on the thread of the screw. The nut may run on the screw, or the screw in the nut. The power may be applied to either, as desired, by means of a wrench or a lever. When the power is applied at the end of a lever, it describes a circle of which the lever is the radius r. The distance through which the power passes is the circumference of the circle; and the height to which the weight is lifted at each revolution of the screw is the distance between two of the threads, called the pitch (p}. Therefore we have P X circumference of circle = W X pitch, or P : W : : p : 2 IT r. The power of the screw may be increased by lengthening the lever or by diminishing the distance between the threads. EXAMPLE. How great a weight can be raised by a force of 40 Ib. applied at the end of a wrench 14 in. long, using a screw with 5 threads per inch? WX$ = 40 X 28X3.1416. W = 17,593 Ib. The wedge usually consists of two inclined planes placed back to back. (Fig. 6.) In theory, r the same formula applies to the wedge as to the inclined plane, Case 2. P : W:: thickness of wedge : length of wedge. ELEMENTS OF MECHANICS. Friction, in the other mechanical powers, materially diminishes their efficiency; in this it is essential, since, without it, after each blow the wedge would fly back and the whole effect be lost. Again, in the others the power is applied as a steady force; in this it is a sudden blow, and is equal to the momentum of the hammer. The pulley is simply another form of the lever that turns about a fixed axis or fulcrum. With a single fixed pulley shown in Fig. 7, there can be no gain of power or speed, as the force P must pull down as much as the weight W, and both move with the same velocity. It is simply a lever of the first class with equal arms, and is used to change the direction of the force. v = velocity of W. v' = velocity of P. P = W. v = v'. Movable Pulley. A form of the single pulley, where it moves with the weight, is shown in Fig. 8. In this, one half of the weight is sus- tained by the hook, and the other half by the power. Since the power is only one-half the weight, it must move through twice the space; in other words, by taking twice the time, we can lift twice as much. Here power is gained and time lost. P = i W. v' = 2 v. Combinations of Pulleys. (1) In Fig. 9, we have the W sustained by three cords, each of which is stretched by a tension equal to the P, hence, 1 Ib. of power will balance 3 Ib. of weight. (2) In Fig. 10, a power of 1 Ib. will in the FIG. 7. same manner sustain a TFof 41b., and must descend 4 in. to raise the W 1 in. (3) Fig. 11 represents the ordinary tackle block used by mechanics, which can be calculated by the following general rule: Rule. In any combination of pulleys where one continuous rope is used, a load on the free end will balance a weight on the movable block as many times as great as the load on the free end as there are parts of the rope support- ing the load, not counting the free end. (4) In the cord marked 1,1, Fig. 12, each part has a tension equal to P; and in the cord marked 2, 2, each part has a tension equal to 2 P, and so on with the other cords. The sum of the tensions acting on iris 16; hence, W = 16 P. If n = number of pulleys, = 2 M P. p = Jl_. Differential Pulley. Fig. 13. W = 2PR FIG. 13. FRICTION AND LUBRICATION. 95 In all combinations of pulleys, nearly one-half the effective force is lost by friction. Composition of Forces. When two forces act on a body at different angles, their result may be obtained by the following rule: Rule. Through a point draw two lines parallel to the directions of the lines of action of the two forces. With any convenient scale, measure off, from the point of intersection, distances corresponding to the magnitudes of the respective forces, and complete the parallelogram. From the common point of application, draw the diagonal of the parallelogram; this diagonal will be the resultant, and its magni- tude can be measured with the same scale that was used to measure the two forces. When more than two forces act on a body simultaneously, find the resultant of any two of them as above; then, by the same method, combine this resultant with a third force, and this resultant with the fourth force, and so on. FRICTION AND LUBRICATION. Friction. Friction is the resistance to motion due to the contact of surfaces. It is of two kinds, sliding and rolling. If the surface of a body could be made perfectly smooth, there would be no friction; but, in spite o'f the most exact polish, the microscope reveals minute projections and cavities. We fill these with oil or grease, and thus diminish friction. Since no surface can be made perfectly smooth, some separation of the two bodies must, in all cases, take place in order to clear such projections as exist on the surfaces. Therefore, friction is always more or less affected by the amount of the perpendicular pressure that tends to keep them together. The ultimate friction is the greatest frictional resistance that one body sliding over another is capable of opposing to any sliding force when at rest. The coefficient of friction is the proportion that the ultimate friction in a given case bears to the perpendicular pressure. The coefficient of friction is usually expressed in decimals; but sometimes, as in the case of cars and engines, it is expressed in pounds (of friction) per ton. The coefficient of friction equals the ultimate friction divided by the perpendicular pressure, and the ultimate friction equals the perpendicular pressure multiplied by the coefficient of friction. Thus, if we have a block weighing 100 Ib. standing on another block, and it takes 35 Ib. pressure to slide it, the coefficient of friction = T 3 ^, or .35. TABLE OF COEFFICIENTS OF FRICTION. Materials. Smooth, Clean, and Dry Plane Surfaces. Smooth Plane Sur- faces, Perfectly Lubricated With Tallow. Oak on oak 40 079 Wrought iron on oak . .. 62 085 Wrought iron on cast iron .19 103 Wrought iron on wrought iron Wrought iron on brass .14 17 .082 103 Cast iron on cast iron 15 100 Cast iron on brass 15 103 Steel on cast iron 20 105 Steel on steel 14 Steel on brass .15 056 Brass on cast iron 22 086 Brass on wrought iron 16 081 Brass on brass 20 Oak on cast iron 080 Oak on wrought iron 098 Cast iron on oak 078 Steel on wrought iron 093 The above coefficients are only approximate, for the coefficient will vary with the intensity of the pressure and the velocity, and also with the condi- tions of the atmosphere. But they are correct enough for practical purposes. ELEMENTS OF MECHANICS. The friction of liquids moving in contact with solid bodies is independent of the pressure, because the forcing of the particles of the fluid over the pro- jections on the surface of the solid body is aided by the pressure of the surrounding particles of the liquid, which* tend to occupy the places of those forced over. Therefore, the coefficients of friction of liquids over solids do not correspond with those of solids over solids. The resistance is directly as the area of surface or contact. COEFFICIENTS OF FRICTION IN AXLES. Axle. Bearing. Ordinary Lubrication. Lubricated Continuously. Bell metal Bell metal .097 Cast iron Wrought iron Bell metal Bell metal .07 .07 .049 05 Wrought iron .. . Cast iron .... 07 0.5 Cast iron Cast iron 07 05 Cast iron Wrought iron Lignum vitse Lignum vitse .10 .12 Friction naturally varies with the character of the surfaces, lubrication, and the nature of the lubricant. The best lubricants for the purposes should always be used, and the supply should be regular. When machinery is well lubricated, the lubricant keeps the surfaces apart, and the frictional resistance becomes very small, or about the same as the friction of liquids. Frictional Resistance of Shafting. Let K = coefficient of friction; W = work absorbed in foot-pounds; p = weight of shafting and pulleys + the resultant stress of belts; H = horsepower absorbed; D = diameter of journal in inches; R = number of revolutions per minute. Then, ORDINARY OILING. CONTINUOUS OILING. W = .0182 X P X D; H = .000000556 XP K = .066. .044. As a rough approximation, 100 ft. of shafting, 3 in. diameter, making 120 revolutions per minute, requires 1 horsepower. For friction of air in mines, see "Coefficient of Friction," under Venti- lation. Friction of Mine Cars. The friction of mine cars varies so much that it is impossible to give a formula for calculating it in every case. No two mine cars will show the same frictional resistance, when tested with a dynamome- ter, and, therefore, nothing but an average friction can be dealt with. The construction of the car, the condition of the track, and the lubrication are important factors in determining the amount of friction. In this connection, we may, however, state some of the requisites of good oil box and journal bearings. Tightness is a prerequisite, and, in dry mines where the dust is very penetrating, this is especially important; the bear- ings should be sufficiently broad; the oil box large enough to hold sufficient oil to run a month without renewal, and so constructed that, while it may be quickly and easily opened, it will not open by jarring or by being acci- dentally struck by a sprag or a lump of C9al. There are a number of patented self-oiling wheels that are improvements on the old-style plain wheels, and each of these has undoubtedly some point of superiority over the old style. Among the most extensively used of these patented wheels are those with annular oil chambers, and those with patent bushings. Their superiority consists in the fact that, if properly attended to, a well-lubricated bearing is secured with greater regularity and less work than when the old-style wheel was used. With a view of adopting a standard wheel, the Susquehanna Coal Co., of Wilkesbarre, Pa., experimented for a number of years with different FRICTION AND LUBRICATION. 97 styles of self-lubricating wheels, and as a result of the experiments it adopted a wheel patented by its chief engineer, Mr. Jas. H. Bowden. Mr. R. Van A. Norris, E. M., Assistant Engineer, made a series of 989 tests with old-style wheels, some of which had patent removable bushings, and others annular oil chambers, and the Bowden wheel. The old wheels were found to be practically alike in regard to friction. All the wheels were of the loose outside type, 16 in. in diameter, mounted on 2} in. steel axles, with journals 5i in. long. The axles passed loosely through solid cast boxes, bolted to the bottom sills of the cars, and were not expected to revolve. The table of friction tests shows the results obtained with both old- and new-style wheels, and is of interest to all colliery managers, inasmuch as the figures given~for the old-style wheels alone are the most complete in existence, and, as stated before, they are good averages. Tests were made on the starting and running friction of each style of wheel, under the conditions of empty and loaded cars, level and grade track, curves, and tangents. The instruments used were a Pennsylvania Railroad spring dynamometer, graduated to 3,000 lb., with a sliding recorder, a hydraulic gauge (not recording) reading to 10,000 lb., graduated to 25 lb., and a spring balance, capacity 300 lb., graduated to 3 lb. All these were tested and found correct previous to the experiments. Most of the observations on single cars were made with the 300-lb. balance. The two types of " old-style " wheels have been classed together in the table. Each car was carefully oiled before testing, and several of each type were used, the results being averages from the number of trials shown in the table. In the experiments on the slow start and motion, the cars were started very slowly by a block and tackle, and the reading was taken at the moment of starting. They were then kept just moving along the track for a considerable distance, and the average tractive force was noted, the whole constituting one experiment. The track selected for these experiments was a perfectly straight and level piece of 42 in. gauge, about 200 ft. long, in rather better condition than the average mine track. The cars were 41 in. gauge, 3i ft. wheel base, 10 ft. long, capacity about 85 cu. ft., with 6-in. topping. To ascertain the tractive force required at higher speeds, trips of one, four, and twenty cars, both empty and loaded, were attached to a mine locomotive and run about a mile for each test, the resistance at various points on the track, where its curve and grade were known, being noted, care also being taken to run at a constant speed. Unfortunately, only four of the "new- style" cars were available 011 the tracks where these trials were made. The remarkably low results for the twenty-car trips are attributed to variations in the condition of the track, and the fact that the whole train was seldom pulling directly on the locomotive, the cars moving by jerks, so that correct observations were impracticable. The hydraulic gauge was used for these twenty-car tests, and the needle showed vibrations from 1 to 4 tons and back. The mean was taken as nearly as possible. The gauge was rather too quickly sensitive for the work, and the Pennsylvania Railroad dynamometer was not strong enough to stand the starting jerks and the strain of accelerating speed. The tests marked " rope haul" were made on an empty-car haulage system, about 500 ft. long, with overhead endless rope running continuously at a speed of 180*11. per min., the cars being attached to the moving rope by a chain, a ring at the end of which was slipped over a pin on the side of the car. The increase of friction on the heavier grades was due to the rope pulling at a greater angle across the car. Correction was not made for this angularity at the time, and the rope has since been rearranged, so that the correction cannot now be made. There were not enough curve experi- ments to permit the deduction of any general formula for the resistance of these cars on curves. The experiments on grade agree fairly well with those on a level, the rather higher values obtained being probably due more to the greater effort required in moving them, and the consequent jerkiness of the motion, than to any real increase in resistance. As the experiments on all styles of wheels were made in an exactly similar manner, the comparative value of the results is believed to be nearly correct, the probable error in each set of experiments, as computed by the method of least squares, varying from about 4ji for slow start and motiojn to 12$ for the rapid motion and twenty-car trips. ELEMENTS OF MECHANICS. (NCOO^ oOf rHiOOt- rH COCO^t^ COCO^t^COCOCOO Ilil SiS nopouj o^ ana uoj, aad aojo.j aApO uopouj o^ ana JBO jo jad aoaoj CO ^ ^ X3 J2-H"5 . fl '. fl '. fl ' 1 & r r2 >.S.S r i d a a a * : '3 ^ f_ -, b : P o> o ooo o.S .S ^ : :-" !!!!!!!! bCbJDbJDbJDbJDbJObcbjo >p^^>>^^^ ^^t>>>>>t>t> <;<<^<<<<^<1^ FRICTION AND LUBRICATION. 99 norjOTJj oj ana U X J3d 30JO.I 8AIJOBJX notjotij 01 ana J1J JBO jad Ill S88S~ GO QO SO QO J C^i C4 r-5 T-H r iO iO tO iO O O* i-H QC (M lOCO il' 8SSS O > S i3^ r of of a o a> o a o fl fi dll Sdi M .c _o ^o o o"o o iaia iZ il -~ i^ C - :^C 100 ELEMENTS OF MECHANICS. Lubrication. There is probably no factor that has a more direct bearing on the cost of production per ton 'of coal and ores than the lubrication of mine machinery, and yet it is doubtful if there is another item connected with the operation of a mine less understood by owners, their managers, and engineers in charge. Steam plants are equipped with boilers of the highest known efficiency; heaters are used that, by utilizing waste steam, will heat the feed water for boilers to the highest point. Modern engines that will develop a horsepower with the least amount of steam are installed; bends, instead of elbows, are placed in steam and exhaust pipes, so that the friction and back pressure may be reduced to a minimum. In a word, everything is done in the equip- ment of a plant to secure economy in its operation. After all this is done, frequently a long step is taken in the opposite direction by the use of an oil unsuited to the existing conditiQns, and those in charge of the plant are led to believe that the lubrication is all that could be desired, simply because the engines and machinery run quietly and the temperature of the bearings does not become alarmingly high. The office of a lubricant is not merely to secure this result, but, primarily, to reduce friction and wear to a minimum; and an oil that will do this is* the best oil to use, no matter what the price per gallon may be. Few realize the great loss in power due to the friction of wearing parts. One of the greatest living authorities on lubrication writes: "It may probably be fairly estimated that one-half the power expended in the average case, whether in mill, mine, or workshop, is wasted on lost work, being consumed in overcoming the friction of lubricated surfaces." He adds that a reduction of 50$ in the work lost by friction has often been secured by a change of lubricants. As one of many instances showing the loss that will occur by the use of inferior lubricants, attention is called to two flour mills located in one of the Middle States. One of the plants was equipped with a condensing engine capable of developing a horsepower on 24 Ib. of water per hour; the other plant had a simple engine, taking 30 Ib. of water per hour. The plant con- taining the condensing engine was purchased by the owner of the plant containing the simple engine. The new owner of the plant was surprised to learn that the cost of operation per barrel of flour manufactured was equally -as great in the new plant as in the old one. The engines were indicated, and valves found to be properly adjusted and the engine working within the economical range, so far as load was concerned. The loss was then attributed to the boilers, but an evaporative test proved that there was no practical difference here, as the boilers, in both instances, were evaporating a fraction over 8 Ib. of water per pound of coal. At this point, the question of lubrication was taken up, and, on the advice of an expert sent by a prominent manufacturer of lubricants to look over the plant, an entire change was made in the lubricants used, and, as a result, a money saving of over $2.25 per day (practically $700 per annum this in a plant of less than 250 horsepower) was effected, "notwithstanding the fact that the new lubri- cants used cost considerably more per gallon than those formerly used. This simply indicates that the price of an oil is of little importance in comparison with its friction-reducing power. Friction costs money, because it means greater cost of operation per unit of output. Among the expenses chargeable to waste power, due to inferior lubrica- tion, may be included: (1) The cost of power produced in excess of that really required to operate the mine per ton of output. In this calculation should -be included the proper proportion of salaries of engineers, and all other items that contribute to the cost of the motive department, as well as the cost of mining the fuel consumed in producing this excess power. (2) Wear and tear of machinery, which is constantly doing more work per ton of coal mined than should be required of it. There is also an element of danger that ought to receive serious consid- eration, as, while it is true that cylinder and bearing lubricants of indifferent merit will, under ordinary conditions, keep the cylinders from groaning and the bearings from becoming hot, experiments have proved that, in accom- plishing such results, the oils in use were being taxed to their utmost; and there is record of many instances where, as a result of using oils of such limited endurance, accidents of a serious nature have occurred, necessarily causing shut-downs just at the time when the operation of a plant to its fullest capacity was imperative. It is most difficult, in an article of this character, to do much more than FRICTION AND LUBRICATION, 101 point out the danger due to the use of inferior lubrieanis, leaving .it. to .-the purchaser himself to determine as to the intrinsic worth of the lubricants offered to him. In making his selection he ~,vou4d do well to consult with and heed the advice of some highly responsible manufacturer of lubricants who has given to the question, in all its phases^, the moat" easeful study,, anci who would most probably have the benefiuof a-vvjdeexpe3k;rr..ce in thearopHca- tion as well as the manufacture of lubricants. 'Some buyers 'have,- to -tht'ir ultimate regret, adopted, as a method of determining the merits of lubri- cants, a schedule of laboratory tests. Such a method is not only useless, but it is misleading to any one other than a manufacturer of lubricants, who makes use of it merely as a means of insuring uniformity in his manu- factured products, and not as a measure whereby to judge their practical value. Indeed, many oils can be very properly described by practically the same schedule of tests, and yet are widely apart when their utility for a given service is considered. As a general guide in purchasing cylinder oil for mine lubrication, it might be said that a dark-colored oil is of greater value, as a rule, than one that has been filtered to a red or light amber color, as the process of filtration necessarily takes from the oil a considerable percentage of its lubricating value, and at the same time the process is an expensive one. In short, if a light-colored oil is insisted upon, a high price must be paid for an inferior lubricant. As a word of caution, however, it would be well to add right here that irresponsible manufacturers frequently take advantage of the fact that the most efficient and best known cylinder oils are dark-colored, and endeavor, with more or less success, to market as "cylinder oil" products absolutely unsuited to the lubrication of steam cylinders, and that would consequently be expensive could they be procured without cost. For the lubrication of engine bearings, where modern appliances for feeding are used, an engine oil of a free running nature is best, as it more quickly reaches the parts requiring lubrication than an oil of a more sluggish nature. It, of course, must not be an oil susceptible to temperature changes, but must be capable of performing the service required of it under the most severe conditions, where an oil of less " backbone " would fail. Such an oil would also be suitable for the lubrication of dynamos, and should also give satisfaction where used in lubricating the cylinders of air compressors. Where the machinery is of an old type and loose-jointed, or when the bear- ings are open and the oil is applied directly to them by means of an oiler, an engine oil of a more sluggish, or viscid, nature is best. Perhaps of equal importance to the lubrication of power machinery must be considered the lubrication of the axles of mine cars. This is important, first, because of the fact that perhaps three-fourths of the oil used about a coal mine is used for this purpose, and, secondly, because there is really a marked difference in the quality and, therefore, in the efficiency of lubricants used for this purpose. Fully nine-tenths of the prominent ' railroads of this country are today using car-axle oil, costing perhaps as much per gallon as much of the so-called cylinder oil that is used in coal mines, they having discovered, by exhaustive experiments, that the increased efficiency gained by using an oil of such quality many times offsets the difference in the cost per gallon and enables them to secure a greater mile- age without any increase in their power or other fixed charges. This, we are certain, would apply just as forcibly to the lubrication of coal cars, no matter whether the power is derived from "long-eared mules" or electric motors, and we believe this feature of lubrication of mine equipment should receive more careful attention than it does receive, as a rule. There is a considerable amount of waste in the lubrication of mine cars. This waste is hard to avoid, and, naturally, makes the buyer hesitate before adopting the use of a car oil that costs very much per gallon; but we believe it can be demonstrated, even in the face of this waste, that the increased efficiency secured by the use "of a high-grade car oil would warrant its use. Such waste is pretty hard to correct in mines where the old-fashioned style of car axles is still in use, and where the oil is applied through an ordinary spout oil can into the axle box, and allowed to drip off the axles and on to the ground. When axles are equipped in the same manner as those of freight cars, or where cars are equipped with one of the several different styles of patent car wheels and axles that are coming into use quite extensively, it is possible to regulate the feeding of the oil to the axles, so as to reduce the waste to a minimum. One of these patent car wheels, which is perhaps better known than any other, is constructed with a hollow hub 102 STRENGTH OF MATERIALS. that actsnas a reservoir forjhe oil, the oil passing from this reservoir through smaH holbs onto a fet' ,w.a,sher, which it must saturate, and by which it is applied- to the axle*. Such wheels require a limpid oil, as a heavy, sluggish oil would not so readily saturate the felt washer referred to. A tight cap is adjusted to' the end of the, ax! 3, to prevent waste of oil. These wheels will ruji,qvq;;o tvleijgth of time- without reoiling after the reservoir is once filled. 13 f course, it costs something to' equip mine cars with these patent axles, but we are convinced that such an outlay would result in more economical operation, particularly if at the same time the very best quality of car oil obtainable is used. BEST LUBRICANTS FOR DIFFERENT PU R POSES (TH U RSTONl). rOC r . mineral lubricating oils. Very great pressures, slow speed. j^ffibriSS^ 11 ^ "* Heavy pressures, with slow speed j T ^her greases^ laPd ' tall W ' and Heavy pressures and high speed S PJ* m _ J^ aslor oil ' and heay y Light pressures and high speed mineral oils. Sperm, refined petroleum, olive, rape, cottonseed. Lard oil, tallow oil, heavy mineral oils, and the heavier vegetable oils. Heavy mineral oils, lard, tallow. Clarified sperm, neat's foot, por- poise, olive, and light mineral lubricating oils. For mixture with mineral oils, sperm is best; lard is much used; olive and cottonseed are good. STRENGTH AND WEIGHT OF MATERIALS Ordinary machinery Steam cylinders Watches and other delicate mechanism. WOODEN BEAMS. To Find the Quiescent Breaking Load of a Horizontal Square or Rectangular Beam Supported at Both Ends and Loaded at the Middle. Multiply the breadth in inches by the square of depth in inches, divide the product by distance in feet between the supports, and multiply the quotient by the constant given in the table on the next page. Take safe working load one-third of break- ing load. To Find the Quiescent Breaking Load of a Horizontal Cylindrical Beam. Divide the cube of the diameter in inches by the distance between the supports in feet, and multiply the quotient by the constant. When the load is uniformly distributed on the beam, the results obtained by the above rules should be doubled. EXAMPLE 1. Find the quiescent breaking load and safe working load of a yellow-pine collar 8 in. square, 12 ft. between legs. 8 V 8 2 Breaking load = ^V^ X 500 = 21,333 Ib. for seasoned, and 10,666 Ib. for green timber. Safe working load = 7,111 Ib. for seasoned, and 3,556 Ib. for green timber. EXAMPLE 2. Find the quiescent breaking load, and the safe working load of a hemlock collar 10 in. diameter, 7 ft. between legs. Breaking load =* 3S X 286 = 33,714 Ib. for seasoned timber, and -~ 16,857 Ib. for green timber. Safe working load = -- = 11,238 Ib. for seasoned, and - or - = 5,619 Ib. for green timber. To Find the Load a Rectangular Collar Will Support When Its Depth Is Increased. When the length and width remain constant, the load varies as the square of the depth. IKON AND STEEL BEAMS. 103 EXAMPLE. A rectangular collar 10 in. deep supports 15,000 Ib. What will it support if its depth is increased to 12 in.? 10- : 12 2 : : 15,000 : 21,600. Ans. Having the Length and Diameter of a Collar, to Find the Diameter of a Longer Collar to Support the Same Weight. For the same load, the strength of collars varies as the cubes of their diameters, and inversely as their lengths. EXAMPLE. If a collar 6 ft. long and 8 in. diameter supports a certain weight, what must be the diameter of a collar 12 ft. long to support the same weight? ff 6 : ^15 : : 8 in. : 10+ in. Ans. Having the Loads of Two Beams of Equal Length and the Diameter of One, to Find the Diameter of the Other. When the lengths are equal, the diameters vary as the cube roots of the loads, or the cubes of the diameters vary as the loads. EXAMPLE 1. A beam 11 in. in diameter supports a load of 32,160 Ib. What will be the diameter of another beam the same length, to support a load of 19,440 Ib.? f 32, 160 : ^19,440 : : 11 : 9. Ans. EXAMPLE 2. A beam 8 in. in diameter will support a load of 10,240 Ib. What load will a beam the same length and 7 in. in diameter support? 8 3 : 7 3 : : 10,240 : 6,860. Ans. TABLE OF CONSTANTS. Calculated for seasoned timber. For green timber, take one-half of these constants. Safe working load is one-third of breaking load. Woods. Square or Rectan- gular. Round. Woods. Square or Rectan- gular. Round. Ash white 650 383 Locust 600 353 Ash swamp 400 236 Lignum vitse 650 383 Ash black 300 177 Larch 400 236 Balsam Canada 350 206 Maple 550 324 Beech, white Beech red 450 550 265 324 Oak, red or black... Oak, white 550 600 324 353 Birch black 450 265 Oak, live 600 353 Birch vellow 450 266 Pine white 450 265 Cedar white 250 147 Pine, yellow 500 295 Chestnut 450 265 Pine, pitch 550 324 Elm 350 206 Poplar '" 550 324 Elm rock 600 353 Spruce 450 265 Hemlock 400 236 Sycamore 500 295 Hickory 650 383 Willow 350 206 Ironwood 600 353 To Find the Diameter of a Collar When the Weight Increases in Proportion to the Length. Find the required diameter to support the same weight as the short collar. Then the length of the short collar is to the length of the long one as the diameter found to support the original weight is to the required diameter. EXAMPLE. If a collar 6 ft. long, 8 in. in diameter, supports a certain weight, what must be the diameter of a collar 12 ft. long to support twice the weight? ^ ^ or 1 : 2 : : 2 X 8' : ( ) 3 , 1 : 2 :: ~ 6 ' 12 :f'2::8, ) = 12.7. Ans. AND STEEL BEAMS. Constants for use in calculating strength of iron and steel beams: Cast iron 2,000 Wrought iron 2,200 Steel 5,000 104 STRENGTH OF MATERIALS. SAFE LOADS UNIFORMLY DISTRIBUTED FOR STANDARD AND SPECIAL I BEAMS. (Tons of 2,000 Pounds.) ^qSpAY ui OS138JOUI qi;'Xj8Aa joj ppy CO CO i! O OS CO !> !> CO CO >O *O iO 't 1 ^ ^ ^ Safe loads given include weight of beam. Maximum fiber stress, 16,000 Ib. per sq. in. For spacings below the heavy lines, the deflections will be greater than the allowable limit for plastered ceilings, equaling 3 J W span. M CO S3 CO^OOCOOOOCOCO COgiOCNOSCO^ rH^r-liHOOOOO OOOOOOOO q^I A"j8A[j joj ppy ^OOiOCOOl^OOSOO CO^gCOCOCOiOiO M S3'" S S ^ ^ g.$ SI ^Sgo^88^8J2 CO3888S3g5 1 i^S^^SSo^S J>COIO^^COCOCOOOOSOrH COtO Tf4 CO C1 (N rHrHOOOSOSO5COCOCO M -3 OS -TJH OS rH OS CN OS O CO OSOCCOOSCOt^COOSI^CO co i> I-H t. CN os 10 co o t^iccoi iocci>-iO'"t | co cot^t > -cocoididididTj5 Tjt-^j5 -^ TJH co co co co co ^qSi8AY ui 8S138JOUI q^I A\i8A3 joj ppy C^OOst^COiO^^CO CNCNrHrHOOOOSOSOS M 83 oBScOOrHci^gS 8g^SoS3lSM OOOSOOOOt-t-cOcO cOOiOiOiOiO^^Tf^ ^uSpAY q-[ A\i8 Ul 88-88 JO UI CO^CO-HOOSOOt-CO lO^^COCOCM^rHrHrH A3 Joj ppy M sS t5^^o1^oSg r^^Cog^^^S^ lOT^COCNrHrHOOOS OS CO OO 1> 1> I> 1> CO CO CO* ^n os co i> tft> -HH r^ co d r-5 rHo'o'osososooco'oor^ rHr l^i li-4i IrH^-li 1, 1, - OQ fss 6 t 26.2 23.0 20.1 17.5 15.2 13.2 11.5 8.6 26.95 6 37.5 33.0 28.8 25.0 21.7 18.9 16.5 12.4 38.59 6 '5- 42.7 37.6 32.8 28.5 24.7 21.5 18.8 14.1 43.96 6 47.6 41.9 36.5 31.8 27.6 24.0 21.0 15.7 49.01 6 It 52.2 46.0 40.1 34.8 30.2 26.3 23.0 17.2 53.76 7 1 47.7 43.1 38.5 34.3 30.4 26.9 23.9 21.2 18.9 14.7 45.96 7 61.1 55.2 49.3 43.8 38.9 34.4 30.6 27.1 24.2 18.9 58.90 7 IF 67.2 60.8 54.3 48.3 42.8 37.9 33.7 29.9 26.7 20.8 64.77 8 57.9 53.3 48.6 44.1 39.7 35.8 32.2 28.9 26.1 17.1 53.29 8 1 74.6 68.7 62.5 56.7 51.1 46.0 41.4 37.3 33.6 22.0 68.64 8 H 89.9 82.8 75.5 68.4 61.7 55.5 49,9 44.9 40.5 26.5 82.71 9 ^. 68.1 63.6 58.9 54.2 49.6 45.2 41.2 37.5 34.1 19.4 60.65 9 l 88.0 82.3 76.2 70.0 64.1 58.4 53.2 48.4 44.1 25.1 78.40 9 H 106.6 99.6 92.2 84.8 77.6 70.8 64.4 58.7 53.4 30.4 94.94 9 1* 123.8 115.7 107.1 98.5 90.1 82.2 74.8 68.1 62.0 35.3 110.26 9 139.6 130.5 120.8 111.1 101.6 92.7 84.4 76.8 69.9 39.9 124.36 10 1 101.4 95.9 83.6 77.4 71.5 65.8 60.5 55.5 28.3 88.23 10 H 123.3 116.5 mi 101.6 94.1 86.8 79.9 73.4 67.5 34.4 107.23 10 it 143.7 135.8 127.3 118.5 109.7 101.2 93.2 85.6 78.7 40.1 124.99 10 l* 162.7 153.8 144.1 134.1 124.2 114.6 105.5 97.0 89.1 45.4 141.65 11 114.8 109.4 103.5 97.3 91.0 84.8 80.2 73.1 67.7 31.4 98.03 11 H 139.9 133.3 126.1 118.6 110.9 103.3 97.8 89.4 82.5 38.3 119.46 11 it 163.5 155.9 147.5 138.6 128.7 120.8 114.3 104.1 96.4 44.8 139.68 11 185.7 177.1 167.5 157.5 147.3 137.2 129.8 118.3 109.5 50.9 158.68 11 2 206.6 196.9 186.3 175.1 163.8 152.6 144.4 131.5 121.8 56.6 176.44 12 1 128.0 122.9 117.2 111.0 104.7 98.4 92.2 86.1 80.4 34.6 107.51 12 H 156.4 150.1 143.1 135.7 127.9 120.2 112.6 105.2 98.2 42.2 131.41 12 it 183.3 175.9 167.7 159.0 149.9 140.9 132.0 123.3 115.1 49.5 154.10 12 l* 208.7 200.4 191.0 181.1 170.7 160.4 150.3 140.5 131.1 56.4 175.53 12 2 232.7 223.4 213.0 201.9 190.4 178.9 167.6 156.6 146.1 62.8 195.75 13 1 141.2 136.3 130.7 124.7 118.5 112.1 105.8 99.5 93.5 37.7 117.53 13 H 172.8 166.8 160.0 152.7 145.0 137.2 129.4 121.8 114.4 46.1 143.86 13 it 203.0 195.9 187.9 179.3 170.3 161.1 152.0 143.1 134.3 54.2 168.98 13 231.6 223.6 214.5 204.7 194.4 183.9 173.5 163.3 153.3 61.9 192.88 13 2 258.9 249.9 239.7 228.7 217.3 205.5 193.9 182.5 171.3 69.1 215.56 14 1 154.3 149.6 144.3 138.5 132.3 125.9 119.5 113.1 106.8 40.8 127.60 14 H 189.2 183.4 176.9 169.7 162.2 154.4 146.5 138.6 131.0 50.1 156.31 14 it 222.6 215.8 208.1 199.7 190.8 181.7 172.3 163.1 154.1 58.9 183.67 14 it 254.4 246.7 237.9 228.3 218.1 207.6 197.0 186.5 176.2 67.4 210.00 14 2 284.8 276.2 266.4 255.6 244.2 232.4 220.6 208.8 197.2 75.4 235.12 15 1 167^4 162.9 157.8 152.1 146.0 139.7 133.3 126.8 120.4 44.0 137.28 15 H 205.5 200.0 193.7 186.7 179.3 171.5 163.6 155.7 147.9 54.0 168.48 15 242.1 235.7 228.2 220.0 211.2 202.1 192.8 183.5 174.2 63.6 198.74 15 1? 277.2 269.8 261.3 251.9 241.9 231.4 220.7 210.1 199.5 72.9 227.45 15 2 310.8 302.5 293.0 282.5 271.2 259.5 247.5 235.5 223.6 81.7 254.90 SPECIFIC GRAVITY. 107 MINIMUM SAFE-BEARING VALUES OF MASONRY MATERIALS. Materials. Tons per Sq. Ft Granite, capstone j 50 Squared masonry | 25 Sandstone, capstone Squared masonry . Rubble, laid in lime mortar Rubble, laid in cement mortar . 25 12 5 10 36 Limestone, capstone Squared masonry I 18 Rubble, laid in lime mortar 5 Rubble, laid in cement mortar Bricks, hard, laid in lime mortar .. Hard, laid in Portland cement mortar Hard, laid in Rosendale cement mortar .... Concrete, 1 Portland, 2 sand, 5 broken stone 10 7 14 10 10 SPECIFIC GRAVITY, WEIGHT, AND PROPERTIES OF MATERIALS, ETC. The specific gravity of a body is the ratio of its weight to the weight of an equal bulk of pure water, at a standard temperature (62 F. = 16.670 C.). Some experimenters have used 60 F. as the standard temperature, others 32 and still others, 39.1. To reduce a specific gravity, referred to water at 39.1 F., to the standard of water at 62 F., multiply by 1.00112. Given specific gravity referred to water at 62 F., multiply by 62.355 to find the weight of a cubic foot of the substance. Given weight per cubic foot, to find specific gravity, multiply by 0.016037. Given specific gravity, to find the weight per cubic inch, multiply by 0.036085. To Find the Specific Gravity of a Solid Heavier Than Water, Weigh the body both in air and in water, and divide the weight in air by the difference of the weights in air and water. EXAMPLE. A piece of coal weighs, say, 480 grains. Loss of weight when weighed in water. 398 grains. Then, ffg = 1.206, specific gravity of the coal compared with water at 1.000. As a cubic foot of water weighs, approximately, 1,000 oz., the weight of a cubic foot of any substance can be found by multiplying its specific gravity by 1,000. To Find the Specific Gravity of a Solid Lighter Than Water-Attach to it another body heavy enough to sink it; weigh severally the compound mass and the heavier body in water, divide the weight of the body in air by the weight of the body in air plus the weight of the sinker in water minus the combined weight of the sinker and body in water. To Find the Specific Gravity of a Fluid. Weigh both in and out of the fluid a solid (insoluble) of known specific gravity, and divide the product of the weight lost in the fluid and the specific gravity of the solid by the weight of the solid. The weight of a cubic foot of water at a temperature of 62 is about 1,000 oz. avoirdupois, and the specific gravity of a body, water being 1,000, shows the weight of a cubic foot of that body in ounces avoirdupois. Then, if the magnitude of the body be known, its weight can be com- puted; or, if its weight be known, its magnitude can be calculated, provided we know its specific gravity; or, of the magnitude, weight, and specific gravity, any two being known, the third may be found. To Find the Magnitude of a Body in Cubic Feet From Its Weight. Divide the weight of the body in ounces by 1,000 times the specific gravity of the body. To Find the Weight of a Bodv in Ounces From Its Magnitude. Divide the weight of the body in ounces by the specific gravity of the substance mul- tiplied by 1,000. NOTE. The specific gravity of any substance is equal to its weight in grams per cubic centimeter. (See table of metric weights and measures.) 108 WEIGHT OF MATERIALS. SPECIFIC GRAVITY OF SUBSTANCES. Substance. Average Average Specific Weight per Gravity. Cu. Ft. Lb. Air, atmospheric; at 60 F. under pressure of 1 at- mosphere, or 14.7 Ib. per sq. in 00123 Alcohol, pure Alcohol, of commerce 834 Aluminum 2.66 Anthracite* coal 1.5 Asphaltum 1.4 Brass, cast 8.1 Brass, rolled 8.4 Bronze, gun metal 8.5 Brick, best pressed Brick, common hard Carbonic-acid gas 00187 Clay, dry, in lumps, loose Clay, potters', dry 1.9 Coke,f loose, of good coal Coal, bituminous^ 1.35 Coal, bituminous, broken loose Coal, bituminous, moderately shaken Copper, cast 8.7 Copper, rolled 8.9 Cork 25 Earth, common loam, perfectly dry, loose Earth, common loam, perfectly dry, shaken Earth, common loam, perfectly dry, moderately packed Earth, common loam, slightly moist, loose Earth, common loam, more moist, loose Earth, common loam, more moist, shaken Earth, common loam, more moist, packed Earth, common loam, as a soft flowing mud Earth, common loam, as a soft mud packed Gold, cast, pure or 24 carat 19.26 Gravel Gutta percha 98 Gypsum (plaster of Paris) 2.27 Gypsum, in irregular lumps Gypsum, ground, loose Gypsum, ground, well shaken Gypsum, calcined, loose Hydrogen gas, 14 times lighter than air and 16 times lighter than oxygen ". Ice .92 Iron, cast 7.21 Iron, rolled bars 7.65 Iron, sheet Iron, wrought 7.77 Lead 11.38 Lime, quick 1.5 Lime, quick, ground, loose, per struck bushel, 66 Ib. Mercury, at 32 F '. 13.62 Mercury, at 60 F 13.58 Mercury, at 212 F 13.38 Nitrogen gas, 3 V part lighter than air Oils, whale, olive .92 * Anthracite increases about 75 per cent, in bulk when broken to any market size. A ton loose, averages from 40 to 43 cu. ft. t A heaped bushel, loose, weighs from 35 to 42 Ib. A ton occupies 80 to 97 cu. ft. t A heaped bushel, loose, weighs about 74 Ib., and a ton occupies from 43 to 48 cu. ft. Bitumi- nous coal, when broken, occupies 75 per cent, more space than in the solid. SPECIFIC GEA VITY. 109 SPECIFIC GRAVITY OF SUBSTANCES (Contin ued). Substance. Average Specific Gravity. Average Weight per Cu. Ft. Lb. Oxygen gas ^ part heavier than air 00136 0846 Petroleum 878 54 g Powder 1.00 62.3 Rosin 1.1 686 Silver 10.5 655.0 Slate 2.8 175.0 Steel 7.85 490.0 Sulphur 2.0 125.0 Tallow .94 58.6 Tin cast 7.35 459.0 Water, pure, rain or distilled, at 32 F., Barom. 30 in. Water, pure, rain or distilled, at 62 F., Barom. 30 in. Water, pure, rain or distilled, at 212 F., Barom. 30 in. Water sea average 1.00 1.028 62.417 62.355 59.7 64.08 Zinc .. 7.00 437.5 The following table gives the specific gravities of various coals: Name of Coal. Sp. Gr. Weight of a Cu. Ft. Lb. Weight of a Cu.Yd. Tons. Newcastle Hartley, England Wigan, 4 ft., England Portland England 1.29 1.20 1 30 80.6 75.0 81 2 .972 .914 .978 Anthracite, Wales 1.39 86.9 1.047 Islington Scotland 1.25 78.1 .941 Anthracite Irish 1 59 994 1.193 Anthracite, Pennsylvania 1.55 96.9 1.167 Bituminous, Pennsylvania Block coal Indiana 1.40 127 87.5 794 1.054 .956 SPECIFIC GRAVITY AND WEIGHT OF PREPARED ANTH RACITE COAL. To Mr. Irving A. Stearns, General Superintendent of the Pennsylvania Railroad Co.'s Coal Department, we are indebted for the following sum- mary of tests made by the mining engineers of the company. In a series of tests to ascertain the specific gravity of the coal from differ- ent seams worked by the company, it was found that the average specific gravity was 1.4784, and the average weight per cubic foot was 92.50 Ib. This was calculated for space filled at breaker without settling. Add 5$ for packed spaces of large heaps. WEIGHT PER CUBIC FOOT OF SUSQUEHANNA COAL Co.'s WHITE ASH ANTHRA- CITE COAL. Size. Size of Mesh. Weight per Cu. Ft. Pounds. Cu.Ft. From 1 Cu.Ft. Solid. Over. Through. Lump Broken Egg 4i" to 9 ' 2|" to 2f 13" to 2*' H"toH' 1 " to H' F' to r i"t f 2f to 2|' ir to2i / H' to H' 1 ' to U' r to f r to i' T 3 8 ' tO f 57 53 52 6U 6i| 51 1.614 1.755 .1.769 1.787 1.795 1.804 1.813 1.813 1.813 Large stove Small stove Chestnut ... Pea No. 1 buckwheat No. 2 buckwheat 110 WEIGHT OF MA TERIALS. LINE SHAFTING. Shafting is usually made cylindrically true, either by a special rolling process, when it is known as cold-rolled shafting, or it is turned up in a machine called a lathe. In the latter case, it is called bright shafting. What is known as black shafting is simply bar iron rolled by the ordinary process and turned where it receives the couplings, pulleys, bearings, etc. Bright turned shafting varies" in diameter by i in. up to about 3| in. in diameter; above this diameter the shafting varies by in. The actual diameter of a bright shaft is ^ in. less than the commercial diameter, it being designated from the diameter of the ordinary round bar iron from which it is turned. Thus, a length of what is called 3" bright shafting is only 2^| in. in diameter. Cold-rolled shafting is designated by its commercial diameter; thus, a length of what is called 3" shafting is 3 in. in diameter. Cold-rolled iron is considerably stronger than ordinary turned wrought iron; the increased strength being due to the process of rolling, which seems to compress the metal and so make it denser not merely skin deep, but practically throughout the whole diameter. STRENGTH OF SHAFTING. Let D = diameter of shaft; ft = revolutions per minute; H = horsepower transmitted; C = constant given in table. CONSTANTS FOR LINE SHAFTING. In the accompanying table the bearings are supposed to be spaced so as to relieve the shaft of Material of Shaft. Steel or cold-rolled iron Wrought iron Cast iron No Pulleys Between Bearings. 65 70 90 Pullevs excessive bending; also, Between in tne third vertical col- umn, an average num- ber and weight of pulleys and power given off is OK f*" 1 assumed. In determining the 120 constants given in the - accompanying table, al- lowance has been made to insure the stiffness as well as strength of the shaft. &XR n 3\&X~H CXH ~C~~' = M~~R~' ~D^' Shafts are subject to forces that produce stresses of two kinds transverse and torsional. When the machines to be driven are below the shaft, there is a transverse stress on the shaft, due to the weight of the shaft itself, of the pulley and tension of the belt. Sometimes the power is taken off horizon- tally on one side, in which case the tension of the belt produces a horizontal transverse stress, while the weight of the pulley acts with the weight of the shaft to produce a vertical transverse stress. When the machinery to be driven is placed on the floor above the shaft, the tension of the belt produces a transverse stress in opposite direction to that due to the weight of the shaft and pulley. The torsional strength of shafts, or their resistance to breaking by twisting, is proportional to the cube of their diameter. Their stiffness or resistance to bending is proportional to the fourth power of their diameters, and inversely proportional to the cube of the lengths of their spans. No simple general formula can be given that will safely apply to engine and other shafting that is subjected to the bending stresses produced by overhung cranks, the weight of heavy flywheels, the pull of large belts, or to severe shocks pro- duced by the intermittent action of the power or load. The calculations for such shafts should always be based on the special conditions involved. In the following table is given the maximum distance between the bear- ings of some continuous shafts that are used for the transmission of power. Pulleys from which considerable power is to be taken should always be placed as close to a bearing as possible. The diameters of the different lengths of shafts composing a line of shaft- ing may be proportional to the quantity of power delivered by each respective length. In this connection, the positions of the various pulleys depend WEIGHT OF CASTINGS. Ill on the distance between the pulley and the bearing, and on the amount of power given off by the pulleys. Suppose, for example, that a piece of shaft- ing delivers a certain amount of power; then, it is obvious that the shaft will deflect or bend less if the pulley transmitting that power be placed close to a hanger or bear- ing, than if it be placed midway between the two hangers or bear- ings. It is impossible to give any rule for the proper distance of bear- ings that could be used univer- sally, as in some cases the require- ments demand that the bearings be nearer together than in others. If the work done by a line of shaft- ing is distributed quite equally along its entire length, and the power can be applied near the middle, the strength of the shaft need be only half as great as would be required if the power were applied at one end of the shaft. WEIGHT OF CASTINGS. To Find the Approximate Weight of a Casting. For iron, multiply the weight of the pattern by 20. Copper is heavier; lead, | heavier; brass, } heavier; and zinc is Jfa as heavy. Distance Between Bearings. Diameter Feet. of Shaft. Inches. Wrought-Iron Shaft. Steel Shaft. 2 11 11.50 3 13 13.75 4 15 15.75 5 17 18.25 6 19 20.00 7 21 22.25 8 23 24.00 9 25 26.00 | g || Weight of a Square Foot. Weight of a Square Bar 1 Ft. Long. Weight of a Round Bar 1 Ft. Long. ! {> gS So Weight of a Square Foot. Weight of a Square Bar 1 Ft. Long. Weight of a Round Bar 1 Ft. Long. g 5~ Pounds. oun . i 9.375 .195 .154 44 168.7 63.33 49.71 | 14.06 .440 .346 4 173.4 66.86 52.52 18.75 .781 .610 4 178.1 70.52 55.39 | 23.44 1.221 .959 41 182.8 74.27 58.34 .3 28.12 1.758 1.381 5 187.5 78.12 61.37 32.81 2.393 1.880 5i 196.9 86.14 67.65 1 37.50 3.125 2.455 5i 206.2 94.54 74.26 H 42.19 3.955 3.107 5| 215.6 103.3 81.16 H 46.87 4.883 3.835 6 225.0 112.5 88.36 if 51.57 5.909 4.640 6i 234.4 122.1 95.89 H 56.26 7.033 5.523 6i 243.8 132.0 103.7 H 60.94 8.253 6.484 6* 253.1 142.4 111.9 l* 65.63 9.572 7.518 7 262.5 153.2 120.2 U 70.32 10.99 8.630 7i 271.9 164.2 129.0 2 75.01 12.50 9.821 7i 281.3 175.8 138.1 2j 79.70 14.11 11.09 7* 290.7 187.7 147.4 2i 84.40 15.83 12.43 8 300.0 200.1 157.0 2f 89.07 17.63 13.85 8i 309.4 212.7 167.0 2i 93.75 19.54 15.34 8| 318.8 225.8 177.3 n 98.44 21.54 16.56 8* 328.2 . 239.3 187.9 2* 103.2 23.64 18.56 9 337.4 253.1 198.8 21 107.8 25.84 20.29 9i 346.8 267.4 210.0 3 112.6 28.13 22.10 9* 356.2 282.1 221.5 3| 117.3 30.52 23.97 9| 365.6 297.0 233.3 3i 121.8 33.01 25.93 10 375.0 312.5 245.5 3| 126.5 35.60 27.95 10i 384.4 328.4 257.8 3i 131.2 38.28 30.07 lot 393.7 344.5 270.6 3| 135.9 41.07 32.25 Ipf 403.1 361.2 283.7 3* 140.6 43.95 34.51 11 412.5 378.2 297.0 31 145.3 46.93 36.85 Hi 421.9 395.5 310.6 4 150.0 50.01 39.27 Hi 431.2 413.3 324.6 4i 154.7 53.18 41.77 H* 440.6 431.4 338.8 8 159.3 56.46 44.33 12 450.0 450.0 353.4 4f 164.0 59.82 46.99 112 WEIGHT OF MATERIALS. WEIGHTS OF SHEETS AND PLATES OF STEEL, WROUGHT IRON, COPPER, AND BRASS. (Cambria Steel Co.) AMERICAN, OR BROWN & SHARPE, GAUGE. No. of Gauge. Thickness. Inch. Weight Per Square Foot. Steel. Iron. Copper. Brass. 0000 .460000 18.7680 18.4000 20.8380 19.6880 000 .409642 16.7134 16.3857 18.5568 17.5327 00 .364796 14.S837 14.5918 16.5253 15.6133 .324861 13.2543 12.9944 14.7162 13.9041 1 .289297 11.8033 11.5719 13.1052 12.3819 2 .257627 10.5112 10.3051 11.6705 11.0264 3 .229423 9.3605 9.1769 10.3929 9.8193 4 .204307 8.3357 8.1723 9.2551 8.7443 5 .181940 7.4232 7.2776 8.2419 7.7870 6 .162023 6.6105 6.4809 7.3396 6.9346 7 .144285 5.8868 5.7714 6.5361. 6.1754 8 .128490 5.2424 5.1396 5.8206 5.4994 9 .114423 4.6685 4.5769 5.1834 4.8973 10 .101897 4.1574 4.0759 4.6159 4.3612 11 .090742 3.7023 3.6297 4.1106 3.8838 12 .080808 3.2970 3.2323 3.6606 3.4586 13 .071962 2.9360 2.8785 3.2599 3.0800 14 .064084 2.6146 2.5634 2.9030 2.7428 15 .057068 2.3284 2.2827 2.5852 2.4425 16 .050821 2.0735 2.0328 2.3022 2.1751 17 .045257 1.8465 1.8103 2.0501 1.9370 18 .040303 1.6444 1.6121 1.8257 1.7250 19 .035890 1.4643 1.4356 1.6258 1.5361 20 .031961 1.3040 1.2784 1.4478 1.3679 21 .028462 1.1612 1.1385 1.2893 1.2182 22 .025346 1.0341 1.0138 1.1482 1.0848 23 .022572 .92094 .90288 1.0225 .96608 24 .020101 .82012 .80404 .91058 .86032 25 .017900 .73032 .71600 .81087 .76612 26 .015941 .65039 .63764 .72213 .68227 27 .014195 .57916 .56780 .64303 .60755 28 .012641 .51575 .50564 .57264 .54103 29 .011257 .45929 .45028 .50994 .48180 30 .010025 .40902 .40100 .45413 .42907 31 .008928 .36426 .35712 .40444 .38212 32 .007950 .32436 .31800 .36014 .34026 33 .007080 .28886 .28320 .32072 .30302 34 .006305 .25724 .25220 .28562 .26985 35 .005615 .22909 .22460 .25436 .24032 36 .005000 .20400 .20000 .22650 .21400 37 .004453 .18168 .17812 .20172 .19059 38 .003965 .16177 .15860 .17961 .16970 39 .003531 .14406 .14124 .15995 .15113 40 .003144 .12828 .12576 .14242 .13456 CAST-IRON PIPE. WEIGHT OF CAST-IRON PIPE PER FOOT IN POUNDS. These weights are for plain pipe. For hautboy pipe, add 8 in. in length for each joint. For copper, add ; for lead, I; for welded iron, 1 ' 5 . Diam- eter of Thickness of Pipe. Inches. Bore. Inches. i I i 1 * T 1 H H If H 2 1 3.07 5.07 7.38 H 3.69 6.00 8.61 a 4.30 6.92 9.84 i* 4.92 7.84 11.10 2 5.53 8.76 12.30 16.2 2i 6.15 9.69 13.50 17.7 6.76 10.60 14.80 19.2 24.0 9 7.37 11.50 16.00 20.8 25.9 3 7.98 12.50 17.20 22.3 27.7 33.4 ft 9.21 14.30 19.70 25.4 31.4 37.7 4 10.30 16.10 22.20 28.5 35.1 42.0 4i 11.70 18.00 24.60 31.5 38.8 46.3 5 12.90 19.80 27.10 34.6 42.5 50.6 51 14.20 21.70 29.50 37.7 46.1 54.9 6 15.40 23.50 32.00 40.8 49.8 59.2 68.9 6* 16.60 25.40 34.50 43.8 53.5 63.5 73.8 84.4 7 17.80 27.20 36.90 46.9 57.2 67.8 78.7 89.4 n 19.10 29.10 39.40 50.0 60.9 72.1 83.7 95.5 108 8 20.30 30.90 41.80 53.1 64.6 76.4 88.6 101.0 114 127 8i 21.50 32.80 44.30 56.1 68.3 80.7 93.5 107.0 120 134 148 9 22.80 34.60 46.80 59.2 72.0 85.1 98.4 112.0 126 140 155 24.00 36.40 49.20 62.3 75.7 89.3 103.0 118.0 132 147 163 10 25.10 38.30 51.70 65.3 79.4 93.6 108.0 123.0 138 164 170 202 11 27.60 42.00 56.60 71.5 86.7 102.0 118.0 134.0 151 168 185 220 12 30.00 45.70 61.50 77.7 94.1 111.0 128.0 145.0 163 181 199 237 275 13 32.50 49.40 66.40 83.8 102.0 120.0 138.0 156.0 175 195 214 254 294 14 35.00 53.10 71.40 89.4 109.0 128.0 148.0 168.0 188 208 229 271 314 15 37.40 56.70 76.30 96.1 116.0 137.0 158.0 179.0 200 222 244 289 334 16 39.10 60.40 81.20 102.0 124.0 145.0 167.0 190.0 212 235 258 306 353 17 42.30 64.10 86.10 108.0 131.0 154.0 177.0 201.0 225 249 273 323 373 18 44.80 67.80 91.00 115.0 139.0 163.0 187.0 212.0 237 262 288 340 393 19 47.30 71.50 96.00 121.0 146.0 171.0 197.0 223.0 249 276 303 357 412 20 49.70 75.20 101.00 127.0 153.0 180.0 207.0 234.0 261 289 317 375 432 21 52.20 78.90 106.00 1 133.0 161.0 188.0 217.0 245.0 274 303 332 392 452 22 54.60 82.60 111.00:139.0 168.0 196.0 227.0 256.0 286 316 347 409 471 23 57.10 86.30 116.00 145.0 175.0 206.0 236.0 267.0 298 330 362 426 491 24 59.60 89.90 121.00 152.0 183.0 214.0 246.0 278.0 311 343 375 444 511 25 26 62.00 64.50 93.60 97.30 126.00 131.00 158.0 164.0 190.0 198.0 223.0 j:U.O 256.0289.0 266.0,300.0 323 335 357 370 391 406 461 478 531 550 27 66.90 101.00 135.00 170.0 205.0 240.0 276.0 311.0 348 384 421 495 570 28 69.40 105.00 140.00 176.0 212.0 i 249.0 286.0 '323.0 360 397 436 512 590 29 30 71.80 109.00 74.20! 112.00 145.00 150.00 182.0 188.0 220.0 257.0 227.0 266.0 295.0334.0 305.0345.0 372 384 411 424 450 465 530 547 609 629 DIAMETER AND NUMBER OF WOOD SCREWS. Formulas for Wood Screws. No. Diameter. No. Diameter. No. Diameter. N = number .056 11 .201 22 .347 D = diameter 1 .069 12 .215 23 .361 D = (NX .01325) + .056 2 .082 13 .228 24 .374 D .056 3 .096 14 .241 25 .387 .01325 4 .109 15 .255 26 .401 5 .122 16 .268 27 .414 6 .135 17 .281 28 .427 7 .149 18 .293 29 .440 8 .162 19 .308 30 .453 9 .175 20 .321 10 .188 21 .334 114 WEIGHT OF MATERIALS. WEIGHT OF WROUGHT IRON. The following table is for wrought iron. Multiply by .95 for weight of cast iron; by 1.02 for steel; by 1.16 for copper; by 1.09 for brass; by 1.48 for lead. Thickness or Diameter. Inches. Weight of a Square Foot. Pounds. Weight of a Square Bar 1 Ft. Long. Pounds. Weight of a Round Bar 1 Ft. Long. Pounds. Thickness or Diameter. Inches. Weight of a Square Foot. Pounds. Weight of a Square Bar 1 Ft. Long. Pounds. Weight of a Round Bar 1 Ft. Long. Pounds. | 5.052 .0526 .0414 4f 176.8 64.47 50.63 I 10.10 .2105 .1653 4 181.9 68.20 53.57 1 15.16 .4736 .3720 4 186.9 72.05 56.59 I 20.21 .8420 .6613 y 192.0 75.99 59.69 I 25.26 1.316 1.033 4 197.0 80.05 62.87 30.31 1.895 1.488 5 202.1 84.20 66.13 I 35.37 2.579 2.025 5* 212.2 92.83 72.91 1 40.42 3.368 2.645 6} 222.3 101.9 80.02 H 45.47 4.263 3.348 5* 232.4 111.4 87.46 l| 50.52 5.263 4.133 6 242.5 121.3 95.23 If 55.57 6.368 5.001 6i 252.6 131.6 103.3 1* 60.63 7.578 5.952 6i 262.7 142.3 111.8 H 65.68 8.893 6.985 6* 272.8 153.5 120.5 1* 70.73 10.31 8.101 7 282.9 165.0 129.6 If 75.78 11.84 9.300 7i 293.0 177.0 139.0 2 80.83 13.47 10.58 7i 303.1 189.5 148.8 2} 85.89 15.21 11.95 7* 313.2 202.3 158.9 3 90.94 17.05 13.39 8 323.3 215.6 169.3 2f 95.99 19.00 14.92 8i 333.4 229.3 180.1 2 101.0 21.05 16.53 8 343.5 243.4 191.1 2| 106.1 23.21 18.23 8| 353.6 247.9 202.5 2* 111.2 25.47 20.01 9 363.8 272.8 214.3 21 116.2 27.84 21.87 % 373.9 288.2 226.3 3 121.3 30.31 23.81 94 384.0 304.0 238.7 3} 126.3 32.89 25.83 9* 394.1 320.2 251.5 si 131.4 35.57 27.94 10 404.2 336.8 264.5 3f 136.4 38.37 30.13 10i 414.3 353.9 277.9 3i 141.5 41.26 32.41 10* 424.4 371.3 291.6 8| 146.5 44.26 34.76 10| 434.5 389.2 305.7 3* 151.6 47.37 37.20 11 444.6 407.5 320.1 8| 156.6 50.57 39.72 Hi 454.7 426.3 334.8 4 161.7 53.89 42.33 11* 464.8 445.4 349.8 4} 166.7 57.31 45.01 11* 474.9 465.0 365.2 8 171.8 60.84 47.78 12 485.0 485.0 380.9 SPIKES AND NAILS. Standard Steel- Wire Nails. Steel- Wire Spikes. Common. Finishing. Length. izes. In. Diam. No. per Diam. No. per Length. Diam. No. per Size Length. No. per In. Lb. In. Lb. In. In. Lb. In. Lb. 2d 1 .0524 1,060 .0453 1,558 3 .1620 41 2d 1 800 3d H .0588 640 .0508 913 Si .1819 30 3d H 400 4d l* .0720 380 .0508 761 4 .2043 23 4d H 300 5d l* .0764 275 .0571 500 4* .2294 17 5d 1* 200 6d 2 .0808 210 .0641 350 5 .2576 13 6d 2 150 7d 2i .0858 160 .0641 315 5| .2893 11 7d 2i 120 8d 2* .0935 115 .0720 214 6 .2893 10 8d 85 9d 2* .0963 93 .0720 195 6* .2249 U 9d 2* 75 lOd 3 .1082 77 .0808 137 7 .2249 1 lOd 3 60 12d 3i .1144 60 .0808 127 8 .3648 5 12d 3i 50 16d 3i .1285 48 .0907 90 9 .3648 4* 16d s 40 20d 4 .1620 31 .1019 62 20d 4 20 30d 4* .1819 22 30d 4* 16 40d 5 .2043 17 40d 5 14 50d 6* .2294 13 50d 6* 11 60d 6 .2576 11 fVV^ 6 8 WROUGHT IRON. 115 WEIGHT, IN POUNDS, OF 1 LINEAL FOOT OF WEOUGHT IRON FLAT. Multiply by .95 for weight of cast iron; by 1.02 for weight of steel; by 1.16 for copper; by 1.09 for brass; by 1.48 for lead. Size. Inches. Weight. Pounds. Size. Inches. Weight. Pounds. Size. Inches. Weight. Pounds. 1 Xi 0.85 5iXI 6.65 4 XI 8.45 HXi 1.06 5iXI 6.97 4iXI 8.98 liX i 1.27 5#Xt 7.29 4iXI 9.51 If Xf 1.48 6 XI 7.60 41X1 10.03 2 X T 1.69 5 XI 10.56 2J- XT 1.90 1 Xi 1.69 5iXI 11.09 2iX i 2.11 H Xi 2.11 5iXI 11.62 2| XT 2.32 HXi 2.53 6f Xf 12.15 3 Xi 2.53 IfXi 2.96 6 XI 12.67 3iXi 2.75 2 X i 3.38 3iXi 2.96 2iXi 3.80 1 XI 2.53 3* XT 3.17 2iXi 4.22 HX* 3.17 4 XT 3.38 2| Xi 4.65 HXI 3.80 4iXi 3.59 3 Xi 5.07 UXI 4.44 4iXi 3.80 3i X i 5.49 2X1 5.07 4| XT 4.01 3i X i 5.92 2iX4 5.70 5 XT 4.22 3* X k 6.33 2iX* 6.33 5iXT 4.44 4 Xi 6.76 2f X I 6.97 5iXi 4.65 4iXi 7.18 3X1 7.60 5* XT 4.86 4Xi 7.60 3iX* 8.24 6 XT 5.07 4*Xi 8.03 3iX* 8.87 5 Xi 8.45 3*X* 9.51 1 XI 1.27 5iXi 8.87 4 X* 10.14 IT XI 1.58 5iXi 9.30 4iX* 10.77 liXt 1.90 5f Xi 9.72 4iX 11.41 11 XI 2.22 6 Xi 10.14 4*X* 12.04 2 XI 2.53 5 XI 12.67 2X I 2.85 1 X* 2.11 5iX 1 13.31 2iXI 3.17 HX4 2.64 5iXl 13.94 2| X I 3.49 HXI 3.17 51 X 1 14.57 3 XI 3.80 uxt 3.70 6 XI 15.21 3iX f 4.12 2 X f 4.22 3i X t 4.44 2iXt 4.75 HX1 5.07 31 Xi 4.75 2iXi 5.28 2X1 6.76 4 XI 5.07 2*Xt 5.81 3 XI 10.14 4* XI 5.39 3X1 6.33 4 XI 13.52 4iX 1 5.70 3iXI 6.87 5 XI 16.90 4| X 1 6.02 3iXI 7.39 6X1 20.28 5X1 6.33 3* XI 7.92 7 XI 23.66 STRENGTH OF METALS IN POUNDS PER SQUARE INCH. Material. Ultimate Tensile. Ultimate Compres- sion. Ultimate Shearing. Modulus of Rupture. Modulus of Elasticity. Millions. Wrought iron Shape iron Structural steel j Cast iron 50,000 48,000 60,000 65,000 18,000 70,000 24,000 50,000 75,000 15,000 44,000 52,000 81,000 70,000 *30,000 120,000 12,000 44,000 52,000 25,000 60,000 36,000 12,000 48,000 60,000 45,000 70,000 20,000 27 26 29 12 30 9 14 11 Steel, castings Brass, cast ... Bronze, phosphor Bronze, aluminum Aluminum, commercial * Unit stress producing 10$ reduction in original length. 116 WEIGHT OF MATERIALS. WEIGHT OF WROUGHT-IRON BOLTHEADS, NUTS, AND WASHERS. Diameter of Bolt. Inches. Hexagon Heads and Nuts. Per Pair. Square Heads and Nuts. Per Pair. Round Washers. Per Pair. I 20 to alb. 16 to alb. 20 to a Ib. 10 to a Ib. 8| to a Ib. 10 to a Ib. f 5 to a Ib. 4 to a Ib. 5 to a Ib. t 2 to a Ib. 2i to a Ib. 3 to a Ib. f 2 to alb. 0.56 Ib. 0.63 Ib. j 0.77 Ib. 0.88 Ib. 0.77 Ib. 1.25 Ib. 1.31 Ib. 1.25 Ib. H 1.75 Ib. 2.10 Ib. ] .75 Ib. H 2.13 Ib. 2.56 Ib. 2.25 Ib. H 3.00 Ib. 3.60 Ib. 3.25 Ib. H 3.75 Ib. 4.42 Ib. 4.25 Ib. if 4.75 Ib. 5.70 Ib. 5.25 Ib. i* 5.75 Ib. 7.00 Ib. 6.50 Ib. H 7.27 Ib. 8.72 Ib. 8.00 Ib. 2 8.75 Ib. 10.50 Ib. 9.60 Ib. WEIGHT OF 100 BOLTS WITH SQUARE HEADS AND NUTS. (The Carnegie Steel Co., Limited.} Diameter of Bolts. Length Head to Point. & ft. Lb. ft. b. b. b . ib. 1" Lb. li 4.0 7.0 10.5 15.2 22.5 39.5 63.0 1* 4.4 7.5 11.3 15.3 23.8 41.6 66.0 2 4.8 8.0 12.0 17.4 25.2 43.8 69.0 109.0 163 tt 5.2 8.5 12.8 18.5 26.5 45.8 72.0 113.3 169 3 5.5 9.0 13.5 19.6 27.8 48.0 75.0 117.5 174 5.8 9.5 14.3 20.7 29.1 50.1 78.0 121.8 180 3 6.3 10.0 15.0 21.8 30.5 52.3 81.0 126.0 185 B* 7.0 11.0 16.5 24.0 33.1 56.5 87.0 134.3 196 4 7.8 12.0 18.0 26.2 35.8 60.8 93.1 142.5 207 4i 8.5 13.0 19.5 28.4 38.4 65.0 99.1 151.0 218 5 9.3 14.0 21.0 30.6 41.1 69.3 105.2 159.6 229 ft 10.0 15.0 22.5 32.8 43.7 73.5 111.3 168.0 240 6 10.8 16.0 24.0 35.0 46.4 77.8 117.3 176.6 251 6* 25.5 37.2 49.0 82.0 123.4 185.0 262 7 27.0 39.4 51.7 86.3 129.4 193.7 273 7i 28.5 41.6 54.3 90.5 135.0 202.0 284 8 30.0 43.8 59.6 94.8 141.5 210.7 295 9 46.0 64.9 103.3 153.6 227.8 317 10 48.2 70.2 111.8 165.7 224.8 339 11 50.4 75.5 120.3 177.8 261.9 360 12 52.6 80.8 128.8 189.9 278.9 382 13 86.1 137.3 202.0 296.0 404 14 91.4 145.8 214,1 313.0 426 15 96.7 154.3 226.2 330.1 448 16 102.0 162.8 238.3 347.1 470 17 107.3 171.0 250.4 364.2 492 18 112.6 179.5 262.6 381.2 514 19 117.9 188.0 274.7 398.3 536 20 123.2 206.5 286.8 415.3 558 Per Inch Addit'al. 1.4 2.1 3.1 4.2 5.5 8.5 12.3 16.7 21.8 RAILROAD IRON. 117 IRON REQUIRED FOR ONE MILE OF TRACK. TONS OF IRON. Rule. To find the number of tons of rails to the mile, divide the weight per yard by 7, and multiply by 11. Thus, for 56-pound rail, divide 56 by 7 equal 8, multi- plied by 11 equal 88 tons, for 1 mile of single track. Weight of Rail per Yard. Pounds. Tons per Mile. Weight of Rail per Yard. Pounds. Tons per Mile. Tons. Pounds. Tons. Pounds. 12 18 1,920 45 70 1,600 14 22 ' 48 75 960 16 25 320 50 78 1,280 18 28 640 52 81 1,600 20 31 960 56 88 22 34 1,280 57 89 1,280 25 39 640 60 94 640 26 40 1,920 62 97 960 27 42 960 64 100 1,280 28 44 65 102 320 30 47 320 68 106 1,920 33 51 1,920 70 110 35 55 72 113 320 40 62 1,920 76 119 960 NUMBER OF RAILS, SPLICES, AND BOLTS PER MILE OF TRACK. Length of Rail. Feet. No. of Rails per Mile. No. of Splices. No. of Bolts, 4 to Each Joint. No. of Bolts, 6 to Each Joint. 18 584 1,168 2,336 3,504 20 528 1,056 2,112 3,168 21 503 1,006 2,012 3,018 22 480 960 1,920 2,880 24 440 880 1,760 2,640 25 422 844 1,688 2,532 26 406 812 1,624 2,436 27 391 782 1,564 2,346 28 377 754 1,508 2,262 30 352 704 1,408 2,112 RAILROAD SPIKES PER MILE OF TRACK. Size Measured Under Head. Average No. per Keg Ties 2 Ft. Between Centers, 4 Spikes to a Tie. Rails Used. Pounds per Inches. of 200 Lb. Pounds. Kegs. Yard. 5* X T 9 g 375 5,870 29i 45 to 70 5 XA 400 5,170 26 40 to 56 5 Xi 450 4,660 23| 35 to 40 4*XH 530 3,960 20 28 to 35 4 Xi 600 3,520 17| 24 to 35 4* X / 5 4 XA 680 720 3,110 2,910 15* 14 ' 20 to 30 3iX T 7 * 4 XI 900 1,000 2,350 2,090 11 ID* - 16 to 25 3Xf 3 XI 1,190 1,240 1,780 1,710 9 M - 16 to 20 2iX| 1,342 1,575 7| 12 to 16 118 WIRE ROPES. WIRE ROPES. Wire ropes for mine use are made of either iron or steel, and are gener- ally round. Flat wire ropes are sometimes used, but the round rope is the favorite for many reasons, and is generally used in American practice, excepting in some of the deep metal mines having small compartment shafts. Taper ropes are sometimes used, the idea being to produce a rope of uni- form strength, that is, to have it less strong and of less diameter at the cage end, where the load is least, and greater in strength and diameter at the drum end, where the load is greatest. The theory is correct, and some weight of rope is saved; but practically there is not much advantage, and it is doubtful whether taper ropes will ever be generally used. The long- established conviction that the best of all ropes for colliery use is a round one made of steel or iron has never been overcome and probably never will be. Steel ropes are in most respects superior to iron ropes, and are therefore gaining in favor every year. The principal advantage of a steel rope is that it has a greater strength than an iron rope of equal diameter; consequently, it can be made lighter and can pass around pulleys and drums with less injury than an iron rope of equal strength. In fastening a rope to a drum there is often a grievous error made. Men who will not think of passing a rope around a pulley of too small diameter will insert it in the drum rim in such a way as to make a very sharp curve, and make a weak point in the rope that would not other- wise exist. In the accompanying cut (a) shows the right and (6) the wrong way of passing the rope througn the drum rim. (a) (I)) The securing of the rope to the drum or the drum shaft by several coils around each is unnecessary. With one coil around either the drum or the shaft, a pull of 1 Ib. will resist a weight of 91b.; if two coils, a pull of 1 Ib. will resist 9 X 9, or 81 Ib.; if three coils, 9 X 9 X 9, or 729 Ib.; and so on, multiplying the former result by 9 for each additional coil. No rope should be subjected to a load greater than the safe working strain. There is, of course, in all cases, a wide margin between the break- ing strain and the working load, and on this account it is supposed that no risk is run by putting on a load considerably in excess of the maker's safe working strain. This is a mistake; and it is false economy. A rope over- loaded is unduly strained, and, although showing no defect at the moment, it will some day give way without warning. Drums and rope pulleys should have as great diameters as the engines will allow. Ropes should be regularly and properly greased. This can best be done with brushes, but brush greasing takes considerable time. While it pays in the long run, it is not always convenient to use brushes. A fairly good and cheap arrange- ment for greasing ropes is to make a wooden trough, wide at top, and small enough at bottom to fit loosely around the rope. Make a mixture of 1 barrel of coal tar or pitch tar to 1 bushel of fresh slaked lime, and boil it well. Then fill the trough with this mixture and run the rope slowly through it. A rope should not be changed from a large drum to a small one, for it will not work so well, neither will it last as long. This is also true, but in a lesser degree, of ropes changed from a small drum to a large one. After having been used for some time on a drum, the rope adapts itself to that diameter and resents a change. Rope sheaves should be made to fit the rope, and should be filled in with well-seasoned blocks of oak or other hard wood, set on end. This will save the rope and increase adhesion. Where great flexibility is required, such as in hoisting ropes, the strands are usually made up of 19* wires each, while haulage ropes have but 7 wires to the strand; yet, both kinds have 6 strands. A hemp core is generally used, and in some cases a core is also placed in each strand, to further increase the flexibility of the rope. The lay of the rope is the twist or pitch of the wires in the strand, or of the strands in the rope. As the lay of the wires is less than that of the strands, each wire is exposed to external wear for short distances at intervals WIRE ROPES. 119 along the rope. In the ordinary lay, Fig. (a), the wires are twisted in the opposite direction to the strands. This method prevents the rope from untwisting when in use, and the wires from unraveling when they are worn through or broken at the surface. In the Lang lay, Fig. (6), the wires are twisted in the same direction as the strands, thus giving each wire a greater wearing surface, while the rope is smoother and will wear longer. After the wires begin to break, unraveling becomes troublesome, and it is more difficult to splice a Lang lay rope than an ordinary lay one. Hoisting ropes, especially those used to raise and lower men, should not be spliced. The locked wire rope, a cross-section of which is shown in Fig. (c), consists of wires of special cross-section formed in concentric layers. The lay of the inner wires is opposite to that of the outer ones, and somewhat longer. This prevents untwisting, and brings the greater stress upon the outside layer, which is supposed to give way first. The inside layer, although inac- cessible, and therefore cannot be inspected or oiled, can be relied upon until the external portion of the rope wears out. This form of rope has a smooth cylindrical surface, but it is not so flexible as the other forms, and is most suitable for haulage purposes or bucket transportation. The life of a steel rope depends largely on the conditions to which it is subjected, and the care it receives. At some mines the ropes must be changed every six months, while at others the ropes last for one year and longer. Where the rope enters the socket by which it is attached to the cage is perhaps the place where signs of weakness will first appear. This point should be fre- quently inspected, and a new connection made every two or three months by cutting a few feet off the end and paying it out from the drum end. WEIGHTS AND STRENGTHS OF WIRE ROPES. FLAT ROPES. ( Trenton Iron Co., Trenton, N. J.) Breaking Stress. Size. Inches. Approximate Weight per Foot. ( Approximate. ) Pounds. Pounds. Iron. Cast Steel. 2 Xt 1.35 20,000 40,000 2| XI 1.70 25,000 50,000 3 Xf 2.05 30,000 60,000 3iXf 2.40 35,000 70,000 4 Xt 2.75 40,000 80,000 5 XI 3.45 50,000 100,000 6 Xt 4.15 60,000 120,000 3 Xi 2.40 37,500 75,000 3iXi 2.85 43,750 87,500 4 X* 3.30 50,000 100,000 5 Xt 4.20 62,500 125,000 6 Xt 5.10 75,000 150,000 7 Xt 6.00 87,500 175,000 8 Xt 6.90 100,000 200,000 For safe working load allow from one-fifth to one-seventh of the break- er stress. ing stress. 120 WIRE ROPES. COMPOSED OF 6 STRANDS AND A HEMP CENTER, 19 WIRES TO THE STRAND. (John A. Eoebling's Sons Co., Trenton, N. J.) SWEDISH IRON. Trade Number. Diameter. Inches. Approximate Circumfer- ence. Inches. _t-j O C< Approximate Breaking Strain. Tons of 2,000 Lb. Allowable Working Strain. Tons of 2, 000 Lb. fir CO 1 2 3 4 5 2| 2 If H H 5 4f 8.00 6.30 4.85 4.15 3.55 78.0 62.0 48.0 42.0 36.0 15.60 12.40 9.60 8.40 7.20 13 12 10 i 7| 6 a 7 8 9 If H I 8 f 4* 3* 3 2f 3.00 2.45 2.00 1.58 1.20 31.0 25.0 21.0 17.0 13.0 6.20 5.00 4.20 3.40 2.60 7 6* 6 4 10 loi 10a i 2 4 H .89 .62 .50 .39 .30 9.7 6.8 5.5 4.4 3.4 1.94 1.36 1.10 .88 .68 4 S 2* 106 lOc lOd 1 I 8 1 .22 .15 .10 2.5 1.7 1.2 .50 .34 .24 H 1 f CAST STEEL. 1 2 3 4 5 2i 2 If H H 8 5i 5 4} 8.00 6.30 4.85 4.15 3.55 156.0 124.0 96.0 84.0 72.0 31.20 24.80 19.20 16.80 14.40 8i 8 7i S 5f f 7 8 9 1! ? f 5 4 3i 3 2f 3.00 2.45 2.00 1.58 1.20 62.0 50.0 42.0 34.0 26.0 12.40 10.00 8.40 6.80 5.20 B| 5 41 4 8| 10 101 104 101 10a [ A 2i 2 If H H .89 .62 .50 .39 .30 19.4 13.6 11.0 8.8 6.8 3.88 2.72 2.20 1.76 1.36 3 2i If H li 106 lOc lOd i 1; .22 .15 .10 5.0 3.4 2.4 1.00 .68 .48 1 f PLOW-STEEL ROPE. Wire ropes of very high tensile strength, which are ordinarily called "plow-steel ropes," are made, of a high grade of crucible steel, which, when put in the form of wire, will bear a stress of from 100 to 150 tons per square inch. Where it is necessary to use very long or very heavy ropes, a reduction of the dead weight of ropes becomes a matter of serious consider- ation. It is advisable to reduce all bends to a minimum, and to use some- what larger drums or sheaves than are suitable for an ordinary crucible rope having a strength of 60 to 80 tons per square inch. ROPES. 121 PLOW-STEEL ROPE WITH 6 STRANDS AND A HEMP CENTER, 19 WIRES TO THE STRAND. *.-d S^S^ a a . fi gs H Sri 2 H a 03 fl 5~ Ifl Pi '*- ogflo ^,0 |i| i8^ .5^X3 S C Caa^ SJS ^ a> *< 02 02 02 22- 8* 11.95 305.00 61.00 11 i 2 2i 2i 2 1 9.85 8.00 6.30 254.00 208.00 165.00 50.80 41.60 33.00 10 9 8 3 H 5i 4.85 moo 25.60 U 4 H 5 4.15 111.00 22.20 6 5 H 42- 3.55 96.00 19.20 5 n U 4i 3.00 82.00 16.40 5^ 6 H 4 i 2.45 67.00 13.40 5 7 H 2.00 56.00 11.20 8 1 3 1.58 44.00 8.80 41- 9 i 2? 1.20 34.00 6.80 10 i 2 .89 25.00 5.00 3 10- 2 .62 18.00 3.60 3 10* T% U .50 14.50 2.90 2i HI H .39 11.40 2.28 2 10a T ? 5 H .30 8.85 '1.77 li 106 | 1? .22 6.55 1.31 1 lOc T S 5 1 .15 4.50 .90 i lOd * * .10 3.00 .60 t PLOW-STEEL ROPE WITH 7 WIRES TO THE STRAND. 11 H 4* 3.55 91.00 18.20 84 12 13 I! 8 3.00 2.45 78.00 64.00 15.60 12.80 8 14 If 3j 2.00 53.00 10.60 64 15 1 3 1.58 42.00 8.40 5$ 15 f 21 1.20 32.00 6.40 5 17 | .89 24.00 4.80 4 18 19 1 2| 2 .75 .62 21.00 17.00 4.20 3.40 31 3 20 A 11 .50 14.00 2.80 2| . 21 22 23 24 i f ? i 8 .39 .30 .22 .15 11.00 8.55 6.35 4.35 2.20 1.71 1.27 .87 2| 2 it 25 A T .125 3.65 .73 1 122 WIRE ROPES. TRANSMISSION OR HAULAGE ROPE. COMPOSED OF 6 STRANDS AND A HEMP CENTER, 7 WIRES TO THE STRAND. SWEDISH IRON. -M 1 CD 1 fl^ CO d o>| ti O> co I s ! 1 . ^^3 |e? || if || M HI If di II pi |2|| % s~ & o5 ^ P-" g'^ <3^''S Jg "** o> -< OQ ^ 11 H 41 3.550 34.00 6.80 13 12 H 4i 3.000 29.00 5.80 12 13 H 4 2.450 24.00 4.80 lOf 14 3 31. 2.000 20.00 4.00 9 f 15 1 3 1.580 16.00 3.20 16 I 2f 1.200 12.00 2.40 7i 17 j .890 9.30 1.86 18 ft 2| .750 7.90 1.58 6 19 1 2 .620 6.60 1.32 5- 20 | If .500 5.30 1.06 4i 21 i li .390 4.20 .84 4 22 H .300 3.30 .66 31 23 U .220 2.40 .48 3 24 1% l .150 1.70 .34 25 | T .125 1.40 .28 2! CAST STEEL. 11 H 4^ 3.55 68.00 13.60 8^ 12 14 s 3.00 58.00 11.60 8 13 H 4 2.45 48.00 9.60 7i 14 3 3^ 2.00 40.00 8.00 N 15 i 3 1.58 32.00 6.40 5* 16 T P 1.20 24.00 4.80 5 17 * s .89 18.60 3.72 A 18 2i .75 15.80 3.16 4 19 | 2 .62 13.20 2.64 3 20 T% If .50 10.60 2.12 3 21 22 I 5 ij 1} .39 .30 8.40 6.60 1.68 1.32 l! 23 IF .22 4.80 .96 2 24 JL 1 .15 3.40 .68 If 25 * J .125 2.80 .56 1* The rope usually employed for transmission of power is a seven-wire iron rope. Ropes of twelve and also of nineteen wires to the strand are frequently substituted, where it is impracticable to use the larger sheaves which seven- wire ropes require. The driving sheaves should always be lined with some flexible material, such as a packing of rubber and leather. The shortest practicable span is found by experience to be about 50 feet. The following table gives the proper deflections at center of span to secure the most economical results: TABLE OF DEFLECTIONS. Span in feet 50 100 150 200 250 300 350 400 450 Deflection in feet 0.17 0.69 1.56 2.78 4.34 6.25 8.52 11.12 14.07 It is frequently convenient to use sheaves of different sizes, in order to obtain the requisite speed in the driven mechanism. In such cases the power transmitted will be the same as if both were of the diameter of the smaller sheave. WIRE ROPES. 123 STRESS IN HOISTING ROPES ON INCLINED PLANES OF VARIOUS DEGREES. (From "Wire- Rope Transportation," published by Trenton Iron Co.) The following table is based upon an allowance of 40 Ib. per ton for rolling friction, but there will be an additional stress due to the weight of the rope and inclination of the plane. Rise per 100 Ft. Horizontal. Ft. Angle of Inclination. Stress in Lb. per Ton of 2,000 Lb. Rise per 100 Ft. Horizontal. Ft. Angle of Inclination. Stress inLb. per Ton of 2,000 Lb. 5 2 52' 140 105 46 24' 1,484 10 5 43' 240 110 470 44 / 1,516 15 8 32' 336 115 49 00' 1,535 20 11 IV 432 120 50 12' 1,573 25 14 03' 527 125 51 21' 1,597 30 16 42' 613 130 52 26' 1,620 35 19 18' 700 135 53 29' 1,642 40 21 49 / 782 140 54 28' 1,663 45 24 14' 860 145 55 25' 1,682 50 26 34' 933 150 56 19' 1,699 55 28 49' 1,003 155 579 11' 1,715 60 30 58' 1,067 160 58 00' 1,730 65 33 02' 1,128 165 58 47' 1,744 70 35 00' 1,185 170 59 33' 1,758 75 36 53' 1,238 175 60 16' 1,771 80 38 40' 1,287 180 60 57' 1,782 85 40 22' 1,332 185 61 37' 1,794 90 42 00' 1,375 190 62 15' 1,804 95 43 32' 1,415 195 62 52' 1,813 100 45 00' 1,450 200 63 27' 1,822 RELATIVE EFFECTS OF VARIOUS SIZED SHEAVES OR DRUMS ON THE LIFE OF WIRE ROPES. Mine officials and other users of wire ropes have often felt the want of a table or set of tables that would enable them to determine at a glance what effect the use of various sized sheaves would have on various sized ropes. The following tables have been specially prepared for the Coal and Metal Miner's Pocketbook by Mr. Thomas E. Hughes, of Pittsburg, Pa. MADE OF 6 STRANDS OF 7 WIRES EACH, LAID AROUND A HEMP CORE. Diameter of uiamt; iei s ui ciieaves ur uiuius 111 reei, ouuwmg .rerceniages of Life for Various Diameters. Rope. Inches. lOO/o 90f, SOfc 75/< 60* 50^ 25/c li 16.00 14.00 12.00 11.00 9.00 7.00 4.75 if 14.00 12.00 10.00 8.50 7.00 6.00 4.50 H 12.00 10.00 8.00 7.25 6.00 5.50 4.25 H 10.00 8.50 7.75 7.00 6.00 5.00 4.00 1 8.50 7.75 6.75 6.00 5.00 4.50 3.75 | 7.75 7.00 6.25 5.75 4.50 3.75 3.25 7.00 6.25 5.50 5.00 4.25 3.50 2.75 I 6.00 5.25 4.50 4.00 3.25 3.00 2.50 * 5.00 4.50 4.00 3.50 2.75 2.25 1.75 NOTE. We do not publish a table of iron ropes for inclines, as the use of iron ropes for this purpose has been generally abandoned, steel ropes being far more satisfactory and economical. 124 WIRE HOPES. MADE OF 6 STKANDS OF 19 WIEES EACH, LAID AROUND A HEMP CORE. TV I Diameters of Sheaves or Drums in Feet, Showing 1 Percentages )iam f ete] of Life for Various Diameters. Rope. Inches. 100$ 90$ 80$ 75$ 60$ 50$ 25$ it 14.00 12.00 10.00 8.50 7.00 6.00 4.50 if 12.00 10.00 8.00 7.00 6.00 5.25 4.25 il 10.00 8.50 7.50 6.75 5.50 5.00 4.00 i| 9.00 7.50 6.50 5.50 5.00 4.50 3.75 i 8.00 7.00 6.00 5.50 4.50 4.00 3.50 i 7.50 6.75 5.75 5.00 4.25 3.50 3.00 1 5.50 4.50 4.00 3.75 3.25 3.00 2.25 i 4.50 4.00 3.75 3.25 3.00 2.50 2.00 | 4.00 3.00 3.00 2.75 2.25 2.00 1.50 3.00 2.00 1.50 MADE OF 6 STRANDS OF 19 WIRES EACH, LAID AROUND A HEMP CORE. Diameter of Diameters of Sheaves or Drums in Feet, Showing Percentages of Life for Various Diameters. Rope. Inches. lOO/o 90$ 80$ 75$ 60$ 50$ 25$ H 12.00 11.00 9.00 7.50 6.00 5.00 3.00 If 10.00 9.00 7.50 7.00 5.25 4.75 4.00 1} 9.00 7.75 6.50 5.75 4.50 4.00 3.50 H 8.00 6.75 5.50 5.00 4.25 3.50 3.00 1 6.75 6.00 5.00 4.75 4.00 3.25 2.75 I 6.75 6.00 5.00 4.50 4.00 3.00 2.50 5.00 4.75 4.00 3.75 3.00 2.75 2.00 1 4.50 3.75 3.25 3.00 2.75 2.25 1.75 I 3.50 3.25 3.00 2.75 2.00 1.50 1.00 3.00 . 2.00 1.25 1.00 Wire rope is as pliable as new hemp rope of the same strength; the former will therefore run on the same sized sheaves and pulleys as the latter. But the greater the diameter of the sheaves, pulleys, and drums, the longer wire rope will last. In the construction of machinery for wire rope, it will be found good economy to make the drums and sheaves as large as possible. The tables of wire-rope manufacturers give " proper diameters of drum or sheave " at from 50 to 65 times the rope diameter; but the expression would more properly be the "minimum, admissible diameter." For ordinary ser- vice, by using sheaves and drums from 75 to 100 times the diameter of the rope, the average life of hoisting ropes would be materially lengthened. For rapid hoisting, during which abnormal strains are most likely to occur, or where a low factor of safety is employed, a sheave diameter of 150 times that of the rope is to be recommended. Experience has demonstrated that the wear increases with the speed. It is therefore better to increase the load than the spe,ed. Wire rope is manu- factured either with a wire or a hemp center. The latter is more pliable than the former, and will wear better where there is short bending. Wire rope must not be coiled or uncoiled like hemp rope. When mounted on a reel, the latter should be mounted on a spindle or flat turntable to pay off the rope. When forwarded in a small coil, without reel, roll it over the ground like a wheel, and run off the rope in that way. All untwisting or kinking must be avoided. WIRE ROPES. 125 PROPER WORKING LOAD For steel hoisting ropes, made with 19 wires to the strand, when used on drums of different diameters. Total strain of wire rope, including bending strain and the strain due to load, assumed at 50,000 Ib. per sq. in. of actual steel section, d = diameter of rope in in.; D = diameter of drum in in.; & = strain per sq. in. due to bending; L = proper working load in pounds. 5 - 1,894,000 X ~- L = 20,000 d* - 757,600 X j^. (By permission of E. T. Sederholm, Chief Enqr., Eraser & Chalmers, Chicago.) n &SOOO 126 WIRE ROPES. Starting Strain on Hoisting Rope. In selecting a hoisting rope, due allow- ance must be made for the shock and extra strain imposed on the rope when the load is started from rest. Experiments made by placing a dynamometer between the rope and the cage have shown that starting stress may be from two to three times the actual load. Experiment 1. Strain in Rope. Pounds. Empty cage, lifted gently 4 030 Empty cage, started with 2| in. of slack rope 5600 Empty cage, started with 6 in. of slack rope .. 8 950 Empty cage, started with 12 in. of slack rope 12 300 Experiment 2. Strain in Rope. Pounds. Cage and loaded cars, as weighed , 11 300 Cage and loaded cars, lifted slowly and gently Cage and loaded cars, started with 3 in. of slack rope Cage and loaded cars, started with 6 in. of slack rope Cage and loaded cars, started with 9 in. of slack rope 11,525 19,025 24,625 26,850 HORSEPOWER OF MANILA ROPES. (Link-Belt Engineering Co.) V bO &0 . 1,000 Ft. 2,000 Ft. 3,000 Ft. 4,000 Ft. 5,000 Ft. dS- A . S .2 a 3 '3 o a 3 "?. per Min. per Min. per Min. per Min. per Min. 1* ~ Si If o H.P. Tens. Wt. H.P. Tens. Wt. H.P. Tens. Wt. H.P. Tens. Wt. H.P. Tens. Wt. 1 0.15 4,000 121 2i 90 4i 90 6i 80 7i 80 8* 70 0.18 5,000 151 2* 110 6* 110 7* 100 f 100 10* 90 i 0.27 7,500 227 4i 170 8i 170 11* 160 14* 150 16 130 1 0.33 9,000 272 5 200 10 200 14 180 17J 170 19 150 1} 0.45 12,250 371 7 280 18* 270 19 250 23^ 230 26 210 H 0.50 14,000 424 8 320 15* 310 22 290 27 270 29 240 It 0.65 18,062 547 10i 410 20 400 28i 370 34* 350 38^ 310 li 0.73 20,250 613 1H 460 :22 440 3H 420 39 390 43i 350 H 0.82 25,000 760 14i 570 27* 550 39 520 49 490 55 448 i* 1.08 30,250 916 17 680 33i 660 47i 630 58i 580 64* 520 2 1.27 36,000 1,000 20^ 810 40 790 56i 740 69i 670 77 620 WIRE-ROPE FASTENINGS. Thimble spliced, in ordinary style, is shown in Fig. 1 (a). In this method, the wires, after being frayed out at the end and the rope bent around the thimble, are laid srfugly about the main portion of the rope and securely fastened by wrapping with stout wire, the extreme ends that project below this wrapping being folded back, as shown. Another style of thimble splicing is shown in Fig. 1 (&). In this case the strands are interlocked as in splicing, and the joint is wrapped with wire as in the former method. The socket fastening is shown in Fig. 1 (c). The hole in which the rope end is fastened is conical in shape. The rope is generally secured by fraying put the wires at the end, the interstices being filled up with spikes driven in tightly. The whole is finally cemented by pouring in molten. Babbitt metal. This makes a much neater fastening 'than either of those shown in (a) and (&), but it does not possess anything like as much strength. The thimble possesses a serious disadvantage; it is usually made of a piece of curved metal bent around into an oval shape, WIRE-ROPE SPLICING. 127 (c) as shown in (a) and (6), with the groove, in which the rope lies, outside, the ends coming together in a sharp point. When weight is placed on the rope, the strain on the thimble is apt to cause one end to wedge itself beyond or past the other, and with its sharp edge it cuts the strands in the splice. Mr. William Hewitt, of Trenton, N. J., while testing the strength of wire ropes, discovered this tendency, and experimented with sockets with the idea of devising some method of fastening the rope securely in the socket. He found that by adopt- ing the' following plan he secured good results: The wires, after being frayed out at the end, were bent upon themselves in hook fashion, the prongs of some being longer than others, so that the bunch would conform to the conical aperture of the socket, and the melted Babbitt metal was finally run in as usual. The rope was subjected to a strain of over 129,000 lb., and the wires in the socket were unaffected. The simplicity of this method commends itself to practical men. RAPID METHOD OF SPLICING A WIRE ROPE,* The only tools needed are a cold cutter and hammer for cutting and trimming the strands, and two needles 12 in. long, made of good steel and tapered ovally to a point. Cut off the ends of the ropes to be spliced and unlay three adjacent strands of each back 15 ft.; cut out the hemp center to this point and relay the strands for 7 ft. and cut them off. Pull the ropes by each other until they have the position shown in Fig. 2 (a), cut off a and d', b and c', Fig. 2 (&), making their lengths approximately 10 and 12 ft., respectively, measured from the point where the hemp centers were cut. Place the ropes together, Fig. 2 (b); unlay e, d, c, Fig. 2 (a), keeping the strands to- Hemp Center FIG. 1. \ gether, and follow with e', d', c',Fig.2(&). Similarly, unlay /, a', b', Fig. 2 (6), and follow with /, a, 6, until the rope appears as in Fig. 2 (c). Next run the p Center strands into the middle of the rope. To do this, cut FIG. 2. off the end of the strand e', Fig. 2 (c), so that when it is put in place it will just reach to the end x of the hemp core, and then push the needle A, Fig. 2 (c), through the rope from the under side, leaving two strands at the front of the needle, as shown. Push the needle B through from the upper side and as close to the needle A as possible, leaving the strands e and e' between them; place the needle A on the knee and turn the needle B around with the coil of the rope, and force the strand e' into the center of the rope. Repeat this *W. H. Morris, " Mines and Minerals," September, 1898. 128 WIRE ROPES. WIRE-ROPE SPLICING. 129 operation with the other ends and cut them off so that the ends coming together in the center of the rope will butt against each other as nearly as possible. . ORDINARY LONG SPLICE. Tools Required. One pair wire nippers, for cutting off strands; one pair pliers, for pulling through and straightening ends of strands; two marline- spikes, one round and one oval, for opening strands; one knife to cut hemp center; two clamps, to untwist rope to insert ends of strands, or, in place of them, two short hemp-rope slings, with a stick for each as a lever; a wooden mallet and some rope twine. Also, a bench and vise are handy. The length of the splice depends on the size of the rope. The larger ropes require the longer splices. The splice of ropes from f in. to in. in diameter should not be less than 20 ft.; from f in. to 1 in., 30 ft.; and from 1| in. up, 40 ft. To splice a rope, tie each end with a piece of cord at a distance equal to one-half the length of the splice, or 10 ft. back from the end, for a I" rope, after which unlay each end as far as the cord. Then cut out the hemp center, and bring the two ends together as close as possible, placing the strands of the one end between those of the other, as shown in Fig. 3 (a). Now remove the cord k from the end M of the rope, and unlay any strand, as a, and follow it up with the strand of the other end M' of the rope that corresponds to it, as a', Fig. 3 (a) . About 6 in. of a are left out, and a is cut off about 6 in. from the rope, thus leaving two short ends, as shown at P in Fig. 3(6), which must be tied for the present by cords as shown. The cord k should again be wound around the end M of the rope, Fig. 3 (a), to prevent the unraveling of the strands; after which remove the cord k' on the other or M' end of the rope, and unlay the strand &; follow it up, as above, with the strand &', leaving the ends out, and tying them down for the present, as before described in the case of strands a and a', see Q, Fig. 3 (6); also, replace the cord k' for the same purpose as stated above. Now, again remove the cord k and unlay the next strand, as c, Fig. 3 (a), and follow it up with c', stopping, however, this time within 4 ft. of the first set. Continue this operation with the remaining 6 strands, stopping 4 ft. short of the preceding set each time. The strands are now in their proper places, with the ends passing each other at intervals of 4 ft., as shown in Fig. 3 (c). To dispose of the loose ends, clamp the rope in a vise at the left of the strands a and a', Fig. 3 (c), and fasten a clamp to the rope at the right of these strands; then remove the cords tied around the rope that hold these two strands down; after which turn the clamp in the oppo- site direction to which the rope is twisted, thereby untwisting the rope, as shown in Fig. 3 (d). The rope should be untwisted enough to allow its hemp core to be pulled out with a pair of nippers. Cut off 24 in. of the hemp core, 12 in. at each side from the point of intersection of the strands a and a', and push the ends of the strands in their place, as shown in Fig. 3 (d). Then allow the rope to twist up to its natural shape, and remove the clamps. After the rope has been allowed to twist up, the strands tucked in generally bulge out somewhat. This bulging may be reduced by lightly tapping the bulged part of the strands with a wooden mallet, which will force their ends farther into the rope. Proceed in the same manner to tuck in the other ends of the strands. CHAINS. The links of iron chains are usually made as short as is consistent with easy play, so as to make them less liable to kink, and also to prevent bending when wound around drums, sheaves, etc. The weight of close-link chain is about three times the weight of bar from which it is made, for equal lengths. Karl von Ott, comparing weight, cost, and strength of three materials, hemp, iron wire, and chain iron, concludes that the proportion between cost of hemp rope, wire rope, and chain is as 2 : 1 : 3, and that, therefore, for equal resistances, wire rope is only half the cost of hemp rope, and a third of cost of chains. Chains of warranted superior iron will stand 25$ more strain before breaking. The report of the U. S. Test Board, 1881, shows that the ultimate strength of chains may be taken at 1.6 that of the iron from which the links are made. 130 HYDROSTATICS. The strength of chains varies, owing to the nature of the iron from which they are made, and their mechanical construction. The following table is approximately correct for ordinary iron chains: TABLE OF WEIGHT AND STRENGTH OF CHAINS. Diameter of Weight of Diameter of Weight of Rod of Which the Links Are Made. Chain per Running Foot. Working Strength. Tons. Breaking Strain. Tons. Rod of Which the Links Are Made. Chain per Running Foot. Working Strength. Tons. Breaking Strain. Tons. Inches. Pounds. Inches. Pounds. ^ .325 .19 .773 7.10 4.40 16.80 J .579 .36 1.37 it 8.14 5.00 19.32 1 6 .904 .45 2.14 1 9.26 5.71 22.00 g 1.30 .85 3.09 u 11.70 7.23 26.44 i 1.78 1.09 4.20 1} 14.50 9.00 32.64 i 2.31 1.43 5.50 a 17.50 10.80 39.42 ^5 2.93 1.80 6.96 . i* 20.80 13.00 47.00 1 3.62 2.23 8.58 ii 24.40 15.24 55.14 ft 4.38 2.70 10.39 i? 28.40 17.65 63.97 1 5.21 6.11 3.21 3.80 12.36 14.42 P 32.60 37.00 20.27 23.10 73.44 83.55 HYDROSTATICS. Hydrostatics treats of the equilibrium of liquids, and of their pressures on the walls of vessels containing them; the science depends on the way in which the molecules of a liquid form a mass under the action of gravity and molecular attraction, the latter of which is so modified in liquids as to give them their state of liquidity. While the particles of a liquid cohere, they are free to slide upon one another without the least apparent friction; and it is this perfect mobility that gives them the mechanical properties considered in hydrostatics. The fundamental property may be thus stated: When a pressure is exerted on any part of the surface of a liquid, that pressure is transmitted undiminished to all parts of the mass, and in all directions. This is a physical axiom, and on it are based nearly all the principles of hydrostatics. Equilibrium of Liquids. This is a property of liquids that can be easily demonstrated, and examples are frequently seen. Thus, if two barrels are connected at the bottom with a pipe, and water is poured in one until it reaches within a foot of the top, the water in the other will be found to have attained the same height. Pressure of Liquids on Surfaces. The general proposition on this point is as follows: The pressure of a liquid on any surface immersed in it is equal to the weight of a column of the liquid whose base is the surface pressed, and whose height is the perpendicular depth of the center of gravity of the surface below the surface of the liquid. The pressure thus exerted is independent of the shape or size of the vessel or cavity containing the liquid. The pressure of a liquid against any point of any surface, either curved or plane, is always perpendicular to the surface at that point. At any given depth the pressure of a liquid is equal in every direction, and is in direct proportion to the vertical depth below the surface. The weight of a cubic foot of fresh water, at ordinary temperature of the atmosphere, that is, from 32 F. to 80 F., is usually assumed at 62.5 Ib. This is a trifle more than the actual weight, but is sufficiently close for purposes of calculation. To Find the Pressure Exerted by Quiet Water Against the Side of a Gangway or Heading. Multiply the area of the side in square feet by the perpendicular distance from the surface of the water to a point equidistant between the top and bottom of the submerged heading or gangway, and multiply the product by 62.5. The result will be the pressure in pounds, exclusive of atmospheric pressure. This latter need not be considered in ordinary mining work. HYDROSTATICS. 131 EXAMPLE. If an abandoned colliery, opened by a slope on a pitch of 25 and 100 yd. long, is allowed to fill with water, what is the average pressure exerted on each square foot of the lower rib of the gangway, assuming that the gangways were driven dead level, and that the length of the slope was measured to a point on the lower rib equidistant between top and bottom of gangway. We here have a perpendicular height of water = 300 X sine of 25 = 126.78 ft. Then, the pressure on each square foot of the lower rib of gangway = 126.78 X 62.5 lb., or the weight of 1 cu. ft., or a pressure on each square foot of surface of 7,923.75 lb., or over 3 gross tons. The total pressure exerted along the gangway may readily be found by multiplying the 7,923.75 lb. by the number of square feet of the lower rib against which it rests. To find the total pressure of quiet water against and perpendicular to any surface whatever, as a dam, embankment, or the bottom, side or top of any containing vessel, water pipe, etc., no matter whether said surface be vertical, horizontal, or inclined; or whether it be flat or curved; or whether it reach to the surface of the water or be entirely below it: Multiply the area, in square feet, of the surface pressed,- by the vertical depth in feet of its center of gravity below the surface of the water, and this product by 62.5. The result will be the pressure in pounds. Thus, assuming that in the annexed three figures the depth of water in each dam is 12 ft., and the wall or embankment is 50 ft. long, then in Fig. 1 the total pressure will equal 12 X 50 X 6 X 62.5 = 225,000 lb. In Figs. 2 and 3 the walls or embankments, being inclined, expose a greater surface to pressure, say 18 ft. from A to B. Then the total pressure equals 18 X 50 X 6 X 62.5 = 337,500 lb. Now, the results obtained are the total pressures without regard to direction. In Fig. 1 the total pressure calculated, or 225,000 lb., is hori- zontal, tending either to overturn the wall or make it slide on its base. The center of pres- FIG. 1. FIG. 2. FIG. 3. sure is at C, or one-third of the vertical depth from the bottom. In Fig. 2 the pressure is exerted in two directions; one pressure, acting horizontally, tends to overthrow or slide the wall, while the other, acting vertically, tends to hold it in place. In Fig. 3 the pressure is also exerted in two directions; one pressure, acting horizontally, tends to overthrow or slide the wall, while the other tends to lift. So long as the vertical depth of water remains the same, the horizontal pressure remains the same, no matter what inclination is given the wall. Thus, in Figs. 2 and 3, the horizontal pressure is the same as in Fig. 1, or 225,000 lb. The total pressure of the water is distributed over the entire depth of the submerged part of the back of the wall, and is least at the top, gradually increasing toward the bottom. But so far as regards the united action of every portion of it, in tending to overthrow the wall, considered as a single mass of masonry, incapable of being bent or broken, it may all be assumed to be applied at C, which is one-third of the vertical depth from the bottom in Fig. 1, or, what is the same thing, one-third of the slope distance from the bottom in Figs. 2 and 3. No matter how much water is in a dam or vessel, the pressure remains the same, so long as the area pressed and the vertical depth of its center of gravity below the level surface of the water remains un- changed. Thus, if the water in dam shown in Fig. 1 extended back 1 mile, it would exert no more pressure against the wall than if it extended back only 1 ft. In'any two vessels having the same base, and con- taining the same depth of water, no matter what quantity, the pressures on the bases are equal. Thus, if Figs. 4 and 5 have the same base and be filled with water to the same depth, the pressure on the bases FIG. 4. FIG. 5. will be equal. This fact, that the pressure on a given surface, at a given 132 HYDROSTATICS. depth, is independent of the quantity of water, is called the hydrostatic paradox. As the pressure of water against any point is at right angles to the surface at that point, it follows that props or other strengthening material for the strengthening of such structures as a sloping dam, should be so placed as to offer the greatest resistance in a line at right angles to the sloping surface, and these supports should be strongest and closest together at the bottom. For the same reason, the hoops on a circular tank should be strongest and closest at the bottom. Transmission of Pressure Through Water. Water, in common with other liquids, possesses the important property of transmitting pressure equally in all directions. Thus, if a vessel is constructed with two cylinders, the area of one being 10 sq. in., and that of the other 100 sq. in., and the vessel is rilled with water (Fig. 6), and pistons fitted to the cylinders, a pressure of 100 Ib. applied at the smaller will balance 1,000 Ib. at the larger. This is the principle of the hydrostatic press. Air and other gaseous fluids transmit pressure equally in all directions, like liquids, but not as rapidly. To Find the Pressure on a Plane Surface at Any Given Depth of Water. For pounds per square inch, multiply depth in feet by .434. For pounds per square foot, multiply depth in feet by 62.5. For tons per square foot, multiply depth in feet by .0279. The pressure per square foot at different depths increases directly as the depths. The total pressure against a plane 1 ft. wide at different depths increases as the square of the depths. PRESSURE IN POUNDS PER SQ. FT. AT DIFFERENT VERTICAL DEPTHS, AND ALSO THE TOTAL PRESSURE AGAINST A PLANE 1 FT. WIDE EXTENDING VERTICALLY FROM THE SURFACE OF THE WATER TO THE SAME DEPTHS. Depth. Feet. Pressure. Pounds per Sq. Ft. Total Pressure. Pounds. Depth. Feet. Pressure. Pounds per Sq. Ft. Total Pressure. Pounds. Depth. Feet. Pressure. Pounds per Sq. Ft. Total Pressure. Pounds. 1 62.5 31 27 1,687 22,781 65 4,062 132,025 2 125 125 28 1,750 24,500 70 4,375 153,124 3 187 281 29 1,812 26,281 75 4,687 175,779 4 250 500 30 1,875 28,125 80 5,000 200,000 5 312 781 31 1,937 30,031 85 5,312 225,775 6 375 1,125 32 2,000 32,000 90 5,625 253,124 7 437 1,531 33 2,062 34,031 95 5,937 282,025 8 500 2,000 34 2,125 36,125 100 6,250 312,500 9 562 2,531 35 2,187 38,281 110 6,875 378,124 10 625 3,125 36 2,250 40,500 120 7,500 450,000 11 687 3,781 37 2,312 42,781 130 8,125 528,100 12 750 4,500 38 2,375 45,125 140 8,750 612,496 13 812 5,281 39 2,437 47,531 150 9,375 703,116 14 875 6,125 40 2,500 50,000 160 10,000 800,000 15 937 7,031 41 2,562 52,531 170 10,625 903,100 16 1,000 8,000 42 2,625 55,125 180 11,250 1,012,496 17 1,062 9,031 43 2,687 57,781 190 11,875 1,128,100 18 1,125 10,125 44 2,750 60,500 200 12,500 1,250,000 19 1,187 11,281 45 2,812 63,281 225 14,062 1,582,025 20 1,250 12,500 46 2,875 66,125 250 15,625 1,953,100 21 1,312 13,781 47 2,937 69,031 275 17,187 2,363,275 22 1,375 15,125 48 3,000 72,000 300 18,750 2,812,500 23 1,437 16,531 49 3,062 75,031 350 21,875 3,828,100 24 1,500 18,000 50 3,125 78,125 400 25,000 5,000,000 25 1,562 19,531 55 3,437 94,531 450 28,120 6,328,100 26 1,625 21,125 60 3,750 112,500 500 31,250 7,812,500 Pressure of Water in Pipes. As water exerts a pressure equally in all directions, it is important that in pipe lines the pipe should be sufficiently thick to assure strength enough to resist a bursting pressure. In ordinary HYDROS TA TICS. 133 practice, the thickness of cast-iron water pipes of different bores is calculated by Mr. J. T. Fanning's formula, given in his Hydraulic Engineering, which is as follows: .Une.es This formula, worked out for different heads and different sizes of bore, yields the following results: THICKNESS OF PIPE FOR DIFFERENT HEADS AND PRESSURES. Head in Ft 50 100 200 300 500 1,000 Pressure in Lb. per Sq. In. 21.7 43.4 86.8 130 217 434 Bore. Inches. Thickness of Pipe. Inches. 2 .36 .37 .38 .39 .42 .48 3 .37 .38 .40 .42 .45 .54 4 .39 .40 .42 .45 .50 .61 6 .41 .43 .47 .50 .57 .75 8 .45 .47 .52 .57 .66 .90 10 .47 .50 .56 .62 .74 1.04 12 .49 .53 .60 .67 .82 1.18 16 .55 .60 .70 .79 .98 1.46 18 .57 .63 .74 .85 1.06 1.60 20 .61 .67 .79 .91 1.15 1.75 24 .66 .73 .87 1.02 1.30 2.03 30 .74 .83 1.01 1.19 1.55 2.46 36 .82 .93 1.15 1.36 1.80 2.88 48 .98 1.13 1.42 1.70 2.28 3.73 In the above table, the ultimate tensile strength of cast iron is taken at 18,000 Ib. per sq. in. The addition of 100 Ib. to the pressure is made to allow for water ram. The valves of water pipes should be closed slowly, and the necessity of this increases as the pipes increase in diameter. If this rule is not observed, the momentum of the running water is arrested suddenly, and a great pressure is created against the pipes in all directions, and through- out the entire length of the line above the valve, even if it be many miles, and there is danger of their bursting at any point. For this reason, stop- gates are shut by screws, because they prevent any very sudden closing; but in pipes of large diameters, even the screws must be worked very slowly to prevent bursting. Compressibility of Liquids. Liquids are not entirely incompressible, but they are so nearly so, that for most purposes they may be considered as incompressible. The bulk of water is diminished about j^ by a pressure of 324 Ib. per sq. in., or 22 atmospheres; varying slightly with its temperature. It is perfectly elastic, regaining its original bulk when the pressure is removed. Construction of Dams in Mines. Dams may be constructed in mines, either to isolate a portion of the workings so that they can be flooded to extinguish fires, or, in cases where an extremely wet formation has been penetrated, it is sometimes expedient to construct a dam so as to prevent the water from flowing into the workings. Mine dams should be of sufficient strength to resist any column of water that will be likely to come against them. The dam should be arched toward the direction from which the pressure comes, and should be given a good firm bearing in both walls and in the floor and roof. Fig. 7 illustrates a brick dam that was constructed in Kehley's Run Colliery, at Shenandoah, Pa., to isolate a portion of the seam so that it might 134 HYDROSTATICS. be flooded to extinguish a mine fire. This is one of the largest mine dams that has ever been constructed. It is composed of three brick arches, each having a thickness of 5 ft., that are placed one against the other so that they act as one solid structure. The gangway at this point is about 20 ft. wide, and the distance to the next upper level is about 119 ft. It was intended that this should be the maximum head of water that the dams would ever have to resist, though they were made sufficiently strong to resist a head of water reaching to the surface. The separate walls were constructed one at a time, and the cement allowed to set before the next wall was placed. The back wall was carried to a greater depth and height than the others, so as to make sure of the fact that all slips or partings had been closed. The total pressure upon the dam when the water was in the mine was about 70,000 Ib. per sq. ft. Dams constructed to permit the flooding of a mine usually require no passages through them, but where dams are constructed to confine the water to certain parts of the workings, and so reduce pumping charges, it may be necessary to provide both man ways and drain pipes through the FIG. 7. dams. Fig. 8 illustrates a plan and cross-section of a dam in the Curry Mine, at Norway, Mich. ("Mines and Minerals," Vol. 18, page 177; Trans. A. I. M. E., XXVII, 402), constructed to keep the water that came from some exploring drifts out of the mine workings. As originally constructed, it consisted of a sandstone dam 10 ft. thick and arched on the back face with a radius of 6 ft. A piece of 20" pipe provided a man way through the masonry and was held in place by three sets of clamps and bolts passing 2 ft. 4 in. back of the dam, the space between being filled with concrete, and the man way and drain pipe extended through the brick wall. Before closing the drain pipe, horse manure was fastened against the face of the brick wall by means of a plank partition. After this the manway and drain pipe were closed, and when the pressure came on, the dam was found to leak a small HYDRAULICS. 135 amount, but this soon practically ceased, showing that the manure had closed the leaks. A gauge in the head of the manway on this dam showed a pressure of 211 lb., which corresponded to a static head of 640 ft. of water. The total pressure against the dam was something over 800 tons, which it successfully resisted. HYDRAULICS. Hydraulics treats of liquids in motion, and in this, as in hydrostatics, water is taken as the type. In theory its principles are the same as those of falling bodies, but in practice they are so modified by various causes that they cannot be relied on except as verified by experiment. The discrepancy arises from changes of temperature that vary the fluidity of the liquid, from friction, the shape of the orifice, etc. As we shall deal with water only, the first cause may be thrown aside as of little account. In theory the velocity of a jet is the same as that of a body falling from the surface of the water. To Find the Theoretical Velocity of a Jet of Water. Let v = the velocity, g = the acceleration of gravity (32.16 ft.), and d = the distance of the orifice below the surface_othe water. Then, v = i/ 2^d, or v = the square root of twice the product of g X d. EXAMPLE. The depth of water above the orifice is 64 ft.; what is the velocity ? Substituting 64 for d, and 32.16 for g, we have, v = j/2 X 32.16 X 64, or 64.16. To Find the Theoretical Quantity of Water Discharged in a Given Time. Multi- ply the area of the orifice by the velocity of the water, and that product by the number of seconds. EXAMPLE. What quantity of water will be discharged in 5 seconds from an orifice having an area of 2 sq. ft., at a depth of 16 ft.? I/ 2 X 32 - 16 X 16 X 2 = 64.16 cu. ft,, or the amount discharged in 1 second, and in 5 seconds the amount will be 5 X 64.16 = 320.8 cu. ft. The above rules are only theoretical, and are only useful as foundations on which to build practical formulas. Flow of Water Through Orifices. The standard orifice, or an orifice so arranged that the water in flowing from it touches only a line, as would be the case in flowing through a hole in a very thin plate, is used for the measurement of water. The contraction of the jet, which always occurs when water issues from a standard orifice, is due to the circumstance that the particles of water as they approach the orifice move in converging directions, and that these directions continue to converge for a short distance beyond the plane of the orifice. This contraction causes only the inner corner of the orifice to be touched by the escaping water, and takes place in orifices of any shape, its cross-section being similar to the orifice until the place of greatest contraction is passed. Owing to this contraction, the actual discharge from an orifice is always less than the theoretical discharge. The Coefficient of Contraction. The coefficient of contraction is the number by which the area of the orifice is to be multiplied in order to find the area of the least cross-section of ,the jet. In this way by experiment this coeffi- cient has been found to be about .62 (Merriman's "Hydraulics"); or, in other words, the minimum cross-section of the jet is, 62$ of the cross-section of the orifice. The Coefficient of Velocity. The coefficient of velocity is the number by which the theoretical velocity of flow from the orifice is to be multiplied in order to nnd the actual velocity at the least cross-section of the jet. This may be taken for practical work as .98; or, in other words, the actual flow at the contracted section is 98$ of the theoretical velocity. The Coefficient of Discharge. The coefficient of discharge is the number by which the theoretical discharge is to be multiplied in order to obtain the actual discharge. This has been found by thousands of experiments to be equal to the product of the coefficients of contraction and velocity, and for practical work it may be taken as .61; or, the actual discharge from standard orifices is 61$ of the theoretic discharge. 136 HYDRA ULICS. NOTE. While the coefficients for standard orifices with sharp edges have been determined fairly close, those for the more complicated cases of weirs, and especially for the flow of water through long pipes, are simply the nearest approximation to the truth that it has been possible to obtain. In all cases, the coefficient should be one that has been determined under con- ditions similar to those in the problem in hand. For instance, it is not prac- ticable to use the coefficient for small pipes in solving problems relating to large ones, or for short pipes in solving problems relating to long ones. Suppression of the Contraction. When a vertical orifice has its lower edge at the bottom of a reservoir, the particles of water flowing through its lower portion move in lines nearly perpendicular to the plane of the orifice, and the contraction of the jet does not form on the lower side. The same thing occurs in a lesser degree when the lower edge of the orifice is within a dis- tance of three times its least diameter from the bottom. The suppression of contraction will occur on the side if it is placed within a distance of three times its least diameter from the side of a reservoir, the suppression of contraction being the greater the nearer the orifice is to the side. By round- ing the edge of the orifice sufficiently, the contraction can be completely suppressed, and the discharge can be increased. As stated before, the value of the coefficient of contraction for a standard square-edged orifice is .62, but with a rounded orifice it may have any value between .62 and 1.00, depend- ing on the degree of rounding. The coefficient of discharge for square- edged orifices has a mean value of .61; this is increased with rounded edges and may have any value between .61 and 1.00, although it is not probable that values greater than .95 can be obtained except by the most careful adjustment of the rounded edges to the exact curve of a completely con- tracted jet. A rounded interior orifice is therefore always a source of error when the object of the orifice is the measurement of the discharge. GAUGING WATER. Water is sold by two methods; i. e., the flowing unit and the capacity unit. The flowing unit is a cubic foot per second. In the western part of North America the miners' inch has come into use quite largely, while in Australia and New Zealand the cubic foot per second is the common measure, 1 cu. ft. per second being 1 " head," and 10 heads of water would be 10 cu. ft. per second, regardless of the actual hydrostatic head under which the water was delivered. Water is sometimes sold for irrigation by the capacity unit, that is, so much land covered to a certain depth, as, for instance, the "acre- foot," which means that 1 acre has been covered to a depth of 1 foot, or that an amount of 43,560 cu. ft. of water has been furnished. Miners' Inch. The miners' inch may be roughly defined as the quantity of water that will flow in 1 minute through a vertical standard orifice having a section of 1 sq. in. and a head of 6 in. above the center of the orifice. This quantity equals 1.53 cu. ft., and the mean quantity may be taken at, approxi- mately, 1.5 cu. ft. per minute. The laws or customs defining the miners' inch in different districts vary so that the amount of water actually delivered varies from 1.2 to 1.76 cu. ft. per minute, the principal reasons for these varia- tions being the method adopted for measuring the water where large quan- tities are used; as, for instance, at Smartsville, in California, an opening 4 in. deep, 250 in. long, with a head of 7 in. above the top edge, is said to furnish 1,000 miners' inches, while it would actually furnish considerably over 1,000. In other places, the size of the opening for measuring the amounts is restricted, and may actually furnish less than the rated amount. In Montana the common method of measurement was formerly through a vertical rect- angle 1 in. high, with a head on the center of the orifice of 4 in. The num- ber of miners' inches discharged was considered to be the same as the number of linear inches in the length of the orifice; thus, under the given head, an orifice 1 in. deep and 60 in. long could discharge 60 miners' inches. The State Legislature of Montana has now passed a law defining the miners' inch as the number of gallons of water discharged in a given time, regardless of the character of the openings or methods of measurement. The statement is as follows: "Where water rights, expressed in miners' inches, have been granted, 100 miners' inches shall be considered equivalent to a flow of 2i cu. ft. (18.7 gal.) per second, and this proportion shall be observed in determining the equivalent flow represented by any number of miners' inches." MINERS' INCH. 137 If this amount is reduced to cubic feet per minute, it will be found to be equal to a ftow of 1.5 cu. ft. per minute, which is the value given above for the miners' inch. Duty or Work Performed by a Miners' Inch of Water. Few tests have been made in regard to the duty of a miners' inch of water, but the North Bloomfield mine and the La Grange mine, in California, have carried on a series of experiments extending over several years. At the La Grange mine the observations were carried on simultaneously upon several differ- ent claims, hence parallel dates appear. The accompanying tables give the results of these experiments. In general it is governed by the size, capacity, character of pavement, and grade of sluices, together with the supply of water. A heavy grade will compensate for a limited supply. With an abundant supply of water and material, the capacity of the sluices will depend on: First, the character of the material washed; second, the size and minimum grade of the sluices; third, the character of the riffles used. DUTY OF MINERS' INCH. (Risdon Iron Works, Evans's Elevator Catalogue.) NORTH BLOOMFIELD MINE. jj j o ^ O " a - W . &*!-< f fc s PQ Years. g| *| Grades. Is |J *o Remarks. 1^ *t2 ^a 2 I .2 * || s,2 w | 3 U 1870-74 3,250,000 710,987 6M in. to 12 ft.. 4.60 18 100 ft, Sluices 6 ft. wide, 32 in. deep. 1875 1876 1,858,000 2,919,700 386,972 700,000 6^ in. to 12 ft. 6J^ in. to 12 ft. 4.80 4.17 17 20 100 ft. 200 ft. Riffles principally blocks (wood), but rock riffles in tail 1877 2,993,930 595,000 6^ in. to 12 ft. 3.86 21 265 ft. sluices. The larger portion Totals 11,021,630 2,392,959 4.60 18 moved was top gravel. LA GRANGE MINE. 1874-76 676,968 624.745 4 in. to 16 ft. 1.08 74.0 10 to 48 ft. 1875-76 1874-76 1875-78 683,244 284,932 459,570 375,155 207,010 302,960 4 in. to 16 ft. 4 in. to 16 ft. 4 in. to 16 ft. 1.82 1.37 1.52 43.9 58.0 52.0 6ft. 50 to 80 ft. 40 to 50 ft. Sluices 4 ft. wide and 30 in. deep, paved with blocks. 1880-81 329,120 203,325 4 in. to 16 ft. 1.57 1.42 50.0 10 to 80 ft. Totals 2,433,834 1,713,195 56.0 The right-angled V notch is frequently used for gauging the flow of compara- tively small streams. The notch is usually fitted into a box provided with baffle boards, Fig. 9, or where this is not practicable the water should be so impounded above the notch as to remove all possibility of surface cur- rents producing a perceptible velocity of approach. The distance a of the surface of the water below the top of the box is taken at a point some dis- tance back from the notch (at least 18 to 20 in.), where the surface of the water is unaffected by the flow through the notch. The distance a, sub- tracted from the total depth of the notch H, gives the head h of the water passing over the notch. The discharge in cubic feet per second may be found by the formula Q = .306 jA& = .306 7*2 ]/ /*, in which Q equals the quantity in cubic feet per minute and h equals the 138 HYDRA ULICS. head in inches. The accompanying table gives the discharge in cubic feet per minute through a right-angled V notch, as shown in Fig. 9, for heads varying from 1.05 in. to 12 in. TABLE I. DISCHARGE OF WATER THROUGH A RIGHT-ANGLED V NOTCH. h Head. Inches. Q Quantity per Min. Cu. Ft. h Head. Inches. Quantity per Miii. Cu. Ft. h Head. Inches. Q Quantity per Min. Cu. Ft. h Head. Inches. Q Quantity per Min. Cu. Ft. ft Head. Inches. Quantity per Min. Cu. Ft. 1.05 .3457 3.25 5.827 5.45 21.22 7.65 49.53 9.85 93.18 1.10 .3884 3.30 6.054 5.50 21.71 7.70 50.34 9.90 94.37 1.15 .4340 3.35 6.285 5.55 22.20 7.75 51.16 9.95 95.56 1.20 .4827 3.40 6.523 5.60 22.70 7.80 51.99 10.00 96.77 1.25 .5345 3.45 6.765 5.65 23.22 7.85 52.83 10.05 97.98 1.30 .5896 3.50 7.012 5.70 23.74 7.90 53.67 10.10 99.20 1.35 .6480 3.55 7.266 5.75 24.26 7.95 54.53 10.15 100.43 1.40 | .7096 3.60 7.524 5.80 24.79 8.00 55.39 10.20 101.67 1.45 .7747 3.65 7.788 5.85 25.33 8.05 56.26 10.25 102.92 1.50 .8432 3.70 8.058 5.90 25.87 8.10 57.14 10.30 104.18 1.55 .9153 3.75 8.332 5.95 26.42 8.15 58.03 10.35 105.45 1.60 .9909 3.80 8.613 6.00 26.98 8.20 58.92 10.40 106.73 1.65 1.0700 3.85 8.899 6.05 27.55 8.25 59.82 10.45 108.02 1.70 1.1530 3.90 9.191 6.10 28.12 8.30 60.73 10.50 109.31 1.75 1.2400 3.95 9.489 6.15 28.70 8.35 61.65 10.55 110.62 1.80 1.3300 4.00 9.792 6.20 29.28 8.40 62.58 10.60 111.94 1.85 1.4240 4.05 10.100 6.25 29.88 8.45 63.51 10.65 113.26 1.90 1.5220 4.10 10.410 6.30 30.48 8.50 64.45 10.70 114.60 1.95 1.6250 4.15 10.730 .6.35 31.09 8.55 65.41 10.75 115.94 2.00 1.7310 4.20 11.060 6.40 31.71 8.60 66.37 10.80 117.29 2.05 1.8410 4.25 11.390 6.45 32.33 8.65 67.34 10.85 118.65 2.10 1.9550 4.30 11.730 6.50 32.96 8.70 68.32 10.90 120.02 2.15 2.0740 4.35 12.070 6.55 33.60 8.75 69.30 10.95 121.41 2.20 2.1960 4.40 12.420 6.60 34.24 8.80 70.30 11.00 122.81 2.25 2.3230 4.45 12.780 6.65 34.89 8.85 71.30 11.05 124.21 2.30 2.4550 4.50 13.140 6.70 35.56 8.90 72.31 11.10 125.61 2.35 2.5900 4.55 13.510 6.75 36.23 8.95 73.33 11.15 127.03 2.40 2.7300 4.60 13.890 6.80 36.89 9.00 74.36 11.20 128.45 2.45 2.8750 4.65 14.270 6.85 37.58 9.05 75.40 11.25 129.90 2.50 3.0240 4.70 14.650 6.90 38.27 9.10 76.44 11.30 131.35 2.55 3.1770 4.75 15.040 6.95 38.96 9.15 77.49 11.35 132.81 2.60 3.3350 4.80 15.440 7.00 39.67 9.20 78.55 11.40 134.27 2.65 3.4980 4.85 15.850 7.05 40.38 9.25 79.63 11.45 135.75 2.70 3.6660 4.90 16.260 7.10 41.10 9.30 80.71 11.50 137.23 2.75 3.8380 4.95 16.680 7.15 41.83 9.35 81.80 11.55 138.73 2.80 4.0140 5.00 17.110 7.20 42.56 9.40 82.90 11.60 140.23 2.85 4.1960 5.05 17.540 7.25 43.30 9.45 84.01 11.65 141.75 2.90 4.3820 5.10 17.970 7.30 44.06 9.50 85.12 11.70 143.28 2.95 4.5740 5.15 18.420 7.35 44.82 9.55 86.24 11.75 144.82 3.00 4.7700 5.20 18.870 7.40 45.58 9.60 87.37 11.80 146.36 3.05 4.9710, 5.25 19.320 7.45 46.36 9.65 88.52 11.85 147.91 3.10 5.1780 5.30 19.790 7.50 47.14 9.70 89.67 11.90 149.48 3.15 5.3880 5.35 20.260 7.55 47.92 9.75 90.83 11.95 151.05 3.20 5.6050 5.40 20.730 7.60 48.72 9.80 92.00 12.00 152.64 1 cu. ft. contains 7.48 U. S. gallons; 1 U. S. gallon weighs 8.34 Ib. Gauging by Weirs. A weir is an obstruction placed across a stream for the purpose of diverging the water so as to make it flow through a desired chan- nel, which may be a notch or opening in the weir itself. The term usually applies to rectangular notches in which the water touches only the bottom and ends, the opening being a notch without any upper edge. Weirs are of two general classes: weirs with end contractions, Fig. 10 (a), and weirs without GAVGING BY WEIRS. 139 end contractions, Fig. 10 (b). The crest arid edges of the weir with end con- tractions should be sharp, as shown at a, Fig. 10 (c) and (d). The head of water H producing the flow over the weir should be measured at a suffi- cient distance .from the crest to avoid the effects of the curve of the surface as it flows over the crest. The water above the weir should be motionless, or if it has any perceptible current toward . , , , , , ^ . ^sK the weir, this should be deter- mined and taken into account in the formula. Fig. 11 illus- trates a weir constructed across a small stream for measuring its flow. The head is measured from the stake JE"some distance FIG. 9. back of the weir, the top of the stake being level with the crest of the weir B. The discharge over the weir may be calculated from the following formula: Let I = length of weir in feet; H = head in feet; v = velocity with which the water approaches the weir in feet; h = a head equivalent to the velocity with which the water approaches the weir; c = coefficient of discharge; Q = theoretic discharge in cubic feet per second; Q' = actual discharge in cubic feet per second. For weirs with end contractions and a velocity of approach, the actual discharge is Q = 5.347 cl V (H + f /ip. Where the water has no velocity of approach, Q = 5.347 c I V W. For weirs without end con- tractions, but with a velocity of approach, the actual dis- charge is Q = 5.347 cZ V(H + 1.4/i) 3 . . Where the water has no velocity of approach, Q = 5.347cJ VH*. The velocity with which the water approaches the weir FIG. 10. may be found by determining the approximate discharge from the stream without any allowance for velocity of approach, and then dividing this discharge in cubic feet per second by the area of the stream in square feet where it approaches the weir, which will give the velocity of approach in feet per second. Having ob- tained the value ofv, the equivalent head h may be found by the formula h = 0.01555V 2 . Since v is small in a properly constructed weir, it is usually neg- lected unless great accuracy is required. The values of coeffi- cients of discharge, as determined from ex- periments for weirs with end contractions, FIG. 11. are given in Table II, and for weirs without end contractions in Table III. The values of the coefficients in Tables II and III are given in feet and tenths. Frequently 140 HYDRA ULICS. in measuring water where only a close approximation is required, it is desired to take all of the measurement in feet and inches. See Table IV. VALUES OF THE COEFFICIENT OF DISCHARGE FOR WEIRS WITH END CONTRACTIONS. Length of Weir. Feet. Effective Head. Feet. .66 1 2 3 5 10 19 .10 .632 .639 .646 .652 .653 .655 .656 .15 .619 .625 .634 .638 .640 .641 .642 .20 .611 .618 .626 .630 .631 .633 .634 .25 .605 .612 .621 .624 .626 .628 .629 .30 .601 .608 .616 .619 .621 .624 .625 .40 .595 .601 .609 .613 .615 .618 .620 .50 .590 .596 .605 .608 .611 .615 .617 .60 .587 .593 .601 .605 .608 .613 .615 .70 .590 .598 .603 .606 .612 .614 .80 .595 .600 .604 .611 .613 .90 .592 .598 .603 .609 .612 1.00 .590 .595 .601 .608 .611 1.20 .585 .591 .597 .605 .610 1.40 .580 .587 .594 .602 .609 1.60 .582 .591 .600 .607 TABLE III. VALUES OF THE COEFFICIENT OF DISCHARGE FOR WEIRS WITHOUT END CONTRACTIONS. Effective Head. Feet. .10 .15 .20 .25 .30 .40 .50 .60 .70 .80 .90 1.00 1.20 1.40 1.60 Length of Weir. Feet. 19 10 7 5 4 3 2 .657 .658 .658 .659 .643 .644 .645 .645 .647 .649 .652 .635 .637 .637 .638 .641 .642 .645 .630 .632 .633 .634 .636 .638 .641 .626 .628 .629 .631 .633 .636 .639 .621 .623 .625 .628 .630 .633 .636 .619 .621 .624 .627 .630 .633 .637 .618 .620 .623 .627 .630 .634 .638 .618 .620 .624 .628 .631 .635 .640 .618 .621 .625 .629 .633 .637 .643 .619 .622 .627 .631 .635 .639 .645 .619 .624 .628 .633 .637 .641 .648 .620 .626 .632 .636 .641 .646 .622 .629 .634 .640 .644 .623 .631 .637 .642 .647 CON VERSION FA CTORS. 141 TABLE IV. WEIR TABLE GIVING CUBIC FEET DISCHARGED PER MINUTE FOR EACH INCH IN LENGTH OF WEIR FOR DEPTHS FROM IN. TO 25 IN. This table should not be used unless the length of the crest is at least 3 or 4 times the depth of water passing over the weir, for if this is not the case, there will be serious errors caused bx end contractions. Inches. i i I i * 1 I .01 .05 .09 .14 .20 .26 .33 1 .40 .47 .55 .65 .74 .83 .93 1.03 2 1.14 1.24 1.36 1.47 1.59 1.71 1.83 1.96 3 2.09 2.23 2.36 2.50 2.63 2.78 2.92 3.07 4 3.22 3.37 3.52 3.68 3.83 3.99 4.16 4.32 5 4.50 4.67 . 4.84 5.01 5.18 5.36 5.54 5.72 6 5.90 6.09 6.28 6.47 6.65 6.85 7.05 7.25 7 7.44 7.64 7.84 8.05 8.25 8.45 8.66 8.86 8 9.10 9.31 9.52 9.74 9.96 10.18 10.40 10.62 9 10.86 11.08 11.31 11.54 11.77 12.00 12.23 12.47 10 12.71 13.95 13.19 13.43 13.67 13.93 14.16 14.42 11 14.67 14.92 15.18 15.43 15.67 15.96 16.20 16.46 12 16.73 16.99 17.26 17.52 17.78 18.05 18.32 18.58 13 18.87 19.14 19.42 19.69 19.97 20.24 20.52 20.80 14 21.09 21.37 21.65 21.94 22.22 22.51 22.79 23.08 15 23.38 23.67 23.97 24.26 24.56 24.86 25.16 25.46 16 25.76 26.06 26.36 26.66 26.97 27.27 27.58 27.89 17 28.20 28.51 28.82 29.14 29.45 29.76 30.08 30.39 18 30.70 31.02 31.34 31.66 31.98 32.31 32.63 32.96 19 33.29 33.61 33.94 34.27 34.60 34.94 35.27 35.60 20 35.94 36.27 36.60 36.94 37.28 37.62 37.96 38.31 21 38.65 39.00 39.34 39.69 40.04 40.39 40.73 41.09 22 41.43 41.78 42.13 42.49 42.84 43.20 43.56 43.92 23 44.28 44.64 45.00 45.38 45.71 46.08 46.43 46.81 24 47.18 47.55 47.91 48.28 48.65 49.02 49.39 49.76 1,728 231 * J. = 7.4805194 gal. 231 CONVERSION FACTORS. Cubic Feet Into Gallons: 1 cu. ft. = 1,728 cu. in. Gallons Into Cubic Feet: 1 United States liquid gal. = 231 cu. in. = ^~- cu. ft. = .133680555 cu. ft. Feet per Second Into Miles per Hour: 3 600 15 1 ft. per sec. = 3,600 ft. per hr. = ^sn, or miles per hour. Miles per Hour Into Feet per Second: 1 mi. per hr. = 5,280 ft. per hr. = ~^^, or ft. per sec. o,oOO 1O Second-Feet per Day Into Gallons: 1 second-foot, or 7.4805194 gal. per sec. for 1 day, or 86,400 sec. = 646,316.87616 gal. Millions of Gallons Into Second-Feet per Day: 1,000,000 gal. per 24 hr cu - ft - Persec., or 1.5472286 second-feet. Second-Feet per Day Into Acre-Feet: 1 second-foot flow for 1 day = 86,400 cu. ft. T' , or 1.983471 acre-feet. 142 HYDRA ULICS. Acre-Feet Into Second-Feet Flow for 24 Hours: One acre-foot each 24 hr. = 43,560 cu. ft. each 86,400 sec. 43 560 121 2nn > or FTJT; second-foot flow for 24 hr. Acre-Feet Into Gallons: 1 acre-foot = 43,560 cu. ft. = ^,560^ 1,728^ ^ 7^680 Millions of Gallons Into Acre-Feet: 1,000,000 United States liquid gal., or 231,000,000 cu. in. = 133,680.555 cu. ft., 1 ^'3 fi80 or = 3.0688832 acre-feet. Second-Feet Into Minute Gallons: FACTORS: 1 cu. ft. contains 1,728 cu. in.: 1 gal. has a capacity of 231 cu. in.; 1 second-foot equals [(1,728 -=- 231) X 60] gal. per min., or 448.831164 minute- gallons. Minute-Gallons Into Second-Feet: FACTORS: 1 gal. contains 231 cu..in.; 1 cu. ft. contains 1,728 cu. in.; 1 gal. per min. equals [(231 -r- 1,728) -*- 60] second-feet, or .0022280092 second-foot. FLOW OP WATER IN OPEN CHANNELS. Ditches. In the case of hydraulic mining and irrigation, water is usually conveyed through ditches. The ditch line should be carefully surveyed and all brush and trees removed, and the underbrush cut away and burned, before beginning to excavate the ditch. The following letters will be used in the formulas for determining the various factors relating to ditches: h = difference in level between ends of canal or ditch, or between two points under consideration; I horizontal length of portion of canal or ditch under consideration; s = slope = ratio j = sin of slope; a = area of water cross-section in square feet; p = wet perimeter = portion of outline of cross-section of stream in contact with channel, in feet; r = hydraulic radius, or hydraulic mean depth = ratio -; c' = coefficient, depending on nature of surface of the ditch; c = coefficient depending on nature of surface of ditch, as determined by Kutter's formula; v = mean velocity of flow in feet per second; v > = surface velocity of a stream; v b = bottom velocity of a stream; x = bottom or one side of a section, the form of which is half a regular hexagon, in feet; Q = quantity of water flowing, in cubic feet per second; n = coefficient of roughness in Kutter's formula. The form of ditch and its grade will depend largely on the amount of water to be conveyed and the character of the soil in the section under consideration. As a general rule, the average flow of water in a ditch should not be less than 2 ft. per second, and under most circumstances should not exceed 4 ft., though in rare cases where the formation is suitable, mean velocities of 5 ft. per second are employed. Sand will deposit from a current flowing at The rate of 1| ft. per second, and if the current does not have a velocity of at least 2 ft. per second, vegetation is liable to block the ditch linei Safe Bottom Velocity. The bottom velocity of a stream may be obtained from the average velocity by the following formula: v h = v 10.87 ]/rs. The following table gives values of safe bottom and mean velocities, cor- responding with certain materials, as given by Ganguillet and Kutter: FLOW OF WATER IN CHANNELS. 143 Material of Channel. Safe Bottom Velocity^. Feet per Second. Mean Velocity v. Feet per Second. Soft brown earth .249 .328 Soft loam .499 .656 Sand 1.000 1.312 Gravel 1.998 2.625 Pebbles 2.999 3.938 Broken stone, flint Conglomerate, soft slate Stratified rock 4.003 4.988 6.006 5.579 6.564 8.204 Hard rook 10.009 13.127 Resistance of Soils to Erosion by Water. W. A. Burr, "Engineering News," February 8, 1894, gives a diagram showing the resistance of various soils to erosion by water. The following values have been selected from Mr. Burr's work for different kinds of soil: Pure sand resists erosion by flow of ................ 1.10 ft. per sec. Sandy soil, 15$ clay ............................................ 1.20 ft. per sec. Sandy loam, 40$ clay .......................................... 1.80 ft. per sec. Loamy soil, 65$ clay .......................................... 3.00ft. per sec. Clay loam, 85$ clay ............................................. 4.80 ft. per sec. Agricultural clay, 95$ clay ................................ 6.20 ft. per sec. Clay ................................................................... 7.35ft. per sec. pacity of Ditches. Ditches should never be run full, but should be constructed large enough so that they will carry the desired amount of ' full. Carrying Capa water when from f 'to f full. For any given cross-section, the greatest flow will be attained when the hydraulic radius or hydraulic mean depth is equal to one-half of the actual depth of the channel. The cross-section of a ditch or conduit that has the greatest possible carrying capacity is a half circle, and the nearest practical approach to this is a half hexagon. Knowing the cross-section of a ditch, its dimensions may be found by the formula: V2a 2^91 2.598 As the obtuse angle between the side and bottom of the ditch is 120, the form can be easily laid off. The carrying capacity of ditches generally increases after they have been in use some time, as the ditch becomes lined with a fine scum that closes the pores in the soil and prevents leakage. This may increase the amount to as much as 10$. Grade. The grade of the ditch must be sufficient to create the desired velocity of flow, and depends largely on the character of the material com- posing the surfaces of the ditch. If the surface is smooth, as, for instance, where the ditch is cut through clay or is lined with masonry, the grade can be considerably less than where the surface is rough, or when cut through coarse gravel or when lined with rough stone. In mountainous countries, where the ground is hard, deep narrow ditches with steep grades are gener- ally preferred to larger channels with gentle slopes, as the cost of excavation is considerably less; but steep grades and narrow ditches are suitable only when the banks can resist the rapid flow. In California, grades of from 16 to 20 ft. per mile are used, and 10 ft. per mile is quite common. Water channels of a uniform cross-section should have a uniform grade, otherwise, the flow will be checked in places, which will result in deposits of sand or silt in some portions of the ditch, which are liable to cause the banks to be over- flowed and the ditch to be ultimately destroyed. In designing any given ditch, the grade is generally assumed to correspond to the formation of the country and the velocity figured from the grade. In case v is found to be so great that it would cut the banks, it will be necessary either to reduce the grade or to change the form of the ditch so as to reduce the velocity. Ditch banks, when possible, should be composed of solid material, but frequently it is necessary to use excavated material. Where this is the case, care must be taken to see that the material is o placed as to avoid settling 144 HYDRA ULICS. and cracking as much as possible. All stumps, roots, etc. should be separated from the material to be used for embankments. If artificial banks are neces- sary, it is best to build them of masonry, provided the expense is not too great; or, the water may be carried across depressions in pipes or flumes. When the character of the material through which the ditch is constructed is not sufficiently firm to resist the desired current velocity, it becomes neces- sary to line the ditch. In some locations the ditches are simply smoothed on the inside and lined with from | in. to 1 in. of cement mortar, made up of Portland cement and sharp sand. In other cases they are lined with dry stonework laid up in order and carefully bonded together. Sometimes the stonework is pointed with cement or mortar on the inside, so as to present a more uniform surface to the flow. In other cases, the sides are simply revetted with stone. Influence of Depth on Ditch. The depth of the flow in a ditch has consider- able influence on the scouring or eroding of the bottom and the banks, owing to the fact that a much greater average velocity can be attained in a deep stream than in a shallow stream, without causing an excessive velocity of the water in contact with the wet perimeter. For this reason, in cases where banks will stand it, it is best to use narrow deep ditches rather than wide flat ditches, though each location has to be treated in accordance with its own special conditions, and no general rule can be laid down. Measuring the Flow of Water in Channels. The laws for the resistance to the flow may be expressed by the relation (see page 142 for significance of letters) : If c = -\ij , the formula becomes = c -\/ rs. The coefficient c is usually found by means of Kutter's formula, one form of which is as follows: 23 + .00155 .5521 + 23 + - - The values for n, the coefficient of roughness, under various conditions, are as follows: Character of Channel. Value of n. Clean, well-planed timber Clean, smooth, glazed iron, and stoneware pipes Masonry, smoothly plastered with cement, and for very clean, smooth, cast-iron pipe Unplaned timber, ordinary cast-iron pipe, and selected pipe sewers, well laid and thoroughly flushed Rough iron pipes and ordinary sewer pipes, laid under the usual conditions Dressed masonry and well-laid brickwork Good rubble masonry and ordinary rough or fouled brickwork Coarse rubble masonry and firm, compact gravel Well-made earth canals in good alinement Rivers and canals in moderately good order and perfectly free from stones and weeds Rivers and canals in rather bad condition and somewhat obstructed by stones and weeds Rivers and canals in bad condition, overgrown with vegeta- tion and strewn with stones and other detritus, according to condition .009 .010 .011 .012 .013 .015 .017 .020 .0225 .025 .030 .035 to .050 FLUMES. 145 As it is quite difficult to obtain the value of c by Kutter's formula, the fol- lowing three approximate formulas for v are given: /100,000r2s For canals with earthen banks, v = \l-z- ; \ 9 r + 36 If the ditch is lined with dry stonework, v -%/ --' - -- - /OO If the ditch is lined with rubble masonry, v = \\-=- \ 7. -- - -- r - /TOO, 000 r-7 -- -- - To find the quantity Q of water flowing through any channel in a given time, multiply the velocity by the area, or Q = a v. Flow in Brooks and Rivers. When a stream is so large that, it becomes impracticable to employ a weir for measuring its flow, fairly accurate results may be arrived at by determining the velocity of the current at various points in a carefully surveyed cross-section of the stream, thus determining both v and a. The greatest velocity of current occurs at a point some distance below the surface, in the deepest part of the channel. When determining the current velocities in the different portions of a stream, it is frequently advantageous to divide the stream into divisions. This may be accomplished by stretching a wire across and tying strings or rags about the wire at various points. The mean velocity of the current between these points can be determined by current meters, or by floats. The points for observation should be chosen where the channel is comparatively straight and the current uniform. Surface floats may be used, in which case the mean velocity of the point where the float is used may be found as follows: If v f equals the observed velocity, then the mean velocity will be v = .9 v'. By taking observations of the velocity of the current in each section of a stream, the amount of water flowing may be determined for each separate section. The total amount of water flowing in the stream will be the sum of the amounts in each section. The average velocity of the entire stream may be found by dividing the total amount of water flowing by .total area of the cross-section of the stream. The correction necessary to reduce surface velocity to mean velocity may be made as follows: Measure off T ^ of the ordinary distance, and figure the time as though for the full distance. For instance, if only 90 ft. were employed, the time would be taken and the problem figured as though it were 100 ft., on account of the fact that the mean velocity is only & of the. surface velocity. Flumes are used for conveying water when a ditch line would be abnormally long, or when the material to be excavated is very hard. They may be constructed of timber or of metal, but metal flumes are compara- tively rare, as piping can be used instead. The line of the proposed flume should be carefully cleared of all standing timber, and the brush burned for at least 20 ft. each side of the flume line to prevent danger from fire. The life of an ordinary flume, which is supported on or constructed of timber, is always short, varying, as a rule, from 10 to 20 years, depending on whether the flume is allowed to run dry a portion of the year or is always full of water, the care with which it was originally constructed, and the attention paid to repairs. Grade of Flumes. Flumes are usually set on a much steeper grade than is possible in ditches, the grade frequently being as much as 25 to 30 ft. per mile, and in special cases even more. The result of this is that the carrying capacity of flumes is much greater than that of ditches of the same size. The form of flume depends largely on the material of which it is constructed. Metal flumes may have a semicircular form, while wooden flumes are either rectangular or V-shaped. The former is used almost exclusively for con- veying water, and the latter quite extensively for fluming timber or cord wood from the mountains to the shipping point in the valley. Timber flumes should be so constructed that the water will meet with but small resistance, and the bottom and side should be enclosed in a frame of timbers so braced or secured that there is no possible chance of the sides spreading or lifting from the bottom, and thus cause leakage. As a rule, all mortised and tenoned joints should be avoided in flume construction. 146 HYDRAULICS. Fig. 12 shows a timber flume in which no joints are cut, the bottoms of the posts being kept in place by stringers spiked on the sills, and the tops tied together by pieces bolted on. Fig. 13 shows a construction in which the posts are let into the sills and supported by diagonal'braces. The ties across the top of the posts are also notched to receive the upper ends of the posts. As a rule, in such a construction these ties are only placed on every third or fourth frame, the diagonal braces being depended on to hold the other posts in place. The joints between the planking may be battened on the in- side with strips of " lumber, 4 or 5 in. wide, or the edges of the planking may be dressed and painted before they are put together, so as to form a tight joint. Connection With Ditches. FIG. 12. FIG. 13. Where flumes connect with ditches or dams, the posts for several boxes should be made longer, so that they may receive another sideboard to prevent the water from splashing over the sides. The flume should also be widened out or flared, both at its entry and discharge ends. Where the flume passes through a bank of earth, an outer siding may be nailed on the outside of the posts, to protect the flume from rotting. Trestles. Where flumes are carried on trestles, the individual frames supporting the flume are usually placed on heavy stringers, which in turn are supported upon trestle bents from 12 to 16 ft. apart, the frames supporting the flume being placed about 4 ft. apart. Curves. Where flumes are laid around curves, the outer edge of the flume should be elevated so as to prevent splashing and to cause the flowing water to have a uniform depth across the width of the flume. It is impossible to give any definite rule as to the amount that the outer edge of the flume should be raised, but this is usually accomplished by judging the amount when the flume is first constructed, and correcting this by wedging up after the water is flowing. The individual boxes of the flume may have to be cut into 2 or 3 portions on curves, and at times the side planks are sawed partially through, so as to enable them to be bent to the desired curve. Waste gates should be placed every half mile, to empty the flume for repairs, or in case of accident. They are also useful for flushing snow out of a flume. In snow regions, flumes are frequently protected by sheds over their exposed portions. Flow of Water Through Flumes. As smooth wooden surfaces offer consider- ably less resistance to the flow of water than earth or stone canals, the coefficients must necessarily be somewhat reduced, and the following formula is useful in giving the flow of water through flumes: 100,000 r- s 6.6 r + 6746' That flumes may have their full carrying capacity, they have to be of sufficient length to get the water in motion, or, as it is technically expressed, " to put the water in train." It is largely on this account that flumes have to be made of a larger cross-section at both the entrance and the exit. In cold countries it may be best to construct the flume narrower than it is deep, as in cold weather the ice in the narrow flume freezes a crust entirely across the surface, thus protecting the water from further action of the elements and frequently prolonging the flow through the flume for several weeks, while wide shallow flumes will not freeze on the surface so quickly, but will freeze in from the bottom and sides until they are practically a solid mass of ice. When a flume is laid on the ground along a bank, it should be laid as close to the bank as possible, so as to protect it from snow or landslides, and so that in the winter the snow will drift in under and behind it, thus preventing the circulation of the air about the flume. This will protect the flume, and may prolong the flow for some time after cold weather sets in. TUNNELS. 147 carrying capacity of the tunnel, they have been lined with wooden-stave pipe, backed with concrete, the pipe requiring no metal bands, but depend- ing on the concrete to keep it in place. When such linings are employed, it TUNNELS. Tunnels are sometimes used for conveying water, in connection with flume or ditch lines. Where a tunnel is unlined, it is best to give the roof the shape of the Gothic arch, owing to the fact that this stands better and resists scaling to a greater extent than the round arch, which usually scales off until it has the form of the Gothic arch. If tunnels are to be used as water conduits, without lining, care should be taken to make the inside of the tunnel as smooth as possible. In some cases, in order to increase the hey have been lined with wooden-stave ie requiring no metal bands, but depend- ice. When such linings are employed, it is not practicable to have them exposed to the alternate action of the water and the atmosphere, hence the tunnel should be kept continually full of water. To accomplish this, the tunnel may be dropped below the grade of the ditch or flume line, so that it is always under a slight hydrostatic pressure, and even if the water were turned off from the line, the tunnel would remain full of water, the same as an inverted siphon. Sometimes tunnels are lined with cement, being given either a circular or oval form, or they may have a flat bottom, with flat sides and an arched roof. The cement may be placed directly on the country rock composing the walls of the tunnel, or the tunnel may be lined with brick or stone, and then cemented on the inside. Flow Through Tunnels. The flow of water through tunnels, when they are only partially filled, is calculated by the formulas for flow in open channels, while in the case of lined tunnels that are run full, the flow is calculated by formulas for calculating the flow through pipes. FLOW THROUGH PIPES. Hydraulic Gradient. If a pipe of uniform cross-section be connected with a reservoir, and water allowed to discharge through its open end, it has been found that the pressure on the pipe at any point is equal to the vertical dis- tance from the center of the pipe at that point to an imaginary line, called the hydraulic gradient or hydraulic grade line. This is a line drawn from a point slightly below the surface of the water in the reservoir to the outlet of the pipe, as ab, Fig. 14. The distance from the sur- face of the water to the point a is equal to the head lost in overcoming the fric- tion at the entrance to the pipe, and is rarely over 1 ft. If the pipe were laid along the line a b, it would carry exactly the same amount of water as when laid hori- zontally, as shown, but there would be practically FIG. 14. no pressure tending to burst the pipe at any point along this line; while if it were laid along the line from the point a' (the reservoir being made deeper), it would still deliver exactly the same amount of water, but the pressure tending to burst the pipe would be greatly increased. In order that a pipe may have a maximum discharge, no point in the line must rise above the hydraulic gradient, and it makes no difference in the discharge how far below the gradient it may fall. In Fig. 15, the pipe rises above the hydraulic gradient a c, and in this case a new hydraulic gradient a b would have to be established, and the flow calculated for this head, the pipe b c simply acting to carry off the water delivered to it at b. If the upper side of the pipe were open at the point 6, the water would have no tendency to escape, but, on the contrary, air would probably enter, and the pipe flow only partially full from 6 to c. Flow in Pipes. Darcy, a French engineer, made a series of experiments on different diameters of cast-iron pipe, with different degrees of internal 148 HYDRA ULICS. roughness, from which he calculated a series of formulas. The following are some of these formulas, as arranged by Mr. E. Sherman Gould, C. E., E. M., one of the most experienced hydraulic engineers in America. Darcy found that the character of the inside surface of the pipe played a very important part in its dis- charge, and he deduced a formula and determined a series of coefficients for it, but Mr. Gould calls attention to the fact that the coefficients for pipes from 8" to 48" in diam- eter practically cancel the numerical factor employed in Darcy's formula, and that a slightly different factor applies to pipes from 3 to 8 in., so that we may have the following simple formulas, in which the factors given apply: Q *= amount of water in cubic feet per second; q = U.S. gallons per second; Z) = diameter of pipe in feet; d = diameter of pipe in inches; H = total head in feet; h = head per 1,000 ft.; V = velocity in feet per second. Pipes above 8 in. in diameter, rough inside surface, Q = For diameter in inches, Q = d 2 ]/ d h. Pipes between 3 and 8 in. in diameter, rough inside surface, = 0.89 Large pipes, smooth inside surface, Jni; V = 1.78 j Small pipes, smooth inside surface, Q = 0.89i/2l^A = 1.25 IT-\/J)h', V = As a rule, it is best to calculate any pipe line by the formula for pipes having a rough internal surface, for if this is not d9ne the results are liable to be disappointing, owing to the fact that all pipes become more or less rough with use. Eytelwein's Formula for the Delivery of Water in Pipes: D = diameter of pipe in inches; H = head of water in feet; L = length of pipe in feet; W = cubic feet of water discharged per minute W = 4.71-1 D = . .X W* H ' Hawkslsy's Formula: G = number of gallons delivered per hour; L == length of pipe in yards; H = head of water in feet; D = diameter of pipe in inches. Neville's General Formula: v = velocity in feet per second; r = hydraulic mean depth in feet; s = sine of inclination, or total fall divided by total length. v = 140 1/ ri ll^fJ. In cylindrical pipes, v multiplied by 47. 124 d- gives the discharge per minute in cubic feet, or v multiplied by 293. 7286 d 2 gives the discharge per minute in gallons, d being the diameter of the pipe in feet. COMPARISON OF FORMULAS. 149 COMPARISON OF FORMULAS. area -r- wet perimeter = for R = mean hydraulic depth in feet circular section of pipe; S = sine of slope = =- ; v == velocity in feet per second; d = diameter- of pipe in feet; L = length of pipe in feet; H = head of water in feet. Prony, v = 97.05 \/'RS .08; or, v = 99.88 v/^RS .154. Eytelwein, Eytelwein, Hawksley, Neville, Darcy, v = 108 i/RS- .13. ; for value of (7, see following Table. Diameter of pipe (inches) Value of C 65 1 80 2 93 3 99 4 102 5 103 6 105 7 106 8 107 Diameter of pipe (inches) Value of C 9 108 10 109 12 109.5 14 no 16 110.5 18 110.7 20 111 22 111.5 24 111.5 Maximum value of Cfor very large pipes, 113.3. v = c y'lts, .00281 S Kutter, where 181 :ya^ s ) Weisbach, h = ^( .0036 + - )-, where h = head necessary to overcome the friction in a pipe; r the mean radius of the pipe in feet; and g = gravity = 32.2. line rises above the source of supply, Siphons. When any part of the pipe 1 ich a line is called a siphon. If this rii PI 1 >f t such "a line is called a siphon. If this rise is greater than the height of the water barometer (34 ft. at sea level), water will not flow through the siphon. The flow through the siphon will be the same as that through any pipe line so long as there is no accumulation of air at the highest point of the line; but such an accumulation will decrease or entirely stop the flow. All siphons should be provided at their highest points with valves for discharging the air and introducing water to fill the siphon, and it is usually best to trap the lower end of the pipe so that air cannot enter it, and to enlarge the upper end so as to reduce the loss of the stream in entering. For a siphon to work well, the fall between the intake and the discharge end should be considerable, if the rise amounts to much. 150 HYDRA VLICS. o p_?3 c t 2 ?2 os ^T iocoi>-aiTt- rH_T^l> OCMLOOrHiOt--COOOI>;CO^TTr >O C^4 ^^ CN C- Tf OS ^ CO Cl T I T I O iC r *O CO !> O C^I CO CO C^ rH 1C C\l i I CO CO O CC >C LC O C^ O *M O CJl O Tf C^l CO GO C^ rH C|CO_-^iO_y^O^Oi_T^cC_CN_<> O5_ CN LO OS CO t^ GO GO I> CO rfi C g38i ^fl^QOl^-i CN Tf 25 GO " " ~ g ^ 1.^ i ^t \T / ~ 7J " C liOGOi c cc cc ^ bGCOrHCNCOTPLOCj as-*tiascccoococ; CNCOCOTTITfLOLOLI ^~o~Tt< cc CN i> "GO c T-r 50uCCOT----i-C. : : i - t I t I i I CN CN CN CN CC CC CC rH CN CO CC Tt< LO iO CO CO t- H* \ ^ ^ ^ as co co o co co as cc c GO Os' OS O ^' GO r^' ' ' ' ' -- I GO rH CN rH C5 CO CN ) I>- O CN Tf lO l> OS rH rH rH CN CN C FRICTION IN PIPES. 151 LOSS OF HEAD IN PIPE BY FRICTION In each 100 ft. in length of different diameters, when discharging the follow- ing quantities of water per minute, as given by Pelton Water Wheel Co. INSIDE DIAMETER OF PIPE. INCHES. . 2 3 4 5 6 1& ** * 2 * r .2 '*& 53 *i *>.9 ** .5 r' e| 51 o" * 51 5 % 51 5 fl J 85 51 9 ~ o ^ 3 a >- K B a ^a & a x n a 2.0 2.37 .65 1.185 2.62 .791 5.89 .593 10.4 .474 16.3 .395 23.5 2.2 2.80 .73 1.404 2.88 .936 6.48 .702 11.5 .561 18.0 .468 25.9 2.4 3.27 .79 1.639 3.14 .093 7.07 .819 12.5 .650 19.6 .547 28.2 2.6 3.78 .86 1.891 3.40 .260 7.65 .945 13.6 .757 21.3 .631 30.6 2.8 4.32 .92 2.160 3.66 .440 8.24 1.080 14.6 .864 22.9 .720 32.9 3.0 4.89 .99 2.440 3.92 .620 8.83 1.220 15.7 .978 24.5 .815 35.3 3.2 5.47 1.06 2.730 4.18 .820 9.42 1.370 16.7 1.098 26.2 .915 37.7 3.4 6.09 .12 3.050 4.45 .040 10.00 1.520 17.8 1.220 27.8 1.021 40.0 3.6 6.76 .19 3.380 4.71 .260 10.60 1.690 18.8 1.350 29.4 1.131 42.4 3.8 7.48 .26 3.740 4:97 .490 11.20 1.870 19.9 1.490 31.0 1.250 44.7 4.0 8.20 .32 4.100 5.23 2.730 11.80 2.050 20.9 1.640 32.7 1.370 47.1 4.2 8.97 .39 4.490 5.49 2.980 12.30 2.240 22.0 1.790 34.3 1.490 49.5 4.4 . 9.77 .45 4.890 5.76 3.250 12.90 2.430 23.0 1.950 36.0 1.620 51.8 4.6 10.60 .52 5.300 6.02 3.530 13.50 2.640 24.0 2.110 37.6 1.760 54.1 4.8 11.45 .58 5.720 6.28 3.810 14.10 2.850 25.1 2.270 39.2 1.900 56.5 5.0 12.33 .65 6.170 6.54 4.110 14.70 3.080 26.2 2.460 40.9 2.050 58.9 5.2 13.24 .72 6.620 6.80 4.410 15.30 3.310 27.2 2.650 42.5 2.210 61.2 5.4 14.20 .78 7.100 7.06 4.730 15.90 3.550 28.2 2.840 44.2 2.370 63.6 5.6 15.16 .85 7.580 7.32 5.060 16.50 3.790 29.3 3.030 45.8 2.530 65.9 5.8 16.17 .91 8.090 7.58 5.400 17.10 4.040 303 3.240 47.4 2.700 68.3 6.0 17.23 1.98 8.610 7.85 5.740 17.70 4.310 31.4 3.450 49.1 2.870 70.7 7.0 22.89 2.31 11.450 9.16 7.620 20.60 5.720 36.6 4.570 57.2 3.810 82.4 INSIDE DIAMETER OF PIPE. INCHES. g 7 8 9 10 11 12 ll ** *"' 2 ** ' a *d ~ f* w C * c . feg ** -" ll tfl 4 31 PO *l ll H . s l| s\ ii X si ll n ** 2.0 .338 32.0 .296 41.9 .264 53.0 .237 65.4 .216 79.2 .198 j 94 2 2.2 .401 35.3 .351 46.1 .312 58.3 .281 72.0 .255 87.1 .234 103.0 2.4 .468 38.5 .410 50.2 .365 63.6 .327 78.5 .297 95.0 .273 113.0 2.6 .540 41.7 .473 54.4 .420 68.9 .378 85.1 .344 103.0 .315 122.0 2.8 .617 44.9 .540 58.6 .480 74.2 .432 91.6 .392 111.0 .360 132.0 3.0 .698 48.1 .611 62.8 .544 79.5 .488 98.2 444 119.0 .407 141.0 3.2 .785 51.3 .686 67.0 .609 84.8 .549 105.0 .499 127.0 .457 151.0 3.4 .875 54.5 .765 71.2 .680 90.1 .612 111.0 .557 134.0 .510 160.0 3.6 .969 57.7 .848 75.4 .755 95.4 .679 118.0 .617 142.0 .566 169.0 3.8 1.070 60.9 .936 79.6 !831 101.0 .749 124.0 .680 150.0 .624 179.0 4.0 1.175 64.1 1.027 83.7 .913 106.0 .822 131.0 .747 158.0 .685 188.0 4.2 1.280 67.3 1.122 87.9 .998 111.0 .897 137.0 .816 166.0 .749 198.0 4.4 1.390 70.5 1.220 92.1 1.086 116.0 .977 144.0 .888 174.0 .815 207.0 4.6 1 .510 73.7 1.320 96.3 1.177 122.0 1.059 150.0 .963 182.0 .883 217.0 4.8 1.630 76.9 1.430 100.0 1.270 127.0 1.145 157.0 1.040 190.0 .954 226.0 5.0 1.760 80.2 1.540 105.0 1.370 132.0 1.230 163.0 1.122 198.0 1.028 235.0 5.2 1.890 83.3 1.650 109.0 1.470 138.0 1 .320 170.0 1.200 206.0 1.104 245.0 5.4 2.030 86.6 1.770 113.0 1.570 143.0 1.410 177.0 1.280 214.0 1.183 254.0 5.6 2.170 89.8 1.890 117.0 1.680 148.0 1.510 183.0 1.370 222.0 1.260 264.0 5.8 2.310 93.0 2.010 121.0 1.800 154.0 1.610 190.0 1.460 229.0 1.340 273.0 6.0 2.460 96.2 2.150 125.0 1.920 159.0 1.710 196.0 1.560 237.0 1.430 283.0 7.0 3.260 112.0 2.850 146.0 2.520 185.0 2.280 229.0 2.070 277.0 1.910 330.0 EXAMPLE. Have 200 ft. head and 600 ft. of 11" pipe, carrying 119 cu. ft. of water per minute. To find effective head: In right-hand column, under 11" pipe, find 119 cu. ft. Opposite this will be found the coefficient of friction for this amount of water, which is .444. Multiply this by the number of hun- dred feet of pipe, which is 6. and you will have 2.66 ft., which is the loss of head. Therefore, the effective head is 200 2.66 = 197.34. 152 HYDRA ULICS. LOSS OF HEAD IN PIPE BY FRICTION In each 100 ft. in length of different diameters, when discharging the follow- ing quantities of water per minute, as given by Pelton Water Wheel Co. INSIDE DIAMETER OF PIPE. INCHES. 13 14 15 16 18 20 *l is, & - a * *^ 5 ** - a v * ^ 2 , -^'.9 ^ -u' a ? ll a* 11 z* ll JS fe 31 u g, ll t, l| dg W 001 a 04 H a a a 2.0 .183 110 .169 128 .158 147 .147 167 .132 212 .119 262 2.2 .216 121 .200 141 .187 162 .175 184 .156 233 .140 288 2.4 .252 133 .234 154 .218 176 .205 201 .182 254 .164 314 2.6 .290 144 .270 167 .252 191 .236 218 .210 275 .189 340 2.8 .332 156 .308 179 .288 206 .270 234 .240 297 .216 366 3.0 .375 166 .349 192 .325 221 .306 251 .271 318 .245 393 3.2 .422 177 .392 205 ".366 235 .343 268 .305 339 .275 419 3.4 .471 188 .438 218 .408 250 .383 284 .339 360 .306 445 3.6 .522 199 .485 231 .452 265 .425 301 .377 382 .339 471 3.8 .576 210 .535 243 .499 280 .468 318 .416 403 .374 497 4.0 .632 221 .587 256 .548 294 .513 335 .456 424 .410 523 4.2 .691 232 .641 269 .598 309 .561 352 .499 445 .449 550 4.4 .751 243 .698 282 .651 324 .611 368 .542 466 .488 576 4.6 .815 254 .757 295 .707 339 .662 385 .588 488 .529 602 4.8 .881 265 .818 308 .763 353 .715 402 .636 509 .572 628 5.0 .949 276 .881 321 .822 368 .770 419 .685 530 .617 654 5.2 1.020 287 .947 333 .883 ' 383 .828 435 .736 551 .662 680 5.4 1.092 298 1.014 346 .947 397 .888 452 .788 572 .710 707 5.6 1.167 309 1.083 1.011 412 .949 469 .843 594 .758 733 5.8 1.245 321 1.155 372 1.078 427 1.011 486 .899 615 .809 759 6.0 1.325 332 1.229 385 1.148 442 1.076 502 .957 636 .861 785 7.0 1.750 387 1.630 449 1.520 515 1.430 586 1.270 742 1.143 916 INSIDE DIAMETER OF PIPE. INCHES. 22 2 4 * 2 8 3 3 6 if '** 2 *i * 9 'o w a f -.9 0) . *i a *' *S -t> a S'S is" 3 t- is 3 -. SS s *~ is g, W g, g, a a a a a a 2.0 .108 316 .098 377 .091 442 .084 513 .079 589 .066 848 2.2 .127 348 .116 414 .108 486 .099 564 .093 648 .078 933 2.4 .149 380 .136 452 .126 531 .116 616 .109 707 .091 1,018 2.6 .171 412 .157 490 .145 575 .134 667 .126 766 .104 1,100 2.8 .195 443 .180 528 .165 619 .153 718 .144 824 .119 1,188 3.0 .222 475 .204 565 .188 663 .174 770 .163 883 .135 1,273 3.2 .249 507 .229 603 .211 708 .195 821 .182v 942 .152 1,357 3.4 .278 538 .255 641 .235 752 .218 872 .204 1,001 .169 1.442 3.6 .308 .570 .283 678 .261 796 .242 923 .226 1,060 .188 1,527 3.8 .340 601 .312 716 .288 840 .267 974 .249 ,119 .207 1,612 4.0 .373 633 .342 754 .315 885 .293 1,026 .273 ,178 .228 1,697 4.2 .408 665 .374 791 .345 929 .320 1,077 .299 ,237 .249 1,782 4.4 .444 .697 .407 829 .375 973 .348 1,129 .325 ,296 .271 1,866 4.6 .482 .728 .441 867 .407 1,017 .378 1,180 .353 ,355 .294 1,951 4.8 .521 760 .476 905 .440 1,062 .409 1,231 .381 ,414 .318 2,036 5.0 .561 792 .513 942 .474 ,106 .440 1,283 .411 ,472 .342 2,121 5.2 .602 823 .552 980 .510 .150 .473 1,334 .441 ,531 .368 2,206 5.4 .645 855 .591 1,018 .546 ,194 .507 1,385 .473 ,590 .394 2,291 5.6 .690 887 .632 1,055 .583 ,239 .542 1,437 .506 ,649 .421 2,376 5.8 .735 918 .674 1,093 .622 ,283 .578 1,488 .540 ,708 .450 2,460 6.0 .782 950 .717 1,131 .662 1,327 .615 1,539 .574 1,767 .479 2,545 7.0 1.040 1,109 .953 1,319 .879 1,548 .817 1,796 .762 2,061 .636 2,968 FRICTION IN PIPES. 153 The following formula, deduced by William Cox, gives practically 3 same results as the foregoing table and will be found useful in many the instances: F = oregoing i - (4 V' 2 + 5 V 2) , where F - friction head; L = length of pipe in feet; D = diameter of pipe in inches; V = velocity in feet per second. Friction of Knees and Bends. This subject has not been investigated suffi- ciently to enable the engineer to make exact allowance for this factor, but FIG. 16. the following formulas may be taken as giving close approximate results. It is well to bear in mind that right angles should be avoided whenever possible, and that bends should be made with as large a radius as circum- stances will allow. A angle of bend or knee with forward line /" ,'A of direction; v = velocity of water in feet per second; -K = radius of center line of bend; v = radius of bore of pipe (or \ diameter); K = coeffic i ent for angles of knees; L = coefficient for curvature of bends; ' H = head of water in feet necessary to ovcr- come the friction of the bends, or knees. H = .0155 V*K. . ' ^ //>j ' FIG. 17. The value of K is as follows for different angles: A = K = 20 .046 40 .139 60 | 8( .364 .7 ) | 90 4 .98 100 1.26 120 1.86 For bends, H = .0155 F 2 =H=J 154 HYDRA ULICS. Values of L with various ratios of the radius of bend to radius of bore: When - *. .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 In circular section L In rectangular L .131 .124 .138 .135 .158 .18 .206 .25 .294 .4 .44 .64 .66 1.01 .98 1.55 1.4 2.3 2.0 3.2 RESERVOIRS. Reservoir Site. In selecting a site for a reservoir, the following points should be observed: 1. A proper elevation above the point at which the water is required. 2. The total supply available, including observations as to the rainfall and snowfall. . 3. The formation and character of the ground, with reference to the amount of absorption and evaporation. The most desirable formation of ground for a reservoir site is one of com- pact rock, like granite, gneiss, or slate; porous rocks, like sandstones and limestones, are not so desirable. Steep bare slopes are best for the country surrounding a reservoir, as the water escapes from them quickly. The presence of vegetation above the reservoir causes a considerable amount of absorption; but, at the same time, the rainfall is usually greater in a region covered with vegetation than in a barren region, hence the streams have a more uniform flow. A reservoir must be made large enough to hold a supply capable of meeting the maximum demand. The area of a reservoir should be determined, and a table made showing its contents for every foot in depth, so that the amount of water available can always be known. Dams are used for retaining water in reservoirs, for diverting streams in placer mining, and for storing debris coming from placer mines in canons or ravines. Foundations for dams must be solid to prevent settling, and water-tight to prevent leakage under the base of the dam. Whenever possible, the founda- tion should be solid rock. Gravel is better than earth, but when gravel is employed it will be necessary to drive sheet piling under the upper toe of the dam, to prevent water from seeping through the formation under the dam. Vegetable soil should be avoided, and all porous material, such as sand, gravel, etc. should be stripped off until hard pan or solid rock is reached. In case springs occur in the area covered by the foundation of the dam, it will be necessary to trace them up, and if they originate on the upper side to confine their flow to that side of the dam, so that they will have no tendency to ultimately become passageways for water from the upper face to the lower face of the dam, thus providing holes which may ultimately destroy the entire foundation of the structure. Wooden Dams. Wooden dams are constructed of round, sawed, or hewn logs. The timbers are usually at least 1 ft. square, or, if round, from 18 to 24 in. in diameter. A series of cribs from 8 to 10 ft. square are constructed by building up the logs log-house fashion and securing them together with treenails. The individual cribs are secured to one another with treenails or by means of bolts. The cribs are usually filled with loose rock to keep them in place, and in many cases are secured to the foundation by means of bolts. A layer of planking on the upper face of the dam makes it water- tight, and if the spillway is over the crest of the dam it will be necessary to plank the top of the cribs, and, in most cases, to provide an apron for the water to fall on. The apron may be set on small cribs, or on timbers pro- jecting from the cribs of the dam itself. Abutments and Discharge Gates. Abutments are structures at the ends of a dam. They may be constructed from timber, masonry, or dry stonework. If possible, abutments should have a curved outline, and should be so placed that there is no possibility of the water overflowing them, or getting behind them during floods. If the regular discharge from a dam takes place from the main face, the gates may be arranged in connection with one of the abutments, or by means of a tunnel and culvert through the dam. In DAMS. 155 either case, some structure should be constructed above the outlet so as to prevent driftwood, brush, and other material from stopping the discharge gates. When the discharge gates are placed at one side of the dam, they are usually arranged outside of the regular abutment, between it and another special abutment, the discharge being through a series of gates into a flume, ditch, or pipe. Spillways or Waste Ways. These are openings provided in a dam for the discharge of water during floods or freshets, or for the discharge of a portion not being used at any time. The spillway may be over the crest of the dam, or, where the topography favors such a construction, the main dam may be of sufficient height to prevent water from ever passing its crest, the spillway being arranged at another outlet over the lower dam. Waste ways, proper, are openings through the dam, and are intended for the discharge of the large quantities of water that come down during freshets or floods. In the case of timber dams, the waste ways are usually surrounded by heavy cribs, and have an area of from 40 to 50 sq. ft. each. There are two general forms of construction employed for waste ways. One consists of a compara- tively narrow opening in the dam, extending to a considerable depth (8 or S^^SM^I ^ . ;v r: ^~ n '-f-3~ ~i ^- ^i& v : "Sir : :7 ?#$$&& :./? ;:<* -j v . .'.4. ' -Ay, ': ';.. :'/: :} '.": '....?:'...: ; J'.'| '. l< \- ' ''.' : .**'::':'L''::. : .''' '''? \ feagS^y^tfe&gjgfe^ FIG. 18. 10 ft.). Water is allowed to discharge through this during flood time, but when it is desired to stop, the flow planks are placed across the up-stream face of the opening in such a manner as to close it. The opening, which is usually not over 3 or 4 ft. wide, is provided with guides on the upper face of the dam, and between which the planks are slid down, the individual pieces of planking being at least 1 ft. longer than the opening that they are to cover. The other device frequently used consists in providing the waste way, at one side of the regular spillway, with a crest 2 or 3 ft. lower than the regular spillway. The crest of this waste way is composed of heavy timber, and 4 or 5 ft. above there is arranged a parallel timber, the space between the two being closed by what are called flash boards. These are made from pieces of 1" or 3" plank, 6 or 8 in. wide. The planks are placed against both timbers so as to close the space. The individual planks are made long enough so that they extend from 1 to 2 ft. above the upper timber, and through the upper end of each plank is bored a hole through which a piece of rope is passed and a knot tied in the end of the rope. These ropes are secured by staples to the upper timber. When it becomes necessary to open the waste way, men go under with peevies, cant hooks, or pinch bars, and pry up the planks in such a way as to draw the longer end out of contact with the lower timber, when the force of the water will immediately carry the plank down the stream as far as the rope will allow it to go. After the first plank has been loosened, the succeeding ones can be pulled up with comparative ease, and two men can open a 25' or 30' section of waste way in a very few minutes. The ropes keep the plank from being lost, and the opening can be closed again by passing the plank down into the water to one side of the opening and moving them into the current. Some skill is required, both in opening and closing the waste ways. Stone Dams. Where cement or lime is expensive, and suitable rubble stone can be obtained, dams are frequently constructed without the use of mortar. The upper and lower faces of the dam should be of hammer- dressed stone, carefully bonded, and the stones in the lower face of the dam are sometimes anchored by means of bolts. The dam can be made water- tight by means of a skin of planking on the upper face. In case water should ever pass over the crest of such a dam, much of it would settle through the openings in the stone into the interior of the dam, and this would subject the stones in the lower portion of the face to a hydrostatic 156 HYDRA ULICS. pressure, provided an opening was not made for the escape of such water. For this reason, culverts or openings should be made through the lower portion of the dam, to discharge any such water. When such dams as this are constructed, the regular spillway is not placed over the face of the dam, but at some other point, and usually over a timber dam. Earth Dams. Earth dams are used for reservoirs of moderate height. They should be at least 10 ft. wide on top, and a height of more than 60 ft. is unusual. When the material of which the dam is composed is not water- tight, as, for instance, gravel, sand, etc., it is sometimes necessary to con- struct a puddle wall of clay in the center of the regular dam. This consists of a narrow dam of clay mixed with a certain proportion of sand. The puddle wall should not be less than from 6 to 8 ft. thick at the top of the dam, and should be given a slight batter on each side. It is constructed during the building of the dam, and should be protected from contact with the water by a considerable thickness of earth on the upper face. The upper face of an earthen dam is frequently protected by means of plank or a pavement of stone. The lower face is frequently protected by means of sod, or sod and willow trees. Sometimes earth dams are provided with a masonry core in place of the puddle wall, to render them water-tight. This consists of a masonry wall carried to an impervious stratum, and up through the center of the dam. The masonry core should never be less than 2 or 3 ft. thick at the top, and should be given a batter of at least lOft on each side. At the regular water level, earthen dams are liable to have a small bench or shelf formed, and on this account, during the construction, such a bench or shelf is sometimes built into the earth dam. Fig. 18 shows a dam with a masonry core, with the upper face covered with rubble and the lower face covered with grass. Debris Dams. These are dams or obstructions placed across the bed of streams to hold back tailings from mines, and to prevent damage to the valleys below. They are made of stone, timber, or brush. No attempt is made to render the debris dam water-tight, the only object being that it- should retard the flow of the stream and give it a greater breadth of dis- charge, so that the water naturally drops and deposits the sediment that it is carrying. The sediment soon silts or fills up against the face of the dam, the area above the dam becoming a flat expanse or plain over which the water finds its way to the dam. When these dams are constructed of stone, the individual stones on the lower face and crest of the dam should be so large that the current will be unable to displace them, while the upper face and core of the dam may be composed of finer material. In case a breach should occur in the debris dam, it will not necessarily endanger the region farther down the stream, as is the case when a break occurs in a water dam. The reason for this is that the d6bris dam is not made water- tight, and hence there is never much pressure against it, or a large volume of water held back that can rush suddenly down the stream should a break occur. The only result of the break would be that more or less of the gravel behind the dam would be washed through the breach. Wing Dams. Wing dams are used for turning streams from their courses, so as to expose all or a portion of the bed for placer mining or other pur- poses. They are usually of a temporary nature, and are constructed of brush and stones, light cribs filled with stones, and of large stones, or timber. Sometimes the course of a stream is turned by an obstruction made of sand bags, and a wing dam constructed behind this of frames of timber, the inter- vening space being filled with gravel or earth, and, in some cases, the timber being covered with stone, and the surface riprapped so that if the flow ever comes over the top of the structure it will not destroy it. Masonry Dams. When high masonry dams are to be employed they should be designed by a competent hydraulic engineer. Masonry dams are not, as a rule, used for hydraulic mining, owing to the fact that the length of time during which the dam is required rarely warrants the expense of the con- struction of a masonry dam. WATER-POWER. The Theoretical Efficiency of the Water-Power. The gross power of a fall of water is the product of the weight of water discharged in a unit of time, and the total head or difference in elevation of the surface of the water, above and below the fall. The term head, used in connection with waterwheels, WATER-POWER. 157 is the difference in height between the surface of water in the penstock and that in the tailrace, when the wheel is running. If Q = cubic feet of water discharged per minute, W = weight of a cubic foot of water = 62.5 lb., and H = total head in feet, then WO H = gross power in foot-pounds per minute, WQ II aild oonnn = the horsepower. oo,UUU Substituting the value for TF, we have = .00189 Q H, as the horsepower of a fall. o 00,000 The total power can never be utilized by any form of motor, owing to the fact that there is a loss of head, both at the entrance to, and exit from, the wheel, and there are also losses of energy, due to friction of the water in passing through the wheel. The ratio of the power developed by the wheel to the gross power of the fall, is the efficiency of the wheel. A head of water can be made use of in any one of the following ways: 1. By its weight, as in the water balance, or overshot wheel. 2. By its pressure, as in the hydraulic engine, hydraulic presses, cranes, etc., or in a turbine water wheel. 3. By its impulse, as in the undershot and impulse wheels, such as Peltons, etc. 4. By a combination of the above. The Horsepower of a Running Stream. The gross horsepower, as seen above, is H. P. 1^ = . 00189^, in which Q is the quantity in cubic 'feet per minute actually impinging oh the float or bucket, and H the theoretical head added to the velocity of the stream, or 77" = ^ = 2g 64.4' in which v is the velocity in feet per second. For example, if the floats of an undershot waterwheel were 2 ft. X 10 ft., and the stream had a velocity of 3 ft. per second, i. e., v = 3, we would have H = ^T = .139, and Q = 2X10X3X60 = 3,600 cu. ft. per min. From this, H. P. = 3,600 X .139 X .00189 = .945 H. P., or a gross horse- power for practically .05 sq. ft. of wheel surface; but, under ordinary circum- stances, it would be impossible to attain more than 40$ of this, or practically .02 horsepower per sq. ft. of surface, which would require 50 sq. ft. of float surface to each horsepower furnished. Current Motors. A current motor fully utilizes the energy of a stream only when it is so arranged that it can take all of the velocity out of the water; that is, when the water leaves the floats or vanes with no velocity. It is evident that in practice we can never even obtain a close approximation to these results, and hence only a small fraction of the energy of a running stream can be utilized by the current motor. Current motors are frequently used to obtain small amounts of power from a large stream, as, for instance, for pumping a limited amount of water for irrigation. For this work, an ordinary undershot wheel having radial paddles is usually employed. At one end of the wheel a series of small buckets are placed, and so arranged that each bucket will dip up water at the bottom of the wheel and discharge it into the launder, near the top of the wheel. The shape of the buckets should be such that only the amount of water which the bucket is capable of carrying to the launder will be dipped up, for, if the bucket is constantly slopping or pouring water as it ascends, a large amount of useless work is performed in raising this extra water and then pouring it out again, as only the portion that reaches the launder can be of any service. Current motors are not practicable for furnishing large amounts of power. UTILIZING THE POWER OF A WATERFALL. The power of a waterfall may be utilized by a number of different styles of motors, but each has certain advantages. Breast and Undershot Wheels. When the head is low (not over 5 or 6 ft.), breast or undershot wheels are frequently employed. If these are properly 158 HYDRA ULICS. proportioned, it is possible to realize from 50$ to 70$ of the theoretical power of the fall, but the wheels are large and cumbersome compared with the duty they perform, and not often installed at present, especially near manufac- turing centers. Overshot Wheels. For falls up to 40 or 50 ft., overshot wheels are very commonly employed, and they have been used for even greater heads than this. The overshot wheel derives its power both from the impulse of the water entering the buckets, and from the weight of the water as it descends on one side of the wheel in the buckets. The latter factor is by far the more important of the two. When properly proportioned, overshot wheels may realize from 70$ to 90$ of the power of the waterfall, but they are large and cumbersome compared with the power that they give, and are not often installed except in isolated regions, where they are made from timber by local mechanics. Impulse Wheels. For heads varying from 50 ft. up, impulse wheels are very largely used. These are also sometimes called hurdy gurdies, and are usually of the Pelton type, consisting of a wheel provided with buckets, so arranged about its periphery that they receive an impinging jet of water and turn it back upon itself, discharging it with practically no velocity, and con- verting practically all the energy into useful work. The efficiency of these wheels varies from 85$ to 90$ under favorable circumstances. This style of wheel is especially adapted for very high heads and comparatively small amounts of water. There are a number of instances where wheels are operating under a head of as much as 2,000 ft. This style of impulse wheel is an American development; in Europe, a style of impulse turbine has been used to some extent, but has not found very much favor in the United States. Turbines. Turbines or reaction wheels are very largely employed, espe- cially for moderate heads. When properly designed to fit the working conditions, they can be used for heads varying from 4 or 5 ft. up to consider- ably over 100 ft., and when properly placed are capable of utilizing the entire head, a factor that gives them a decided advantage over any other style of waterwheel. Turbines are capable of returning 85$ to 90$ of the theoretical energy as useful power, and are largely used, especially where a considerable volume of water at a low head, or a smaller volume at a moderate head, can be obtained. PUMP MACHINERY. Pumps are employed for un watering mines, handling water at placer mines, irrigation, water-supply systems, boiler feeds, etc. For unwatering mines, two general systems of pumping are employed. (1) The pump is placed in the mine and is operated by a motor on the sur- face, the power being transmitted through a line of moVing rods. (2) Both the motor and pump are placed in the mine, the motor being an engine driven by steam, compressed air, hydraulic motor, or an electric motor. Cornish Pumps* Any method of operating pumps by rods is commonly called a Cornish system. Formerly, the motor in the Cornish system con- sisted of a steam engine placed over the shaft head, which operated the pump by a direct line of rods. With this arrangement, there is great danger of accident to the engine from the settling of the ground around the shaft, or from fire in the shaft; also, the position of the motor renders access to the shaft difficult. To overcome these objections, the engine is frequently placed at one side of the shaft, and the rods operated by a bob; this has. become the common practice, and is generally called the Cornish rig. The engine employed in ,the most modern plants is generally of the Corliss type, and is provided with a governor to guard against the possibility of the engine running away, in case the rods should break. This system requires no steam line down the shaft, and is independent of the depth of water in the mine, so that the pump is not stopped by the drowning of a mine, but the moving rods are a great inconvenience in the shaft, and they absorb a great amount of power by friction. Simple and Duplex Pumps. In the simple pump, a steam cylinder is con- nected directly to a water cylinder, and the steam valves are operated by tappets. Such a pump is more or less dependent on inertia at certain points of the stroke to insure the motion of the valves, hence will not start from P UMP MA CIIINER Y. 159 FIG. 19. any place, but is liable to become stalled at times. In the duplex pump, two steam cylinders and two water cylinders are arranged side by side, and the valves so placed that when one piston is at mid-stroke it throws the steam valve for the other cylinder, etc. With this arrangement, the Sump will start from any point, and can never be stalled for lack of steam, ue to the position of the valves. Ordinarily, duplex pumps are to be pre- ferred for mine work. The packing for the w r ater piston of a pump maybe either inside or outside. Any form of packing that is inside the cylinder, either upon a moving piston or surrounding the ram, and so situated that any wear will allow communi- cation between the oppo- site ends of the cylinder, is called inside packing. It may consist simply of piston rings about the pis- ton, as in the case of an ordinary steam-engine pis- ton G, Fig. 19, or stationary rings may be employed about the outside of a mov- ing ram or long piston P. In either case, the cylinder heads have to be removed before the condition of the packing can be inspected, and any leak does not make itself visible. When outside packing is employed, separate rams are used in opposite ends of the cylinder, there being no internal communication between the chambers in which the rams work. The rams are packed by ordinary outside stuffingboxes and glands. The arrangement consists practically of two single-acting pumps arranged to work alternately, so that one is forcing water while the other is drawing water. Fig. 20 shows a horizontal section of a cylinder so arranged, together with the yoke rods that operate the ram at the farther end of the cylinder. As a rule, inside-packed pumps should be avoided in mines, on account of the fact that acid or gritty waters are liable to cut the packing, and make the pumps leak in a very short time. For dipping work in single stopes or entries, small single or duplex outside-packed pumps may be employed. It is generally best to operate such pumps by compressed air, for the exhaust will then be beneficial to the mine air. If steam is employed, it is frequently necessary to introduce a trap and remove entrailed water from the steam before it enters the pump, and to dispose of the exhaust by piping it out or condensing it. Such isolated steam pumps are about the most wasteful form of steam-driven motor in existence. For sinking, center-packed single or duplex pumps are usually employed, the duplex style being the better. For station work, where much water is to be handled, large compound, or triple-expansion, condensing, duplex pump- ing engines are employed. They may, or may not, be provided with cranks and a flywheel. Engineers differ greatly upon this point, and, as a rule, for very high lifts and great pressures, the flywheel is employed. The main points in consideration are the first cost of the pump, and the amount that will be saved by using the more expensive engine. The large flywheel pumping engines are several times as expensive as the direct- acting steam pumps, and the question is as to whether their greater efficiency will more than coun- terbalance the in- creased outlay. Most engineers favor fly- wheel pumps for handling large vol- umes of water where the work is approxi- FIG. 20. mately constant, and direct-acting pumps, without flywheels or cranks, for handling small amounts of water, or for very irregular service, owing to the fact that if the flywheel pump is driven below its normal speed it does not govern properly, nor work economically. Until recently, water was removed from mines in lifts of about 300 to 350 ft., pumps being placed at stations along the shaft. While a series of station pumps are still employed, in some cases they are 160 PUMP MACHINERY. generally intended to take care of water coming into the shaft, or workings at or near their level, and are not employed for handling water in successive stages or lifts. For handling the bulk of the water from the bottom of the shaft, large pumping enplnes are employed that frequently force the water to the surface from depths of over 1,000 ft. These high-duty pumping plants, when near the shaft and operated by steam with a condenser, frequently show a very high efficiency. When air is employed to operate such a plant, a much higher efficiency can be obtained if the compressed air is heated before using in the high-pressure cylinder, and during its passage from the high-pressure to the low-pressure cylinder. This has been very successfully accomplished by means of a steam reheater, the small amount of steam necessary being conveyed to the station in the small pipe, and entirely con- densed in the reheater, from which it is trapped as water. The duty of steam pumps is approximately as follows: For small-sized steam pumps, the steam consumption is from 130 to 200 Ib. per horsepower per hour, when operating in the workings of a mine at some distance from the boiler. For larger sizes of simple steam pumps, the consumption runs from 80 to 130 Ib. of steam per horsepower per hour. Compound-condensing pumps, such as are commonly used as station pumps, consume from 40 to 70 Ib. of steam per horsepower per hour. Triple-expansion, condensing, high-class pumping engines consume from 24 to 26 Ib. per horsepower per iiour. The Cornish pump consumes varied amounts of steam in proportion to the water delivered, depending largely on the friction of the gearing, bobs, rods, etc., but its efficiency is usually considerably below the best class of pumping engines. Speed of Water Through Valves, Pipes, and Pump Passages. The speed of water through the valves and passages of a pump should not exceed 250 ft. per minute, and care should be taken to see that the passages are not too abruptly deflected. The flow of water through the discharge pipe should not exceed 500 ft. per minute, but for single-cylindered pumps it is usually figured at between 250 and 400 ft. per minute. In the case of very large pumps, greater velocities may be allowed. The suction pipe for the pump should be larger than the discharge pipe. Ordinarily, the suction pipe for a pump should not exceed 250 ft. in length, and should not contain more than two elbows. The following formula gives the diameter of the suction and discharge pipes of a pump: G = U.S. gallons per minute; d ' = diameter of suction pipe in inches; d"= diameter of discharge pipe in inches; v' = velocity of water in feet per second in the suction pipe = from .50v"to .75 v"; v" == velocity of water in feet per second in the discharge pipe. RATIO OF STEAM AND WATER CYLINDERS IN A DIRECT-ACTING PUMP. A = area of steam cylinder; H = head of water = 2.309 p; D = diameter of steam cylinder; a = area of pump cylinder; P = steam pressure in pounds per d = diameter of pump cylinder; square inch; p = pressure per square inch, corresponding to the head H = .433 H; work done in pump cylinder E = efficiency of pump = work done injte^m "cylinder 1 A _ W_. _ IEP A p .433 H TEF d = D \-jT' a = E~P = ~EP-' - EAP . P - a P- p ' EA' CAPACITY AND HORSEPOWER OF PUMPS. 161 If E = 75$, then H = 1.732 P X ^. is commonly taken at from .7 to .8 for ordinary direct-acting pumps. For the highest class of pumping engines it may amount to .9. The steam pressure P is the mean effective pressure, according to the indicator dia* gram; the pressure p is the mean total pressure acting on the pump plunger or piston, including the suction, as would be shown by the indicator dia- gram of the water cylinder. The pressure on the pump cylinder is frequently much greater than that due to the height of the lift, on account of the friction in the valves and passages, which increases rapidly with the velocity of the flow. Piston Speed of Pumps. For small pumps, it is customary to assume a speed of 100 ft. per minute, but, in the case of very small short-stroke pumps, this is too high, owing to the fact that the rapid reverses make the flow through the valves and change in the direction of the current too frequent. When the stroke of the pump is somewhat longer (18 in. or more), higher speeds can be employed, and in the case of large pumping engines having long strokes, speeds of as much as 200 to 250 ft. per minute are successfully used without jar or hammer. Boiler Feed-Pumps. In practice, it has been shown that a piston speed greater than 100 ft. per minute results in excessive wear and tear on a boiler feed-pump, especially when the water is warm. This is due to the fact that vapor forms in the cylinders, and results in a water hammer. In determining the proper size of a pump for feeding a steam boiler, not only the steam employed in running the engine, but that necessary for the pumps, heating system, etc. must be taken into consideration. THEORETICAL CAPACITY OF PUMPS AND THE HORSEPOWER REQUIRED TO RAISE WATER. Let Q = cubic feet of water per minute; G = U. S. gallons per minute; G f = U. S. gallons per hour; d = diameter of cylinder in inches; I = stroke of piston in inches; N = number single strokes per minute; v = speed of piston in feet per minute; W = weight moved in pounds per minute; P = pressure in pounds per square feet = 62.5 X H ; p = pressure in pounds per square inch = .433 X H' H = height of lift in feet; H. P. = horsepower. Then, Q = . = .0004545 JVef-/. G = ~ . = .0034 NcPl. G' = The diameter of piston requiredjbr a given capacity per minute will be l* - 17 - 15 Vi- or d r 13 The actual capacity of a pump will vary from 60$ to 95$ of the theoretical capacity, depending on the tightness of the piston, valves, suction pipe, etc. _Q P_ = QHX144 X.433 Q1T _Gp_ 33,000 33,000 529.2 1,714.5* The actual horsepower required will be considerably greater than the theoretical, on account of the friction in the pump; hence, at least 20$ should be added to the power for friction and usually about 50$ more is added to cover leaks, etc., so that the actual horsepower required by the pump is about 70$ more than the theoretical. EXAMPLE 1. If it is desired to find the size of a pump that will throw 30 gal. of water per minute up 125 ft., from the bottom of a pit or prospect shaft to the station pump at the main shaft, it may be accomplished as follows: An allowance of probably 25$ should be made with a small pump of this character, to overcome slippage or leaking through the valves, past the piston, 162 PUMP MACHINERY. etc., and hence we will call the total amount of water to be handled 40 gal. per minute. The formula for the diameter of piston is Assuming that v = 100 ft. per minute, we have d = 4.95]/^4 = 4.95 X .63 = 3.13. In practice, a 3F' pump would probably be employed. EXAMPLE 2. If it is desired to find the approximate horsepower necessary to lift 30 gal. per minute in the above example, without determining the size of the pump, it can be done as follows: - m In order to cover leakage through valves, friction, etc., an addition of at least 75$ should be made to a very small pump like this, and so we would count on If H. P. Depth of Suction. Theoretically, a perfect pump will raise water to a height of nearly 34 ft. at the sea level; but, owing to the fact that a perfect vacuum can never be attained with the pump, that the water always con- tains more or less air, and that more or less watery vapor will form below the piston, it is never possible to reach this theoretical limit, and, in practice, it is not possible to draw water much, if any, over 30 ft. at the sea level, even when the water is cold. Warm water cannot be lifted as high as cold water, owing to the fact that a larger amount of watery vapor forms. With boiler feed-pumps handling hot water, the water should flow to the pumps by gravity. Amount of Water Raised by a Single-Acting Lift Pump. In the case of all pumps having a piston or ram, the amount of water lifted is usually con- siderably less than the piston displacement, owing to the leakage through the valves, etc., but with single-acting lift pumps, having bucket plungers with a clack valve in the plunger, the amount lifted may actually exceed the plunger displacement, that is, the volume of water may actually be greater than the length of the stroke multiplied by the number of strokes, for, during the up stroke, the water both above and below the piston is set in motion, and during the down stroke, the inertia of the water actually carries more water through the valve than would pass through it on account of the space passed through. This increases as the speed or number of strokes increases. Pump Valves. As a rule, a large number of small valves having a compar- atively small opening are preferable to a small number of large valves with a greater opening, and most modern pumps are built upon these lines. A small valve represents a proportionately larger, surface of discharge with the same lift than the large valve, hence whatever the total area of the valve- seat opening, its full contents can be discharged with less lift through numerous small valves than through one large valve. Cornish pumps generally have one large metal valve. Power Pumps. Where comparatively small amounts of water are to be handled, and power is available, belt-driven power pumps are very much more efficient than small steam pumps. Electrically Driven Power Pumps. Where water is to be delivered from isolated workings to the sumps for the large station pumps, electrically driven power pumps are far more efficient than steam pumps. In some cases it is probably best to equip the entire mine with electric pumps, both in the isolated workings and at the stations, on account of the fact that they can be driven by a high-class compound-condensing engine on the surface, directly connected to a generator, and furnishing electricity through con- ductors to the various pumps. The total efficiency of a series of small electric pumps that aggregate a sufficient amount of power to enable this arrangement to be used, is very much higher than the total efficiency of a number of small isolated steam or compressed-air pumps introduced into the workings. With compound- condensing engines upon the surface, operating electric pumps underground, the steam consumption per pump horsepower per hour, for the smaller sizes, would only be about 40 Ib. per horsepower per hour; for medium-sized electric pumps, about 30 Ib. of steam per hour, and larger sizes from 20 to 30 Ib. per horsepower per hour. It will be seen from these figures that for PUMP AND WATER MEMORANDA. 163 pumping from isolated portions of the mine the electric pump is much more efficient than the steam pump, and owing to the fact that the current can frequently be obtained from the lines operating the underground haulage system, furnishing light, etc., it is evident that this system of pumping has a great future before it in connection with mining. The following table gives the gallons per minute delivered from various sized pumps operating at different piston speeds: PUMP AND WATER MEMORANDA. ~~ ~~ cocoppppppppppppppppppppppppppppppppp COrHOOOOOOOOOOOO O O O O O'O O O O O O O O O O O O O O O O (NOpppppppppppppppppppppppppppOpp p~~p * 10 50 -O 1> 00 05 rH CNpppppppppppppppppppppppppppOppppp O iC t5 O C^ i i Tt< Oi LC i-C O CC C 1^ <"2 :'. 7 I 7_1 TJ '~" ; ^ " ~f ^ ^- ^' ^ O5 "^ OS iC T-H 1^- Tf OQ O S CC t- OO t^ ''''''' pppppppppppppp O O O O O O > QO ^ rji O O 5 1> rH O5 rH l> O !>' TJ? CO O Tf CO GO Tf? O (N i idCOCOiOOt>>OOOiOT ICOTf^iOt-G Dpppppppppppppp rH CO '-C O "^ t- O CC jp C sssiii'iisiiii ^ ^ i: i: ^ -i^ -iS: -i^ -i^ -iv -!i -ii: ^i^ -w^ -i^ ^ : -i5: - r^ fi 'M co co -t 1 ~f uf >c ^o cc i^ t-- oo ac o o o - OI^l^COOOOiOirHrHiHrHi^rHrHiHiHi^rHrHiHTHrHrHrHrHrHrHC^C 1 gal. - 231 cu. in. - .13368 cu. ft. 1 gal. of water at 39.2 = 8.33888 Ib. 1 cu. ft. of water = 7.48052 gal., and weighs 62.423 Ib. 164 PUMP MACHINERY. MISCELLANEOUS FORMS OF WATER ELEVATORS. Jet Pump. In this form, the energy of the jet of water is utilized for raising a larger volume through a small distance, or a mixture of water and solid material through a short distance. Vacuum Pump. The pulsometer, which is the most important representa- tive of this class, consists of two chambers in a large casting, with suitable automatic valves arranged at the top and bottom of the chambers., Steam is introduced into one of the chambers, then the valve at the top closed. This steam will condense, forming a vacuum that draws water from the suction into the chamber. When the chamber is filled with water, steam is again introduced and forces the water out through the discharge pipe. The operation is then repeated, more water being drawn in by the condensation of the steam. The two chambers work alternately, one being engaged in drawing water in while the other forces it out. The total steam efficiency of this form of pump is small, though it may actually be above that of small steam pumps employed in isolated portions of a mine. The advantages are that the pump possesses no intricate mechanism, no reciprocating parts, requires no lubrication, and is not injured by gritty or acid materials. On this account it may be employed for pumping water in concentration works, coal-washing plants, and similar places where the water is liable to contain grit or dirt. Air-Lift Pumps. By introducing compressed air at the bottom of a pipe submerged in any liquid, the air in the pipe rises as bubbles, and so reduces the specific gravity of the fluid in the pipe. This causes the fluid in the pipe to rise above the level of that surrounding the pipe. The difference in specific gravity can never be great, and hence the fluid can never be elevated to any considerable height without having the lower end immersed to a correspondingly great depth. On this account it is frequently necessary to drill a well considerably below the water-bearing strata, so as to obtain the proper ratio between the submerged portion of the pipe and the height to which the water is to be lifted. Some advantages of this form of pump are that there are no moving parts, no lubrication is required, and gritty material does not interfere with the operation. If the pump is constructed of suitable material, it may be employed for handling acids or solutions in electrolytic or chemical works. This style of pump is also quite extensively employed for pumping water from Artesian wells. It has not been successful as a mine pump, owing to the ratio between the part immersed and the lift. Centrifugal Pumps. The height of lift depends on the tangential velocity of the revolving disk of pump and the quantity of water discharged, and is proportional to the area of the discharge orifices at the circumference of the disk. The most efficient total lift for the centrifugal pump is, approximately, 17 ft., and for small lifts the centrifugal pump is much more efficient than any style of piston pump. For a given lift, the total efficiency of a centrif- ugal pump increases with the size of the pump. Centrifugal pumps are always designated by the size of their outlet, as, for instance, a 2" or 4" pump, meaning with a 2" or 4" discharge pipe. Centrifugal pumps are not at all effective for dealing with great heads, and hence have never come into competition with piston pumps for this class of work. For lifting large volumes of water against a low head, as in irrigation or drainage problems, they are remarkably efficient. Under the most favorable circum- stances, the efficiency of the centrifugal pump may be practically 70$; that is, the pump may do an amount of work upon the water that is theoretically equal to 70$ of the power furnished to the pump. Pumping engines work- ing against high heads, and operated by the most improved class of engines., may attain an efficiency of practically 85$. Centrifugal Pump as a Dredge. When dredging is done by means of centrif- ugal pumps, a greater amount of power is necessary, and the pump has to be run at a greater speed than when pumping water, owing to the fact that the fluid being handled has a greater density than water. When dealing with fine sand, as much as 50$ of the bulk of the material handled may be sand, though, as a rule, the amount of solid material in the water dredged only runs from 30$ to 35$ of the total. Water Buckets. Where only a limited amount of water collects in the mine workings, it is frequently removed by means of a special water bucket or water car during the hours that the hoisting engine would otherwise be "idle. Where very large amounts of water are to be removed, it has also SINKING PUMPS. 165 been found economical to remove them by means of special water buckets. This is especially true in the case of deep shafts. One of the best illustrations of this class of work is the Gilberton water shaft, which has been equipped at the Gilberton Colliery of the Phila- delphia and Reading Coal & Iron Co. The collieries draining to this shaft require the removal of 6,000,000 gal. of water per 24 hours during the wet season, and this has to be lifted from a depth of 1,100 ft. In order to accom- plish the work by means of steam pumps, it required a number of pump stations in different parts of the mine, each of which had to be attended by a pumpman, and a large number of steam lines were required in the mine. In order to remove the danger of fire caused by these steam lines, and to dispense with the large amount of labor otherwise necessary, it was decided to hoist the water, and a shaft 22 ft. X 26 ft. 8 in. outside of timbers, was sunk. This shaft contains two compartments 7 ft. X 7 ft., in which the water buckets are operated, and two compartments 7 ft. X 11 ft. 8 in. that are utilized for cages to lower men, timber, and other supplies. The water tanks employed in the special water compartments are 5 ft. 6 in. in diameter, and 14 ft. long. They are provided with a special device sliding on regular cage guides, and empty themselves automatically at the surface by means of a trip or sliding valve. Two pairs of direct-acting hoisting engines, with 45" X 60" cylinders, operating drums 14 ft. 8 in. in diameter by 15 ft. face, are employed. These operate the water buckets in cages by means of 2" crucible steel ropes, at 50 revolutions per minute, which is equivalent to a piston speed of 500 ft. per minute. The drums will hoist two tanks of 2,400 gal. per minute. This gives an output of 7,000,000 gal. per 24 hours. By slightly increasing the speed of the engine this amount can be increased HK, which is 25/ c in excess of the calculated maximum demand on the shaft. The cages in the cage compartments are so arranged that they can be discon- nected, and water buckets substituted for them. This would be a total output of over 14,000,000 gal. per 24 hours at the normal speed of the engine. One great advantage of this style of pumping plant is that there is absolutely no fear of drowning the pumps. Some years ago the Hamilton iron mine, in Michigan, was drowned by a sudden inrush of water that drove the pumpmen from the pumps. In order to remove this large volume of water, special bailing buckets were v substituted for the ordinary mine skips. These .bailing buckets ran on the inclined skip road, and un watered the mine in a remarkably short time. Sinking Pumps. Sinking pumps may be either single or duplex in their action, and may be inside or outside packed. Outside-packed single-acting pumps are in many ways preferable, owing to the fact that they are less liable to get out of order. One requisite of any sinking pump is that it should have as few exposed parts as possible, and that these parts should be so placed that they will be protected from injury by blasting to as great an extent as possible. Sinking pumps are usually provided with a telescopic section in the suction pipe, and sometimes also in the discharge pipe, so that they can be moved down several feet without having to break the joints of the piping. Pumps for Acid Waters. Where mine waters are acid in their nature, brass or brass-lined pumps are usually employed, and in some cases even wooden pumps have been used, as, for instance, in the Swedish copper mines, though this prac- tice is disappearing in favor of the use of brass or copper linings. The pipes for such pumps should be of brass or copper tubing, or should be lined with some substance that will not be affected by the acid of the water. Sometimes wooden linings are em- ployed, placed as shown in Figs. 21 and 22, Fig. 21 being a section of the pipe with the lining complete, and Fig. 22 a cross-section of one of the individual boards used in the lining. These are usually made of pine FIG. 21. FIG. 22. about f in. thick, and are grooved on each end as shown. They are sprung in so as to complete a circle on the inside of the pipe, and then long, thin, wooden keys driven into the grooves. When the water is allowed to go into the pipes, the linings swell and make all joints perfectly tight. Elbows and other crooked sections are lined with sheet lead beaten in with a mallet. 166 FUELS. FUELS. The value of any fuel is measured by the number of heat units that its combustion will generate, a unit of heat being the amount required to heat 1 Ib. of water 1 F. The fuels used in generating steam are composed mainly of carbon and hydrogen, ash, and moisture, with sometimes small quantities of other substances not materially affecting their value. Combustible is that portion which will burn; the ash or residue varies from 20 to 36$ in different fuels. The following table gives, for the more common combustibles, the air required for complete combustion, the temperature with different proportions of air, the theoretical value, and the highest attainable value under a steam boiler, assuming that the gases pass off at 320, the temperature of steam at 75 Ib. pressure, and the incoming draft to be at 60; also, that with chimney draft twice and with blast only the theoretical amount of air is required for combustion. TABLE OP COMBUSTIBLES. 11 Temperature of Combustion. Theoretical Value. Highest Attainable Value Un- der Boiler. A S * , , As | & ' * . g^ O *H 5 H 2 1*4 51 1 11 Kind of Combustible. EC m 2 I"* ys o> >> ft 0) O it HH O 03 5t ill > 8^0- 'ounds p< of Comb th H Tim 3al Suppl ith Twic( cal Supp th Three itical Sui mdsofW 1 per P( Combu II ^3 ith Chim to O oj m ?" ' SI 1 S-2'S % m Hydrogen 36.00 5,750 3,860 2.860 1,940 62,032 64.20 Petroleum 15.43 5,050 3,515 2,710 1,850 21,000 21.74 18.55 19.90 (Charcoal ) Carbon -j Coke > 12.13 4,580 3,215 2,440 1,650 14,500 15.00 13.30 14.14 (Anthracite J Coal, Cumberland, 12.06 4,900 3,360 2,550 1,730 15,370 15.90 14.28 15.06 Coal, Coking bituminous 11.73 5,140 3,520 2,680 1,810 15,837 16.00 14.45 15.19 Coal, Cannel 11.80 4,850 3,330 2,540 1,720 15,080 15.60 14.01 14.76 Coal, Lignite 9.30 4,600 3 210 2490 1,670 11,745 12.15 10.78 11.46 Peat, Kiln dried Peat, Air dried, 25^ water 7.68 5.76 4,470 4,000 3,140 2,820 2,420 2,240 1,660 1,550 9,660 7,000 10.00 7.25 8.92 6.41 9.42 6.78 Wood, Kiln dried 6.00 4,080 2,910 2,260 1,530 7,245 7.50 6.64 7.02 Wood, Air dried,20$ water 4.80 3,700 2,607 2,100 1,490 5,600 5.80 4.08 4.39 The effective value of all kinds of wood per pound, when dry, is substan- tially the same. This is usually estimated at .4, the value of the same weight of coal. The following are the weights and comparative values of different woods by the cord: Wood. Weight. Wood. Weight. Hickory (shell bark) 4 469 Beech 3 126 Hickory (red heart) 3705 Hard maple 2878 White oak 3821 Southern pine 3 375 Red oak 3,254 Virginia pine 2,680 Spruce 2325 Yellow pine 1 904 New Jersey pine 2137 White pine 1 868 SLACK. 167 Much is said nowadays about the wonderful saving that is to be expected from the use of petroleum for fuel. This is all a myth, and a moment's attention to facts is sufficient to convince any one that no such possibility exists. Petroleum has a heating capacity, when fully burned, equal to from 21,000 to 22,000 B. T. U. per lb., or, say, 50$ more than coal. But, owing to the ability to burn it with less losses, it has been found, through extended experiments by the pipe lines, that under the same boilers, and doing the same work, 1 lb. of petroleum is equal to 1.8 lb. of coal. The experiments on locomotives in Russia have shown practically the same value, or 1.77. Now, a gallon of petroleum weighs 6.7 lb. (though the standard buying and selling weight is 6.5 lb.), and therefore an actual gallon of petroleum is equivalent under a boiler to 12 lb. of coal, and 190 standard gallons are equal to a gross ton of coal. It is very easy with these data to determine the relative cost. At the wells, if the oil is worth, say, 2 cents a gallon, the cost is equivalent to $3.80 per ton for coal at the same place, while at, say, 3 cents per gallon, the lowest price at which it can be delivered in the vicinity of New York, it costs the same as coal at $5.70 per ton. The Standard Oil Company estimates that 173 gal. are equal to a gross ton of coal, allowing for incidental savings, as in grate bars, carting ashes, attendance, etc. Sawdust can be utilized for fuel to good advantage by a special furnace and automatic feeding devices. Spent tan bark is also used, mixed with some coal, or it may be burned without the coal in a proper furnace. Its value is about one-fourth that of the same weight of wood as it comes from the press, but, when dried, its value is about 85$ of the same weight of wood in same state of dryness. It has been estimated that, on an average, 1 lb. of coal is equal, for steam- making purposes, to 2 lb. dry peat, 2i to 2i lb. dry wood, 2i to 3 lb. dried tan bark, 2 to 3 lb. cotton stalks, 3 to 3f lb. wheat or barley straw, and 6 to 8 lb. wet tan bark. Natural gas varies in quality, but it is usually worth 2 to 2 times the same weight of coal, or about 30,000 cu. ft. are equal to a ton of coal. Slack, or the screenings from coal, when properly mixed anthracite and bituminous and burned by means of a blower on a grate adapted to it, is nearly equal in combustible value to coal, but its percentage of refuse is greater. The accompanying, table of proximate analyses and heating values of American coals was compiled by Mr. William Kent, for the 1898 edition of the Babcock & Wilcox Co.'s book, " Steam." The analyses are selected from various sources, and, in general, are averages of many samples. The heating values per pound of combustible are either obtained from direct calorimetric determinations or calculated from ultimate analyses, except those marked (?), which are estimated from the heating values of coals of similar composition. The figures in the last column are obtained by dividing the figures in the preceding column by 965.7, the number of heat units required to evaporate 1 lb. of water at 212 into steam of the same temperature. The heating values per pound of combustible given in the table, except those marked (?), are probably within 3$ of the average actual heating values of the combustible portion of the coals of the several districts. When the .percentage of moisture and ash in any given lot of coal is known, the heating value per pound of coal may be found, approximately, by multi- plying the heating value per pound of combustible of the average coal of the district by the difference between 100$ and the sum of the percentages of moisture and ash. The heating effect is calculated on the basis of the coal burned to carbon dioxide and liquid water at 100 C., and is stated either in calories per kilo- gram or English heat units per pound. The theoretical evaporative effect is calculated by dividing the number of calories per kilogram by 536, or the number of English heat units per pound by 965. In either case, it expresses the theoretical number of kilograms or pounds of water converted into steam from and at 100 C., by 1 kilogram or 1 lb. of coal. A committee of the Western Society of Engineers, of Pittsburg, report that 1 lb. of good coal = 7i cu. ft. of natural gas. When burned with just enough air, its temperature of combustion is 4,200 F. The Westinghouse Air Brake Co. found from experiment that 1 lb. Youghiogheny coal = 12i cu. ft. natural gas, or 1,000 cu. ft. natural gas = 81.6 lb. coal. Indiana natural gas gives 1,000,000 B. T. U. for 1,000 cu. ft. and weighs .045 lb. per cu. ft. 168 FUELS. PROXIMATE ANALYSES AND HEATING VALUES OF AMERICAN COALS. .j tj g .0 ,0 O "2 5 If J g $** sj 1 *" o3 o * Coal. E 1 s ' -g I ft s S.Q || y *J ||| *8 1 1 3 02 fl 1" 1* U fl iSl 3 S3 o a j "o & I o Anthracite. Northern Coal Field . . 3.42 4.38 83.27 8.20 .73 13,160 5.00 95.00 14,900 15.42 East Middle Coal Field . 3.71 3.08 86.40 6.22 .58 13,420 3.44 96.56 14,900 15.42 West Middle Coal Field . 3.16 3.72 81.59 10.65 .50 12,840 4.36 95.64 14,900 15.42 Southern Coal Field . . 3.09 4.28 83.81 8.18 .64 13,220 4.85 95.15 14,900 15.42 Semianthracite . Loyalsock Field . . . 1.30 8.10 83.34 6.23 1.63 13,920 8.86 91.14 15,500 16.05 Bernice Basin .... .65 9.40 83.69 5.34 .91 13,700 10.98 89.02 15,500 16.05 Semibituminous. Broad Top, Pa .79 15.61 77.30 5.40 .90 14,820 17.60 82.40 15,800 16.36 Clearneld Co., Pa. . . . .76 22.52 71.82 3.99 .91 14,950 24.60 75.40 15,700 16.25 Cambria Co., Pa. ... .94 19.20 71.12 7.04 1.70 14,450 22.71 77.29 15,700 16.25 Somerset Co., Pa. ... 1.58 16.42 71.51 8.62 1.87 14,200 20.37 79.63 15,800 16.36 Cumberland, Md. . . . 1.09 17.30 73.12 7.75 .74 14,400 19.79 80.21 15,800 16.36 Pocahontas, Va 1.00 21.00 74.39 3.03 .58 15,070 22.50 77.50 15,700 16.25 New River, W. Va. . . .85 17.88 77.64 3.36 .27 15,220 18.95 81.05 15,800 16.36 Bituminous. Connellsville, Pa. ... 1.26 30.12 59.61 8.23 .78 14,050 34.03 65.97 15,300 15.84 Youghiogheny, Pa. . . 1.03 36.50 59.05 2.61 .81 14,450 38.73 61.27 15,000 15.53 Pittsburg, Pa 1.37 35.90 52.21 8.02 1.80 13,410 41.61 58.39 14,800 15.32 Jefferson Co., Pa. ... 1.21 32.53 60.99 4.27 1.00 14,370 35.47 64.53 15,200 15.74 Middle Kittaning Seam, Pa. 1.81 35.33 53.70 7.18 1.98 13,200 40.27 59.73 14,500 15.01 Upper Freeport Seam, Pa. and Ohio 1.93 35.90 50.19 9.10 2.89 13,170 43.59 56.41 14,800 15.32 Thacker, W. Va. . . . 1.38 35.04 56.03 6.27 1.28 14,040 39.33 60.67 15,200 15.74 Jackson Co., Ohio . . . 3.83 32.07 57.60 6.50 13,090 35.76 64.24 14,600 15.11 Brier Hill, Ohio . . . 4.80 34.60 56.30 4.30 13,010 38.20 61.80 14,300 14.80 Hocking Valley, Ohio . . 6.59 34.97 48.85 8.00 1.59 12,130 42.81 57.19 14,200 14.70 Vanderpool, Ky. . . . 4.00 34.10 54.60 7.30 12,770 38.50 61.50 14.400 14.91 Muhlenberg Co., Ky. . . 4.33 33.65 55.50 4.95 1.57 13,060 38.86 61.14 14,400(7) 14.91 Scott Co., Tenn. 1.26 35.76 53.14 8.02 1.80 13,700 34.17 65.83 15 100(7) 15.63 Jefferson Co., Ala. . . . 1.55 34.44 59.77 2.62 1.42 13,770 37.63 62.37 14,400(7) 14.91 Big Muddy, 111 7.50 30.70 53.80 8.00 12,420 36.30 63.70 14,700 15.22 Mt. Olive, 111 11.00 35.65 37.10 13.00 10,490 47.00 53.00 13,800 14.29 Streator 111 12.00 33.30 40.70 14.00 10,580 45.00 55.00 14,300 14.80 Missouri 6.44 37.57 47.94 8.05 12,230 43.94 56.06 14,300(7) 14.80 Lignite and Lignitic Coals. 8.45 37.09 35.60 18.86 8,720 51.03 48.97 12,000(7) 12.42 W mine 8.19 38.72 41.83 11.26 10,390 48.07 51.93 12,900(7) 13.35 Utah 9.29 41.97 44.37 3.20 1.18 11,030 4860 51.40 12,600(7) Oregon lignite .... 15.25 42.98 33.32 7.11 1.66 8,540 54.95 45.05 11,000(7) ll!39 A British thermal unit (B. T. U.) is the quantity of heat required to raise the temperature of 1 Ib. of wetter 1 F. at or near the temperature of maximum density, 39.1 F. A calorie is the quantity of heat required to raise the temperature of 1 kilogram of water 1 C. at or about 4 C. A pound calorie is the quantity of heat necessary to raise the temperature of 1 Ib. of water 1 C. 1 French calorie = 3.968 British thermal units. 1 B. T. U. = .252 calorie. 1 Ib. calorie = f B. T. U. = .4536 calorie. The heating value of any coal may be calculated from its ultimate analysis, with a probable error not exceeding 2$, by Dulong's formula: Heating value per Ib. = 146 C -f 620 (ff- ^ }, \ o / in which (7, H, and are, respectively, the percentages of carbon, hydrogen, and oxygen. CLASSIFICATION OF COALS. 169 Heat in pound calorie = 8,080 C + 34,462 H ~ or = 8,080 C+ 34,462 (#- f ) + 2 .250 S. Heat in B. T. U. - 14,650 C- 62,100 (H- %- ), \ of in which (7, 0, H, and /S represent the weights of carbon, oxygen, hydro- gen, and sulphur in 1 Ib. of the substance. COMPOSITION OF FUELS. (Mechanical Draft, B. F. Sturtevant Co.) Description. Carbon. Hydro- gen. Oxy- gen. Nitro- gen. Sul- phur. Ash. Anthracite. France 909 1.47 1.53 1.00 .80 43 Wales 91.7 3.78 1.30 1.00 .72 1.5 Rhode Island 850 3.71 2.39 1.00 .90 7.0 Pennsylvania 786 2.50 1.70 .80 .40 148 Semibituminous. Maryland 800 5.00 2.70 1.10 1.20 8.3 Wales 88.3 4.70 .60 1.40 1.80 3.2 Bituminous. Pennsylvania . . 755 4.93 12.35 1.12 1.10 50 Indiana 697 5 10 19 17 1.23 1 30 35 Illinois 61.4 4.87 35.42 1.41 1.20 5.7 Virginia 570 4.96 26.44 1.70 1.50 8.4 Alabama 53.2 4.81 32.37 1.62 1.30 6.7 Kentucky 491 4.95 41.13 1.70 1.40 7.2 Cape Breton 67.2 4.26 20.16 1.07 1.21 6.1 Vancouver Island Lancashire gas coal Boghead cannel 66.9 80.1 63.1 5.32 5.50 8.90 8.76 8.10 7.00 1.02 2.10 .20 2.20 1.50 1.00 15.8 2.7 19.8 Lignite. California brown 49.7 3.78 30.19 1.00 1.53 13.8 Australian brown 73.2 4.71 12.35 1.11 .63 8.0 Petroleum. Pennsylvania (crude) Caucasian (light) 84.9 86.3 13.70 13.60 1.40 .10 Caucasian (heavy) 86.6 12.30 1.10 Refuse 87.1 11.70 1.20 CLASSIFICATION, COM POSITION, AN D PROPERTIES OF COALS. Coals may be broadly divided into two classes: Anthracite, or hard, coal; and bituminous, or soft, coal. Anthracite, or Hard, Coal. Specific gravity, 1.30 to 1.70. This is the densest, hardest, and most lustrous of all varieties. It burns with little flame and no smoke, but gives a great heat. Contains very little volatile combustible matter. Color, deep bla conchoidal. matter. Color, deep black, shining; sometimes iridescent. Fracture, Semianthracite coal is not so dense nor so hard as the true anthracite. Its percentage of volatile combustible matter is somewhat greater, and it ignites more readily. Bituminous, or Soft, Coal. Specific gravity, 1.25 to 1.40. It is generally brittle; has a bright pitchy or greasy luster, and is rather fragile as compared with anthracite. It burns with a yellow smoky flame, and gives, on distil- lation, hydrocarbon oils or tar. Under the term "bituminous " are included a number of varieties of coal that differ materially under the action of heat, giving rise to the general classification: Coking or caking coals, and free-burning coals. Semibituminous coal has the same general characteristics as the bituminous, although it is usually not so hard, and its fracture is more cuboidal. The 170 FUELS. percentage of volatile combustible matter is less. It kindles readily, and burns quickly with a steady fire, and is much valued as a steam coal. Coking coals are those that become pasty or semiviscid in the fire; and, when heated in a close vessel, become partially fused and agglomerate into a mass of coherent coke. This property of coking may, however, become greatly impaired, if, indeed, not entirely destroyed, by weathering. Free-burning coals have the same general characteristics as the coking coals, but they burn freely without softening, and do not fuse or cake together in any sensible degree. Splint coal has a dull black color, and is much harder and less frangible than the coking coal. It is readily fissile, like slate, but breaks with difficulty on cross-fracture. It ignites less readily, but makes a hot fire, constituting a good house coal. WEIGHTS AND MEASUREMENTS OP COAL. (Coxe&ros. & Co., Chicago, III.) Coal. Weight per Cubic Foot. Pounds. Cubic Feet per Ton, 2,000 Lb. Coal. Weight per Cubic Foot. Pounds. Cubic Feet per Ton, 2,000 Lb. Lehigh lump 55 26 36 19 Free-burning egg 56 07 35 67 Lehigh cupola 5552 3602 Free-burning stove 5633 3550 Lehigh broken Lehigh egg 56.85 57 74 35.18 34.63 Free-burning nut ... Pittsburg 56.88 4648 35.16 4303 Lehigh stove 58 15 3439 Illinois 47 22 4235 Lehigh nut 5826 34.32 Connellsville coke 2630 7604 Lehigh pea 53 18 37 60 Hocking 4930 4056 Lehigh buckwheat... Lehigh dust 54.04 5725 37.01 3493 Indiana block Erie 43.85 4807 45.61 41 61 Ohio cannel 49.18 40.66 Cannel coal differs from the ordinary bituminous coal in its texture. It is compact, with little or no luster and without any appearance of a banded structure. It breaks with a smooth conchoidal fracture, kindles readily, and burns with a dense smoky flame. It is rich in volatile matter, and makes an excellent gas coal. Color, dull black and grayish black. Lignite, or brown coal, often has a lamellar or woody structure; is some- times pitch black, but more often rather dull and brownish black. It kindles readily and burns rather freely with a yellow flame and comparatively little smoke, but it gives only a moderate heat. It is generally non-coking. The percentage of moisture present is invariably high from 10$ to 30$. The subdivisions given above are entirely arbitrary, as the different varieties of coal are found to shade insensibly into one another. The follow- ing are two classifications according to percentages of volatile combustible matter: CLASSIFICATION OF COAL ACCORDING TO VOLATILE COMBUSTIBLE. Coal. Per Cent. Kent. Per Cent. Anthracite 2.5 to 6 to 7 Semianthracite 7 to 10 7 5 to V> Semibituminous 12 to 20 12.5 to 25 Bituminous over 20 25 to 50 Lignite over 50 The Composition of Coals. A proximate analysis determines the proportion of those products of a coal having the most important bearing on its uses. These substances as usually presented are: Moisture, or water, volatile com- PROPERTIES OF COALS. 171 bustible matter, fixed carbon, sulphur, and ash. In addition to these, the following physical properties are generally given: Color of ash, specific gravity, and strength or hardness. The determination of these eight factors gives a fair general idea of the adaptabilities of a coal. Moisture, or water, in coal, has no fuel value, is an inert constituent, dug, handled, and hauled, and finally expelled at a cost of fuel. Each per cent, of moisture means 20 Ib. less fuel for each ton of coal. Volatile combustible matter is an important constituent of coal, the amount and quality deciding whether a coal is suitable for the manufacture of illuminating gas. The coking of coal also is largely dependent on this constituent. When a large percentage of volatile combustible matter is present, coals ignite easily and burn with a long yellow name, and, in ordinary combustion, give out dense smoke, and form soot. This quality makes a fuel objectionable for railway and sometimes for naval use. The fixed carbon is the principal combustible constituent in coal, and, in bituminous and semibituminous coals, the steaming value is in proportion to the percentage of fixed carbon. Though the fixed carbon of a coal evapo- rates much less water than an equivalent weight of the volatile combustible matter when properly burnt, in practice, so much of the latter is lost through, careless firing, or improper furnace construction, that the relative steaming value of a coal may be fairly approximated by assuming the carbon to be the only useful constituent. Sulphur will burn and develop heat, and is not inert like moisture and ash. But it corrodes grates and boilers; in the blast furnace it injures iron, and produces a hot short pig, and is objectionable in coal for forge use. In gas making, the sulphur must be removed. It usually occurs in coal in the form of iron pyrites, which, oxidizing, causes disintegration, and sometimes spontaneous combustion. It is then an element of danger and loss. Ash is an inert constituent, which means 20 Ib. of weight to be handled and 20 Ib. loss per ton of coal for each per cent, present. Water in coal is removed at the cost of fuel, while ashes are removed at extra cost of labor. It is estimated that if the cost of stoking coal is 6f$ of the cost of coal (coal at $3.00 per ton, and labor at $1.00 per day), and with cost of handling ashes double that of stoking coal, 5$ of ash will lessen the fuel value of coal over 6$; 10$ ash, over 12$; and so on. The color of the ash furnishes a rough estimate of the amount of iron con- tained in a fuel. Iron in an ash makes it more fusible, and increases its tendency to clinker. In domestic consumption, where the temperature is low, the quantity of ash is of more importance than its fusibility, but for steam purposes, where an excessive heat is required, ashes of a clinkering coal will fuse into a vitreous mass and accumulate upon the grate bars and exclude the passage of necessary air. The practicability of employing a coal will often be determined by the quality of the clinkering of the ashes. Under such conditions, such coals are best whose ashes are nearly pure white and w r hich contain little or no alkali nor any lime, and do not contain silica and alumina. The specific gravity is an important factor when there is restriction of space, as on railway cars and in ship bunkers. A given bulk of anthracite coal will weigh from 10$ to 15$ more than the same bulk of bituminous coal, so that from 10$ to 15$ more pounds of fuel can be carried in the same place. The average specific gravity of anthracite coal is 1.5, and a cubic yard weighs about 2,531 Ib. The average specific gravity of American bituminous coals, and of grades intermediate between them and anthracite, is about 1.325, and 1 cu. yd. weighs about 2,236 Ib. Strength or hardness is valuable in preventing waste. In soft coal, much is ground to dust in mining and at the tipple. In railway transportation, soft coal is crushed, which further increases the loss, and the coal reaches market in bad condition. A very soft coal is shipped in lump, and is not in so wide demand. For marine use, a soft coal is objectionable, because of disintegra- tion by the motion of the ship. Strength is a requisite for the use of raw coal in the blast furnace, and also to prevent excessive loss of coal through the grates in ordinary furnaces. Steaming Coals. For steam making, the superiority of coals high in com- bustible constituents is admitted, and those with the higher percentage of fixed carbon are the most desirable. But the consideration of the steaming qualities of a coal involves, also, a consideration of the form of furnace and of all the conditions of combustion. The evaporative power of a coal in 172 FUELS. practice cannot be stated without reference to the conditions of combustion, and every practical test of a coal, to be thorough, should lead to a determi- nation of the best form of furnace for that coal, and should furnish knowl- edge as to what class of furnaces in actual use such coal is specially adapted. It is not sufficient that in comparative tests of coals the same conditions should exist with each, but there should also be determined the best conditions for each coal. Of coals high in fixed carbon, the semianthracites and the semibitumi- nous rank as high as the anthracites in meeting the various requirements of a quick and efficient steaming coal. For railway use, these coals have been found to excel anthracites in evaporating power. The comparative absence, in semibituminous coals, of smoke, which means loss of combustible matter as well as discomfort to the traveler, is sufficient to suggest the superiority of these coals over bituminous coals for such use. In fact, the high rate of combustion and the strong draft necessary in locomotives is particularly unfavorable to the economic com- bustion of bituminous coal. Such semibituminous coals are also specially well suited for small tubular boilers, firebpx steam boilers, or other forms with small unlined combustion chambers, in which the gases from bitumi- nous coals become cooled, are not burnt, and deposit soot in the tubes. Steaming coal should kindle readily and burn quickly but steadily, and should contain only enough volatile matter to insure rapid combustion. It should be low in ash and sulphur, should not clinker, and when it is to be transported should not easily crumble and break. Coals for Iron Making. For the manufacture of iron and for metallurgical purposes, coal is chiefly used after being converted into coke, though it is also used to a limited extent in the raw state. Coal directly used must be strong and not swell nor disintegrate so as to choke the furnace. It should be capable of producing a high heat and should not contain a large amount of sulphur or phosphorus. Coke. Coke is me fixed carbon of a coal, a fused and porous product pro- duced by the distillation of the gaseous constituent. For metallurgical use, it should be firm, tough, and bright, with a sonorous ring, and should contain not over K of sulphur. For blast-furnace use, a dense coke is objectionable, and the best is the one with the largest cell structure and the hardest cell wall. A high percentage of volatile hydrocarbon is, as a rule, necessary for a good coking coal. The fusibility of the carbon, the amount of disposable hydrogen, the tenacity with which the gaseous constituents are held, all affect the results in coking. Further, coal that is mined near the outcrop, and has been sub- jected to the influence of the weather, loses its capacity for coking. The process of manufacture should, however, be adapted to the character of the coal, as it has an important, though secondary, influence on the physical character, uniformity of quality, and dryness of a coke. Coals of inferior grade are made to produce good coke by using coke ovens in which the heat of the gases is applied externally to the coke chamber, but the coal is generally first carefully crushed and washed. Further, the depth of the charge and length of heating have an important bearing. As at present understood, and in the present mode of manufacture, the essential qualities of a good coking coal are: that it shall contain not less than 20$ nor more than 30$ of volatile hydrocarbons, and not too much ash; that on being heated it must pass through a thoroughly fused or pasty condition; and that when in this condition, it must part with its volatile matter in such a manner as to form innumerable small pores. If a coal contains less than 20$ of volatile matter, it will not fuse properly, while if it has more than 30$ the porous structure will be unduly developed at the expense of the strength of the pore walls; on the other hand, many coals lying between these limits will not fuse at all, and therefore do not coke, while others fuse properly but t give off" their gas so as to form large and thin-walled pores. Ordinary analyses do not indicate whether or not a coal is a good coking coal, and they indicate simply by giving the amount of carbon, ash, and sulphur, what will be the probable purity of the coke formed. The coal of the Pittsburg bed in the Connellsville basin of Pennsylvania is considered by many as the standard coking coal, but coals whose analysis differ very materially from that of Connellsville undoubtedly give most excellent cokes, which are equal to or very nearly equal to, that from Connellsville, as, for instance, the Pocahontas coke, Virginia. ANALYSIS OF COAL. 173 Domestic Coals. In domestic use, coal is burned In open grates, in closed stoves with ordinary fire bowls and flat grates, or with basket grates in small furnaces for hot-air heating, and in cooking stoves. In all these, the coal that sustains a mild, steady combustion, and remains ignited at a low tem- perature with a comparatively feeble draft, is the best. A coal burning with a smoky flame is objectionable as producing much soot and dirt, especially for open grates or cooking purposes. For self-feeding stoves, or for base burners, a dry non-coking coal is necessary. A very free and fiercely burn- ing coal is not desirable, particularly in stoves, as the temperature cannot be easily regulated. A sulphurous coal is also bad, as it produces stifling gases with a defective draft, and corrodes the grates and fire bowls. The difficulty from clinkering is not so great in domestic uses, as the temperature is not generally high enough to fuse the ash. A stony, hard ash that will not pass between the grate bars is bad, and light pulverulent ash is best. Gas Coals. Mr. H. C. Adams, of The American Gas Light Association, says: "The essentials of a good gas coal are a low percentage of ash, say 5$, and of sulphur, say of 1$, a generous share, say 37$ to 40$ of volatile matter, charged with rich illuminating hydrocarbons. And it should yield, under present retort practice, 85 candle-feet to the pound carbonized. It should be sufficiently dense to bear transportation well, so that, when carried long distances/it may not arrive at its destination largely reduced to slack or fine coal of the consistency of sand. And it should possess coking qualities that will bring from the retorts, after carbonization, about 60$ of clean, strong, bright coke." Blacksmith Coals. A good coal for blacksmith purposes should have a high heating power, should contain a very small amount of sulphur, if any, should coke sufficiently to form an arch on the forge, and should also be low in ash. From the above, it is readily seen that the analysis of a coal does not necessarily determine its value or the uses to which it can be put. How- ever, by examining the analyses given in the table on page 168, certain standards may be adopted as showing in a general way about what the analysis of coal should be for certain purposes. For steam purposes, the semibituminous coals have established reputations. For gas coals, that from Youghiogheny, Pa., is well known. For blacksmiths, Broad Top and Tioga County, Pennsylvania, coals are standards; while for coking, Connells- ville is recognized as a standard. The sizes of anthracite coal vary. The sizes of screen mesh and bar open- ings used for separating, range as follows: Lump, over bars placed 7 to 9 in. apart. Steamboat, over bars placed 3i to 5 in. apart and through bars 7 in. apart. Grate, over 2| in. and through 4 in. square mesh. Egg, over 2 in. and through 2f in. square mesh. Stove, over If in. and through 2 in. square mesh. Chestnut, over in. and through If in. square mesh. Pea, over | in. and through in. square mesh. Buckwheat, over i in. and through in. square mesh. No. 2 Buckwheat, or Bird's-eye, over in. and through -f s in. square mesh. The sizes of bituminous coal are Lump, Nut, and Slack. All coal that passes over bars H in. apart is called Lump. All coal that passes through bars 1 in. apart and over bars in. apart is called Nut. All coal that passes through bars in. apart is called Slack. ANALYSIS OF COAL. The following is the outline of the method recommended for the analysis of coal by a committee of the American Chemical Society, Messrs. \V. F. Hillebrand, C. B. Dudley, and W. A. Noyes: Sampling. At least 5 Ib. of coal should be taken for the original sample, with care to secure pieces that represent the average. These should be broken up and quartered down to obtain the smaller sample, which is to be reduced to a fine powder for analysis. The quartering and grinding should be carried out as rapidly as possible, and immediately after the original sample is taken, to prevent gain or loss of moisture. The pow- dered coal should be kept in a tightly stoppered tube, or bottle, until analyzed. Unless the coal contains less than 2$ of moisture, the shipment of large samples in wooden boxes should be avoided. 174 FUELS. In boiler tests, shovelfuls of coal should be taken at regular intervals and put in a tight covered barrel, or some air-tight covered receptacle, and the latter should be placed where it is protected from the heat of the furnace. In sampling from a mine, the map of the mine should be carefully examined and points for sampling located in such a manner as to fairly represent the body of the coal. These points should be placed close to the working fac'e. Before sampling, make a fresh cut of the face from top to bottom to a depth that will insure the absence of possible changes or of sulphur and smoke from the blasting powders. Clean the floor and spread a piece of canvas to catch the cuttings. Then, with a chisel, make a cutting from floor to roof, say 3 in. wide and about 1 in. deep. Do not chisel out the shale or other impurities that it is the practice at that mine to reject. Measure the length of the cutting made, but do not include the impurities in this measurement. With a piece of flat iron and a hammer, break all pieces to quarter-inch cubes or less, without removing from the cloth. Quarter down and transfer to a sealed bottle or jar. For the " run-of-mine " sample, samples taken at several points in this manner should be mixed and quartered down. If the vein varies in thickness at different points, the samples taken at each point should correspond in amount to the thickness of the vein. For instance, a small measure may be filled as many times with the coal of the sample as the vein is feet in thickness. Should there appear differences in the nature of the coal, it will be more satisfactory to take, in addition to the generat sample, samples of such portions of the vein as may display these differences. Moisture. Dry Ig. of the coal in an open porcelain or platinum crucible at 104 to 107 C. for 1 hour, best in a double-walled bath containing pure toluene. Cool in a desiccator and weigh covered. Volatile Combustible Matter. Place 1 g. of fresh, undried coal in a platinum crucible, weighing 20 to 30 g., and having a tightly fitting cover. Heat over the full flame of a Bunsen burner for 7 minutes. The crucible should be supported on a platinum triangle with the bottom 6 to 8 cm. above the top of the burner. The flame used should be fully 20 cm. high when burning free, and the determination made in a place free from drafts. The upper surface of the cover should burn clear, but the under surface should remain covered with carbon. To find "volatile combustible matter," subtract the percentage of moisture from the loss found here. Ash. Burn the portion of coal used for the determination of moisture at first over & very low flame, with the crucible open and inclined, until free from carbon. If properly treated, this sample can be burned much more quickly than the dense carbon left from the determination of volatile matter. Fixed Carbon. This is found by subtracting the percentage of ash from the percentage of coke. Sulphur (Eschka's Method). Mix thoroughly 1 g. of the finely powdered coal with 1 g. of magnesium oxide and i g. of dry sodium carbonate, in a thin 75 to 100 c. c. platinum dish or crucible. The magnesium oxide should be light and porous, not a compact, heavy variety. The dish is heated on a triangle over an alcohol lamp, held in the hand at first. Gas must not be used, because of the sulphur it contains. The mixture is frequently stirred with a platinum wire and the heat raised very slowly, especially with soft coals. The flame is kept in motion and barely touching the dish, at first, until strong glowing has ceased, and is then increased gradually until, in 15 minutes, the bottom of the dish is at a low red heat. When the carbon is burned, transfer the mass to a beaker and rinse the dish, using about 50 c. c. of water. Add 15 c. c. of saturated bromine water and boil for 5 minutes. Allow to settle, decant through a filter, boil a second and third time with 30 c. c. of water, and wash until the filtrate gives only a slight opalescence with silver nitrate and nitric acid. The volume of the filtrate should be about 200 c. c. Add H c. c. of concentrated hydrochloric acid, or a corresponding amount of dilute acid (8 c. c. of an acid of 8#). Boil until the bromine is expelled, and add to the hot solution, drop by drop, especially at first, and with constant stirring, 10 c. c. of a 10$ solution of barium chloride. Digest on the water bath, or over a low flame, with occasional stirring until the precipitate settles clear quickly. Filter and wash, using either a Gooch crucible or a paper filter. The latter may be ignited moist in a platinum crucible, using a low flame until the carbon is burned. Jn the case of coals containing much pyrites or calcium sulphate, the STEAM. 175 residue of magnesium oxide should be dissolved in hydrochloric acid and the solution tested for sulphuric acid. When the sulphur in the coal is in the form of pyrites, that compound is converted almost entirely into ferric oxide in the determination of ash, and, since 3 atoms of oxygen replace 4 atoms of sulphur, the weight of the ash is less than the weight of the mineral matter in the coal by | the weight of the sulphur. While the error from this source is sometimes considerable, a correction for "proximate" analyses is not recommended. When analyses are to be used as a basis for calculating the heating effect of the coal, a correction should be made. The analysis of a coal may be reported in three different forms, as per- centages of the moist coal, of the dry coal, or of the combustible. Thus, suppose 1 g. of coal is analyzed, and the first heating shows a loss of weight of .1 g., the second of .3g., the third .5g., the remainder, or ash, weighing .1 g., the complete report would be as follows: Per Cent, of the Moist Coal. Per Cent, of the Dry Coal. Per Cent, of the Combustible. Moisture 10 Volatile matter 30 33.33 37.50 Fixed carbon 50 55.56 6250 Ash 10 11.11 Total 100 100.00 10000 STEAM. A calculation of the power that coal possesses, compared with the useful work which steam engines exert, shows that probably in the very best engines not one-tenth of the power is converted into useful work, and in some very bad engines, probably not one one-hundredth. There are many causes for this; some we can never remedy, because to do so it would be necessary to exhaust the steam at a lower temperature than is practical. There are other causes that can and ought to be removed. We want good engines, good boilers, high-pressure steam, expansive working, and con- densing appliances. High-Pressure Steam. Why should we use high-pressure steam? There are several good reasons. Whatever pressure we have available at the steam boiler, a certain amount is absorbed in overcoming the resistances of the engine and without doing any useful work. Suppose our available steam pressure is 20 lb., and 10 Ib. are so absorbed; that leaves us only one-half; but, if we have 100 lb. available, it would leave us nine-tenths. High-pressure steam means fewer boilers and smaller engines, with founda- tions and houses of less dimensions. Then, again, the amount of work that it is possible to get out of a given quantity of steam depends on the differ- ence between the temperature at the commencement of the stroke and the temperature at the end of the stroke. Now, there is a limit as to how low the temperature can be at the end, and as we raise the commencing temperature, we enlarge the available difference. We may put the advantages of high-pressure steam in this way. By taking a fixed temperature in the condenser of, say, 100 F., and initial temperatures when the steam enters the cylinder, of varying amounts, the theoretic efficiency of that steam can be determined. Commencing with atmospheric pressure, we have an efficiency of 16.6$. Lb. 10 Per Cent. 20 Lb. 100 Per Cent. 29 8 9Q 22.1 125 31.1 30 237 150 322 40 250 200 . 339 50 26 1 250 353 60 2'.0 300 36.5 80 .... .. 28.6 176 BOILERS. We can only get in practice with steam a certain proportion of the theoretic power, and that proportion varies with the pressure of the steam. In early days we used steam at atmospheric pressure, the efficiency being 16.6$; afterwards, we had, in compound engines of two cylinders, steam of 60 lb., the efficiency being 27$. Now we have triple-expansion engines, using steam at 150 lb., the efficiency being 32.2$. It will be observed that, although the efficiency increases as the steam pressure increases, the amount of that increase is a diminishing quantity, and it becomes so small at and beyond 150 lb. pressure that probably any gain in efficiency is not a satisfactory set-off to the additional expense of strength- ening the parts of the engine. But then, how very few of our engines work nearly so high as 150 lb. pressure. The advantages of high-pressure steam are not yet sufficiently appreciated. It is not merely the difference between 60 lb. and 120 lb. Suppose we use steam at 60 lb.; probably we shall get 50 lb. at engine, and resistances of engine will absorb 10 lb., leaving 40 lb. Now, suppose we use 120 lb., we can get at engine 110 lb., and if resistances of engine absorb 10 lb., we shall have 100 lb. as against 40 lb. Expansion of Steam. By "expansion of steam" we mean that at a certain point of the stroke we shut off steam supply from the boiler to the cylinder, and the steam already within the cylinder performs the remainder of the stroke unaided. Now, suppose we do not expand at all. Suppose we allow free admission of steam into the cylinder all through the stroke; we shall have at the end of the stroke pressure exactly similar to the pressure with which we commenced. Now, we cannot work a seam of coal and still have the coal left; we cannot get work out of steam and still have the work left in it, and so, if our steam pressure is the same at the end of the stroke as at the beginning, we simply discharge twice in each revolution a whole cylinder full of steam that has done no work at all, and waste it just the same as if we had discharged it from the boiler without passing through the engine at all. But some one will say, work has been done upon the engine while that steam was in the cylinder. True and the explanation is, that while the steam is performing work its heat and pressure must diminish, and so long as the communication with the boiler is open, fresh heat comes from the boiler into the cylinder to take its place, and at the end of the stroke we have expended heat represented by the capacity of two cylinders, and have performed work as represented by the capacity of one cylinder. Now, suppose we close the communication, and beyond a certain point of the stroke allow no more steam to enter, we get an amount of work from the steam already in the cylinder, represented by the diminishing pressure of the steam by expansion. Condensers. The effective power of an engine does not depend on, and is not measured by, the pressure pushing the piston. There is always what is termed a back pressure holding the piston back, and the real effective pressure is evidently the difference between the two. Suppose we have a locomotive engine, or a winding engine, throwing exhaust into the open air. The back pressure cannot be less than the pressure of the open air, and, indeed, to overcome it, it must be something more. But if we can discharge our exhaust into some vessel from which atmospheric pressure and all other pressure has been removed, we know that atmospheric pres- sure amounts to about 15 lb., and the removal of that from the front of the piston is as good as adding 15 lb. behind. BOILERS. The steam boiler that will be the most suitable for a certain mine will depend on the nature of the feedwater, the cost of fuel, and the amount of steam required. When the acid water from the mine is used for feedwater, and fuel is cheap, the type of boiler generally used is either the plain cylindrical or flue boiler, because it is simple in construction and can therefore be easily cleaned and cheaply replaced when eaten by the mine water. The tubular or locomotive type is used where good water can be obtained, except in the best equipped plants, where the water-tube boiler is used. Feedwater taken from the mine, or containing acid, should be neutralized by lime or soda before being used. In case it contains minerals in solution, a feedwater separator should be employed to precipitate the mineral substance before the water is allowed to enter the boiler. HORSEPOWER OF BOILERS. 177 We always calculate the strength of a boiler in the direction of its diameter, because, theoretically, a boiler is twice as strong in the direction of length as direction of diameter. Many causes may bring about boiler explosions. First, bad materials; second, bad workmanship; third, bad water, which eats away the plates by internal corrosion; fourth, water lying upon plates, bringing about external corrosion; fifth, overpressure; sixth, safety valves sticking; seventh, water getting too low; eighth, excessive firing; ninth, hot gases acting on plates above water level; tenth, choking of feedpipes; eleventh, insufficient provision for expansion and contraction; twelfth, insufficient steam room and too sudden a withdrawal of a large quantity of steam; thirteenth, getting up steam, or knocking off a boiler too suddenly; fourteenth, allowing wet ashes to lie in contact with plates. The probable causes suggest their several remedies. Wherever possible, and except under certain circumstances, steam engines should not be placed in the mine, and certainly steam boilers should be in all cases placed upon the surface. Steam injures the ventila- tion, increasing the temperature where already too high, doing injury and causing inconvenience by condensation, and many fires in mines have been caused by underground boilers. The Lancashire Boiler. The colliery boiler that finds much favor in Eng- land is that class of Lancashire boiler which is 28 or 30 ft. long and 7 or 8 ft. in diameter, and has two large flues running through. There is no doubt that the marine type will generate more steam with a given amount of coal, and, consequently, is gaining ground, and will gain ground where coal is dear. But the Lancashire boiler is a good steam generator, and will not only work longer without repairs, but is less troublesome and expensive to repair. The favorite construction some few years ago was wrought iron with double-riveted horizontal joints and Galloway tubes (Galloway tubes are simply taper tubes running across the flues in the boiler), and expansion weldless hoops strengthening the flues and allowing for expan- sion and contraction. The dimensions were 7 ft. diameter, and from 28 to 30 ft. long, with internal flues each 2 ft. 9 in. diameter, the circular plates being about i in. and the end plates about f- in. The safe working pressure was about 60 Ib. per sq. in. Now the conditions are somewhat altered. Steel has taken the place of iron, giving increased strength, and allowing increased diameter and increased pressure. Ring plates have also abolished a great source of weakness in a boiler, namely, horizontally riveted joints. A good Lancashire boiler now will measure 8 ft. in diameter and 30 ft. long, with ring plates f in. thick, end plates probably f in., and will work very well at 120 Ib. pressure per sq. in. Horsepower of Boilers. The horsepower of a boiler is a measure of its capacity for generating steam. Boilermakers usually rate the horsepower of their boilers as a certain fraction of the heating surface; but this is a very indefinite method, for with the same heating surface, different boilers of the same type may, under different circumstances, generate different quantities of steam. In order to have an accurate standard of boiler power, the American Society of Mechanical Engineers has adopted as a standard horsepower an evaporation of 30 Ib. of water per hour from afeedwater temperature of 100 F. into steam at 70 Ib. gauge pressure, which is considered equivalent to 34.5 units of evaporation; that is, to 34.5 Ib. of water evaporated from a feedwater temperature of 212 F. into steam at the same temperature. EXAMPLE. A boiler evaporates per hour 1,980 Ib. of water from a feed temperature of 100 into steam at 70 Ib. gauge pressure. What is the horsepower of the boiler? Since, under the given conditions, an evaporation of 30 Ib. is equivalent to 1 horsepower, the number of horsepower is 1,980 -f- 30 = 66. In the various types of boilers there is a nearly constant ratio between the water-heating surface and the horsepower, and also between the heating surface and the grate area. These ratios are given in the table on page 178. If the heating surface of a boiler is known, the horsepower can be found roughly; thus, if a return-tubular boiler has a heating surface of 900 sq. ft., its horsepower lies between e T g - = 50 H. P. and &>- = 64.3 H. P., say about 57 H. P. The heating surface of a boiler is the portion of the surface exposed to the action of flames and hot gases. This includes, in the case of the multi- tubular boiler, the portions of the shell below the line of brickwork, the exposed heads of the shell, and the interior surface of the tubes. In the 178 BOILERS. ease of a water-tube boiler, the heating surface comprises the portion of the shell below the brickwork, the outer surface of the headers, and outer surface of tubes. In any given case, the heating surface may be calculated RATIO OF HEATING SURFACE TO HORSEPOWER AND OF HEATING SURFACE TO GRATE AREA. TVDC of Boiler . Heating Surface Ratio Heating Surface Horsepower Grate Area Plain cylindrical Flue . 6 to 10 8 to 12 12 to 15 20 to 25 Return - tubular Vertical 14 to 18 15 to 20 25 to 35 25 to 30 Water-tube 10 to 12 35 to 40 Locomotive 1 to 2 50 to 100 by the rules of mensuration. The following example will show the method of calculating the heating surface of a return-tubular boiler: EXAMPLE. A horizontal return-tubular boiler has the following dimen- sions: Diameter, 60 in.; length of tubes, 12 ft.; internal diameter of tubes, 3 in.; number of tubes, 82. Assume that f of the shell is in contact with hot gases or flame, and f of the two heads are heating surface. Circumference of shell = 60 X 3.1416 = 188.496 = 188.5 in., say. Length of shell = 12 X 12 = 144 in. Heating surface of shell = 188.5 X 144 X I = 18,096 sq. in. Circumference of tube = 3 X 3.1416 = 9.425 in., nearly. Heating surface of tubes = 82 X 144 X 9.425 = 111,290.4 sq. in. Area of one head = 60 2 X .7854 = 2,827.44 sq. in. Two-thirds area of both heads = f X 2 X 2,827.44 = 3,769.92 sq. in. From the heads must be subtracted twice the area cut out by the tubes; this is 82 X 3 2 X .7854 X 2 = 1,159.26. Total heating surface in square feet = 18,096 + m.290.44^ 8.769.92- 1,159.26 = mM ^ An , PROBABLE MAXIMUM WORK OF A PLAIN CYLINDRICAL BOILER OF 120 SQ. FT. HEATING SURFACE AND 12 SQ. FT. GRATE SURFACE, AT DIFFERENT RATES OF DRIVING. Rate of driving; Ib. water evaporated per sq. ft. of heating surface per hour .... Total water evapora- ted by 120 sq. ft. heating surface per hour, Ib Horsepower; 34.5 Ib. per hour = 1 H. P. Pounds water evapo- rated per Ib. com- bustible Pounds combustible burned per hour ... Pounds combustible per hour per sq.ft. of grate Pounds combustible per hour per horse- power 240.00 360.00 420.00 480.00 540.00 600.00 720.00 840.00 960.00 6.96 10.88 22.10 1.85 3.17 10.43 11.30 31.90 2.65 3.05 3.5 12.17 11.36 37.00 3.08 3.04 13.91 11.29 42.50 3.55 3.06 4.5 15.65 11.20 48.20 4.02 3.08 17.3 11.05 54.30 4.52 3.12 20.87 10.48 68.70 5.72 3.30 24.35 9.48 7.38 27.83 8.22. 88.60 116.80 9.73 4.16 From the figures in the last line, we see that the amount of fuel required for a given horsepower is nearly 37$ greater when the rate of evaporation is 8 Ib. than when it is 3.5 Ib. DANGER OF EXPLOSION. 179 The figures in the preceding table that represent the economy of fuel, viz., " Pounds water evaporated per Ib. combustible" and " Pounds combustible per hour per horsepower," are what may be called "maximum" results, and they are the highest that are likely to be obtained with anthracite coal, with the most skilful firing anfl with every other condition most favorable. Unfavorable conditions, such as poor firing, scale on the inside of the heating surface, dust or soot on the outside, imperfect protection of the top of the boiler from radiation, leaks of air through the brickwork, or leaks of water through the blow-off pipe, may greatly reduce these figures. Choice of a Boiler. Questions that arise under this head in regard to any 1. Is the grate surface sufficient for burning the maximum quantity of coal expected to be used at any time, taking into consideration the availa- ble draft, the quality of the coal, its percentage of ash, whether or not the ash tends to run into clinker, and the facilities, such as shaking grates, for getting rid of the ash or clinker? 2. Is the furnace of a kind adapted to burn the particular kind of coal used? 3 ' Is the heating surface of extent sufficient to absorb so much of the heat generated that the gases escaping into the chimney shall be reasonably low in temperature, say not over 450 F. with anthracite, and 550 F. with bituminous coal? 4. Are the gas passages so designed and arranged as to compel the gas to traverse at a uniform rate the whole of the heating surface, being not so large at any point as to allow of the gas finding a path of least resistance, or short-circuiting, or, on the other hand, so contracted at any point as to cause an obstruction to the draft? These questions being settled in favor of any given boiler and they may be answered favorably for boilers of many of the common types the relative merits of the different types may now be considered with reference to their danger of explosion; their probable durability; the character and extent of repairs that may be needed from time to time, and the difficulty, delay, and expense that these may entail; the accessibility of every part of the boiler to inspection, internal and external; the facility for removal of mud and scale from every portion of the inner surface, and of dust and soot from the exterior; the water and steam capacity; the steadiness of water level, and the arrangements for securing dry steam. Each one of the points referred to above should be considered carefully by the intending purchaser of any type of boiler with which he is not familiar by experience. The several points may be considered more in detail. Danger of Explosion. All boilers may be exploded by overpressure, such as might be caused by the combination of an inattentive fireman and an inoperative safety valve, or by corrosion weakening the boiler to such an extent as to make it unable to resist the regular working pressure; but some boilers are much more liable to explosion than others. In consider- ing the probability of explosion of any boiler of recent design, it is well to study it to discover whether or not it has any of the features that are known to be dangerous in the plain cylinder, the horizontal tubular, the vertical tubular, and the locomotive boilers. The plain cylinder boiler is liable to explosion from strains induced by its method of suspension, and by changes of temperature. Alternate expansion and contraction may produce a line of weakness in one of the rings, which may finally cause an explosion. A boiler should be so suspended that all its parts are free to change their posi- tion under changes of temperature without straining any part. The circulation of water in the boiler should be sufficient to keep all parts at nearly the same temperature. Cold feedwater should not be allowed to come in contact with the shell, as this will cause contraction and strain. The horizontal tubular boiler, and all externally-fired shell boilers, are liable to explosion from overheating of the shell, due to accumulation of mud, scale, or grease, on the portion of the shell lying directly over the fire, to a double thickness of iron with rivets, together with some scale, over the fire, or to low water uncovering and exposing an unriveted part of the shell directly to the hot gases. Vertical tubular boilers are liable to explosion from deposit of mud, scale, or grease, upon the lower tube-sheet, and from low water allowing the upper part of the tubes to get hot and cease to act as stays to the upper tube-sheet. Locomotive boilers may explode from deposits on the crown sheet, from low water exposing the dry crown sheet 180 BOILERS. to the hot gases, and from corrosion of the staybolts. Double-cylinder boilers, such as the French elephant boiler, and the boilers used at some American blast furnaces, have exploded on account of the formation of a "steam pocket" on the upper portion of the lower drum, the steam being prevented from escaping from out of the rings of the drum by the lap joint of the adjoining ring, thus making a layer of steam about i inch thick against the shell, which was directly exposed to the hot gases. Questions to Be Asked Concerning *New Boilers. The causes mentioned above are only a few of the causes of explosions, but they are the principal ones that are due to features of design. These features should be looked for in any new style of boiler, and if they are found they should be considered elements of danger. Such questions as the following may be asked: Is the method of suspension of the boiler such as to allow its parts to be free to move under changes of temperature? Is the circulation such as to keep all parts at practically the same temperature? Is there a shell with riveted seams exposed to the fire? Is there a shell exposed to the fire that may at any time be uncovered by water? Is there a crown sheet on which scale may lodge? Are there vertical or inclined tubes acting as stays to an upper sheet, the upper part of which tubes may become overheated in case of low water? Are there any stayed sheets, the stays of which are liable to become corroded? Is there any chance for a steam pocket to be formed on a sheet that is exposed to the fire? In addition to the above-mentioned features of design, which are elements of danger, all boilers, as already stated, are liable to explosion due to corrosion. Internal corrosion is usually due to acid feedwater, and all boilers are equally liable to it. External corrosion, however, is more liable to take place in some designs of boilers than others, and in some locations rather than others. If any portion of a boiler is in a cold and damp place, it is liable to rust out. For this reason the mud-drums of many modern forms of boilers are made of cast iron, and resist rusting better than either wrought iron or steel. If any part of a boiler, other than a part made of cast iron, is liable to be exposed to a cold and damp atmosphere, or covered with damp soot or ashes, or exposed to drip from rain or from leaky pipes, and especially if such part is hidden by brickwork or otherwise so that it can- not be seen, that part is an element of danger. Durability. The question of durability is partly covered by that of danger of explosion, which has already been discussed, but it also is related to the question of incrustation and scale. The plates and tubes of a boiler may be destroyed by internal or external corrosion, but they may also be burned out. It may be regarded as impossible to burn a plate or tube of iron or steel, no matter how high the temperature of the flame, provided one side of the metal is covered with water. If a steam pocket is formed, so that the water does not touch the metal, or if there is a layer of grease or hard scale, then the plate or tube may be burned. In a water tube that is horizontal, or nearly so, and in which the circulation of water is defective, it is possible to form a mass of steam that will drive the water away from the metal, and thus allow the tube to burn out. In considering the probable durability of a boiler, we may ask the same questions as those that have been asked concerning danger of explosion. There are, however, many chances of burning out a minor part of a boiler without serious danger, to one chance of a disastrous explosion. Thus the tubes of a water-tube boiler, if allowed to become thickly covered with scale, might be burned out again and again without causing any further destruction at any one time than the rupture of a single tube. A new type of boiler should be questioned in regard to the likelihood of frequent small repairs being necessary, as well as in regard to. its liability to complete destruction. We may ask: Is the circulation through all parts of the boiler such that the water cannot be driven out of any tube or from any portion of a plate, so as to form a steam pocket exposed to high temperature ? Are there proper facilities for removing the scale from every portion of the plates and tubes ? Repairs. The questions of durability and of repairs are, in some respects, related to each other. The more infrequent and the less extensive the repairs the greater the durability. The tubes of a boiler, where corroded or burnt out, may be replaced and made as good as new. The shell, when it springs a leak, may be patched, and is then likely to be far from as good as new When the shell corrodes badly it must be replaced, and to replace the shell is the same as getting a new boiler. Herein is the advantage of the sectional water-tube boilers. The sections, or parts of a section, may be WATER AND STEAM CAPACITY. 181 renewed easily, and made as good as new, white the shell, being far removed from the fire and easily kept dry externally, is not liable either to burning out or external corrosion. In considering the merits of a new style of boiler, with reference to repairs, we may ask whp t parts of the boiler are most likely to give out and need to be repaired or replaced? Are these repairs easily effected, how long will they require, and, after they are made, is the boiler as good as new ? Facility for Removal of Scale and for Inspection. These questions have already been discussed to some extent under the head of durability. Some water-tube boilers, now dead and gone, were some years ago put on the market, which had no facilities for the removal of scale. It was claimed by their promoters that they did not need any, because their circulation was so rapid. Every few years boilers of these types are reinvented, and the same claim is made for them, that their rapid circulation prevents the formation of scale. The fact is that if there is scale-forming material in the water it will be deposited when the water is evaporated, and no amount or kind of circulation will keep it from accumulating on every part of the boiler, and in every kind of tubes, vertical, horizontal, and inclined. I have seen the nearly vertical circulating tubes of a water-tube boiler, in which the circulation is nine times as fast as the average circulation in the inclined tubes, nearly full of scale; that is, a 4" tube had an opening in it of less than 1 in. in diameter. This was due to carelessness in blowing off the boiler, or exceptionally bad feedwater, or both. If circulation would prevent scaling at all, it would prevent it here. Water and Steam Capacity. It is claimed for some forms of boilers that they are better than others because they have a larger water or steam capacity. Great water capacity is useful where the demands for steam are extremely fluctuating, as in a rolling mill or a sugar refinery, where it is desirable to store up heat in the water in the boilers during the periods of the least demand, to be given out during periods of greatest demand. Large water capacity is objectionable in boilers for factories, usually, especially if they do not run at night, and the boilers are cooled down, because there is a large quantity of water to be heated before starting each morning. If " rapid steaming" or the ability to get up steam quickly from cold water, or to raise the pressure quickly, is desired, large water capacity is a detriment. The advantage of large steam capacity is usually overrated. It is useful to enable the steam to be drained from water before it escapes into the steam pipe, but the same result can be effected by means of a dry pipe, as in locomotive and marine practice, in which the steam space in the boiler is very small in proportion to the horsepower. Large steam space in the boiler is of no importance for storing energy or equalizing the pressure during the stroke of an engine. The water in the boiler is the place to store heat, and if the steam pipe leading to an engine is of such small capacity that it reduces the pressure, the remedy is a steam reservoir close to the engine or a large steam pipe. Steadiness of Water Level. This requires either a large area of water sur- face, so that the level may be changed slowly by fluctuations in the demand for steam or in the delivery of the feed-pump, or else constant, and preferably automatic, regulation of the feedwater supply to suit the steam demand. A rapidly lowering water level is apt to expose dry sheets or tubes to the action of the hot gases, and thus be a source of danger. A rapidly rising level may, before it is seen by the fireman, cause water to be carried over into the steam pipe, and endanger the engine. Water Circulation. Positive and complete circulation of the water in a boiler is important for two reasons: (1) To keep all parts of the boiler of a uniform temperature, and (2) to prevent the adhesion of steam bubbles to the surface, which may cause overheating of the metal. It is claimed by some manufacturers that the rapid circulation of water in their boilers tends to make them more economical than others. I have as yet, however, to find any proof that increased rapidity of circulation of water beyond that usually found in any boiler will give increased economy. We know that increased rate of flow of air over radiating surfaces increases the amount of heat transmitted through the surface, but this is because by the increased circulation, cold air is continually brought into contact with the surface, making an increased difference of temperature on the two sides, which causes increased transmission. But by increasing the rapidity of circulation in a steam boiler we cannot vary the difference of temperature to any appreciable extent, for the water and the steam in the boiler are at 182 BOILERS. about the same temperature throughout. The ordinary or " Scotch " form of marine boiler shows an exception to the general rule of uniformity of temperature of water throughout the boiler, but the temperature above the level of the lower fire tubes is practically uniform. INCRUSTATION AND SCALE. Nearly all waters contain foreign substances in a greater or less degree, and though this may be a small amount in each gallon, it becomes of importance where large quantities are evaporated. For instance, a 100 H. P. boiler evaporates 30,000 Ib. of water in 10 hours, or 390 tons per month; in comparatively pure water there would be 88 Ib. of solid matter in that quantity, and in many kinds of spring water as much as 2,000 Ib. The nature and hardness of the scale formed of this matter will depend on the kind of substances held in solution and suspension. Analyses of a great variety of incrustations show that carbonate and sulphate of lime Form the larger part of all ordinary scale, that from carbonate being soft and granular, and that from sulphate, hard and crystalline. Organic substances in connection with carbonate of lime will also make a hard and troublesome scale. The presence of scale or sediment in a boiler results in loss of fuel, burning and cracking of the boiler, predisposes to explosion, and leads to extensive repairs. It is estimated that the presence of ^ in. of scale causes a loss of 13$ of fuel; in., 38$; and in., 60$. The Railway Master Mechanics' Association of the United States estimates that the loss of fuel, extra repairs, etc., due to incrustation, amount to an average of $750 per annum for every locomotive in the Middle and Western States, and it must be nearly the same for the same power in stationary boilers. Causes of Incrustation. 1. Deposition of suspended matter. 2. Deposition of salts from concentration. 3. Deposition of carbonates 9f lime and magnesia, by boiling off carbonic acid, which holds them in solution. 4. Deposition of sulphates of lime, because sulphate of lime is soluble in cold water, less soluble in hot water, insoluble above 270 F. 5. Deposit of magnesia, because magnesium salts decompose at high temperatures. 6. Deposition of lime soap, iron soap, etc., formed by saponification of grease. Method of Preventing Incrustation. 1. Filtration. 2. Blowing off. 3. Use of internal collecting apparatus, or devices, for directing the circulation. 4. Heating feed water. 5. Chemical or other treatment of water in boiler. 6. Introduction of zinc in boiler. 7. Chemical treatment of water outside of boiler. Troublesome Substance. Trouble. Remedy or Palliation. Sediment, mud, clay, etc. Incrustation. Filtration; blowing off. Readily soluble salts. Incrustation. Blowing off. Bicarbonates of lime, magnesia, and iron. Incrustation. Heating feed; addition of caustic soda, lime, or magnesia, etc. Sulphate of lime. Incrustation. Addition of carbonate of soda, barium chloride, etc. Chloride and sulphate of magnesium. Corrosion. Addition of carbonate soda, etc. Carbonate of soda in large amounts. Priming. Addition of barium chloride, etc. Acid (in mine water). Corrosion. Alkali. Dissolved carbonic acid and oxygen. Corrosion. Heating feed; addition of caustic soda, slaked lime, etc. Grease (from condensed water). Corrosion. Slaked lime and filtering. Substitute mineral oil. Organic matter (sewage). Priming. Precipitate with alum or ferric chloride, and filter. Organic matter. Corrosion. Precipitate with alum or ferric chloride, and filter. PREVENTION OF SCALE. 183 Means of Prevention. It is absolutely essential to the successful use of any boiler, except in pure water, that it be accessible for the removal of scale, for though a rapid circulation of water will delay the deposit, and certain ' chemicals will change its character, yet the most certain cure is periodical inspection and mechanical cleaning. This may, however, be rendered less frequently necessary, and the use of very bad water more practical by the employment of some preventives. The following are fair samples of those in use, with their results: M. Bidard's observations show that " anti-incrustators " containing organic matter help rather than hinder incrustations, and are therefore to be avoided. Oak, hemlock, and other barks and woods, sumac, catechu, logwood, etc. are effective in waters containing carbonates of lime or magnesia, by reason of their tannic acid, but are injurious to the iron and not to be recom- mended. Molasses, cane juice, vinegar, fruits, distillery slops, etc. have been used with success so far as scale is concerned, by reason of the acetic acid that they contain, but this is even more injurious to the iron than tannic acid, while the organic matter forms a scale with sulphate of lime when it is present. Milk of lime and metallic zinc have been used with success in waters charged with bicarbonate of lime, reducing the bicarbonate to the insoluble carbonate. Barium chloride and milk of lime are said to be used with good effect at Krupp's works, in Prussia, for waters impregnated with gypsum. Soda ash and other alkalies are very useful in waters containing sulphate of lime, by converting it into a carbonate, and so forming a soft scale easily cleaned. But when used in excess they cause foaming, particularly where there is oil coming from the engine, with which they form soap. All soapy substances are objectionable for the same reason. Petroleum has been much used of late years. It acts best in waters in which sulphate of lime predominates. Sulphate of lime is the injurious substance in nearly all mine waters, and petroleum, when properly prepared, is a good preventive of scale and pitting. Crude petroleum should not be used, as it sometimes helps in forming a very injurious scale. Refined petroleum, on the other hand, is useless, as it vaporizes at a temperature below that of boiling water. Therefore, only such prepara- tions should be used as will not vaporize below 500 F. Tannate of soda is a good preparation for general use, but in waters con- taining much sulphate, it should be supplemented by a portion of carbonate of soda or soda ash. A decoction from the leaves of the eucalyptus is found to work well in some waters in California. For muddy water, particularly if it contain salts of lime, no preventive of incrustation will prevail except filtration, and in almost every instance the use of a filter, either alone or in connection with some means of precipita- ting the solid matter from solution, will be found very desirable. In all cases where impure or hard waters are used, frequent "blowing" from the mud-drum is necessary to carry off the accumulated matter, which if allowed to remain would form scale. When boilers are coated with a hard scale, difficult to remove, it will be found that the addition of i Ib. caustic soda per horsepower, and steaming for some hours, according to the thickness of the scale, just before cleaning, will greatly facilitate that operation, rendering the scale soft and loose. This should be done, if possible, when the boilers are not otherwise in use. COVERING FOR BOILERS, STEAM PIPES, ETC. The losses by radiation from unclothed pipes and vessels containing steam are considerable, and in the case of pipes leading to steam engines, are magnified by the action, of the condensed water in the cylinder. It there- fore is important that such pipes should be well protected. The following table gives the loss of heat from steam pipes naked, and clothed with wool or hair felt, of different thickness, the steam pressure being assumed at 75 Ib., and the exterior air at 60. There is a wide difference in the value of different substances for protec- tion from radiation, their values varying nearly in the reverse ratio to their conducting power for heat, up to their ability to transmit as much heat as 184 BOILERS. the surface of the pipe will radiate, after which they become detrimental, rather than useful, as covering. This point is reached nearly at baked clay or brick. TABLE OF Loss OF HEAT FROM STEAM PIPES. i Outside Diameter of Pipe, Without Felt. 2 In. Diameter. 4 In. Diameter. 6 In. Diameter. 8 In. Diameter. 12 In. Diameter. S S3 S3 I pX jj p:| .k 1 1 O i || 1 "3 o 2* lg. ri o of Loss 1 9 .s* m i .2 bo o J5 o w to o of Loss 1 a ifa "" W Jh 1 'Z w * jjj ofe 8 H-' ofe 1 '" W 1-3 S3 M $ fe M i 1-1 S3 P5 i *"* S3 M ^ H i H fe i* & P, Si 219.0 1.00 132 390.8 1.00 75 624.1 1.000 46 729.8 1.000 40 1,077.4 1.000 26 ^- 100.7 .46 288 180.9 .46 160 1 65.7 .30 441 117.2 .30 247 187.2 .300 154 219.6 .301 132 301.7 .280 92 1 43.8 .20 662 73.9 .18 392 111.0 .178 261 128.3 .176 225 185.3 .172 157 2 28.4 .13 1,020 44.7 .11 648 66.2 .106 438 75.2 .103 385 98.0 .091 294 4 19.8 .09 1,464 28.1 .07 1,031 41.2 .066 703 46.0 .063 630 60.3 .056 486 6 23.4 .00 1,238 33.7 .054 8t;o 34.3 .047 845 45.2 .042 642 A smooth or polished surface is of itself a good protection, polished tin or Russia iron having a ratio, for radiation, of 53 to 100 for cast iron. Mere color makes but little difference. TABLE OF CONDUCTING POWER OF VARIOUS SUBSTANCES. (From Peclet.) Substance. Conducting Power. Substance. Conducting Power. Blotting paper .274 Wood, across fiber. 83 Eiderdown 314 Cork 1 15 Cotton or Wool, ) any density j -- .323 Coke, pulverized India rubber 1.29 1 37 Hemp canvas .418 Wood, with fiber 1.40 Mahogany dust .523 Plaster of Paris 3.86 Wood ashes .531 Baked clay 4.83 Straw 563 Glass 6.60 Charcoal powder .636 Stone ., 13.68 Hair or wool felt has the disadvantage of becoming soon charred from the heat of steam at high pressure, and sometimes of taking fire therefrom. This has led to a variety of "cements" for covering pipes composed gen- erally of clay mixed with different substances, as asbestos, paper fiber, charcoal, etc. A series of careful experiments, made at the Massachusetts Institute of Technology in 1871, showed the condensation of steam in a pipe covered by one of them, as compared with a naked pipe, and one clothed with hair felt, was 100 for the naked pipe, 67 for the "cement" covering, and 27 for the hair felt. The presence of sulphur in the best coverings and its recognized injurious effects make it imperative that moisture be kept from the coverings, for, if present, it will surely combine with the sulphur, thus making it active. Stated in other words, keep the pipes and coverings in good repair. Much of the inefficiency of coverings is due to the lack of attention given them; they are often seen hanging loosely from the pipe which they are supposed to protect. CARE OF BOILERS. 185 TABLE OF RELATIVE VALUE OF NON-CONDUCTORS. (From Chas. E. Emery, Ph. D.) Non-Conductor. Value. Non-Conductor. Value. Wool felt 1.000 Loam, dry and open .550 Mineral wool No 2 832 Slaked lime .480 Mineral with tar 715 Gas-house carbon .470 Sawdust .680 Asbestos .363 Mineral wool No 1 676 Coal ashes .345 Charcoal .632 Coke in lumps .277 Pine wood across fiber .553 Air space undivided .136 Carbonate of magnesia, as compared with wool felt at 1.000, has a rela- tive value of .472. This is determined from tests by Prof. Ordway, of Boston, and adjusted to results shown in Prof. Emery's tests. " Mineral wool," a fibrous material made from blast-furnace slag, is a good protection, and is incombustible. Cork chips, cemented together with water glass, make one of the best coverings known. A cheap jacketing for steam pipes, but a very efficient one, may be applied as follows: First, wrap the pipe in asbestos paper, though this may be dispensed with; then lay slips of wood lengthways, from 6 to 12, accord- ing to size of pipe, binding them in position with wire or cord, and around the framework thus constructed wrap roofing paper, fastening it by paste or twine. For flanged pipe, space may be left for access to the bolts, which space should be filled with felt. If exposed to weather, use tarred paper, or paint the exterior. A French plan is to cover the surface with a rough flour paste, mixed with sawdust until it forms a moderately stiff dough. Apply with a trowel in layers of about in. thick; give 4 or 5 layers in all. If iron surfaces are well cleaned from grease, the adhesion is perfect. For copper, first apply a hot solution of clay in water. A coating of tar renders the composition impervious to the weather. DATA FOR PROPORTIONING AN ECONOMIZER. (The Green Fuel Economizer Co., Matteawan, N. Y.) The following estimate is given for the amount of heating surface to be provided in an economizer to be used in connection with a given amount of boilers: By allowing 4 sq. ft. of heating surface per boiler horsepower (Centennial rating, 34 Ib. of water evaporated from and at 212 = 1 H. P.), we are able to raise the feedwater 60 for every 100 reduction in the temperature enter- ing the economizer with gases from 450 to 600. These results are cor- roborated by Mr. Barrus's tests. With the temperature of the gases entering the economizer at 600 to 700, we have allowed 4i to 5 sq. ft. of heating surface per boiler horsepower, and for every 100 reduction of gases we have obtained about 65 rise in temperature of the water; the temperature of the feedwater entering aver- aging from 60 to 120. With 5,000 sq. ft. of boiler heating surface (plain cylinder boilers) develop- ing 1,000 H. P., we should recommend using 5 sq. ft. of economizer heating surface per B. H. P., or an economizer of about 500 tubes, and it should neat the feedwater about 300. CARE OF BOILERS. 1. Safety Valves. Great care should be exercised to see that these valves are ample in size and in working order. Overloading or neglect frequently leads to the most disastrous results. Safety valves should be tried at least once every day, to see that they act freely. 2. Pressure Gauge. The steam gauge should stand at zero when the pressure is off, and it should show same pressure as the safety valve when that is blowing off. If not, then one is wrong, and the gauge should be tested by one known to be correct. 186 BOILERS. 3. Water Level. The first duty of an engineer before starting, or at the beginning of his watch, is to see that the water is at the proper height. Do not rely on glass gauges, floats, or water alarms, but try the gauge-cocks. If they do not agree with water gauge, learn the cause arid correct it. 4. Gauge-cocks and water gauges must be kept clean. Water gauges should be blown out frequently, and the glasses and passages to them kept clean. The Manchester, England, Boiler Association attributes more accidents to inattention to water gauges than to all other causes put together. 5. Feed-Pump or Injector. These should be kept in perfect order, and be of ample size. No make of pump can be expected to be continuously reliable without regular and careful attention. It is always safe to have two means of feeding a boiler. Check-valves and self-acting feed-valves should be frequently examined and cleaned. Satisfy yourself frequently that the valve is acting when the feed-pump is at work. 6. Low Water. In case of low water, immediately cover the fire with ashes (wet if possible) or any earth that may be at hand. If nothing else is handy, use fresh coal. Draw fire as soon as it can be done without increas- ing the heat. Neither turn on the feed, start nor stop engine, nor lift safety valve until fires are out and the boiler cooled down. 7. Blisters and Cracks. These are liable to occur in the best plate iron. When the first indication appears, there must be no delay in having it carefully examined and properly cared for. 8. Fusible plugs, when used, must be examined when the boiler is cleaned, and carefully scraped clean on both the water and fire sides, or they are liable not to act. 9. Firing. Fire evenly and regularly, a little at a time. Moderately thick fires are most economical, but thin firing must be used where the draft is poor. Take care to keep grates evenly covered, and allow no air holes in the fire. Do not "clean" fires oftener than necessary. With bituminous coal, a "coking fire," i. e., firing in front and shoving back when coked, gives best results if properly managed. 10. Cleaning. All heating surfaces must be kept clean outside and in, or there will be a serious waste of fuel. The frequency of cleaning will depend on the nature of fuel and water. When a new feedwater supply is introduced, its effect upon the boiler should be closely observed, as this new supply may be either an advantage or a detriment as compared with the working of the boiler previous to its introduction. As a rule, never allow over T y scale or soot to collect on surfaces between cleanings. Handholes should be frequently removed and surfaces examined, particularly in case of a new boiler, until proper intervals have been established by experience. The exterior of tubes can be kept clean by the use of blowing pipe and hose through openings provided for that purpose. In using smoky fuel, it is best to occasionally brush the surfaces when steam is off. 11. Hot Feedwater. Cold water should never be fed into any boiler when it can be avoided, but when necessary it should be caused to mix with the heated water before coming in contact with any portion of the boiler. 12. Foaming. When foaming occurs in a boiler, checking the outflow of steam will usually stop it. If caused by dirty water, blowing down and pumping up will generally cure it. . In cases of violent foaming, check the draft and fires. 13. Air Leaks. Be sure that all openings for admission of air to boiler or flues, except through the fire, are carefully stopped. This is frequently an unsuspected cause of serious waste. 14. Blowing Off. If feedwater is muddy or salt, blow off a portion fre- quently, according to condition of water. Empty the boiler every week or two, and fill up afresh. When surface blow cocks are used, they should be often opened for a few minutes at a time. Make sure no water is escaping from the blow-off cock when it is supposed to be closed. Blow-off cocks and check-valves should be examined every time the boiler is cleaned. Never empty the boiler while the brickwork is hot. 15. Leaks. When leaks are discovered, they should be repaired as soon as possible. 16. Filling Up. Never pump cold water into a hot boiler. Many times leaks, and, in shell boilers, serious weaknesses, and sometimes explosions are the result of such an action. THICKNESS OF BOILER IRON. 187 17. Dampness. Take care that no water comes in contact with the exterior of the boiler from any cause, as it tends to corrode and weaketfi the boiler. Beware of all dampness in seatings and coverings. 18. Galvanic Action. Examine frequently parts in contact with copper or brass, where water is present, for signs of corrosion. If water is salt or acid, some metallic zinc placed in the boiler will usually prevent corrosion, but it will need attention and renewal from time to.time. 19. Rapid Firing. In boilers with thick plates or seams exposed to the fire, steam should be raised slowly, and rapid or intense firing avoided. With thin water tubes, however, and adequate water circulation, no dam- age can come from that cause. 20. Standing Unused. If a boiler is not required for some time, empty and dry it thoroughly. If this is impracticable, fill it quite full of water, and put in a quantity of common washing soda. External parts exposed to damp- ness should receive a coating of linseed oil. 21. Repair of Coverings. All coverings should be looked after at least once a year, given necessary repairs, refitted to the pipe, and the spaces due to shrinkage taken up. Little can be expected from the best non-conductors if they are allowed to become saturated with water, or if air-currents are permitted to circulate between them and the pipe. 22. General Cleanliness. All things about the boiler room should be kept clean and in good order. Negligence tends to waste and decay. THICKNESS OF BOILER IRON REQUIRED AND PRESSURE ALLOWED BY THE LAWS OF THE UNITED STATES. PRESSURE EQUIVALENT TO THE STANDARD FOR A BOILER 42 IN. IN DIAM- ETER AND i IN. THICK. Diameter. Aiiiuji-iicoa. 16ths 34 In. 36 In. 38 In. 40 In. 42 In. 44 In. 46 In. Lb. ^Lb. Lb. Lb. Lb. Lb. Lb. 5 169.9 160.4 152.0 144.4 137.5 131.2 125.5 44 158.5 149.7 141.8 134.7 128.3 122.5 117.2 4 135.9 128.3 121.6 115.5 110.0 105.0 100.0 3| 124.5 117.6 111.4 105.9 100.8 96.2 92.0 3| 113.2 106.9 101.3 96.2 91.7 87.5 83.0 3 101.9 96.2 91.2 82.6 82.5 78.7 75.1 The rule for finding the proper sectional area for the narrowest part of the nozzle is given by Rankine, S. E., page 477, as follows: Area in square inches = cubic feet per hour gross feedwater 800 1/ pressure in atmospheres Delivery in Gallons per Hour with a Pressure Diameter of Throat. Decimals per Square Inch of of an Inch. 30 Lb. 45 Lb. 60 Lb. 75 Lb. 90 Lb. .10 56 69 80 89 98 .15 127 156 180 201 221 .20 226 278 321 360 393 .25 354 434 502 561 615 .30 505 624 722 807 884 188 BOILERS. PRESSURE OF STEAM AT DIFFERENT TEMPERATURES. (Results of Experiments Made by the Franklin Institute.} Pressure. Inches of Tempera- ture. Pressure. Inches of Tempera- ture. Pressure. Inches of Tempera- ture. Mercury. Degrees F. Mercury. Degrees F. Mercury. Degrees F. 30 212.0 135 298.5 225 331.0 45 235.0 150 304.5 240 336.0 60 250.0 165 310.0 255 340.5 75 264.0 180 315.5 270 345.0 90 275.0 195 321.0 285 349.0 105 284.0 210 326.0 300 352.5 120 291.5 MAXIMUM ECONOMY OF PLAIN CYLINDER BOILERS. Pounds of Water Evaporated From and at 212. Per sq. ft. heating surface per hour Per Ib. combustible, maximum of other boilers, Centennial tests 1.70 11.90 1.32 10.58 2.00 12.00 1.12 10.88 2.60 12.10 .87 11.23 12.05 .75 11.30 3.50 12.00 .64 11.36 4.00 11.85 .56 11.29 4.50 11.70 .50 11.20 5.00 11.50 .45 11.05 6.00 10.85 .37 10.48 7.00 9.80 .32 9.48 8.00 8.50 .28 8.22 Subtract extra radia- tion loss for cylin- der boilers Probable maximum per Ib. combus- tible, cylinder boilers SCHEME FOR BOILER TEST. Number of test Made by Type of boiler > Date of test Duration of test Dimensions and Proportions. Number of boilers tested Diameter, boiler Length, boiler Width, grate Length, grate Number of tubes Diameter of tubes Length of tubes Total water heating surface Total steam heating surface Grate surface per boiler Per cent, air space in grate Ratio water heating to grate surface Area of stack Height stack above dead plates Ratio stack area to grate surface Average Pressures. Atmosphere by barometer Steam pressure by gauge Hr. In. Ft. In. Ft. In. Ft. In. No. In. Ft. In. Sq. Ft. Sq. Ft. Sq. Ft. Sq.Ft. Ft. In. Lb. CHIMNEYS. 189 SCHEME FOR BOILER TEST (Contin ued). 24 Force chimney draft, inches water In. 25 Force blast in ash pit, inches water In. Average Temperatures. 26 Of external air F. 27 Offireroom P. 28 Of steam F. 29 Of feedwater before heater F. 30 Of feed water after heater.: F. 31 Of stack gases F. Fuel. 32 Kind of coal 33 Total coal consumed Lb. 34 Moisture in coal % 35 Total dry coal consumed Lb. 36 Total ash and refuse Lb. 37 Per cent, ash and refuse in dry coal $ 38 Total combustible consumed Lb. CALORIMETRIC TESTS. 39 Percent, moisture in steam ..... $ 40 Degrees superheat in steam F. Water. 41 Total water pumped into boiler Lb. 42 \Vaterevaporatedcorrectedforqualityofsteam Lb. 43 Equiv. water evap. to dry steam from and at 212 Lb. 44 Equiv. water evap. to dry steam from and at 212 per hour Lb. Economic Evaporation. 45 Water evap. per Ib. dry coal actual pressures and temp Lb. 46 Equiv. water evap. Ib. dry coal from and at 212 Lb. 47 Equiv. water evap. Ib. combustible from and at 212 Lb. Rate of Combustion. 48 Dry coal burned per hr. per sq. ft. grate surface Lb. 49 Combustible burned per hr. per sq. ft. grate surface Lb. 50 Dry coal per hour per H. P. developed Lb. Rate of Evaporation. 51 Water evap. from and ) Per sq. ft. grate surface Lb. 52 at 212 per hour /Per sq. ft. heating surface Lb. Commercial Horsepower. 53 Basis 20 Ib. water from 100 feed to 70 Ib. steam per hour H. P. 54 Horsepower builders rating , H. P. 55 Heating surface to one horsepower developed Sq. Ft. 56 Per cent, total horsepower due to feedheater. $ CHIMNEYS. Chimneys have two important duties to perform, the first being to carry off the waste furnace gases, which requires size, and the second, to produce a draft sufficient to insure the complete combustion of the fuel, which requires height. The area of a chimney is usually made from f to A as large as the area of the furnace grates, or of about the same cross-section as the cross-sectional area of the flues or tubes; we have, therefore, a comparatively simple method of determining one of the required dimensions of a chimney, and, \vhen this is known, it becomes an easy matter to determine the height of the chimney when the horsepower of the boiler has been ascertained. The horsepower of a boiler being given, and the necessary chimney area having been determined, the following rule gives the required height that the chimney must be to produce the necessary draft: Rule. From 3.33 times the area of the chimney in square feet, subtract twice the square root of the area of the chimney in square feet, and divide the given horsepower by the remainder. The square of the quotient will be the height of the chimney in feet. Let A area of chimney; H = horsepower of boiler; h = height of chimney. Then, h = \3.33 A 2}/A 190 STEAM ENGINES. EXAMPLE. What must be the height of a chimney that is to have a cross- sectional area of 7 sq. ft., and to supply the draft for a 141-horsepower boiler ? = 6L3fL Ans - V 7 - 2j/ 7/ ^ 9 3 - 33 X 7 - (2 Forced Draft. The use of forced draft as a substitute for, or as an aid to, natural chimney draft is becoming quite common in large boiler plants. Its advantages are that it enables a boiler to be driven to its maximum capacity to meet emergencies without reference to the state of the weather or to the character of the coal; that the draft is independent of the tempera- ture of the chimney gases, and that therefore lower flue temperatures may be used than with natural draft; and in many cases that it enables a poorer quality of coal to be used than is required with natural draft. Forced draft may be obtained: First, by a steam jet in the chimney, as in locomotives and steam fire-engines; second, by a steam-jet blower under the grate bars; third, by a fan blower delivering air under the grate bars, the ash-pit doors being closed; fourth, by a fan blower delivering air into a closed fireroom, as in the " closed stoke-hold " system used in some ocean-going vessels; and fifth, by a fan placed in the flue or chimney drawing the gases of combustion from the boilers, commonly called the induced-draft system. Which one of these several systems should be adopted in any special case will usually depend on local conditions. The steam jet has the advantage of lightness and compactness of apparatus, and is therefore most suitable for locomotives and steam fire-engines, but it also is the most wasteful of steam, and there- fore should not be used when one of the fan-blower systems is available, except for occasional or temporary use, or when very cheap fuel, such as anthracite culm at the coal mines, is used. STEAM ENGINES. What Is a Good Steam Engine? It should be as direct acting as possible; that is, the connecting parts between the piston 'and the crank-shaft should be few in number, as each part wastes some power. Formerly, beam engines were all the rage. They were well enough in their time for pump- ing, when the pump was at one end of the beam and the piston at the other. Few of our modern colliery engines have such an appendage, except in some instances for pumping, and even for that kind of work the better engines have no beams. The moving parts of an engine should be strong, to resist strains, and light, so as to offer no undue resistance to motion; parts moving upon each other should be well and truly and smoothly finished, to reduce resistances to a minimum; the steam should get into the cylinder easily at the proper time, and the exhaust should leave the cylinder as exactly and as easily. The steam pipes supplying steam should have an area one-tenth the combined areas of the cylinders they supply, and exhaust pipes should be somewhat larger. The cylinder and the steam pipes and the boiler should be well protected. The engine should be capable of being started and stopped and reversed easily and quickly. Rule. To find the indicated horsepower developed by an engine, multiply together the M. E. P. per square inch, the area of the piston, the length of stroke, and the number of strokes per minute. This gives the work per minute in foot- pounds. Divide the product by 83,000; the result will be the indicated horse- power of the engine. Let I. H. P. = indicated horsepower of engine; P = M. E. P. in pounds per square inch; A = area of piston in square inches; L = length of stroke in feet; N = number of strokes per minute. Then, the above rule may be expressed thus: _PLAN ' 33,000 ' The number of strokes per minute is twice the number of revolutions per minute. For example, if an engine runs at a speed of 210 revolutions per minute, it makes 420 strokes per minute. A few types of engines, however, are single acting; that is, the steam acts on only one side of the piston. In this case, only 1 stroke per revolution does work, and, consequently, the RULES FOR ENGINE DRIVERS. 191 number of strokes per minute to be used in the above rule is the same as the number of revolutions per minute. EXAMPLE. The diameter of the piston of an engine is 10 in. and the length of stroke 15 in. It makes 250 revolutions per minute, with a M. E. P. of 40 Ib. per sq. in. What is the horsepower ? As it is not stated whether the engine is single or double acting, assume that it is double acting. Then, the number of strokes is 250 X 2 = 500 per minute. Hence, T TT T> - PLA N - 40 X if X (10 2 X .7854) X 500 r H * p ' ~3poo~ : 33,000 To find the horsepower, the value for the M. E. P. must be substituted for P in the formula I. H. P. = ^^p Reducing the stroke to feet, and substituting the values of P, L, A, and N, we have 46.92 X fg X (18 2 X .7854) X (200 X 2) 33,000 Approximate Determination of M. E. P. To approximately determine the M. E. P. of an engine, when the point of apparent cut-off is known and the boiler pressure, or the pressure per square inch in the boiler from which the supply of steam is obtained, is given: Ru\t.Add 1U.1 to the gauge pressure, and multiply the result by the number opposite the fraction indicating the point of cut-off in the following table. Subtract 17 from the product, and multiply by .9. The result is the M. E. P. for good, simple non-condensing engines. Or, letting p = gauge pressure; k = a constant (see following table); M. E. P. = mean effective pressure. Then, M. E. P. = .9[&(p + 14.7) - 17]. TABLE. Cut-Off. Constant. Cut-Off. Constant. Cut-Off. Constant. 1 .566 1 .771 .917 I .603 .4 .789 .7 .926 I .659 f .847 .937 3 .708 .6 .895 .8 .944 i .743 i .904 I .951 If the engine is a simple condensing one, subtract the pressure in the condenser instead of 17. The fraction indicating the point of cut-off is obtained by dividing the distance that the piston has traveled when the steam is cut off by the whole length of the stroke. For a | cut-off, and 92 Ib. gauge pressure in the boiler, the M. E. P. is, by the formula just given, .9 [.917(92 + 14.7) - 171 = 72.6 Ib. per sq. in. EXAMPLE. Find the approximate 1. H. P. of a 9" X 12" non-condensing engine, cutting off at i stroke, and making 240 revolutions per minute. The boiler pressure is 80 Ib. gauge. 80 + 14.7 = 94.7. The constant for cut-off is .847, and .847 X boiler pressure = .847 X 94.7 = 80.21. M. E. P. = (80.21 17) X .9 = 56.89 Ib. per sq. in. - Then, PLAN 56.89 X H X (.7854 X 9) X 24 X 2 *~~ 33,000 RULES FOR ENGINE DRIVERS. If a gauge glass breaks, turn off the water first and then the steam, to avoid scalding yourself. Don't buy oil or waste simply because it is very cheap; it will cost more than a good article in the end. 192 STEAM ENGINES. In cutting rubber for gaskets, etc., have a dish of water handy, and keep wetting the knife blade; it makes the work much easier. Don't forget that there is no economy in employing a poor fireman. He can, and probably will, waste more coal than would pay the wages of a first- class man. An ordinary steam engine having two cylinders connected at right angles on the same shaft consumes one-third more steam than a single-cylinder engine, while developing only the same amount of power. A fusible plug ought to be renewed every three months, by removing the old metal and refilling the case; and it should be scraped clean and bright on both ends every time that the boiler is washed out, to keep it in good working order. When you try a gauge-cock, don't jerk it open suddenly, for if the water happens to be a trifle below the cock, the sudden relief from pressure at that point may cause it to lift and flow out, deceiving you in regard to its height. Whereas, if you open it quietly, no lift will occur, and you ascertain surely whether there is water or steam at that level. Always open steam stop-valves between boilers very gently, that they may heat and expand gradually. By suddenly turning on steam a stop- valve chest was burst, due to the expansive power of heat unequally applied. The same care is also recommended when shutting off stop- valves. A fearful explosion once occurred by shutting a communicating stop-valve too suddenly due to the recoil. In order to obtain the driest possible steam from a boiler, there should be an internal perforated pipe (dry pipe, so called) fixed near the top of the boiler, and suitably connected to the steam pipe. The perforations in this pipe should be from one-quarter to one-half greater in area than that of the steam pipe. Domes are of no use as steam driers; they only add a very little to the steam space of a boiler, and are often a source o*f loss by radiation. If a glass gauge tube is t9O long, take a triangular file and wet it; hold the tube in the left hand, with the thumb and forefinger at the place where you wish to cut it, saw it quickly and '.lightly two or three times with the edge of the file, and it will mark the glass. Now take the tube in both hands, both thumbs being on the side opposite the mark, and an inch or so apart, and then try to bend the glass, using your thumbs as fulcrums, and it will break at the mark, which has weakened the tube. A stiff charge of coal all over a furnace will lower the temperature 200 or 300 in a very short time. After the coal is well ignited the temperature will rise about 500, and as it continues burning will gradually drop about 200, until the fireman puts in another charge, when the sudden fall before mentioned takes place again. This sudden contraction and expansion frequently causes the bursting of a boiler, and it is for this reason that light and frequent charges of coal, or else firing only one-half of the furnace at a time, should be always insisted on. Be careful when using a wrench on hexagonal nuts that it fits snugly, or the edges of the nut will soon become rounded. Be careful how you use a monkey wrench, for if it is not placed on the nut properly the strain will often bend or fracture the wrench. The area of grate for a boiler should never be less than sq. ft. per I. H. P. of the engine, and it is seldom advisable to increase this allowance beyond I sq. ft. per I. H. P. The area of tube surface for a boiler should not be less than 2i sq. ft. per I. H. P. of the engine. The ratio of heating surface to grate area in a boiler should be 30 to 1 as a minimum, and may often be increased to 40 to 1, or even more, with advantage. Lap-welded pipe of the same rated size has always the same .outside diameter, whether common, extra, or double extra, but the internal diame- ter is of course decreased with the increased thickness. A good cement for steam and water joints is made by taking 10 parts, by weight, of white lead, 3 parts of black oxide of manganese, 1 part of litharge, and mixing them to the proper consistency with boiled linseed oil. To harden a cutting tool, heat it in a coke fire to a blood-red heat and plunge it into a solution of salt and water (1 Ib. of salt to 1 gal. of water), then polish the tool, heat it over gas, or otherwise, until a dark straw and purple mixed color shows on the polish, and cool it in the salt water. Small articles can be plated with brass by dipping them in a solution of 9i gr. each of sulphate of copper and chloride of tin, in If pt. of water. BELTING AND VELOCITY OF PULLEYS. 193 Don't be eternally tinkering about your engine, but let well enough alone. Don't forget that with a copper hammer you can drive a key just as well as with a steel one, and that it doesn't leave any marks. Keep on hand slips of thin sheet copper, brass, and tin, to use as liners, and if you shape some of them properly, much time will be saved when you need them. A few wooden skewer pins, such as butchers use, are very useful for many purposes in an engine room. Try them. In running a line of steam pipe where there are certain rigid points, make arrangements for expansion on the line between those points, or you will come to grief. Arrange the usual work of the engine and firerooms systematically, and adhere to it. It pays well. Don't forget that cleanliness is next to godliness. Rubber cloth kept on hand for joints should be rolled up and laid away by itself, as any oil or grease coming in contact with it will cause it to soften and give out when put to use. When using a jet condenser, let the engine make three or four revolutions before opening the injection valve, and tnen open it gradually, letting the engine make several more revolutions before it is opened to the full amount required. Open the main stop-valve before you start the fires under the boilers. When starting fires, don't forget to close the gauge-cocks and safety valve as soon as steam begins to form. An old Turkish towel, cut in two lengthwise, is better than -cotton waste for cleaning brass work. Always connect your steam valves in such a manner that the valve closes against the constant steam pressure. Turpentine well mixed with black varnish makes a good coating for iron smoke pipes. Ordinary lubricating oils are not suitable for use in preventing rust. You can make a hole through glass by covering it with a thin coating of wax, warming the glass and spreading the wax on it. Scrape off the wax where you want the hole, and drop a little fluoric acid on the spot with a wire. The acid will cut a hole through the glass, and you can shape the hole with a copper wire covered with oil and rottenstone. A mixture of 1 oz. of sulphate of copper, i oz. of alum, i teaspoonful of powdered salt, 1 gill of vinegar and 20 drops of nitric acid will make a hole in steel that is too hard to cut or file easily. Also, if applied to steel and washed off quickly, it will give the metal a beautiful frosted appearance. BELTING AND VELOCITY OF PULLEYS. Belts should not be made tighter than necessary. Over half the trouble from broken "pulleys, hot boxes, etc. can be traced to the fault of tight belts, while the machinery wears much more rapidly than when loose belts are employed. The speed of belts should not be more than 3,000 or 3,750 ft. per minute. The motion of driving should run with and not against the laps of the belts. Leather belts should be run with the stronger or flesh side on the outside and the grain (hair) side on the inside, nearest the pulley, so that the stronger part of the belt may be subject to the least wear. It will also drive 30$ more than if run with the flesh side nearest the pulley. The grain side adheres better because it is smooth. Do not expose leather belts to the weather. When the length of a belt cannot be conveniently ascertained by measuring around the pulleys with a tape line, the following rule will be serviceable: Add the diameters of the 2 pulleys together and divide by 2; multiply this quotient by 3i, and to the product add twice the distance between the centers of the shafts; the sum will be the length required. 194 COMPRESSED AIR. COMPRESSED AIR.* BY PROF. ROBERT PEELE. An air compressor consists essentially of a cylinder in which atmospheric air is compressed by a piston, the driving power being steam or water. Classification of Compressors. Steam-driven compressors in ordinary use may be classed as follows: (a) Straight-line type, in which a single horizontal air cylinder is set tandem with its steam cylinder, and provided with two flywheels. This pattern is generally adapted for compressors of small size. (6) Duplex type, in which there are two steam cylinders, each driving an air cylinder, and coupled at 90 to a crank-shaft carrying a flywheel. (c) Horizontal, cross-compound engines, each steam cylinder set tandem with an air cylinder, as in (6). (d) Vertical, simple, or compound engines, with the air cylinders set above the steam cylinders. (e) Compound or stage compressors, in which the air cylinders themselves are compounded. The compression is carried to a certain point in one cylinder and successively raised and finally completed to the desired pres- sure in the others. They may be either of the straight-line or duplex form, with simple or compound steam cylinders. Classes (a), (6), (c), and (e) are those commonly employed for mine service. The principle of compound, or two-stage, air compression is recognized as applicable for even the moderate pressures required in mining, and the compressors of class (e) are frequently employed. Construction of Compressors. Compressors are usually built with a short stroke, as this is conducive to economy in compression as well as the attain- ment of a proper rotative speed. In ordinary single-stage compressors, the usual ratio of length of stroke to diameter of steam cylinders is 1 to 1 or 1 to 1. In some makes, such as the Rand, the ratio is considerably greater, varying from H to If to 1, as in several large plants built for the Calumet & Hecla Mining Co. Many compressors have length and diameter of steam cylinders equal. The relative diameters of the air and steam cylinders depend on tne steam pressure carried, and the air pressure to be produced. In mining operations, there is usually but little variation in these con- ditions. For rock-drill work, the air pressure is generally from 60 to 80 Ib. In usmg water-power, a compressor is driven most conveniently by a bucket impact wheel, such as the Pelton or Knight. The waterwheel is generally mounted directly on the crank-shaft, without the use of gearing. Since the power developed is uniform throughout the revolution of the wheel, the compressor should be of duplex form, in order to equalize the resistance so far as possible. The rim of the wheel is made extra heavy, to supply the place of a flywheel. When direct-connected, the wheel is of relatively large diameter, as its speed of rotation must of necessity be slow. With small high-speed wheels, the compressor cylinders may be operated through belting or gearing. In most cases, however, the waterwheel may be large enough to render gearing unnecessary. Impact wheels may be employed with quite small heads of water, by introducing multiple nozzles. To prevent the water from splashing over the compressor, the wheel is enclosed in a tight iron or wooden casing. The force of the water is regu- lated usually by an ordinary gate valve. If the head be great, it may be necessary to introduce means for deflecting the nozzle, so that, when the compressor is to be stopped suddenly, danger of rupturing the water main will be avoided. Theory of Air Compression. The useful effect or efficiency of a compressor is the ratio of the force stored in the compressed air to the work that has been expended in compressing it. This probably never reaches 80$, and often falls below 600. *See "Mines and Minerals," Vols. XIX and XX, for complete discussion of this subject by the same author. RATING OF COMPRESSORS. 195 Free air is air at ordinary atmospheric pressure as taken into the com- pressor cylinder. As commonly used, this means air at sea-level pressure (14.7 Ib. per sq. in.) at 60 F. The absolute pressure of air is measured from zero, and is equal to the assumed atmospheric pressure plus gauge pressure. Air-compression calcu- lations depend on the two well-known laws: 1. Boyle's Law. The temperature being constant, the volume varies inversely as the pressure; or P V = P' V = a constant; in which V equals volume of given weight of air at the freezing point, and the pressure P; V equals the volume of the same weight of air at the same temperature and under the pressure P. 2. Gay-Lussac's Law. The volume of a gas under constant pressure, when heated, expands, for each degree of rise in temperature, by a constant pro- portional part of the volume that it occupied at the freezing point; or, V = V (1 + a ), in which a equals 5 } 3 for centigrade degrees, or T for Fahrenheit degrees. Theoretically, air may be compressed in two ways, as follows: 1. Isothermally, when the temperature is kept constant during compres- sion, and in this case, the formula P V = P' V is true. 2. Adiabatically, when the temperature is allowed to rise without check during the compression. Since the pressure rises faster than the volume diminishes, the equation pr I y\n p V = P' V no longer holds, and we have -= = (-y^J . in which n equals 1.406. The specific heat of air at constant pressure is .2375, and at constant 2375 volume .1689, and n = '^ = 1.406. In practice, compression is neither isothermal nor adiabatic, but inter- mediate between the two. The values of n for different conditions in practice are as follows, as determined from a 2,000-horsepower stage com- pressor at Quai de la Gare, Paris. For purely adiabatic compression, with no cooling arrangements, n = 1.406; in ordinary single-cylinder dry compressors, provided with a water-jacket, n is roughly 1.3; while in the best wet compressors (with spray injection), n becomes 1.2 to 1.25. In the poorest forms of compressor, the value n = 1.4 is closely approached. For large, well-designed compressors with compound air cylinders, the exponent n may be as small as 1.15. Rating of Compressors. Compressors are rated as follows: (1) In terms of the horsepower developed by the steam end of the compressor, as shown by indicator" cards taken when running at full speed, and when the usual volume of air is being consumed. (2) Compressors for mines are often rated roughly as furnishing sufficient air to operate a certain number of rock drills; a 3" drill requires a volume of air at 60 Ib. pressure, equal to 100 or 110 cu. ft. of free atmospheric air per minute. (3) In terms of cubic feet of free air compressed per minute to a given pressure. As the actual capacity of a compressor depends on the density of the intake air, it will obviously be reduced in working at an altitude above sea level, because of the diminished density of the atmosphere. The following table gives the percentages of output at different elevations: EXAMPLE. Calculate the volume of air furnished by an 18" X 24" compressor work- ing at an elevation of 5,000 ft. above sea level, revolving 95 times per minute, and having a piston speed of 380 ft. per minute. 9 2 X 3.14 = 254.3 sq. in. = piston area. 254 3 X 380 = 668.8 cu. ft. = volume dis- 144 placed per minute by the piston; deducting 10$ for loss gives 602 cu. ft. At sea level at 80 Ib. gauge pressure, this equals X 602 = 95 cu. ft. At an elevation of 5,000 ft., the output of a compressor would be 95 X 85$ = 80.7 cu. ft. per minute. Cooling. Compressor cylinders may be cooled by either of the following methods: Altitude. Feet. Atmospheric Pressure. Pounds. Percentages of Output at Sea Level. 14.7 100.0 1,000 14.2 97.2 2,000 13.6 93.5 3,000 13.1 90.8 4,000 12.7 88.4 5,000 12.2 85.0 6,000 11.7 82.0 7,000 11.3 79.3 8,000 10.9 77.0 9,000 10.5 75.0 10,000 10.1 72.0 196 COMPRESSED AIR. (1) by injecting water into the cylinder, known as wet compressors; or (2) by jacketing the cylinder in water, known as dry compressors. Dry Versus Wet Compressors. Up to about the year 1885 there seemed to be little doubt among mechanical engineers that wet compressors were, on the whole, superior to dry, because, by bringing the air into direct contact with water, the heat is most effectually absorbed. This view is correct, so far as heat loss alone is concerned, provided the water in the cylinder is Eroperly applied. But the question of heat loss is not the only consideration, ow first cost and simplicity of construction are often more advantageous than a close approximation to isothermal compression. Latterly, the wet svstem has lost ground, owing to the fact that moisture is objectionable in the air, as it forms frost in the exhaust ports of the drills, and stops them up, and probably no wet compressors are now being built in the United States. In Europe, also, dry compressors have grown in favor, at least for mining plants and others of moderate size. TRANSMISSION OF AIR IN PIPES. The actual discharge capacity of piping is not proportional to the cross- sectional area alone, that is, to the square of the diameter. Although the periphery is directly proportional to the diameter, the interior surface resistance is much greater in a small pipe than in a large one, because, as the pipe becomes smaller, the ratio of perimeter to area increases. To pass a given volume of compressed air, a V pipe of given length re- quires over three times as much head as a 2" pipe of the same length. The character of the pipe, also, and the condition of its inner surface, have much to do with the friction developed by the flow of air. Besides imper- fections in the surface of the metal, the irregularities incident on coupling together the lengths of pipe must increase friction. There are so few relia- ble data that the influences by which the values of some of the factors may be modified are not fully understood; and, owing to these uncertain condi- tions, the results obtained from formulas are only approximately correct. Among the formulas in common use, perhaps the most satisfactory is that of D'Arcy. As adopted for compressed-air transmission, it takes the form: D = cJ^'T* . \ \l in which D = volume of compressed air in cubic feet per minute discharged at final pressure; c = coefficient varying with diameter of pipe, as determined by experiment; d = diameter of pipe in inches (the actual diameters of 1" and H" pipe are 1.38" and 1.61", respectively; the nomi- nal diameters of all other sizes may be taken for calcu- lations); I = length of pipe in feet; Pi = initial gauge pressure in pounds per square inch; p 2 = final gauge pressure in pounds per square inch; wl = density of air, or its weight in pounds per cubic foot, at initial pressure pi. The values of the coefficients c for sizes of piping up to 12" are: 1" 45.3 5" 59.0 9" 61.0 2" 52.6 6" 59.8 10" 61.2 3" 56.5 7" 60.3 11" 61.8 4" 58.0 8" 60.7 12" 62.0 Some apparent discrepancies exist for sizes larger than 9", but they cause no very material differences in the results. Another formula, published by Mr. Frank Richards, is as follows: H= V * L 10,000 D 5 a' in which H = head or difference of pressure required to overcome friction and maintain the flow of air; V = volume of compressed air delivered in cubic feet per minute; L = length of pipe in feet; D = diameter of pipe in inches; a = coefficient, depending on the size of pipe. TRANSMISSION OF AIR IN PIPES. 197 Values of a for nominal diameters of wrought-iron pipe: 1" 350 3" 730 8" 1.125 U" 500 Zk" 787 10" 1.200 li" 662 4" .840 12" 1.260 1" 565 5" 934 2i" 650 6" 1.000 The values of a for li" and li" pipe are not consistent with those for other sizes, for the reason stated above. In using this formula with its constants, the calculated losses of pressure are found to be smaller, and, conversely, the volumes of air discharged are larger, under the same condi- tions, than those obtained from D'Arcy's formula. It must be remembered that, within certain limits, the loss of head or pressure increases with the square of the velocity. To obtain the best results, it is found in practice that the velocity of flow in the main air pipes should not exceed 20 or 25 ft. per second. When the initial velocity much exceeds 50 ft. per second, the percentage loss becomes very large; and, conversely, by using piping large enough to keep down the velocity, the friction loss may be almost eliminated. For example, at the Hoosac tunnel, in transmit- ting 875 cu. ft. of free air per minute, at^an initial pressure of 60 lb., through an 8" pipe, 7,150 ft. long, the average loss including leakage was only 2 lb. A volume of 500 cu. ft. of free air per minute, at 75 lb., can be transmitted through 1,000 ft. of 3" pipe with a loss of 4.1 lb., while if a 5" pipe were used the loss would be reduced to .24 lb. The velocity of flow in the latter case is only 10 ft. per second. In driving the Jeddo mining tunnel, at Eberyale, Pa., two 3" drills were used in each heading, with a 6" main, the maximum transmission distance being 10,800 ft. This pipe was so large in proportion to the volume of air required for the drills (230 cu. ft. free air per minute) that the loss was reduced to an extremely small quantity. A calculation shows a loss of .002 lb., and the gauges at each end of the main were found to record practically the same pressure. A due regard for economy in installation, however, must limit the use of very large piping, the C9st of which should be considered in relation to the cost of air compression in any given case. Diameters of from 4 to 6 in. for the mains are large enough for any ordinary mining practice. Up to a length of 3,000 ft., a 4" pipe will carry, per minute, 480 cu. ft. of free air compressed to 82 lb., with a loss of 2 lb. pressure. This volume of air will run four 3" drills. Under the same conditions, a 6" pipe, 5,000 ft. long, will carry 1,100 cu. ft. of free air per minute, or enough for 10 drills. A mistake is often made in putting in branch pipes of too small a diam- eter. For a distance of, say, 100 ft., a H" pipe is small enough for a single drill, though a 1" pipe is frequently used. While it is, of course, admissible to increase the velocity of flow in short branches considerably beyond 20 ft. per second, extremes should be avoided. To run a 3" drill from a 1" pipe 100 ft. long, would require a velocity of flow of about 55 ft. per second, causing a loss of 10 lb. pressure. The piping for conveying compressed air may be of cast or wrought iron. If of wrought iron, as is customary, the lengths are connected either by sleeve couplings or by cast-iron flanges into which the ends of the pipe are screwed or expanded. Sleeve couplings are used for all except the large sizes. The smaller sizes, up to l in., are butt-welded, while all from \\ in. up are lap-welded, to insure the necessary strength. Wrought-iron spiral-seam riveted or spiral-weld steel tubing* is sometimes used. It is made in lengths of 20 ft., or less. For convenience of transport in remote regions, rolled sheets in short lengths may be had. They are punched around the edges, ready for riveting, and are packed closely 4, 6, -or more sheets in a bundle. All joints in air mains and branches should be carefully made. Air leaks . are more expensive than steam leaks because of the losses already suffered in compressing the air. The pipe may be tested from time to time by allow- ing the air at full pressure to remain in the pipe long enough to observe the gauge. In case a leak is indicated, it should be traced and stopped imme- diately. In putting together screw joints, care should be taken that none of the white lead or other cementing material is forced into the pipe. This would cause obstruction and increase the friction loss. Also, each length as put in place should be cleaned thoroughly of all foreign substances that may have lodged inside. To render the piping readily accessible for inspection 198 COMPRESSED AIR. and stoppage of leaks, it should, if buried, be carried in boxes sunk just below the surface of the ground; or, if underground, it should be supported upon brackets along the sides of the mine workings. Low points in pipe lines, which would form "pockets" for the accumulation of entrained water, should be avoided, as they obstruct the passage of the air. In long pipe lines, where a uniform grade is impracticable, provision may be made near the end for blowing out the water at intervals, when the air is to be used for pumps, hoists, or other stationary engines. For long lengths of piping, expansion joints are required, particularly when on the surface. They are not often necessary underground, as the temperature is usually nearly constant, except in shafts, or where there may be considerable variations of temperature between summer and winter. LOSSES IN THE TRANSMISSION OF COMPRESSED AIR. BY E. HILL, NORWALK IRON WORKS Co. The increasing use that is being made of compressed-air engines for mine and underground work stimulates the inquiry regarding their efficiency. The situation is apparently very simple. An engine drives an air com- pressor, which forces air into a reservoir. The air under pressure is led through pipes to the air engine, and is there used after the manner of steam. The resulting power is frequently a small percentage of the power expended. In a large number of cases the losses are due to poor designing, and are not chargeable as faults of the system or even to poor workmanship. The losses are chargeable, first, to friction of the compressor. This will amount ordinarily to 15$ or 20$, and can be helped by good workmanship, but cannot probably be reduced below 10$. Second, we have the loss occasioned by pumping the air of the engine room, rather than air drawn from a cooler place. This loss varies with the season, and amounts to from 3$ to 10$. This can all be saved. The third loss or series of losses arises in the compressing cylinder. Insufficient supply, difficult discharge, defective cooling arrangements, poor lubrication, and a host of other causes, perplex the designer and rob the owner of power. The fourth loss is found in the pipe. This has heretofore received by no means the consideration that the subject demands. The loss varies with every different situation, and is sub- ject to somewhat complex influences. The fifth loss is chargeable to fall of temperature in the cylinder of the air engine. Losses arising from leaks are often serious, but the remedy is too evident to require demonstration. No leak can be too small to require immediate attention. An attendant who is careless about packings and hose couplings will permit losses for which no amount of engineering skill can compensate. We can only realize 100$ efficiency in the air engine, leaving friction out of our consideration, when the expansion of the air and the changes of its temperature in the expanding or air-engine cylinder are precisely the reverse of the changes that have taken place during the compression of the air in the compressing cylinder. But these conditions can never be realized. The air during compression becomes heated, and during expansion it becomes cold. If the air immediately after compression, before the loss of any heat, was used in an air engine and there perfectly expanded back to atmospheric pressure, it would, on being exhausted, have the same tem- perature it had before compression, and its efficiency would be 100$. But the loss of heat after compression and before use cannot be pre- vented, as the air is exposed to such very large radiating surfaces in the reservoir and pipes, on its passage to the air engine. The heat, which escapes in this way, did, while in the compressing cylinder, add much to the resistance of the air to compression, and since it is sure to escape, at some time, either in reservoir or pipes, it is evidently the best plan to remove it as fast as possible from the cylinder, and thus remove one element of resistance. Hence, we find compressors are almost universally provided with cooling attachments more or less perfect in their action, the aim being to secure isothermal compression, or compression having equal temperature throughout. Where the temperature rises, without check, during com- pression, the term adiabatic compression is employed. If air compressed isothermally is used with perfect expansion and the fall of temperature during expansion be prevented, then we will have 100$ efficiency. But air will grow cold on being expanded in an engine, and hence we conclude that warming attachments have the same economic place on an air engine that cooling attachments have on an air compressor. In fact, we find attachments of this kind more particularly in large and TRANSMISSION OF COMPRESSED AIR. 199 permanently located engines, but, for practical reasons, their use on most of the engines for mine work is dispensed with, and the engines expand the air adiabatically, or without receiving heat. The practical engineer, therefore, has to deal with nearly isothermal compression, and nearly adiabatic expansion, and must also consider that the air in reservoirs and pipes becomes of the same temperature as surround- ing objects. Consideration must also be had for the friction of the com- pressor and the air engine. For the pressure of 60 lb., which is that most commonly used, the decrease in resistance to compression secured by the cooling attachments, is almost exactly equaled by the friction of the com- pressor. Hence it is safe, in calculating the efficiency of the air engine, to consider the compressor as being without cooling attachments, and also as working without friction. The results of such calculations will be too high efficiencies for light pressures, which are little used; about correct for medium pressures, which are commonly employed; and too low for higher pressures, and will thus have the advantage of not being overestimated. This result is occasioned by the fact that, owing to the slight heat in compressing low pressures of air, the saving of power by the cooling attachments is not equal to the friction of the machine, but at high pressures, on account of the great heat, the cooling attachments are of great value and save very much more power than friction consumes. In the expanding engines; the expansion never falls as low as the adiabatic law would indicate, owing to a number of reasons, but we will consider the expansion as being adiabatic, as an error in calculations caused thereby will be on the " safe side" and the actual power will exceed the calculated power. We therefore consider the compressor and engine as following the adiabatic law of compression and expansion, and as working without friction. With this view of the case, the efficiency of an air engine, working with perfect expansion, stated in percentages of the power required to operate the compressor, can be placed as below for the various pressures above the atmosphere. Pressure above the atmosphere, 2.9 lb. 94.85$ efficiency. Pressure above the atmosphere, 14.7 lb. 81.79$ efficiency. Pressure above the atmosphere, 29.4 lb. 72.72$ efficiency. Pressure above the atmosphere, 44.1 lb. 66.90$ efficiency. Pressure above the atmosphere, 58.8 lb. 62.70$ efficiency. Pressure above the atmosphere, 73.5 lb. 59.48$ efficiency. Pressure above the atmosphere, 88.2 lb. 56.88$ efficiency. We observe that the efficiencies for the lower pressures are very much greater than for the high pressures, and the conclusion is almost irresistible that to secure economical results we must design our air engines to run with light pressures. And, in fact, the consideration of tables similar to the above, heretofore published by writers on this subject, has led many engineers into grave errors. The pipe has been entirely neglected. We notice that a pressure of 2.9 lb. is credited with an efficiency of 94.85$. It is clear that if the air were conveyed through a pipe, and the length of the pipe and the velocity of flow were such that 2.9 lb. pressure was lost in friction, then its efficiency, instead of being 94.85$. would be absolutely zero. It is, therefore, the power that we can get from the air, after it has passed the pipe and lost a part of its pressure by friction, which we must consider when we state the efficiency of our entire apparatus. Our table of efficiencies with a loss of 2.9 lb. in the pipe, now gives us dif- ferent values for the efficiencies at the various pressures. Pressure above the atmosphere, 2.9 lb. 00.00$ efficiency. Pressure above the atmosphere, 14.7 lb. 70.44$ efficiency. Pressure above the atmosphere, 29.4 lb. 68.81$ efficiency. Pressure above the atmosphere, 44.1 lb. 64.87$ efficiency. Pressure above the atmosphere, 58.8 lb. 61.48$ efficiency. Pressure above the atmosphere, 73.5 lb. 58.62$ efficiency. Pressure above the atmosphere, 88,2 lb. 56.23$ efficiency. It will be noticed that the light pressures have lost most by the pipe friction, 2.9 lb. having lost 100/: 14.7 lb. 11$, and 88.2 lb. only a trifle over of K. We see that now 14.7 lb. is apparently the economical pressure to use. But a further careful analysis of the subject shows, that when the loss in the pipe is 2.9 lb., then 20.5 lb. is the most economical pressure to use, and that 200 COMPRESSED AIR. the efficiency is 71$. But 2.9 Ib. is a very small loss between compressor and air engine, and cases are extremely exceptional where the friction of valves, ipes, elbows, ports, etc. does not far exceed this. Yet, with these con- itions, which are very difficult to fill, we see that 20.5 Ib. is the lightest pressure that should probably ever be used for conveying power, and that 71$ is an efficiency scarcely to be obtained. Continuing our investigation and taking examples where the pipe friction amounts to 5.8 Ib., we find the following efficiencies to correspond to the stated pressure: Pressure above the atmosphere, 14.7 Ib. 57.14$ efficiency. Pressure above the atmosphere, 29.4 Ib. 64.49$ efficiency. Pressure above the atmosphere, 44.1 Ib. 62.71$ efficiency. Pressure above the atmosphere, 58.8 Ib. 60.12$ efficiency. Pressure above the atmosphere, 73.5 Ib. 57.73$ efficiency. Pressure above the atmosphere, 88.2 Ib. 55.59$ efficiency. We again notice that as friction increases, or in other words, when we begin to use more air and make greater demands on the carrying capacity of the pipe, then we must increase pressure very considerably to attain the most economical results. If the demands are such as to increase the friction and loss in pipe to 14.7 Ib., the air of 14.7 Ib. pressure at the compressor is entirely useless at the air engine. The table will stand thus: Pressure above the atmosphere, 14.7 Ib. 00.00$ efficiency. Pressure above the atmosphere, 29.4 Ib. 48.53$ efficiency. Pressure above the atmosphere, 44.1 Ib. 55.13$ efficiency. Pressure above the atmosphere, 58.8 Ib. 55.64$ efficiency. Pressure above the atmosphere, 73.5 Ib. 54.74$ efficiency. Pressure above the atmosphere, 88.2 Ib. 53.44$ efficiency. It is to be noticed that 88.2 Ib. pressure has lost only about 3|$ of its efficiency by reason of as high a friction as 14.7 Ib., while the efficiency of the lower pressures has been greatly affected. As the friction increases we see that the most efficient, and, consequently, most economical, pressure increases. In fact, for any given friction in a Eipe, the pressure at the compressor must not be carried below a certain mit. The following table gives the lowest pressures that should be used at the compressor, with varying amounts of friction in the pipe: 2.9 Ib. friction. 20.5 Ib. at compressor. 70.92$ efficiency. 5.8 Ib. friction. 29.4 Ib. at compressor. 64.49$ efficiency. 8.8 Ib. friction. 38.2 Ib. at compressor. 60.64$ efficiency. 11.7 Ib. friction. 47.0 Ib. at compressor. 57.87$ efficiency. 14.7 Ib. friction. 52.8 Ib. at compressor. 55.73$ efficiency. 17.6 Ib. friction. 61.7 Ib. at compressor. 53.98$ efficiency. 20.5 Ib. friction. 70.5 Ib. at compressor. 52.52$ efficiency. 23.5 Ib. friction. 76.4 Ib. at compressor. 51.26$ efficiency. 26.4 Ib. friction. 82.3 Ib. at compressor. 50.17$ efficiency. 29.4 Ib. friction. 88.2 Ib. at compressor. 49.19$ efficiency. So long as the friction of the pipe equals the amounts given above, an efficiency greater than the corresponding sums stated in the table cannot be expected. If we should have a case that corresponded to any of these cited in the table, we could only increase efficiency by reducing the friction. An increase in the size of pipe will reduce friction by reason of the lower velocity of flow required for the same amount of air. But many situations will not admit of large pipes being employed, owing to considerations of economy outside of the question of fuel or prime motor capacity. An increase of pressure will decrease the bulk of air passing the pipe, and in that proportion will decrease its velocity. This will decrease the loss by friction, and, as far as that goes, we have a gain. But we subject ourselves to a new loss, and that is the diminishing efficiencies of increasing pressures. Yet as each cubic foot of air is at a higher pressure, and, therefore, carries more power, we will not need as many cubic feet as before for the same work. It is obvious that with so many sources of gain or loss the question of selecting the proper pressure is not to be decided hastily. As an illustration of the combined effect of these different elements, we will suppose a very common case. Compressor 102 revolutions, pressure 52.8 Ib., loss in pipe 14.7 Ib., machine in mine running at 38.2 Ib., efficiency 55.73$. FRICTION OF AIR IN PIPES. 201 So long as^the friction of the pipe amounts to 14.7 lb., we have seen that 52.8 lb. is the best pressure and 55.73$ the greatest efficiency. We will reduce the friction by reducing the bulk of air passing through the pipe. We reduce the cylinder of the air engine so that it requires 47 lb. pressure to do the same work as before. W T e lind now that the friction of pipe drops to 11.7 lb. The pressure on the compressor rises to 58.8 lb., its number of revolu- tions falls to 100, and the resulting efficiency is 57.22$. Another change of pressure on compressor to 64.7 lb. would decrease its revolutions to 93, friction to 8.8 lb., and efficiency would rise to 57.94$. Still again increasing the pressure to 73.5 lb., we have only 84 revolutions of com- pressor, 5.8 lb. loss in pipe, and efficiency of 57.73$. In this last case the efficiency begins to fall off a little, and higher pressures would now show less efficiency; but, in comparison with the first example, we find we are doing the same work in the mine with a trifle less power and with a decrease of nearly 20$ in the speed of the compressor. Other common examples can be shown where an increase of pressure would result in wonderful increase in efficiency and economy. There are many cases where light pressures and high velocity in the pipe will convey a given power with greater economy than higher air pressures and lower speed of flow through the pipe. But these cases arise mostly when the higher air pressures become very much greater than are at present in com- mon use. Therefore, in estimating the efficiency of the complete outfit, we find that the pipe and the pressure are very important elements, and must be deter- mined with care and skill to secure the most satisfactory results. As the volume and power of air vary with its pressure, the size and consequent cost of compressor for a certain work would also be affected by the pressure. To plan an outfit for a mine, due regard must be had to cost of fuel or prime motor power, and also to cost of compressor, pipes, and machinery, as the saving in one is often secured by a sacrifice in the other. Next to determining the size of pipe, the skilful engineer has need of further care in the proper position of reservoirs, branches, drains, and other attachments, as only by the exercise of good judgment in this can satis- factory working be secured. The fact that, on account of the diminished density of the atmosphere at high altitudes, air compressors do not give the same results as at sea level, should also be taken into consideration when a compressor is to be installed in a mountainous region. Friction of Air in Pipes. Air in its passage through pipes is subject to friction in the same manner as water or any other fluid. The pressure at the compressor must be greater than at the point of consumption in order to overcome this resistance. The power that is needed to produce the extra pressure representing the friction of the pipe is lost, as there can be no use- ful return for it. The friction is affected by very many circumstances, but chiefly to be noted is the fact that it increases in direct proportion to the length of the pipe and also as the square of the velocity of the flow of air. The pressure of the air does not affect it. The losses by friction may be quite serious if the piping system is poorly designed, and, 'on the other hand, extravagant expenditure in pipe may result from a timid overrating of the evils of friction. A thorough knowl- edge of the laws governing the whole matter, as well as a ripe experience, is necessary to secure true economy and mechanical success. The loss of power in pipe friction is not always the most serious result. When a number of machines are in use in a mine, and the pipes are so small as to cause a considerable loss of pressure by friction, then there will be sudden and violent fluctuations in pressure whenever a machine is started or stopped. Breakages will be of common occurrence, as the changes are too quick to be entirely guarded against by the attendant. Perfectly even pres- sure at the compressor is no safeguard against this class of accidents. The trouble arises in the pipe, and the remedy must be applied there. A system of reservoirs and governing valves will regulate these matters and allow successful work to be done with pipes, which would otherwise be entirely inadmissible. The ordinary formulas for calculating the volume of air transmitted through a pipe do not take into account the increase of volume due to reduction of pressure, i. e., loss of head. To transmit a given volume of air at a uniform velocity and loss of pressure, it would be necessary to construct the pipe with a gradually increasing area. This, of course, is impracticable, 202 COMPRESSED AIR. and in pipe of uniform section both volume and velocity must increase as the pressure is reduced by friction. The loss of head in properly propor- tioned pipes is so small, however, that in practice the increase in volume is usually neglected. Loss OF PRESSURE IN POUNDS PER SQUARE INCH, BY FLOW OF AIR IN PIPES. Calculated for pipes 1,000 ft. long; for other lengths, the loss varies directly as the length. Velocity of Air at Entrance V Pipe. 2" Pipe. 2i" Pipe. J to Pipe. $*t a 5* $4 A . t. <& 1 | i ||gi if si a g So P 1 |8 ! S k " CO j COrH^S W Weath- er-Proof. Rubber- Covered. 0000 460.0 211,600.0 640.50 3,381.4 .0489 312 210 000 409.6 167,805.0 508.00 2,682.2 .0617 262 177 00 364.8 133,079.4 402.80 2,126.8 .0778 220 150 324.9 105,534.5 319.50 1,686.9 .0981 185 127 1 289.3 83,694.2 253.30 1,337.2 .1237 156 107 2 257.6 66,373.0 200.90 1,060.6 .1560 131 90 3 229.4 52,634.0 159.30 841.1 .1967 110 76 4 204.3 41,742.0 126.40 667.4 .2480 92 65 5 181.9 33,102.0 100.20 529.1 .3128 ' 77 54 6 162.0 26,250.5 79.46 419.5 .3944 65 46 7 144.3 20,816.0 63.02 332.7 .4973 8 128.5 16,509.0 49.98 263.9 .6271 46 33 9 114.4 13,094.0 39.63 209.2 .7908 10 101.8 10,381.0 31.43. 165.9 .9972 32 24 11 90.7 8,234.0 24.93 131.6 1.257 12 80.8 6,529.9 19.77 104.4 1.586 23 17 13 71.9 5,178.4 15.68 82.8 1.999 14 64.1 4,106.8 12.43 76.2 2.521 16 12 15 57.1 3,256.7 9.86 52.0 3.179 16 50.8 2,582.9 7.82 41.3 4.009 8 6 17 45.2 2,048.2 6.20 32.7 5.055 18 40.3 1,624.3 4.92 25.9 6.374 5 3 19 35.9 1,288.1 3.90 20.6 8.038 20 31.9 1,021.5 3.09 16.3 10.14 21 28.5 810.1 2.45 12.9 12.78 22 25.3 642.4 1.94 10.3 16.12 23 22.6 509.4 1.54 8.1 20.32 24 20.1 404.0 1.22 6.4 25.63 25 17.9 320.4 .96 5.1 32.31 26 15.9 254.1 .76 4.0 40.75 27 14.2 201.5 .61 3.2 51.38 28 12.6 159.7 .48 2.5 64.79 29 11.2 126.7 .38 2.0 81.7 30 10.0 100.5 .30 1.6 103.0 31 8.93 79.70 .24 1.27 129.9 32 7.95 63.21 .19 1.01 163.8 33 7.08 50.13 .15 .801 206.6 34 6.30 39.75 .12 .635 260.5 35 5.61 31.52 .095 .504 328.4 36 5.00 25.00 .075 .400 414.2 37 4.45 ,19.83 .060 .317 522.2 38 3.96 15.72 .047 .251 658.5 39 3.53 12.47 .038 .199 830.4 40 3.14 9.89 .030 .158 1,047.0 ELECTRIC WIRING. 209 The following table gives a comparison of the properties of aluminum and copper: COMPARISON OF PROPERTIES OF ALUMINUM AND COPPER. Aluminum. Copper. Conductivity ( for equal sizes^ .54 to .63 1 Weight (for equal sizes) . . . .33 1 Weight (for equal length and resistance).... Price (per pound) aluminum, 29 cents; cop- per, 16 cents (bare wire) Price (equal length and resistance, bare line wire) .48 1.81 .868 1 1 1 Temperature coefficient per degree F. .002138 .002155 Resistance of mil-foot (20 C.) 18 73 105 Specific gravity 2 5 to 2 68 8 89 to 8 93 Breaking strength (equal sizes) 1 1 In case a conductor larger than that given in the table is required, stranded cables are used. These are made in various sizes. The table below gives some of the more common sizes, with their allowable current capacity. CARRYING CAPACITY OF CABLES. Current. Amperes. Current. Amperes. Area. Area. Circular Mils. Exposed. Concealed. Circular Mils. Exposed. Concealed. 200,000 299 200 1,200,000 1,147 715 300,000 405 272 1,300,000 1,217 756 400,000 503 336 1,400,000 1,287 796 500,000 595 393 1,500,000 1,356 835 600,000 682 445 1,600,000 1,423 873 700,000 765 494 1,700,000 1,489 910 800,000 846 541 1,800,000 1,554 946 900,000 924 586 1,900,000 1,618 981 1,000,000 1,000 630 2,000,000 1,681 1,015 1,100,000 1,075 673 Estimation of Resistance. The resistance of any conductor is directly pro- portional to its length, and inversely proportional to its area of cross-sec- tion, or R = K -T-, where K is a constant. If L is expressed in feet and A A is expressed in circular mils, then the constant 7T must be the resistance of a foot of the wire in question of 1 circular mil cross-section. The resist- ance of 1 mil-foot of copper wire at 75 F. is about 10.8 ohms. Hence, for copper wire, we have R = - ; but A = d 2 when d is the diameter in mils; hence, we also have R 10.8 L This formula is easily remembered, and is very convenient for estimating the resistance of any length of wire of given diameter when a wire table is not at hand, or when the diameter of the given wire does not correspond to anything given in the table. EXAMPLE. Find ther esistance of 1 mile of copper wire .20 in. in diameter. 1 mile = 5,280 ft. .20 in. = 200 mils. Area of cross-section = (200) a = . ., 10.8 X L 10.8 X 5,280 40,000 circular mils. Hence, R = -r = = 1.42 ohms. d 'iU,UUU 210 ELECTRICITY. CALCULATION OF WIRES FOR ELECTRIC TRANSMISSION. Direct-Current Circuits. No matter how large a wire may be, some energy must always be expended in forcing a current through it, because no con- ductor can be entirely devoid of resistance. It is true that the loss may be made as small as we please by using a very large conductor, but, in practice, this would not pay, because the interest on the cost of the copper would more than counterbalance the gain in the efficiency of transmission. In starting out, then, to estimate the size of wire to transmit a given amount of power over a given distance, one of the first things to be decided is the amount of power that may be allowed for loss in the line, because it is evi- dent that the greater the power lost, the higher may be the line resistance, and hence the smaller the wire. The pressure required to force a current C through a wire of resistance R is C X R. This pressure is generally spoken of as the drop, for the reason that the pressure necessary to set up the current through the line is lost, and, consequently, the pressure falls off' or drops from the dynamo to the receiving end of the line. In all cases, the pressure at the end of the line, or point where the power is delivered, is equal to the pressure at the dynamo less the drop in the line, and, conversely, the pres- sure that must be maintained by the dynamo in order to obtain a given pressure at the end will be equal to the pressure at the receiving end plus the drop in the line. To illustrate the above, take the case shown in Fig. 3, where a dynamo D supplies current to a motor M situated 1 mile distant. In order that the motor may operate properly, the pressure at its terminals must be kept constant at, say, 500 volts. It is evident, then, that the pressure between a and b (the dynamo terminals) must be more than 500 volts, by the drop or pressure necessary to force the current through the line. If the motor is taking very little current, i. e., if it is running on a very light load, the current will be small, and hence the drop in the line will be small. In order, then, that the pressure at the motor may remain constant, or nearly so, the pressure at the dynamo must automatically increase as the load increases. The way in which this is done will be explained later; for the present, we are concerned only with the calculation of the line. The line must evidently be designed with regard to the maximum current it has to carry. We will suppose, for the sake of illustration, that the motor takes 50 amperes at full load and that the line wire is of such size that it has a resist- ance of .2 ohm per mile. ' The current has to pass through 2 miles of wire ( because it has to flow out through 1 mile and back through 1 mile), and hence encounters a resistance of .4 ohm. The drop in the FIG. 3. line will then be .4 X 50 = 20 volts, and in order to obtain a pressure of 500 volts at the motor, the pressure at the dynamo would have to be 520 volts. The loss of power in the line would be current X drop = 50 X 20 = 1,000 watts, or about U horsepower. The drop in an electrical transmission line is analogous to the loss in pressure due to the friction encountered by water flowing through a pipe line. If, in the illustration just given, a size of wire were used such that its resistance would be .1 ohm per mile, it is evident that the loss in the line would be halved, but the weight of copper required doubled, because the wire would have to be double the cross-section. The question as to whether it would pay better to invest more money in the line or to put up with the larger loss is something that must be determined in each case by the relative cost of power and copper. In many cases, the loss allowed in the line is about 10$ of the power to be delivered, though sometimes the loss may be allowed to run as high as 15$ or 25$. This applies only to transmission lines. For local electric-light or power-distributing systems, the amount of drop allowed is usually about 2$ for the former and 5$ for the latter. The problem of calculating line wires usually presents itself in the following form: Given, a certain amount of power to transmit over a known CALCULATION OF WIRE. 211 distance with a certain allowable loss, to determine the cross-section of the wire required. Let P = power to be delivered, expressed in watts; P will be equal to horsepower delivered at end of line multiplied by 746; = allowable percentage of loss in line, i. e., percentage of power delivered that may be lost in transmission; E = voltage at end of line where power is delivered; C = current at full load; L = length of wire through which current flows. The cross-section of the copper conductor will then be given by the following formula: _ 10.8 X LX C X 100 n . A = EXt A will be expressed in circular mils, and the corresponding size of wire may be found by consulting the wire table. It should be noticed, particu- larly, that in this formula, L is the average length of conductor through which the current C flows. The application of distance of transmission in the formula will be understood from what follows. EXAMPLE. A mine pump, driven by an electric motor, is situated 2 miles from the power station. The electrical input of the motor at full load is 50 H. P., and the voltage at its terminals is to be 500. Estimate the size of line wire necessary to supply the motor, the allowable loss in the line being 15$ of the power delivered. The actual length of line through which th.e current will flow will be 4 miles, because the current has to flow out to the motor and back again. We have = 74.6 amperes. ^ = = Applying formula (1), we have A = 10.8 X 2X2X5,^0X74.6X100 000 X ! By consulting the wire table it is found that this calls for a wire a little larger than No. 0000, which has a cross-section of 211,600 circular mils; No. 0000 wire would probably be used in this case, as it is near enough to the calculated size for all practical purposes. In case the calculated size comes out larger than any size given in the table, a number of wires may be used in multiple to make up the required cross-section, or, what is 'better, a stranded cable may be used. These heavy stranded cables may now be obtained in different sizes, up to 2,000,000 circular mils cross-section. It is evident that, in the above examples, if it were allowable to waste twice as much power in the line, or what is equivalent to having a line drop of 150 volts instead of 75 volts, the cross-section of wire required would have been one-half of that found above. Such a large amount of loss would, however, be objectionable unless power was very cheap. A large drop in the line is in any case objectionable, because the voltage at the receiving end of the circuit will fall off greatly unless the voltage at the generating station is raised, as the load comes on, in order to compensate for the line drop. Most of the uses to which electricity is put, in mines or other places, requires that the pressure at the point where the power is utilized shall be kept approximately constant. For example, in the case of incandescent lights, the lamps will fall off greatly in brightness if the pressure decreases even by a comparatively slight amount. Also, if motors are being operated, the speed will vary considerably if the pressure is not kept constant, and it may be stated, in general, that a large line loss tends to poor regulation at the end of the circuit where power is delivered. From the above considerations, it will be seen that, in the majority of cases, the size of wire to be used under given conditions is determined by the allowable amount of drop. In some cases, however, especially if the current is to be used near at hand, the size of wire so determined might not be large enough to carry the current without overheating. Of course, in such cases, the safe carrying capacity of the wire determines the size to be used, and the drop will be correspondingly less. The amount of current that a given wire can carry without overheating depends very largely on the location of the wire. For example, a wire strung in the open air will carry a greater current, with a given temperature rise, than the same wire would if boxed up in a molding or conduit. The 212 ELECTRICITY. table on page 209 gives the approximate safe carrying capacity of wires when strung in the air. In order to keep down the size of wire required to transmit a given amount of power over a given distance, with a certain allowable loss, the current must be kept as small as possible. Now, for a given amount of power, the current can only be made small by increasing the pressure, because the number of watts, or power delivered, is equal to the product of the current and the pressure. As a matter of fact, if the pressure in any given case be doubled, the amount of copper required will be only one- fourth as great; in other words, for a given amount of power transmitted, the weight of copper required decreases as the square of the voltage. It is at once seen, then, that if any considerable amount of power is to be trans- mitted over long distances, a high line pressure must be used or else the cost of copper becomes prohibitory. The use of high pressures in power trans- mission will be taken up in connection with alternating currents. Insulated Wires. For most overhead line work using modern voltages, weather-proof insulated wire is used. This wire is covered with two or three braids of cotton, and treated with insulating compound. For inside work, and in places where a better quality of insulation is required, rubber-covered wires are used. The following table gives the approximate weight of weather-proof line wire. The cost of the wire per pound varies considerably, owing to the variations in the price of copper; about 18 cents per pound may be taken as an approximate figure in making calculations. WEATHER-PROOF LINE WIRE (ROEBLING'S). Double Braid. Triple Braid. Number. B.&S. Gauge. Outside Diameter. Weight. Pounds. Outside Diameter. Weight. Pounds. 32ds Inch. Per Per 32ds Inch. Per Per 1,000 Ft. Mile. 1,000 Ft. Mile.' 0000 20 716 3,781 24 775 4,092 000 18 575 3,036 22 630 3,326 00 17 465 2,455 18 490 2,587 16 375 1,980 17 400 2,112 1 15 285 1,505 16 306 1,616 2 14 245 1,294 15 268 1,415 3 13 190 1,003 14 210 1,109 4 11 152 803 12 164 866 5 10 120 634 11 145 766 6 9 98 518 10 112 591 8 8 66 349 9 78 412 10 7 45 238 8 55 290 12 6 30 158 7 35 185 14 5 20 106 6 26 137 16 4 14 74 5 20 106 18 3 10 53 4 16 85 For high-tension lines, it is customary to use bare wires and insulate them thoroughly on special porcelain insulators. The ordinary weather- proof wire insulation is of little or no use as a protection when these high pressures are used, and it only makes the line more dangerous because of the appearance of false security that it gives. In many cases, it is also better to use bare feeders for mine-haulage plants, because the ordinary insulation soon becomes defective in a mine, and a wire in this condition is really more dangerous than a bare wire, because the latter is known to be dangerous and will be left alone. CURRENT ESTIMATES. Before calculating the size of wire required for any given case, it is necessary to know the current, and the method of getting at this will depend on what the current is to be used for. INCANDESCENT LAMPS. 213 Incandescent Lamps. These are usually operated on 110-volt circuits, Fig. 4, or on the three-wire system, as shown in Fig. 5. In the three-wire system, two 110-volt dynamos are connected in series so that the voltage across the outside wires is 220. The neutral wire a a connects to the point b where the machines are connected together. The wire a a merely serves to carry the difference in the currents on the two sides of the system, in case more lamps should be burning on one side FIG. 4. than on the other. The outside wires for such a system are calcu- lated as if the lights were operated two in series across 220 volts. The middle wire is usually made equal in size to the outer wires. An ordinary 16 c. p. incandescent lamp requires about 55 watts for its operation; a 32 c. p. lamp requires about 110 watts. Hence, in the case of ordinary parallel dis- tribution, as shown in Fig. 4, the dy- namo will deliver about i ampere for each 16 c. p. lamp operated, and 1 am- pere for each 32 c. p. lamp. In the case of the three-wire sys- FIG. 5. tern, each pair of 16 c. p. lamps will take i ampere, and the total number of amperes in the outside wires will be one-fourth the num- ber of lamps operated. EXAMPLE. A certain part of a mine is to be illuminated by fifty 16 c. p. lamps and ten 32 c. p. lamps. This portion of the mine is 1,000 ft. from the dynamo room, and the allowable drop in pressure is 5#. The lamps are to be run on a 110-volt system. Find the size of wire required. Fifty 16 c. p. lamps require ................... 25 amperes Ten 32 c. p. lamps require ..................... 10 amperes Total current ....................................... 35 amperes We have, then, circular mils = 10-S X 1.000 X 2 X 35 X 100 = ^^ circular mils , 11U X O or about a No. 00 B. & S. wire. EXAMPLE. Take the same case as in the last example, but suppose the lights to be operated on the three-wire system. There will then be twenty- five 16 c. p. lamps and five 32 c. p. lamps on each side of the circuit, and the total current in the outside wires will be 17.5 amperes. The voltage between the outside wires will be 220, and we will have circular mils 10.8X1.000X2X17.5X100 or about a No. 5 B. & S. wire. If we make the central wire also of this size, it is seen that this system would require three-eighths the amount of copper called for by the plain 110-volt system. There is the disadvantage that two dynamos are needed. NOTE. The length to be used in the wiring formula is the average dis- tance traversed by the current in the conductor. For example, if, as in Fig. 6 (a), the lamps were all grouped or bunched at the end of the line, the length used in the formula would be twice that from G to A, because the whole current has to flow out to A through one main and back through the other. In other words, the whole current here passes through the whole length of the line. In case the load is uniformly distributed all along the line, as shown in Fig. 6 (6), it is evident that the current decreases step by step from the dynamo to the end. In such a case, the length or distance to be used in the formula is one-half that used in the former case, or simply the distance from the dynamo to the end, instead of twice this distance. 214 ELECTRICITY. Arc Lamps. Arc lamps are frequently run on constant-potential circuits, and usually consume from 400 to 500 watts. There are so many types of these lamps that it is difficult to give any current estimates that will be gen- erally applicable. Enclosed arc lamps usually take from 3 to 5 amperes when run on 110- volt circuits. Motors. Practically all the motors used in mining work are run on the constant-potential system, either at 250 or 500 volts. The efficiency of ordi- nary motors will vary from 70$ to 95$ or higher, depending on the size. The efficiency is greater with the larger machines, and, for the ordinary run of motors, it will probably lie between 80$ and 90$. By efficiency is here meant the ratio of the useful output at the pulley or pinion of the motor to the total input. The accompanying table gives the efficiency of motors of ordinary size: APPEOXIMATE MOTOR EFFICIENCY. to 1| H. P., inclusive = 75$ efficiency 3 to 5 H. P., inclusive = 80$ efficiency 7^ to 10 H. P., inclusive =F 85$ efficiency 15 H. P. and upwards = 90$ efficiency If the required output in horsepower is known, the input will be w = H. P. X 746 efficiency ' W and the current required at full load will be C = -=-, where E is the voltage JCj between the mains at the motor. , Conductors for Electric-Haulage Plants. In electric-haulage plants, the rails take the place of one of the conductors, so that, in calculating the size of feeders required, only the overhead conductors are taken into account. It is a difficult matter to assign any definite .value to the resistance of the track circuit, as it depends very largely on the quality of the rail bonding at the HHHfiii (*>) FIG. 6. joints. If this bonding is well done, the resistance of the return circuit should be very low, because the cross-section of the rails is comparatively large. For calculating the supply feeders, we may use the approximate formula, circular mils _MXXCX100. E X $ drop In this case, L is the average length of feeder over which the power is to be transmitted. It will be noticed that the constant 10.8 appearing in the previous formulas has here been increased to 14. This has been done to allow, approximately, for the track resistance, but this constant might vary con- siderably, depending on the quality of the rail bonding. If the load is all bunched at the end of the feeder, Lis the actual length of the feeder in feet. If the load is uniformly distributed all along the line, as it would be if a number of locomotives were continually moving along the line, the dis- tance L in the above formula would be taken as one-half that used in the case where the load was bunched at the end. In other words, the whole current C would only flow through an average of one-half the length of the line. DYNAMOS AND MOTORS. 215 EXAMPLE. In Fig. 7, a & represents a section of track 4,000 ft. long. From the dynamo c to the beginning of the section, the distance is 1,200 ft. The trolley wire is No. 00 B. & S., and is fed from the feeder at regular intervals. Two mining locomotives are operated, each of which takes an average cur- rent of 75 amperes. The total allowable drop to the end of the line is to be 5^c of the terminal voltage, which is 500 volts. - Calculate the size of feeder required, assuming that the constant 14, in the formula, takes account of the resistance of the return circuit. Since the locomotives are moving from place to place, the center of dis- tribution for the load may be taken at the center of the 4,000 ft. The fc- 1200 FlG. 7. distance L will then be 1,200 + 2,000 = 3,200 ft. The total current will be 150 amperes; hence, we have circular mils - " X 8.2M X ISO X 100 = 268i800 . ouu x o This would require either a stranded cable or the use of two No. 00 wires in parallel from c to a. From a to b we have the No. 00 trolley wire in parallel with the feeder; hence, the section of feeder ab may be a single No. 00 wire. In many cases, the drop is allowed to run as high as 10$, because the loads are usually heavier, and the distances longer, than in the example given above. DYNAMOS AND MOTORS. A dynamo is a machine for converting mechanical energy into electrical energy by moving conductors relatively to a magnetic field. An electric motor is a machine for converting electrical energy into mechanical energy by the relative motion between conductors carrying a current and a magnetic field. In the case of a dynamo, a number of conductors are made to move across a magnetic field by means of a steam engine or other prime mover, and the result is that an E. M. F. is set up in the conductors, and this E. M. F. will set up a current if the circuit is closed. In the case of a motor, a number of conductors are arranged so that they are free to move across a magnetic field, and a current is sent through these conductors from some source of electric current. The current flowing through these conductors reacts on the magnetic field and causes the conductors to move, thus converting the electrical energy delivered to the motor into mechanical energy. As far as mechanical construction goes, dynamos and motors are almost identical, and the operation of the motor is exactly the reverse to that of the dynamo. Dynamos and motors may be divided into two general classes: (a) Dyna- mos and motors for direct current; (b) dynamos and motors for alternating current. DIRECT-CURRENT DYNAMOS. Principle of Action. Direct-current dynamos are those that furnish a current that always flows in the same direction. This kind of dynamo is largely used for incandescent lighting, and also for the operation of street railways. A dynamo generates an E. M. F. by the motion of conductors across a magnetic field; hence, at the outset, it is seen that there must be at least two essential parts to a dynamo; namely, a magnet of some kind to set up a magnetic field, and a series of conductors arranged so that they may be moved or revolved in the magnetic field. The first part is known as the 216 DYNAMOS AND MOTORS. field magnet, or very often, simply as the field. The second part is known as the armature. The field is supplied by means of a powerful electromagnet which is magnetized by the current in the field coils. Fig. 8 shows a typical six-pole magnet of this kind; B, B are the magnetizing coils, which, when a current is sent through them, form powerful magnetic poles at N, S. The framework A of such a field magnet is usually made of cast iron or cast steel. These field magnets may have any number of poles, but machines of ordinary size are usually provided with from two to eight poles. The armature usually con- sists of a number of turns of insulated copper wire, arranged around the periph- ery of a ring or drum built up of soft iron sheets. Fig. 9 shows the construction of a typical armature of the ring type. The winding is divided into a number of sections, and the terminals connected to the commutator. This commutator consists of a number of copper bars, insulated from each other by means of mica, the bundle of bars being clamped firmly into place and turned up to form a true cylindrical sur- face. The sections in the commutator correspond with those in the armature, and the use and operation of the commutator will be described later. The winding on the ring is endless, i. e., it consists of a number of coils or sections c, the end of one section ^-Binding- u>ir*$: FIG. 9. being joined to the beginning of the next, thus forming an endless coil, as shown in Fig. 10. The construction of such a ring armature would be as shown in Fig. 9. DIRECT-CURRENT DYNAMOS. 217 Suppose the ring shown in Fig. 10 with its endless winding to be rotated between the poles of a 2-pole field magnet. We will then have the condi- tion of affairs as indicated in Fig. 10. The magnetic lines will flow from the N pole of the field magnet across through the iron core of the armature and enter the S pole on the other side. Since all the conductors on the right- hand face of the ring are moving upwards, they will have an E. M. F. gen- erated in them in one direction, while the E. M. F. in the conductors on the left side will have an E. M. F. in the opposite direction, because all the conductors on this side are moving downw;ards, or in the opposite direction, to those on the other side. These two opposing E. M. F.'s will meet at a, as shown by the arrowheads, and will neutralize each other so that no current will flow through the windings of the armature. Suppose, however, that taps are connected at the points a and a', as shown by the dotted lines, and these taps connected to two rings r, r' ', mounted so as to revolve with the armature. By allowing brushes b, b' to press on these rings, we can make connection with an outside circuit d, which may consist of a number of lamps or any other device through which we wish to send a current. By putting in the taps at a and a', we have allowed the two opposing E. M. F.'s to set up a current through the common connections to the rings, and thence through the outside circuit. Current now flows in each halt of the armature winding, unites at a, flows out by means of ring r' and brush 6', thence through the outside circuit d to brush b and ring r, from whence it passes to a', and thus completes the circuit. When the ring makes a half revolution from the position shown in the figure, it is seen that the current in the ouside circuit will flow in the opposite direction. In fact, an arrange- ment of this kind would deliver a current that would be periodically revers- ing in the outside circuit, or it would be what is known as an alternating current. Instead of simply bringing out two terminals to rings, suppose the winding to be tapped at a fairly large number of points, and connections brought down to a number of insulated strips, as shown in Fig. 11. If the armature be now revolved, it is seen that the brushes will come in contact with successive bars and keep the outside circuit in such re- lation to the armature winding that the current will always flow through it in the same direction . Moreover, if the num- FIG. 11. ber of divisions in the armature be large, the current will fluc- tuate very little, being nearly as steady as that obtained from a battery. The arrangement made up of insulated bars is called the commutator, because it commutes or changes the relation of the outside circuit to the armature winding so that the current in the outside circuit always flows in the same direction. All practical machines used for the generation of direct current must be provided with such a commutator. When alter- nating currents are used it is only necessary to use plain collector rings, as 2L8 DYNAMOS AND MOTORS. shown in Fig. 10. The foregoing brief description will give a general idea as to the construction of an ordinary direct-current dynamo or motor. Drum-wound armatures are more frequently used than the ring type shown, but the action is the same in either case. Factors Determining E. M. F. Generated. A dynamo should be looked upon as a machine for maintaining an electrical pressure rather than as a machine for generating a current. A pump does not manufacture water it merely maintains a head or pressure that causes water to flow wherever an outlet is provided for it to flow through. In the same way, a dynamo maintains a pressure, and this pressure will set up a current whenever the circuit is closed, so that the current can flow. The important thing to consider, therefore, is the E. M. F. that the dynamo is capable of generating. The E. M. F. generated by an armature depends on the total number of magnetic lines cut through per second by the armature conductors. This means that, in the first place, the faster the armature runs, the higher will be the E. M. F.; in the second place, the greater number of conductors or turns there are on the armature, the higher will be the E. M. F.; and in the third place, the stronger the magnetic field, the higher will be the E. M. F. The E. M. F. in terms of these quantities may be written ' nCN 100,000,000' where n = speed in revolutions per second; C = number of conductors on face of the armature; N = number of magnetic lines flowing from one pole. The constant 100,000,000 is necessary to reduce the result to volts. This equation enables us to make calculations relating to any two-pole dynamo, and with slight modification it is applicable to machines with field magnets FIG. 12. FIG. 13. having a number of poles. It will not be necessary to consider this formula further here, as the main thing to fix in mind is that the E. M. F. is propor- tional to the three quantities: speed, number of conductors, and strength of field. Field Excitation of Dynamos. In, the earliest form of dynamo, the magnetic field in which the armature rotated was set up by means of permanent magnets. Permanent magnets are, however, very weak compared with electromagnets, which are excited by means of current flowing around coils of wire wound on a soft-iron core, as shown in Fig. 13. As soon as the current ceases flowing around the coils of an electromagnet, the magnetism almost wholly disappears, but a small amount, known as the residual magnet- ism remains. It is to this residual magnetism that the dynamo owes its ability to start up of its own accord and excite its own field magnets. When the armature is first started to revolve, a very feeble E. M. F. is gener- ated in it, but the armature is connected to the field coils in such a way that this small E. M. F. is able to force a small current through the field coils, and thus set up a larger amount of magnetism in the field. This in turn increases the E. M. F. in the armature, and the building-up process goes on rapidly until the dynamo generates its full pressure. There are three different methods in use for supplying the field coils with current, and con- tinuous-current dynamos are divided into three classes, according to the method used for exciting their fields. These three classes are: (a) Series- wound dynamos; (6) shunt-wound dynamos; (c) compound- wound dynamos. SHUNT- WOUND DYNAMOS. 219 (a) Series-Wound Dynamos. In this class of machine, the field coils are connected in series with the armature, and all the current that passes through the armature also passes through the field and the outside circuit. This arrangement is shown in Fig. 12, where A T and S represent the poles of the magnet, + B and B the brushes, and Re the outside cir- cuit, which may consist of lamps, motors, or any other device in which it is desired to utilize the current. It will be noticed that with an arrangement of this kind, the E. M. F. will increase as the current increases, because the field will become stronger and the speed is sup- posed to remain constant. This will be true up to the point where the field carries all the mag- netism it is capable of, or, in other words, until it becomes saturated. After this point is reached, the E. M. F. will increase very little with increase of current. In most of the work connected with lighting or power trans- mission, it is desirable to have the voltage FIG. 14. remain nearly constant. For this reason, therefore, the series method of excitation has not been very largely used for dynamos. The only style of generator to which it has been applied at all generally is the arc-light dynamo, and these machines are provided with an automatic regulator of some kind to vary the voltage as desired. The series field winding has, however, been largely used in connection with the motors operated on constant-pressure circuits, as will be taken up later in connection with motors. (&) Shunt-Wound Dynamos. This style of machine has not been used largely of late years, although it was formerly very common. Its use is at present confined more particularly to machines of small size. In this method of excitation, the field is connected as a shunt or by-pass to the armature; i. e., the field winding is connected in parallel with the armature. This winding consists of a large number of turns of fine wire, so that its resistance is high and only a small part of the total current flows through it. Fig. 13 shows the connections for this kind of field excitation. An adjust- able resistance r is usually inserted in the field circuit, and by cutting this resistance in or out, the field may be weakened or strengthened and the voltage varied accordingly. With this type of machine, the current through the field does not vary greatly from no load to full load, and if the dynamo is well designed, the pressure at the brushes will keep approxi- mately constant. The pressure will, however, always fall off more or less, on account of the drop in the armature, due to its resistance, and also upon the tendency that the current in the armature has of weakening the field. The shunt winding is used quite largely for motors. (c) Compound-Wound Dynamos. The compound-wound dynamo is the one most largely used for direct-current power and light distribution, and it is so called because the winding used for exciting the field is a combination of the series and shunt windings previously described. The series winding serves the purpose of keeping up the field strength while the load is increased, and thus keeps the pressure constant, or even makes it rise with increased load, if so desired. When the series winding is so adjusted that the pressure rises as the load is increased, the machine is said to be overcom- pounded. Fig. 14 shows the connections for such a machine. It will be seen that the shunt winding is connected as before, a field resistance or rheostat, not shown in the figure, being inserted for the purpose of adjusting the volt- age. One brush connects directly to one terminal of the machine + T, while the other brush connects to one end of the series winding on the field. The other end of the series winding forms the other terminal T, to which the outside circuit R e is connected. It is thus seen that the shunt coil supplies a certain amount of initial magnetization that is augmented by the magnet- ism supplied by the series coils. Of course, care must be taken to see that the current in the series coils circulates around the field in the same direc- tion as that in the shunt coils, otherwise the effect would be to make the E. M. F. fall off with increasing load instead of keeping it up. This is the style of dynamo used almost exclusively for electric haulage plants, as well as plants for direct-current illuminating purposes. 220 DYNAMOS AND MOTORS. DIRECT-CURRENT MOTORS. Direct-current motors are in general almost identical, so far as construc- tion goes, with direct-current dynamos. Motors are often required to oper- ate under very trying conditions, as for example, in mine haulage or pump- ing plants or on the 9rdinary street car. For this reason, their mechanical construction often differs somewhat from that of the dynamo, the design being modified in such a way as to enclose the working parts as completely as possible, and thus protect them from dirt and injury. The two kinds of motors most commonly used are the series and shuni varieties. Compound- wound motors are only used for a few special kinds of work. Practically all of the motors in use are operated from constant-pressure mains; i. e., the pressure at the terminals of the motor is practically constant, no matter what load it may be carrying. We will here consider constant-potential motors only. Principles of Operation. If the fields of an ordinary constant-potential dynamo are excited and a current supplied to the armature from some out- side source, such as another dynamo D, Fig. 15, so that the current enters at +.B, and passing through the winding in the direc- tion indicated by the arrow heads, leaves at brush B, it will be found that all of the conductors under the S pole face, 6, c, d, e, /, and g, will tend to move downwards, and all those under the N pole face, j, k, I, m, n, and o, will tend to move upwards, as indicated by the small arrows. These forces combine to produce a tendency of the armature to rotate about its axis as indicated by the large arrows, which ten- dency is called the torque of the motor. The amount of this torque which is usually expressed in pound-feet; FIG. 15. that is, a certain number of pounds acting at a radius of a certain number (usually 1) of feet depends on (1) the strength of the field, (2) the number of conductors, (3) their mean distance from the axis of the armature, and (4) the amperes in each conductor. In any given machine, the second and third conditions are constant, so that the torque depends on the strength of the field and the current. If the armature is stationary, the E. M. F. required to send the current through the winding is only that necessary to overcome the drop, which is due to the resistance of the winding. If the torque exerted by this current is greater than the opposition to motion, so that it causes the armature to revolve, the motion of the conductors through the field generates in them an E. M. F. that is opposed to the E. M. F. that is sending the current through the armature. This opposing E. M. F., or counter E. M. F. as it is called, then diminishes the effect of the applied E. M. F., so that the current is reduced, reducing the torque. Should the torque still be greater than the opposition to motion, the speed of the armature will continue to increase, increasing the counter E. M. F., and thereby further reducing the current and the cor- responding torque, until the torque just balances the opposition to the motion, when the speed will remain constant. At all times, the drop of potential through the armature is equal to the difference between the counter and the applied E. M. F.'s, and as the product of this drop and the current, represents energy wasted, it is desirable to make it as low as possible. In good motors of about 10 H. P. output, the drop in the armature is seldom more than about 5# of the applied E. M. F., and is less in larger machines. This being the case, it is evident that if the armature is at rest, so that it DIRECT-CURRENT MOTORS. 221 has no counter E. M. F M and is connected directly to the mains, a very large current will flow through it, which would be liable to damage the armature. On this account an external resistance, called a starting resistance, is con- nected in series with the armature when it is to be started. This resistance is made great enough to prevent more than about the normal current from flowing through the armature when it is at rest; as the armature speeds up and develops some counter E. M. F., this resistance is gradually cut out. until the armature is connected directly to the mains, and is running at normal speed. The energy represented by the product of drop in the armature and the current is wasted; that represented by the product of the current and the rest of the E. M. F., that is, the counter E. M. F., is the energy required to keep the armature in motion. Aside from the comparatively small amount of current required to furnish the torque necessary for overcoming the frictional losses in the motor itself, which are practically constant, the amount of current taken from the mains is directly proportional to, and varies automatically with, the amount of the external load; for, if this external load is increased, the current which has been flowing in the armature cannot furnish sufficient torque for this increased load, so that the machine slows down. This decreases the counter E. M. F., which immediately allows more current to flow through the arma- ture, increasing the torque to the proper amount. If the external load is decreased, the current flowing furnishes an excess of torque, which . causes the speed to increase, increasing the counter E. M. F., and de- creasing the current until it again furnishes only the required amount of torque. Since the counter E. M. F. is very nearly equal to the applied, it is only necessary for it to vary a small amount to vary the current within wide limits. For example, if the resistance of a certain armature is 1 ohm, and it is supplied with current at a constant potential of 250 volts, then, when a current of 10 amperes is flowing through it, the drop is 10 X 1 = 10 volts, and the counter E. M. F. is 250 10 = 240 volts. Now, if the current is reduced to 1 ampere, the drop is 1 X 1 = 1 volt, and the counter E. M. F. is 250 1 = 249 volts; that is, the counter E. M. F. only varies , or 3.750, 9 while the current varies , or 90$. As stated before, the field magnets of constant-potential motors are usually either shunt-wound or series-wound. If shunt-wound, and supplied from a constant-potential circuit, the mag- netizing force of the field coils is constant, giving a practically constant field. This being the case, the counter E. M. F. is directly proportional to the speed, so that variations of the load make only slight variation in the speed. A shunt- wound motor is then (practically) a constant-speed motor. With series-wound motors, the strength of the field varies with the cur- rent; if the load on such a motor is reduced, the excess of torque makes the armature speed up, but as the resulting decrease of the current decreases the field strength, the armature must speed up to a much greater extent, in order to increase the counter E. M. F. to the right degree, than would be necessary if the field were constant. If the load is increased, the increase in the current so increases the field strength that the speed must decrease considerably, in order to decrease the counter E. M. F. by the right amount. The speed of a series-wound motor, then, varies largely with variations in the load. An advantage of the series nrotor is that if a torque greater than the normal is required, it can be obtained with less current than with a shunt motor, since the increased current increases the field strength, and the torque is proportional to both these factors. It would not be practicable to make the field strength of a shunt motor as great as is possible to get with a series motor, since it would require a very large magnetizing force, and with the shunt winding, this extra magnetizing force would have to be expended all the time, whether the strong field was required or not, which would be very wasteful; in the series motor, however, this extra magnetizing force is only expended while it is needed. 222 DYNAMOS AND MOTORS. A disadvantage of the series winding is that if all the load is taken off, the current required to drive the motor is very small, making a weak field, which requires such a high speed to generate the proper counter E. M. F. that the armature is liable to be damaged. In other words, the motor will race, or run away, if the load is all removed. This cannot occur with the shunt motor as long as the field circuit remains unbroken. . On account of the above features, shunt motors are used to drive machinery that requires a nearly constant speed with varying loads, or which would be damaged if the speed should become excessive, such as ordinary machinery in shops and factories, pumps, etc. Series motors are used on street cars, to operate hoists, etc., where, on account of the gearing used, the load cannot be entirely thrown off, and the torque required at starting and getting quickly up to speed is much greater than the normal amount. Speed Regulation of Motors. The torque of a motor depends on the current; that is, for a given current, the torque will be the same whatever may be the speed, provided the field strength remains the same. The speed at which the armature runs is a matter of E. M. F. only; that is, with a given current the speed will be proportional to the applied E. M. F., or, more strictly, the counter E. M. F., other conditions remaining the same. It has been shown that the torque will automatically regulate itself for changes in the load. The speed, however, may be varied by varying the applied E. M. F. or the strength of the field. A change in speed may or may not result in a change in the torque required, depending on the character of the work done by the motor. The simplest way to vary the applied E. M. F. is to insert a resistance, in series with the armature, similar to the starting resistance. By varying this resistance, the applied E. M. F. at the terminals of the motor is also varied, although the E. M. F. of the mains remains constant. It is evident FIG. 16. that the energy represented by the product of the current and the drop through the resistance is converted into heat, and is thereby wasted; therefore, for great variati9ns in speed, this method is not economical, though often very convenient. The applied E. M. F. may also be varied by varying the E. M. F. of the generator supplying the current, but this can only be done where a single generator is supplying a single motor, or several motors, whose speed must all be varied at the same time; so that this method is only used in special cases. If the strength of the field is changed, the speed necessary to give a cer- tain counter E. M. F. will also be changed, which gives a convenient method of varying the speed. If the strength of the field is lessened, the speed will increase, and if the field is strengthened, the speed will decrease. With shunt motors, the field may be weakened by inserting a suitable resistance in the field circuit, as in shunt dynamos; with series motors the same result may be obtained by cutting out some of the turns of the field coils or by placing a suitable resistance in parallel with the field coils. This method of regulation is also of limited range, since it is not econom- ical to maintain the strength of the field much above or below a certain density. The resistance method described above being rather more simple, it is generally used. For special cases, such as street-railroad work, various special combinations of the above methods of regulation are used. One of the most common of these is known as the series-parallel method, and is the method of regulation generally used at present for operating street cars. This method is equivalent to the method of cutting down the speed by reducing the E. M. F. applied to the motor, and is only applicable where at least two motors are used. It is also used, to some extent, in haulage plants. When a low speed is desired, or when the car is to be started up, the motors are thrown in series, as shown in Fig. 16, thus making the voltage across each motor equal to one-half the voltage between the lines, and cutting down the speed accordingly. When a high speed is CONNECTIONS FOR MOTORS. 223 desired, the motors are thrown in multiple, as shown in Fig. 17, and each motor runs at full speed because it gets the full line pressure. In practice, starting resistances are used in connection with the' above to make the starting smooth, but the two running positions are as shown, the motors being connected in series in the one case, and in parallel in the other. Connections for Continuous-Current Motors. Fig. 18 shows the manner in which a shunt motor is connected to the terminals + and of the circuit. It will be seen that the current through the shunt field does not pass through the resistance E which is connected in the arma- ^_ 7 ture circuit. This is necessary, Trolley since to keep the field strength constant, the full difference of potential must be maintained be- tween the terminals of the field coil, which would not be the case if the rheostat were included in the field current, for then the difference of potential would be only that existing between the brushes -f B and B. As on starting the motor this difference of potential is small, only a small current would flow through the field coils, which would generate such a weak field that an excessive current would be required to furnish the necessary torque for starting the motor. When connected as shown, however, the field is brought up to its full strength before any current passes through the armature; so this difficulty does not arise. Since in a series motor the same current flows through both armature and field coils, the starting resistance may be placed in any part of the circuit. The diagram in Fig. 19 illustrates one method of connecting a series motor to the line terminals -f and ; here the starting or regulating resistance R is placed between the line terminal and the brush B of the motor. To reverse the direction of rotation of a motor it is necessary to reverse either the direction of the field or the direction of the current through the armature. It is usual to reverse the direction of the current In the arma- ture, a switch being used to make the necessary changes in the connections. Fig. 20 shows the connectiops of one form of reversing switch. Two metal bars B and B\ are pivoted at the points T and T, ; one is extended and supplied with a handle H, and the two bars are joined together by a link L of some insulating material, such as fiber. Three contact pieces a, 6, and c are arranged on the base of the switch so that the free ends of the FIG. 18. FIG. 19. bars B and BI may rest either on a and 6, as shown by the full lines, or on b and c, as shown by the dotted lines. The line is connected to the terminals T and T lf and the motor armature between a and b, or vice versa, a and c being connected together. When the switch is in the position shown by the full lines, T is connected to a by the bar B, and 2\ to 6 by the bar ,. If the switch is thrown by means of the handle H into the position indicated by the dotted lines, Tis connected to b by the bar B, and T\ to a by the bar BI and the connection 224 DYNAMOS AND MOTORS. between c and a. The direction of the current through the motor armature, or whatever circuit is connected between a and 6, is thus reversed. In order to reverse only the current in the armature, the reversing switch must be placed in the armature circuit only. Fig. 21 represents the connec- tion for a reversing-shunt motor (a) and a reversing- series motor (6); + and are the line terminals; R, the starting resistance; B and JBi, the brushes of the motor, and F, the field coil of the motor. Some man- ufacturers combine the starting resistance and revers- ing switch in one piece of apparatus. In connecting up motors, some form of main switch is used to entirely disconnect the motor from the line when it is not in use. To prevent an excessive current from flowing through the motor circuit from any cause, short strips of an easily melted metal, known as fuses, mounted on suitable terminals, known as fuse boxes, are placed in the circuit. These fuses are made of such a sectional area that a current greater than the normal heats FIG. 20. them to such an extent that they melt, thereby breaking the circuit and preventing damage to the motor from an excessive current. The length of fuse should be proportioned to the voltage of the circuit, a high voltage requiring longer fuses than a low voltage, in order to prevent an arc being maintained across the terminals when the fuse melts. If desired, measuring instruments (ammeter and voltmeter) may be connected in the motor circuit, so that the condition of the load on the motor may be observed while it is in operation. All these appliances, regulating resistance, reversing switch, fuses, instruments, etc., are placed FIG. 21. inside the main switch; that is, the current must pass through the main switch before coming to any of these appliances, so that opening the main switch entirely disconnects them from the circuit, when they may be handled without fear of shocks. ALTERNATING-CURRENT DYNAMOS. An alternating-current dynamo is one that generates a current that periodically reverses its direction of flow. It was shown in connection with Fig. 10 that an armature provided simply with collector rings produced an alternating current in the outside circuit. This current may be represented by a curve such as that shown in Fig. 22. The complete set of values that the current or E. M. F. passes through repeatedly is known as a cycle. For example, the values passed through during the interval of time represented by the distance a c would constitute a cycle. The set of values passed through during the interval a 6 is known as an alternation. An alternation is, therefore, half a cycle. The number of cycles passed through per second is known as the frequency of the current, or E. M. F. Alternating-current dynamos are now largely used both for lighting and power transmission, especially when the transmission is over long distances. The reason that the alternating current is specially suitable for long-distance FIG. 22. ALTERNATORS. 225 work is that it may be readily transformed from one pressure to another. We have already seen that in order to keep down the amount of copper in the line, a high line pressure must be used. Pressures much over 500 or 600 volts cannot be readily generated with direct-current machines, owing to the troubles that are likely to arise due to sparking at the commutator. On the other hand, an alternator requires no commutator or even collecting rings, if the armature is made stationary and the field revolving, as is frequently done. Alternators are now built that generate as high as 8,000 or 10,000 volts directly. If a still higher pressure is required on the line, it can be easily obtained by the use of transformers, to be explained later. It is thus seen that where power is to be carried over long distances, the alternating current is indispensable. Alternating-current dynamos, like direct-current machines, consist of two main parts, i. e., the field and armature. Either of these parts may be the revolving member, and in many modern ma- chines the armature, or the part in which the current is induced, is the revolving member. Fig. 23 shows a typical alternator of the belt-driven type, having a revolving armature. It is not unlike a direct-current machine as regards its gen- eral appearance. The number of poles is usually large, in order to secure the required frequency without running the ma- chine at a high rate of speed. The frequencies met with in practice vary all the way from 25 to 150. The higher frequencies are, however, passing out of use, and at present a frequency of 60 is very FIG. 23. common. This frequency is well adapted both for power and lighting pur- poses. When machines are used almost entirely for lighting work, frequen- cies of 125 or higher may be used. The frequency of any machine may be readily determined when the number of poles and the speed is known, as follows: Frequency = number of poles rev. per min. X - 60 For example, if an eight-pole alternator were run at a speed of 900 R. P. M., the frequency would be 8 900 / = -2 X -gQ = 60 cycles per second. Alternators may be divided into the two following classes: (a) Single- phase alternators; (b) Multiphase alternators. (a) Single-Phase Alternators. These machines are so called because they generate a single alternating current (as represented by the curve shown in Fig. 22). The armature is provided t with a single winding and the two terminals are brought out to collector rings, as previously described. Single- phase machines have been largely used in the past for lighting work, but they are gradually being replaced by multiphase machines, because the single-phase machines are not well suited for the operation of alternating- current motors. (6) Multiphase Alternators. These machines are so called because they deliver two or more alternating currents that differ in phase; i. e., when one current is, say, at its maximum value, the other currents are at some other value. This is accomplished by providing the armature with two or more distinct windings which are displaced relatively to each other on the armature. One set of windings, therefore, comes under the poles at a later instant than the winding ahead of it, and the current in its winding comes 226 DYNAMOS AND MOTORS. to its maximum value at a later instant than the current in the first wind- ing. In practice, the two types of multiphase alternator most commonly used are (1) two-phase alternators, (2) three-phase alternators. Two-phase alternators are machines that deliver two alternating currents that differ in phase by one-quarter of a complete cycle; i. e., when the current in one circuit is at its maximum value, the current in the other circuit is passing through its zero value. By tapping four equidistant points of a regular ring armature, as shown in Fig. 24, and connecting these points to four collector rings, a simple two-pole two-phase alternator is obtained. One circuit connects to rings 1 and l f , the other circuit connects to rings 2 and 2 f . It is easily seen from the figure that when the part of the winding connected to one pair of rings is in its position of maximum action, the E. M. F. in the other coils is zero, thus giving two currents in the two different circuits that differ in phase by one-quarter of a cycle or one-half an alternation. Three-phase alternators are machines that deliver three currents that differ in phase by one-third of a complete cycle; i. e., when one current is flowing in one direction in one circuit, the currents in the other two circuits are one- half as great, and are flowing in the opposite direction. By tapping three equidistant points of a ring winding, as shown in Fig. 25, a simple three- phase two-pole alternator is obtained. Three mains lead from the collecting rings. In order to have three distinct circuits, it would ordinarily be necessary to have six collecting rings and six circuits; but this is not necessary in a three-phase machine if the load is balanced in the three different circuits, because one wire can be made to act alternately for the return of the other two. Uses of Multiphase Alternators. Multiphase alternators are coming largely into use, because, by using them, alternating-current motors can be readily operated. By using multiphase machines, motors can be operated that will FIG. 24. FIG. 25. start from rest under load, whereas with single-phase machines the motor has to be brought up to speed from some outside source of power before it can be made to run. For this reason, such machines are used for the operation of modern power-transmission plants. As far as the general appearance of three-phase machines goes, they are similar to ordinary single-phase alter- nators, the only difference being in the armature winding and the larger number of collector rings. The multiphase alternator is also adapted for the operation of lights, so that by using these machines, both lights and motors may be operated from the same plant. They are well adapted for power-transmission purposes in mines, especially for the operation of pump- ing and hoisting machinery, because the motors operated by them are very simple in construction and therefore not liable to get out of order. ALTERNATING-CURRENT MOTORS. Alternating-current motors may be divided into two general classes: (a) Synchronous motors; (b) Induction motors. (a) Synchronous motors are almost identical, so far as construction goes, with the corresponding alternator. For example, a two-phase synchronous motor would be constructed in the same way as a two-phase alternator. ALTERNATING-CURRENT MOTORS. 227 They are called synchronous motors because they always run in synchro- nism, or in step, with the alternator driving them. This means that the motor runs at the same frequency as the alternator, and if the motor had the same number of poles as the alternator, it would run at the same speed, no matter what load it might be carrying. This type of motor has many good points, and is especially well suited to cases where the amounts of power to be transmitted are comparatively large and where the motor does not have to be started and stopped frequently. Multiphase synchronous motors will start up from rest and will run up to synchronous speed without aid from any outside source. They will not, however, start with a strong starting torque or effort, and will not, there- fore, start up under load, and can- not be used in places where a strong starting effort is required. For this reason synchronous motors are not suitable for intermittent work. (6) Induction motors are so called FIG. 26. because the current is induced in the armature instead of being led into it from some outside source. Fig. 26 shows a typical induction motor. There are two essential parts in these machines, viz., the field, into which multiphase currents are led from the line, and the armature, in which currents are induced by the magnetism set up by the field. Either of these parts may be the stationary or revolving member, but in most cases the field, or part that is connected to the line, is stationary. Fig. 27 shows the construction of the stationary member or field. This con- sists of a number of iron laminations, built up to form a core and provided with slots around the inner periphery. The form-wound coils constituting the field winding are placed in these slots and connected to the mains. This winding is arranged in the same way as the armature winding of a multi- phase alternator. When the alternating currents differing in phase are sent through the winding, magnetic poles are formed at equidistant points around the periphery of the field, and the constant changing of the currents causes these poles to shift around the ring, thus set- ting up what is known as a revolving magnetic field. This armature, Fig. 28, consists of a laminated iron core provided with a number of slots, in each of which is placed a heavy copper bar b. The ends of these bars are all connected together by two heavy short- circuiting rings r, r running around each end of the arma- ture. The bars and end rings thus form a number of closed circuits. When such an arma- ture is placed in the revolv- ing field, the magnetism will cut across the armature con- ductors, inducing E. M. F.'s in them, and since the conduc- tors are joined up into closed circuits, currents will flow in them. These currents will react on the field, and the armature will be forced to revolve. Such an armature will not run exactly in synchronism, because if it did, it would revolve just as fast as the magnetic field, and there would be no cutting of 228 DYNAMOS AND MOTORS. lines of force. The speed drops slightly from no load to full load, but if the motor is well designed, this falling off in speed is slight. Induction motors possess many advantages for mine work. One of the chief of these is the absence of the commutator or any kind of sliding con- tacts whatever. Such motors can therefore operate with absolutely 110 sparking a desirable feature for mine work. The motors are also very simple in construction, and are therefore not liable to get out of order. They have an additional advantage over the syn- chronous motor in that they start up with a strong starting effort, and, in fact, behave in most re- spects like any good shunt-wound direct-current motor. They are used quite successfully for all kinds of stationary work, such as pumping, hoisting, etc., but so far have not been used to any great extent for haulage purposes. When these motors are used for purposes where a variable speed is FIG. 28. required, it is customary to pro- vide the armature with a winding similar to that of the field and bring out the terminals to collecting rings, so that resistance may be inserted in the armature circuit. TRANSFORMERS. Reference has already been made to the use of transformers for changing an alternating current from a higher to a lower pressure, or vice versa, with a corresponding change in current. Transformers used for raising the volt- age are known as step-up transformers; those used for lowering the pressure are known as step-down transformers. The transformer consists of a laminated iron core upon which two coils of wire are wound. These coils are entirely distinct, having no connection with each other. One of these coils, called the primary, is connected to the mains; the other coil, called the secondary, is connected to the circuit to which current is delivered. Fig. 29 shows the arrangement of coils and core for a common type of transformer. The secondary -* coil is wound in two parts S, S', and the primary coil, C also in two parts P, P', is placed over the sec- ondary. C is the core, built up of thin iron plates. Fig. 30 shows a weather-proof cast-iron case for this transformer. When a current is sent through the primary it sets up a magnetism in the core which rapidly alte mates with the changes in the current. This changing magnet- ism sets up an alterna- ting E. M. F. in the sec- ondary, and this second- ary E. M. F. depends FIG. 29. FIG. 30. upon the number of turns in the secondary coil. If the secondary turns are greater than the primary, the secondary E. M. F. will be higher than that of the primary. The relation between the primary E. M. F. and secondary E. M. F. is given by the following: , secondary turns. Secondary E. M. F. = primary E. M. F. ) primary turns ' BATTERIES. 229 . second The ratio _ secondary turns _ ^ secondary turns ratio of transformation of the transformer. For example, if a transformer had 1,200 pri- mary turns and 60 secondary turns, its ratio of traiisforma- Phase 1. Phase 2. 1OOOV. P * ~1OOO FT* P' FIG. 32. tion would be 20 to 1, and the secondary voltage would be one-twentieth that of the primary. Transformers are made for a number of different ratios of transformation, the more common ones being 10 to 1 or 20 to 1. Of course, a transformer never gives out quite as much power from the sec- ondary as it takes in from the primary mains, because there is always some loss in the iron core and in the wire making up the coils. The efficiency ( *10OO F *j P /Tnnnnnnrinnr^ ~-1000 V-+ p' FIG. 33. -U00V FIG. 31. of transformers is, however, high, reaching as high as 97^ or 98$ in the larger sizes. Transformers are always connected in parallel across the mains, and if they are well designed, will furnish a very nearly constant secondary pressure at all loads, when furnished with a constant primary pressure. Fig. 31 shows transformers connected on a single-phase circuit, Fig. 32 shows the connection for a two-phase circuit, and Fig. 33 shows one method of connection for a three-phase circuit. . ELECTRIC SIGNALING. BATTERIES. Batteries are used for various purposes in connection with mining work, principally for the operation of bells and signals. The Leclanchi cell is one that is widely used for bell and telephone work. It is made in two or three different forms, one of the most com- mon of these being as shown in Fig. 34 (a). The zinc element of this battery is in the form of a rod Z, and weighs about 3 oz. The other electrode is a car- bon plate placed in a porous cup and sur- rounded with black oxide of manganese, mixed with crushed coke or carbon. The electrolyte used in the battery is a satura- ted solution of sal FIG. 34. 230 ELECTRIC SIGNALING. ammoniac. The E. M. F. of this cell is about 1.48 volts when the cell is in good condition. In another form of the cell, known as the Gonda type, the black oxide of manganese is pressed into the form of bricks and clamped against each side of the carbon plate by means of rubber bands. This cell will do good work if it is only used intermittently, i. e., on circuits where the insulation is good and where there is no leakage causing the cell to give 8 i ' - til i ~/\ J * FIG. 35. FIG. 36. out current continuously. If current is taken from it for any length of time, it soon runs down, but will recuperate if allowed to stand. In cases where the insulation is apt to be poor, as it often is in mines, it is best to use a battery that will stand a continuous deli very of current and that will at the same time operate all right on intermittent work or on work where the circuit is open most of the time. For work of this kind, cells of the Edison- Lalande or Gordon type are excellent. Fig. 34 (b) shows the Edison-Lalande cell. The elements consist of two zinc plates Z, hung on each side of a plate of compressed cupric oxide C, The electrolyte is a satu- rated solution of caustic potash, and this should be kept covered with a layer of heavy paraffin oil, to prevent the action of the air on the solution. The voltage of the cell is only .7 volt, but its internal resistance is very low and its current capacity correspondingly large. The electrolyte used in the Gordon cell is also caustic-potash solution, and the two cells are much the same, so far as their general characteristics are concerned. The table on page 231 gives data relating to a number of different types of cell. BELL WIRING. The simple bell circuit is shown in Fig. 35, where p is the push button, b the bell, and c, c the cells of the battery connected up in series. When two or more bells are to be rung from one push button, they may be joined up <> FIG. 37. FIG. 38. in parallel across the battery wires, as in Fig. 37 at a and &, or they may be arranged in series, as in Fig. 36. The battery B is indicated in each diagram by short parallel lines, this being the conventional method. In the parallel arrangement of the bells, they are independent of each other, and the failure of one to ring would not affect the others; but in the series grouping, all but one bell must be changed to a single-stroke action, so that each impulse of current will produce only one movement of the hammer. The current is then interrupted by the vibrator in the remaining bell, the result BATTERIES. 231 ri g 66 be larizing eandde in porou Si ^g^ a 'go >3 O> 5S Cj S'i'^^^aJ ^o g'^O^Oa? ^ * a) 1 " 1 oj 1 " 1 "^ o o a Polariz For lar, 1*" w> 4 '|Sa2f oft -s.| 03 Q q g^ {2 ^3 ^ ^ Q o M *~ 5 & oft56a"og, 5-?r^i O CO CO CJ I fe ^ c* M ^3 _o 8 3 P4 1-5 ** : ' A : : o>^ : > '3 o o ^ Q o ^ o a o> a a $ a I 4 s 'oT^ : ^ "oT 'O a O ^^ : o '' " 5 3 S : ^ 1 Lj ft 3 : 3 ! 1 "C ^ ; 1 "B CO 8. 5 si s I 2 ST "C 6 i -s -a ^ j H 'E e c 5 1 a o !o c s S * 2 .2 ' o3 ^o _ "^ 1 1 'ft < r-H _, oi 03 .2 : 1 i'-=I 1 .2 ft ft 2 : oj TD i ji p || 1|^ .2 5 || l o ^ ^ I ! S in io o ' 3 c a 'XCC coCU^ fc CO a "* CO cB"" 3 1 s II 1 i' a 5 o v-V^ 3 ! i i'O.S bo . a ^ 'o "" *j o : a c o o o 0; O o c. a CJ a a a a e a c a a is XX N '~K ^ a N S K N N N N N N a s ^c : 1 i Grenet .... Pabst Bunsen... 1 1 SJ ? .-s'S ^- l 5 Q Q r5 * ^'f'di !^!^ -J J OW CJ Gordon,... 232 ELECTRIC SIGNALING. being that each bell will ring with full power. The only change necessary to produce this effect is to cut out the circuit-breaker on all but one bell by connecting the ends of the magnet wires directly to the bell terminals. When it is desired to FIG. 39. FIG. 40. FIG. 41. FIG. 42. ring a bell 1 ' from one of two places some distance apart, the wires may be run as shown in Fig. 38. The pushes p, p' are located at the required points, and the battery and bell are put in series with each other across the wires joining the pushes. A single wire may be used to ring signal bells at each end of a line, the connections being given in Fig. 39. Two batteries are required, B and B', and a key and bell at each sta- tion. The keys Jfc, k' are of the double-contact type, making connections normally between bell b or b' and line wir6 L. When one key, as A:, is depressed, a current from B flows along the wire through the upper contact of k' to bell b' and back through ground plates G', G. When a bell is intended for use as an alarm apparatus, a constant-ringing attachment may be introduced, which closes the bell circuit through an extra wire as soon as the trip at door or window is disturbed. In the diagram, Fig. 40, the main circuit, when the push p is depressed, is through the automatic drop d by way of the terminals a, 6 to the bell and battery. This current releases a pivoted arm which, on falling, completes the circuit between b and c, establishing a new path for the current by way of e, independent of the push p. For operating electric bells, any good type of open-circuit battery may be used. The Leclanche' cell is largely used for this purpose, also several types of dry cells. Annunciator System. The wiring dia- gram for a simple annunciator system is shown in Fig. 42. The pushes 1, 2, 3, etc. are located in various places, one side being con- nected to the battery wire b, and the other to the leading wire I in communication with the annun- ciator drop corresponding to that place. A bat- tery of two or three Leclanch6 cells is placed at B in any convenient location. The size of wire used throughout may be No. 18 annuncia- tor wire. A return-call system is illustrated in Fig. 41, in which there is one battery wire 5, one return wire r, and one leading wire Z t ,o, etc. for each place. The upper portion of the annunciator board is provided with the usual drops, and below these are the return-call pushes. These are double-contact buttons, held normally against the upper contact by a spring. When in this SELL WIRING. 233 position, the closing of the circuit by the push button in any room, such as No. A, rings the office bell and releases No. k drop, the path of the current 111 ( FOOT BBL1 Q ^M1 U TO ENGINE ROOH 0J i L JIEAD ISX. U SBD.L ^ T 1 (FOOT BELL pZr e 8 - T'p ' !> ' I>S! M> UEAJ> BUTTOJf ' I -v ri^ D FOOT BUTT* \ 1] TELEPBOtt FIG. 4 this case being from push j> back to the push button, nal being made by pressing lower part of the annui office-bell circuit is broke circuit formed through k the battery B to g-m-r-n-o the room bell being in th eral fire-alarm may be adc consisting of an automati ratus for closing all the ro once, or as many at a tim ring. When this system is tery wire should be either Four or five Leclanche' ce quired in this case. It will be seen that th so arranged that the room the push in that room is not desired, a double-con substituted, so that the r broken at the same time made through the annunc push should be so connec is normally complete thr leading wire bein^ conne< and the battery wire bein second contact point, whi of circuit. Telephones are also use communicating purposes, that a first-class long-dist phone is the best type to phones are so called becau or connected in parallel a are not connected in series should get out of order, likely to be disabled. Fi plete bell annunciator an or ^ 3. ^ to a-c-d-e-f-g-B-h-b On the return sig- * the button at the iciator board, the i at rf, and a new as follows: From -a-c-k-p to battery, is circuit. A geh- ied to this system, B clockwork appa- om-bell circuits at e as a battery can installed, the bat- No. 14 or No. 16. 11s are usually re- e connections are jell will ring when pressed. If this be tact push may be oom-bell circuit is that the circuit is iator. This double ted that the circuit Dugh the bell, the ited to the tongue, connected to the ch is normally out 8 3 for signaling and It has been found ance bridging tele- use. Bridging tele- se they are bridged cross the line, and . If one telephone __ 9 the others are not ~*^~* g. 43 shows a com- d telephone outfit, 234 ELECTRIC SIGNALING. Hoisting ng/ne House. Battery. as installed in one of the anthracite coal mines of the D., L. & W. R. R. Co. It will be noticed that bridging instru- ments are used and that each bell in the shaft is provided with a return- call button. This bell wiring should be put up in a substantial manner, and it is best, if possible, to run all the wires down the shaft in the shape of a lead-covered cable. Another shaft-signaling apparatus is shown in Fig. 44, as used at the West Vulcan mines, Mich. Fig. 45 9 f -?Lerl 10'-* Level. fS^Le FIG. 44. FIG. 45. shows a form of waterproof push but- ton used at the same mine. Fig. 46 shows the arrangement of flash signals as used in Montana. This consists of a switch cut into this main circuit at PROSPECTING. 235 each level of the mines. By pulling out the handle bar of the switch, the lights, on this circuit can all be flashed at once, and by a properly arranged code of flash sig- nals, the system can be used for communicating between the surface to any part of the mine, and bet ween different portions of the mine. A system of signaling by which signals can be sent to the engine room from any point along the haulage road is shown in FIG. 47. Fig. 47. The conductors a and b, leading from the battery run parallel to ach other along the roadside, and about 6 in. apart. A short iron rod, placed across the wires a, 6, signals to the engineer, or by simply bringing the two wires together a signal may be sent. When the engineer hauls from different roads, the signal- ing system should be supplemented with indicators, so that when the bell rings the indicator would show from which point the signal came, and in case several signals were given at the same time, the engineer should not heed any until the indicator shows that a complete signal came from one place. A system of signaling for showing whether or not a section of track is occupied by another motor is shown /oo' -400' FIG. 48. in Fig. 48. White lights indicate a clear track and dark- ness an occupied section. A single-center hinge, double- handle switch at each signal station is used and a touch of FIG. 46. the handle throws the switch in the desired direction. The switches are placed in the roof, 4 ft. above rails within easy reach of motor- man. Fig. 48 shows the connections. Each switch is provided with a spring (not shown in the figure) which, drawing across the center hinge, when the handles are in their central position, insures a perfect contact when the switch is inclined toward either the trolley or rail-terminal plug. PROSPECTING. The prospector should have a general knowledge of the mineral-bearing strata, and should know from the nature of the ledges exposed whether to expect to find mineral or not. He should also possess such a knowledge of the use of tools as will enable him to construct simple structures, and a sufficient experience in blacksmithing to enable him to sharpen picks and drills, or to set a horseshoe, if necessary. Outfit Necessary. The character of the prospecting being carried on will have considerable effect on the outfit necessary, which should always be as simple as possible. In general, when operating in a settled country, the outfit is as follows: A compass and clinometer for determining the dip and strike of the various measures encountered; a pick and shovel for excavating, and, where rock is liable to be encountered, a set of drills, hammer, spoon for cleaning the holes, tamping stick, powder and fuse, or dynamite fuse and cap; a blowpipe outfit; a small magnifying glass; an aneroid barometer for determining elevations, and a small hand pick; the latter should weigh about 12 lb., and should have a pick on one end and a square-faced ham- mer on the other, the handle being from 12 to 14 in. long. If the region under consideration has been settled for some time, there will probably be geological, county, railroad, or other maps available. 236 PROSPECTING. These may not be accurate as to detail, but will be of great assistance in the work on account of the fact that they give the course of the railroads, streams, etc. When operating in a mountainous region, away from a settled country, and especially when searching for precious metals, the following materials, in addition to that already mentioned, may be required: A donkey or pony packed with a couple of heavy blankets, an A tent, cooking utensils, etc.; a supply of flour, sugar, bacon, salt, baking powder, and coffee, sufficient for at least a month. It is also well to take some fruit, but all fruit containing stones or pits should be avoided, as they are only dead weight, and every pound counts. For the same reason, canned goods should be avoided, on account of the large amount of water they contain. A healthy man will require about 3 Ib. of solid food per day. Many prefer to vary the diet by taking rice, corn meal, beans, etc., in place of a portion of the flour. The additional tools necessary are an ax, a pan for washing gold ore, making concentrating tests, etc., and, in some cases, an assay furnace and outfit packed upon another animal. Where game is abundant, a shot- gun or rifle will be found useful for supplying fresh meat. In regions abounding in swamps it becomes necessary to operate from canoes, or to take men for porters or packers, who carry the outfit on their backs or heads. These men will carry from 60 to 125 Ib. Plan of Operations. When the presence of mineral is suspected in a tract of land, a thorough examination of the surface and a study of the exposed rocks, in place, may result in its immediate discovery, or in positive proof of its absence; or it may result in still further increasing the doubt of, or the belief that, it does exist. The first procedure in prospecting a tract of land is to thoroughly traverse it, and note carefully any stains or traces of smut, and all outcrops of every description; and, whenever possible, take the dip and the course of the outcrop with a pocket compass. Any fossils should also be carefully noted, to assist in determining the geological age of the region. These outcrops are frequently more readily found along roads or streams than any other place on the tract. In traveling along the streams, the prospector should pay particular attention to its bed and banks, to see whether there are any small particles of mineral in the bed of the stream, or any stains or smut exposed along the washed banks. If small pieces of mineral are found in the stream, a search up it and its tributaries will show where the outcrop from which the find came is located. When the ravines and valleys are so filled with wash that no exposures are visible, and nothing is gained by a careful examination of them, the prospector must rely on topographical features to guide him. Any gold present in the vein material usually remains in the float as free or metallic gold, but other valuable metals are often leached out. The fact that the float itself may be barren does not indicate that it may not have come from a very rich deposit, and hence it will often pay to follow barren float, since the outcrop of the vein itself is often either entirely barren, low grade, or of a different nature from the deeper deposits. In cases where there are no outcrops or any other surface indications, it would become necessary to sink shafts or test pits, or to proceed by drilling. The absence of any indication of mineral in the soil may not prove that there is not an outcrop near at hand, for the soil is frequently brought from a distance, and bears no relation to the material underlying it. In like manner, glacial soil often contains debris transported from, deposits many miles away; but such occurrences can usually be distinguished by the gen- eral character of the associated wash material. Frequently, the weathered outcrop of a deposit has been overturned or dragged back upon itself, so as to indicate the presence of a very thick deposit. For this reason, any openings made to determine the character of the material should be continued until the coal or other mineral is of a firm character, and both floor and roof are well exposed. Sometimes, in the case of steeply pitching coal beds, the surface may be overturned for a consider- able depth, so that it is difficult to tell which is the roof and which is the floor. Usually, if Stigmariae are found in the rocks of one wall, it is supposed that this wall is the floor of the seam, while if Sigillariae, fern leaves, etc. are found in the wall rock, it is probably the roof of the deposit. These indi- cations are not positive proof, for both of these fossils may occur in either the top or bottom wall of a coal deposit, though they are usually found in the positions noted. Coal, clay, gypsum, salt, etc. usually occur in unaltered deposits, i. e., in rocks that have not undergone metamorphism. PROSPECTING. 237 The accompanying table gives the names of the various geological periods, both as they occur in America and their foreign equivalents, together with the name of the principal form of life during each period. The various terms employed in geology are denned in the glossary. 238 PROSPECTING. Metals and metallic ores usually occur in rocks that have undergone more or less metamorphism. This change may have been accompanied by heat and volcanic disturbances sufficient to render the rocks thoroughly crystalline, or it may simply have been the converting of limestone into dolomite. The prospector for metals usually avoids regions in which the rocks have been wholly unaltered; while, on the other hand, a region covered by extensive flows of basalt is generally barren. As the vein filling of most metal-bearing deposits has been deposited from circulating water, it stands to reason that porous rock formations are more favorable to the occurrence of metallic ores than are hard, dense, rock formations. As a rule, ore deposits are more common at the junction of two dissimilar rock formations, as, for instance, the contact between limestone and porphyry. When a prospector is operating in any particular region, it is best to study carefully the conditions of that region before proceeding, as such factors as lack of rain, frozen ground, etc. may have played an important part in determining the character of placer or fragmentary deposits, and the outcrop and surface appearance of other deposits. Experience obtained in one region is frequently very misleading when applied in another. Coal or Bedded Materials. The presence of the outcrop of any bed may often be located by a terrace caused by the difference in the hardness of the strata; but as any soft material overlaying a hard material will form a ter- race, it is necessary to have some means of distinguishing a coal or ore terrace from one caused by worthless material. Usually, the outcrop of a coal terrace will be accompanied by springs carrying a greater or less amount of iron in solution, which is deposited as ochery films upon the stones and vegetable matter over which the water flows. The outcrops of beds of iron or other ores are very frequently marked by mineral springs. Sometimes the outcrop of a bed will be characterized by a marked difference in the vegetation, as, for instance, the outcrop of a bed of phosphate rock by a luxuriant line of vegetation, the outcrop of a mineral bed by a lack of vegetation, the outcrop of a coal bed contained between very hard rocks by more luxuriant vegetation than the surrounding country, etc. Some indication as to the dip and strike of the material composing the bed may be obtained by examining the terrace and noting the deflections from a straight line caused by the changes in contour of the ground. If the varia- tion occasioned by a depression is toward the foot of the hill, the bed dips in the same direction with the slope of the ground; but if the deflection is toward the top of the hill, the dip is the reverse from the slope of the ground, or into the hill. After any terrace or indication of the outcrop of a bed has been discovered, it will be necessary to examine the outcrop by means of shafts, tunnels, or trenches. The position of such openings will depend on the general character of the terrace. If the dip appears to be with the hill, a trench should be started below the terrace and continued to and across it; while if the dip appears to be into the hill, it may be best to sink a shallow shaft above the terrace. Formations Likely to Contain Coal. No coal beds of importance have as yet been found below the Carboniferous period, but coal may be looked for in any stratified or sedimentary rocks that were formed after this period, although the bulk of the best coal has, up to the present time, been found in the Carboniferous period. As a rule, highly metamorphic regions con- tain no coal, and the same may be said of regions composed of volcanic or igneous rocks. An examination of the fossils contained in the rocks of any locality will usually determine whether they belong to a period below or above the Carboniferous, and hence whether there is a probability of the formations containing coal. On account of this fact, the prospector should familiarize himself with the geological periods, and, by referring to any elementary geology, with the most common fossils of the various periods. The rocks 'most common in coal measures are sandstones, limestones, shale, conglomerates, fireclays, and, in some localities, the coal deposits are frequently associated with beds of iron ore. Ore deposits, as is well known, are generally found in mountainous districts, rather than in the undisturbed horizontal strata of the plains and mountain parks usually deep in the core and center of the mountain system, rather than along their flanking foot-hills. Consequently, not only are the prairies a,nd flat portions of the mountain parks to be avoided, but also the zone of uptilted strata on the edges of prairies and parks, commonly Called hogbacks. These hogbacks are the natural "habitat" of such ORE DEPOSITS. 239 economic products as coal, petroleum, building stone, clays, etc., but not often of the precious metals. The reason for this appears to be that the latter are commonly found to be associated with evidences of more or less heat. In the Rocky Mountains they are rarely found except where volcanic eruptions have at some time been active, or where the strata have been changed or metamorphosed and crystallized by heat. As metallic ore bodies occupy fissures and other openings in the earth's crust, we must go to regions where the greatest disturbances and uplifts have occurred, accompanied by the greatest rending and contortions of the rocks, and eruptions of volcanic matter. As a broad assertion, we may say that the greater part of any mountain region is a prospecting field, with the exception of those areas we have restricted as unpromising. But over this wide area of more or less metamor- phosed and crystalline rocks, there are regions and localities where the precious metals have already been found, and others where on geological grounds they are most likely yet to be found, and those are generally where eruptive forces have been especially active, where once molten eruptive rocks are most abundant, and the disturbance and crystallizing of the strata most pronounced. Position of Veins and Ore Deposits. Ores, as a rule, are to be looked for at the junction of any two dissimilar rocks, rather than in the mass of those rocks. However, there are many exceptions to this, where the mass of a decomposed dike or sheet of porphyry has been impregnated by free gold or gold-bearing pyrites, and the whole rock is practically a gold vein. In this mass, the richest gold is often found in a network of little quartz veins run- ning through the porphyry mass. Some of our richest gold mines are found in " rotten," decomposed, oxidized dikes and sheets of porphyry; but this is rarely the case with lead-silver ores, which frequent rather the lines of con- tact in limestones or in fissure veins in granite. The Cambrian quartzites a few years ago were rather avoided by the prospectors, their extreme hardness pre- senting great difficulties in mining, and from the fact that they were generally supposed to be barren. The late discov- eries of very rich gold deposits in them, and of similar deposits in quartzites of a later age, have drawn more attention to them. The gold has been found in a free state associated with oxide of iron in cavernous deposits, and in close prox- imity to eruptive rocks. In the granitic FIG. 1. rocks, both gold and silver occur in fissure veins associated with pyrites, galena, etc. These fissures, occupied by mineralized quartz veins, may occur in the granite or gneiss alone, or be at the contact of these rocks with a porphyry dike. Veins in overflows of volcanic lava generally fill a fissure having a more or less steep inclination, penetrating the lava sheets, caused probably by shrinkage of the molten lava on cooling. These fissures, in some cases, are likely to be limited in depth to the thickness of the lava sheet. Where, in a few rare cases, the fissure has been traced down to the underlying granite or some other rock, it has come abruptly to an end. Underground Prospecting. Frequently a seam or deposit becomes faulted or pinched out underground, and it is necessary to continue the search by means of underground prospecting. Underground prospecting is, to a large extent, similar to surface prospecting, the underground exposures being simply additional faces for the guidance of the engineer. In the case of coal beds or similar seams, if a fault or dislocation is encountered, the man- ner of carrying on the search will depend on the character of the fault. Where sand faults or washouts are encountered, the drift or entry should be driven forwards at the angle of the seam until the continuation of the formation is encountered, when a little examination of the rocks will indi- cate whether they are the underlying or overlying measures. In the case of dislocations or throws, the continuation of the vein may be looked for by Schmidt's law of faults, which is as follows: Always follow the direction of the greatest angle. It has been discovered by observation that, in the majority of cases, the hanging- wall portion of the fault has moved down, and on this 240 PROSPECTING. account such faults are commonly called normal faults. For instance, if the bed a b, Fig. 1, were being worked from a toward the fault, upon encoun- tering the fault, work would be continued down on the farther side of the fault toward d, until the continuation of the bed toward b was encountered. In like manner, had the work been proceeding from 6, the exploration would have been carried up in the direction of the greatest angle, and the continuation toward a thus discovered. A reverse fault is one in which the movement has been in the opposite direction to a normal fault. Espe- cially in the case of precious metal mines, where the material occurs as perpendicular or steeply pitching veins, faults are liable to displace the deposit, both horizontally and vertically, in which case it may be difficult to determine the direction of the continuation of the ore body; but fre- quently pieces of ore are dragged into the fault, and these serve as a guide to the miner, and indicate the proper direction for exploration. Where a bed or seam is faulted, its continuation can frequently be found by breaking through into the measures beyond, when an examination of the formation will indicate whether the rocks are those that usually occur above or below the desired seam. Prospecting for Placer Deposits. Placers are fragmental deposits from water in which the heavier minerals have been concentrated in certain portions, usually next the underlying, or bed, rock. The materials that are recovered from placer deposits are metallic gold, tinstone, monazite, sand, or precious stones. Placer deposits are modern or ancient. Modern placers are deposits of washed material, or debris, in the beds or along the banks of streams that are either now in existence or existed in comparatively recent times. Placer deposits may also occur in deposits along the seashore. Ancient placers are fragmental accumulations, similar to the modern placers, which have been buried under accumulations of strata or flows of lava, and they may or may not have become consolidated into rock. At times, placers are very compact, owing to the presence of large quanti- ties of oxide of iron or calcium carbonate, or similar cementing material. Often, in the case of modern placers, the streams, or other sources of water that deposited the material, have changed their course so that the placer deposit is now high up in the benches bordering the streams, or, possibly, even on the top of the present hills. Such deposits are commonly called bench deposits, while those along the sides of the streams below the high- water mark are called bar deposits, diggings, or placers. Frequently, a large portion of the gold or other valuable material is found in pockets or irregularities in the bed rock, but the pot holes under waterfalls are frequently barren of gold, on account of the fact that the current there was sufficiently swift to wash everything out, either heavy or light. When the soil is saturated with water, the mass may partake of the nature of a semifluid through which the heavy particles of gold settle until they accumulate on the bed rock. When prospecting for placers, the miner examines the country for any indications of present or ancient watercourses in which the deposits of placer material have been formed. He pans the dirt from any deposits dis- covered, to see if it contains colors (small particles of metallic gold). If colors are found, more extensive operations are in order, and hence he sinks to bed rock and examines the material thoroughly, to see if it contains a paying quantity of the valuable mineral. The form of placer deposit in dry or arid regions differs from that in regions where the rivers have a continuous flow, on account of the fact that the deposits are largely the result of sudden rushes of water partaking of the nature of cloudbursts, hence the rich portions in the placer material are very irregular, and are rarely situated on bed rock, but are usually found on any strata that formed the bottom of the ravine during the sudden rush of water. During the rainy season in arid regions, the surface soil is some- times softened for a few inches, so that it becomes practically a mud, and particles of gold that it may contain tend to settle to the bottom of the soft portion, thus rendering the surface barren. This barren surface may be subsequently washed away by the rain, or blown away as dust during the dry season. The repeating of this process year after year results in the removal of considerable of the original surface and the formation of a rich stratum just below the grass roots. Prospectors in arid regions, who have been used to operating in an ordinarily well-watered country, are frequently deceived by finding this rich ground so high up in the deposit, not knowing that it is no indication as to the value of the material at a greater depth, GEMS AND PRECIOUS STONES. 241 In many cases, in the arid regions the portion of the deposit upon bed rock is entirely barren. In like manner, frozen ground may play an important part in the formation and distribution of the values in placer deposits. Gems and precious stones are prospected for in a manner similar to that employed in searching for placer material, and are usually found in alluvial deposits, from which they are obtained by washing. In a few cases, gems are found in the rocks themselves; as, for instance, diamonds in the hard matrix that occurs as pipes or chimneys in metamorphic rocks, and which, upon exposure to the atmosphere, becomes decomposed, so that the stones are easily removed. Some of the corundum minerals are found in lime- stone and metamorphic or crystalline rocks. Turquoise usually occurs in veins, the outcrop of which is stained with carbonate of copper. In most cases, it does not pay to extract gems from rock formations when the rock is extremely hard, owing to the fact that the gems are liable to become broken in separating them from the rock matrix. For gem prospecting, the following outfit has been recommended: A shovel and pick; two sieves, one of 2 or 3 meshes to the linear inch, and the other of 20 or more meshes to the inch (the coarse sieve should be arranged to fasten on top of the finer one for use together); a tub in which the sieves can be submerged in water; an oilcloth on which to sort the gravel; several stones and crude gems as a scale of hardness; a small pocket magnifying glass, and a dichroscope. In some cases, a portion of the outfit is dispensed with. The use of the outfit may be explained as follows: The tub is partially filled with water, the two sieves fastened together, and a shovelful of material placed in the upper one, when they are submerged in water, the large stones cleaned and examined, and all of the fine material worked through the upper sieve, which is then removed, the material on it examined and disposed of. The material in the fine sieve is then washed until free from clay, when a little jigging motion in the water will carry the lighter material to the top. The sieve is then quickly inverted and the material dumped out on the oilcloth, thus bringing the heavier stones to the top. The various pieces should now be examined with the magnifying glass, scale of hardness, etc., and the identity of any doubtful colored gems settled, by means of the dichroscope. Few precious stones are of sufficient specific gravity to be concentrated in distinct beds, like gold or tinstone, but they are usually fairly well concentrated and freed from much of the lighter worthless material. Value of Free Gold per Ton of Ore. The accompanying table was prepared by Mellville Atwood, F. G. S., and its use may be explained as follows: If a 4-lb. sample of quartz be crushed, the gold separated by panning and VALUE OF FREE GOLD PER TON OF ORE. (Risdon Iron Works.) Weight, Washed Gold. Fineness, 780. Fineness, 830. Fineness, 875. Fineness, 920. 4-Lb. Sample. Grains. Value per Oz., $16.12. Value per Oz., 817.15. Value per Oz., 818.08. Value per Oz., 819.01. 5.0 883.97 889.36 894.20 899.05 4.0 67.18 71.49 75.36 79.24 3.0 50.38 53.61 56.52 59.43 2.0 33.59 35.74 37.68 39.62 1.0 16.79 17.87 18.84 19.81 .9 15.11 16.08 16.95 17.82 .8 13.43 14.29 15.07 15.84 .7 11.75 12.51 13.19 13.86 .0 10.07 10.73 11.30 11.88 ."> 8.40 8.93 9.42 9.90 .4 6.71 7.14 7.53 7.92 .3 5.03 5.36 5.65 5.94 .2 3.36 3.57 3.76 3.96 .1 1.68 1.78 1.88 1.98 amalgamation, the quicksilver volatilized by blowpiping or otherwise, and the resulting button weighed, the value of the ore per ton of 2,000 Ib. will 242 PROSPECTING. be found opposite the weight of the button. The values are given for fine- ness of gold varying from 780 to 920. To determine the value of gravel, a 6-lb. sample will give the same results as that obtained from a 4-lb. sample of quartz, on account of the fact that 18 cu. ft. of gravel measured in a bank weigh 1 ton, or 2,000 lb.; hence, a cubic yard of gravel measured in a bank weighs 3,000 lb., and for this reason a sample one and one-half times as large as that required for quartz must be taken. In case the gravel is of low grade, a sample ten times as large, or 60 lb., may be taken, in which case the value opposite the weight of the button will have to be divided by 10. As an example, in the use of the table we may suppose that a button from 4 lb. of ore or 6 lb. of gravel weighs 3.8 gr., and that the fineness of the gold is 830. Opposite 3 in the table we will find $53.61 as the value of the button in dollars containing 3 gr. of gold, and opposite .8 we will find $14.29. The sum of these is $67.90, the value of the ore per ton, or the gravel per cubic yard. EXPLORATION BY DRILLING OR BORE HOLES. Earth Augers. When testing soil or searching for placer gold, sand, soft iron, or manganese ores, and similar materials that usually occur compara- tively near the surface, hand augers may be employed to great advantage. A good form of hand auger consists of a piece of flat steel or iron, with a steel tip, twisted into a spiral about 1 ft. long, and having four turns. The point is split and the tips sharpened and turned in opposite directions and dressed to a standard width, usually 2 in. The auger is attached to a short piece of V pipe, and is operated by joints of 1" pipe, which are coupled together with common pipe couplings. The auger is turned by means of a double-ended handle having an eye in the center through which the rod passes. The handle is secured by means of a setscrew. In addition to the auger, it is well to have a straight-edged chopping bit for use in comparatively hard seams. This may be made from a piece of If" octagon steel, with a 2" cut- ting edge. The upper end of the steel is welded on to a piece of pipe similar to that carrying the auger. When the chopping bit is employed, it is necessary to have a heavy sinking bar, which may be made from a piece of solid H" iron bar, fitted with ordinary V pipe threads on the ends. Pros- pecting can be carried on to a depth of from 50 to 60 ft. with this outfit. The number of men necessary to operate the rods varies from 2 to 4, depending on the depth of the hole being drilled. When more than 30 ft. of rods are in use, it is usually necessary to have a scaffold on which some of the men can stand to assist in withdrawing the rods. When withdrawing the rods, to remove the dirt, they are not uncoupled unless over 40 ft. of rods are in use at one time, and sometimes as many as 50 or 60 ft. are drawn without uncoupling. Percussion or churn drills are frequently employed in drilling for oil, water, or gas, and were formerly much used in searching for coal and ores, but, owing to the fact that they all reduce the material passed through to small pieces or mud, and so do not produce a fair sample, and to the fact that they can only drill perpendicular holes, they are at present little used in prospecting for either ore or coal. The cost and rate of drilling by means of a percussive or churn drill varies greatly, being affected much more by COST OF WELL-DRILLING. the character of the strata penetrated than is - the case with the diamond drill. In the case Size of Well. r f of highly inclined beds of varying hardness, Inches. per * oot ' the holes frequently run out of line and be- come so crooked that the tools wedge, and drilling has to be suspended. For drilling $1.50 through moderately hard formations, usually 2.25 encountered in searching for gas or water, 10 3.00 such as sandstones, limestones, slates, etc., the 12 5.00 accompanying costs, from the American Well 15 8.00 Works, Aurora, 111., may be taken per foot , for wells from 500 to 3,000 ft. deep for the central or eastern portion of the United States at present (1900). This cost includes the placing of the casing, but not the casing itself. DRILLING OR BORE HOLES. 243 When drilling wells for oil or gas to a depth of approximately 1,000 ft., using the ordinary American rig with a cable, the cost is sometimes reduced to as little as 65 cents per foot for 6" or 8" wells. This is when operating in rather soft and known formations. From 15 to 40 ft. per day of 24 hours is usually considered a good rate of drilling, though in soft materials as much as 100 ft. may be drilled in a single day, and at other times, when very hard rock is encountered, it is impossible to make more than from 1 to 2 ft. per day. The diamond drill is the only form that has been universally successful in drilling in any direction through hard, soft, or variable material. Even in the use of the diamond drill, many difficulties present themselves, and demand careful study in adapting the form of apparatus to the work in hand, and in rightly interpreting the results obtained from any set of observations. NOTE. See "Mines and Minerals" for articles on Diamond-Drilling Practice, by H. M. Lane, August, 1899, to January, 1900, Vol. XX. Selecting the Machine. It is not economy to employ a machine of large capacity in shallow explorations, as the large machines are provided with powerful motors, and hence do not work economically under light loads. When a large machine is operating small rods on light work, the driller cannot tell the condition of the bit, or properly regulate the feed. The machine should possess a motor of sufficient capacity to carry the work to the required depth, but where much drilling is to be done, it is usually best to have two or more machines, and to employ the small ones for shallow holes, and the large ones for deep holes. All feed mechanisms employed in diamond drilling may be divided into two classes: (1) Those that are an inverse function of the hardness of the material. This class includes friction, spring, and hydraulic feeds. (2) Those in which the feed is independent of the material being cut, as in the case of the positive gear-feed. The first class is advantageous when drilling through variable measures in search of fairly firm material, which does not occur in very thin beds or seams. On account of the fact that this "class of feed insures the maximum amount of advance of which the bit is capable in the material being cut, the danger is that the core from any thin soft seam may be ground up and washed away, without any indication of its presence having been given. The second class, or positive gear-feed, if properly operated, requires somewhat greater skill, but if used in connection with a thrust register, it gives reliable information as to the material being cut, and is especially useful when prospecting for soft deposits of very valuable material. Size of Tools. The size of tools and rods, and consequently the size of the core extracted, depends on the depth of the hole and the character of the material being prospected. When operating in firm measures, such as anthracite coal, hard rock, etc., it is best to employ a rather small bit, even when drilling up to 700 ft., or more, in depth. For such work, a core of from Jg in. to 1 T 3 S in. is usually extracted. The rate of drilling with a small outfit is very much greater than with a large one, owing to the fact that there is a small cutting surface exposed, and the rate of rotation of the rods can be much greater. When prospecting for soft materials, such as bituminous coal, valuable soft ores, or for disseminated ores, such as lead, copper, gold, silver, etc., it is best to employ a larger outfit and extract a core 2 or 3 in. in diameter, and sometimes even larger, even though a comparatively small machine is used to operate the rods. Drift of diamond-drill holes, or the divergence from the straight line, often becomes a serious matter. This trouble may be minimized by keeping the tools about the bit as nearly up to gauge as possible. Core barrels, with spiral water grooves about them, answer this purpose very well if they are renewed before excessive wear has taken place. Surveying of diamond drill-holes may be carried on by either one of two methods, depending on the magnetic conditions of the district. Where there is no magnetic disturbance, the system developed by -Mr. E. F. MacGeorge, of Australia, may be employed. This consists in introducing into the hole, at various points, small tubes containing melted gelatine, in which are suspended magnetic needles and small plummets. After the gelatine has hardened the tubes are removed, and the angles between the center line of the tube, the plummet, and the needle noted, thus furnishing the data from which the course of the hole can be plotted. This method gives both the vertical and the horizontal drift. 244 PR OSPECTING. Where there is magnetic disturbances the needle cannot be used, but a system brought out by Mr. G. Nolten, of Germany, has been quite exten- sively employed. In this case, tubes partly filled with hydrofluoric acid are introduced into the hole, at various points, and the acid allowed to etch a ring on the inside of the tube. After the acid has spent itself the tubes are withdrawn, and by bringing the liquid into such a position that it corre- sponds with the ring etched on the inside of the tube, the angle of the hole at the point examined can be determined. This method gives a record of the vertical drift of the hole only. The value of the record furnished by the diamond drill depends largely on the character of the material sought. The core extracted is always of very small volume when compared with the large mass of the formation pros- pected, and hence will give a fair average sample only in the case of very uniform deposits. The value of the diamond drill for prospecting may be stated as follows: More dependence can be placed on the record furnished by the diamond drill when prospecting for materials that occur in large bodies of uniform composition than when prospecting for materials that occur in small bunches or irregular seams. To the first class belong coal, iron ore, low-grade finely disseminated gold and silver ores, many deposits of copper, lead, zinc, etc., as well as salt, gypsum, building stone, etc. To the latter class belong small but rich bunches of gold, silver mineral, or rich streaks of gold telluride. The arrangement of holes has considerable effect upon the results fur- nished. If the material sought lies in 'beds or seams (as coal), the dip of which is fairly well known, it is best to drill a series of holes at right angles to the formation. If the material sought occurs in irregular bunches, pockets, or lenses, it will be necessary to drill holes at two or more angles, so as to divide the ground into a series of rectangles, thus rendering it prac- tically impossible for any vein or seam of commercial importance to exist without being discovered. Where the surface of the ground is covered with drift and wash material, it may be best to sink a shaft or drill pit to bed rock, and locate the machine on bed rock. After this, several series of fan holes may be drilled at various angles from the bottom of the pit. Owing to the upward drift of diamond-drill holes, the results furnished from a set of fan holes drilled from a single position would make a flat bed appear as an inverted bowl, or the top of a hill. On this account, it is best to drill sets of fan holes from two or more locations, so that they will correct one another. If fan holes from different positions intersect the same bed, a care- ful examination of them will usually furnish a check on the vertical drift of the holes. The cost and speed of drilling depend greatly on the formation being penetrated. As a rule, it is more expensive to sink the stand pipe than to do the subsequent drilling. Stand pipes may cost $5 or more per foot to sink, while the cost of drilling in firm rock varies from $0.50 to $2 per foot; in the case of difficult drilling, the cost may run over $4 per foot. Where a large amount of drilling has to be done, a fair average estimate for shallow holes up to 700 ft. deep would be $2 per foot, under such conditions as exist in most mineral districts of the United States. The cost of labor, fuel, etc., enter into the problem, and frequently affect it to a considerable extent. The rate of drilling varies considerably, but in firm rock an average of 1 ft. per hour, including all delays for changing rods, etc., would be a fair average up to 700 ft. Greater speed than this could be made in soft shales or sandstones, and somewhat less in hard rock. The hardness of the rock affects the rate of drilling much less than does its character. A conglomer- ate rock containing loose pebbles that come out during the drilling, or a crystalline rock containing angular pieces that come out during drilling, will cause far greater trouble than the hardest material ever encountered in diamond drilling. The following tables will give some idea as to the cost of diamond drilling under various conditions. The cost of drilling 2,084 ft. of hole in prospecting the ground through which the Croton aqueduct tunnel was to pass is given as follows: 814 ft. of soft rock (decomposed gneiss), in which an average of 23.1 ft. per day was drilled, at a cost of SI. 15 per ft. 347 ft. of hard rock (gneiss), in which an average of 11.1 ft. per day was drilled, at a cost of $3.97 per ft. 923 ft. of clay, gravel, and boulders, in which from 6 to 9 ft. per day were drilled, at a cost of $4.07 per ft. The average progress per day in drilling the entire 2,084 ft. was 10.2 ft per day. DRILLING OR BORE HOLES. 245 In the Minnesota Iron Co.'s mines, at Soudan, Minn., the diamond drill is used for drilling holes from 10 to 40 ft. in depth in the back of the stopes, practically all the work being done in iron ore. The average cost per foot of drilling 13,512 ft. of hole was 80.7703, which was divided as follows: Carbons 80.34 Supplies, oil, etc 0.07 Fuel :.. 0.04 Repairs 0.05 Labor 0.2703 Total : $0.7703 The following tables give the cost of boring at two Ishpeming, Mich., mines: TABLE I. Total Cost f 400i days setter at 83.00 $1,200.751 Cost. per Ft. TflhnrJ 372 days runner at 2.25 837.00 Labor 1 2304 days runner at 2.00 460.50 t 4^ days laborer at 1.75 7.85 Carbon 68f carats at $15.144 1,035.47 0.276 Bits, lifters, shells, barrels, and repairs 433.81 0.115 Oil, candles, waste, and supplies 128.09 0.035 Estimated cost compressed air 374.60 0.100 Total $4,478.07 $1.195 Number holes drilled 28 Drilled in hematite 193 ft. Drilled in jasper 646 ft. Drilled in mixed ore 986 ft. Drilled in dioritic schist 1,921 ft. Total drilling 3,746 ft. Number of 10-hour shifts drill was running, including moving and setting up 603 Amount drilling per 10-hour shift 6.2 ft. TABLE II. Underground drilling 6,075 ft. Surface drilling 1,414ft. Stand pipe sunk 470 ft. Total distance run 7,959 ft. Actual drilling time underground 672 shifts Actual drilling time on surface -. 165 shifts Time of foreman, setter; moving, and stand-piping 1,314 shifts Total time worked :.... 2,151 shifts Average progress per man per shift 3.70 ft. Average progress per drill per shift actually run- ning 8.95 ft. Weight of carbon consumed 111.00 carats Distance drilled per carat of carbon consumed 67.38 ft. Amount. Per Ft. Cost of carbon $1,887.00 $0.237 Cost of supplies and oils 134.13 0.017 Cost of fuel 360.73 0.045 Cost of shop material, etc 663.36 0.083 Pay roll 4,000.03 0.502 Total cost $7,045.25 246 PROSPECTING. RECORDS OF COST PER FOOT IN DIAMOND DRILLING. A B C D E F G * / J K L M N O Labor . . . .707 1.040 2.483 1.150 .581 1.615 1.030 1.720 1.189 1.284 .721 1.200 .939 .812 .984 Fuel ... . '.094 .270 .256 .019 .000 .216 .090 .214 .157 .339 .419 .329 .126 .182 .251 Camp account .373 .559 .789 .538 .295 .621 .384 .549 .516 .495 .519 .595 .644 .722 .636 Repairs . . .139 .110 .294 .171 .135 .144 .103 .185 .154 .165 .040 .087 .138 .126 .116 Supplies Carbon . . .034 .263 .065 .658 .039 .859 .074 .860 .023 .843 .032 1.587 .011 .934 .039 .684 .048 .684 .097 .733 .020 .227 .092 .209 .076 .553 .097 .239 .088 .330 Supt. . . . .239 .322 .628 .040 .063 .192 .140 .305 .259 .172 .347 .220 .106 .196 .199 Total . . . 1.849 3.024 5.348 2.852 1.940 4.407 2.692 3.696 3.007 3.285 2.293 2.732 2.582 2.374 2.604 1 1 1 A 5 holes, 1,066 ft. Sandstone and marble. B 1 hole, 1,293 ft. Black slate and jasper. C 3 holes, 478 ft. Jasper, very hard. D 5 holes, 780 ft. Jasper, hard. . E 1 hole, 216 -ft. Iron slates. F 1 hole, 174 ft. Jasper and slate. G 2 holes, 267 ft. Jasper and s^te. H 3 holes, 410 ft. Jasper. / Average cost of total work of drilling 21 holes. Total of 4,684 ft. J* 2 holes, 634 ft. Iron slates. K 2 holes, 360 ft. Schist and jasper. L 6 holes, 1,350 ft. Iron slates. M 2 holes, 611 ft. Schist, jasper, and quartzite. N 6 holes, 2,091 ft. Quartzite. Average cost of drilling 18 holes, 5.046 ft. The following figures, taken from a letter written by T. F. Richardson, Departmental Engineer of Dam and Aqueduct Department, Metropolitan Water Board of Boston, and published by the U. S. Geological Survey, are of interest, as they show the rate and cost of diamond drilling under certain conditions. The costs do not take into account depreciation of machinery nor losses of time in moving machines, etc. The machines employed in this work were a Badger drill, manufactured by the M. C. Bullock Manu- facturing Co., of Chicago, 111., and an S-510 drill, manufactured by the Sullivan Machinery Co., Claremont, N. H. The total amount drilled was 2,814 ft., the deepest hole being 286 ft. deep, and the average depths of holes about 60 ft. The amount accomplished per day was from to 32 ft., the average amount being probably about 10 or 12 ft. per day. The cost of drilling varied very largely, both with the hard- ness of the rock and the condition of the rock as to being seamy. The following was .the cost of drilling 321.2 ft. of rather hard, tough diorite rock: Labor $341.25 Diamonds 74.30 Coal 17.50 Total 3433.05 Costperfoot 1.34 (86.6 ft. of this was drilled with a If" bit, and 237.6 ft. was drilled with a If "bit.) Drilling 150.7 ft. of very hard syenite rock: Labor $158.00 Diamonds 298.69 Coal 10.50 Total 3467.19 Cost per foot 3.10 (Size of drill, l$in.) DRILLING OR BORE HOLES. 247 The following was the cost of drilling 28G.1 ft. of soft schist rock: Labor $190.00 Diamonds 87.75 Coal 11.50 Total $289.25 Cost per foot 1.01 (Sizeof drill, lUn.) The following figures will be of considerable interest, owing to the fact that the work is practically all of the nature of sinking stand pipes, the object of the exploration being to ascertain the depth of wash material and the character of the bed rock over the area of certain proposed dam sites in the southwestern portion of the United States, the work being carried on by the government. The machines used were made by the American Diamond Rock Drill Co., of New York, and had previously been employed in similar exploration along the line of the Nicaragua Canal. Cost of operation per month of bed-rock exploration: Foreman $150.00 6 laborers, at $1.50 per day, 28 days 234.00 1 cook 45.00 $429.00 240 rations, at 60 cents 144.00 Total repairs, pipe and lumber for one party for 10 months 500.00 Total commissary charges for team, feed, etc 350.00 Total moving 670.00 Total sundry incidentals 200.00 Total supervision 350.00 Total, 10 months $2i070XX) Sundry expenses per month 230.00 Total cost per month 803.00 10 months, at $803 8,030.00 Total number of feet sunk 3,254.20 Total cost : $8,030.00 Cost per foot 2.46 Cost per hole, 7,227 H- 52 154.42 The drills were purchased second-hand from the Nicaragua Canal Co., and the other apparatus was new. If the original cost of all this machinery were distributed over the work, the results would be as follows: Operation $8,030.00 Machinery 1,600.00 Total cost $9,630.00 Or average cost per foot 2.86 Both machines are still in good repair, after having been used in Nicara- gua and in various localities in Arizona and California. The total depths penetrated in all materials at the various dam sites are as follows : Covering. Rock. Total. TheButtes Queen Creek.. Riverside Dikes San Carlos Total 1,621.2 357.8 729.8 80.0 143.2 2,932.0 196.0 55.6 40.2 0.0 30.4 322.2 1,817.2 413.4 770.0 80.0 173.6 3,254.2 248 PROSPECTING. Magnetic Prospecting. Bodies of magnetic iron ore are frequently discov- ered or located on account of their magnetic properties. Two forms of compasses are employed in this work: the dipping needle, or miners' compass, and the ordinary compass. The ordinary compass is used to find the center of magnetic attraction in the horizontal plane, and after this has been found the ground may be run over with the di PP in g needle, to locate the center of attraction by this means. The ordinary compass does not give good results when operating over a mag- netic deposit, but is only useful in determining its outside edge, and thus locating its general position. The dipping needle differs from the ordinary compass in that the needle is hung in a vertical plane in place of horizontally, so that the needle is free to assume any position varying FlG 2 from the horizontal, depending on the downward component of magnetic attraction at that point. The vertical magnetic component at the point should be compensated for by balancing the dipping needle so that it will ordinarily stand horizontally when not affected by local disturbances. The actual work of prospecting may be carried on as follows: If there were an outcrop of a vein of magnetic material, as shown in Fig. 2, covered with a capping of wash material, the preliminary prospecting would be carried on as shown in Fig. 3, the dipping needle being carried backwards and forwards zigzag across the deposit, noting the point of maximum dip in each case and establishing a stake there as indi- cated by the crosses. After these stakes had all been established, an average straight line would be struck through them that would follow the course of the deposit as nearly as possible. Stakes would be placed at the ends of this line, as at X and Y, and the line XY divided off into 100' dis- tances by means of stakes marked A, B, etc. Lines at right angles to the original line would then be turned off at these 100' points, and stakes placed every 10 ft. upon the branch lines. These points on the branch lines would be lettered with small letters, corresponding to the large letter on the line X Y, as shown in Fig. 4, which represents the obser- vations taken at the first station. The dip would be noted at each one of the 10' stations, and recorded in the note book. A convenient method of keeping the notes is to have a vertical line down the center of the page for the line X F, and other lines to the right and left of it for the indi- FIG. 3. vertical vidual stations 10 ft. apart, each side of the main line, the horizontal lines across the page being lettered A, B, etc., the sta- tions to the right and left being marked with primes and subscripts of the small letters corresponding to the line. After the observations have been taken, lines may be drawn through points of equal dip and equal deflection (isogonic lines). Bythis means the general form of the bed is determined. The maximum dip, in the case of an inclined deposit like that shown in Fig. 2, would occur at c, over the hanging wall of the outcrop, the dip at b being consider- ably less, and the dip at a FIG. 4. After the center of magnetic attraction has been discov- ered, prospecting may be continued by means of the diamond drill, or by sinking shafts or test 'pits. Sometimes, where deposits of magnetic iron ore have been eroded, the sands near the surface may contain such a considerable amount of magnetic disturbance as to indicate the presence of a body of iron ore, while in reality there may be such a small quantity disseminated through the sand that it could not be made to pay for its removal. I GEOLOGICAL MAPS AND CROSS-SECTIONS. 249 Any body of magnetic iron ore is affected by polarity, and one end of it will attract one end of the dipping needle, while the other end will attract the opposite end. Where the body is badly broken up, this dip of the needle may be reversed several times in a comparatively short distance. Prospecting for Petroleum, Natural Gas, and Bitumen. Among the surface indications of petroleum and bitumen may be mentioned white leached shales or sandstones, shales burned to redness, fumaroles, mineral springs, and deposits from mineral springs. Also natural gas, springs of petroleum oil and naphtha, porous rocks saturated with bitumen, cracks in shale, and other rock partly filled with bitumen. Petroleum is never found in any quantity in metamorphic rocks, but always in sedimentary deposits. Bitumen can be told from coal, vegetable matter, iron, manganese, and other minerals, which it sometimes closely resembles, by its odor and taste, also by the fact that it melts in the flame of a match or candle, giving a bituminous odor. (Iron and manganese do not fuse, and coal and vegetable matter burn without fusion.) Bitumen is also soluble in bisulphide of carbon, chloroform, and turpentine, usually giving a dark, black, or brown solution. Frequently, springs or ponds have an iridescent coating of oil upon the surface. Sometimes iron compounds give practically the same appearance, but the iron coating can always be distinguished from the oil by agitating the surface of the water, when the iron coating will break up like a crust of solid material, while the oil will behave as a fluid, and tend to remain over the entire surface even when it is agitated. Frequently, bubbles of gas are seen ascending from the bottoms of pools or creeks. These may be composed of carbureted hydrogen or natural gas, which is a good indication of the presence of petroleum or bitumen; they may be composed of sulphureted hydrogen or carbonic-acid gas. Carbu- reted hydrogen can be distinguished by the fact that it burns with a yellow luminous flame, whereas sulphureted hydrogen burns with a bluish flame, and carbon dioxide will not support combustion, but, on the contrary, is a product of combustion. When carbureted hydrogen gas is discovered ascending from water, the bottom of which is not covered with decaying vegetation, it is almost a certain sigh that there is petroleum or bitumen somewhere in the underlying or adjacent formations. If natural gas or bitumen is found upon the surface of shale, it is probable that the material ascended vertically through cracks in these rocks from porous strata below; while if it is found in connection with sandstones, it is probable that the material was derived from the porous sandstone itself. This is especially liable to be true if the sandstone has a steep pitch. As a rule, deposits of bitumen or petroleum occur in porous formations overlaid by impervious strata, such as shales, slates, etc. Anticlines are more liable to contain such deposits, though they are not absolutely neces- sary to retain them, as at times portions of the' underlying porous strata have been rendered impervious by deposits of calcium salts, silica, etc., and hence the petroleum or bitumen will be confined to the porous portions. Natural gas also occurs under similar conditions, but usually in anticlines only. Construction of Geologjcal Maps and Cross-Sections. After the surface exam- ination of a property is complete, the data should be entered on the best map procurable, or a map constructed. The scale depends on the size of the property, the complexity of the geological formation, the value of the property, and the material to be mined from it. The amount of work that it will pay to put on the survey will depend largely on the value of the property, more detail being justified in the case of high-grade properties. If a property 1,200 ft. X 3,000 ft. (the size of four U. S. mining claims) were to be surveyed and mapped with a scale of 1 in. equal to 100 ft., the map would be 12 in. X 30 in. A vein of strata 10 ft. wide on this map would appear as T V of an inch wide, which is about the smallest division that could be shown with its characteristic symbol; for greater detail, a larger scale, or larger scaled sheets of the most important portions of the deposit, will be necessary. If the geologist constructs the topographical contour map, he can take notes on the geology at the same time. When the boundaries of the property are being surveyed, certain points should be established, both vertically and horizontally, as stations in future topographical work. If the map is on government surveyed land, the government lines may be used for horizontal locations, but it will be necessary to determine the elevation of the different points. If the property is much broken, it is well to run a 250 PROSPECTING. few lines of levels across it, to establish points from which to continue the work. This work is usually done with a Y level and chain, the other details being subsequently filled in with a transit and stadia, the levels of the other points being taken either by using the transit as a level, by vertical angles, by bar- ometric observations, or by means of a hand level. Where lines of levels are run across the property in various directions, it is best to run them in such a direction that they will cross the strike of the strata as nearly at right angles as possible, so that the profile thus de- termined may be used in constructing a cross- section. Sometimes, for preliminary work, simply a sketch map is all that may be neces- sary. All of the outcrops and exposures, together with their proper dip, should be entered on the map. To Obtain Dip and Strike From Bore-Hole Records. Before the results obtained from bore holes are available for use in map construction, the dip and strike of the various strata must be ascertained. The process, in the case of stratified rock, is as follows: If three holes were drilled, as at A, B, and C, Fig. 6, each intersecting a given bed, the strike and angle of dip of the bed may be obtained by reducing the results from the three holes to a plane passing through the highest point of intersection, which is at A. The hole B intersected the bed at the distance Be, and C at the distance Cd below the point A. By continuing the line CB indefinitely, and erecting two lines Be and Cd perpendicular to it, each representing the distance from the hori- zontal plane through A to the intersection of the strata, two points in the line de are obtained, which line intersects CB produced at/: / is one point in the line of strike through A. In order to find the angle of dip, the perpendicular Cg is dropped from the deepest hole C upon the line of FIG. 6. FIG. 7. strike Af. The distance Ch, equal to Cd, is laid off at right angles to Cg, when the angle Cg h gives the maximum dip. The results obtained from bore holes may thus be reduced to such form that the dips can be projected on the surface to obtain the line of outcrop for each stratum. Bore holes also furnish data for constructing underground curves in cross-sections of stratified rocks, and in locating the probable outline of ore bodies in other formations. SAMPLING AND ESTIMATING AVAILABLE MINERAL. 251 Having recorded on the map all exposures, whether surface or those obtained from underground work, draw the line of strike and the outcrops. Also construct a cross-section. If the vein is perpendicular, the outcrop will be a straight course across the map. If the bed or seam is horizontal, the outcrop will correspond with the contour line. For beds or veins dipping at any other angle, results between these limits will be obtained. If the property being examined is cut by synclines or anticlines, the dips will not all be in the same direction, and if there is a dip along the axis of the synclines or anticlines, the construction of the map will be considerably complicated. Fig. 5 represents a plan or map on which there is an axis xy toward which the strata dip from both sides. Outcrops are indicated at A, B, C, A', and B', each having a dip in % the direction of the arrow. The lines mn, op, qr are contours. If the cross-section were constructed on the line FG, perpendicular to the axis x y, the various beds or deposits would be cut at such an angle as to show a thickness in the cross-secti9n greater than that which actually exists. In order to show the actual thickness for each seam, the cross-section must be taken along the line perpendicular to the strike of the strata, which, in the present case, is along the line IHK. In other words, the cross-section must be constructed in two parts. Where a general sketch is all that is necessary, a single cross-section with notes correcting the thickness of the seams may answer. In order to construct the cross-section IHK, the outcrops A, B, C, A', and B f must be projected to the points a, 6, c, a', and 6', this projection being along their contours. If the points on the line of the intended cross-section were not upon the contour, it would be necessary to project them on the plane of the cross-section, as shown in the figure, and then from the dip of the strata and the difference in elevation to obtain a corrected point along the line IHK. The cross-section is constructed as shown in Fig. 7, each seam having its actual thickness as shown at the outcrop. If the upper surface of the cross-section is nojt a true profile of the surface, and the points are not projected in the plane on the cross-section, on this cross-section, according to their dips, there is considerable danger of exaggerating their thickness one way or the other. On mine maps, the supposed course of the beds should be sketched in, subject to revision, as more data are brought out by later development work. Even in the case of stratified rocks, it is difficult to form a definite idea as to the underground conditions from surface indications, and, in the case of metamorphic or crystalline rocks, it is absolutely necessary to determine the underground conditions by drilling, or actual development work. If the property being examined is liable to become a large and valuable mining property, the original survey should be tied to monuments or natural landmarks, so that it can be checked by future observations, and these monuments or landmarks should become the basis of future and more careful mining surveys. Some of the advantages of a careful geological examination of a property are that other materials of economic value would probably be discovered, if any should exist on the property; also, such an examination of the property gives information as to the drainage system of the country that may be of great advantage in laying out the mine, and future exploration by drilling or sinking can be done to better advantage after a careful surface examination. Sampling and Estimating the Amount of Mineral Available. In many cases, it is necessary to do some development or exploration work before fair average samples can be obtained. The samples as taken should fairly represent the material as it will be extracted. Such gangue as cannot be separated from the ore in mining, or slate that would be sold with the coal, should be included in the sample. When sampling any property it is well to divide the deposit up into blocks, and sample each one separately. The samples may then be assayed and an average obtained later, or the different samples may be mixed and an average assay obtained. The amount of material broken for sample may vary from a few pounds to many tons, depending on the nature of the material under consideration. Large samples may be reduced by shoveling (that is, taking a proportionate number of shovelfuls for the sample, as every third or fourth shovelful). After the sample has been partially reduced, the operation may be carried on by quartering, which may be described as follows: The material is shoveled into a conical pile by throwing each shovel- ful on to the apex of the cone. After this, the cone may be reduced by 252 PROSPECTING. scraping it down with a shovel, passing slowly around it. If the amount of material is small, a flat plate may be introduced into the cone, and the pile flattened by revolving the plate. The pile is then divided into quarters by drawing lines across it. After this, two alternate quarters are scraped out and shoveled away, and the other two quarters are left as the sample. Thfc process may be repeated until the block has been sufficiently reduced. In shoveling away the discarded portions, care should be taken to see that the fine dust under them is brushed away also, as they often contain fine and valuable mineral that would unduly increase the value of the resulting sample. When the sample consists of only a few pounds, it may be reduced by means of a riffle. Large samples consisting of several tons are sometimes sent to sampling works to be reduced by automatic sampling machines. If the property being examined is a mine in active operation, samples may be taken from the working faces, and also from cars, loading chutes, etc. Usually the samples from the face are kept separate from those from the cars and loading chutes, the latter being intended as a check on the former. In the case of ores of the precious metals, large samples are sometimes taken and used for mill runs. Stock piles, or dumps, may be roughly sampled by taking pieces from intervals over the surface, being careful to obtain a fair average of coarse and fine material, and of rock and ore. These samples are quartered down and assayed, but if a close valuation is d esired, it will be necessary to drive cuts or tunnels through the mass, and to take a certain amount, as every fifth or tenth shovelful, for the sample. When sampling dumps of fine material (as, for instance, tailings) it is possible to take samples from the pile by means of a drill, an auger 1 in. or 2 in. in diameter usually being employed for this purpose. The human factor always plays a large part in the value of a sample as finally selected, and hence it should be taken by a man who has had con- siderable experience in this class of wort. For this reason, it is best to employ a mining engineer. One not accustomed to sampling very rarely undervalues a property, owing to the fact that it seems to be human nature to pick up a rich piece of ore or coal, rather than the barren gangue material or slate. When only surface exposures or shallow prospect openings are available, it is impossible to determine the amount of ore in sight, or to form more than a guess as to the size of the deposit. It is not safe to count any ore in sight unless it is exposed on at least three faces. Ore that is exposed on one or two faces can be counted as probable ore, while slight exposures can be counted only as chances indicated. The amount of material available in coal deposits can be estimated much closer than in the case of ores. If a seam is penetrated by a number of bore holes, or by workings extended over a considerable area, it is fair to esti- mate that the material will run practically as exposed for a considerable area; but especially in the case of bituminous coal, it is a comparatively easy matter to form some estimate as to the amount of material available. When dealing with ores, it is impossible to form reliable estimates, owing to the fact that horses or other masses of rock may be exposed at any point, and the ore bodies themselves are usually very irregular, hence it will be necessary to do careful blocking out before making any estimates. When estimating the amount of mineral available, only that portion which can actually be removed in stoping should be counted, and if the seam is so narrow that it is necessary to break material from the walls, or if there are masses of country rock that have to be removed with the ore, the expense of removing them should be estimated and deducted from the value of the ore. DIAGRAM FOR REPORTING ON MINERAL LANDS. The following diagram will be useful as a guide in making out a report on a mining property: ;1. Location, if on surveyed land. 2. Nearest town or village. Q ATinoT-ol Hicfyint AND SUR- 3. Mineral district. L 4. County, state, or territory. ^ 2. Distance and direction from one or more points. REPORTS ON MINERAL LANDS. 253 DIAGRAM FOR REPORTING ON MINERAL LAN DS~ ( Continued). {1. Hills or mountains. 2. Character of surface, vegetation, and timber. . -^^ x ^'S x a ' P & Ipttxit* J i 5 1* , gg os feS'S 2fi'0 f a * a ! S ^LN_TH_ - I Q cc 02 ^^^M i-i PH O ^ T I 5 XXX XX X XXXXX X XX X XX^^X* b b C4 Tt*Tt< b bbc^^r^f ^ boo b bb^5oo^-i v o c^ uo f-ogiboo gj gib os -raoojo -ON cq ca 01 bb C X X X X> b b b 3^ b bb b *} ox Kb x3 ^ io ox CO S 5 g= ? SB 8 II ^ ;^ i ; S.a'd.s ^i-H^CO g g 098 | ^OOOCftOCMCO^O^gOrHCO^^grH^ OD <*4 nno % .S UU J " ""rHrH'r^THPirHrHrHgi?Jg^egigS^g!(giS I GO o co loooocoioaoocoioogocoioaoocoiooooco COiOCCt^GOOrHCMCOLOtOt^OOOrHC-lCOiOOt^-OOOrH i' a ! g ^ 100200 ^^^^^^^^;^^^^^^ QUa I CO^iQgO t ^ QOqil ^^j^ r ^ rHrH ^^^^ CMCMC^CMCMCM 099 ' ^^ ?2?2:?< ^ I2 ^' :C! - fS5 s a2PrtEi?ac^' I rHrHrHrHrHrHrHrHrHrHCMCMCMCM 091 a ooe "^ I ^g^^SSo^SggcSogg^^ 2 ^-- 2 ^ i rHQOiOCMO5t-COO5OSOrH ^097 H 001 ^ 09 I " 3 H T ^ _q u a O H r- oo CD o evi cr> >* PILLAR DRAWING. 289 Compressive Strength of Anthracite. Attention has recently been called by Mr. Williain Griffith, of Scranton, Pa., to the advisability of testing the strength of the different coals and of using this data as a basis for the proper proportioning of the pillars and for determining the probability of a squeeze. In some crude experiments, which Mr. Griffith carried on, he found that different coals from even the same locality varied greatly in their strengths. If attention were given to this matter, probably the sizes of pillars could be calculated on a much more certain basis than is possible at present, and the liability to squeeze lessened. The table on page 290 gives the results of some preliminary and crude tests made by Mr. Griffith, which supply the only data available as to the crushing strength of anthracite coal. Drawing pillars is about the most dangerous work the miner has to perform, but the fact of its being so is no doubt the reaspn why, comparatively speaking, so few serious accidents happen in it. It is not so much that the best, most skilled workmen are chosen to perform pillar drawing, as that the men, being alive to the dangers, are more on the alert and careful to protect themselves. Sometimes, if not very often, in chamber or room-and-pillar working it is the custom to work out the rooms or chambers and leave pillars all the way from the shaft to the boundary line over large areas; in other words, the portion of the roof left standing on pillars is very extensive. Mines so worked have sometimes been spoken of as mines on stilts. To this mode of proceeding there are several serious objections. By leaving the pillars until the boundary has been reached, a large number of airways and roadways have to be kept open and in repair, and this number is constantly increasing until the limits of the workings have been reached. This circumstance renders the ventilation more difficult, and thereby increases risks of accident. Moreover, the length of time during which the old rooms and pillars are left open and standing increases the danger of squeeze and creep FIG. 5. FIG. 6. setting in, by which a large area may in a short time be overrun. Also, by this method, the pillars first formed are last removed, and hence it happens that a large number of them crack and give way under the combined action of atmospheric agencies and great pressure. Even if they resist these actions well, the quality of the coal greatly deteriorates by the long exposure. For the above reasons, it is the best practice to carry on the two workings (working the rooms and drawing the ribs and pillars) simultaneously. By so doing, the length, mean duration of the roadways, etc. are reduced, and the pillar coal obtained in much better condition; and, in order to concen- trate the workings as much as possible, the two operations should go on as closely together as practicable. With fairly thick and very soft coals, the rapid working up of the rooms and equally quick drawing of the ribs, as soon as the rooms are driven their full distance, is essential to economical working; for delay in extracting ribs and pillars in such circumstances results in their getting crushed and the coal lost or largely ground to slack, waste of props and material, disordered ventilation, and shortened life of the mine. Methods of drawing pillars vary according to the inclinations of the seams, the nature of the roof ajid floor, and the character of the coal. Figs. 5 and 6 show the common methods. In Fig. 5, A, B, and C, the drawing begins by cross-cutting the fast ends of the pillars to obtain a retreating face. A shows a method for soft coal and narrowing pillars, B for wide 290 METHODS OF WORKING. fc <5 p h O 1 w H a P a rC pillars, the end being taken in two lifts, while C is for harder coal and shows it taken in three lifts. D and E show the pillars cut into stocks to be drawn by side or end lifts, according to the character of the coal, the inclination of the seam, thickness of the cover, and the strength or weak- ness of the roof and floor. Fig. 6 shows some of the methods used in robbing the pillars in steep pitch- ing, thick beds of anthra- cite. To get the coal out of the pillar at the left of A, a skip is taken off the side, as shown. Suc- cessive skips are thus taken off until the whole is removed, the miner keeping the m a n w a y open to the heading be- low as a means of retreat. The pillar bet ween A and B is very similarly worked. To remove that between B and (7, a nar- row, chute or heading is driven up the middle, and cross-cuts put to the right and left a few yards from the upper end. Shots are placed in the four blocks of coal thus formed, as shown, and they are fired simultane- ously by battery. This operation is repeated in each descending portion unless the pillar begins to run. A pillar from which the coal has started to run is shown to the right of C. To secure the highest percentage of pillar coal, a method should be adopted that will pre- vent squeezing or crush- ing, if possible. All the pillars in a panel may be taken out at the same time by end lifts in such a way as to keep the face of all the lifts in line and perpendicular to the sides of the pillars, or the pillars are drawn in lifts of three or more pillars each, the centers of the face of the lifts lying in a straight line that makes an angle of about 40 with the sides ROOM-AND-PILLAR METHODS. 291 of the pillars. (See also " Flushing of Culm," which is described fully on page 314.) Gob fires are due to the spontaneous ignition of coal, and are most likely to occur in pack walls and gobs where there is an insufficiency of air. Ample ventilation is the best preventive. Spontaneous Combustion. According to Prof. Able, Dr. Percy, and Prof. Lewes, the causes of the spontaneous ignition of coal are: First, and chiefly, the condensation and absorption of oxygen from the air by the coal, which of itself causes heating, and this promotes the chemical combination of the volatile hydrocarbons in the coal and some of the carbon itself with the condensed oxygen. This process may be described as self-stimulating, so that, with conditions favorable, sufficient heat may be generated to cause the ignition of portions of the coal. The favorable conditions are: A mod- erately high external temperature; a broken condition of the coal, affording the fresh surfaces for absorbing oxygen; a supply of air sufficient for the purpose, but not in the nature of a strong current adequate to remove the heat; a considerable percentage of volatile combustible matter or an extremely divided condition. Second, moisture acting on sulphur in the form of iron pyrites. The heating effect of this second cause is very small, and it acts rather by breaking the coal and presenting fresh surfaces for the absorption of oxygen. Coal Storage. Prof. Lewes gives the following recommendations for the storage of coal: "The coal store should be well roofed in, and have an iron floor bedded in cement; all supports passing through and in contact with the coal should be of iron or brick; if hollow iron supports are used, they should be cast solid with cement. The coal must never be loaded or stored during wet weather, and the depth of coal in the store should not exceed 8 ft., and should only be 6 ft. where possible. Under no condition must a steam or exhaust pipe or flue be allowed in or near any wall of the store, nor must the store be within 20 ft. of any boiler, furnace, or bench of retorts. No coal should be stored or shipped to distant ports until at least a month has elapsed since it was brought to the surface. Every care should be taken during loading or storing to prevent breaking or crushing of the coal, and on no account must a large accumulation of small coal be allowed. These precautions, if properly carried out, would amply suffice to entirely do away with spontaneous' ignition in stored coal on land." When the coal pile has ignited, the best way to extinguish the fire is to remove the coal, spread it out, and then use water on the burned part. The incandescent portion is invariably in the interior, and when the fire has gained any headway usually forms a crust that effectually prevents the water from acting efficiently. MODIFICATIONS OF ROOM-AND-PILLAR METHODS. Some modifications of the room-and-pillar plan shown in Fig. 1 can usually be applied to seams whose dip does not exceed 3. When the pitch is greater, rooms are often turned off toward the rise only, and the cross- entries driven correspondingly closer together. When the pitch is from 5 to 10, the cars may still be taken to the face if the rooms are driven across the pitch, thus making an oblique angle with an entry or gangway, the rooms being known as room breasts. Buggy Breasts. For inclinations between 10 and 18, that is, after mule haulage becomes impossible and until the coal will slide in chutes, buggies are often used. Fig. 8 shows a buggy breast in plan and section. Coal is loaded into a small car or buggy c, which runs to the lower end of the breast and there delivers the coal upon a platform I, from which it is loaded into the mine car. The refuse from the seam is used in building up the track, and if there is not sufficient refuse for this, a timber trestle is used. Another form of buggy breast is shown in Fig. 7. Here the coal is dumped directly into the mine car from the buggy. If the breast pitches less than 6, the buggy can be pushed to the face by hand, but in rooms of a greater pitch, a windlass is permanently fastened to timbers at the bottom of the breast, while the pulleys at the face are temporarily attached to the props by chains, so that they' can be advanced as the face advances. The rope used is from i in. to f in. in diameter, and any form of ordinary horizontal windlass can be used. With the windlass properly geared, one man can easily haul a buggy to the face of a breast in a few minutes time. The buggy runs upon 20-lb. T rails spiked with 2" X I" spikes upon 2" X 4" 292 METHODS OF WORKING. hemlock studding sawed into lengths of 14 ft. This system has been thoroughly tested by the Delaware & Hudson Canal Co., Scranton, Pa., and has proved a very successful and economical one. Chute Breasts. Seams pitching more than 15 are usually worked by chutes, or self-acting inclines. When the pitch is between 15 and 30, sheet iron is laid to furnish a good sliding surface for the coal. On inclinations of less than 18 to 20, it "is usually necessary to push the coal down the chute. Sheet iron is not required on pitches above 30. It must be remem- bered that these pitches are only fair averages, as much depends on the character of the coal. Anthracite slides more easily than bituminous. To secure the best returns from a coal seam, the slope or shaft should be driven to the basin, and the lowest gangways or levels first driven to the property limits, and the coal then worked retreating toward the slope or shaft. Practice is, however, usually contrary to this, and the upper levels or gang- ways are turned off first, and working places opened out as rapidly as the gangway is driven. Fig. 9 shows a method of grouping rooms that may be FIG. 7. used where the pitch is from 8 to 20, the straight heading being driven on the strike and the other headings at such angles as will give a good grade for haulage purposes. The pillar-and-stall system is a modification of the room-and-pillar, to which it is similar in all respects excepting in the relative size of the pillars and breasts. The stalls are usually opened narrow and widened inside, according to conditions of roof, floor, coal, depth, etc., being from 4 to 6 yd. in the single-stall method, with the pillars about the same width. Fig. 10. A and B, shows single and double stalls. This system is adapted to weak roof and floor, or strong roof and soft bottom, to a fragile coal, or wherever ample support is required, and is particularly useful in deep seams with CONNELLSVILLE METHOD. 293 great roof pressure. Double stalls are often driven from 12 to 15 yd. wide, with an intervening pillar of sometimes 30 yd. The following are a few of the applications of the pillar-and-stall method of working as they are carried out in some of the leading coal fields of America: Connellsville Region (//. L. Auchmuty) . Fig. 11 shows the common method used in the Connellsville, Pa., region. The average dip is about 5#. The face and butt headings are driven, respectively, at right angles to each other on the face and the butt of the coal. The face headings leave the main butts about 1,000 ft. apart, while from these face headings, and 400 ft. apart, secondary butts are driven, and again from these butts on the face of the coal the rooms or wide work- ings are excavated to a length of 300 ft., this having proved the most convenient length for economical working. Room pillars have a thickness of 30 to 40 ft., while the rooms are 12 ft. in width and are spaced 42 to 52 ft. between centers, de- pending on depth of strata over the coal. The headings are 8 ft. wide, and in all main butts and faces the dis- ._. _ tance between centers PIG. 9. of parallel headings is 60 ft., leaving a solid rib of 52 ft. A solid rib of 60 ft. is also left on the side of each main heading. The average thickness of cover at the Leith mine, which 294 METHODS OF WORKING. is here described and which may be considered as a type of the region, is 250 ft., the overlying measures being alternated layers of soft shale and coal for 4 ft. The bottom is an 18" layer of hard flreclay and slate. These floor and roof materials are soft, and are easily disintegrated by air and water. At some mines, cover will reach as much as 700 ft., and the dip of 5$ (as at Leith) is much heavier at some points on eastern out- crop, and will run as high as 12& flattening off as the synclinal line of the basin is reached, until it is almost level. In some localities, the material below coal is hard limestone, requiring blasting to remove it, and at other places the roof slates are much more solid than at Leith, and not read- ily disintegrated. The method of drawing ribs is one of the beauties of the system, since it is harder to do successfully in a soft coal like the Connellsville coal than in hard coal. The FIG. 10. FIG. 11. CLEARFIELD METHOD. 295 coal uself is firm. When necessary to protect the top or bottom, 4 to 6 in. of coal are left covering the soft material. The method as given above is often applied to a whole series of butts (4 or 5) at once instead of to butt by butt, as shown in Fig. 11. In this case, work is started at the upper end of the uppermost butt and progresses, as shown in Fig. 11; but, after cutting across the butt heading from which the rooms were driven, the butt heading itself and the upper rooms from the second butt, or that just before, are likewise drawn back by continuous slices being removed from the rooms of the upper butt, and on across the next lower butt, etc., all 9n an angle to the butts, and so continued as the operations progress, until another butt is reached, etc., thus gradually making a longer and longer line of fracture, which is only limited by the number of butts it is desired to include at one time in the section thus mined. This works very nicely and makes long even lines of fracture, the steps of the face of the workings (in the rib drawing) being about 30 ft. ahead of one another. Pittsburg Region (H. L. Auchmuty). The coal is worked in much the same way as in the Connellsville region, except that a different system of drawing ribs is used. The coal is worked on the room-and-pillar system, with double entries, with cut-throughs between for air, and on face and butt, entries are about 9 ft. wide, and the rooms 21 ft. wide and about 250 ft. long; narrow (or neck) part of room, 21 ft. long by 9 ft. wide; room pillars, 15 to 20 ft. wide, depending on depth of strata over the coal, which is from a few feet to several hundred feet. The mining is done largely by machines of various types. Coal is hard, of course, and, in many places, the roof immediately over the coal is also quite hard. There are about 4 ft. of alternate layers of hard slate and coal above the coal seam. Rooms are mined from lower end of butt as fast as butt is driven, the ribs being drawn as mining progresses. As the coal is harder than in the Connellsville region, thickness of coal pillar between parallel entries is somewhat less. Clearfield Region (G. F. Duck). The butt and face are not strongly marked in the B or Miller seam, the one chiefly worked in this region. Where possible, these cleavages are followed in laying out the workings, but the rule is to drive to the greatest rise or dip and* run headings at right angles to the right and left, regardless of anything else. The main dip or rise heading is usually driven straight, and is raised out of swamps or cut down through rolls very common here unless they are too pronounced, when the head- ing is curved around them. The same is true of room headings, except that they are more usually crooked, not being graded except over very minor disturbances. As the B seam rarely runs over 4 ft. in thickness, and is worked as low as 2 ft. 8 in. in the haulage headings, the roof is taken down to give 5 ft. to 5 ft. 2 in. above the rail, or 5 ft. 8 in. to 5 ft. 10 in. in the clear. Where the resulting rock is taken outside, the headings are driven 10 ft. wide with 24 ft. of pillar, roof taken down in haulage heading but not in air-course. Where the rock is gobbed underground, the haulage heading is 18 to 24 ft. wide, air-course 10 ft., pillar 24 ft., and roof taken down in haulage heading only. The thinner the coal, the wider the heading. It is more economical to haul the rock to daylight. The bottom generally consists of 3 ft. to 5 ft. of hard fireclay, frequently carrying sulphur balls. In numerous places, the sand rock is immediately over the coal, but in most cases there is from 3 to 5 ft. of slate before the sand rock is reached. Room headings are driven 280 ft. apart, haul rock to daylight, heading 10 ft. wide with 24 ft. pillar to 10 ft. air-course, in which roof is left up. A 15 ft. to 25 ft. chain pillar is left between air-course and faces of rooms from the lower heading, every fourth to eighth of which is driven through to the air-course to shorten the travel of the air. The rooms are therefore 180 to 200 ft. long, and the men push the cars to the face, an important economical item in this thin coal. Rooms are 21 ft. wide with a 15 ft. pillar, and a 15 ft. chain pillar is left between the first room on any room heading and the main heading, and roof is not taken down in rooms. Main-heading track is usually 30-lb. iron, room heading, 12 lb., and 1" X i" strap iron set on edge is used in the rooms in low coal. Mine cars hold from 600 to 800 lb. in low seams, and 1,500 to 2,000 lb. in the so-called thick seams, i. e., 3 ft. 8 in. to 4 ft. thick. Reynoldsville Region. The measures are very regular, and the method employed the typical one shown in Fig. 1. The average thickness of the principal seam is 6i ft. and the pitch is 3 to 4. The coal is hard and firm, 296 METHODS OF WORKING. and contains no gas; the cover is light, and on top of the coal there are 3 or 4 ft. of bony coal; the bottom is fireclay. Drift openings and the.double- entry system are used. Both main and cross-entries are 10 ft. wide, with a 24-ft. pillar between. The cross-entries are 600 ft. apart, and a 24 ft. chain pillar is left along the main headings. The rooms are about 24 ft. wide and open inbye, the necks being 9 ft. wide and 18 ft. long. The pillars are from 18 to 30 ft. thick. West Virginia (James W, Paul}. The general plan of working the Pitts- burg coal in the northern part of West Virginia is as follows. The coal measures vary from 7 to 8 ft. in thickness, and have a covering varying from 50 to 500 ft. The coal does not dip at any place over 5#. In most places the coal is practically level, or has just sufficient dip to afford drainage. The usual method of exploitation is to advance two parallel headings, 30 ft. apart, on the face of the coal. At intervals of 500 to 600 ft., cross-headings are turned to right and left, and from these headings rooms are turned off. These cross-headings are driven in pairs about 20 or 30 ft. apart. Between the main headings and FIG. 12. the first room is left a block of coal about 100 ft., and on the cross-headings there is often left a barrier pillar of 100 ft. after every tenth room. The headings are driven from 8 to 12 ft. wide, and the rooms are made 24 ft. wide and 250 to 300 ft. long. A pillar is left between the rooms about 15 to 20 ft. wide. These pillars are withdrawn as soon as the panel of rooms has been finished. The rooms are driven in from the entry about 10 ft. wide for a distance of 20 ft., and then the room is increased in width on one side. The track usually follows near the rib of the room. Cross-cuts on the main and cross-headings are made every 75 to 100 ft., and in rooms about every 100 ft. for ventilation. The double-heading system of mining and ventilation is in vogue. Over- casts are largely used, but a great many doors are used in some of the mines. Rooms are worked in both directions. This is the general practice when the grades are slight. When the coal dips over 1$, the rooms are driven in one direction only. In this case, the rooms are made longer, as much as 350 ft. It is the custom then to break about every third room into the cross-heading above (a practice ill advised). The floor of this bed of coal, being composed of shale and fireclay, often ALABAMA METHODS. 297 heaves, especially when it is made wet. Some trouble is at times experi- enced by having the floor heave by reason of the pillars being too small for the weight they support. The dimensions of rooms and pillars given are for a mine (with covering 300 to 500 ft. thick) having a fairly good and strong roof. Where roof, bottom, and thickness of cover change, these dimensions are altered to suit the requirements. The main-heading pillars may be reduced to 30 or 40 ft.; the rooms may be made 15 ft. wide with 12 ft. pillars, and no barrier pillars may be left on the cross-headings. The foregoing plan is very much followed in other parts of the State; at least an attempt is made to do so, but local disturbances often require changes in the plan. This plan is followed on soiae parts of New River, and also in the Flat Top field. Alabama Methods (/. E. Strong). Fig. 12 shows the common methods used in working the Alabama coals. The seams now working vary from 2 to G ft. thick, and they pitch from 2 to 40. Where the seams are thin, the coal is hard, and pillars of about 20 to 30 ft. are used to support the roof. pi t FIG. 13. The thick seams are soft and easily broken, and much larger pillars are left. The character of bottom and top varies; fireclay bottom and slate roof are usually found with the thick seams, and hard bottom and sandstone roof with the thin seams. The general plan of laying out the mine is to drive the slope straight with the pitch of the seam; this is usually on the butts of the coal. A single-track slope is 8 ft. wide, and a double-track slope 16 ft. Cross-headings are driven or turned from the slope water level every 300 ft.; air-courses are driven parallel on either side of the slope. Where an 8 ft. slope is driven, 30 ft. of pillar are left between the slope and airway, and for a 16 ft. slope, 30 ft. of pillar. The size of pillar, however, depends largely on the character of the roof and thickness and strength of coal. On the lower side of the headings, pillars from 20 to 60 ft. are left on the entry before turning the first room. The rooms are worked across the pitch on an angle of about 5 on the rail, Fig. 12, A, when the coal does not itch greater than 20; where the pitch is greater, chutes are worked and he rooms are driven straight up the pitch (Fig. 12, B}. In a few cases, where the pitch is not greater than 15, double rooms are worked with two roadways in each room (Fig. 12, C). A rope with two pulleys is used, and each track keeps the rib side of the room, the loaded car pulling up the empty on the opposite side of the room; distance between room centers, about 42 ft. Where single rooms are worked, the room is driven narrow (8 ft. wide) for 21 ft., when connections are made with the room outside of it; the room is then widened out to about 25 ft., sloping gradually until this width is at tained; pillars of from 10 to 20 ft. thick are left between the rooms, and cross-cuts for ventilation are made about every 50 ft.; every third or fourth room is driven through to the entry above; pillars are then drawn back to the entry stumps or pillars. The average cover over the coal now working is from 100 to 600 ft. Air-courses usually have an area of 30 ft., and sufficient coal is taken out to give this area, the roof and bottom being left. George's Creek District, Md. Fig. 13 shows the method used in the George's Creek field, Maryland. The coal shows no indication of cleats, and the butts and headings can be driven in any direction. The main heading is driven to secure a light grade for hauling toward the mouth. Cross- headings making an angle of 35 to 40 are usually driven directly to the 298 METHODS OF WORKING. rise, and of the dimensions shown. Pillars are drawn as soon as the rooms are completed, being attacked on the ends and from the rooms on either side, the coal being shoveled to the mine car on a track in the room. Very wide pillars are split. No effort is made to hold up the overlying strata, and the entire bed is removed as rapidly as possible. An extraction of 85# of the bed is considered good work. A section of the seam is as follows: Roof coal, 10 in.; coal, 7 ft.; slate, i in.; coal, 10 in.; slate, in.; coal, 10 in.; fireclay; slate. The top bench is bony and frequently left in place to prevent FIG. 14. disintegration of the roof by the air. Above this coal is from 8 to 10 ft. of " rashings," consisting of alternating thin beds of coal and shale, that is very brittle, and requires considerable timber to keep it in place. (" Mines and Minerals," Vol. 19, page 422.) Blossburg Coal Region, Pa. Coal is generally mined from drifts, but in a few cases by slopes. Fig. 14 shows the general method adopted; the breasts are run at right angles to the slips; the breast pillars are split by a center heading .and taken out as soon as the breasts are finished. The gangway pillars are taken out retreating from the crop or boundaries of the property. FIG. 15. The general average of the coal seams is not over 31 ft., accompanied by fireclay and some iron ore. The dip of the veins is about 3#. (" Mines and Minerals," Vol. 19, page 126.) Indiana Coal Mining. Fig. 15 shows the double-entry room-and-pillar method as used in Indiana. The entries are generally 6 ft. high, 8 ft. broad, IOWA IfETIlOl). 299 the minimum height required by law being 4 ft. 6 in. The rooms are from 21 to 40 ft. in width. The mines are generally shallow. The rooms in Fig. 15 are shown as widened on both ribs, but a more usual method in this locality is to widen the room on the inbye rib, leaving one straight rib for the protec- tion of the road in the room. ("Mines and Minerals," Vol. 20, page 202.) Iowa Coal Mining. The coal lies at a depth of 200 ft. below the surface, and is geologically similar to that of the Missouri and Illinois fields. It lies in lenticular basins extending northwest and southeast and outcropping in the larger river beds. The seams are practically level, non-gaseous, and gen- erally underlaid by fireclay and overlaid by a succession of shales, sand- stones, and limestones, \yhich are generally of a yielding nature, giving a strong, good roof for mining. There are three distinct seams, the lower one, which varies from 4 to 7 ft. in thickness, being the only one worked. The coal is a hard, brittle, bituminous coal that shoots with difficulty, but is excellent for steam and domestic uses. About Centerviile, the coal has a distinct cleat, but elsewhere in the State this is lacking. The entry pillars along the main roads are 6 to 8 yd. thick, for the cross-entries 5 to 6 yd., and for the rooms 3 to 5 yd. Room pillars are drawn in when approaching a cross-cut. Both room-and-pillar and longwall methods are in use, with modifications of each. In the room-and-pillar system, the double-entry system is almost invariably used in the larger mines. Rooms are driven off each entry of each pair of cross-entries at distances of 30 to 40 ft., center to center; the rooms are 8 to 10 yd. in width, and pillars 3 to 4 yd. The rooms are narrow for a distance of 3 yd., and then widened inbye at an angle of 45 to their full width. They vary from 50 to 100 yd. in length, and the road is carried along the straight rib. When double rooms are driven, the mouths of the rooms are 40 to 50 ft. apart, and they are driven narrow from the entry a distance of 4 or 5 yd. FIG. 16. A cross-cut is then made connecting them, and a breast 16 yd. wide is driven up 50 to 60 yd. The pillar between each pair of rooms is 12 to 15 yd. In pillar-and-stall work, the stalls are usually turned off narrow and widened inside, the pillar varying from 5 to 8 yd. The stalls are 30 to 40 yd. in length, and the pillars are drawn back. When the stalls are driven in pairs, the pillar 8 to 10 yd. in width is carried between them. Longwall. The main haulage road runs in each direction from the foot of the shaft, and on both sides of this diagonal roads are turned at an angle of 45, or parallel to the main haulageway. These are spaced 10 yd. apart and driven 50 to 60 yd., when they are cut off by another diagonal road. Panel breasts are used where the conditions are such as to induce a squeeze. Rooms are turned narrow off entries and are arranged in sets of 6 to 12 rooms, with a pillar 10 to 20 yd. wide between the sets of rooms. When the rooms have progressed a short distance from the entry, they are connected by cross-cuts, and the longwall face is carried forward from this point. Packs are built and the roof allowed to settle, as in longwall. The wide pillars are taken out after the roof has settled. 300 METHODS OF WORKING. Ventilation. The system of ventilating the workings usually employed is that of conducting the air to the inside workings by means of an air-course forming the back entry of each haulage road. From this point it is carried along the face of the rooms, through the breakthroughs or cross-cuts in the room pillars, returning thence to the haulage road, which is usually made the return airway. When, however, the mine is ventilated by means of a furnace or an exhaust fan, the intake airway is usually made the haulage road, in order to avoid doors at the shaft bottom. The Tesla, California, method is shown in Fig. 16. The coal seam averages 7 ft. of clear coal, and pitches 60. This system was adopted in a portion of the mine to get coal rapidly; for, at this point, a short-grained, slate cap rock came in over the coal, making it difficult to keep props in place. The floor is a close blue slate and has a decided heaving tendency. The roof is an excellent sandstone. There is a small but troublesome amount of gas. Two double chutes are driven up the pitch at a distance of 36 ft. apart, con- nected every 40 ft. by cross-cuts. One side of each chute is used for a coal chute and the other for a manway and air-course. At a distance of 12 yd. apart small gangways are driven parallel with the main mine gangways. Tnese are continued from each chute a distance of 300 ft., if the conditions warrant it. The top line is then attacked from the back end and the coal is worked on the cleavage planes; the breast, or room, therefore consists of a 12-yd. face, including the drift or gangway through which the coal is carried to the chutes; a rib of coal (2 or 3 ft.) is left between the breasts to keep the rock from falling on the breast below. Thus in each breast the FIG. 17. miners have a working face of about 15 or 16 yd., and as the coal is directed to the car by a light chute, moved along as the face advances, the coal is delivered into the cars at small cost, and but little loss results from the falling coal, as a minimum of handling is thus obtained. Immediately above each gangway, and starting from these main chutes, an angle chute is driven at about 45, connecting with the breast gangway above it, and into these chutes the coal from that breast is delivered, runs into the main chute, and from it is loaded into the mine cars in the main gangway. These angle chutes serve as a means of keeping the main chute full, and at the same time giving each breast an opportunity to send out coal continuously. They also serve the purposes primarily intended, of saving the coal from breakage, by giving it a more gradual descent into the full chute. The breast gangways are driven 5 ft. wide. No timbers are needed in these gangways, as they are driven in the coal, except on the foot-wall or floor TESLA METHOD. 301 side, which, as before stated, is a firm sandstone. It is found safest to leave a rib of coal on the top of the breast 2 or 3 ft. thick, until the working face has passed on 12 or 15 ft., when this rib is cut out and thus all the coal extracted, the roof caving behind and filling in the opening. As cross-cuts are driven every 36 ft., ventilation is kept along the working faces, and a safe and effectual means of securing all the coal in the seam is thus attained. Fig. 17 shows another svstem used in No. 7 vein at the same place. The seam averages 7 ft. of coal. The roof is shelly and breaks quickly, hence the coal must be mined rapidly. In this system the gangway chutes are driven at right angles with the strike of the seam, 40 ft. up the pitch; a cross-cut 5 ft. X 6 ft. is then driven FIG. 18. parallel with the gangway. From this cross-cut, chutes are driven at same distance apart as the gangway chutes (30 ft.), at an angle of 35, and cross- cuts are driven every 40 ft. between chutes, for ventilation. After a panel of five or more chutes is driven up the required distance, work is com- menced on the upper outside pillar and the pillars on that line are drawn and the next line is attacked, and this is continued until the panel or block is worked down to the cross-cut over the gangway. About every 80 ft. in this level it is found advantageous to build a row of cogs parallel with the strike of the seam as the pillars are drawn. This serves to save the crushing of the pillars, and prevents any accidents from falls of rock. But few timbers are required by this system. ("Mines and Minerals," Vol. 19, page 145.) 302 METHODS OF WORKING. New Castle, Colorado, Method. The following method as described by Mr. R. M. Hosea, Chief Engineer of the Colorado Fuel and Iron Co., is used at New Castle, Colo., for highly inclined bituminous seams. The coals mined are only fairly hard, contain considerable gas, and make much waste in mining. Fig. 18 shows the method used for extracting the Wheeler or thicker vein to its full width of 45 ft., and the E seam 18 ft. thick, excepting that left for pillars. Rooms and pillars are laid out under each other in the two seams whenever practicable. Entries are along the foot-wall; 30 ft. up the pitch is an air-course. Rooms and breasts are laid out as shown in B and C, Fig. 18. In the Wheeler vein, the man ways go through the entry pillars to the air-course and thence along the ribs each side of the room, one man way to the main entry serving for two double rooms. A lower bench of 6 ft. is first mined the full length of the rooms, 120 ft., side man ways being protected by vertical or leaning props, bordered with 3" planks outside, and the chute or battery is then put in. At the top the rooms are connected by cross-cuts, and, occasionally, intermediate cross-cuts are required. The room is kept full of loose coal, only sufficient being drawn to keep the working floor at the proper height for the mining. When driven to the limit and with cross-cuts connected, the coal is all drawn out at the chutes, which have receptacles for rock and waste at their sides, to be picked out by the loaders. The next operation is to drive across the seam at the air-course until the hanging wall is reached, manways, called back man- ways, being maintained as before. A triangular section of coal is mined off, as shown in A, Fig. 18, and the room filled with loose coal. The full thick- ness of the seam is now taken off, shots being first placed at > ft Month. Ton- nage. ftp January . February 107,952 98,109 7.94 7.37 May June 179,752 164,062 12.84 11.92 September October.... 161,213 198,161 11.52 13.90 March.... April 141,991 136,375 9.95 9.69 July August .. 145,445 177,241 10.59 12.96 November December 228,433 123,406 17.15 8.87 320 COSTS OF MINING ANTHRACITE. PERCENTAGES OF DIFFERENT SIZES. Mouth. ,, ump . Steamer. Broken. Egg. Stove. Chestnut. Pea. January 821 02 17 53 20 31 21 46 18 04 14 43 February 8 29 12 17 75 20 41 20 85 17 44 15 14 March 620 55 17 64 20 04 20 65 is'oo 16 9 -> April 7 01 38 16 76 20 17 20 92 18 1 16 64 May 4.79 27 1863 20 33 21 42 18 23 16 33 June 3.29 .21 22.43 1972 2021 1857 15 57 July 7.84 .42 1942 1954 19 46 18 58 14 74 August 5.05 .57 19.84 20 69 1892 18 62 16 31 September October 4.25 4.72 .27 .01 18.81 16.77 21.98 2200 19.98 21 27 19.32 19 88 15.39 15 35 November December 2.69 440 .16 57 15.56 14 03 22.42 22 62 22.66 21 27 20.71 21 41 15.80 15 70 Year 5.23 .29 17.96 20.95 20.80 19.03 15.74 COSTS OF MINING AND PREPARATION PER TON. Months. Outside. Inside. I Credits. Net Cost. i 5 Supplies. Repairs. OJ e e 1 5 1 3 CO ! I I January February March April .363 .376 .297 .305 .270 .290 .309 .286 .284 .267 .262 .344 .297 .042 .042 .031 .034 .022 !032 .046 .030 .039 .036 .029 .045 .034 .014 .014 .010 .023 .011 .011 .019 .017 .012 .013 .010 .018 .014 .419 .432 .338 .362 .303 .333 .374 .333 .335 .316 .301 .407 .345 .934 .947 .872 .870 .839 .874 .879 .873 .890 .856 .860 .954 .881 .249 .273 .182 .203 .164 .206 .266 .194 .201 .188 .214 .307 .214 .028 .030 .022 .020 .015 .018 .033 .026 .024 .020 .018 .028 .023 1.211 1.250 1.076 1.093 1.018 1.098 1.178 1.093 1.115 1.064 1.092 1.289 1.118 1.630 1.682 1.414 1.455 1.321 1.431 1.552 1.426 1.450 1.380 1.393 1.696 1.463 .120 .104 .096 .103 .101 .105 .098 .102 .105 .100 .104 .120 .104 1.510 1.578 1.318 1.352 1.220 1.326 1.454 1.324 1.345 1.280 1.289 1.576 1.359 May June July August September ... October November .... December ... Year COAL PRODUCTION OF UNITED STATES. "Vaar Bituminous. Anthracite. Tons of 2,000 Lb. Value. Tons of 2,240 Lb. Value. 1890 111,302,322 $110,420,801 46,468,641 $66,383,772 1895 135,118,193 115,779,771 57,999,937 82,019,272 1897 147,609,985 119,567,224 52,611,680 79,301,954 1898 166,592,023 . 132,586,313 53,382,644 75,414,537 1899 193,321,987 167,935,304 53,944,647 88,142,130 PRICES OF COAL. The table on page 327, given by the IT. S. Geological Survey, will be of interest as showing the fluctuations in the average prices ruling in each State since 1886. Prior to that year, the statistics were not collected with sufficient accuracy to make a statement of average prices of any practical value. These averages are obtained by dividing the total value by the total product, except for the years 1886, 1887, and 1888, when the item of colliery consumption was not considered, PRICES OF COAL. 327 si i B&vai O CO CO iO i 1 t~ CO i 1 I"* 1>- ' O T ' CO 1C l 4 i-H GO CC S- r COiMrHTjHiO Oi5C5 OSC<1COC<100 00 ^ S * " ' I> T^ rH p TH lO l^ r-J GO 00 1> O CO ^ t>- CC 1> ' * " * '' ' A I J3 fi fl i-HOOi-HCi 'ci " co 83 H CO CO rH . ' C4 ' r-i rH c4 rH C^ ' CO* I rH rH ee If - H g ..>> s PH 328 COST OF COKING COAL. COST OF COKING COAL. The cost for labor alone of coking coal has been given by a number of companies in the Connellsville district as 61 cents per ton of coke produced, or 40j cents per ton of coal coked, exclusive of royalties, taxes, rents, and such fixed charges. In the "American Manufacturer" for July 27, 1899, Mr. F. C. Keighley gave the following as the proportional costs of the several items of mining and coking Connellsville coal: Coke Yard. Per Cent. Coke Yard. Per Cent. Drawing 70.01 Shifting cars 1.28 Leveling 8.96 Yard bosses 1 12 Charging 3.48 Masons on repairs 6.12 Carters 2.48 Forking 1 60 Bookkeeper and superin- Individual cars .52 tendent, i of total for Sundry 51 mine and yard 204 Yard pumps 76 Cleaning tracks 1.20 Total 1.00^08 Mine. Per Cent. Mine. Per Cent. Room coal 52 15 Machinist . . 49 Drivers 807 Bookkeeping i of total for Heading coal Rope haulage 11.15 281 mine and yard Outside labor .49 203 Roads ... 3.03 Stable boss .96 Mine bosses 1 31 Teams 65 Fire boss 1.44 Blacksmith .98 Timber 283 Carpenters 1 01 Trappers Superintendence i of total .43 Lamp cleaners Inside pumps .82 59 for mine and yard .49 Steam pumps .55 Cagers 66 Survevs 41 Runners and oilers .80 Extra men .51 Engineers 101 Supplies .92 Firemen 1.13 Betterments 1.05 Dumpers 1.25 Total 100 02 The mine labor is 67.20$ of the total labor cost, and the coke-yard labor is 32.80$ of the total labor cost. The cost of equipping a coke plant and opening a mine to furnish the coal in the Connellsville region is from $500 to $1,000 per oven, dependent on the kind of opening for the mine and local considerations. $500 per oven is a fair price for a plant when the conditions are favorable and the mine is a drift mine, and $1,000 is a fair price for a shaft mine about 300 ft. deep, under rather unfavorable conditions. Fulton gives the cost of the various types of coke ovens as follows: Not saving by-products: Beehive, $300; Thomas, $800; McLanahan, $800; Belgian, $1,000; Coppee, $1,000; Bernard, $1,000. Saving by-products: Simon Carves, $1,300; Semet-Solvay, $1,600; Hiiessner, $1,400; G. Seibel, $1,300; Otto-Hoffman, $1,600; Festner-Hoffman, $1,500. The usual quantity of coal required to make 1 ton of coke is 1.4 to 1.6 tons. The loss in loading coke at the ovens and again unloading it at the furnaces or steel works is 2$ to 3$. During the winter and in wet seasons coke takes on 2$ to 3$ of moisture in transit between the ovens and the furnaces. EXPLOSIVES 329 EXPLOSIVES. The characteristics of a good blasting explosive are: (1) sufficient stability and strength; (2) difficulty of detonating by mechanical shock; (3) handy form; (4) absence of injurious effects on the user. Explosives are divided into two general classes: (1) low explosives or direct-exploding materials; (2) high explosives or indirect-exploding mate- rials that require a detonator. Low Explosives. Gunpowder or black powder is the type of this group. Its composition varies, depending on the purpose for which it is to be used, but the ingredients commonly used in its manufacture are saltpeter, sulphur, and charcoal. The following table gives the composition of blasting powder in different countries: COMPOSITION OF BLASTING POWDER (Guttmann). Ingredients. Great Britain. Germany. Austria- Hungary. France. Russia. Italy. United States. Saltpeter Sulphur 75 10 66.0 125 64 16 62 -20 66.6 167 70 18 64 16 Charcoal 15 21.5 20 18 16.7 12 20 High Explosives. These are a mixture of nitroglycerine with an absorbing dope, the composition of which is such that, in addition to thoroughly and permanently absorbing the nitroglycerine, it is itself a gas-producing com- pound. Nitroglycerine at 60 F. has a specific gravity of 1.6. It is odorless, nearly or quite colorless, has a sweetish burny taste, is poisonous even in very small quantities, and is insoluble in water. All nitroglycerine com- pounds freeze at 42 F., and explode when confined at 360 F. It takes fire at 306 F., and, if unconfmed, burns harmlessly unless in large quantities, so that a part of it, before coming in contact with the air, becomes heated to the exploding point. Thawing Dynamite. All frozen cartridges should be thawed, as, when frozen, cartridges are very hard to explode, and even if they do explode, the results are not nearly as satisfactory as when properly thawed. When cartridges are frozen, do not expose to a direct heat, but thaw by one of the following methods: First, place the number of cartridges needed for a day's work on shelves in a room heated by steam pipes (not live steam) or a stove. Where regular blasting is done, a small house can be built for this purpose, fitted with a small steam radiator. Exhaust steam through these pipes gives all heat necessary. Bank your house around with earth, or, preferably, fresh manure. Second, use two water-tight kettles, one smaller than the other, put cartridges to be thawed in smaller kettle, and place it in larger kettle, filling space between the kettles with hot water at, say, 130 to 140 F., or so that it can be borne by the hand. To keep water warm, do not try to heat it in the kettle, but add fresh warm water. Cover kettles to retain heat. In thawing do not allow the temperature to get above 212 F. Third, where the number of cartridges to be thawed is small, they may be placed about the person of the blaster until ready for use, the heat of the body thawing the cartridges. Keep cartridges away from all fires this applies to all explosives. Do not be in a hurry, but thaw slowly. Do not thaw before an open fire. Do not put cartridges in an oven, on a hot stove, against hot iron plates, or against brick casing of a boiler. Do not put cartridges in hot water, or expose them to live steam. And do not take any kind of powder, fuse, or caps near a blacksmith shop. A large number of high explosives are made that vary but little in their composition, the main difference being in the character of the dope and in the percentage of nitroglycerine. The trade name is usually determined by the percentage of nitroglycerine, thus 10$ dynamite means that the dyna- mite contains 10# of nitroglycerine, etc. Safety explosives, or, as they are called in England, perm itted explosives, are compounds intended for use in gaseous mines, and they are so constituted 330 EXPLOSIVES. that they will ignite without producing the extremely high temperature given by ordinary explosives. The term flameless explosives was formerly used, but it has been replaced by safety explosives, as the absence of a flame is not now necessary to a permitted explosive. COMMON BLASTING EXPLOSIVES. Atlas. Brands Equivalent in Strength to Atlas. Q I o5 , 6 jj i| a qj S fe +->' 5 ^ 10 H3 33 .. | T3 S "oS o te a o o O o o 3 o O B * 1 to ft o m Pk (2 d ! 3 o 1 1 "S 1 oS CJ % P< 0) o> 0) '6 o n ^ tf w w A 75 A No. 1 XX No. 1XX Old No. 1 No. 1 A No. 1 XX B + 60 B-f No.l No. 1 No. 1 A No. 1 | No. 1 XS No.l B 50 fi No. 2 SS No. 2SS New No. 1 No. 2 No. 1 X No. 2 XX C + 45 C + No. 2 S No. 2S No. 2 Extra No. 2 X c 40 C No. 2 No. 2 No. 2 No. 3 C No.l No. 2 D+ 33 No.2C No. 2C No.2X No. 3 A D 30 No. 3 No. 3 No. 2 No. 3 E + 27 No.3B XXX No.3X No. 3 B E 20 No.4B xxxx No. 3 No. 4 Drilling. Adapt the size and depth of the hole to the work to be accom- plished. As a rule, for ordinary rock blasting, the distance between the holes should be equal to from one-half to the total depth of the holes, the holes set back from the face twice as far for dynamite as for common black powder, say a distance equal to the depths of the holes or slightly less, and load one-third the length of the hole. These directions are only general, and do not apply to very deep holes. Much depends on character and hard- ness of the rock, also on size of drill holes. In all cases, the experience and judgment of the blaster must be his guide. Diameter of Holes. In driving headings or sinking shafts, experience shows that holes having a diameter varying from | to H in. at the bottom are most economical in hard rock, if charged with the strongest high explosive. On the contrary, holes of large diameter, say H to 2 in. in diameter, and charged with strong, low, and cheap explosive, are the best when operating in weak rock. All the holes in the heading or shaft should have the same diameter, and the best arrangement is to give an equal resistance of rock to each, and to so place each hole that it will receive the greatest benefit from the free faces formed by firing the previous holes. Relation of Diameter of Hole to Length of Charge. By experiment, it has been proved that, as a rule, the length of the charge of explosive for single holes should not exceed from 8 to 12 times the diameter of the hole; that is, a V hole should never have a charge of more than 12 in. of explosive placed in it. Where several holes are fired together, this rule is sometimes slightly deviated from. It is usually best to employ a length of charge between these two limits, as, for instance, about 10 times the diameter of the hole. Chambering or squibbing is the blasting out of a cavity at the bottom of a drill hole to allow of a larger charge of explosive being used. Bulling a drill hole is the working of clay into any cracks opening into a drill hole, to prevent the power of the blast being scattered through these cracks. Charging. The charge must fit and fill the bottom of bore and be packed solid. If holes are comparatively dry, slit the paper of the cartridges length- wise with a knife, and as each is dropped into the hole, strike a wooden BLASTING. 3'Jl rammer on it with sufficient force to make the powder completely fill the bottom and diameter of the bore. Where water is not present, a more per- fect loading is made by taking powder out of cartridge and dropping it in loosely, ram each 6 or 8 in. of the charge, using the paper of each cartridge as a wad, to take down any powder that may have stuck to the sides of the hole. If water is standing in the hole, do not break the paper of the car- tridges and avoid ramming more than enough to settle the charge on the bottom, using cartridges of as large diameter as will readily run into the bore. When cartridges are used, the last cartridge placed in the hole should contain an electric exploder, or cap with fuse attached. When loose powder is used, a piece of cartridge 2 or 3 in. in length, with exploder or cap attached, should be pressed firmly on top of charge. Some blasters put an exploder or cap in the first cartridge put in the hole, placing remainder of charge on top. The charge should be placed in a solid part of the material to be broken. If possible, the face should be undercut and then the overhanging material shot down. Best results are obtained when the bore holes cross the faces or layers of the material at right angles. The charges should be placed so as to disturb the sides and roof of a tunnel through material of medium hardness as little as possible. The charge at the bottom of the tunnel should be placed from 6 to 12 in. below the permanent level. Amount of Charge. No invariable rule can be laid down as to the diameter and length of cartridges to be used under any and all circumstances, nor the amount or grade of powder required for all kinds of work. Much depends on the good sense and judgment of the persons using the explosive. Guttmann, in his well-known handbook on blasting, says: ''There is no lack of theories for the determination of blasting charges, but their application depends on empirical facts determined by practical work. I therefore advise that the calculation of charges under ordinary conditions be neg- lected, and recommend watching actual operations for some weeks, asking for explanation from the most expert miners. In this way experience will be gotten in a short time that will enable one to estimate with some precision the proper charge to use after inspecting the spot to be blasted." A good rule by which to determine the weight of black powder to use in any given hole in bituminous workings is the following: Find the distance in feet from the charge out in the line of least resistance. Multiply the fourth power of this distance by ^ the diameter of the hole in inches, and divide this product by the thickness of the seam in inches. The result will be the weight of the charge in pounds. Thus, for a 1\" hole in a seam of bituminous coal 6 ft. thick, where the charge is placed 4 ft. deep from the face of the coal, or cutting, we have for the weight of charge to be used, Tamping. In deep holes, water makes a good tamping, but fine sand, clay, etc. are generally used. Fill in for the first 5 or 6 in. carefully, so as not to displace cap and primer; then with a hardwood rammer pack bal- ance of material as solid as possible, ramming with the hand alone, and not using any form of hammer. Never use a metal tamping rod. Firing. If the work is wet, or the charge used under water, use water- proof fuse, and protect the end of the fuse by applying bar soap, pitch, or tallow around the edge of the cap. Water must not be allowed to reach the powder in the fuse or the fulminate in the cap. Exploding by electricity is best under water at great depth, as the pressure of water is so great on the fuse that it is forced through and dampens it so as to prevent firing. Seam Blasting. If a seam is found in the rock, remove the powder from. the cartridges and push it into the seam and fire a cap beside it. This will open the seam so that a larger quantity of explosive can be used, and the rock broken without drilling. In blasting coal, slate, marble, granite, free- stone, or any other material that it is desirable to obtain in large blocks, cartridges of small diameter should be used in wide bore holes, the charge being rolled in several folds of paper, to prevent its touching the sides of the bore holes. The intensity of action and the crushing effect of the explosive are thus lessened. Firing by Detonation. Nitroglycerine explosives always require detonation by a cap or exploder in order to develop their full force. Fig. 1 illustrates the method of attaching such an exploder to the end of a fuse and the pla- cing of it in the cartridge. The exploders are loaded with fulminate or mer- cury and are slipped over the end of the fuse, after which the upper end is 332 EXPLOSIVES. crimped tightly against the end of the fuse, as shown. (Miners sometimes bite the caps on. to the fuse with their teeth. This is a very dangerous pro- ceeding and should never be allowed, as, with strong caps, one of them exploding in a man's mouth would prove fatal.) In placing the cap or FIG. 2. FIG. 3. exploder into the dynamite or giant-powder cartridge, care should be taken that only about two-thirds of the cap be embedded in the material of the cartridge, for if the fuse had to pass through a portion of the material before reaching the cap, there would be danger of its igniting the material, thus causing deflagration of the cartridge in place of detonation. The fumes given off by high explosives are much worse in the case of detonating a cartridge. The electric exploder, Fig. 2, has wires A and B, which carry the current to the exploder. D is a cement (usually sulphur) that protects the explosive compound C (usually mercury fulminate) and the whole is contained in a copper shell. A small platinum wire E is heated by the passage of a current and ignites the explosive. Fig. 3 shows the method of placing a cap or an electric exploder in a cartridge of powder. When a number of holes are ex- ploded at one time, the electric exploders are connected in series, as shown in Fig. 4, for a small number of holes, and as in Fig. 5 for a larger number. The battery for furnishing the current of electricity is a magneto machine that is worked by either pulling up or by depressing a handle or rack bar, or else by turning a crank. Directions for Blasting by Electricity. Drill the number of holes desired to be FIG. 5. fired at one time; depth and spacing of holes depending on character of rock, size of drill holes, etc., the blaster, of course, using his judgment in this matter. Load the hole in the usual manner, fitting one cartridge with a fuse ARRANGEMENT OF DRILL HOLES. 333 (electric exploder) instead of cap and fuse. The fuse head is fitted into the bottom end of the cartridge, or into the middle of one side of the cartridge, where a hole has been punched with a pencil or small sharp stick to receive it; push the powder close around the fuse head. The fuse can then be held in position by tying a string around the cartridge and the fuse wires, binding the wires to the cartridge, as shown in Fig. 3. A shows head of fuse, B the two fuse wires, C string used to tie wires to cartridge. Avoid taking hitches in fuse wires, as by this very common practice, the insulation of the wires may be injured and the current of electricity may pass from one wire to the other, without passing through the cap, hazarding a misfire. The cartridge containing the fuse is put in on top of the charge by some blasters; by others, at bottom of the charge. The best place for it is in the center of the charge, having part of the charge above and part below it. In tamping the hole, great care must be taken not to cut the wires, or injure the cotton covering of fuse wires, or to pull the fuse out of the cartridge. Allow at least 8 in. of the fuse wire to project above the hole, to make connections. When all the holes to be fired at one time are tamped, separate the ends of the two wires in each hole, and, by the use of connecting wire, join one wire of the first hole with one of the second, the other or free wire of the second with one of the third, and so on to the last hole, leaving a free wire at each end hole. All connections of wires should be made by twisting together the bare and clean ends; it is best to have the joined parts bright. Scrape off the cotton FIG. 7. covering at the ends of the wires to be connected, say for 2 in., then rub the wire with a small hard stone. This makes a bright fresh wire. Be sure that all connections are clean, bright, and well twisted. Do not hook or loop wires in making connections. Bare joints in wire should never be allowed to touch the ground, particularly so if the ground is wet. This can be prevented by putting dry stones under the joints. The charges having all been connected, as directed above, the free wire of the first hole should be joined to one of the leading wires, and the free wire of the last hole to the other of the two leading wires. The leading wires should be long enough to reach a point at a safe distance from the blast, say 250 ft. at least. All being ready, and not till the men are at a safe distance, connect the leading wires, one to each of the projecting screws on the front side or top of the battery, through each of which a hole is bored for the purpose, and bring the nuts down firmly on the wires. Now, to fire, take hold of the handle for the purpose, lift the rack bar (or square rod, toothed on one side) to its full length, and press it down, for the first inch of its stroke with moderate speed, but finishing the stroke with all force, bringing rack bar to the bottom of the box with a solid thud, and the blast will be made. Do not churn rack bar up and down. It 33 i EXPLOSIVES. is unnecessary and harmful to the machine. One quick stroke of the rack bar is sufficient to make the blast. Never use fuses (exploders) made by different manufacturers in the same blast. Connecting wire should be of FIG. same size as the fuse wire; leading wire should be at least twice as large. Covering on wire should not " strip " or come off easily. The power of an explosive cannot be exactly calculated from the quantity and temperature of the gas resulting from its detonation, as it is impossible to determine the exact composition of gas at the moment of explosion and during the subsequent cooling period. Tables that give the relative strength FIG. 10. FIG. 11. of explosives are apt to be misleading, as so much depends on the compo- sition of the explosive, and since there are so many explosives of varying compositions that are sold under the same name. Pressures Developed by Explosives. According to experiments conducted ARRANGEMENT OF DRILL HOLES. 335 by Sarrau, Vielle, Xoule, and Abel, the following approximate maximum pressures, in tons per square inch, developed by various explosives, have been arrived at: Mercury fulminate, 193; nitroglycerine, 86; guncotton, 71; blasting powder, 43. Values of Explosives. Taking gunpowder (containing 61$ saltpeter) as a standard, and calling its value 1, the following are the comparative values FIG. 12. FIG. 13. FIG. 14. FIG. 15. of the other explosives: Dynamite, containing 75$ nitroglycerine, 2.2; blasting gelatine, containing 92$ nitroglycerine, 3.2; nitroglycerine, 3.3. The arrangement of drill holes for driving and sinking should be such as to permit the easy handling of the drills and also to minimize the number of holes and the weight of explosive. Two distinct systems are in use: (1) the center cut, by which a center core or key is first removed, and after that concentric layers about this core; (2) the square cut, in which th,Q lines, of 336 MACHINE MINING. holes are parallel to the sides of the excavation, the rock being removed in wedges instead of in concentric circles. The center-cut method is shown in Figs. 6, 7, 8, and 9, Fig. 6 showing the face of a heading, Fig. 7 an elevation or vertical section, and Figs. 8 and 9 plans. The numbers of the holes correspond in the several views. The holes are supposed to be drilled by rock drills, and they are so placed that all except the breaking-in holes have an equal line of resistance. The num- ber of holes given is supposed to take out a clean cut of the whole section abed to the extent of 3 ft. 6 in. The order of firing the holes is: (1) break- ing-in shots 1, 2, 3, and U simultaneously; (2) 5, 6, 7, 8; (3) 9, 10, 11 12- (4) 13, U, 15, 16', (5) 17, 18, 19, 20. The square-cut arrangement is shown in Figs. 12 (face), 10, 11 (plans), and 13 (vertical elevation). The entering wedge, Fig. 11, is best removed in two stages: First, the part e# A by the shots 1, 2, 5, and k; and second, part efh by shots 5, 6, 7, and 8. The other shots are then fired: (1) 9, 10, 11, 12: (2) 13, U, 15, 16-, (3) 17, 18, 19, %0, each volley being fired either simultaneously or consecutively. Where there is a natural parting in the heading, advan- tage is, of course, taken of this in the location of the shots. Figs. 14 and 15 show two arrangements of drill holes used in sinking the Parker shaft at Franklin Furnace, N. J. The size of the shaft was 10 ft. X 20 ft. in the rock. At first, only 6' cuts were put in, but these were gradually increased until 11' and 12' cuts were pulled. The best average obtained was 66 ft. of shaft from 6 consecutive cuts. MACHINE MINING. The number of coal-mining machines in use has increased rapidly within a very short time. In 1896 there were 1,446 in use in the United States. During 1897 there was an increase of 542, or 37.5$, while the average yearly gain from 1891 to 1896 was only about 22$. The total tonnage won by machines in 20 States in 1897 was 22,649,220 short tons, or 16.17$ of the total product of these States, and 15.3$ of the total bituminous product of the United States. A universal mining machine has not yet been brought out, and one of the principal reasons for the failure of mining machines in a number of instances has been the attempt to use a machine under condi- tions to which it was not adapted. When a mining machine is designed and built to suit the conditions under which it is to be operated, it is safe to say that there are but few mines in which they cannot be successfully utilized. They are of particular advantage where there is a long working face and where the coal is over 3 ft. in thickness. Low seams require more under- cutting for the given output than high seams. As a rule it has not been found economical to use machines in seams pitching over 12 to 15, though pick machines have been used in mines having an inclination of 23, the difficulty being not so much in the cutting as in moving the machine from place to place. There are four general types of mining machines in use; pick machines, chain-cutter machines, cutter-bar machines, and longwall machines. The first two are the types almost universally used in America. Cutter-bar machines have almost entirely disappeared from use excepting one type which is at present used in Iowa. Longwall mining machines have not been very generally adopted in America, as the longwall method of mining is not extensively used. Both compressed air and electricity are used for operating mining machines. Pick machines driven by compressed air are made by three separate concerns. Four companies make electric chain machines and one of these four is also making a compressed-air chain machine. One makes a longwall machine, and one has brought out a pick machine for electric power. Pick machines work very similarly to a rock drill. They can be used wherever mining machines are applicable, and their particular advantage is that they are more perfectly under the control of the operator, who can cut around pyrites and similar obstructions without cutting them with the machine. This renders such a machine particularly applicable for seams cf VENTILATION OF MINES. 337 coal having rolls in the bottom and containing pyrites or other hard impuri- ties. They are also applicable for working pillars on which there is a squeeze, as they are light and can be easily handled and readily removed. Chain-cutter machines consist of a low metal bed frame upon which is mounted a motor that rotates a chain to which suitable cutting teeth are attached. To operate chain machines to the best advantage, the coal should be comparatively free from pyrites. They also require more room than pick machines, and a space from 12 to 15 ft. in width is necessary along the face to work them to advantage. These machines have proved failures in some mines on account of the incessant jarring of the roof by the rear jack. Chain-cutter machines cannot be used to undercut coal when a squeeze is upon it. Coal seams that are comparatively level and free from pyrites and have a comparatively good roof can undoubtedly be more satisfactorily and economically cut with chain-cutter machines than with any other type. The average height of cut is 4 to 5 in., and at this height, the chain- cutter machines makes only about 60$ as much small coal as a pick machine. This is not always an advantage, as it does not always allow sufficient height for the coal to fall down after the cut is made. In a 3i' seam, 3 men are required to handle the machine to advantage. Shearing. All the pick machines can be converted into shearing machines and can be used for longwall work by using a longer striking arm and a longer supply hose. The chain machines are used to do shearing work by having the cutting parts turned vertically. Capacity. The average producing capacity of each mining machine used in the United States was 11,398 tons in 1891, 11,373 tons in 1896, and 11,393 tons in 1897. So much depends on the local conditions that it is almost impossible to give specific data of rates of working and costs, but the following are fair working approximations. A good pick machine will undercut 450 sq. ft. in 10 hours, while an ordi- nary miner will undercut 120 sq . ft. in the same time. In a seam varying from 4 to 6 ft. in thickness, the machine will undercut from 50 to 100 tons of coal in 10 hours. The cost of undercutting under these conditions has been given as approximately 10 cents per ton. Extraordinary records show 1,400 sq. ft. to have been cut in 9 hours in Western Pennsylvania, and in an 8' seam, 240 tons have been undercut in a shift of 10 hours. A good chain cutter will make from 30 to 45 cuts, 44 in. wide and 6 ft. deep, in 10 hours under moderately fair conditions, while in high seams two men handling the same machine under ordinary conditions can make 60 cuts per shift, and under particularly favorable conditions, 80 to 120 cuts per shift. VENTILATION OF MINES. This subject is divided naturally into (a) gases occurring in workings, explosive conditions, quantity of air, distribution of air, and (6) ventilating methods and machinery. THE ATMOSPHERE. Composition. Air consists chiefly of oxygen and nitrogen, with small and varying amounts of carbonic-acid gas, ammonia gas, and aqueous vapor. These gases are not chemically combined, but exist in a free state in uniform proportion, as follows: By Volume. By Weight. Nitrogen 79.3 77.0 Oxygen 20.7 23.0 TOOO 100.0 Wherever air is found, its composition is practically the same. Weight. The weight of 1 cu. ft. of air at 32 F. and under a barometric pressure of 30 in. is .080975 Ib. Air decreases in weight per cubic foot as we ascend in the atmosphere, and increases as we descend below the surface of the earth. 338 VENTILATION OF MINES. The weight of 1 cu. ft. of dry air at any temperature and barometric pressure is found by means of the formula = L3253 X B 459 + 1 ' in which w = weight of 1 cu. ft. of dry air; B = barometric pressure (inches of mercury); t = temperature (degrees F.). The constant 1.3253 is the weight in pounds avoirdupois of 1 cu. ft. of dry air at an absolute temperature of 1 F. and 1 in. barometric pressure. EXAMPLE. Find the weight of 1 cu. ft. of dry air at a temperature of 60 F. and a barometric pressure of 30 in. TABLE OP WEIGHT OF DRY AIR. Weight of 1 cu. ft. of dry air at different temperatures and barometric 1 S253 V B pressures, as calculated by the formula w = ^ . -- Temperature. Degrees F. t Weight of 1 Cu. Ft. of Dry Air (Lb. Avoirdupois). Barometer (In.). B = 27. Barometer (In.). B = 28. Barometer (In.). B = 29. Barometer (In.). B = 30. .07796 .08085 .08373 .08662 5 .07718 .08002 .08285 .08569 10 .07631 .07914 .08196 .08478 15 .07550 .07830 .08109 .08388 20 .07470 .07747 .08023 .08300 25 .07393 .07667 .07941 .08215 30 .07318 .07589 .07860 .08131 32 .07288 .07558 .07828 .08098 35 .07244 .07512 .07780 .08048 40 .07171 .07435 .07701 .07967 45 .07099 .07362 .07625 .07888 50 .07031 .07291 .07551 .07811 55 .06961 .07219 .07477 .07735 60 .06895 .07150 .07405 .07660 65 .06828 .07081 .07324 .07587 70 .06766 .07016 .07266 .07516 75 .06701 .06949 .07197 .07445 80 .06648 .06884 .07130 .07376 85 .06576 .06820 .07064 .07308 90 .06519 .06760 .07001 .07242 95 .06490 .06699 .06938 .07177 100 .06401 .06638 .06875 .07112 110 .06288 .06521 .06754 .06987 120 .06180 .06409 .06638 .06867 130 .06075 .06300 .06525 .06750 140 .05974 .06195 .06416 .06637 150 .05874 .06092 .06310 .06528 160 .05781 .05995 .06209 .06423 170 .05688 .05899 .06110 .06321 180 .05601 .05808 .06015 .06222 190 .05514 .05718 .05922 .06126 200 .05430 .05631 .05832 .06033 220 .05271 .05466 .05661 .05856 240 .05119 .05309 .05498 .05688 260 .04978 .05162 .05346 .05530 280 .04840 .05020 .05200 .05380 300 .04714 .04888 .05063 .05238 350 .04423 .04587 .04751 .04915 400 .04166 .04321 .04475 .04629 THE BAROMETER. 339 Atmospheric Pressure. The term barometric pressure is the pressure caused by the weight of the atmosphere above a given point. It is measured by the barometer, and this gives rise to the synonymous term barometric pressure, Atmospheric pressure is usually stated in pounds per square inch, while barometric pressure is stated in inches of mercury. Thus, at sea level, the atmospheric pressure under normal conditions of the atmosphere is 14.7 Ib. per sq. in., while the barometric pressure at the same level is 30 in. of mercury column, or simply 30 in. Barometric Variations. The pressure of the atmosphere is not constant, but is subject to fluctuations depending on the condition of the atmosphere. Besides these, there are fluctuations that are more or less regular and are called barometric variations. There is both a yearly and a diurnal, or daily, variation. Of these two, the more important and the more regular is the daily variation, in which the barometer attains a maximum height from 9 to 10 o'clock A. M., and a minimum about 4 o'clock p. M. Other maximum and minimum readings are obtained at 10 P. M. and 3 A. M., respectively; but these are not as pronounced as those occurring in the daytime. The daily barometric variations range from .01 to .08 in. Mercurial Barometer. This barometer is often called the cistern barometer; or, when the lower end of the tube is bent upwards instead of the mouth of the tube being submerged in a basin, it is known as the siphon barometer. The instrument is constructed by filling a glass tube 3 ft. long, and having a bore of | in. diameter, with mercury, which is boiled to drive off the air. The thumb is now placed tightly over the open end, the tube inverted, and its mouth submerged in a basin of mercury. When the thumb is withdrawn, the mercury sinks in the tube, flowing out into the basin, until the top of the mercury column is about 30 in. above the surface of the mercury in the basin, and after a few oscillations above and below this point, comes to rest. The vacuum thus left in the tube above the mercury column is as perfect a vacuum as it is possible to form, and is called a Torricelli vacuum, after its discoverer. There being evidently no pressure in the tube above the mercury column, and as the weight of this column standing above the sur- face of the mercury in the basin is supported by the pressure of the atmos- phere, it is the exact measure of the pressure of the atmosphere on the surface of the mercury in the basin. If the experiment is performed at sea level, the height of the mercury will be found to average about 30 in., at higher elevations it is less, while if we descend deep shafts below this level, it ; s greater. Roughly speaking, an allowance of 1 in. of barometric height is made for each 900 ft. of ascent or descent from sea level (see calculation of barometric elevations). A thermometer is attached to each mercurial barometer to note the temperature of the reading, as it is customary in all accurate work with this instrument to reduce each reading to an equivalent reading at 32 F., which is the standard temperature for barometric readings. A scale is provided at the top of the mercury column with its inches so marked upon it as to make due allowance for what is called the error of capacity. In other words, the inches of the scale are longer than real inches, since the level.of the mercury in the basin rises as it sinks in the tube, and vice versa. The" top of the mercury column is always oval, convex upwards, owing to capillary attraction, and the scale is read where it is tangent to this convex surface. Aneroid Barometer. This is a more portable form than the mercurial barometer. It consists of a brass box resembling a steam-pressure gauge, having a similar dial and pointer, the dial, however, being graduated to read inches, corresponding to inches of mercury column, instead of reading pounds, as in a pressure gauge. Within the outer case is a delicate brass box having its upper and lower sides corrugated, which causes it to act as a bellows, moving in and out as the atmospheric pressure on it changes. The air within the box has been partially exhausted, to render it sensitive to atmospheric changes. The movement of the upper surface of the box is communicated to the pointer by a series of levers, and the dial is graduated to correspond with the mercurial barometer. Calculation of Atmospheric Pressure. The weight of the mercury column of the barometer is the exact measure of the pressure of the atmosphere, since it is the downward pressure of the atmosphere that supports the mercury column, area for area; that is to say, the pressure of the atmosphere on 1 sq. in. supports a column of mercury whose area is 1 sq. in., and whose height is such that the weight of the mercury column is equal to the weight of the atmospheric column. Hence, since 1 cu. in. of mercury weighs .49 Ib., 340 VENTILATION OF MINES. the atmospheric pressure that supports 30 in. of mercury column is .49 X 30 = 14.7 Ib. per sq. in. In like manner, the atmospheric pressure correspond- ing to any height of mercury column may be calculated. It will be observed that the sectional size of the mercury column is not important, since it is supported by the atmospheric pressure on an equal area, but the calculation of pressure is based on 1 sq. in. Water Column Corresponding to Any Mercury Column. The density of mercury referred to water is practically 13.6; hence, the height of a water column corresponding to a given mercury column is 13.6 times the height of the mercury column. For example, at sea level, where the average barometric pressure is 30 in. of mercury, the height of water column that the atmos- Eheric pressure will support is 13.6 X f = 34 ft. This is the theoretical eight to which it is possible to raise water by means of a suction pump, but the length of the suction pipe should not exceed 75fc or 80$ of the theoretical water column. Calculation of Barometric Elevations. Such elevations, although approxi- mate, are useful for many purposes. The barometric readings are reduced to equivalent readings at the standard temperature of 32 F., and for deter- mining differences in elevation, the readings of two barometers should be taken, if possible, at the same time. It must not be supposed, however, that the barometer always reads the same for the same elevation at this tempera- ture. The temperature of the atmosphere has indeed very little effect on the atmospheric pressure, which is due to the weight of air above the point of observation, aerial currents, and other phenomena. In the more accurate determinations of vertical height or elevation by means of the barometer, the following formula is usually employed: R = reading of barometer (inches) at lower station; r = reading of barometer (inches) at higher station; T = temperature (F.) at lower station; t = temperature (F.) at higher station; H = difference of level in feet between the two stations. More simply: H = 49,000(1^) (l + g. = . [-49,000 (900 + T+ t) + 900 H~\ = r L49,000 (900 + T 4- 900 5J ' Correction for Temperature. Mercury expands about .0001 of its' volume for each degree Fahrenheit. To reduce, therefore, a reading at any tem- perature to the corresponding reading at the standard temperature of 32 F., subtract TTy ^ of the observed height for each degree above 32; or, if the temperature is below 32, add -^h for each degree. Thus, 30.667 in. at 62 F. is equivalent to a reading of 30.555 in. at 32 F., ff) 00 since 30.667 -^^(30.667) = 30.667 -.092 = 30.555 in. Depth of Shafts. The barometer is often employed to determine the depth of a shaft or the depth of any point in a mine below a corresponding point on the surface. The aneroid is employed for this work, being more portable. Allowance must always be made in such cases for the venti- lating pressure of the mine. A simple formula often used for such calcu- lations is the following: H = 55,000(1 --J.M, in which the letters stand for the same factors as designated above. The most important use of the barometer in mining practice, however is found in the warning that it gives of the decrease of atmospheric pressure, ' and the expansion of mine gases that always follows. CHEMISTRY OF GASES. 341 CHEMISTRY OF GASES. All matter exists in one of three forms, solid, liquid, or gaseous, according to the predominance of the attractive or the repulsive forces existing between the molecules. For example, water exists as ice, or in a solid form, when the attractive force exceeds the repulsive force between its molecules. As the temperature is raised or heat is applied, the ice assumes the liquid form due to the more rapid vibration of the molecules of which it is composed. In other words, the repulsive force existing between the molecules is increased, and the result is a liquid. If we still further raise the tempera- ture by applying more heat, the vibration of the molecules becomes yet more rapid, the repulsive force is increased between the molecules, and a gas or vapor called steam is formed. An atom is the smallest conceivable division of matter. A molecule is a collection of two or more atoms, united by affinity. The atom cannot consist of more than one element. The molecule may be either simple or compound. If compound, it is a chemical compound, its atoms being chemically united. Chemical Compounds. A chemical compound is one formed by the union of two or more atoms chemically, such atoms uniting always in fixed or definite proportions. The properties of a chemical compound are always the same. Mechanical Mixture. A mechanical mixture is composed of different sub- stances that are not chemically united, and which are mixed in no fixed proportion. The properties of a mechanical mixture present a regular gradation from a maximum to a minimum state. Thus, a solution of common salt NaCl in water is not a chemical compound of salt and water, but simply a mechanical mixture of the salt in the water. If more salt is added to the water, the strength of the mixture or the brine is increased; and when less salt is present, the strength is less. On the other hand, salt itself is a chemical compound formed by the union of 1 atom of sodium with 1 atom of chlorine, the two atoms being bound together by chemical affinity, and always uniting in the same proportion, 1 atom of each, to form salt. The air that we breathe is a mechanical mixture of nitrogen and oxygen gases, with small amounts of other ingredients. The nitrogen and oxygen gases are in a free state; that is to say, they are not combined as in a chem- ical compound. This is true, although the proportion of these two gases, oxygen and nitrogen, in the atmosphere, is uniformly in the ratio of; say, 1 volume of oxygen to 4 of nitrogen. Firedamp is another example of true mechanical mixture, consisting chiefly of a mixture of marsh gas CH^ and air, with small amounts of other hydrocarbons and a varying amount of carbonic-acid gas, which is always present in firedamp. These gases are not combined chemically, but are mixed in varying proportions. Atomic volume, or specific volume, means simply relative volume. These terms refer to the relative volume of gases resulting from any particular reaction. By means of the laws of atomic volume, we can ascertain the volumes of the different gases resulting from any particular reaction. The chemical reaction that takes place between the elements constituting the different gases is expressed by means of a chemical equation. When we have expressed such reaction by a chemical equation, we can then calculate the volumes of the gases formed, with respect to the original volumes of the gases entering into the reaction. It must be observed, how- ever, that the atomic volumes express merely the relative volumes of gases; or, in other words, the ratio of the volumes of gases before and after the reaction takes place. Laws of Volume. The following laws of volume refer to gases only, and never to solids or liquids: First. Equal volumes of all gases, under the same conditions of tempera- ture and pressure, contain the same number of molecules. Hence, the molecules of all simple gases are of the same size. Second. The molecules of compound gases, under like conditions of tem- perature and pressure, occupy twice the volume of an atom of hydrogen gas. There are very few exceptions to these two laws of gaseous volume, and the exceptions are unimportant so far as mining practice is concerned. An element is a form of matter that is composed wholly of like atoms. Thus, hydrogen, oxygen, iron, copper, gold, and silver are elements. Chemical Symbols and Equations. To facilitate the writing of chemical 342 VENTILATION OF MINES. equations expressing the reaction that takes place between elements under certain conditions, it is usual to express the elements by letters called symbols. These symbols stand for the elements that they represent, and are written as capital letters, except where two letters are used to express a symbol, in which case the first letter only is a capital. Thus, C is the symbol for the element carbon, but Cu is the symbol for copper (cuprum) and Co is the symbol for cobalt. It is important that these symbols be written exactly in this manner; otherwise they are liable to be frequently misconstrued. For example, Co stands for cobalt, while the symbol CO TABLE OF ELEMENTS. Element. 1 a OQ Al Sb A As Ba Be Bi B Br Cd Cs Ca C Ce Cl Cr Co Cb Cu D Er F Ga Ge Au He H In I Ir Fe La Pb Li Mg Atomic Weight. Element. 3 | Mn Mo Nd Ni Nb N Os Pel P Pt K Pr Rh Rb Ru Sa Sc Se Si Na Sr S Ta Te Tl Th Sn Ti W U V Yb Y Zn Zr Atomic | Weight. Aluminum Antimony (stibium) Argon(?) 27.5 120.0 75.0 137.0 9.4 208.0 11.0 80.0 112.0 133.0 40.0 12.0 138.0 35.5 52.5 59.0 93.7 63.0 147.0 169.0 19.0 69.0 196.7 1.0 113.4 127.0 193.0 56.0 139.0 207.0 7.0 24.0 200.0 Manganese 55.0 96.0 58.8 94.0 14.0 191.0 16.0 106.5 31.0 197.0 39.0 104.0 85.0 104.0 79.0 28.0 108.0 23.0 87.5 32.0 182.0 127.0 205.0 231.5 108.0 48.0 184.0 240.0 51.2 89.0 65.0 90.0 Molybdenum Neodymium(?) Arsenic Barium - ... Niobium Nitrogen Beryllium Bismuth Osmium Oxygen Boron Bromine Palladium Phosphorus. Cadmium Csssium Platinum Pottasium (kalium) Praseodymium(?) : Calcium Carbon Cerium .... Chlorine Rubidium Ruthenium Chromium Cobalt Samarium(?) Scandium Selenium Columbium Copper (cuprum) Didymium Silicon Erbium(') Silver (argentum) Sodium (natrium) Strontium Fluorine Gallium Germanium Sulphur Tantalum Gold (aurum) HeliumC') Tellurium Thallium Hydrogen Indium Thorium Tin (stannum) Titanium Tungsten (wolfram) ... Uranium Iodine Iridium Iron (ferrum) Lanthanum Lead (plumbum) Lithium Vanadium Ytterbium Magnesium Mercury ( hydrargy- rum) Yttrium Zinc Zirconium stands for carbonic-oxide gas, which is a chemical compound composed of two elements, carbon and oxygen A molecule is expressed by writing the symbols of its elementary atoms. Where more than 1 atom of a substance or element enters into the compo- sition of a molecule, the number of atoms of such element is expressed by a small subscript letter written immediately after the symbol of the element. Thus carbonic-acid gas is composed of 1 atom of carbon chemically united with '2 atoms of oxygen, and is expressed by the symbol (70 2 . Where the symbol is written without such subscript figure, 1 atom only is meant. Thus carbonic-oxide gas being composed of 1 atom of carbon chemically united to 1 atom of oxygen, is expressed by the symbol CO. CHEMISTRY OF GASES. 343 A large figure written before the symbols expressing the molecule indi- cates the number of molecules entering into the reaction. A large figure is sometimes used before the symbol of a single element to indicate the number of atoms of that element that enter the reaction. In any reaction occurring between atoms of matter, no matter is destroyed. In any reaction, there are always the same number of atoms after the reaction as before the reaction took place. A chemical equation is therefore an expression of equality between the atoms before and after a reaction takes place. The first member of the equation contains the substances that act upon each other, while the second member of the equation contains the substances that are formed by the reaction. The number of atoms is the same in each member of the equation. EXAMPLE. To express the reaction that takes place when carbonic- oxide gas burns in the air to produce carbonic-acid gas, we write CO + O + 4N = COz + N In this equation, each molecule of carbonic-oxide gas CO takes up 1 atom of the free oxygen of the atmosphere to form carbonic-acid gas COz. The nitrogen in the atmosphere being 4 times the volume of oxygen, is expressed as 4 atoms in the equation. This nitrogen, however, remains inactive, and takes no part in the reaction. It is written on both sides of the equation for the purpose of determining the atomic volumes of the gases before and after the reaction, as explained below. The reaction for an explosion of firedamp is CH* + 40 + 16^ = C0 2 + 2H 2 + IGN In this equation, each molecule of marsh gas CH 4 is dissociated; that is to say, its atoms are separated. The atom of carbon in the molecule unites with 2 atoms of the oxygen of the air to form carbonic-acid gas 6'0 2 . The 4 atoms of hydrogen, in like manner, combine with two atoms of oxygen in the air to form 2 molecules of water or steam 2 (H<>0), or 2H 2 0. The nitro- gen in this equation is equal to 4 times the volume of the oxygen consumed, and is therefore written as I6N, since a total of 4 atoms of oxygen have been used. The nitrogen is however inert, and plays no part in the reac- tion itself, but is written here on both sides of the equation, as in the previous equation, in order to properly represent the atomic volumes of the gases or their relative volumes before and after the reaction takes place. Calculation of the Relative Volumes of Gases. To calculate the relative volumes of the gases before and after the reactions expressed in each of the equations given in the preceding paragraphs, write beneath the symbol of each molecule or atom its atomic volume. In the chemical equation expressing the reaction that takes place when carbonic-oxide gas CO burns to carbonic-acid gas COz, we have as follows: CO + + 4JV = C0 2 + 4N Atomic volumes, 2+1+4= 2 + 4 or, in this reaction, 7 volumes have been reduced to 6 volumes. Such a change of volume often takes place in chemical reactions. All attempts to explain the cause of this change of volume, however, have thus far failed; but that the change of volume does take place has been demonstrated by a large number of experiments. To calculate the volume of air consumed in the complete explosion of 100 cu. ft. of carbonic-oxide gas CO, we write the ratio of the relative volumes of carbonic-oxide gas and air, which is 2 : (1 + 4), or 2 : 5; and to obtain the actual volume of air consumed in the explosion of 100 cu. ft. of carbonic- oxide gas, we write the proportion 2 : 5 : : 100 : x, or x = = 250 cu. ft. To find the volume of carbonic-acid gas CO 2 produced in the complete explosion of 100 cu. ft. of carbonic-oxide gas CO, write the ratio of the atomic volumes of these two gases 2 : 2, which shows no change of volume, and, therefore, the volume of carbonic-acid gas C0 2 produced will be the same as the volume of carbonic-oxide gas CO burned. To find the volume of air consumed in the complete explosion of 100 cu. ft. of marsh gas CH^ write the equation expressing the reaction that takes place in this explosion as given above, CH + 4O + 16N = COz + 2T 2 + 16A" Atomic volumes, 2 +4+ 16 =2+ 4+16 There is no change of volume caused by the explosion, since 22 volumes on one side of the equation produce, likewise, 22 volumes on the other side; or 22 volumes before the explosion produce 22 volumes after the explosion. 344 VENTILATION OF MINES. To find the volume of air consumed, we write the ratio of the atomic volumes of marsh gas and air 2 : (4 + 16), or 2 : 20, or 1 : 10; that is to say, roughly speaking, the amount of air consumed in the complete explo- sion of marsh gas is 10 times the volume of the marsh gas. This is not exact, however, as the volume of nitrogen in the air is 3.83 times the volume of oxygen. Making this correction, the volume of air consumed in the complete explosion of marsh gas is 9.66 times the volume of the gas. To determine the percentage of pure marsh gas in the above firedamp mixture (marsh gas and air), we write the ratio of the atomic volumes of these two, 2 : (2 + 4 + 15.32), or 1 : 10.66; and j^ X 100 = 9.38$ of CH. The volume of carbonic-acid gas formed in this reaction is equal to the volume of marsh gas consumed, and the volume of watery vapor is double the volume of marsh gas consumed; the total volume of gas and vapor formed by the reaction is the same as the original volume of marsh gas and air, or firedamp mixture, since the sum of the atomic volumes on each side of the equation is the same. Atomic weight is the relative weight of an atom of an element compared with an atom of hydrogen. Atomic weight is, then, not an absolute weight to be expressed in pounds, ounces, or any other denomination, but is simply relative weight. The atomic weight of each of the elements is given in the table on page 342. Molecular weight is the sum of the atomic weights of the elements forming the molecule, taking the atomic weight of each element as many times as there are atoms of that element in the molecule. A molecule of water is composed of 2 atoms of hydrogen and 1 atom of oxygen, and as the atomic weight of hydrogen is 1 and that of oxygen 16, the molecular weight of water is (2 X 1) + 16 = 18. In the same manner, since a molecule of marsh gas Cff 4 is composed of 4 atoms of hydrogen and 1 of carbon, and the atomic weight of hydrogen is 1 and that of carbon 12, the molecular weight of marsh gas is (4X 1) + 12 = 16. The density of a gas is the weight of any volume compared with the weight of the same volume of hydrogen or some other standard. The density of a gas is constant at all temperatures and pressures, the change of temperature and pressure affecting the gas in question and the standard alike. The density of air referred to hydrogen is 14.38. (a) The density of any simple gas, referred to hydrogen as unity, is equal to its atomic weight, (b) The density of any compound gas, referred to hydrogen as unity, is one-half of its molecular weight. Specific Gravity of Gases. The specific gravity of a gas is the weight of that gas referred to the weight of a like volume of air as a standard. It is, in other words, the ratio between the weight of like volumes of any gas and air, both the air and gas being subject to the same temperature and pressure. Thus, since the weight of 1 cu. ft. of air at a temperature of 60 F. and 30 in. barometric pressure is .0766 lb., and the weight of 1 cu. ft. of carbonic-acid gas C0 2 is .11712 lb. at the same temperature and pressure, the specific gravity of carbonic-acid gas is ' = 1.529. Weight of Gases. The weight of 1 cu. ft. of any gas at any given tempera- ture and pressure is found by first calculating the weight of 1 cu. ft. of dry air at the same temperature and pressure by means of the formula given on page 338 for air, and then multiplying this weight by the specific gravity of the gas referred to air as a standard. EXAMPLE. To determine the weight of 1 cu. ft. of carbonic-acid gas at a temperature of 60 F., and 30 in. barometric pressure, we multiply the weight of 1 cu. ft. of dry air, at this temperature and pressure, as found above (.0766 lb.), by the specific gravity of carbonic-acid gas (1.529). Thus, .0766 X 1.529 = .11712 lb. The table on page 349 gives the specific gravity of the gases common in mining practice, referred to air as a standard. Expansion of Air and Gases. All air and gases expand uniformly at the same rate. The expansion and contraction of air and gases follow two simple laws that we will consider under the heads (a) Ratio of volume and absolute temperature and (6) Ratio of volume and absolute pressure. Absolute temperature means the temperature as reckoned from absolute zero, which is the point on the temperature scale below which it is assumed that no substance can exist in a gaseous state. The absolute zero of the PRESSURE. 345 Fahrenheit scale is assumed in mining practice as 459 below zero. Hence, the absolute temperature corresponding to any common temperature is found by adding 459 to the common temperature. Thus, the absolute temperature corresponding to 60 F. is 459 + 60 = 519. Absolute Pressure. The term absolute pressure refers to the total pressure supported by air or gas; i. e., the pressure above a vacuum. Gauge pressure is the pressure above the atmosphere. Absolute pressure is always the atmospheric pressure plus the gauge pressure. If a gauge pressure on a boiler indicates 60 Ib. per sq. in., the absolute pressure supported by the steam in the boiler will be 60 + 14.7 = 74.7 Ib. per sq. in. Or, if the ventila- ting pressure in a mine is equal to 13 Ib. per sq. ft., the absolute pressure supported by the air in the airways will be 13 + (14.7X144) = 2,129.8 Ib. per sq. ft. Relation of Volume and Absolute Temperature (Charles' or Gay Lussac's law). The volume of any air or gas varies directly as its absolute temperature. Relation of Volume and Absolute Pressure (Boyle's or Mariotte's law). The volume of any air or gas varies inversely as the absolute pressure it supports. For example, if we double the absolute pressure supported by air or gas, the volume of the air or gas will be reduced to one-half its original volume; if we multiply the absolute pressure 3 times, we reduce the volume to one- third the original volume; etc. EXAMPLE. The intake current of a mine is 50,000 cu. ft. of air per minute; the ventilating pressure is 13 Ib. per sq. ft. The temperature of the intake is 20 F.; the temperature of the return air is 70 F. Calculate the volume of the return air-current per minute, according to the rules of expansion of air, due to the increase of temperature and decrease of pressure, in the return current. The increased volume of the return air, due to the decrease of pressure and increase of temperature, is found by writing a compound proportion, the first member of which consists of two ratios, viz., the direct ratio of the absolute temperatures, and the inverse ratio of the absolute pressures, accord- ing to the two laws stated above. That is, we write (459 + 20) : (459 + 70) ) . . , n nnn . _. 2,116.8 : 2,129.8 / ' ' 50 ' 000 ' x ' Or x - 529 X 2 ' 129 ' 8 X 50 ' 00 - 55 558 cu ft r ' ^~~ 55 ' 558 EXAMPLE. In a compressed-air plant, the gauge shows a pressure of 80 Ib. per sq. in.; the area of the piston is 20 sq. in., and its stroke 10 in. The pump makes 100 strokes per minute. Assuming there is no leakage of air past the piston, what will be the volume of air discharged from the pump into the mine per minute ? The volume of air discharged from the pump cylinder per minute = 11.57 eu. ft. (cylinder pressure). The absolute pressure 1, / 2o on the air in the cylinder is 80 + 14.7 = 94.7 Ib. The absolute pressure on the discharged air is simply the atmospheric pressure (14.7 Ib.). Hence, we QA n write the proportion 14.7 : 94.7 : : 11.57 : x; or, x = -~ X 11.57 = 74.54 cu. ft. per minute, nearly. In calculating the expanded volume of air or gas, it will be observed that the ratio of the original volume to the expanded volume is always equal to the product of the direct ratio of the absolute temperatures and the inverse ratio of the absolute pressures, which gives a compound proportion, the first member of which consists of two ratios, the one a direct ratio and the other an inverse ratio. Weight Produces Pressure. In the study of the barometer as a means of measuring atmospheric pressure, we observe that the weight of the atmos- phere produced the atmospheric pressure. In like manner, the weight of all fluids produces pressure, and this pressure acts equally in all directions. This is an important consideration in the study of mine ventilation, since it has given rise to the measurement of pressure by air or motive columns. Calculation of Pressure. An air column, or motive column, in ventilation, is a column of air having a base of 1 sq. ft., and of such height that its weight shall be equal to any given pressure. To calculate the height of air column corresponding to any given pressure, divide the pressure in pounds per square foot by the weight of 1 cu. ft. of the air. Mine pressure is also 346 VENTILATION OF MINES. measured by the water column that it will support, as in the water gauge, or by the mercury column, as in the barometer. In the measurement of pressure by means of the water column, the weight of the water column must be equal to the pressure, area for area. Since the weights of these columns are proportional to their sectional areas, it makes no difference what this area may be, the weight of the column calculated for a sectional area of 1 sq. in. will equal the pressure per square inch that supports the same. Hence, since 1 cu. in. of mercury weighs .49 lb., .49 X 30 = 14.7 lb. is the atmospheric pressure corresponding to a height of 30 in. of mercury, or, as we say, 30 in. of barometer. If we consider a cubical box, as shown in the accompanying figure, holding exactly 1 cu. ft. of water, and assume the weight of the water to be 62.5 lb., as is usual in practice, and divide the bottom of the box into 144 sq. in., as shown in Fig. 1, we - , observe: FIG. 1. (a) The pressure of the water on the bottom of the box is equal to the weight of the water, 62.5 lb.; that is to say, the pressure per square foot due to 1ft. of water column is 62.5 lb. (b) The pressure on the bottom of the box, when the water is only 1 in. deep, is equal to the weight of a layer of water 1 in. thick, or -r^- = 5.2 lb.; or, the pressure per square foot due to 1 in. of water column is 5.2 lb. (c) The pressure per square inch on the bottom of the box is equal to the weight of a prism of water 1 ft. high, and having a base of 1 sq. in. j-j- = .434; or, the pressure per square inch due to 1 ft. of water column is .USU lb. These principles relating to the pressure of fluids are important to the student of mining, of which the following are examples: 1. In a mountainous country, several thousand feet above sea level, where the barometer registers, say, only 21 in., it is desired to know the theoretical height a pump will draw. .49 X 21 = 10.29 lb. atmospheric pressure, and ' = 24 ft., nearly. The theoretical suction, in this instance, is 24 ft., nearly, but the actual draft or suction would vary from f to | of this, according to the perfection of the pump. 2. The water-gauge reading between the intake and return airways of a certain mine is 2.5 in.; to determine the pressure per square foot, we have, 2.5 X 5.2 = 13 lb. per sq. ft. 3. To determine the pressure per square foot on a mine dam, due to a vertical head of 200 ft., 62.5 X 200 = 12,500 lb. 4. To express in air column or motive column, a mine pressure equivalent to a water-gauge reading of 3 in., assuming the temperature of the air to be 60 F. and the barometric pressure 30 in., we have for the weight of 1 cu. ft. of air at this temperature and pressure w = = .0766 lb. The pressure per square foot due to 3 in. of water gauge is 3 X 5.2 = 15.6. Then, we have for motive column, m = - '- = 204 ft. .0/66 Diffusion and Transpiration of Gases. Diffusion of gases means the mixing of the gaseous volumes. Graham took several glass tubes, and inserting in one end of each a plug of plaster of Paris that was porous, he filled each tube with a different gas; as for example, oxygen, hydrogen, nitrogen, etc. He then placed the open end of each inverted tube in a basin of mercury, supporting the tubes in an erect position. The gas in each tube immedi- ately began to diffuse through the porous plaster plug into the atmosphere, and it was observed that the mercury rose in each tube to take the place of the gas that passed into the atmosphere. The mercury rose in the hydrogen tube 4 times as fast as in the oxygen tube, and in the other tubes the mer- cury rose at different rates. Rate of Diffusion (Graham's Law). The rate of diffusion of gases into air is DIFFUSION OF GASES. 347 in the inverse ratio of the square roots of their densities. The density of oxygen being 16 and hydrogen 1, the rate of diffusion of oxygen as compared with hydrogen is 1 to 4; that is to say. the rate of diffusion of oxygen is only one-fourth that of hydrogen. TABLE SHOWING THE CORRESPONDING MERCURY AND AIR COLUMNS, AND PRESSURE PER SQUARE FOOT FOR EACH INCH OF WATER COLUMN. & It O,c Column, hes. d l g l So- ^ ' J3CO & g* 0^ Column, hes. I* I! II 5" rO Si "5 S glrH K <5 i> * M 8 1 ^ r g 3 ., 1 .0735 68 5.2 6 .4412 407 31.2 2 .1471 136 10.4 7 .5147 475 36.4 3 .2206 204 15.6 8 .5882 543 41.6 4 .2941 272 20.8 9 .6618 611 46.8 5 .3676 340 ; 26.0 10 .7353 679 52.0 TABLE SHOWING THE CORRESPONDING WATER COLUMN, AND PRESSURE PER SQUARE FOOT FOR EACH INCH OF MERCURY COLUMN. Barometer. Water Column. Pressure. Barometer. Water Column. Pressure. Inches. Feet. Lb. per Sq. In. Inches. Feet. Lb. per Sq. In. 1 1.13 .49 16 18.13 7.84 2 2.27 .98 17 19.27 8.33 3 3.40 1.47 18 20.40 8.82 4 4.54 1.96 19 21.53 9.31 5 5.67 2.45 20 22.67 9.80 6 6.80 2.94 21 23.80 10.29 7 7.93 3.43 22 24.93 10.78 8 9.06 3.92 23 26.07 11,27 9 10.20 4.41 24 27.20 11.76 10 11.33 4.90 25 28.33 12.25 11 12.46 5.39 26 29.47 12.74 12 13.60 5.88 27 30.60 13.23 13 14.73 6.37 28 31.73 13.72 14 15.87 6.86 29 32.87 14.21 15 17.00 7.35 30 34.00 14.70 NOTE. One foot of water column is equivalent to a pressure of .434 Ib. per sq. in. The weight of air at 60 F., barometer 30 in., is ^ the weight of water; but the ratio of air to water is often assumed as 1.2 : 1,000, for quick calculation. The specific gravity of mercury at 32 F. (standard tempera- ture for barometric readings) is 13.62; and a cubic foot of mercury at this temperature weighs 849 Ib. For ordinary calculation, the weight of 1 cu. ft. of water is taken as 62.5 Ib. The exact weight of 1 cu. ft. of pure water, at a temperature of 32 F., is, however, 62.418 Ib. The diffusion of marsh gas (Sp. Gr. .559) is much more rapid than that of carbonic-acid gas (Sp. Gr. 1.529). The diffusion of gases, however, is greatly assisted by the movement of the air-current; or by the movement of the gas as it tends to rise or fall, according to its relative density and position in the airway. For example, suppose a gas feeder to be located in the floor of an airway. The marsh gas given off from the feeder, being lighter than air, 348 VENTILATION OF MINES. tends to rise toward the roof. The action of rising helps a diffusion of this gas very much. On the other hand, a feeder located in the roof gives off the same gas, which tends to accumulate along the roof, and if the air-current is at all sluggish at this point, the diffusion of the marsh gas will be compar- atively slow. It often happens that a feeder in the roof or other high point of the workings gives off gas more quickly than diffusion can take place, where the air-current is sluggish. This results in the accumulation of a body of pure marsh gas at this point. In like manner, we often have an accumulation of a large body of carbonic-acid gas, or blackdamp, near the floor or other low place in the mine workings, where the air-current is sluggish and where the blackdamp is formed quicker than diffusion takes place. Limit of Diffusion. The diffusion of gases continues to take place until the mixture of the gases is uniform. It is a curious fact that this takes place earlier or quicker in the case of gases whose densities differ widely, than where the densities 9f the two gases are nearly alike. Thus, saturation will take place more quickly in the diffusion of carbonic-acid gas into air than in the diffusion of firedamp into air, although the rate of diffusion of the latter is greater than of the former, firedamp being lighter than carbonic-acid gas. The property of diffusion is of the greatest importance in the ventilation of mines, since it is owing to this that the air-current is enabled to sweep away these gases from their lurking places in the workings more rapidly and effectually than it otherwise could. Transpiration of gases is the exuding of the gases from the pores of the coal in which they are contained. It is a well-known fact that transpiration takes place more rapidly from a newly exposed face of coal. This is owing to the fact that the gas pent up in the coal, or occluded in the seam, tends to escape at the first opportunity, when the seam is exposed to the atmos- phere. The gas is under a certain pressure, as we have previously observed, and, as the mine workings penetrate the coal seam, the gases are forced outward from the coal by their own pressure, thus expanding into the air of the mine. The transpiration of gas from coal seams differs very widely, in some seams it being so rapid and violent as to splinter and break the coal in its effort to escape. It frequently causes a crackling sound peculiar to a very gaseous seam, and in some cases, causes fine coal to be thrown into the face of the miner. GASES FOUND IN MINES. Oxygen is a colorless, odorless, tasteless, non-poisonous gas. It is heavier than air, having a specific gravity of 1.1056. It is the great supporter of life and combustion. Oxidation, or the union of any of the elements with oxygen, is simply another term for combustion in its broadest sense. Most forms of matter containing carbon are easily decomposed at certain temper- atures, through carbon seeking to combine with the oxygen of the air to form carbonic-acid gas C0 2 . This union of the oxygen with other elements, or oxidation, takes place at all temperatures. It is less active when the temperature is low, and is then known as slow combustion. An example of this is found in the gob fires that occur so frequently in mine workings. The fine coal that is so often thrown back into the gob is acted on first by moisture, and as its temperature rises, carbonic-oxide gas is formed in small quantities by the union of the carbon of the coal with the oxygen of the air; as the temperature rises, more gas is formed. Heat is caused by the chemical action due to the interchange of the atoms, this heat being often sufficient to ignite the gas formed, spontaneous or active combustion resulting. Oxygen is the element in the atmosphere on which all life depends. Nitrogen N is a colorless, odorless, and tasteless gas; it is neither combus- tible nor a supporter of combustion; it is not poisonous, and is lighter than air, having a specific gravity of .9713. Nitrogen is a particularly inert gas; it takes no active part in any combustion, in the sense of causing such com- bustion. Its province is to dilute oxygen of the atmosphere, on which life depends. Were it not for this dilution, oxidation would be too rapid, and not as completely under control as at present. The effect of nitrogen on human life would be to suffocate, if breathed pure, inasmuch as it would exclude oxygen from the lungs. Nitrogen itself has no life-giving power. Marsh gas CH 4 , often called light carbureted hydrogen, or methane, is a chemical compound, consisting of 4 atoms of hydrogen to 1 atom of carbon. GASES FO UXD MIXES. 349 It is one of the chief gases occluded in coal seams, and results from the metamorphism of the carbonaceous matter from which coal is formed, when such metamorphism has taken ' of water. Pure marsh gas is than air. Its specific gravity is ._, a firedamp mixture. Marsh gas burns with a blue name, but it will not support combustion, and a lamp placed in it is immediately extinguished. In the mine, it is a difficult matter to pla^e a lamp in a body of pure marsh gas, since the gas diffuses so rapidly that a firedamp mixture always sur- rounds a body of pure gas, which may exist high up in some cavity of the roof, or at the face of a steep pitch where the circulation is slow and the feeder at the face is giving off a large amount of gas. The naming of the lamp in passing through a nredamp mixture would at once cause the withdrawal of the lamp before reaching the body of pure marsh gas. But could a lamp be placed in a body of pure marsh gas, it would be extinguished at once. Marsh gas is not poisonous, and when mixed with air in sufficient proportion, it may be breathed for a considerable time with impunity (see Firedamp) . Pure marsh gas does not support life, but suffocates by exclu- ding oxygen from the lungs. Other Hydrocarbons. All gases that are compounds of carbon and hydrogen are called hydrocarbons. Of these, the. chief member is marsh gas, or light carbureted hydrogen, described in the preceding paragraph; the other hydrocarbons'are called heavy hydrocarbons. The chief of these are olefiant gas C 2 Hi, and ethane Q>HQ. Both of these gases, like marsh gas, are the result of the metamorphism of carbonaceous matter, during the formation of the coal, but unlike marsh gas, they have been produced in the absence of water, and as a result they contain a larger percentage of carbon than marsh gas. They afways exist in common with marsh gas, as occluded gases in coal seams, but to a far less extent. Each of these gases possesses a higher illuminating power, burning with a brighter flame than marsh gas. This is due to the larger percentage of carbon present in their composition. Their remaining properties are very similar to the properties given for marsh gas; they, however, when present in a nredamp mixture, lower the temperature of ignition, and render the mixture more dangerous than it would be otherwise. Constants for Mine Gases. The following table shows the symbols, specific gravities, and relative velocities of diffusion and transpiration of the principal mine gases, arranged in the order of their specific gravities, air being taken asl. The values given in the next to the last column of this table were obtained by experimenting with the gases, and agree quite closely with the calculated values given in the preceding column. From this column we see that 1,344 volumes of marsh gas will diffuse in the same time as 1,000 volumes of air, or 812 volumes of carbonic-acid gas. TABLE OF MINE GASES. Name of Gas. Symbol. Specific Gravity. J/SpTGr. Relative Velocity of Diffusion. (Air = 1.) Relative Velocity of Transpiration. (Air = 1.) Air 1.00000 1 0000 1.000 1 0000 Carbonic acid Sulphureted hy- drogen CO, 1.529 1.1912 .8087 .9162 .812 .95 1.2371 Oxygen Olefiant Nitrogen Carbonic oxide ... Steam Marsh gas Hydrogen CO H* 1.1056 .978 .9713 .967 .6235 .559 .06926 .9510 1.0112 1.0147 1.0169 1.2664 1.3375 3.7794 .9487 1.0191 1.0143 1.0149 1.344 3.83 .903 1.788 1.0303 1.034 1.639 2.066 Carbonic-oxide gas CO. often called ichitcdamp, is a chemical compound consisting of 1 atom of carbon united to 1 atom of oxygen. To a certain 350 VENTILATION OF MINES. extent it occurs as an occluded gas in coal. It is chiefly formed, however, in coal mines, by the slow combustion of carbonaceous matter in the gobs or waste places of the mine, where the supply of air is limited. It is al ways the product of the slow combustion of carbon in a limited supply of air. It is therefore one of the chief products of gob fires, and is also a product of the explosion of powder in blasting. This gas often fills the crevice made behind a standing shot, and causes the Hash that takes place when the miner puts his lamp behind such shot to examine the same. This gas is formed in large quantities whenever the name of a blast or explosion is projected into an atmosphere in which coal dust is suspended. The force of a blast often blows the dust into the air, and the flame acting on it distils carbonic-oxide gas. Carbonic-oxide gas is lighter than air, having a specific gravity of .967, and it therefore accumulates near the roof and in the higher working places. It is colorless, odorless, and tasteless. It is combustible, burning with a light-blue flame. This is the flame often seen over a freshly fed anthracite fire. It is also a supporter of combustion, being the only mine gas that burns and also supports combustion. This property leads to very important results in mines, inasmuch as it lengthens the flame of a lamp or the flame of a blast. Any flame is fed by this gas, and is thereby transmitted through the mine airways, from one point to another. The same property extends very widely an otherwise local explosion. This gas has the widest explosive range of any gas known to mining, except hydrogen. The effect of its presence in firedamp mixtures is always to widen the explosive range of the firedamp, causing it to become explosive in larger and smaller proportions than it otherwise would. Carbonic-oxide gas is a very poison- ous gas, and acts on the human system as a narcotic, producing drowsiness or stupor, followed by acute pains in the head, back, and limbs, and after- ward by delirium. It acts, when breathed into the lungs, to absorb the oxygen from the blood, or, in other words, poisons the blood. Carbonic-oxide gas is detected in mine workings by its effect on the flame of a lamp, which burns more brightly in the presence of the gas, and reaches upwards as a slim, quivering taper, having often a pale-blue tip that, however, is not readily observed. Carbonic-acid gas CO*, often called blackdamp or chokedamp, is a chemical compound consisting of 1 atom of carbon united to 2 atoms of oxygen. It is heavier than air, having a specific gravity of 1.529. It therefore accumulates near the floor or in the low places of the mine workings. It is always the result of the complete combustion of carbon in a plentiful supply of air, and is a product of the breathing of men and animals, burning of lamps, or any other complete combustion. It is always present in occluded gases. Carbonic-acid gas is a colorless, odorless gas, but possesses a peculiarly sweet taste, which may be detected in the mouth when it is inhaled in large quantities. It is not combustible, nor is it a supporter of combustion. Lamps are at once extinguished by it. It diffuses slowly into the atmosphere, and is a difficult gas to remove in ventilating. It is not poisonous, but acts to suffocate by excluding oxygen from the lungs. Its effect, when breathed for any length of time, is to cause headache and nausea, followed by weak- ness and pains in the back and limbs; when present in larger quantities, it causes death by suffocation. This gas, when present in firedamp mixtures, has the opposite effect from, that of carbonic-oxide gas, inasmuch as it narrows the explosive range of the firedamp, and renders such mixtures inexplosive, which would otherwise be explosive (see Firedamp). Carbonic-acid gas is detected in the mine air by the dimness of the lamps and by their extinguishment when present in larger quantities. It should always be looked for at the floor, and in low places of the mine workings. Sulphureted hydrogen H Z S occurs at times as an occluded gas in coal seams, but more often exudes from the strata immediately underlying or over- lying those seams. It is generally supposed to be formed by the disintegra- tion of pyrites in the presence of moisture. It is heavier than air, having a specific gravity of 1.1912. It is a colorless gas, having a very disagreeable odor resembling that of rotten eggs, and is known to the miners as stinkdamp. It is an exceedingly dangerous gas when occurring in considerable quan- tities. When mixed with 7 times its volume of air, it is violently explosive. It is extremely poisonous, acting to derange the system when breathed in small quantities, and, when inhaled in larger quantities, it produces unconsciousness and prostration. Its smell serves as the best means for its detection. GASES FOi'XJ) IX MIXES. 351 Firedamp. The general term firedamp relates to any explosive mixture of marsh gas and air, although in some localities this term is understood as referring to any mixture of marsh gas and air whatever, whether explosive or otherwise. Many persons speak of pure marsh gas as firedamp. The first meaning given above, however, is the general acceptation of the term. Pure marsh gas when present in small quantities in the air burns in the flame of the lamp without explosion. As the quantity of the gas is increased, the effect on the flame of the lamp is at once noticeable. As the proportion of gas in the air is further increased, and approaches the lower explosive limit, the lamp flame enlarges, snaps, and crackles. When the proportion of gas to air is 1 to 13, slight explosions occur within the lamp, the flame of the lamp jumping violently. As the proportion of gas is increased, the violence of the explosion is augmented until it reaches a maximum, when the proportion of gas to air is 1 to 9 (exactly, 1:9.38). This is the proportion of gas and air in firedamp, when at its maximum explosive violence. From this point, as the quantity of gas is still further increased, the violence of the explosion decreases, until it becomes very feeble when the proportion of gas and air is 1 to 5i, and ceases altogether beyond this point. The explosive limits of marsh gas, or the limits of fire- damp mixtures, are then as follows: Lower limit, 1 volume of gas to 13 volumes of air; higher limit, 1 volume of gas to 5 volumes of air. These limits refer to pure firedamp, or, in other words, a firedamp mixture con- sisting of pure marsh gas and air. It rarely happens that firedamp, as found in mine workings, is pure, but contains admixtures of other gases, such as carbonic-acid gas C0 2 , carbonic- oxide gas CO, and heavy hydrocarbons. Afterdamp. The term afterdamp relates to the gaseous mixture that exists in mine workings after an explosion of gas. The composition of afterdamp is exceedingly variable, and admits of no general analysis that can be applied with certainty to any one explosion. The conditions that obtain in an explosion are so manifold, and control so completely the character of the gases formed, that it is impossible to give more than a general analysis of afterdamp. The chief products of the complete explosion of pure firedamp are car- bonic-acid gas, watery vapor, and nitrogen (see page 343). The explosion of firedamp is seldom, however, complete. Where a large body of gas has exploded, the air-current in the mine workings does not furnish sufficient air for the complete combustion of the firedamp, and as a result, a large amount of carbonic-oxide gas is formed, and is present in the afterdamp of the explosion. The presence of this gas (CO) renders the afterdamp far more dangerous than it would otherwise be, for two reasons: The gas itself is very poisonous, and its presence is not at once detected by the zealous men that are working to rescue their fellow workmen. The lamps burn very brightly in this gas, and the rescuers press forward unconscious of their real danger until overcome by the effects of the gas. The presence of coal dust in suspension in the mine air at the time of the explosion, or thrown into the air by the force of the explosion, results at once in the production of a large amount of carbonic-oxide gas. It is a well-known fact, also, that carbonic-acid gas CO?, formed as a direct product of the explosion, or which may be present in the mine air before the explosion, coming in contact with the incandescent carbon of the coal dust, is converted by it, at the high temperature of the flame, into carbonic-oxide gas CO. We observe, there- fore, that an explosion, in all its effects, tends to the rapid and abundant production of this most dangerous gas. The other products of an explosion are numerous, but for the larger part, unimportant, except as they do not support life. We have mentioned and described only those gases forming the larger portion of the afterdamp, or constituting the active agents in an explosion. Occurrence of Gases in Mines. Most of the gases occurring in mines are occluded in the coal or the strata adjacent to the coal seam. These occluded gases differ widely in different coals, but are chiefly marsh gas with varying quantities of heavy hydrocarbons (olefiant gas, ethane, etc.) and carbonic- acid gas to a limited extent. In some coals, a large percentage of nitrogen gas is occluded, which, however, transpires very slowly into the atmosphere. Sulphureted hydrogen, when present, usually exudes from the underlying or overlying strata of the coal seam. These occluded gases are the result of coal formation, according to the best authorities and evidence. They exist in the pores of the coal under considerable pressure due to the weight of the 352 YEN TIL A TION OF MINES. superincumbent strata. When the strata adjacent to the coal seam are impervious to gases, the occluded gases remain pent up, and we have what is called a gaseous seam. The tendency of the gas is always to escape to the surface or into the mine workings, at the first opportunity. These gases have each their separate effects, and their combined effect is sometimes very complicated. We can only study to become familiar with the separate characteristics of each of these gases, and judge of their com- bined effect when present in firedamp mixtures. For example, one effect of all these gases when present in firedamp mixtures is to dilute the firedamp, and to that extent weaken its explosive force. Dilution of the firedamp by carbonic-acid gas CO? decreases very rapidly the explosiveness of the fire- damp. When carbonic-acid gas is present in firedamp to the extent of one- seventh its volume, explosion ceases altogether; in other words, the firedamp is rendered inexplosive. The effect of smaller quantities of this gas is to contract the explosive limits of the firedamp as well as to weaken the explosion. The effect of carbonic-oxide gas CO when present in fire- damp mixtures is likewise to dilute the firedamp. The flame, however, is lengthened by this gas, and the explosive limits of the firedamp mixture are widened. In other words, mixtures of marsh gas and air, which were not explosive mixtures, are rendered explosive by the presence of carbonic- oxide gas. The chief source of the other mine gases lies in the slow combustion of carbonaceous matter in the gob, gob fires, burning of lamps, breathing of men and animals, etc. The table on page 353 shows the percentage of occluded gases in a number of coals and their volume at normal temper- ature and pressure. Gas Feeders (Pockets). The occluded gas of a coal seam escapes when- ever opportunity is offered, and accumulates in the pockets and crevices of the adjoining strata, forming what are called gas feeders. These consti- tute a very dangerous element in the mining of gaseous seams, inasmuch as when such a crevice or feeder is tapped by the miner's drill, the gas, which is usually under heavy pressure, blows out in a large volume, at times even blowing *the drill from the hole. Pressure of Occluded Gases. Occluded gases exist under a pressure that is proportionate to the weight of the overlying strata. Numerous experiments in England, France, and Belgium show that the pressure of gases occluded in coal seams frequently amounts to from 10 to 16 atmospheres, and in some cases has reached 32 atmospheres. These high pressures of occluded gases manifest themselves frequently in the boring of gas wells, where the tools are at times blown from the bore hole. PRESSURE OF OCCLUDED GAS. - Name of Mine. Depth of Hole. Feet. Pressure. Pounds. Elmore mine, main bed Hetton mine, Hutton bed Eppleton mine, Hutton bed... Balden mine, Benshambed... Harris Navigation mine Merthyr Vale mine Celynen mine 8.53 8.98 46.90 31.85 32.80 49.20 5448 4.36 6.96 36.14 71.41 22.04 39.67 6832 Harton mine (1,214 ft. deep) Harton mine . 16.24 27.55 196.30 23044 Harton mine 37.13 294.45 Amount of Gas. Experiments made by the Prussian Firedamp Commission have given results varying from 357 to 2,400 cu. ft. of gas liberated per ton of coal mined. Mr. Chesneau gives 1,377 cu. ft. at the Herin mine, Anzin. Experiments at the Ronchamp mines give 883 cu. ft. Outbursts of gas are frequent occurrences in some coal seams. They are caused by the occluded gas' finding its way to a vertical crevice or cleat in the GASES FOUND IX MINES. 353 GASES ENCLOSED IN THE PORES OF COAL AND EVOLVED IN VACUO AT 212 F. ( Thomas.) Name of Colliery. Quality. C0 2 CHi N Quantity. c. c. per 100 Grams. -Cu. Ft. per Short Ton. Navigation Steam. Steam. Steam. Steam. Anthracite. Anthracite. Bituminous. Bituminous. Bituminous, 13.21 5.46 18.90 9.25 2.62 14.72 36.42 5.44 22.16 .49 .44 1.02 .34 .80 1.05 6.09 81.64 84.22 67.47 86.92 93.13 84.18 63.76 2.68 4.66 9.88 12.61 3.49 4.25 1.10 62.78 29.75 69.07 250.0 218.0 147.0 375.0 555.0 600.0 55.9 55.1 24.0 80 70 47 120 178 192 18 18 8 Dunraven Cyfarthfa .*. Bute Bonville's Court Watney's Plymouth Iron Works Cwm Clydach Bettwys GASES ENCLOSED IN THE PORES OF COAL AND EVOLVED IN VACUO AT 212 F. (IT. LeChatellier.) Locality. CH 4 C0 2 N Analyst. Dunraven mine (blowers) Dunraven mine (bore hole) Gars wood, mine 96.70 96.50 8416 .47 .44 86 2.79 3.02 12.30 265 J. W. Thomas. J. W. Thomas. W. Kellner. Gars wood mine (blowers) Glamorgan mine (blowers) Dombranmine (blowers) Karwin mine 88.86 93.01 95.11 94.59 .41 .27 .48 .18 8.90 5.94 4.07 4.48 1.83 .78 .34 .75 W. Kellner. W. Kellner. ( Austrian Firedamp ( Commission. Karwin mine (blowers) Hruschau mine 99.10 7916 .20 19 .70 1704 61 Hruschau mine (blowers) Peterswald mine (blowers) Segen Gottes mine Segen Gottes mine ( bore hole ) Liebe Gottes mine (borehole) 87.93 90.00 83.51 87.16 77.69 .83 .15 1.17 1.11 3.77 10.25 9.25 15.02 11.73 18.48 .99 .60 .30 .06 Sauer. Sauer. Sauer. GASES ENCLOSED IN THE PORES OF COAL AND EVOLVED IN VACUO AT 212 F. ( Schondorff. ) Locality. Cfli C 2 #6 H C0 2 N+0 Blowers. Bonifacius mine at Kray (Essen) Consolidation mine at Schalk ( Westphalia) Konig mine at Neunkirchen (Saarbruck) 90.94 89.88 84.89 1.62 1.40 5.84 .30 .67 .65 7.36 3.61 12.84 Oberkirchen mine at Schaumburg f 60.46 \93.66 37.64 .88 2.11 2.56 .63 4.80 Cavities in the roof. Lothringen mine at Castrop (Westphalia) 27 95 1.35 .45 70.25 New Iserlohn mine at Lawgendren (West- f 4.75 .09 1.34 65.00 phalia) \ 400 06 .40 95.00 354 VENTILATION OF MINES. FIG. 2. coal seam, as illustrated in Fig. 2, and the pressure of the gas thus becomes distributed over a large area. Thus, a pressure of 10 atmospheres of a gas feeder becoming distributed over an area of 200 sq. ft. results in a total pres- sure of upwards of 2,000 tons, upon a comparatively small area of coal. As mine openings approach proximity to such a locality, this pressure man- ifests itself by bursting the coal from its position in the face, and throwing it into the entries, in some cases com- pletely blocking the openings or pas- sageways. Such an occurrence is termed an outburst. It is frequently accompanied by thunderings and poundings, which manifest themselves for several days previous to the actual outburst of gas. These poundings are taken as a warning by the miners experienced in such regions. The poundings are probably the result of the gas working its \vay from one crevice to another, always advancing closer and closer to the mine openings, where they finally burst forth with extreme violence. Testing for Gas by Lamp Flame. Marsh gas and firedamp are detected in mine workings by the small flame cap that envelopes and surmounts the flame of the lamp in a firedamp mixture. This flame cap is caused by the gaseous mixture, which burns as it comes in contact with the flame. The proportion of gas in the mixture determines the height of the flame cap. When testing for gas, the lamp flame is first reduced to a small, uniform size, and although this is not a universal practice, it has the advantage of giving uniform results. The lamp is held in an upright position, in one hand, while the eyes are carefully screened by the other hand from the glare of the light, the lamp being slowly raised toward the roof where gas is suspected. The flame is carefully watched for the first appearance of a cap, and the height of the cap is carefully noted. Many lamps are provided with a graduated scale set opposite to the flame, so that the height of a cap may be estimated with accuracy. After the observation, the lamp is quietly and promptly withdrawn from' the gas. Should flaming occur within the lamp, as sometimes happens when it is raised too quickly, or when the gaseous mixture is strong, the lamp should be withdrawn carefully and not with undue haste, as there is danger of the flame of the gases burning within the lamp being forced through the gauze by a rapid movement. This requires great presence of mind on the part of the person using the lamp. In Fig. 3 the heights of flame cap due to the presence of different proportions of marsh gas are shown. These heights, as given, refer to the experimental heights of flame cap ob- tained with pure marsh gas. It should be ob- served, however, that the presence of other gases in the firedamp will vary its explosive character, and this fact very mate- rially modifies the explo- siveness of certain caps. For example, in the ex- periments on pure marsh gas, a 2" flame cap was found to be inexplosive; while, in the mine, and with the variable char- acter of the firedamp mixtures usually found there, a flame of 1 T ^ in. is often found to indicate explosive conditions. Again, flames of even less height than this often indicate dangerous conditions, especially where the coal is inflammable and there is much fine dust present in the atmosphere. These conditions account readily for the various statements that we commonly see in regard to the explosiveness of certain flames. In fact, each fire boss learns, after years of experience, to depend wholly on his 1:18 1:16 SAFETY LAMP*. 355 own knowledge, guided by the conditions that exist in the workings and with which he has become familiar. SAFETY LAMPS. The safety lamp is designed to give light in gaseous workings without the danger of igniting the gases present in the atmosphere. The principle of the safety lamp depends on the cooling effect that an iron-wire gauze exerts on flame. It is a well-known fact that all gases ignite at certain fixed temperatures, and if this temperature is decreased from any cause, the flame is extinguished. Use of Safety Lamps. Safety lamps are used for two general purposes in the mine, and may be classified under two heads: (a) lamps for general use; (b) lamps for testing for gas. Safety Lamps for General Work. The essential features of a lamp designed for general mine work are: (1) safety in strong currents; (2) good illuminating power; (3) security of lock fastening; (4) freedom from flaming; (5) security against accident; (6) simplicity of construction. The conditions under which a lamp is placed at the working face differ from those that attend the testing for gas. The illuminating power of the lamp must be good, so that the workman can see clearly what he is doing. The lamp must not be too sensitive to gas, or its tendency to flame will necessitate that a care- ful watch be kept of it, and this would interfere with the prosecution of the miner's work. Again, the miner is too often careless or neglectful of his lamp, and would fail to give it the required attention. The lamp is often upset, and is apt to be broken by flying coal, or by a fall, unless carefully protected. The lamp should be so securely locked as not to permit of any tampering on the part of the miner without its being detected in the lamp room. In order that the lamp may be thoroughly and rapidly cleaned, its construction should be simple. The lamp should be easily taken apart and put together again after it is cleaned. Lamps for Testing. The essential features of a lamp for testing purposes are: (1) free admission of air below the flame; (2) no reflecting surface behind the flame; (3) ability to test for a thin layer of gas at the roof. When testing for gas, it is important to have a free admission of the air below and around the flame, as the flame cap is very sensitive and is inter- fered with seriously by the conflicting ascending and descending currents in a lamp in which the air enters above the flame. A more uniform cap will be given where the currents ascend quietly around the flame. This feature is very important to the production of a good flame cap, and it is this feature that makes the Davy lamp such a favorite among fire bosses. In order that a flame cap shall be readily observed, there should be no reflection behind it, as the eye is easily deceived under these conditions. A scale by which the height of the flame cap may be accurately measured, is a convenient feature in many lamps for testing purposes. In the use of the common Davy lamp in testing for gases, it is a common, although dangerous, practice to turn the lamp on its side and place it close up against the roof. In this position, the flame is very apt to pass through the gauze, from two causes: The gauze is readily heated, because the flame cap is close against it, and when heated, affords no protection against the passage of the flame and the ignition of the gas outside the lamp. Again, in this position, small particles from the roof are apt to fall upon the gauze, and this may often assist in the passage of the flame through the gauze. A dirty gauze is unsafe. When the lamp is turned sideways, the gauze may become smoked by contact with the flame, and this smoke, or deposit of carbon, assists greatly the passage of flame through the gauze. Another common and dangerous practice on the part of the fire boss is to brush the gas down on the lamp with his cap. By so doing, there is great danger of the flame being blown through the gauze and igniting the gas that may be present. On these accounts, it is essential that a good lamp for testing pur- poses shall be able to draw its air from a point close to the roof, in cases where it is necessary to do so. This is often accomplished by an extra tube, which is supplied with the lamp, and which may be taken off the lamp when not in use. This tube extends up the outside of the lamp to the top. An important feature of a lamp for testing purposes is the uniformity of its flame. A more uniform flame is obtained in the use of alcohol instead of the lard oil commonly used in the safety lamp. 356 SAFETY LAMPS. Detection of Small Percentages of Gas. The Davy lamp in the hands of a careful person may be made to detect the presence of gas in quantities as low as 3fc. It is claimed by some fire bosses that 2$ of gas may be detected with a good Davy. For the detection of small quantities of gas, specially constructed lamps have been used. These lamps are designed to burn alcohol or hydrogen, giving a non-luminous flame. Among these may be mentioned the Pieler lamp, burning alcohol, which it is claimed will detect as small a quantity of gas as fyt. A device known as the Clowes gas tester has been invented, and may be attached to many safety lamps. It consists of a hydrogen tube that is designed to furnish a small stream of hydrogen to the lamp flame when testing for gas. Surrounding the wick of the lamp is a closely fitting cone, to which the hydrogen from the tube is supplied. When the lamp is to be used for testing for gas, the wick is lowered, extinguishing the oil flame after the hydrogen is turned on. It is claimed that gas may be detected in as small quantities as ffl, by this apparatus attached to any good safety lamp admitting its air below the flame. The Shaw gas tester is useful for determining the percentage of marsh gas in the mine air, but it cannot be applied at the face, and samples of gas must be taken to the surface for analysis. Oils for Safety Lamps. Most safety lamps burn vegetable oils, which are considered the safest for mining use, and so reported by the English Mine Commission. Such oils are rape-seed oil and colza oil, made from cabbage seed. Seal oil is also largely used, and was regarded as a safe oil by the English Mine Commission. Seal oil affords a better light than vegetable oils, and in its use there is less charring of the wick. A mixture of 1 part of coal oil to 2 parts of rape or seal oil is often used, and improves the light, but the smoke from the flame is increased. The Ash worth-Hepple white-Gray lamp is constructed to burn coal oil, or a mixture of coal and lard oil. The Wolf lamp is especially designed for burning naphtha or benzine. Special tests have been made to prove the safety of using such a fluid in this lamp, and resulted in demonstrating the fact that the lamp was safe under any condi- tions that might arise. A thorough test was made, the oil vessel of the burning lamp being heated to 180 F., at which point the lamp was extinguished without manifesting any dangerous results. Types of Safety Lamps. In the year 1815, Sir Humphrey Davy and George Stevenson, the latter a poor miner, discovered, simultaneously, that flame would not pass through small openings in a perforated iron plate. This led to the construction of what are known as the Davy, and the Stevenson or " Geordy," lamps. The Davy lamp is still a great favorite among fire bosses for the detection of gas in mine air. Inasmuch as all safety lamps, of which there are a large number, depend on the same principle, we will only describe such lamps as possess essential features, and which show important improvements and the gradual developments in safety -lamp construction. Davy Lamp. Fig. 4 (a) shows a wire gauze cylinder about 5 in. in height and If in. in diameter, surmounted by a gauze cap 2 in. in depth. The gauze, which has 28 wires to the inch, or 784 apertures to the square inch, is fastened to a brass standard, which secures it to the oil cup or lamp below. The gauze at the top of the lamp is doubled by the cap, which gives greater security at this point, where the flame tends to pass through the gauze more quickly, and where the gauze is more readily burned out. The mixture of gas and air enters the lamp in the lower part of the gauze, and burns within the lamp, the products of combustion passing out through the upper portion of the gauze cylinder. This lamp gives a good flame cap, on account of the free access of the air below the flame, which prevents smoking and increases the illuminating power of the lamp. As a lamp for general use, the Davy lamp, however, is unsafe, on account of its liability to flame. In many mining localities the use of this lamp is prohibited by law, except for purposes of examining for gas, when it must be used solely by properly authorized fire bosses. The flame of the lamp is also unprotected from the force of rapid air-currents, and is not safe when the velocity of the current exceeds 6 ft. per second. The illuminating power of the lamp is also not sufficient for general work. Clanny Lamp. The unbpnneted Clanny lamp, Fig. 4 (&), is constructed according to the same principles as the Davy lamp, differing only in the fact that the lower part of the wire gauze surrounding the flame is replaced by a strong glass cylinder or chimney. The purpose of this is to increase the illuminating power of the lamp. The lamp, when clean, gives a good light, but the entrance of the air at a point above the flame, and its descent YA7) OF LAMPS, (dJ (e) FIG. 4. (f) 358 SAFETY LAMPS. within the lamp to the flame, causes the lamp to smoke, due to the conflict of the ascending and descending air-currents within the lamp. The smoke becomes deposited on the glass chimney, which interferes greatly with the light. This lamp is not a good one for gas testing, and in fact cannot be used for that purpose to any advantage. The unbonneted Clanny is not safe in an air-current having a velocity greater than 8 ft. per second. The bonneted Clanny obviates this difficulty to a large extent, but increases the tendency of the lamp to smoke. Mueseler Lamp. This lamp, Fig. 4 (c), in all respects resembles the Clanny lamp just described, except that the tendency in the Clanny lamp to smoke is overcome in the Mueseler by increasing the draft by means of an interior wrought-iron chimney or tube, supported within the lamp, and reaching down to within an inch of the base of the flame. The air enters the lamp as in the Clanny, above the flame, but is deflected downwards by the central tube, and passes under the edge of this tube, ascending through it to the top of the lamp, where it escapes. The Mueseler lamp is a better lamp for illuminating purposes than the Clanny, and presents more security, when bonneted, against explosions within the lamp. This lamp will withstand a current of very much higher velocity than the Clanny lamp, and is reputed to be safe in a current having a velocity of 100 ft. per second. The lamp is not a good lamp for the detection of gas. It does not flame, however, as quickly as the Clanny lamp. Marsaut Lamp. This lamp, Fig. 4 (rf), is built after the Clanny lamp in every respect, but is supplied with multiple-gauze chimneys, one within the other, the effect of which is to increase the security against explosion of gas within the lamp. The bonneted Marsaut lamp is a peculiarly strong lamp in this respect. The gauze used in the caps of this lamp has 934 apertures to the square inch. This lamp is often extinguished in an explosive mixture by the force of the explosion within itself. .It gives a good light and is a good lamp for general work; it is not, however, a good lamp for testing for gas. Ashworth-Hepplewhite-Gray Lamp. This lamp, Fig. 4 (e), combines a number of characteristic features. It is designed for general work, as well as for testing for gas. It often happens that gas accumulates in a thin layer along the roof of an entry or working place, and is not detected by the use of the Davy lamp or any ordinary lamp. The Gray lamp is so arranged that it can be made to draw its air from the top of the lamp, by means of openings in the top of the four standards of the lamp, the air passing down through the standards, and into the lamp, below the flame. When not in use for testing, openings can be made in the lower part of the stand- ards by moving a slide, and air enters at these openings. The lamp is essen- tially a bonneted Clanny. The glass chimney, however, as well as the gauze that surmounts it, is made in a conical form, the purpose of this being to diffuse the light upward for examination of the roof of the mine. The conical form given to the gauze also strengthens the lamp against explo- sions of gas within. This lamp is a very good all-around lamp, and possesses good illuminating power. Wolf Lamp. The Wolf lamp, Fig. 4 (/), is rapidly growing in popularity, having been already introduced in a large number of mines in America and England, and on the Continent. This lamp is essentially a Clanny lamp with a free admission of air. It is compact and efficient, and has good illuminating power, and is also constructed in different forms, combining, as desired, any or all of the features of previous lamps. Two of its charac- teristic features, however, consist in a self-lighting arrangement accom- plished by means of a percussive device, which ignites a wax taper within the lamp, and a locking device, which can be opened only with a powerful magnet. This relighting device is an important feature in any safety lamp for general use, inasmuch as the most dangerous conditions exist immedi- ately after an explosion, and the miners are always left to grope their way in the dark. A large number of lives are lost, owing to the confusion that ensues, the men becoming bewildered and losing their way, when they are shortly overcome by the afterdamp of the explosion. This lamp permits of immediate relighting with safety to the men. Locking Lamps. The ordinary lock consists of a lead plug, which, when inserted in the lamp, will show the least tampering on the part of the miner. Other locks consist of an ordinary turnbolt operated by a peculiar key. Magnetic locks allow of the opening of the lamp only by means of a Strong magnet kept in the lamp room. Cleaning Safety Lamps. Safety lamps should be thoroughly and regularly CARE OF SAFETY LAMPS. 359 cleaned and filled between each shift. Each lamp should then be lighted and inspected by a competent person before being given to the miner. A careful inspection of the gauze of the lamp is necessary, as well as of all the joints by which air may enter the lamp. It should be known to a certainty that each lamp is securely locked before leaving the lamp room. Relighting Stations. These stations are located at certain places in gaseous mines where they can be supplied with a current of fresh air, and where there is no danger from the gases of the mine. The lamp is apt to be overturned, or to fall, and is often extinguished thereby; and if these stations were not provided, the man would have to return with his lamp to the surface in order to have it relighted. Such a station is always located at the entrance of the gaseous portion of a mine, in cases where the entire mine does not liberate gas. Illuminating Power of Safety Lamps. The following table gives the illumi- nating power or candlepower of some of the principal lamps. The light of a sperm candle is taken as 1, or unity. Name of Lamp. Illuminating Power of Lamp. Daw .16 Geordy .10 Clanny .20 Mueseler .35 Evan Thomas .45 Marsaut, 3 gauzes. .45 Marsaut, 2 gauzes .55 Marsaut, with Howat's deflector .65 Ashworth-Hepplewhite-Grav .65 Wolf . .90 EXPLOSIVE CONDITIONS IN MINES. In the ventilation of gaseous seams, the air-current may be rendered explosive by the sudden occurrence of any one of a number of circum- stances that cannot be anticipated. Among these are the following: (1) Derangement of the ventilating current. (2) Sudden increase of gas due to outburts, falls of roof, feeders, fall of barometric pressure, etc. (3) Presence of coal dust thrown into suspension in the air, in the ordinary working of the mine, or by the force of blasting at the working face, or by a blown-out, or windy, shot. (4) Pressure due to a heavy blast, or any concussion of the air caused by closing of doors, etc. (5) Rapid succession of shots in close workings. (6) Accidental discharges of an explosive in a dirty atmosphere. Any or all of these causes may precipitate an explosion at any moment. Hence, the condition of the air-current should be maintained far within the explosive limit. The explosive conditions vary considerably in different coal seams. The nature of the coal and its enclosing strata, its friability and inflammability, together with the character of its occluded gases, deter- mine, to a large extent, the explosive conditions in the seam. Experience in any particular seam or district must always be the best guide, and furnish the best standard for determining the explosiveness of any given lamp flame. For example, a 2" flame may be comparatively safe in a small mine where the coal is hard and not particularly flammable, while a U" flame cap would be considered unsafe in mines where the conditions are more favorable to the generation of gas and formation of coal dust. The daily output of the mine and the general care that is enforced upon the miners at the working face are factors that should always be considered and taken into serious account in determining explosive conditions (see Testing for Gas by Lamp Flame). Derangement of Ventilating Current. The flow of the air-current must be uniform and continuous. Doors must be kept closed, since the mere setting open of a door, for a short period of time, is sufficient to precipitate a serious explosion. Any contemplated change in the current, by the erection of brattices, air bridges, stoppings, etc., should be carefully considered before the work is begun, and every precaution adopted to secure the safety of the 360 VENTILATION OF MINES. men. Derangement of the current may occur through a fall of roof upon the main airway, by which the area of the airway is reduced, which results in the reduction of the quantity of air passing in the mine. If this fall is not noticed at once, serious results may happen. The utmost vigilance is therefore required on the part of fire bosses and all connected with mine workings. The failure of the ventilating apparatus is another source that gives rise to the derangement of the current. As a rule, furnaces are not now employed for the ventilation of gaseous seams. There are, however, some furnaces in use in such seams, and these require constant attention lest the fire should burn low. Upon any accident occurring to the ventila- ting machinery, notice should at once be given to the inside foreman, and the men withdrawn as rapidly as possible. A sudden increase of gas may occur at any time in a gaseous seam, owing to an outburst, which suddenly yields a large volume of gas and may render the mine air in that section extremely explosive. The men working on the return of such a current must be hastily withdrawn, and all lights extinguished. A heavy fall of coal in the mine workings or in the airways, or the tapping of a large gas feeder, produces the same effect in a less degree. The nearer the fall of roof takes place to the face of the workings, the more liable it is to be followed with a large flow of gas, inasmuch as the gas near the face has not had time to drain off, as in the case of old workings. This fact is always true in reference to new workings in a gaseous seam. The gas continues to flow freely for a considerable period, when its flow gradually decreases until it about ceases. When a large feeder has been tapped, it may be plugged for a time, if necessary, but the better practice is to allow it to flow freely and diffuse into the air-current, which should be sufficiently increased to dilute the quantity of gas given off and to render it inexplosive. The men upon the return air should be notified. It is dangerous practice to light these feeders. When there is a large area of abandoned workings in the mine, any considerable fall of barometric pressure is usually followed by a large outflow of gas from the gobs or waste places of the mine. A fall of 1 in. in .5 hours represents a very rapid decrease of barometric pressure. At all large collieries there is, or should be, a good standard barometer located upon the surface near the shaft. In many cases, these barometers are self-recording, and are often provided with an automatic alarm that gives warning when- ever a fall of barometric pressure occurs. This warning should at once be conveyed to the men in the workings, and every precaution adopted to avoid evil results. The fact is fairly well established that a fall of atmos- pheric pressure is not followed by an outflow of gas from the mine workings for the space of, say, 3 hours after such fall occurs. This statement must be regarded with caution, however, as it largely depends on the condition and extent of the abandoned workings. Where these are full of gas, its expan- sion affects the condition of the airways much more quickly than in cases where these working places are partly ventilated. Effect of Coal Dust in Mine Workings. According to the greater or less flam- mability of the coal, the presence of fine dust in the airways and workings of the mine becomes a dangerous factor. Certain coals are extremely friable and are reduced readily to fine dust, which is thrown into suspension in the air-current by the ordinary operations of the miners in their work, as well as by the concussion of the air from numerous causes, and by the movement of cars and the traveling of men and animals upon the various haul- ways and passageways. For a long time it was questioned whether the presence of dust was a dangerous factor, except where there was also a small percentage of gas in the air. Evidence, however, has well established the fact that coal dust of itself is a dangerous element, and may often be the sole cause of an explosion, when acted upon by a flame of sufficient intensity and magnitude. The action of the flame is to distil carbonic-oxide gas CO from the fine particles of dust suspended in the air. The explosion of the gas thus formed causes a further disturbance and raises a larger supply of dust, which likewise contributes to the liberation of fresh quantities of gas, and thus an explosion is generated and transmitted. Small quantities of marsh gas greatly increase the violence of this action, but explosions in flouring mills and well-ventilated coal bins establish the fact that such occurrences are not dependent on the presence of marsh gas. Too much faith must not be placed in the use of water by sprinkling for ffect in the immediate vicinity, but nder an untidy working place safe laying the dust. This has a beneficial effect in the immediate vicinity, but a large amount of water is required to rend MINE EXPLOSIONS. 361 at firing time. Better practice is to allow no accumulations of dust at the face. This should be regularly loaded out with the coal. Pressure as Affecting Explosive Conditions. Gaseous mixtures that are not explosive in the ordinary condition of a mine, often become explosive under the momentary pressure to which they are subjected by heavy blasting, and, in some instances, this may occur from the concussion of the air caused by the quick shutting of a door. In the latter case, how- ever, the explosive condition of the air would necessarily have to be close to the limit, in order for such a slight occurrence to precipitate an explosion. The factor of pressure as increasing the explosiveness of gaseous mixtures should be considered and constantly borne in mind. Rapid Succession of Shots in Close Workings. It constantly happens that two, three, or more shots are fired by means of fuse or touch squibs in a single chamber or heading, where the circulation of air is not always the best. The practical effect is that a considerable quantity of carbonic-oxide gas CO is produced by the firing of the first shot, and this gas does not have time to diffuse or become diluted by the air-current before it is fired by the flame of the following shots. An explosion may often be precipitated by such an occurrence, if the workings are at all dusty. Two shots at the most are all that should be fired at one time in a close chamber- or heading. Mine Explosions. The explosion of gas in a mine usually arises from the ignition or an explosive mixture of gas and air called firedamp, which has accumulated in some unused chamber or cavity of the roof, or in the waste places of the mine, and has been ignited by a naked light, by the flame of a shot, or by a mine fire. The initial force of an explosion is generally expended locally, but the flame continues to feed upon 'the carbonic-oxide gas generated by the incomplete combustion of the firedamp mixture, and distilled also from the coal dust thrown into the air by the agitation. Air is required to burn this carbonic-oxide gas; this causes the flame to travel against the air-current, or in the direction in which fresh air is found. In the other direction, or behind the explosion, the flame is soon extin- guished in its own trail when the initial force of the explosion is expended. The explosion continues to travel along the airways against the current as long as there is sufficient gas or coal dust for it to feed upon, or until its temperature is cooled below the point of ignition, by some cause such as, for example, the rapid expansion of the area of the workings. We observe the chief factor in transmitting an explosion is the presence of carbonic-oxide gas, which lengthens the flame and extends the effect. The recoil of an explosion is the return of the flame along the path that it has just traversed. In the recoil, the flame burns more quietly, advances more slowly, and travels close to the roof. The evidence found at the point where a recoil took place, or an explosion turned back, has been sufficient to establish the fact that the recoil is caused primarily by a cooling of the tem- perature, probably caused very largely by an expansion of the area of the airway. Soot is often deposited at this point in considerable quantity, if the action of the flame is not such as to consume it. This fact alone shows the combustion at this point to have been incomplete. Immediately in the rear of the flame is a mixture of carbonic-oxide gas CO, which bursts into flame at the sudden stoppage of the advancing explosion. This is rendered possible by the flow of cold air from the adjacent chambers and workings along the floor of the airway. The flame now retreats, burning the trail of carbonic-oxide gas along the roof, fed by the cold air along the floor. To Explore Workings After a Serious Explosion. The shafts or slopes and 'the ventilating machinery should claim the first attention of those on the surface, and an effort should be made to reach the bottom as expeditiously as possible. Assistance from neighboring collieries, both in the way of skilled labor and advice, should also be requested. Should the shaft or slope need repairs before communication between top and bottom is restored, the person in charge on the surface should, in the meantime, see that props of the lengths in ordinary use, brattice boards, brattice cloth, and nails are brought to a convenient place for putting on the cage or car, and he ought also to collect all the tools likely to be required, such as axes, saws, ham- mers, etc. It is also important that rough tracings of the workings be prepared for the use of the leader of each squad of explorers. Officials will understand how useful these will be to those that are penetrating into work- ings about which every man of his squad may have been heretofore ignorant, When the explorers have arrived at the bottom and are ready to proceed, there should be for each section, if more than one is operated upon, two 362 VENTILATION OF MINES. managers, each having his own squad of men, and his own particular duty to do. One may take charge of restoring the ventilation, the inspection of the workings, and the clearing of the roads; the other may appoint and have charge of the bottom man, the conveying of material, and the detailing of stretcher companies where required. They can consult and help each other in every difficulty, but system is necessary if the work is to be done in the shortest possible time. The manager who has charge of the men in front should appoint two experienced men with good nerves to act as foremen, instructing them to inspect and report to him the condition of the workings within a short radius. He should then form the rest of his men into, say, three squads of three each, who will work together at stoppings or falls until separated by him, or until the end of the shift. Being near the bottom, it will probably be found that all is clear for three or four breast or stoop lengths, and stop- pings are required to be put up. Material will be required for this, and when the cage is first sent to the top for it, it should not be kept there to enable the top man to put on a big load, but it should be sent down with all despatch, loaded with a half dozen each of props and brattice boards, with one piece of cloth and nails. This will allow a start to be made, and will prevent the anxious men from worrying over what to them is an unac- countable delay. Larger loads can be sent down in subsequent trips. For convenience in carrying, the brattice cloth may be cut in lengths to suit the gangways or headings with 2 or 3 ft. to spare. Squad No. 1 should be detailed to the first stopping. This may be put up with boards at top and bottom and cloth between. If the air-current is strong, a few of the follow- ing stoppings may be put up by squads No. 2 and No. 3, with cloth only stretched between two props. These can be very rapidly put up and will drive the ventilation forwards, thus allowing the firemen to extend rapidly the area of inspection. These stoppings can be completed by No. 1 detail. In a short time it may become impossible to proceed in this manner. The foul air will in all probability become more difficult to dislodge, and eventu- ally one detail may be able to put up stoppings as quickly as the firedamp or chokedamp can be carried off. Part of what may be called the ventilating detail can now be transferred to the bearer detail, the duties of the latter having become heavier as the stoppings advanced. It is not an easy task to carry props long distances in a stooping posture, and when to that is added, it may be, the carrying out of the living or dead bodies, the men begin to fag very soon. But the person in charge here must see that the forward party is kept in material for stoppings so that no delay may occur on that account. A system of staging gives relief to the carrying parties. To conclude with a few general remarks: Let those that have never yet assisted to explore a mine after an explosion be assured of this, that the chief requisites in a leader are a capacity for hard work and the ability to organize his men into a system, however roughly, whereby work will be best forwarded. It will not speed the work to say to a dozen or more men, generally, do this or that, neither is it beneficial to allow all the workmen to discuss matters and suggest plans. Those in charge ought to arrange what is to be done. Anything else results in noise and confusion. And let men that are sent from other collieries take with them their own tools and lamps. Those in charge ought to take note of the position, etc. of bodies found, and of every point which is likely to throw light on the cause or origin of the explosion. This can be more correctly done before the roads are disturbed by dust and travel. These notes might not only be the means of ascertain- ing the cause of explosion, but also of pointing out a way of prevention in the future. In no case after an explosion should the air-current of the mine be reversed from its usual course, except only after careful consideration, because of the reliance placed by the entombed workmen on their knowl- edge of the direction in which the air should be moving; and the reversal of the current may drive the gases of the explosion upon them with disas- trous results. Conditions must be allowed to remain as they exist, and the rescuers conform themselves to such conditions in the best manner possible. QUANTITY OF AIR REQUIRED FOR VENTILATION. The quantity of air required for the adequate ventilation of a mine can- not be stated as a rule applicable in every case. Regulations that would supply a proper amount of air for the ventilation of a thick seam would be ELEMENTS IN VENTILATION. 363 found to cause great inconvenience if applied without modification to the workings in a thin seam. Likewise, the ventilation of an old mine with extended workings, a large area of which has been abandoned, and in many cases not properly sealed off, will require, naturally, a larger quantity of air per capita than a newly opened mine or shaft. The natural conditions existing in rise and dip workings, with respect to the gases that may be liberated or generated in those workings, call for the modification of the quantity of air required in each case. For example, dip workings, where much blackdamp is generated, will require a larger quantity of air, or higher velocity at the working face, to carry off such damps; and rise work- ings, liberating a large amount of marsh gas, will likewise require a higher velocity at the .working face. On the other hand, a reversal of these conditions, such as a large quantity of marsh gas being liberated in dip workings, or a similar amount of blackdamp being generated in rise work- ings, will require a comparatively low velocity of the air at each respective working place. Quantity Required by State Laws. The quantity of air required by the laws of the several States is generally specified as 100 cu. ft. per man per minute, and in many cases an additional amount of 500 cu. ft. per animal per minute is stated. This quantity is in no case stated as the actual amount of air required for the use of each man or animal, but is only the result of experience, as showing the quantity of air required for the proper ventilation of the average mine, based on the number of men and animals employed. The number of men employed in a mine is an indica- tion of the extent of the working face, while the number of animals employed is an indication likewise of the extent of the haulage roads, or the development of the mine. These amounts refer particularly to non-gaseous seams. The Bituminous Mine Law of Pennsylvania specifies that there shall be not less than 100 cu. ft. per minute per person in any mine, while 150 cu. ft. are required in a mine where firedamp has been detected. The Anthracite Mine Law of Pennsylvania specifies a minimum quantity of 200 cu. ft. per minute per person. Each of these laws contains modifying clauses, which specify that the amount of air in circulation shall be sufficient to "dilute, render harmless, and sweep away" smoke and noxious or dangerous gases. Quantity of Air Required for Dilution of Mine Gases. To determine this requires a knowledge of the quantity of gas generated or liberated in the workings. The quantity of air for dilution should be ample, and should be such as not to permit the condition of the current to approach the explosive point. The ventilation should be ample at the face. Quantity of Air Required to Produce the Necessary Velocity of Current at the Face. This consideration modifies considerably the quantity of air required for the ventilation of thick and thin seams. The velocity of the current is dependent not only on the quantity of air in circulation, but on the area of the air passage. This area is quite small in thin seams, and often very large in thick seams. As a result, the velocity is often low at the face of thick seams, and insufficient for the proper ventilation of the face, although the quantity of air passing into such a mine may be very large. A certain velocity of the current is always required in order to sweep away the gases. This velocity depends on the character of the gases and the position of the workings. Heavy damps are hard to move from dip workings where they have accumulated; and, likewise, lighter damps accumulating at the face of steep pitches are hard to brush away, and the velocity of the current in these cases must be equal to the task of driving out these gases. ELEMENTS IN VENTILATION. The elements in any circulation of air are (a) horsepower, or power applied; (6) resistance of the airways, or mine resistance, which gives rise to the total pressure in the airway; (c) velocity generated by the power applied against the mine resistance. Horsepower or Power of the Current. The power applied is often spoken of as the power upon the air. It is the effective power of the ventilating motor, whatever this may be. including all the ventilating agencies, whether natural or otherwise. The power upon the air may be the power exerted by a motive column due to natural causes, or to a furnace, or may 364 VENTILATION OF MIXES. be the power of a mechanical motor. The power upon the air is always measured in foot-pounds per minute, which expresses the units of work accomplished in the circulation. Mine Resistance. The resistance offered by a mine to the passage of an air-current, or the mine resistance, is due to the friction of the air rubbing along the sides, top, and bottom of the air passages. This friction causes the total ventilating pressure in the airway, and is equal to it. Calling the resistance JR, the unit of ventilating pressure (pressure per square foot) p, and the sectional area of the airway a, we have, R pa; that is to say, the total pressure is equal to the mine resistance. Velocity of the Air-Current. Whenever a given power is applied against a given resistance, a certain velocity results. For example, if the power u (foot-pounds per minute) is applied against the resistance p a, a velocity v (feet per minute) is the result; and since the total pressure p a moves at the velocity v, the work performed each minute by the power applied is the product of the total pressure by the space through which it moves per minute, or the velocity. Thus, u = (p a) v. Relation of Power, Pressure, and Velocity. The relation of these elements of ventilation is not a simple relation. For example, a given power applied to move air through an airway establishes a certain resistance and velocity in the airway. The resistance of the airway is not an independent factor; that is to say, it does not exist as a factor of the airway independent of the velocity, but bears a certain relation to the velocity. Power always produces resistance and velocity, and these two factors always sustain a fixed relation. This relation is expressed as follows: The total pressure or resistance varies as the square of the velocity; i. e., if the power is sufficient to double the velocity, the pressure will be increased 4 times; if the power is sufficient to multiply the velocity 3 times, the pressure will be increased 9 times. Thus, we observe that a change of power applied to any airway means both a change of pressure and a change of velocity. Again, since the power is expressed by the equation u = (p a] v, and since p a, or the total pressure, varies as i/ 2 , the work varies as v*. From this it follows that, if the velocity is multiplied by 2, and, consequently, the total pressure by 4, the work performed (pa) v will be multiplied by 2 3 = 8. We thus learn that the power applied varies as the cube of the velocity. MEASUREMENT OF VENTILATING CURRENTS. The measurement and calculation of any circulation in a mine airway includes the measurement of (a) the velocity of the air-current, (b) of pres- sure, (c) of temperature, (d) calculation of pressure, quantity, and horse- power of the circulation. These measurements should be made at a point in the airway where the airway has a uniform section for some distance, and not far from the foot of the downcast shaft or the fan drift. Measurement of Velocity. For the purpose of mine inspection, the velocity of the air-current should be measured at the foot of the downcast, at the mouth of each split of the air-current, and at each inside breakthrough, in each split. These measurements are necessary in order to show that all the air designed for each split passes around the face of the workings. The measurement of the velocity of a current is best made by means of the anemometer. This instrument consists of a vane placed in a circular frame and having its blades so inclined to the direction of its motion that 1 ft. of lineal velocity in the passing air-current will produce 1 revolution of the vane. These revolutions are recorded by means of several pointers, each having a separate dial upon the face of the instrument, the motion being communicated by a series of gear-wheels arranged decimally to each other. Most anemometers are provided with a large central pointer that makes 1 revolution for each 100 revolutions of the vane. The dial for this pointer is marked by 100 divisions, which record the number of lineal feet of velocity. In very accurate work with the anemometer, certain constants are used as suggested by the instrument maker, but these constants are of little value in ordinary practice and are of doubtful value even in more accurate observations. The measurement of the velocity of an air-current must necessarily represent only approximately the true velocity in the airway. The air travels with a greater velocity in the center of the airway, and is retarded at MEASUREMENT OF PRESSURE. 365 the sides, top, and bottom by the friction of these surfaces. Hence, the air to a large extent rolls upon these surfaces, which naturally generates an eddy at the sides of airways. When measuring the air, the anemometer should be held in a position exactly perpendicular to the direction of the current, and moved to occupy different positions in the airway, being held an equal time in each position, or it may be moved continuously around the margin of the airway, and through the central portion. The person taking the observation should observe the caution of not obstruct- ing the area of the airway by his body, as the area is thereby reduced, and the velocity of the current increased. The area of the airway is accurately measured at the point where the observations are taken (see Calculation of Quantity). To obtain the quantity of air passing (cubic feet per minute), multiply the area of the airway, at the point where the velocity is measured, by the velocity. EXAMPLE. The anemometer gives a reading of 1,320 ft. in 2 minutes, the height of the airway is 6 ft. 6 in., and its average width 8 ft. 8 in. What volume of air is passing in the airway per minute ? X 8} X = 37,180 cu. ft. per min. The measurement of the ventilating pressure is made by means of a water column in the form of a water gauge. Water Gauge. The water gauge is simply a glass U tube open at both ends. Water is placed in the bent portion of the tube, and stands at the same height in both arms of the tube when each end of the tube is subjected to the same pressure. If, however, one end of the tube is subjected to a greater pressure than the other end, the water will be forced down in that arm of the tube, and will rise a corre- sponding height in the other arm, the differ- ence of level in the two arms of the tube repre- senting the water col- umn balanced by the excess of pressure to which the water in the first arm is subjected. An adjustable scale graduated in inches measures the height of the water column. The zero of the scale is ad- justed to the lower water level, and the upper water level will FIG. 5. FIG. 6. then give the reading of the water gauge. One end of the glass tube is drawn to a narrow opening to exclude dust, while the other end is bent to M**K angle, and passing back through the standard to which the tube is attached, is cemented into the brass tube that passes through a hole in the partition or brattice, when the water gauge is in use. The bend of the tube is contracted to reduce the tendency to oscillation in the height of water column. (See Fig. 5.) When in use, the water gauge must be in a perpendicular position. It is placed upon a brattice occupying a position between two airways, as shown ; f* 6> The brass tube Arming one end of the water gauge is inserted in a cork, and passes through a hole bored in the brattice. The water gauge must not be subjected to the direct force of the air-current, as in this case the true pressure will not be given. Fig. 6 shows the instrument as occupying a position in the breakthrough, between two entries. It will oe observed that the water gauge records a difference of pressure, each end of the water gauge being subject to atmospheric pressure, but one end in addition being subject to the ventilating pressure, which is the difference of 366 VENTILATION OF MINES. pressure between the two entries. The water gauge thus enables us to measure the resistance of the mine inbye from its position between two airways. If placed in the first breakthrough, at the foot of the shaft, it measures the entire resistance of the mine, but if placed at the mouth of a split, it measures only the resistance of that split. It never measures the resistance outbye from its position in the mine, but always inbye (see Calcula- tion of Pressure). Measurement of Temperature. It is important to measure the temperature of the air-current at the point where the velocity is measured, as the tem- perature is an important factor of the volume of air passing (see Expan- sion of Air and Gases, etc.). Thermometers. Thermometers measure changes in the temperature of the atmosphere by the contraction and expansion of mercury or spirits; or they may be made entirely of metal, and the changes of temperature are then measured by the expansion and contraction of the sensitive metallic portion. These latter are known as aneroid thermometers. The Fahren- heit thermometer is the one most commonly used in America. By this scale, the freezing point of water at the sea level is placed at 32 above zero; the boiling point of water at sea level is placed at 212 above zero, so that the space between these two points is divided into 180. Reaumur and Centigrade thermometers are used on the continent of Europe. Of these two, the first is generally used in Germany, and the second in France, but the latter is almost exclusively used by the scientists of all nations. In the Reaumur thermometer, the freezing and boiling points are placed at and 80, respectively. In the Centigrade, the freezing and boiling points are placed at and 100, respectively. To Convert Fahrenheit Into Centigrade. (1) Subtract 32 and divide the remainder by 1.8, or multiply by f. If a Fahrenheit thermometer registers 167, what will be the register by a Centigrade thermometer ? ^=^ = 75 Centigrade. (167 ~ 32)5 = 75 Centigrade. To Convert Centigrade Into Fahrenheit. (1) Multiply by 1.8, or , and add 32. If the Centigrade thermometer registers 75, what will be the register by a Fahrenheit thermometer? 75 X 1.8 + 32 = 167 Fahrenheit. - + 32 = 167 Fahrenheit. o To Convert Fahrenheit Into Reaumur. (1) Subtract 32, and divide by 2.25, or multiply by $. If the Fahrenheit thermometer registers 113, what will be the register by the Reaumur thermometer ? 113 2 ~ 32 = 3C Reaumur. <"1=J*>* = 36 Reaumur. To Convert Reaumur Into Fahrenheit. (1) Multiply by 2.25, or multiply by f , and add 32. If the Reaumur thermometer registers 36, what will be the register by the Fahrenheit thermometer? 36 X 2.25 + 32 = 113 Fahrenheit. --^- + 32 = 113 Fahrenheit. To Convert Reaumur Into Centigrade. Multiply by 1.25. If a Reaumur thermometer registers 32, what will be the register by a Centigrade thermometer? 32 X 1.25 = 40 Centigrade. To Convert Centigrade Into Reaumur. Multiply by .8. If a Centigrade thermometer registers 40, what will be the register by a Reaumur thermometer? 40 X .8 = 32 Reaumur. Calculation of Mine Resistance. The mine resistance is equal to the total pressure p a that it causes. This mine resistance is dependent upon three factors: (a) The resistance k offered by 1 sq. ft. of rubbing surface to a current having a velocity of 1 ft. per minute. The coefficient of friction k, or the unit of resistance, is the resistance offered by the unit of rubbing sur- face to a current of a unit velocity. This unit resistance has been variously estimated by different authorities (see following table). The value most universally accepted, however, is that known as the Atkinson coefficient THE EQUIVALENT ORIFICE. 367 (.0000000217). (b) The mine resistance, which varies as the square of the velocity, (c) The rubbing surface. Hence, if we multiply the unit resist- ance by the square of the velocity, and by the rubbing surface, we will obtain the total mine resistance as expressed by the formula pa = ksv' 2 . TABLE OF VARIOUS COEFFICIENTS OF FRICTION OF AIR IN MINES. Pressure per Sq. Ft. Decimals of a Pound. J. J. Atkins9n's treatise ................................................................. 0000000217 A. Devillez in Ventilation des Mines: Forchies ............................................................................ ....... 000000008211 Crachet-Picquery ................................................................... 000000008928 Grand Baisson .............................. . ............................................ 000000008611 Average of 2, 3, and 4 ...................................................... . ....... 000000008585 Used in Ventilation des Mines ................................................ 000000009511 Arched Tunnels ........... . ........................................................... 000000002113 Along a working face of coal ............................... .................. 000000014266 G. G. Andre, Atmosphere of Coal Mines ....................................... 000000022424 Peclet, Cheminee (Devillez, p. 112) .............................................. 000000003697 D. K. Clark .................................................................................... 000000002272 According to Goupilliere's Cours d' Exploitation des Mines, Vol. II, p. 389: D'Aubuisson ............................................................................. 000000001955 Navier ...................................................................................... 000000001872 W. Fairley ....................................................................................... 00000001 J. Stanley James .............................................................................. 00000000929 It will be observed that J. J. Atkinson's coefficient is greatly in excess of any other, with the exception of Andre's. Fairley's is derived from an average taken betvyeen Atkinson, Devillez, and Clark, and, undoubtedly, it is an exceedingly simple coefficient to work out calculations with, as it will save a great mass of figures. James, in his work on colliery ventilation, reduces the coefficient still further on the authority of the Belgian Mine Commission, but he gives a most unwieldy figure to use. Atkinson's figure is the one most in use, and if it is too high, it errs on the side of safety, and it is always advisable to have plenty of spare ventilating power at a mine. For this reason, and until a regular and thorough investi- ation, made by a commission of competent men, provides a standard coef- cient, we prefer to abide by Atkinson's coefficient, and it is used in all our calculations. Calculation of Power, or Units of Work per Minute. If we multiply the total pressure by the velocity (feet per minute) with which it moves, we obtain the units of work per minute, or the power upon the air. Hence, u = p a v = k s v\ which is the fundamental expression for work per minute, or power. The Equivalent Orifice. This term, often used in regard to ventilation, evaluates the mine resistance, or, as will be seen from the equation given below for its value, it expresses the ratio that exists between the quantity of air passing in an airway and the pressure or water gauge that is produced by the circulation. This term was suggested by M. Daniel Murgue, and refers to the flow of a fluid through an orifice in a thin plate, under a given head. The formula expressing the velocity of flow through such an orifice is v = i/2<7/i; multiplying both members of this equation by A, and substi- tuting for the first member A v, its value q, we have, after transposing and correcting for vena contracta, A = - ^ __ , in which .62 is the coefficient for g fi . the vena contracta of the flow. Reducing this to cubic feet per minute and inches of water gauge represented by i, we have, finally, the equation A = .0004 X -~. By this formula, Murgue has suggested assimilating the yi flow of air through a mine to the flow of a fluid through a thin plate; since, in each case, the quantity and the head or pressure vary in the same ratio. Thus, applying this formula to a mine, Murgue multiplies the ratio of the quantity of air passing (cubic feet per minute) and the square root of the water gauge (inches) by .0004. and obtains an area A, which he calls the equivalent orifice of the mine. Potential Factor of a Mine. (Proposed by J, T< tfmrd.) Equations 8 and, 2.7,. 368 VENTILATION OF MINES. pages 370-371, give, respectively, the pressure and the power that will circu- late a given quantity of air per minute in a given airway. These equations may be written as equal ratios, expressed in factors of the current and the airway, respectively; thus, =?. and ^ = ~, which show that the ratio q 2 a 3 q* a 3 between the pressure and the square of the quantity it circulates in any given airway is equal to the ratio between the power and the cube of the quantity it circulates. Solving each of these equations with respect to q, we have the following: With respect to pressure, With respect to power, Hence, we observe that, in any airway, for a constant pressure, the quan- tity of air in circulation is proportional to the expression a-% / a --; and, for a * a constant power, the quantity is proportional to the expression - , which y ks terms are called the potentials of the mine with respect to pressure and power, respectively; and their values t and = are the potentials of the Vp fu current with respect to pressure and power, respectively. These factors, it will be observed, evaluate the airway, as they determine the quantity of air a given pressure or power will circulate in that airway (cubic feet per minute). By their use, the relative quantities of air any given pressure or power will circulate in different airways are readily determined. The rule may be stated as follows: Rule. For any given pressure or power, the quantity of air in circulation is always proportional to the potential for pressure, or the potential for power, as the case may be. This rule finds important application in splitting (see Calculation of Natural Splitting). In all cases where the potential is used as a ratio, the relative potential may be employed by omitting the factor Jfc; or it may be employed to obtain the pressure and power, in several splits by multiplying the final result by k (see Formulas 46, 47, etc., page 378). EXAMPLE. 20,000 cu. ft. of air is passing in a mine in which the airway is 6 ft. X 8 ft., and 10,000 ft. long, under a certain pressure; it is required to find what quantity of air this same pressure will circulate in a mine in which the airway is 6 ft. X 12 ft., and 8,000 ft. long. Calculating the potential X p with respect to the pressure for each of these mines, or airways, we have, using the relative potential, = 6 >< 8 - - 62845 ' a " d * = 6 >< = 1.1384. Since the ratio of the quantities is equal to the ratio of the potentials with respect to pressure, in these two mines, we write the propor- 90 000 V 1 1^84 tion 20,000 : q 2 : : .62845 : 1.1384, and q 2 = *~- = 36,229 cu. ft. per min. .62845 EXAMPLE. 20,000 cu. ft. of air is passing in a mine in which the airway is 6 ft. X 8 ft., and 10,000 ft. long, under a certain power; it is required to find what quantity of air will be circulated by this same power in a mine in which the airway is 6 ft. X 12 ft., and 8,000 ft. long. We calculate the potential X u with respect to power for each of these 6X8 mines, using, as before, the relative potential. Thus, X\ = 10 F2(6 + 8)X10,000 - .7337, and X 2 = - = 1.0905. Then, in this case, since the V 2(6 + 12) X 8,000 ratio of the quantities is equal to the ratio of the potentials with POTENTIAL FACTOR. 369 respect to power, we write the proportion, 20,000 : q : : .7337 : 1.0905, and = 20.000X1.0905 .7337 fl . The following table will serve to illustrate the use of the formulas employed in these calculations. It will be observed that there are several formulas for quantity, and for velocity, and for work or horse- power, but in each respective case the several formulas are derived by simple transposition of the terms of the original formula, and are tabulated here for convenience. Choice must be made in the use of any of these for- mulas, according to the known terms in each example. Thus, an example may ask: What pressure will be produced in passing a given quantity of air through a certain mine, the size and length of the airways being given ? We then use the formula p = ~. But if the question asks what quan- tity of air a given pressure will produce in this same mine, we use the formula q = A/fr" X It will be observed that this second formula is a \ K S simple transposition of the first. In like manner the question may be asked, what power will produce a certain quantity of air in a certain airway; and the expression used, in this - -. Or, the question may be asked, what quantity of air will case, is u be produced in a given airway by means of a certain power or work applied to the airway. In this case, the formula used is q = a i \Mf--. If the ques- tion asks for the power required to produce a given velocity in a given air- way, the formula employed is u = ksv*. All of these formulas are derived by combining the simple formulas p = - , q = av, and u = qp. To illustrate the use of the formulas, we take as an example an under- ground road, 5 ft. wide by 4 ft. high, and 2,000 ft. in length, and calculate the value of each symbol or letter, assuming a velocity of 500 ft. per minute. Symbol. Value of Symbol for this Particular Example. Area of airway (5 ft X 4 f t ) ft 20 sq ft Horsepower * h 2 959 H P Coefficient of friction f k 0000000217 Ib l^ength of airway I 2 000 ft Perimeter of airway, 2(5 ft. + 4 ft.) o 18ft. Pressure (Ib per sq ft ) P 9 765 Ib Quantity of air ( cu ft per min ) Q 10 000 cu ft Area of rubbing surface s 36 000 sq ft Units of work per minute (power) u 97 650 ft -Ib Velocity (ft per min ) V 500 ft Water gauge . i 1.87788 in Equivalent orifice of the mine Potential for power A x 2.919 sq. ft. 217 16 units Potential for pressure X n 3,200 units. Weight of 1 cu. ft. of downcast air Motive column (downcast air) w M .08098 Ib. 120 5 ft Depth of furnace shaft . D 306.77 ft. Average temperature of the upcast column.. Average temperature of the downcast column T t 350 F. 32 F. * A horsepower is equal to 33,000 units of work. t This coefficient of friction is an invariable quantity, and is the same in every calculation relating to the friction of air in mines. NOTE. The water gauge is calculated to five decimal places to enable all the other values to be accurately arrived at. In practice, it is only read to one decimal place. 370 VENTILATION OF MINES. FORMULAS. On the right side of each formula, the various calculations, based on the example given, are worked out in figures. To Find: Rubbing sur- face of an air- way. (Sq.ft.) Area of an airway. (Sq.ft.) Velocity. (Ft. per min.) Pressure. (Lb. persq. ft.) Water gauge. (Inches.) Resistance of an airway. (Total pressure, Ib.) No. 1:5 Formula. Specimen Calculation. s = lo 2,000 X 18 = 36,000 sq. ft. = - V 10,000 ^^ 20 sq. it. oi area. . = -- a 8 1 U -\n ^-Mt 3 / 97,650 _ \ .0000000217 X 36,000 IP a / 9.765X20 = \ks u \ .0000000217 X 36,000 97 ' 65 500 ft pa 9.765X20 k s V* .0000000217 X 36,000 X 500 2 ft _.._ lx P a ksqi 20 .0000000217 X 36,000 X 10,000 2 P - a* u p = -j p = Mw p = 5.2 i X T ~ t }0fi 77 V 35 ~ 32 101 ^ ff upcast air. (Feet.) 39 X 459 + < M = 2- w X 459 f 32 ;& -" Variation of the Elements. In the illustration of the foregoing table, we have assumed fixed conditions of motive column, as well as fixed conditions in the mine airways. It is often convenient, however, to know how the different elements, as velocity v, quantity q, pressure p, power u, etc., will vary in different circulations; since we may, by this means, compare the circulations in different airways, or the results obtained by applying different pressures and powers to the same airway. These laws of variation must always be applied with great care. For example, before we can ascertain how the quantity in circulation will vary in different airways, we must know whether the pressure or the power is constant or the saine for each airway. The following rules may always be applied: For a constant pressure: v varies as A/T-; q varies as a \J7~ (relative poten- tial for pressure). For a constant power: v varies as -; q varies as -_ (relative potential ylo F Lo for power). For a constant velocity: q varies as a; p varies as ; u varies as lo. For a constant quantity: v varies inversely as a; p varies inversely as X u s (potential for power); u varies inversely as X u 3 (potential for power) or directly as p. For the same airway: The following terms vary as each other: r, q, SIMILAR AIRWAYS. r = length of similar side, jDr similar dimension. For a constant pressure: v varies as A/^; q varies as r /? \T ; rvane DISTRIBUTION OF AIR. 373 For a constant power: v varies as - ^=; q varies as r x "V/y! r varies as For a constant velocity: q varies as r 2 ; p varies as -; u varies as lr; /- I u r varies as y q , , or . For a constant quantity: v varies inversely as r 2 ; p and u vary inversely as r 5 1 5 IT 5/7 -', r varies as - ^ 'V~ or v~ FURNACE VENTILATION. p (motive column) varies as D; q varies as \/D. FAN VENTILATION. It has been customary in calculations pertaining to the yield of centrif- ugal ventilators to assume as follows: q varies as n; p varies as n' 2 ; u varies as n 3 . More recent investigation, however, shows that when we double the speed we do not obtain double the quantity of air in circulation; or, in other words, the quantity does not vary exactly as the number of revolutions of the fan. Investigation also points to the fact that the efficiency of centrif- ugal ventilators decreases as the speed increases. To what extent this is the case has not been thoroughly established. The variation between the speed of a fan and the quantity, pressure, power, and efficiency, as calculated from a large number of reliable fan tests, may be stated as follows: For the same fan, discharging against a constant potential: q varies as n- 97 . p varies as n > 94 . Complement of efficiency (I K) varies as n-^. The efficiency here referred to is the mechanical efficiency, or the ratio between the effective work qp and the theoretical work of the fan. DISTRIBUTION OF AIR IN MINE VENTILATION. When a mine is first opened, the air is conducted in a single current around the face of all the headings and workings, and returns again to the upcast shaft, where it is discharged into the atmosphere. As the develop- ment of the mine advances, however, it becomes necessary to divide the air into two or more splits or currents. This division or splitting of the air- current is usually accomplished at the foot of the downcast, or as soon as possible after the current enters the mine. There are several reasons why the air-current should be thus divided. The most important reason is that the mine is thereby divided into separate districts, each of which has its own ventilating current, which may be increased or decreased at will. Fresh air is thus obtained at the face of the workings, and the ventilation is under more perfect control. It often happens that certain portions of a mine are more gaseous than others, and it is necessary to increase the volume of air in these portions, which can be readily accomplished when each district has its own separate circulation. Again, the gases and foul air are not conducted from one district to another, but each district is supplied with fresh air direct from the main intake. Should an explosion occur in any part of the mine, it is more apt to be confined to one locality when a mine is thus divided into separate districts. Another consideration is the reduced power necessary to accomplish the same circulation in the mine; or the increased circulation obtained by the use of the same power. Requirements of Law in Regard to Splitting. The Anthracite Mine Law of Pennsylvania specifies that every mine employing more than 75 persons must be divided into two or more ventilating districts, thus limiting the number that are allowed to work on one air-current to 75 persons. The Bituminous Mine Law of Pennsylvania limits the number allowed to work upon one current to 65 persons, except in special cases, where this number may be increased to 100 persons at the discretion of the mine inspector. Practical Splitting of the Air-Current. When the air-current is divided into two or more branches, it is said to be split. The current may be divided one or more times; when split or divided once, the current is said to be traveling 374 VENTILATION OF MINES. in two splits, each branch being termed a split. The number of splits in which a current is made to travel is understood as the number of separate currents in the mine, and not as the number of divisions of the current. Primary Splits. When the main air-current is divided into two or more splits, each of these is called a primary split. Secondary Splits. Secondary splits are the divisions of a primary split. Tertiary Splits. Tertiary splits result from the division of a secondary split. Equal Splits of Air. When a mine is spoken of as having two or more equal splits, it is understood to mean that the length and the size of the separate airways forming those splits are equal in each case. It follows, of course, from this that the ventilating current traveling in each split will be the same, inasmuch as they are all subject to the same ventilating pressure. When an equal circulation is obtained in two or more splits by the use of regulators, these splits cannot be spoken of as equal splits. Unequal Splits of Air. By this is meant that the airways forming the splits are of unequal size or length. Under this head we will consider (a) Natural Division of the Air- Current; (b) Proportionate Division of the Air- Current. Natural Division of the Air-Current. By natural division of air is meant any division of the air that is accomplished without the use of regulators; or, in other words, such division of the air-current as results from natural means. If the main air-current at any given point in a mine is free to traverse two separate airways in passing to the foot of the upcast shaft, and each of these airways is free or an open split, i. e., contains no regulator, the division of the air will be a natural division. In such a case, the larger quantity of air will always traverse the shorter split of airway. In other words, an air-cur- rent always seeks the shortest way out of a mine. A comparatively small current, however, will always traverse the long split or airway. Calculation of Natural Splitting. It is always assumed, in the calculation of the splitting of air-currents, that the pressure at the mouth of each split, starting from any given point, is the same. Since this is the case, in order to find the quantity of air passing in each of several splits starting from a common point, the rule given under Potential Factor of a Mine is applied. This rule may be stated as follows: The ratio between the quantity of air passing in any split and the pressure potential of that split is the same for all splits starting from a common point. Also, the ratio between the entire quantity of air in circulation in the several splits and the siim of the pressure potentials of those splits is the same as the above ratio, and is equal to the square root of the pressure. Expressed as a formula, indicating the sum of the pressure potentials (Xi + JT 2 + etc.) by the expression *2X P , this rule is ~-^r = -^- = i/p. Hence, p = j^> v - ^ and u = 7^C?-ri express the pressure and power, (2 X p Y (2, Ap) respectively, absorbed by the circulation of the splits. These are the basal formulas for splitting, from which any of the factors may be calculated by transposition. They will be found illustrated in the table at the end of this section. We will give here two examples only, showing the calculation oi the natural division of an air-current between several splits. We have, from the above formulas, q\ = -=-^- Q. EXAMPLE. In a certain mine, an air-current of 60,000 cu. ft. per minute is traveling in two splits as follows: Split A, 6 ft. X 8 ft., 5,000 ft, long: split B, 5 ft. X 8 ft., 10,000 ft. long. It is required to find the natural division of this air-current. Calculating the relative potentials for pressure in each split, we have for split A, X l = 48 V-^ ^ . (6 + 8)0.000 I and 2 Xp = j 3849; for split *, X 2 = 40 V 2(5 + 8)10,000 = ' 4%1 J and substituting these values, we have, <7i = ~~ Q X 60,000 = 38,506 cu. ft. per min.; and q z = ~ X 60,000 = 21,494 cu. ft. per min. DISTRIBUTION OF AIR. 375 EXAMPLE. In a certain mine, there is an air-current of 100,000 cu. ft. per minute traveling in three splits as follows: Split A, 6 ft. X 10 ft., 8,000 ft. long; split B, 6 ft. X 12 ft., 15,000 ft. long; split C, 5 ft. X 10 ft., 6,000 ft. long. Find the natural division of this current of air. Calculating the respective relative potentials with respect to pressure, we have for split A, X, = > - ' 9185; for split B, X 2 = 72- = .8314; for split C, X 3 = 50-J- V 2(5 + 10) X 6,000 Adding these potentials, we have 2 X p = .9185 + .8314 + .8333 - 2.5832. Then, applying the foregoing rule, we have 9185 9i = 7^^ X 100,000 = 35,556 cu. ft. per min.; Z.oooZ x 100,000 = 32,184 cu. ft. per min.; and q s = ^ X 100,000 = 32,260 cu. ft. per min. Z.OooZ Total, 100,000 . Proportional Division of the Air-Current. It continually happens that differ- ent proportions of air are required in the several splits of a mine than would be obtained by the natural division of the air-current. It is usually the case that the longer splits employ a larger number of men, and require a larger quantity of air passing through them. They, moreover, liberate a larger quantity of mine gases, for which they require a larger quantity of air than is passing in the smaller splits. The natural division of the air-current would give to these longer splits less air, and to the shorter ones a larger amount of air, which is directly the reverse of what is needed. On this account, recourse must be had to some means of dividing this air pro- portionately, as required. This is accomplished by the use of regulators, of which there are two general types, the box regulator and the door regulator. Box Regulator. This is simply an obstruction placed in those airways that would naturally take more air than the amount required. It consists of a brattice or door placed in the entry, and having a small shutter that can be opened to a greater or less amount. The shutter is so arranged as to allow the passage of more or less air, according to the requirements. The box regulator is, as a rule, placed at the end or near the end of the return air- way of a split. It is usually placed at this point as a matter of convenience, because, in this position, it obstructs the roads to a less extent, the haulage from the back entry in this split being^ carried over to the main haulway, through a cross-cut, before this point is reached. The difficulty, however, can be avoided, in most cases, by proper consideration in the planning of the mine with respect to haulage and ventilation. The objection to this form of regulator is that, in effect, it lengthens the airway, or increases its resistance, making the resistance of all the airways, per foot of area, the same. It is readily observed that, by thus increasing the resistance of the mine, the horsepower of the ventilation is largely increased, for the same circulation. This is an important point, as it will be found that the power required for ventilation is thus increased anywhere from 50$ to 100$ over the power required when the other form of regulator can be adopted. Door Regulator. In this form of regulator, which was first introduced by Beard, the division of the air is made at the mouth of the split. The regu- lator consists of a door hung from a point of the rib between two entries, and swung into the current so as to cut the air like a knife. The door is provided with a set lock, so that it may be secured in any position, to give more or less air to the one or the other of the splits, as required. The posi- tion of this regulator door, as well as the position of the shutter in the box regulator, is always ascertained practically by trial. The door is set so as to divide the area of the airway proportionate to the work absorbed in the 376 VENTILATION OF MINES. respective splits. The pressure in any split is not increased, each split retaining its natural pressure. Calculation of Pressure for Box Regulators. When any required division of the air-current is to be obtained by the use of box regulators, these are placed in all the splits, save one. This split is called the open, or free, split, and its pressure is calculated in the usual way by the formula p = -"--. The natural pressure in this open split determines the pressure of the entire mine, since all the splits are subject to the same pressure in this form of splitting. First, determine in which splits regulators will have to be placed, in order to accomplish the required division of the air. Calculate the natural pres- sure, or pressure due to the circulation of the air-current, for each split, when passing its required amount of air, using the formula p = -~g-. The split showing the greatest natural pressure is taken as the free split. In each of the other splits, box regulators must be placed, to increase the pressure in those splits; or, in other words, to increase the resistance of those splits per unit of area. EXAMPLE. The ventilation required in a certain mine is: split A, 6 ft. X 9 ft., 8,000 ft. long; 40,000 cu. ft. per min. split J5, 5 ft. X 8 ft., 6,000 ft. long; 40,000 cu. ft. per min. split C, 9 ft. X 9 ft., 8,000 ft. long; 10,000 cu. ft. per min. split Z>, 6 ft. X 8 ft., 10,000 ft. long; 30,000 cu. ft. per min. In which of these splits should regulators be placed, to accomplish the required division of air, and what will be the mine pressure ? Calculating the pressure due to friction in each split when passing its required amount of air, we find, for split A, p = 000000217 X 2(6 + 9)8,000X40,000* = ^ ]b ^ ^ ft ; for split B, p = .0000000217X2(5^+8)6,000X40.000; _ ^ ^ per ^ ft _. for split C, p = .0000000217X2(9^+9)8.000X10.000; = im , per ^ ft . for split D. p = :0X)000217X2(6+ a 8)10,OOOX30.00g = ^ ]b per ^ ft Split B has the greatest pressure, and is therefore the free split. Box regulators are placed in each of the other splits to increase their respective pressures to the pressure of the free split or the mine pressure. Therefore, the mine pressure in this circulation is 84.63 Ib. per sq. ft. The Size of opening in a box regulator is calculated by the formula for determining the flow of air through an orifice in a thin plate under a certain head or pressure. The difference in pressure between the two sides of a box regulator is the pressure establishing the flow through the opening, which corresponds to the head h in the formula v = \/2gh. This regulator is usually placed at the end of a split or airway, and since the regulator increases the pressure in the lesser split so as to make it equal to the pressure in the other split, the pressure due to the regulator will be equal to the ventilating pressure at the mouth of the split, less the natural pressure or the pressure due to friction in this split. Hence, when the position of the regulator is at the end of the split, the pressure due to friction in the split is first calculated by the formula p = f-, and this pressure is deducted from the ventilating pressure of the free or open split, which gives the pressure due to the regulator. This is then reduced to inches of water gauge, and substituted for i in the formula A = ' / _ q . The value of A thus obtained is yi the area (square feet) of the opening in the regulator. EXAMPLE. 50,000 cu. ft. of air is passing per minute in a certain mine, in two equal splits, under a pressure equal to 2 in. of water gauge, and it is required to reduce the quantity of air passing in one of these splits, by a box regulator placed at the end of the split, so as to pass but 15,000 cu. ft. per DISTRIBUTION OF AIR. 377 minute in this split. Find the area of the opening in the regulator, assu- ming that the ventilating power is decreased, to maintain the pressure con- stant at the mouth of the splits after placing the regulator. The size and length of each split is 6 ft. X 10 ft. and 10,000 ft. long. The natural pressure for the split in which, the regulator is placed will be ksq* .0000000217 X 2(6 + 10) X 10,000 X 15,000 2 ,. _ ., ,, = - . ~ - (6 X 10)' Then, ~ = 1.4 in. of water gauge (nearly), due to friction of the air- current in this split. And, 2 1.4 = .6 in. water gauge due to regulator. Finally, A - ^^ = - .0004 q _ .0004 X 15,000 = 7.746 sq. ft., area of opening. I/ .6 I/ .6 Size of Opening for a Door Regulator. The sectional area at the regulator is divided proportionately to the work to be performed in the respective splits according to the proportion A\ : A% : : u\ : u$. Or since A\ + A% = a, we have - X a. This furnishes a method of pro- portionate splitting in which each split is ventilated under its own natural pressure. The same result would be obtained by the placing of the box regulator at the intake of any split, thereby regulating the amount of air passing into that split, but the door regulator presents less resistance to the flow of the air-current. The practical difference between these two forms of regulators is that in the use of the box regulator each split is ventilated under a pressure equal to the natural pressure of the open or free split, which very largely increases the horsepower required for the ventilation of the mine; while in the use of the door regulator each split is ventilated under its own natural pressure, and the proportionate division of the air is accomplished without any increase of horsepower. This is more clearly explained in the two following paragraphs, and the table showing the com- parative horsepowers of the two methods. Calculation of Horsepower for Box Regulators. By the use of the box regu- lator, the pressure in all the splits is made equal to the greatest natural pressure in any one. This split is made the open or free split, and its natural pressure becomes the pressure for all the splits, or the mine pressure. This mine pressure, multiplied by the total quantity of air in circulation (the sum of the quantities passing in the several splits), and divided by 33,000, gives the horsepower upon the air, or the horsepower of the circulation. Thus, in the first example given on page 376, in which for split B the pressure p 84.63 lb. per sq. ft. and the total quantity of air passing per minute is 120,000 cu. ft., we have h = - 84.63 X 120,000 - = 307.745 H. P. 33,000 Calculation of Horsepower for Door Regulators. In the use of the door regulator, each split is ventilated under its own natural pressure, and, hence, in the calculation of the horsepower of such a circulation, the power of each split must be calculated separately, and the sum of these several powers will be the entire power of the circulation. For the purpose of com- parison, we tabulate below the results obtained in the application of these two methods of dividing the air in the above example. Splits. Horsepower. Natural Division. Required Division. Door Box Regulator. Regulator. Splits, 6ft. X 9 ft., 8,000 ft. long 28,277 40,000 64.145 102.582 Split B, 5 ft. Split C, 9 ft. Split J>, 6 ft. X 8 ft., X 9 ft,, X 8 ft., 6,000 ft. long 8,000 ft. long 10,000 ft. long 22,360 47,423 21,940 40,000 10,000 30,000 102.582 .356 44.955 102.582 25.645 76.936 Totals 120,000 120,000 212.038 307.745 3*"O /o VENTILATION OF MINES. SPLITTING FORMULAS. The following table of formulas will serve to illustrate the methods of calculation in splitting. The example assumes the same airway as that given on page 369 and used to illustrate the table of formulas, page 370, but the air- current is divided, as specified in the table: NATURAL DIVISION. Primary Splits. Split (1) = 4 ft. X 5 ft., 800 ft. long. Split (2) = 4 ft. X 5 ft., 1,200 ft. long. To Find: No. Formula. Specimen Calculation. Y ! a V20 ^ OP0 Potential for a ^ks' .0000000217 X 14,400 pressure. 35 V20 4 10-1 ^X p = (Xi + Xt + etc.). .0000000217X21,600 ^ 5,060 + 4,131 = 9,191. Natural divi- 41 n Xp V (1) |^j X 10,000 = 5,505 cu. ft. sion. q zx p XQ ' (2) ^ X 10,000 = 4,495 cu. ft. Or the natural division may be calculated from the pressure at the mouth of the several splits by using formula (23); thus, 23 q = X p ]/p. (1) 5,0601/1.1838 (2) 4,131 1/1.1838 See formula (42) = 5,505 cu. ft. = 4,495 cu. ft. Pressure. 42 * -(rf |^ = 1 , 18 381 b . Power. Q 3 10,000' ,838 units. 9,191 a Quantity. 44 45 10,000 cu. ft. = 10,000 cu. ft. Q = ?,X p Vp. 9,191 V 1.1838 = Q = f(^,X p ^u. 1^9,191 2 X11,838 Increase of quantity due to splitting. ( Pressure con- stant.) 46 Q'' V n |^ X 10,000 - = 28,722 cu. ft. -A-y Increase in quantity due to splitting. ( Power con- stant.) 47 - 20,205 cu. ft. I/"S,X P \* 10 000 A/( 9 ' 191 ) 2 - M t ,-.| \ \Q,^UU/ SPLITTING FORMULAS. Secondary Splits.-(l) 4 ft. X 5 ft., 800 ft. long. (2) 4 ft. X 5 ft., 500 ft. long. (3) 4 ft. X 5 ft., 400 ft. long. (4) 4 ft. X 5 ft., 300 ft. long. The calculation is often shortened, when many splits are concerned, by using the relative potential, omitting the factor k; but the final result must then be multiplied by k to obtain the pressure or power; or, these factors must be divided by k, when finding the quantity, as in formulas (49) to (51). * s la II 1 lo t T r ^ O gl 380 VENTILATION OF MINES. PROPORTIONATE DIVISION. Primary Splits (only). (1) 4 ft. X 5 ft., 800 ft. long = 3,500 cu. ft. (2) 4 ft. X 5 ft., 1,200 ft. long = 6,500 cu. ft. To Find: No Formula. Specimen Calculatio Pressure due to . (i) 3,500 2 5,0602 ~~ .47845 Ib. friction. 13 p = "5? (2) 6,500 2 _ 2.4757 Ib. 4,131* To accomplish this division of air, the pressure in split (1) must be increased by means of a regulator to make it equal to the pressure in the free or open split (2), and, hence, the pressure due to the regulator- is equal to the difference between the natural pressures in these splits. Pressure due to the regulator in split (1). 53 P * P-2-Pi- 2.4757 .47845 = 1.99725 Ib. Area of the opening in regulator. 37 .0004<7 1 Vi .0004 X 3,500 2.259 sq. ft. V 1.99725 5.2 Secondary Splits. (1) 4 ft. X 5 ft., 800 ft. 3,500 cu. ft. (2) 4 ft. X 5 ft., 500 ft. 6,500 cu. ft. (3) 4 ft. X 5 ft., 400 ft. 4,000 cu. ft. (4) 4 ft. X 5 ft., 300 ft. 2,500 cu. ft. NOTE When using the relative potential, multiply the result by k, to obtain the pressure, or the power. Pressure due to friction. Free 13 split second- ary pressure. P (1) .0000000217^^)* (3} ftnnnnnn9i7/ 4,000 \ = .47848 Ib. = 1.0314 Ib. 31^48 Ib 17 V 1.0541 / = .091546 Ib. Since the natural pressure in (3) is greater than that in (4), (3) is the free split, and its natural pressure is the pressure for the secondary splits. The pressure for the primary splits is then found by first adding the pressures in (2) and (3), and if their sum is greater than the natural pressure for (1), it becomes the pressure for the primary splits, or the mine pressure. If the natural pressure for (1) is the greater, this is made the free split, and its natural pressure becomes the primary or mine pressure. In this case, the secondary pressure must be increased by placing a regulator in split (3). Primary or mine pressure. Pressure due to the regula- tors. Areas of open- ings in the regulators. 37 p 2 +PS- 1.0314 + .31248 = 1.34388. Ps Pi- (Pz + Ps)Pi- (4) (1) .31248 .091546 = .220934 Ib. (1.0314 + .31248) .47848 = .86540 Ib. .0004 q (4) (1) .0004X2,500 iS5 ft V '.220934 5.2 .0004X3,500 31328sqft /.8654 METHODS AND APPLIANCES. 381 METHODS AND APPLIANCES IN THE VENTILATION OF MINES. Ascensional Ventilation. Every mine, as far as practicable, should be venti- lated upon the plan known as ascensional ventilation. This term refers particularly to the ventilation of inclined seams. The air should enter the mine at its lowest point, as nearly as possible, and from thence be conducted through the mine to the higher points, and there escape by a separate , shaft, if such an arrangement is practicable. Where the seam is dipping considerably and is mined through a vertical shaft, the upcast shaft should be located as far to the rise of the downcast shaft as possible. The intake air is then first conducted to the lowest point of the dip workings, which it traverses upon its way to the higher workings. In the case of a slope working where a pair of entries is driven to the dip, one being used as the intake and the other the return, there being cross-entries or levels driven at regular intervals along the slope, the air should be conducted at once to the inside workings, from which point it returns, ventilating each pair of cross- entries from the inside, outwards. Where the development of the cross- entries or levels is considerable, their circulation is considered separately, and a fresh air split is made in the intake at each pair of levels. In all ventilation, the main point to be observed is to conduct the air-current first to the inside workings, from whence it is distributed along the working face as it returns toward the upcast. General Arrangement of Mine Plan. Every mine should be planned with respect to three main requirements, viz.: (a) haulage; (b) drainage; (c) ventilation. These requirements are so closely connected with one another that the consideration of one of them necessitates a reference to all. The mine should be planned so that the coal and the water will gravitate toward the opening, as far as possible. There are many reasons, in the consideration of non-gaseous mines, why the haulage should be effected upon the return airways. The haulage road is always a dusty road, caused by the traveling of men and mules, as well as by the loss of coal in transit, which becomes reduced to fine slack and powder. If the haulage is accomplished upon the intake entry or air-course, this dust is carried continually into the mine and working places, which should be avoided whenever possible. When the loaded cars move in the same direction as the return air, the ventilation of the mine is not as seriously impeded. It is often the case that fewer doors are required upon the return airway than upon the intake, which is a feature favorable to haulage roads. Again, in this arrangement, the hoisting shaft is made the upcast shaft, which prevents the formation of ice, and conse- quent delay in hoisting in the winter season. The arrangement, however, presupposes the use of the force fan or blower, since if a furnace or exhaust fan is employed, a door, or probably double doors, would have to be placed upon the main haulage road at the shaft bottom, which would be a great hindrance. In the ventilation of gaseous mines, however, other and more important considerations demand attention. The gaseous character of the return current prevents making the return airway a haulage way. In such mines, the haulage should always be accomplished upon the intake air, as any other system would often result in serious consequences. In such gaseous mine, men and animals must be kept off the return airways as far as this is possible. As far as practicable, ventilation should be accomplished in sections or districts, each district having its own split of air from the main intake, and its own return connecting with the main return of the mine. Reference has been made to this under Distribution of the Air in Mine Ventilation. This splitting of the air-current is accomplished preferably by means of an air bridge, either an under crossing or an over crossing. There are, in general, three systems of ventilation, with respect to the ventilating motor employed: (a) natural ventilation; (6) furnace ventilation; (c) mechanical ventilation. Natural ventilation means such ventilation as is secured by natural means, or without the intervention of artificial appliances, such as the furnace, or any mechanical appliances by which the circulation of air is maintained. In natural ventilation, the ventilating motor or air motor is an air column that exists in the downcast shaft by virtue of the greater weight of the downcast air. This air column acts to force the air through the airways 382 VENTILATION OF MINES. of the mine. An air column always exists where the intake and return currents of air pass through a certain vertical height, and have different temperatures. This is the case whether the opening is a shaft or a slope; since, in either case, there is a vertical height, which in part determines the height of air column. The other factor determining the height of air column is the difference of temperature between the intake and return. The calculation of the ventilating pressure in natural ventilation is identical with that of furnace ventilation, which is described later. Ventilation of Rise and Dip Workings. We have referred to the air column existing either in vertical shafts or slopes as the motive column or venti- lating motor. Such an air column will be readily seen to exist in any rise or dip workings within the mine, and may assist or retard the circulation of the air-current through the mine. It is this air column that renders the ventilation of dip workings easy, and that of rise workings correspondingly difficult, depending, however, on the relative temperature of the intake and return currents; the latter usually is the warmer of the two, which gives rise to the air column. The influence of such air columns must always be taken into account in the calculation of any ventilation. This is often neglected. The influence of air columns in rise or dip workings, within the mine, becomes very manifest where, from any reason, the main intake current is increased or decreased. For example, a mine is ventilated in two splits, a rise and a dip split; a current of 50,000 cu. ft. of air is passing in the main airway, 30,000 cu. ft. passing into the dip workings, and 20,000 into the rise workings. A fall of roof in the main intake airway, or other cause, reduces the main current from 50,000 to 35,000 cu. ft. Instead, now, of 21,000 cu. ft. going to the dip workings and 14,000 to the rise workings, we find that this proportion no longer exists, but that the dip workings are taking more than their proportion of air, and the rise workings less. Thus, the circulation being decreased to 35,000 cu. ft., the dip workings will probably take 25,000 cu. ft., and the rise workings 10,000 cu. ft. On the other hand, had the intake current been increased instead of decreased, the rise workings would then take more than their proportion, while the dip workings would take less. The reason for this distribution is evident; suppose, for example, the intake or mine pressure is 3 in. of water gauge, and in the dip workings there is i in. of water gauge acting to assist ventilation, while a like water gauge of i in. in the rise workings acts to retard ventilation. The effective water gauge in the dip workings is therefore 3 in., while the effective water gauge in the rise workings is 2i in., or they are to each other as 7 : 5. If, now, the mine pressure is decreased to, say,* 2 in., the effective rise and dip pressures will be, respectively, 2i in. and H in., or as 5 : 3. We observe, before the decrease, the dip pressure was , or 1.4, times the rise pressure, while after the decrease took place in the mine pressure, the dip pressure became , or 1.66, times the rise pressure. The relative quantities passing in the dip split before and after the decrease took place, as compared with the quantities passing in the rise split, will be as the y 1.4 : j/1.66, showing an increase of proportion. Now, instead of a decrease taking place in the mine pressure, let us suppose it is increased^ say, from 3 in. to 4 in. The effective pressures in the dip and rise workings will then be, respectively, 4 in. and 3i in., or they will be to each other as 9 : 7, instead of 7 : 5. Here we observe that the dip pressure is If or 1.15, times the rise pressure, instead of 1.4. The relative quantities, therefore, passing in the dip split, before and after the increase of the mine pressure, as compared with the quantities passing in the rise split, will be in the ratio of \/ L4 : 1/1.15, showing a decrease of proportion. We observe that any alteration of the mine pres- sure by which it is increased or decreased does not affect the inside dip or rise columns, and hence the disproportion obtains. In case of a decrease of the mine pressure, the dip workings receive more than their proportion of air, and in case of an increase of the mine pressure, they receive less than their proportion of air. Influence of Seasons. In any ventilation, air columns are always established in slopes and shafts, owing to the relative temperatures of the outside and inside air. The temperature of the upcast, or return column, may always be assumed to be the same as that of the inside air. The temperature of the downcast, or intake column, generally approximates the temperature of the outside air, although, in deep shafts or long slopes, this temperature may be changed considerably before the bottom of the shaft or slope is reached, and METHODS AND APPLIANCES. 383 consequently the average temperature of the downcast, or intake, is often different from that of the outside air. The difference of temperatures will also vary with the season of the year. In winter the outside temperature is below that of the mine, and the circulation in shafts and slopes is assisted, since the return columns are warmer and lighter than the intake columns for the same circulation. In the summer season, however, the reverse of this is the case. The course of the air-current will thus often be changed. When the outside temperature approaches the average temperature of the mine, there will be no ventilation at all in such mines, except such as is caused by accidental wind pressure. In furnace ventilation the temperature of the upcast column is increased above that of the downcast column by means of a furnace. The chief points to be considered in furnace ventilation are in regard to the arrange- ment and size of the furnace. Furnace ventilation should not be applied to gaseous seams, and in some cases is prohibited by law. It is, however, in use in many mines liberating gas. In such cases the furnace fire is fed by a current of air taken directly from the air-course, sufficient to maintain the fire, and the return current from the mine is conducted by means of a dumb drift, or an inclined passageway, into the shaft, at a point from 50 to 100 ft. above the seam. At this point, the heat of the furnace gases is not sufficient for the ignition of the mine gases. The presence of carbonic-acid gas in the furnace gases also renders the mine gases inexplosive. In other cases, where the dumb drift is not used, a sufficient amount of fresh air is allowed to pass into the return current to insure its dilution below the explosive point before it reaches the furnace. Construction of a Mine Furnace. In the construction of a mine furnace, a sufficient area of passage must be maintained over the fire and around the furnace to allow the passage of the air-current circulating in the mine. The velocity of the current at the furnace should be estimated not to exceed 20 ft. per second, and the entire area of passage calculated from this velocity. Thus, for a current of 50,000 cu. ft. of air per minute, the area of passage through and around the furnace should be not less than This is a safe method of calculation, notwithstanding the fact that the velocity of the air is often much more than 20 ft. per second, yet the volume of the air is largely increased owing to the increase of temperature. The length of the furnace bars is limited to the distance in which good firing can be accomplished, and should not exceed 5 ft. The width of the grate will therefore determine the grate area. The grate area must, in every case, be sufficient for the heating of the air of the current to a temperature such as to maintain the average temperature of the furnace shaft high enough to produce the required air column, or ventilating pressure, in the mine. The area A of the grate of the furnace is best determined by the formula 34 A = X H. P., in which A = grate area in square feet; H. P. = horse- V D power of the circulation; and D = depth of shaft in feet. The horsepower for any proposed circulation may always be determined by dividing the quantity of air (cubic feet per minute) by the mine potential X u , and cubing and dividing the result by 33,000; thus, The furnace should have proper cooling spaces above and at each side; upon one side, at least, should be a passageway or manway. The furnace should be located at a point from 10 to 15 yd. back from the foot of the shaft, at a place in the airway where the roof is strong. This is well secured by railroad iron immediatley rover the furnace. A good foundation is obtained in the floor, and the walls of the furnace carried up above the level of the grate bars, when the furnace arch is sprung. If possible, a full semicircle should be used in preference to a flat arch. The sides and arch of the furnace should be carried backwards to the shaft; this is necessary in order to prevent ignition of the coal. The walls and arch are constructed of firebrick a sufficient distance from the furnace, and after- wards of a good quality of hard brick; the shaft is also lined with brick or protected by sheet iron a sufficient height to prevent the ignition of the curbing. 384 VENTILATION OF MINES. Air Columns in Furnace Ventilation. As previously stated, natural ventilation and furnace ventilation are identical, in so far as in each the ventilating motor is an. air column. This air column is an imaginary column of air whose weight is equal to the difference between the weights of the upcast and downcast columns. The upcast and downcast columns in furnace ventilation are sometimes referred to as the primary and secondary columns, respectively. The primary or furnace column is, in nearly every case, a vertical column, and consists of a single air column whose average temperature is easily approximated. According to the manner of opening the mine, whether by shaft, slope, or drift, the secondary column may be a vertical column in the shaft, an inclined column in the slope, or an outside air column in case of a drift opening. Again, it is to be observed that in case of a slope opening where the top of the furnace shaft is much higher than the mouth of the slope, and the dip of the slope is considerable, the secondary column consists of two columns of different temperatures, an outside air column and the slope column. These two parts of the secondary column must be calculated separately, and their sum taken for the weight of the secondary column. The level of the top of the furnace shaft determines the top of both the primary and secondary columns, whether these columns are in the outer air or in the mine. The weight of the upcast or primary column is largely affected by its gaseous condition. For example, if the return current from the mine is laden with blackdamp C0 2 , its weight will be much increased, since this gas is practically H times as heavy as air, while, if laden with marsh gas, or firedamp mix- ture, its weight will be considerably reduced. These causes decrease and increase, respectively, the ventilating pressure in the mine. Inclined Air Columns. In a slope opening, the air column is inclined; it is none the less, how- ever, an air column, and must be calculated in ~ ,_ the same manner as a vertical column whose ver- IG - ' tical height corresponds to the amount of dip of the slope. Fig. 7 shows a vertical shaft and a slope, the air column in each of these being the same for the same tem- perature. The air column in all dips and rises must be estimated in like manner, by ascertaining the vertical height of the dip. Calculation of Ventilating Pressure in Furnace Ventilation. The ventilating pressure in the mine airways, in natural or in furnace ventilation, is caused by the difference of the weights of the primary and secondary columns. Air always moves from a point of higher pressure toward a point of lower pressure, and this movement of the air is caused by the difference between these two pressures. In this calculation each column is supposed to have an area of base of 1 sq. ft. Hence, if we multiply the weight of 1 cu. ft. of air at a given barometric pressure, and having a temperature equal to the average temperature of the column, by the vertical height D of the column, we obtain not only the weight of the column but the pressure at its base due to its weight. Now, since the ventilating pressure per square foot in the airway is equal to the difference of the weights of the primary and secondary columns, we write /1.3253XB 1-3253 X B\ n 459 +T J~ EXAMPLE. Find the ventilating pressure in a mine ventilated by a furnace, the temperatures of the upcast and downcast columns being, respectively, 350 F. and 40 F., the depth of the upcast and downcast shafts being each 600 ft., and the barometer 30 in. Substituting the given values in the above equation, we have p = 1.3253 X 30 X 600 ( ^ 4F"^Kn) = 18 ' 32 lb- per sq ' ft> Calculation of Motive Column or Air Column. It is often convenient to express the ventilating pressure p (Ib. per sq. ft.) in terms of air column or motive column M, in feet. The height of the air column M is equal to the pressure p divided by the weight, w of 1 cu. ft. of air, or M = The expres- sion for motive column may be written either in terms of the upcast air or of the downcast air, the former giving a higher motive column than the latter for the same pressure, since the upcast air is lighter than that of the MECHANICAL VENTILATORS. 385 downcast. As the surplus weight of the downcast column of air produces the ventilating pressure, it is preferable to write the air column in terms of the downcast air, or, in other words, to consider the air column as being located in the downcast shaft, and pressing the air downwards and through the airways of the mine. If we divide the expression previously given for the ventilating pressure by the weight of 1 cu. ft. of downcast air ( *" ^g * t ) (y _ i \ T^Q - m ) ' X A which is the expression for motive column in terms of the downcast air. If, on the other hand, we divide the expression for the ventilating pressure by the weight of 1 cu. ft. of upcast air / ~ L ^ ifr ) > we obtain (if _ ^ \ . j X -D, which is the expression for motive column in terms of the upcast air. Influence of Furnace Stack. To increase the height of the primary or furnace column, a stack is of ten erected over the mouth of the furnace shaft. The effect of this is to increase the ventilating pressure in the mine in proportion to the increased height of the primary column, and to increase the quantity of air passing in the mine in proportion to the square root of this height. Thus, the square root of the ratio of the heights of the primary column, before and after the stack is erected, is equal to the ratio of the quantities of air passing before and after the erection of the stack. Or, calling these quantities (ft and q 2 , and the height of stack d, we have D MECHANICAL VENTILATORS. A large number of mechanical ventilators have been invented and applied, with more or less success, to the ventilation of mines. The earliest type of ventilator was the wind cowl, by which the pressure of the wind at the sur- face was brought to bear effectively upon the mine airways by the action of a cowl whose mouth could be turned toward the wind; this was naturally very unreliable. The waterfall was also extensively applied at one time, but its application could only be made where there was a reliable source of water supply, and where the drainage of the mine could be effected through a tunnel, or where the mine opening could be placed in connection with such a waterfall outside of the mine. Where these conditions are obtained, as is the case in some mountainous districts, the waterfall is still in use, as it is an effective means of ventilation, and is economical. Its application, however, must be limited to the ventilation of small mines. The steam jet is another mechanical device for producing an air-current in the mine. The steam is allowed to issue from a jet at the bottom of an upcast shaft, and, by the force of its discharge, causes an upward current in the shaft. Its use, however, is very limited, and is practically restricted to the ventilation of shafts while sinking. In this connection it may be mentioned, however, that the discharged steam from the mine pumps, where practicable, may be conducted into the upcast shaft; or the discharge pipe from the pumps may be carried up the upcast shaft, its heat increasing the temperature of the shaft, and thereby increasing the motive column and the ventilation. Fan Ventilation. Mechanical motors of this type present two distinct modes of action in producing an air-current: (a) by propulsion of the air; .and (b) by establishing a pressure due to the centrifugal force incident to the revolution of the fan. Fans have been constructed to act wholly on one or the other of these principles, while others have been constructed -to act on both of these principles combined. Disk Fans. The action of this type of fan resembles that of a windmill, except that in the latter the wind drives the mill, while in the former the fan propels the air or produces the wind. This type of fan consists of a number of vanes radiating from a central shaft, and inclined to the plane of revolution. The fan is set up in the passageway between the outer air and .the mine airways. Power being applied to the shaft, the revolution of the 386 VENTILATION OF MINES. vanes propels the air, and produces a current in the airways. The fan may force the air through, or exhaust the air from, the airways, according to the direction of its revolution. This type of fan is most efficient under light pressures. It has found an extensive application in mining practice, and has a large number of devotees, but has been replaced to a large degree in the ventilation of extensive mines. This type of fan acts wholly by propulsion. Centrifugal fans include all fans that act solely on the centrifugal principle, and those that combine the centrifugal and propulsion principles. The action of the fan, whether by centrifugal force alone, or combined with propulsion, depends on the form of the fan blades. In this type of fan, the blades are all set at right angles to the plane of revolution, and not inclined, as in the disk fan just described. The blades may, however, be either radial blades, sometimes spoken of as paddle blades, or they may be inclined to the radius either forward in the direction of revolution, or backward. When the blades are radial, the action of the fan is centrifugal only. The inclina- tion of the blades backward from the direction of motion gives rise to an action of propulsion, in addition to the centrifugal action of the fan. The blades in this position may be either straight blades in an inclined position, as in the original Guibal fan, or they may be curved backward in the form of a spiral, as in the Schiele and Waddle fans. Centrifugal fans may be (a) exhaust fans or (6) force fans or blowers. In each, the action of the fan is essentially the same; i. e., to create a difference of pressure between its intake or central opening, and its discharge at the circumference. The centrifugal force developed by the revolution of the air between the blades of the fan causes the air within the fan to crowd toward the circumference; as a result, a depression is caused at the center and a compression at the circumference, giving rise to a difference of pressure between the intake and the discharge of the fan. Exhaust Fans. If the intake opening of the fan be placed in connection with the mine airways, and the discharge be open to the atmosphere, the fan will act to create a depression in the fan drift leading to the mine, which will cause a flow of air through the mine airways and into and through the fan. In this case, the fan is exhausting, its position being ahead of the current that it produces in the airway. The atmospheric pressure at the intake of the mine forces the air or propels the current toward the depression in the fan drift caused by the fan's action. Force Fans and Blowers. If the discharge opening of the fan be placed in connection with the mine airways, a compression will result in the fan drift owing to the fan's action, and the air will flow from this point of compres- sion through the airways of the mine, and be discharged into the upcast, and thence into the atmosphere. The ventilating pressure in the case of either the exhaust fan or the force fan is equal to the difference of pressure created by the fan's action. In the former case, when the fan is exhausting, the absolute pressure in the fan drift is equal to the atmospheric pressure less the ventilating pressure, while in the latter case, when a fan is forcing, the absolute pressure in the fan drift is equal to the atmospheric pressure increased by the ventilating pressure. This gives rise to two distinct systems of ventilation, known as (a) vacuum system and (b) plenum system. Vacuum System of Ventilation. In this system, the ventilation of the mine is accomplished by creating a depression in the return airway of the mine. This depression may be created by the action of an exhaust fan, as just described, or by the action of a furnace. In either case, the absolute pres- sure in the mine is below that of the atmosphere, or, we may say, the mine is ventilated under a pressure below the atmospheric pressure. This system has many points of advantage over the plenum system, and for years was considered by many the only practicable system of ventilation. Its appli- cation, however, is controlled by conditions in the mine with respect to the gases liberated, the arrangement of the haulage system, etc. Plenum System of Ventilation. In this system, the air-current is propelled through the mine airways by means of the compression or ventilating pressure created at the intake opening of the mine. This ventilating pres- sure may be established by a fan, waterfall, wind cowl, or any other mechanical means at hand, in this system, the absolute pressure in the mine is above that of the atmosphere; or, as we say, the mine is ventilated under a pressure above the atmospheric pressure. Comparison of Vacuum and Plenum Systems. No hard-and-fast rule can be made to apply in every case, as each system has its particular advantages. TYPES OF FANS. 387 In case of a sudden stoppage of the ventilating motor at a mine, there is, in the vacuum system, a rise of mine pressure, instead of a fall, and the gases are driven back into the workings for a while, while, in the plenum system, any stoppage of the ventilating motor is followed at once by a fall of pressure in the mine, and mine gases expand more freely into the passage- ways at the very moment when their presence is most dangerous. This point must be carefully considered in the ventilation of deep workings. In shallow workings, the plenum system is often advantageous, especially if there is a large area of abandoned workings that have a vent or opening to the atmosphere, either through an old shaft or through crevices extending to the surface. Every crevice or other vent becomes a discharge opening by which the mine gases find their way to the surface, and the gases accumu- lating in the old workings are driven back into the workings, and find their way to the surface instead of being drawn into the mine airways, as would be the case in an exhaust system.- Any given fall of the barometer affects the expansion of mine gases to a less extent in the plenum system than in the vacuum system, but this small advantage would not give it consider- ation in determining between the adoption of the one or the other of these two systems; regard must be had, however, to other conditions more vital than this. In the ventilation of gaseous seams, owing to the necessity of making the intake airway the haulage road, the exhaust system has usually been adopted, as the main road is thereby left unobstructed by doors. TYPES OF CENTRIFUGAL FANS. We shall only mention the more prominent types of fans that have been or are still in use, giving the characteristic features, as nearly as possible, of each fan. Many fans have been built, however, combining many of the features that originally characterized a single type of fan. Nasmyth Fan. Fig. 8 is the original type of fan representing straight paddle blades radiating from the center, which is its characteristic feature. This was probably the earliest attempt to apply the centrifugal principle to a mine ventilator, and al- though not recognized at the FIG. time, the fan embodied some of the most essential principles in centrifugal ventilation. It possessed certain disadvantages, however, chief of which was a contracted central or intake opening. The blades, also, were straight throughout their entire length, being normal both to the inner and outer circles of the fan, and thus did not provide for receiving the air without shock at the throat of the fan. The depth of Nasmyth' s blades equaled one-half the radius of the fan, which was, under ordinary conditions of mine practice, far too great, and gave the fan a low efficiency. Biram's Ventilator. About 1850, Biram at- tempted to improve upon the Nasmyth ventilator by reducing the depth of blade so that it was but one-tenth of the radius. The blades were straight, as in Nasmyth's ventilator, but inclined backwards from the direction of motion at a considerable angle. A large number of these blades were employed. This fan was run at a considerable speed, but proved very inefficient. It depended more on the effort of propulsion given to the air than on the centrifugal principle, as the depth of the blade was as much too small as that of Nasmyth's was too great. The intake or central opening in this fan was as contracted as in the former type. See Fig. 9. Waddle Ventilator. In this fan, Fig. 10, the inventor attempted to reenforce the discharge pressure at the circumference against the pressure of the FIG. 9. 388 VENTILATION OF MINES. atmosphere. The discharge took place all around the entire circumference of the fan, which was entirely opened to the atmosphere. The blades were curved backward from the direction of motion in spiral form. The width of the blade decreased from the throat toward the circumference, so as to present an inverse ratio to the length of radius. Thus, the area of passage between the fan blades was maintained constant from the throat to the circumfer- ence of the fan. The pur- pose of this was to maintain the velocity of the air through the fan constant, and to fortify the pressure due to the fan against the atmospheric pressure at the point of discharge. The es- sential features of the Wad- dle ventilator were, there- fore, curved blades tapered toward the circumference, and a free discharge into the atmosphere all around FIG. 10. the circumference. This type is the best type of the open-running fan having no peripheral casing, and discharging air into the atmosphere all around the circumference. Schiele Ventilator. This ventilator, Fig. 11, was constructed on the same principles as the Waddle ventilator just described, but differed from the latter, as the discharge was made into a spiral chamber surrounding the fan and leading to an expanding or evase chimney. There was some advan- tage in this feature, as it protected the fan against the direct influence of the atmosphere, and reduced the velocity of discharge: but, in each of these fans, the intake opening was contracted, and the depth of blade was very great, yielding a comparatively low efficiency. Guibal Ventilator. The next important step in the improvement of centrif- ugal ventilators was introduced by M. Guibal, who constructed a fan, Fig. 12, embodying the features of the Nasmyth ventilator, with the addition of a casing built over the fan to protect its circumference. This casing was, however, a tight-fitting casing, and as such, differed very materially from the Schiele casing. In the Guibal fan the blades were arranged upon a series of parallel bars passing upon each side of the center and at some distance from it. By this construction, the blades were not radial at their inner edge or the throat of the fan. They were curved, however, as they approached the circumference of the fan, so as to be normal or radial at the circumference. FIG. 12. The advantage of this construction was to give a strong skeleton or frame- work to the revolving parts, and. further, each blade was inclined to the radius at its inner extremity, the effect of which was to receive the air upon the blade with less shock than was the case in the Nasmyth ventilator. The intake or central opening, however, was very contracted, and the tight-fitting EFFICIENCY OF FANS. 389 casing about the circumference prevented the effective action of the fan during a considerable portion of its revolution. The fan was supplied with an Svase" chimney, which was a feature of the Schiele fan, but vibration was so strong that a shutter was required at the cut-off below FIG. 13. the chimney, to prevent it. This shutter was made adjustable, and is known as the Walker shutter, having been applied to the fan later. The Guibal ventilator presents some important and valuable features in the protecting cover, and in the blades meeting the outer circumference radially, and in the air being received with less shock than before. On the whole, it has proved a very efficient ventilator, although much work is lost by reason of its contracted central orifice and tight casing, where the same is used. Murphy Ventilator. Fig. 13 consists of twin fans supported on the same shaft and set a few feet apart. Each fan receives its air on one side only, the openings being turned toward each other. This ventilator is built with a small diameter, and is run at a high speed. The blades are curved back- wards from the direction of motion. The intake opening is considerably enlarged; a spiral casing generally surrounds the fan, and in every respect this fan makes an efficient high-speed motor. It has received considerable favor in the United States, where it has been introduced into a large number of mines. Capell Ventilator. Perhaps none of the centrifugal ventilators have been as little understood in regard to their principle of action as the Capell fan. The fan is constructed along the lines of the Schiele ventilator, but differs from that ventilator in the manner of receiving its intake air and delivering the same into the main body of the fan. Here, and revolving with it, is a set of smaller supernumerary blades. These blades occupy a cylindrical space within the main body of the fan, and are inclined to the plane of revolu- tion so as to assist in deflecting the entering air through small ports or openings into the main body of the fan, where it is revolved and discharged at the circumference into a spiral space resembling that surrounding the Schiele fan. The larger blades of this fan are curved backwards as the Schiele blades, but are not tapered toward the circumference. The fan is capable of giv- ing a high water gauge, and is efficient ' as a mine ventilator. The space surround- ing the fan is extended to form an ex- panding chimney. The fan may be used either as an exhaust fan or a blower. The best results in the United States have been obtained by blowers. In Germany, where this fan is in general use, there are no blowers. The position of the fan, whether used as an exhaust or blower, should be suffi- ciently removed from the fan shaft to avoid damage to the fan in case of ex- plosion in the mine. Even in non-gaseous FIG. 14. mines, the fan should be located a short distance back from the shaft mouth, to avoid damage due to settlement. Connection should be made with the fan shaft by means of an ample drift, which should be deflected into the shaft so as to produce as little shock to the current as possible. In :)90 VENTILATION OF MINE*. case of gaseous seams, explosion doors should be provided at the shaft mouth. The ventilator at every large mine should be arranged so that it may be converted from an exhaust to a blow-down fan at short notice. This is managed by housing the central orifices or intake of the fan in such a manner as to connect them directly with the fan drift. A large door a 6, Fig. 15, is arranged at the foot of the expanding chimney, the latter being placed between the fan and the shaft. This door, when the fan is exhausting, is in the lower position a 6, and then forms a portion of the spiral casing leading to the chimney. When the fan is blowing, however, the door is swung upwards so as to oc- cupy the position ac, being tangent to the cut-off at c, thereby closing the discharge into the chimney and causing it to enter the fan drift behind the door. At the same time, the positions of the two doors, ed and/d, in the fan drift, are changed to e t and /s, respec- tively, to open the fan drift to the discharge from the fan, and to close the openings lead- ing from the fan drift to the housing upon each side of the fan, while another set of doors A A upon each side of the fan, in the housing, which were previously closed tightly, are now set wide open to admit FIG. 15. the outside air to the intake openings of the fan. The fan is thus made to draw its air from the atmosphere, and discharge it into the fan drift, instead of drawing its air from the fan drift and discharging into the chimney, as before. The manometrical efficiency of a fan is the ratio between its effective and theoretical pressures. It has been assumed that the theoretical pressure due lyfit ifi V 1 2 X 12 to the fan's action is given by the equation h = , or i = ' /" , u being, as before, the tangential speed (feet per second), and g the force of gravity (32.16); h = head of air column in feet; i = water gauge in inches. The term mechanical efficiency, as applied to the ventilator, is the ratio between its effective and theoretical powers. In estimating the efficiency of a ventilator, it is customary, though incorrect, to estimate the theoretical power of the fan from an engine card taken from the steam cylinder of the fan engine. The efficiency of the steam engine is thus confused with the efficiency of the ventilator. Mr. Beard gives the following formula for the theoretical work of the fan per minute: U = .001699 m ~ j/1^12 3 6 n 2 , in which m = ratio between outer and inner diameters of fan (D = m d), and V = velocity (feet per minute) of air in fan drift; R = outer radius of fan blades (feet); b = breadth of fan blades (feet); n = number of revolu- tions of fan per minute. If we divide the power upon the air, as determined by the expression qp, by the theoretical work given in the last equation, we obtain the value of the coefficient of efficiency. According to this formula the efficiency of the ventilator changes with the speed, decreasing as the speed increases, but not in the same ratio. An expression for the coefficient of efficiency of a ventilator is given by Beard as follows: K = _L IfiS 6002' The factor c is a constant of design whose value may vary from 2 to 7, but for an ordinary design, the value c = 4 may be taken. This factor has refer- ence to the equipment of the machine with respect to its efficiency for pass- ing an air-current through itself with least resistance. Thus, where the ventilator is to be equipped with intake blades for the deflection of the air- current into the motor, and with straight radial blades having only a forward FAN CONSTRUCTION. 391 curve at the lip of the blade to avoid the shock of the entry air against the revolving blades, and the spiral casing starting a short distance upon the cut-off and extending uniformly around the circumference of the fan, the value of this constant may be 2 or 3. Where none of these accessories to the efficiency of the fan is employed, the value of c. may be as high as 7. FAN CONSTRUCTION. Size of Central Orifice. The velocity of the intake should vary between 1 ,000 ft. and 1,500 ft. per minute, while 1,200 ft. may be used for fan calcula- tions. If d = diameter of opening, and q = quantity of air passing per minute, d = ^~ m ? ^ for single-intake fans, and d = -^00 x .7854 for double-intake fans. Upon entering the fan the air travels in a radial direction; this change of direction is accompanied by a slight reduction of the velocity, hence the throat area of the fan must be slightly in excess of the intake area. The throat is the surface of the imaginary cylinder that has for its two bases the two intake openings of the fan, and for its length the width of the fan, = TT d b. [The throat area is commonly made 1.25 times the total area of the intake orifices, which gives for breadth of blade 6 = f d for double intake, and b = T 5 5 d for single intake. Beard.] Diameter of Fan. Murgue assumes the tangential velocity of the blade tips (u) to create a depression double that due to the velocity as expressed by the equation H = , or if the manometrical efficiency = K, and the effective head produced = h, h = KH = K , or u = -\fe. From this 9 \'JL equation, the tangential velocity (feet per second) may be calculated for any given effective head h. This effective head h is the head" of air column effective in producing the circulation in the airway. To convert the effective head of air column into inches of water gauge (i), we have 1 000 h = ' i. Having found the tangential speed required in feet per 1.2 X 1^ second, this is multiplied by 60, to obtain the speed in feet per minute, and dividing this result by the desired number of revolutions per minute, or the desired speed of the ventilator, the outer circumference of the fan blades is obtained. No reference is made in the equation to the quantity of air in circulation, which is determined from the equivalent orifice of the mine and of the fan by the equation V = ' 2 ^ n which ^ + y V = volume of air (cu. ft. per sec.); a = equivalent orifice of the mine: o = the equivalent orifice of the fan. M. Murgue also uses the equation h = - - , and suggests that the value of K for any particular type of machine should be first decided, after which the tangential speed required to produce any given effective head of air column (h) is easily calculated from the formula u = AJ'^- The breadth of the blade is left largely to judgment, while this method of calculation gives the same size of fan for any given effective head desired, regardless of the quantity of air to be circulated, which is the same as saying that the ventilator will present the same efficiency when a large amount of air is crowded through its orifice of passage as when a smaller amount of air is necessary. Mr. Beard uses the following formulas for determining the several dimen- sions of a ventilating fan: 385,000,000 p _1 4,'X3 AT2 F. \ P 392 VENTILATION OF MINES. in which m = -r, which is the ratio between the outer diameter of the fan d blades D and the inner diameter of the blade d, which equals the diameter of the intake orifice; b = width of fan blade; e = expansion of spiral casing at point of cut-off. The other symbols stand for the same quantities as previously indicated. Curvature of Blades. It was at one time supposed that the curvature of the blades should be such that the radial passage of the air-current would be undisturbed, by the revolution of the fan; but fans constructed on this principle gave no adequate results, and the theoretical spiral thus developed was entirely abandoned. A certain curvature of the blade backward, however, is assumed by many to increase the efficiency of the fan. This has not been proved in practice, but the effect of the backward curvature appears simply to necessitate a higher speed of revolution in the fan, in order to obtain the same results as are obtained with radial blades. The Guibal blade, radial at its outer extremity, or normal to the outer circumference, and curved forward in the direction of motion, at its inner extremity, so that the lip of the blade approaches tangency to the throat circle, seems the most effective blade in centrifugal ventilation. Tapered Blades. The object of the taper is to produce a constant area of passage from the throat to the circumference of the fan, and thus prevent the reduction of the velocity of the current in its passage through the fan. This feature presents an attempt similar to that attempted by the curvature of the blades, to hasten the passage of the air through the fan. It has not been proved, however, to have produced any beneficial result, except in the strengthening of the discharge pressure against the atmos. pheric pressure, in open-running fans. On the other hand, the slowing up of the air in its passage through a covered fan has by no means been proved a detriment, but is assumed by many to be an advantage, inasmuch as the air thus remains longer within the influence of the fan blades. The number of blades depends on the size of the fan. An increased number strengthens the fan's action at the circumference, or supports the air at that point, and thus prevents the backlash or the reentry of air into the fan, due to the eddies occurring at the circumference when the blades are too far apart. To a certain extent, the number of blades is modified by the speed of revolution, high-speed motors requiring a somewhat lesser number, while low-speed motors require more. In any case, the number of blades should not be so great as to abnormally increase the resistance to the air- current. In general, the distance upon the outer circumference from tip to tip of the fan blades should be from 2 to 3 times the depth of the blade. The spiral casing gradually reduces the velocity of the air and reduces the shock incident to the discharge of the air into the atmosphere. The spiral casing should be so proportioned that the velocity of the flow from the fan blades will be maintained constant around the entire circumference, and this should not be less than the velocity of the blade tips. The expansion e. of the casing at the cut-off should be such as to provide a velocity of the air at this point equal to the velocity of the blade tips, according to the equation e = ^ , in which D = diameter of fan; n = number revolu- irDnb tions per minute; b = breadth of fan blade. The evase chimney reduces the velocity of the air, as it is discharged into the atmosphere, to a minimum. The chimney should be sufficiently high to protect the fan from the effect of high winds, but should not extend too far above the fan casing, the point of cut-off being situated below this, at about the level of a tangent to the throat circle at its lower side. High-Speed and Low-Speed Motors. The question of speed of the venti- lating motor is largely an open one, inasmuch as the same work may be performed by a small ventilator running at a high speed as is performed by a large ventilator running at a low speed. It is important to design a mine ventilator at a speed such as to admit of its being increased in case of emergency. If the ventilator has been designed at a high speed, a demand for an increase of speed cannot be met as readily as when the ventilator is designed at a medium or low speed; in other words, the exigencies of mine ventilation demand that a ventilator shall be capable of greatly increased speed. Fan Tests. A large number of fan tests have been made, from time to CONDUCTING AIR-CURRENTS. 393 time, on different types of fans and under different conditions, with respect to the resistance against which the fan is operated, and the quantity of air required, and the speed of the ventilator. The experiments have resulted, to a large extent, in tabulating a mass of contradictory data. The condi- tions that affect the yield of the centrifugal ventilator are so numerous, and the tabulation of the necessary data has been so often neglected in these experiments, as to render them practically useless for the purpose of scientific investigation. In conducting a reliable fan test, the following points should be observed: (1) Take the velocity, pressure, and temperature of the air at the same point in the airway, as nearly as practicable. This point should be selected near the foot of the downcast shaft, or in the fan drift at a suitable distance from the fan, to avoid oscillations of pressure and velocity. (2) The area of the fan drift should be uniform for a suitable distance in each direction from the point of observation, and this area should be carefully measured. (3) Take the anemometer readings at differ- ent positions in the airway, so as to obtain an average reading over the entire sectional area. Do not interpose the body in this area so as to decrease the sectional area of the airway. (4) Take outside temperature of the air and the barometric pressure at the time of making the test. (5) The intake and discharge openings of the fan should be protected against wind pressure. (6) At least three observations should be made, at as many different speeds of the ventilator, and the number of revolutions of the fan carefully observed and recorded for each observation. Mr. R. Van A. Norris (Trans. A. I. M. E., Vol. XX, page 637) gives the results of a large number of experiments performed upon different mine ventilating fans. This table, like all other tabulated fan tests, shows a large amount of contradictory data. The conclusions drawn by Mr. Norris from these tests are interesting and would be given here excepting that they might be misleading if considered apart from the description of the experi- ments and the discussion leading up to the conclusions. CONDUCTING AIR-CURRENTS. Doors. A mine door is used for the purpose of deflecting the air-current from its course in one entry so as to cause it to traverse another entry, at the same time permitting the passage of mine cars through the first entry. The essential points in the construction of a mine door are that it shall be hung from a strong door frame in such a manner as to close with the current. The door should be hung so as to have a slight fall. If necessary, canvas flaps may be supplied to prevent leakage around the door, and particularly at the bottom. Double doors are used on main entries at the shaft bottom, or at any point where the opening of the door causes a stoppage of the entire cir- culation of the mine. Such doors should be placed a sufficient distance apart to allow an entire trip of mine cars to stand between them, so that one of the doors will always be closed while the other is open. Stoppings. Stoppings are used to close break-throughs that have been made through two entries, or rooms, for the purpose of maintaining the cir- culation as the workings advance; also to close or seal off abandoned rooms or working places. Stoppings must be air-tight and substantially built. A good form of stopping is constructed by laying up a double wall of slate, having about 8 or 10 in. of space between the two walls. This space is filled, as the building progresses, with dirt taken from the roadways, or other fine material. In the building of stoppings to seal off' mine fires, it is important to begin the work at the end nearest the return air, and work toward the intake end, which should be sealed off last. This method avoids the danger of an explosion occurring within the workings that are being sealed off, as the necessary dilution of the gases within is accomplished by the fresh air- current, until the intake is finally sealed. Where the intake is sealed first, an explosion is almost inevitable, as has been proved in many instances. Air Bridges. An airbridge is a bridge constructed for the passage of air across and over another airway, this being called an overcast; or, the cross- ing may be made to pass under the airway, this being called an undercast. In almost every instance, overcasts are preferable to undercasts for several reasons. An undercast is liable to be filled with water accumulating from mine drainage; it is also liable to fill with heavy damps from the mine, when the ventilation is sluggish, and to offer considerable resistance to the free passage of the air-current. An undercast can never be maintained as air- tight as an overcast, on account of the continual travel through the 394 HOISTING AND HAULAGE. haulageway or passageway leading over it. This continual passing over the bridge causes a fine dust to sift into the airway and mingle with the air-current. All these objections are overcome in the construction of the overcast. An air brattice is any partition erected in an airway for the purpose of deflecting the current. A thin board stopping is sometimes spoken of as a brattice; but the term applies more particularly to a thin board or canvas partition running the length of an entry or room and dividing it into two airways, so that the air will be obliged to pass up one side of the partition and return on the other side of the partition, thus sweeping the face of the heading or chamber. Such a temporary brattice is often constructed by nailing brattice cloth or heavy duck canvas to upright posts set from 4 to 6 ft. apart along one side of the entry a short distance from the rib. Curtains. These are sometimes called canvas doors. Heavy duck, or canvas, is hung from the roof of the entry to divide the air or deflect a portion of it into another chamber or entry. Curtains are thus used very often previous to setting a permanent door frame. They are of much use in longwall work, or where there is a continued settlement of the roof, which would prevent the construction of a permanent door; also, in tempo- rary openings where a door is not required. HOISTING AND HAULAGE. HOISTING. There are two general systems of hoisting in use: (a) Hoisting without attempting to balance the load. In this system, the cage and its load are hoisted by an engine and lowered by gravity, (b) Hoisting in balance. In this system, the descending cage or a special counterbalance assists the engine to hoist the loaded ascending cage. Hoisting in balance is usually effected by the use of (1) double cylindrical drums; (2) flat ropes winding on reels; (3) conical drums; (4) the Koepe system; (5) the Whiting system. 1. Double cylindrical drums are widely used: they consist essentially of an engine coupled directly or else geared to the common axis of the drums. The drums are usually provided with friction or positive clutches, and brakes, so that they can be run singly if desired, or the load can be lowered by gravity and the brake. 2. Flat ropes wound on reels are sometimes used either for unbalanced hoisting with a single reel or for balanced hoisting with a double reel. With the double reels, the load on the engine is balanced throughout the entire hoist, for, as the rope is wound on the reel, the diameter of the reel is increased, and the lever arm through which the power of the engine is applied is also increased and the mechanical efficiency of the hoisting system de- FIG. 1. creased. Thus, when the cage is at the bottom of the shaft and the entire weight of the rope is out, giving the maximum load to be hoisted, the drum is of a minimum diameter and the engine has, therefore, its greatest lever- age to start the load. A flat rope has the advantage of preventing fleeting, but its first cost, extra weight, wear, and difficulty of repairing have prevented its very general adoption. 3. Conical Drums. A conical drum, Fig. 1, equalizes the load on an engine just as a flat rope on a reel does. On account of the fleeting of the rope, however, the drum must be set at a considerable distance from the shaft to prevent the rope leaving the head-sheave. A tail-rope gives the most HOISTING. 395 perfect counterbalance, the weight of the cage and rope on each side being exactly equal. 4. In the Koepe system. Fig. 2, one rope runs over and the other under driving sheaves S. A tail-rope R is 'used, and the head-sheaves x, x' are placed vertically and at such an angle to each other that their grooves and the groove in the dri- ving sheave are in line. As the main driving shaft is short, the en- gines can be placed close together, thus requiring a smaller foundation and engine house than for a drum hoist. The objection to the system is the liability of the rope to slipping about the driving sheave, and for this reason a hoisting indicator can- not be depended on. The system is also inconvenient for hoisting from different levels in the same shaft, and, in case of the rope breaking, both cages fall to the bottom. 5. The Whiting system, Fig. 3, uses two narrow- grooved drums placed tandem instead of a single- driving sheave as is used in the Koepe system. The rope passes from the cage A over a head-sheave, under the guide sheave T and around the sheaves M, F three times, then out to the fleet sheave C, back under another guide sheave, and up over another head-sheave to the cage B. The sheave M is driven by a motor either coupled direct to its shaft, or geared. The drums F and M are coupled together by a pair of connecting-rods like the drivers of a locomotive, and this arrangement FIG. 2. makes it possible to utilize all the friction of both drums to drive the rope. Thus a tail-rope is not depended on to produce more friction, though one is generally used as a balance to the loads. It is best to incline the follower sheave F from the vertical an amount equal in its diameter to the distance between the centers of two adjacent grooves, the object being to eliminate chafing between the ropes around the drums and to prevent them from running off by enabling the rope to run from each groove in one drum straight to the proper groove in the other. This throws the shaft and crankpins out of parallel with those of the main drum, but this difficulty is overcome by the connections in the ends of the parallel rods. The fleet sheave C is arranged to travel back- wards and forwards, as shown by the dotted lines, in order to change the working length of the rope, whereby hoisting can be done from different levels in the The power used for hoisting is generally steam for the main hoists, tricity is, however, coming rapidly into use, particularly for smaller shaft. Elec- hoists 396 HOISTING AND HAULAGE. and local installations, and for main hoists in locations where fuel is expensive and water-power available. Gasoline engines are also being used to an increasing degree, particularly for smaller hoists and in local installa- tions, and they are said to give very satisfactory results. PROBLEMS IN HOISTING. To Balance a Conical Drum. Having given the diameter of one end of a conical drum, to determine the diameter of the other end that will equalize the load on the engines. In Fig. 1, call total load at bottom A, empty cage at top B, loaded cage at top C, empty cage plus rope at bottom D, small diameter of drum x, and large diameter y\ then, Ax By = Cy Dx. EXAMPLE. In a shaft, the cage weighs 2 tons, the empty car 1 ton, the loaded car 2 tons, and the rope 2 tons. What should be the small diameter of a conical drum whose large diameter is 30 ft.? (2 -1- 2 + 3)z (2 + 1)30 = (2 + 3)30 - (2 + 2 + 1)*, or 7x 90 = 150-5z. .'. 12 z = 240, x = 20 ft. To Find the Size of the Hoisting Engine. Let D = diameter of cylinder, P = mean effective steam pressure in cylinders, r = ratio of stroke to diam- eter of cylinder, and w = work per revolution required to be done; then, by making one cylinder capable of doing the work, n = number of strokes, u work per minute (ft.-lb.). EXAMPLE. What should be the size of the cylinders of a hoisting engine that is to perform 152,580 ft.-lb. of work per revolution, if the mean effective pressure is 45 Ib. per sq. in. and the stroke of the piston is twice its diameter? To get up speed in a few seconds, more power than would be represented by the load to be lifted is required. Mr. Percy gives the following rule for this case: In a properly balanced winding arrangement, with uniform load, multiply the weight of coal in pounds by the average speed of the cage in feet per minute; add one-half to cover the Motional resistances, and call that the Load. Then the power that must equal this must be the average effective pressure of steam in pounds per square inch on the piston, multi- plied by the area of one cylinder in square inches, and multiplied again by the average speed of the piston in feet per minute. Approximately, the average effective pressure of steam will be two-thirds of the pressure shown on the gauge near the engines. A good average piston speed is 400 ft. per minute. To Find the Actual Horsepower of an Engine for Hoisting Any Load Out of a Shaft at a Given Rate of Speed To the weight of the loaded car add the weight of the rope and cage. This will give the gross weight. Then H P = gross wei S ht in lb - x speed in ft - per minute . add i for 33,000 contingencies, friction, etc. EXAMPLE. Haying a shaft 600 ft. deep, gross weight of load 20,000 lb., to be hoisted in H minutes, what horsepower is required? on nnn \x Aftf) H - p - = oon = 243 H - p - nearly. To which add | for contingen- 00,000 cies, and we have 324 H. P. In a shaft with two hoistways, use the net weight + the weight of one rope, instead of the gross weight. The following rules regarding winding engines are given by Percy: 1. To Find the Load That a Given Pair of Direct-Acting Engines Will Start. Multiply the area of one cylinder by the average pressure of the steam per square inch in the cylinder, and twice the length of the stroke. Divide this by the circumference of the drum, and deduct j for friction, etc. HE A D-FRAMES. 397 EXAMPLE. Given a pair of engines, cylinders 20 in. diameter by 40 in. stroke, the drum 12 ft. diameter, and the pressure at steam gauge 50 lb., steam cut-off at f , average pressure of steam in cylinder 48.2 lb. Then, area of cylinder = 314.16 sq. in. 314.16 X 48.2 X 80 = 1,211,400.96. The circumference of the drum = 452.4 in. 1,211,400.96 -r- 452.4 = 2,677 f of 2,677 = 1,784 lb., or the net load. The gross load would include the weight of rope, cage, and car, but as these are balanced by the descending rope, cage, and car, the net load only is found. The drum mentioned is cylindrical. 2. Knowing the Load and the Diameter of a Cylindrical Drum, and the Length of Stroke, the Cut-off and Pressure of Steam at Steam Gauge, to Find the Area and Diameter of Cylinders of a Pair of Direct-Acting Engines. Multiply the load by the circumference of the drum, and add one-half for friction, etc. Divide this by the mean average steam pressure, multiplied by twice the length of the stroke. EXAMPLE. Having the drum 10 ft. in diameter, the stroke 6 ft, the steam pressure at gauge 60 lb., the cut-off at of stroke, and the load 5 tons, or 11,200 lb. Then 11,200 X 31.416 (circumference of drum) = 351,859. 351,859 + i of 351,859 (or 175,930) = 527,789. The mean average pressure = 57.8 lb. 57.8 X (6 X 2) = 693.6. 527,789 -f- 693.6 = 761 sq. in., area of piston. 761 -4- .7854 = 969. >/969 = 31.13 in., or diameter of cylinder. 3 To Find the Approximate Period of Winding on a Cylindrical Drum With a Pair of Direct-Acting Engines. Assume the piston to travel at an average velocity of 400 ft. per minute, and divide this by twice the length of the stroke, and multiply by the circumference of the drum. This gives the speed of cage in feet per minute. Divide the depth of shaft by this, and the result will be the period of winding. EXAMPLE. Drum, 31.416 ft. circumference; stroke, 6 ft.; depth of shaft, Then, 400 -f- 12 = 33.33. 33.33 X 31.416 = 1,047.1. 1,500 -4- 1,047.1 = 1.43 min., or about 1 min. 26 sec. 4. To Find the Useful Horsepower During a Winding. Multiply the depth of shaft by net weight raised; divide this by number of minutes occupied in winding, and divide again by 33.000. EXAMPLE. Net weight, 2 tons = 4,480 lb.; depth, 1,500ft.; period of wind- ing, 1.43 minutes. Then, 4,480 X 1,500 = 6,720,000. 6,720,000 -~ 1.43 - 4,699,301. 4,699,301 -4- 33,000 = 142+ H. P. HEAD-FRAMES. Head -frames are built of wood or steel, and some of the typical forms are shown on pages 275 and 276. They vary in height from 30 to 100 ft., depending on local conditions. The inclined leg of a head-frame should be placed so as to take up the resultant strain due to the load hanging down the shaft and the pull of an engine. Fig. 4 shows the graphical method of determining the direction and mag- nitude of this resultant force. Produce the direction of the two portions of the rope lead- ing to the drum and down the shaft until they intersect at G, measure off a distance G K to scale to represent the load hanging down the shaft; similarly, measure off G H to the same scale to represent the pull of the engine, com- plete the parallelogram GH LK; the direction of the line G L represents the direction of the resultant force, and its length represents the amount of this force. The inclined leg of the head-frame should be placed as nearly as possible parallel to this resultant line, and should be designed to withstand a compressive FIG. 4. strain equal to this resultant. Head-sheaves are made of iron, being sometimes entirely cast, or else the 398 HOISTING AND HAULAGE. rim and hub are cast separately and wrought-iroii spokes are used. The former are cheaper and quite satisfactory, but the latter are lighter and stronger, and therefore usually better. The diameter of the sheave depends on the diameter of the rope, and the table giving this will be found on page 120. The groove in the sheave should be wood-lined, to reduce wear on the rope. Wrought-iron spokes should be staggered in the hub and not placed radially. Guides and conductors are usually of timber rigidly attached to the sides of a shaft. In England and certain parts of Europe, wire ropes are used for guides and are strongly advocated, but they have never found favor in America. These ropes when used are weighted at the bottom, and Percy gives 1 ton for each 600 ft. in depth for each wire as a good weight to be used. When not thus weighted, the ropes are fastened at the bottom and attached to levers at the top, the levers being weighted to produce the requisite tension. Safety catches usually consist of a pair of toothed cams placed on either side of the cages and enclosing the guides. When the load is on the hoisting rope, these cams are kept away from the guides by suitable springs; but if the rope breaks, the springs come into action and throw the catches or dogs so that they grip the guides, and the tendency to fall increases the grip on the guides. Detaching hooks are devices that automatically disconnect the rope from the cage in case of overwinding. HAULAGE. The magnitude of modern mines and the practice of loading or of treating the coal or ore at a large central station makes the underground haulage of the material one of the most important problems in connection with mining. A good haulage system is now essential to make most mines a commercial success. Haulage may be considered under the following heads: 1. Inclined Roads. Gravity planes, engine planes. 2. Level Roads. Mule haulage, rope haulage (tail-rope and endless rope), motor haulage (steam, electricity, compressed air, or gasoline). Gravity Planes. The loaded car or trip hauls the empty car up the grade. Two ropes are attached to a drum so that the rope attached to the loaded car unwinds from the drum as the car de- scends, while the rope attached to the empty thu car is wound on the drum and the car thus hauled up the plane. The natural slope of the ground, in a large measure, determines the grade of the incline, but where it is pos- sible to alter the direction of the incline, the grade may be lessened by constructing the incline across the slope of the ground. The grade of the incline may be increased by carrying the upper landing forwards till a point is reached from which the required grade is obtained. The following rule gives suggestions based on practice that has been successful: For lengths not exceeding 500 ft., the minimum grade for the incline should be 5^ when the weight of the descending load is 8,000 Ib. and that of the ascending load 2,800 Ib. Or the inclination should not be less than 5i# if the respective descending and ascending loads are one-half of those just given. When the length of the plane is from 500 to 2,000 ft., the grade should be increased from 5$ to 10$, according to the loads. A load of 4,000 Ib. on a 10# grade 2,000 ft. long will hoist a weight of 1,400 Ib. The angle of inertia is that angle or inclination at which a car will start to move down the slope or plane. The car, when it has once started on this grade, will continue to accelerate its speed as it descends the plane A B, Fig. 5. If we decrease the angle of inclination until the plane A B occupies the position A C, such that the moving car will continue to move at a uniform velocity instead of accelerating its speed, the angle D C A will be the angle of rolling friction, and the tangent of this angle will be the coefficient of rolling friction for the car. The upper portion of a plane is made steeper than the lower portion so that the trip may start quickly at the head and afterwards maintain a uniform velocity. With a good brake to control the cars, the uniform grade of a central portion of a gravity plane should not fall much below 3, which corresponds practically to a 5i^ grade. HA ULAGE, 399 The acceleration f of the haulage system is given by the formula '-B| X * where PI and p 2 are the descending and ascending pulls, respectively. The length of steep pitch is given by the formula where v = velocity at which the trip is desired to run. The maximum tension or pull on the rope which may occur, if it is required to haul the loaded trip up, is T = ( W + w 1) sin a + ( W + w 1) cos a X /*, where W = weight of loaded trip; w I = weight of rope; a = slope angle; /u. = coefficient of friction. EXAMPLE. Find the possible tension of a rope used to lower a loaded trip of two cars upon a plane 800 ft. long, having a uniform grade of 5$ at a speed of 20 miles per hour, using a factor of safety of 10, and letting p. = A, the empty cars weighing 1.000 Ib. each and carrying a load of 2,000 Ib. each. Assuming w = .88 Ib., T = (6,000 + .89 X 800) (.05 + .04994) = 671 Ib. To find the number of cars that must run in a trip on a self-acting incline, use the formula _ (40 sin a -f cos a) W s (40 sin a cos a) Wi (40 sin a + cos a) W* in which N = number of cars; a = angle of inclination of plane; W\ == weight in pounds of one loaded car; W% = weight in pounds of one empty car; W 3 = weight in pounds of haulage rope; & = coefficient of friction. EXAMPLE. A gravity plane has an inclination of 8; it is 2,000 ft. long, the rope weighs 4,000 Ib., a loaded car weighs 3,000 Ib., and an empty car weighs 1,800 Ib. What number of cars must be in the trip to start it? Substituting values in the above formula, we have = _ (40 X .13917 + .99027)4,000 _ ~ (40 X .13917 .99027) 3,000 (40 X .13917 + .99027)1^00 ~~ Engine Planes. With an engine plane, the load is delivered at the foot of the plane and has to be hoisted. The engine may be either at the top or the bottom. The grade of the plane is usually uniform from top to bottom, and there may be a single track, a double track, or three rails with a turnout. Size of Engines Required for Engine-Plane Haulage. (a) Engine at Head of Plane, Single Track. Calling the load on the engine or the tension of the rope at the winding drum T, the weight of the ascending loaded trip W, the weight of the rope per lineal foot w, and the length of the plane I, the angle of inclination or the slope angle being a, as before, we have T= (W+wl)(sma + ncosa). Assume an approximate value for w, and determine T approximately. The size of rope required for this load is then obtained from the table for haulage ropes, and with this new value of w, the correct load on the engine is calculated. EXAMPLE. What size of rope will be required to haul up an incline a loaded trip of 10 mine cars weighing 1,000 Ib. each, and carrying a load of 2,000 Ib. each, the inclination of the plane or the slope angle being 16 and its length 500 yd., assuming for the coefficient of friction M. = ^,? W = 30,000 Ib., and assuming w; = .89 Ib., W + wl = 30,000 + (.89 X 1,500) = 31,335 Ib. Sin a + = .27564 + -- = .29967. Hence, T = 31,320 X .29967 = 9,394 Ib. To provide against shock, we double the load or pull on the rope in calculating the size of rope required; thus, 9,394 X 2 = 18,788 Ib., and using a factor of safety of 6, we have for the breaking strain of the rope 18,788 X 6 2,000 L = 57 tons. In the table of wire ropes, a ly" plow-steel rope 400 HOISTING AND HAULAGE. presents a breaking strain of 56 tons. Since a If" rope weighs 2 Ib. per lineal foot, we have W + wl = 30,000 + (2 X 1,500) = 33,000 Ib. Then T = 33,000 X .29967 = 9,889 Ib. (6) Engine at Head of Incline, Double Track. The load on the engine equals the difference between the gravity pulls of the ascending and descending trips, including the rope, plus the friction pull of both the trips and one rope, since there is only one rope on the plane at any time. Calling the weight of the ascending trip W, as before, and that of the descending trip W\, we have for the difference of the gravity pulls when the loaded trip is at the foot of the incline, ( W Wi + w t) sin a, and for the friction pull of the entire moving system ( W + W\ + w 1) /u. cos a, and L = (W W\-\- wl) sin a + ( W + W\ + w 1) ju. cos a. Assuming the same conditions as given in the example of the preceding paragraph, we have for the load L on the engine, L = [10 X 2,000 + 2 X 1,500] .27564 + [10 X (3,000 + 1,000) + 2 X .1,500] X - ~ = 23,000 X .27564 -f 43,000 X .02403 = 7,373 Ib. instead of 9,394, the unbalanced load for single track. (c) Engine at Foot of Incline. The load on the engine is the same as in (a), except that the gravity pull is the pull due to the weight of the loaded cars only, the weight of the ascending rope being balanced by the descend* ing rope, while the friction pull is increased by the friction of the descend- ing rope. Calling the load on the engine L, as before, we have, in this case, L = W sin a + ('W + 2 w I) /u. cos a. Assuming the conditions of the previous example and calculating the load on the engine for this case, we have L = 30,000 X .27564 + [30,000 + 2(2X1,500)]. 02403 = 9,134 Ib. To Find the Horsepower of an Engine Required to Hoist a Given Load Up a Single- Track Incline in a Given Time. Multiply the length of the incline in feet by the natural sine of the angle of inclination, which will give you the vertical lift. Divide the vertical lift by the given time in minutes. Multiply this by the gross load, including weight of rope, and divide the product by 33,000. EXAMPLE. Length of incline, 600 ft.; angle of inclination, 35; weight of loaded car and 600 ft. of rope, 5,000 Ib. ; time of hoisting, 2 minutes. Required. the horsepower. Sine of 35 = .573576. .573576 X 600 - 344.1456. 344.1456 -=- 2 = 172.728. 172.728 X 5,000 =26+H.P. Add from 25$ to 50$ for contingencies, friction, etc. In mine practice, 50$ is not any too much to add, because the condition of track, cars, etc., is not as good, as a general rule, as on railroad planes. To Find the Horsepower of an Engine Required to Hoist a Given Load Up a Double- Track Incline in a Given Time. Proceed as above, using the net load, to which should be added the weight of one rope, instead of the gross load. ROPE HAULAGE. The tail-rope system of haulage uses two ropes and a pair of drums on the same shaft. The main rope passes from one drum directly to the front of the loaded trip, and the tail-rope passes from the other drum to the large sheave wheel at the end of the road and back to the rear of the loaded trip. While hauling the loaded trip, the drum on which the tail-rope is wound is allowed to turn freely on its journal by throwing its clutch out, while the engine turns the other drum. When the empty trip is being hauled, the clutch on the main-rope drum is thrown out and the one on the tail-rope drum is thrown in. The engine then turns the tail-rope drum and allows the other one to pay out rope as the trip advances. The tail-rope system is suitable for steep, circuitous, and undulating roads. The trip can be kept stretched at all points, and thus the cars will be prevented from bumping together or from being jerked apart as the trip is passing over changes in the grade. It is undoubtedly the most satisfactory system of rope haulage under the natural conditions of most haulage roads in mines, and especially so where but one road is available for haulage purposes. ROPE HAULAGE. 401 CALCULATION OF THE TENSION OF HAULING ROPE. T = tension or pull upon rope (lb.). W = weight of loaded trip (lb.). w = weight of rope per lineal foot (lb.). I = length of two ropes; equals 2 times the distance from winding drum to tail-sheave (ft.). d = vertical drop of rope (ft.). a = slope angle of maximum grade. T = TF(sina + /u. cos a) + w (d + n I) . EXAMPLE. What size of steel wire rope will be required to haul a trip of 20 mine cars, the weight of the loaded cars being 3,000 lb. each, the depth of the shaft 300 ft., and the distance from the foot of the shaft to the tail-sheave 900 yd., the maximum grade in .this haulage being 10, /u. = jfo? Assuming a |" rope, weighing .89 lb. per lineal ft. .89 (300 + ^~\ = say 12,300 lb., or some- T= 60,000 (. 17365 + ^ what over 6 tons. Referring to the tables for steel haulage ropes with 6 strands of 7 wires each, we find the breaking strain of a f" rope, weighing .89 lb. per lineal ft., is 18.6 tons, which will give a factor of safety of about 3. We would, however, use a \" or even a V rope, as a change of ropes would then be required less often. Making the necessary corrections for 1" rope weighing 1.58 lb. per lineal ft., T = 12,607 lb. The endless-rope system uses an endless rope, which is kept running con- tinuously by a pair of drums geared together and set tandem. The drums are comparatively narrow and provided with grooves for the rope to run in. Two drums are necessary to get sufficient fric- tion to drive the rope when the trip is at- tached to it. The rope is passed around both drums a num- ber of times, depend- ing on the amount of friction desired, without completely encircling either. It then passes to a ten- sion wheel at the rear of the drums and thence to the sheave wheel at the far end of the road and back to the drums. To be used to best advan- FIG. 6. tage, this system re- quires that the grade be in one direction and that it be necessary to haul cars from a number of places en route. The cars are attached to the rope by friction grips in a manner quite similar to the way in which street cars are attached to cable lines. It is evident, therefore, that any jerking due to the cars bumping together or stretching the hitchings would seriously injure the rope where the grip takes hold. A double road is an essential feature of endless-rope haulage. The endless-rope system of haulage is best adapted to roads presenting a fairly uniform grade, particularly when the trips are not spaced at fairly regu- lar intervals along the road. Owing to delays in the delivery of the cars by the drivers and to irregularity in unloading at the tipple, it is practically im- possible to have the several trips regularly spaced, and in consequence the load on the engine varies greatly. In order to take up any elongation of the rope due either to change in temperature or to stretching, some form of balance car or balance weight is used. This weight should be sufficient to keep the empty rope taut, and any tendency of the rope to slip on the 402 HOISTING AND HAULAGE. winding drum may be overcome by increasing the weight in the bal- ance car. Fig. 6 shows a device for working a district haulage by connecting it with the main haulage. The main rope makes one or two complete turns around a fleet wheel located at the mouth of each district, and then continues on its course. This fleet wheel d is directly connected with the driving sheave m for the district by means of beveled gears g, h, as shown. The driving sheave m is thrown in or out of gear by levers o and q. To Determine the Friction Pull on an Endless-Rope Haulage. Let = output (Ib. per min.); ~wi = weight of mine car (lb.); v = speed of winding (ft. per min.); w = weight of rope (lb.); 1= length of haulage road (ft.); ' T = load on the rope (lb.); c = capacity of mine car (lb.); /u, = coefficient of friction. = weight of material in transit; 2 wi = weight of moving cars, loaded and empty; 21 w = weight of rope; 1 1 H --- - j -f 2 w I = entire moving load. And if the coefficient of friction equals 3 a , EXAMPLE. Find the horsepower for an endless-rope system 5,000 ft. long for an output of 1,000 tons per day of 10 hours in a flat seam, the mine cars having a capacity of 2,000 lb. each and weighing 1,200 lb. each. Assuming a speed of winding of 8 miles per hour or 704 ft. per minute, and for the coefficient of friction /u, = ,V T = 704 1 = J + 2 X 1.58 X 704 J - 36.2 H. P. or, 36 9 assuming an efficiency for the engine of 60f c , -g~ = 60 H. P. Inclined Roads. The calculation of power for inclined roads is the same as that just given, excepting that the work due to lifting the coal through a height h must be added to that found by the previous formulas. If h equals the elevation due to the grade of the incline, the additional work of the engine due to hoisting the load from this elevation will be h and the total work per minute u will be u = p A 0(i + 2 J^\ -|- 2 w v\ + h. L \ c I J EXAMPLE. Assuming the same conditions as given above, and, in addi- tion, a rise or elevation of 100 ft. in the entire length of the haulageway, we have it = ^[3,333(l + 2 --jjjjp) + 2 X 1.58 X 704J + 3,333 X 100 = 1,528,050 ft.-lb. per minute = 46.3 H. P., or assuming an efficiency of 60$ 4fi ^ for the engine, ~ = 77 H. P. MOTOR HAULAGE. Locomotive Haulage. Wire-rope haulage is very efficient in headings, on heavy grades, and against large loads, but in crooked passages it entails great costs for renewals and repairs. When the grades do not exceed 5j6 for short distances and average 3$ against, or for short distances 8$ and 5$ average in favor of loads, locomotives have been found the most economical form of haulage. MOTOR HAULAGE. 403 The chief advantages of locomotive over rope haulage are the flexibility of the system, it being able to serve any number of side tracks in various parts of the mine, and the closeness of the source of power to the point of application. In the event of an accident due to a car jumping the track, a broken wheel, etc., it often happens that a large number of cars are piled up before the man in charge outside the mine is signaled to stop, whereas with locomotive haulage the engineer or trip rider affords immediate relief. In high seams and under favorable conditions, steam locomotives are very economical, but there is a limit to their use, for it is not well to fire while running in the mine when using bituminous coal; hence the length of trip is practically limited to the steam furnished with one firebox of fuel. On account of their many disadvantages and of the improvements in the methods of using other forms of energy, steam locomotives are fast going out of use and are being replaced by locomotives operated by compressed air and electricity, of which a number of types have been designed in recent years, and which have been very successful and have shown a marked efficiency over the mule. Compressed-Air Haulage. (See also page 194.) Compressed air is particularly applicable in gaseous mines, as it improves ventilation and is perfectly safe under all conditions. The great disadvantage in compressed-air haulage is the size of the locomotive. Mr. H. K. Myers, of the Baldwin Locomotive Works, gives the following in regard to compressed-air haulage: In order that compressed-air locomotives may be able to make a fair length of run, the tanks for storage purposes must necessarily be rather cumbersome, and constructed to carry high-storage pressures. In order that they may be designed correctly and get a minimum of storage for the maximum work expected, it is necessary to have a complete profile of the proposed haulage road, and to make a tabulated statement of the air con- sumption on the various grades, noting the ' ' cut-off" necessary to produce the requisite tractive effort. By making a summation of these various amounts, and adding 20$, we will have the possible amount of air used in doing cer- tain work as specified. It is necessary, therefore, to provide storage on the locomotive for this amount of air at a much greater pressure than that used in the cylinders. In order that the locomotive may receive a quick charge at the stations specially provided for the purpose, it is necessary to have stationary storage of adequate pressure and capacity for the purpose. At the present time, it is the custom to compress for the stationary storage to 800 lb., and to have the volume of this storage at least double the tank capacity of the locomotives comprising the system. This allows an equalized pressure in the locomotive storage of approximately 600 lb. The following formula is useful in determining the capacity of stationary p V + P X storage: P f = * v+ x > in which V = volume of storage on locomotive; X = volume of stationary storage desired; p = cylinder pressure; P = stationary storage pressure: and F = locomotive storage pressure. If the average time for each trip is 30 minutes, the compressor must be able to compress in that time to pressure P, the calculated amount of air required for one trip or series of trips for the various locomotives included in the haulage. In general, it is customary to extend extra-strong pipe into the mine and of such length and diameter as to have the required volume for the stationary storage. There are times however when it would be found more economical to arrange for tank storage either inside or outside the mine, but in general, especially when the mine is advancing, it is the better practice to install pipe storage since it increases the range of the locomotive as the workings advance. The following table gives the various tractive efforts of different sizes of compressed-air locomotives, when working at 100 lb. cylinder pressure, and various cut-offs. If other pressures or strokes are used, the tractive efforts are directly proportionate. This table is calculated by means of the formula, tractive effort = &lJP. in which d = diameter of cylinder; D = diameter of driver: ; = length of stroke; p = working pressure of the cylinders; and x = variable due to the various cut-offs. 404 HOISTING AND HAULAGE. TRACTIVE EFFORTS OF COMPRESSED-AIR LOCOMOTIVES. Cylinder. Diam- eter of Driver. Inches. Weight on Driver. Pounds Tractive Effort for Each 100-Lb. Cylinder Pressure at Various Cut-Offs. Diam. Inches. Stroke. Inches. T * 990 1,425 2,150 2,750 4,140 5,150 6,450 7,800 1 *. t i I 5 6 7 8 9 10 11 12 10 10 12 12 14 14 16 16 24 24 26 26 26 26 28 28 6,000 8,500 13,000 18,000 25,000 32,000 42,000 52,000 1,020 1,470 2,200 2,880 4,340 5,280 6,770 8,050 920 1,320 1,990 2,600 3,840 4,740 5,980 7,200 835 1,200 1,810 2,360 3,490 4,310 5,440 6,550 710 1,020 1,540 2,000 2,960 3,660 4,620 5,580 530 760 1,140 1,510 2,220 2,630 3,470 4,150 325 445 700 900 1,350 1,670 2,140 2,550 On account of certain losses due to radiation, etc. for cut-off at full length of stroke in steam practice, x is taken as .85. While cylinder surface acts as a detriment to the use of steam, it acts entirely opposite in the use of air, for the reason that, in the expansion of the air, very low temperatures are produced, and, with a maximum of cylinder surface exposed, we absorb a maximum of heat from the surrounding air, which virtually adds new energy to the air, thus acting as a reheater. Therefore in air practice, x is made .98 for full-stroke cut-off, with the others proportionately high. If simple-expansion cylinders are used, the working pressure should not exceed 130 lb., while, with compounds, one can easily use from 180 to 225 lb. with great economy. Where it is imperative to have a minimum- sized locomotive storage with a maximum run, this can be accomplished with compound locomotives. Originally, it was the custom to lag the cylin- ders as in steam practice, but now it is found advantageous to leave them bare and to corrugate both sides and ends so as to present a maximum surface to the surrounding atmosphere while running, thus absorbing new energy. EXAMPLE. It is desired to haul trips of 60 cars, empties weighing 2,000 lb. and loads 6,000 lb. each, over a track having the following profile, and with one charge of air. All grades are in favor of loads. (The following calcu- lations have been made with the slide rule.) PROFILE OF ROAD. Grade. Distance. Grade. Distance. Grade. Distance. 1.3$ 2.0$ 1.3$ 800ft. 600ft. 800ft. 0.30$ 1.77$ 0.90$ 700ft. 1,025 ft. 300ft. 2.4$ 3.5$ 1.2* 400ft. 425 ft. 320 ft. The maximum grade being 3.5$, and the car friction in this case being 1$, the total resistance when ascending a 3.5$ grade due to cars is, hence, 3.5$ + 1$ = 4.5$. Since it is desired to haul 60-car trips, and all grades are in favor of loads, it is only necessary to provide a locomotive capable of hauling 60 empties weighing 120.000 lb. up the above-mentioned grade. The drawbar pull necessary to do this is 4.5$ of 120,000 lb. = 5,400 lb. In general, it will require a locomotive having a weight on drivers of 5 times the tractive effort desired if steel tires are used, as is the practice in the con- struction of air locomotives, and 6 times the tractive effort if cast-iron chilled wheels are used, as is the practice in electric locomotives. We will there- fore assume the necessary weight of the locomotive to give the proper adhesion as 32,000 lb., and we calculate that the tractive effort necessary to haul itself up the 3.5* grade would be 3.5$ + .5$ = 4$ (.5$ covering the fric- tion of the locomotive on the level) of 32,000 lb., or 1,280 lb., to which we add the necessary drawbar pull to haul the desired load, 1,280 -f 5,400, and have a total tractive effort of 6,680, which is about the limit of a locomo- tive on dry rail with sand. MO TOR HA VIA GE. 405 By consulting the table of tractive efforts of compressed-air locomotives, we see that, at 100 Ib. working pressure, a 10" X 14", 26" driver locomotive has a maximum tractive effort at cut-off, which is practically full stroke, of 5,280 Ib., and by dividing this into our necessary tractive effort, we find that the necessary working pressure would be about 130 Ib. On this basis, we then make up the following table in order to ascertain the necessary air consumption: GOING IN WITH EMPTIES. Grade. Distance. T. E. Strokes. Cut-Off. Cu. In. Air Used. 1.3 800' 3,375 120 i 126,000 2.0 600' 4,450 80 i 176,000 1.3 800' 3,375 120 126,000 0.3 700' 1,830 105 55,125 1.77 1,025' 4,100 150 315,000 0.9 300' 2,750 40 42,000 2.4 400' 5,075 60 i 157,500 3.5 425' 6,760 65 239,000 1.2 320' 2,220 50 i 52,500 COMING OUT LOADED.* 0.3 700' 2,600 105 i 110,000 1,399,125 20$ additional 279,825 Total 1,678,950 cu. in. This equals 975 cu. ft. at 130 Ib. pressure used in hauling the required loads on a single round trip. Since we should return to the starting point with 130 Ib. in the locomotive storage, it is evident that the volume of the tanks shall allow for the use of 975 cu. ft. in addition to 1 volume at 130 Ib. Let V = volume of storage on locomotive; P' = pressure of storage on locomotive; p = working pressure; V = volume at working pressure nec- essary to do the work required. Then the product of the volume of the locomotive storage by its pressure must equal the sum of the volume necessary to do the work required multiplied by the working pressure, and the locomotive storage volume by the working pressure, thus, P' v = p V + p V', or, V = V P' ~p If P' = 650, then V = 975 X ^~^Q = 244 cu - ft - With one locomotive, making trips every 30 minutes, we must arrange for a compressor capable of compressing 975 cu. ft. at 130 Ib. in this time. Since it is customary to rate compressors at their capacity in free air per minute, (V7K \s 1 QA the above is equivalent to = 288 cu. ft. free air per minute. This must be compressed to 800 Ib. in the compressor, and stored in stationary storage. If X is the volume of the stationary storage, pV+PX V+X ' The length of the haulage is 5,370 ft., hence the cross-section of the pipe 84fi necessary to furnish the requisite storage is =^r = .157 sq. ft. 5,370 From the following table, this would require a 5i" pipe, but for practical purposes it is possible that a 5" pipe would be selected. * Returning with loads, it is possible that there is only one grade that the trip will hare to be hauled. 406 HOISTING AND HAULAGE. STANDARD STEAM AND EXTRA-STRONG PIPE USED FOR COMPRESSED-AIR HAULAGE PLANTS. Trade Diam- eter. In. Cu. Ft. in 1 Lineal Ft. Lineal Ft. Necessary to Make 1 Cu. Ft. Steam. Extra Strong. Trade Diam- eter. In. Thick- ness. Weight per Ft. Thick- ness. Weight per Ft. 2 .0218 45.41 .15 3.61 .22 5.02 > 2* .0341 29.32 .20 5.74 .28 7.67 24 3 .0491 20.36 .21 7.54 .30 10.20 3 3i .0668 15.00 .22 9.00 .32 12.50 3i 4 .0873 11.52 .23 10.70 .34 15.00 4 4i .1105 9.05 .24 12.30 .35 17.60 4i 5 .1364 7.33 .25 14.50 .37 20.50 5 5* .1650 6.06 .26 16.40 .40 24.50 5* 6 .1963 5.10 .28 18.80 .43 28.60 6 From the following table we see that it would require 2.88 X 32.5 = 93.6 H. P.; hence, we would be compelled to arrange for a boiler capacity of practically 100 H. P., provided we used a three-stage compressor, as is the general custom. HORSEPOWER NECESSARY TO COMPRESS 100 Cu. FT. OF FREE AIR TO VARIOUS PRESSURES AND WITH Two-, THREE-, AND FOUR-STAGE COMPRESSORS. Gauge Pres- sure. Horsepower Necessary. Gauge Pressure. Horsepower Necessary. Two- Stage. Three- Stage. Four- Stage. Two- Stage. Three- Stage. Four- Stage. 100 200 300 400 500 600 700 800 15.7 21.2 24.5 27.7 29.4 31.6 33.4 34.9 15.2 20.3 23.1 25.9 27.7 29.5 31.2 32.5 14.2 18.8 21.8 24.0 25.9 27.4 28.9 30.1 900 1,000 1,200 1,400 1,600 1,800 2,000 2,500 36.3 37.8 39.7 41.3 43.0 44.5 - 45.4 33.7 34.9 36.5 37.9 39.4 40.5 41.6 43.0 31.0 31.8 33.4 34.5 35.6 36.7 37.8 39.0 Electric Haulage. Mr. H. K. Myers says in regard to mine haulage by electricity: In general, it costs from 6 to 10 cents per ton to deliver coal from face of workings to shaft, slope, or tipple, where the haul is 1 mile and the tracks approximately level; yet I know three mines that at present haul from parting with the trolley system, the miner delivering from face of room, making an average round trip of 9,000 ft., at a total cost of 1 cent per ton. These mines have never had a mule in them, and it would be almost an impossibility to introduce them, for the reason that the seam is of such thickness that the clearance between tie and roof is only about 4 ft. Since the advent of the electric-mining locomotive, there has been a change in the mine wagons universally used. Formerly it was customary to find as much as 60 Ib. per ton car resistance on the level, while at present it is as low as 15 Ib. In dimensioning mining locomotives, it is customary to make the weight from 6 to 8 times the necessary tractive effort, dependent entirely on the nature of the work. If the work is constant and a maximum, then the weight will be only 6 times the torque of the motors, while if the work is intermittent with 'a short-time maximum tractive effort, then the factor will be 8. The weight of an electric locomotive running at a speed of 6 to MOTOR HAULAGE. 407 8 miles per hour with intermittent load may also be expressed on a basis of 400 Ib. for each rated horsepower of the motor, and the weight should be 8 times the rated drawbar pull, regardless of speed. For continuous work, these weights should be decreased 25$. DRAWBAR PULL ON VARIOUS GRADES FOR DIFFERENT SIZED LOCOMOTIVES. Horse- power. Weight. Grades. Level. 1$ 2$ 3# 4$ 5* ty 10 4,000 500 460 420 380 340 300 260 20 8,000 1,000 920 840 760 680 600 520 30 12,000 1,500 1,380 1,260 1,140 1,020 900 780 50 20,000 2,500 2,300 2,100 1,900 1,700 1,500 1,300 70 28,000 3,500 3,220 2,940 2,660 2,380 2,100 1,820 100 40,000 5,000 4,600 4,200 3,800 3,400 3,000 2,600 In mines it is found that the friction between wheel and rail is less than on the surface, due to dampness and powdered coal on the rail. The tractive efforts with chilled wheels is usually considered of the weight. The table on page 408 and diagram on page 409 give hauling capacities of locomotives in tons of 2,000 Ib. For maximum continuous work, it is necessary to have a grade such that the efforts to haul the same number of empty wagons as loaded are equal. With the car resistance considered 1$ and the loaded cars weigh- ing 3 times as much as the empties, this is found to be i of 1$. The most critical point in the designing of mining locomotives is to make the limiting dimensions a minimum. The demands for various dimensions are wonder- ful. The headings in mines are never of more generous proportions than really necessary, and all clearances a minimum. The minimum dimensions for mining locomotives are as small as 2 ft. for wheel base, 8 ft. for length over all, and 3 ft. width. Scarcely two orders carry the same dimensions, and it is impossible to have any kind of a standard. In consequence of this, it is necessary to have a great variety of motors suitable for gauges as nar- row as 18 in. and for wheels as small as 20 in. in diameter. With such a variety, it becomes possible to construct a locomotive weighing 40,000 Ib. on 3' gauge, having the width over all 62 in., height 35 in., and length 12 ft. In construction, it is necessary to have the most modern form of motors and the most rigid mechanical construction. The motors now used are of the best possible construction and efficiency. They are of the slow-speed street-car type, 6 to 8 miles per hour winding, and range in size from 4 to 50 H. P. It is customary to use the rheostatic type of controller for mining locomotives, on account of its small dimensions and apparent efficiency for this class of work, but it is doubtless but a short time until a very compact form of series-parallel type will be devised. On account of the use of this rheostatic controller, it becomes necessary to pro- vide for large diverter capacity, and since the locomotive is designed for the maximum tractive effort, it is hardly ever possible to run without resist- ance and, hence, a large amount of current must be dispersed with the consequent heating. If the motors are overloaded, they heat rapidly, this heating varying as the square of the current. A motor that has a rating of 40 amperes for regular work, if worked for 3 minutes at 100 amperes, should not be subjected to such a strain oftener than once in 18 minutes, as shown by the following equation: 40 2 X x == 3 X 100 2 ; x = 18* minutes. Using the same problem given under compressed-air locomotives, in which the maximum tractive effort was 6,760 Ib., we find from the table of drawbar pulls that a locomotive equipped with two 50 H. P. motors (equals 100 H. P.) will carry the load with an overload, these motors being rated for continuous work at approximately 32 amperes of 500 volts. Using the formula . \ - T = 64, in which t -= various times at which 408 HOISTING AND HA ULAGE. various amounts a of current are used on the corresponding grades, 2 the summation of the items t a 2 calculated for each section or grade, and T = total time that should be taken for each trip, we calculate the following table: Grade. Dist. T. E. Time. Minutes. Amperes. to? Empties. 1.30 800 3,375 1.5 114 19,600 2.00 600 4,450 1.1 134 19,900 1.30 800 3,375 1.5 114 19,600 .30 700 1,830 1.3 74 7,100 1.77 1,025 4,100 2.0 128 32,800 .90 300 2,750 .6 100 6,000 2.40 400 5,075 .8 148 17,300 3.50 425 6,760 .8 182 26,500 1.20 320 2,220 .6 86 4,400 Loads. .30 700 2,600 1.3 96 13,900 167,100 = 2< 2 4,096 T = 167,100; T = 40. By this means we can make 60-car trips every 40 minutes without injury to the motors, based upon a speed of 6 miles per hour. (See also page 215. ) Speed of haulage depends on the system of haulage used and on the con- dition of the haulage road. The law in Pennsylvania provides for a speed of haulage not over 6 miles per hour, and this is the speed at which electric and HAULING CAPACITY OF ELECTRIC LOCOMOTIVES. i is fi*3 Ifl Grades. I I 05 O Q |'lo ,_ o> *i 2 * ^ 3* 3* 4* * <* 10 4,000 500 20 23 15 10 8 6.3 5.2 4.2 3.5 3.0 2.2 1.6 30 15 11 8.4 6.7 5.4 4.5 3.8 3.2 2.7 2.0 1.5 40 12 9 7 5.7 4.7 4.0 3.4 3.0 2.5 1.8 1.4 20 8,000 1,000 20 46 29 21 16 13 10.3 8.4 7.1 6.0 4.3 3.1 30 31 22 17 13 11 9 7.5 6.4 5.4 4.0 3.0 40 23 18 14 11 9.5 8 6.8 5.9 5.0 3.7 2.8 30 12,000 1,500 20 69 44 32 24 19 15 13 10.7 9.0 6.5 4.7 30 43 33 25 20 16 13 11 9.6 8.2 6.0 4.4 40 34 26 21 17 14 12 10 8.8 7.5 5.6 4.1 50 20,000 2,500 20 115 73 52 40 32 26 21 18 15 11 7.9 30 77 55 42 33 27 122 19 16 14 10 7.3 40 58 44 35 29 24 20 17 15 13 9.3 6.8 70 28,000 3,500 20 161 103 74 56 44 36 30 25 21 15 11 30 107 77 59 47 38 31 26 22 19 14 10 40 81 61 50 40 33 28 24 20 18 13 9.6 100 40,000 5,000 20 230 147 105 80 63 52 42 36 30 22 16 30 153 110 84 67 54 45 38 32 27 20 15 40 115 88 70 57 47 40 34 29 25 19 14 MOTOR HAULAGE. 409 compressed-air haulages are usually calculated and at which loaded trips are usually run. Empty trips are usually run at a slightly higher speed. The speed for tail-rope haulage is given by three prominent makers of such plants, as follows: (a) 600 to 700 ft. per minute; (6) 8 to 10 miles per hour; (c) 6 to 8 miles per hour. The speed for endless-rope haulage is given by the same makers as (a) 140 to 150 ft. per minute; (b) 1 to 2 miles per hour; (c) 150 to 200 ft. per minute. A slow speed for endless rope is to be preferred as being much more economical in the wear of the rope'and cars, and many prefer a single- car system to a trip system, thus doing away with the trip rider. By han- dling the cars singly or even in trains of two and at a slow speed, the load can be picked up without any slippage of the rope through the grips; while if trains of from 12 to 25 'cars are used, with the rope traveling 3 to 3 miles per hour, it is impossible to pick up the load without having the rope slip Approximate Weight of Locotnet/'ris 2 3j 7 1O 12i Tons height of Load Hau/ec* 9 25 SO 75 ' 100 12S ISO 175 2OO Tons / x ^ ^, -' / / / ^ > L J / ^ ^ ' s --- ^ ~- / / / / ^ ^ ^~ \ ^ ^ -" X ^ J / / / ^ / / I ( / / X / f / / s ! 1 f 1 Hou/i "7 e Co? at f\ 1 1 f / \ \ 2 l 1 1 / f/e e/ tc MineV.o COWOJ'/*' f, 0) 1 i/ 1 1 Varying ^w4?s| 1 1 / \ \ T 1 i / (f g^o ?2 Ofb. brc ~*&3rKh /o rh e To TOf a iri 01 id / I 1 H& ufect efe/ 7>- 7Ct f) / 1 / I / 1 , 1 1 / j 1 / / 1 / 1 1 \\\\ 1 1 , I III! / through the grip, thus heating the rope and cutting it. The slow-speed, single-car or small-train, system requires more cars, but this is counterbal- anced by the life of the cars and rope. Those that have tried both systems prefer the slow-speed small trip to the high-speed large trip. It has been found in general practice that the maximum pulling power of a mule as well as a locomotive is, approximately, one-fifth its weight, or, in other words, a locomotive will pull as much as the same weight of mules will pull, and at a speed about three times as great. Cost of Haulage. So much depends on local considerations that it is difficult to give costs of haulage that will be of service. Mule haulage has been given as costing, under different conditions, 5.74 cents and 7.92 cents per ton-mile, and in other locations 2.35 cents, 2.95 cents, and 7.15 cents per ton of coal hauled. The Ber wind-White Coal Mining Co., at Windber, Pa., uses 30 electric loco- motives at various mines, which average, approximately, 400 tons per day of 9 hours, per locomotive, over an average haul of 2 miles for the round trip. The approximate cost for operating one of these locomotives, including the wages of motorman, trip rider, and proportion of power-house expense, is about $6.00 per day. or H cents per ton of coal haul per mile. If the total load, in cludinsr weight of cars, is considered, it figures of 1 cent per ton per mile. These figures do not, however, include grades, which is an important factor in equating costs per ton per mile. In these mines there are no mules 410 HOISTING AND HAULAGE. whatever, the locomotives distributing the empty cars to room partings, for the men to push to the face. If the haul is done between side tracks and under similar grade conditions, the same locomotives could easily handle 1,000 to 1,200 cars per day. Mr. F. J. Platt, of Scranton, Pa., gives the following comparative costs of electric and mule haulage per ton of coal hauled and under approximately the same conditions in the same mine: Name of Mine. Mule Haulage. Cents. Electric Haulage. Cents. Green Ridge Colliery New York & Scranton Coal Co '.... New York & Scranton Coal Co Mt. Pleasant Colliery 7.15 6.58 2.35 2 95 2.76 2.62 1.07 1 ">7 Hillside Coal & Iron Co 1077 4 56 Hillside Coal & Iron Co. . 9 10 4 65 The following costs of electric haulage, per ton of material hauled, are given in the catalogue of the General Electric Co. : Name of Mine. Mule Haulage. Cents. Electric Haulage. Cents. Wythe Lead & Zinc Co 10 2 56 Blossburg Coal Co. Cleveland-Cliffs Iron Co. ('94, '95, '96) 7.9 3.9, 4.5, 4.8 At Carbondale, Pa., compressed-air locomotives have hauled coal for 1.5 cents per ton-mile, at Mill Creek, Pa., for 3.77 cents per ton-mile, and at Glen Lyon, Pa., for 1.89 to 1.93 cents per ton-mile. MINE ROADS AND TRACKS. Underground or mine-car tracks should be solidly laid on good sills, rest- ing on the solid floor of the mine. They should be well ballasted, and should have good clean gutters on the lower side of the entry, so that the rails may be protected as much as possible from the action of the mine water. Much of the following data, on mine roads is based on an article on "Mine Roads," by Mr. H. L. Auchmuty, "Mines and Minerals," March, 1900. Grade. The grades depend entirely on circumstances, but, when possible, the grade should be in favor of the load, and should be at least 5 in. in 100 ft. to insure flow in the gutters alongside the track. On main roads, where wagons having a capacity of 1.5 to 2.5 tons are hauled by animal power, the grades should not exceed 1$ to 2# in favor of the loaded wagon. Such a rate of grade provides for an easy return haul of the empty trip without wearing out the stock, and likewise insures good drainage. With grades under 14, unless the ditches are kept perfectly clean, the drainage is apt to be sluggish, and then, in low places, we are sure to find a wet and muddy track, which is a great source of waste energy. Where hauling is done by locomotives, whether by compressed air or steam, the adverse grades should not be over 1.5$ to 2.5$ if it can possibly be avoided. When gradients are heavy, too great a percentage of the tractive power of the locomotive is consumed in drawing itself up the grade. Ties should be spaced about 2 ft. apart, center to center, making 15 to a 30' rail. The rail should be well spiked to the ties with four spikes to each tie, the joint between two rails on one side of the track being located about midway between two joints on the opposite rail. Care should be taken in locating the spikes that they are not all in the center of the tie, thereby MINE ROADS A XI) TRACK*. 411 causing a tendency to split the same. It is best to place them each side of the center vyith two spikes between the rails, on one side, and the two spikes on the outside of the rail on the other side of the center of the tie. With the spikes so located, there is no tendency for the tie to slide, as there is if an outside and inside spike are on the same side of the center of the tie. Ties having a 5 in. face and 4 in. deep by 5 ft. in length should be used for the ordinary sizes of rail, i. e., 16 lb. to 20 lb., and, in general, the thickness should be sufficiently great that the spike does not pass entirely through the tie, as then its holding power is greatly diminished. On haulage tracks where 35-lb. to 40-lb. rail is used, the ties should be at least 5 in. deep and have a face of 6 in., the ties ordinarily used for lighter sizes of rails being entirely too thin for rails of this weight, as a larger spike than the ordinary 3 in. X t in* is required to securely hold the rails to place. The ends of the ties should be lined up along one side of the track, so that they are all the same distance from the rail, and, with each tie placed at right angles to the rail as it should be, we have a well-spaced, neat-looking track, which, when well tamped with the ballast, is perfectly solid. On curves, the ties should be laid so as to form radii of the curves of the track. Rails. The weight of rail to be chosen in any individual case depends entirely on the weight of wagons used, and the motive power. For wagons whose capacity is about 1.5 tons, the weight of rail, when the motive power is live stock, should not be less than 16 lb. per yd., while for wagons having a capacity of 2 tons or over, a 20-lb. rail should be used. There is no economy in using a very light rail, as the base is gradually eaten away by the mine water when it comes in contact with the metal, and in the case of a heavy section of rail, it will be much longer before the rail becomes weakened. On main roads, where haulage machinery of one kind or another is used, the weight of rail for 2-ton wagons should be from 25 lb. to 35 lb. per yd., and on steep slopes as high as 40 lb. per yd. In the case of locomotive haulage, authorities claim that the weight of rail should be regulated by allowing 1 ton for each driver for each 10 lb. weight of rail per yd. Gauge. The gauge of the track in coal mines should not be less than 30 in. nor more than 48 in. A mean between these two, or a gauge of from 38 in. to 42 in. is desirable, because it combines, to a certain extent, the advantages claimed for the extremes. The advocates of broad gauges believe that the greater stability of the track and the consequent reduction in haulage expen- ses, the increased capacity of the broad-gauged mine cars, the reduction in the outlay for rolling stock, and for repairs to the same, more than equal the disadvantages of broad as compared to the narrow gauges. Advocates of the narrow gauges think that the ease of hauling around sharp curves, the reduction in cost of construction, and the use of mine cars with inside wheels, are advantages greater than those advanced by the advocates of the broad gauges. An allowance of about i in. should always be made between the wheel gauge and the track gauge. By so doing, the resist- ance to hauling is greatly overcome, and there is no binding of the wagons on the track, hence a less likelihood of having derailed wagons. With an average running wagon, there is a resistance of 15 to 20 lb. per ton tractive force on a level track, which would be equal to the resistance occasioned by a grade of .75$ to K, and with wagons that bind on the track, this resistance is greatly increased. Curves should be of as large a radius as possible, and never, if possible, of less radius than 25 ft. The resistance of curves is very considerable. The less the radius of the curve, and the greater the length of the curved track occupied by the trip, or train, the greater the resistance. The length of wheel bases of the cars, the condition of rolling stock and of the track, and the rate of speed, all influence the resistance, and there is no formula that will apply to all cases. In practice on surface railroads, engineers compensate for curves on grades at the rate of T foj ft. in each hundred feet for each degree of curvature, the grade being stated in feet per hundred. In mine work, this compensation is not made, as the gain will not pay for the labor that must necessarily be employed to do work in a thoroughly scientific manner. Sharper curves can be used on narrow-gauge roads than on broad-gauge roads, because the difference in length of the inner and outer rails on curves on the same degree is not quite so great, and also because the wheel bases of cars are less. The track should be spread about in. on easy curves, and 412 HOISTING AND HAULAGE. on very short curves about 1 in., or as much as the tread of the wheels will permit. A good rule is to widen the track Jg in. for each 2| of curvature. Short and irregular curves are to be avoided whenever possible, as they increase the load and are destructive to rails and rolling stock. When a sharp curve is necessary, the rail should be bent to the right curvature by a portable rail bender, or by a jack and clamps. To Bend Rails to Proper Arc for Any Radius. Rails are usually 30 ft. long, and the most convenient chord to use in bending mine rails is 10 ft. Then, having the radius and chord, we find the rise of middle ordinate by squaring the radius, and from it take i the square of the chord. Extract the square root of the remainder and subtract it from the radius; the result will be the rise of the middle ordinate. Thus, having a radius of 30 ft. and a chord of 10 ft., the middle ordinate will be 30 - Vw* - 5-, or 0.42 ft. Rail Elevation. In elevating rails on curves, consider whether the hauling is to be done by a rope, or by a locomotive, or electric motor. For either of the latter, elevate the rail on the outside of the curve; but for the first, elevate the inner rail, since as the power is applied by a long flexible rope, there is always a tendency for both rope and wagons to take the long chord of the curve as soon as the point of curve is reached. On slope haulages, operated by a single rope, when the weight of the wagons traveling on the grade of the slope is sufficient to draw the rope off the hoisting drum, the rails on curves should be elevated on the outside, the effect then being similar to that of a locomotive, i. e., the centrifugal force tends to throw the wagon to the outside of the track. In such cases, the elevation should be moderate so as not to interfere with the trip when drawn out again by the rope the opposite effect being then experienced. On an 18 curve (319 ft. radius), an elevation of 2 in. or 3 in. in the outer rail, where the haulage was by slope rope, has never given any trouble in operating. In general, the elevation of rail necessary for different degrees of curvature for a 42" track gauge should be made in accordance with the following table: TABLE OF ELEVATIONS. For outer rail of curves for a speed of 10 to 15 miles per hour and a gauge of track of 42 in. for locomotives; or for slope haulages where cars run down grade by gravity. Degree of Radius of Elevation of Outer Degree of Radius of Elevation of Outer Curve. Curve (Ft.). Rail (In.). Curve. Curve (Ft). Rail (In.). 1 5,729.6 i 10.0 573.7 1? 2 2,864.9 ' I 12.0 478.3 IT'S 3 1,910.1 A 15.0 383.1 11 4 1,432.7 TB 18.0 319.6 IT! 5 1,146.3 20.0 287.9 2i% 6 955.4 U 57.3 100.0 4i 7 819.0 M 95.5 60.0 4* 8 716.8 8" 114.6 50.0 4i . 9 637.3 1 No elevation should be over 4i in., which would be equivalent to an elevation of 6 in. for standard track gauge of 4 ft. 9 in., the latter being con- sidered as the maximum for standard gauge. Rollers. The rollers on level tracks should not be more than about 20 ft. apart to properly carry the rope, and on gravity slopes where the lower end of the slope gradually flattens off, the distance between rollers should not be more than 12 to 15 ft., as this spacing allows the trip of wagons to run much farther, by keeping the rope well off the ties, than if they are farther apart, thereby not supporting the rope, and causing a great amount of friction between the rope and the ties. With tracks in fair shape and rollers 12 to 15 ft. apart, the resistance, due to the rope in running empty wagons down grades varying from 3.8# to 6.2$, varied from 6$ to 15$ of the weight of ropes by actual trial. MINE ROADS AND TRACKS. 413 FIG. Switches. The switch, or latch, most commonly used in mines is shown in Fig. 7. When the branch or siding is in constant use, an ordinary railway frog is substituted for the bar 6. The latches a, a are wedge-shaped bars of iron (made as high as the rail) with an eye in the thick end. They are sometimes connected together by a rod attached to a lever so that they may both be moved at once from the side of the track, or by a person situated some distance away. This switch is made self- closing or automatic whenever it is necessary to run all the cars off at the branch (the switch then being used only to admit cars to the main track) by attaching the latches through a bar or lever to a metallic spring, a stick of some elastic wood, or a counter weight, to pull them back into a certain position whenever they have been pushed to one side or the other by the passage of a car on the main track. Figs. 10, 11, 12, and 13 show some of the applications of these spring latches or automatic switches. A modification of this switch is shown in Fig. 8, which represents a form of double switch. These latches are set by the drivers, who kick them over and drop a small square of plate iron between them to hold them in place This switch costs more than the other style and is better adapted to outside roads than to inside roads. The ordinary movable rail switch in common use on all surface railways is sometimes used in mine roads. It is commonly used in slopes arranged as shown by Fig. 12, to replace latches set by the car, and is also largely used in outside roads. For crossings, ordinary railway frogs and grade crossings are sometimes used, as is also a small turntable, which then answers two < purposes. More frequently the plan shown in Fig. 9, in which, four movable bars are thrown across the main track whenever the other road is to be used, is adopted. " The subordinate road is built from H to 2 in. higher than the main road, to allow the FIG. 8. bars to clear the main-track rails. Turnouts. On gangways or headings used as main haulage roads, turnouts should be constructed at convenient intervals to allow the loaded and empty trips to pass. These turnouts should be long enough to accommodate from 5 or 6 up to 15 or 20 cars. The switches at each end may be made self- acting so that the empty trip, coming in, is thrown on the turnout, and in running out on the main track at the otner end, the loaded cars open the switch, which immediately closes. As there is constant trouble with self-setting switches, either from small fragments of coal or slate clogging them up, or from insufficient power of the spring to move them, they are viewed with dis- favor by many mine managers, who do not care to use them under any conditions. Slope Bottoms. At the foot of a slope, or at the landing on any lift, the gang- way is widened out to accommodate at* least two tracks one for the empty and one for the loaded cars. The empty track should be on the upper side of the gang- way, or that side nearer the floor of the seam, and the loaded track on that side of the gangway nearer the roof of the seam. An arrangement of tracks often used is shown in Fig. 10. At a distance of 40 or 50 ft. above the gangway, the slope is widened out to accommodate the branch leading into the gangway loaded track. This branch descends with a gradually lessening inclination until nearly at the level of the gang- way it turns into the main loaded track. A short distance above the gangway. FIG. 9. 414 HOISTING AND HAULAGE. FIG. 10. a bridge or door is placed, which, when closed, forms a latch by which the empty cars are taken off the slope. The empty track is about 6 ft higher than the loaded track, and is carried over it on a trestle. The illustration in Fig. 10 shows the plan as arranged for a single slope, or one side only of a slope taking the coal from both directions When coal is being raised from this lift,' the bridge is closed; the empty car comes down and is run off over the bridge; the car is unhooked from the rope, and the chain and hook attached to the rope are thrown down to the branch below on which a loaded car is standing; the loaded car is attached, the signal given, the car ascends to the main track on the slope opening the switch or the switch may be set each time by the bottom men, by a lever at the bottom of the branch. This plan can only be economically applied in thick seams, as the height necessary to allow one track to cross the other on a trestle cannot be obtained in seams of moderate thick- ness without taking down a large amount of top. A more simple plan, which dispenses with the bridge, is often used. The branch is laid off, as shown by Fig. 10, but, near the point where it enters the gangway, a switch opening into the empty track is placed. By this arrangement, the tracks cannot be as well arranged for handling the cars by gravity as in the former plan, in which the empty cars when detached from the rope run by gravity into the empty siding, and the loaded cars descend by gravity around the curve to the foot of the branch, where they lie ready to be attached to the rope. When the pitch of the slope is so steep that the coal or ore falls out of the cars, during hoisting a gunboat is used or the cars are raised on a slope carriage in either case, the arrangement of the tracks ^at lift landings is entirely different. With either a gunboat or a slope carriage, the arrangement of tracks on the slope is the same; but, in the former case, a connection between the slope and gangway tracks is often advisable. When a gunboat is used, the gangway tracks run direct to the slope, and a tipple, or dump, is placed on each side to dump the mine cars over the gunboat; but when the cars are raised on a slope carriage, the gangway tracks run direct (at right angles) to the slope, to carry the car to the cage or carriage. The floor of the cage is horizontal, and has a track on it that fits on the end of the gangway track when the car- riage is at the bottom, and this track is arranged with stops similar to those on cages used in shafts. Another common arrangement of tracks at the bottom of a slope is shown in Fig. 11. A branch is made by widening the slope out near the bottom, and this, being a few feet higher than the main track, is used to run off the empties by gravity. The loaded cars run in by gravity around the curve to the foot of the* slope in position to be attached to the rope. In ascending, the loaded car forces its way through the switch, or the switch may be set by a lever located at the foot of the slope. When the empty car descends, it runs in on the branch, where the chain is unhooked and thrown over in front of the loaded car, and runs around the curve into FIG. 11. FIG. 12. the gangway by gravity. 1 be observed that in this plan the loaded car (and consequently the MINE ROADS AND TRACKS. 415 bottom men) stands on the track in line with the slope, and is in danger from any objects falling down the slope, or from the breakage of the rope or coup- lings; but this can be obviated by making the bottom on the curve. The illustration in Fig. 11 shows only one side of the slope; the other side is, of course, similar. All these plans necessitate the location of that part of the gangway near the slope, in the tipper benches of the coal or near the top rock. The gang- way is then curved gently around toward the floor, so that, when it has been driven far enough to leave a sufficiently thick pillar, the bottom bench is reached and the gangway is then driven along the bottom rock. A very different bottom arrangement is shown by Fig. 12, which also represents a plan frequently adopted on surface planes. The two slope, tracks are merged into one a short distance from the bottom of the slope, and on the opposite sides of the bottom two tracks curve around into the gang- way on opposite sides of the slope. As these branches curve into the main gangway tracks, a switch sends off a side track for the empty cars. The switch on the slope is either set by the car and this can be done because the next loaded goes up on the same side on which the last empty descended or by a lever located at the bottom. It will at once be seen that in this plan no opportunity is afforded of handling the cars by gravity. The curved branches are made nearly level, and the momentum of the descending car, if quickly detached, is often sufficient to carry it partly or wholly around the curve, even against a slight FIG. 14. adverse grade. The disadvantage above noted of having the bottom in direct line with the slope ( where there is danger from breakage and falling material) also obtains in this plan. In the plan shown by Fig. 13, the grades may be so arranged that the cars can be entirely handled by gravity. The latches on the main-slope track may be closed automatically by a spring or weight, the loaded car running through them in its ascent on the slope, or both sets may be operated by a single lever at the bottom. The switch at the upper end of the central track (loaded) is set by a hand lever. All three sets may be linked together, so that they can all be properly set by a single lever. Reference to Fig. 11 will show that this is only a modification of that method. It requires space at the bottom for only three tracks, while Fig. 13 requires width to accom- modate four tracks, and is objectionable because it is more complicated. The extra set of latches at the top of the central track, and the curvature of both main tracks into this central one, must inevitably cause much trouble and delay from cars jumping the track at this point. The plan shown in Fig. 14 is open to many of the objections pertaining to some of those already described, and which need not be reiterated here. It can only be employed in thick seams, or in seams of moderate thickness lying at a slight angle or dip. In planning the arrangement of tracks on a slope, it is advisable to place as few switches as possible on the slope itself, to keep the main track 416 HOISTING AND HAULAGE. unbroken, to make the tracks as straight as possible, to have nothing stand- ing at the bottom in direct line with the slope tracks, and to arrange the tracks so that cars are handled by gravity. The arrangement of tracks near the top of the slope, and on the surface, is often very similar to the bottom arrangements, as already described; but as all loaded cars (except rock and slate cars, which are run off on a separate switch) are to be sent off on one track, and all the empties come in on the same track to the head of the slope, and as there is usually abundance of room for tracks and sidings, these top arrangements are, in a measure, much more easily designed. In some instances, the two main-slope tracks run into a single track near the head of the slope a plan somewhat similar to the bottom arrangement shown by Fig. 12 and the cars are then brought to the surface on one track, which, after passing the knuckle, bifurcates into a loaded and empty track. A similar arrangement is frequently adopted at slopes on which a carriage or gunboat is used. When the two main-slope tracks are continued up over the knuckle to the surface the most common and best plan the arrangement of tracks and switches may be planned entirely with a view to the quickest and most economical method of handling the cars. Vertical Curves. The vertical curves at the knuckle and bottom of a slope or plane should have a sufficiently large radius, so that when passing over _ them the car will rest on the rail with both front and back wheels. The wheel base of the car must be considered in adopting the radius for these curves, for if the curve is of too short a radius, there is danger of the car jumping the track every time it passes over the curve. Tracks for Bottom of Shaft Fig. 15 shows the arrangement of tracks at the foot of a shaft, with one of the cages at surface. The grades should be so arranged that from the inside latches of the crossings the empty track should have a slight down grade from the shaft, and the loaded track a slight down grade toward the shaft. The cross- ings and the short straight piece of road close to the shaft should be level. As it is often desired to move empty FIG. 15. cars from one side of the shaft to the other, without stopping the hoisting, a narrow branch road should be cut through the shaft pillar, and used for this purpose. Where the pitch of the seam prevents this, a road should be laid alongside the shaft, room to accommodate it being cut out of the rock on the side most desirable. (See also Shaft Bottom, page 276.) In arranging tracks for shaft bottoms, at tops and bottoms of slopes, on coal bins, for mechanical-haulage landings, at foot of slopes or shafts, or in the body of the mine, it is customary to provide double tracks of sufficient length to hold the requisite number of wagons for economically operating the plant and with sufficient distance from center to center of tracks, and from centers of tracks to sides of entries, to easily pass around the wagons where it may be necessary, either in handling them, or in lubricating the wheels. For wagons with a capacity of from H to 2 tons, it generally requires an entry to be about 15 to 17 ft. wide in the clear for ordinary land- ings in the body of the mine, while at shaft bottoms the necessary width may attain 17 to 18 ft. in the clear, owing largely to location and local requirements. The curved crossovers connecting the tracks at shaft bot- toms should be designed with radii of as great length as can be introduced, thereby giving an easy running track. They should not be less than from 20 to 50 ft. on center lines for ordinary gauge of tracks, i. e., 36 to 44 in. On landings constructed in the body of the mine for the reception of empty and full wagons handled by mechanical haulage from shaft or slope, and from this point transported by animal power to the various working places in the mine, a grade of about Ij6 in favor of the loaded wagons to be handled by the stock will be found quite an assistance in delivering the wagons to the haulage. The frogs and switches for these landings, as well as those required at the shaft or slope, should be formed of regular track rails, and can generally be arranged to be thrown by a spring or a con- veniently located hand lever, as has been described, instead of being kicked to position, as was the custom at one time. Besides these usual arrangements of shaft-bottom landings, at many plants the natural grades of the entries can be taken advantage of in designing convenient and economical methods for handling the mine cars. MINE ROADS AND TRACKS. 417 For instance, where the coal is to be hauled from the dip workings of a mine by some form of mechanical haulage, and a summit can conveniently be arranged for in the track on the same side of the hoisting shaft, at the proper distance therefrom, to accommodate the requisite number of loaded wagons to be hauled, thus allowing them to run by gravity over, say, a 1# grade to the shaft, several varieties of empty -track arrangements can be made. The most simple form is to have the empty wagon descend a short grade of from 4% to 5# when pushed from the cage by the succeeding full one. The momentum thus secured is quite sufficient to carry the car up an opposing grade of about 1.5$. It again descends on the same track, and passing through an automatic switch, continues to the empty-car siding. From this latter point it is handled by the regular haulage machinery, and in its route passes around the shaft through an entry especially prepared for this arrangement. A shaft bottom so constructed is very economical to operate, requiring but few men to handle the wagons. Occasionally, it becomes more expedient to have a separate short haulage to draw the empty wagons to the main haulage when it cannot be easily arranged to construct a complete gravity landing. Several other modifica- tions of such a general design can be made. All the different devices, however, depend largely on the local requirements of the particular mine under consideration. When endiess-rope haulage is employed, it is generally found to be most convenient to have the landings for full and empty wagons, in the body of the mine, reached by switches off of the main-haulage track, the cars coming on and leaving the main track at slight knuckles introduced in the track, in order to allow a place for the passing of the rope, which then moves along through a short cut or channel through the switch rails. The flanges of the wagons pass over the rope in this manner without any injury to it. Surface Tracks for Slopes and Shafts. The arrangement of the tracks on the surface naturally differs at every mine, owing to the different existing conditions. All surface roads should be so arranged that the loaded cars can be moved with the least possible power, always looking out for the return of the empties with as little expenditure of power as possible. To secure the running of the loaded cars from the mouth of the shaft or slope by gravity, a slight grade is necessary, the amount of which depends on the friction of the cars, which varies greatly. Care should be take that an excessive grade is not constructed, or there will be trouble in returning the empties from the dump to the head of the shaft or slope. The tracks connecting the top of the shaft and the tipple may be very short, or of considerable length, depending on the conditions at each mine. Usually from 20 to 60 ft. will be sufficient, although no definite rule can be given for this. There are two general arrangements of tracks about the head of a shaft: First, where the loaded cars are removed from the cage and the empty cars placed upon it from the same side of the shaft; second, where the loaded cars are removed from one side of the shaft and the empty cars returned to the cages from the opposite side of the shaft. In either case there are usually several empty cars on the platform ready to be put on the cages when the loaded cars have been removed. Where the conditions are such that the loaded cars can be run by gravity to the dump, a good plan is to have a short incline, equipped with an endless chain, in the empty track. The empty cars can be run to the foot of this, hoisted by machinery to the top, and thus gain height enough to run them back to the shaft or slope by gravity. At the Philadelphia & Reading Coal & Iron Co.'s Ellangowan colliery, where the tipple at the head of the breaker is above the level of the head of the shaft, the following plan is used: The loaded cars are taken off the east side of the cages, and run by gravity to the foot of an incline, where the axles of the car are grasped by hooks on an endless chain and the car pulled up to the tipple. After being dumped, the car is run back from the tipple to the head of the incline, and is carried to the foot of the empty track of the incline by an endless chain. The foot of the empty track is several feet higher than that of the loaded track, and the cars are run by gravity around to the west side of the cages, and are put on from that side. The empty cars, as they run on the cage, have momentum enough to start the loaded car off the cage and on toward the foot of the incline. There are a number of hooks attached to both the empty and 418 ORE DRESSING AND PREPARATION OF COAL. loaded chain on the incline, and there are often several loaded and several empty cars on different parts of the plane at once. This arrangement permits of the hoisting of from 700 to 800 cars per day out of a shaft 110 yd. deep, with single-deck cages. Another excellent arrangement for handling coal on the surface is the invention of Mr. Robert Ramsey, and has been adopted by the H. C. Frick Coke Co. and a number of other prominent operators. A description of this arrangement as applied at the H. C. Frick Coke Co.'s Standard Shaft is as follows: The landing of the shaft is made slightly higher than the level of the tipple, which is north of the shaft. South of the shaft is located a double steam ram, one ram being directly in line with the track on each cage. Directly in front of the rams is a transfer truck, worked east and west by wire rope. The loaded car on the cage is run by gravity to the tipple, where it is dumped by means of a nicely balanced dumping arrange- ment. As soon as it is empty it rights itself and runs by gravity alongside the shaft to the transfer truck, which carries it up a grade to a point directly in line with the cage that is at the landing, and one of the steam rams pushes it on the cage, and at the same time starts the loaded car off to ward the tipple. This second loaded car is then returned by the same means to the opposite cage. The whole mechanism is operated by one man, by means of conveniently arranged levers, each of which is automatically locked, except when the proper time to use it arrives. It is therefore impossible for the topman to work the wrong lever and put an empty car into the wrong compartment of the shaft. Besides the one man at the levers, there is but one other man employed at the tipple, and his work is solely to look after the cars when dumping. All switches are worked automatically, and the average hoisting at this shaft is at the rate of 3 wagons per minute. The shaft is about 250 ft. deep, and single-deck cages are used. The Lehigh & Wilkes-Barre Coal Co. has a system in use at a number of collieries that has also proven very effective. In this system the loaded cars are run by gravity from the cage to the dump, and the empties are hauled from the dump back to a transfer truck by a system of endless-rope haulage. The transfer truck carries the car to a point opposite the back of the cage. The empty car runs by gravity to the cage, and its momentum starts the loaded car on the cage on its way to the dump. This system necessi- tates the employment of more topmen, but is a very good one. At the Not- tingham shaft, which is 470 ft. from landing to landing, from 140 to 150 cars per hour are hoisted on single-deck cages. ORE DRESSING AND THE PREPARATION OF COAL CRUSHING MACHINERY. The object of crushing ore or coal is: first, to free the mineral or other valuable constituents from the gangue, slate, pyrites (sulphur), or other worthless or objectionable constituents so that they can be subsequently separated; or, second, simply to reduce the size of the individual pieces and so get the material into a more salable or convenient condition for use. Selection of a Crusher. The style of crusher employed is influenced by the following conditions: (a) The amount of material to be crushed in a given time. (6) The size of the material as it goes to the crusher, (c) The physical characteristics of the material to be crushed; that is, whether it is hard or soft, tough or brittle, clayey or sticky, (d] The object of the crush- ing; that is, whether it is to free the mineral constituents or simply to reduce the size of the individual pieces, (e) The character of the product desired; that is, whether an approximately sized product is desirable and whether dust or fine material is objectionable. All crushing machinery may be divided into the following classes: Jaw crushers, gyratory crushers, cracking rolls, disintegrating rolls, crushing rolls, roller mills, ball mills, stamp mills, hammers, and miscellaneous forms of crushers. CRUSHING MACHINERY. 419 JAW CRUSHERS. With jaw crushers, the material is crushed between two jaws, one or both being movable. All jaw crushers have the common defect of imparting a considerable amount of vibration or shake to the framework of the build- ing containing them, owing to the reciprocating motion of the heavy masses that comprise their crush- ing parts. There are three styles of jaw crushers in common use. The Blake crusher is shown in Fig. 1, a being a fixed jaw and b a movable jaw that is operated by a toggle joint and the pitman d from a suitable crank- shaft. The jaw b is hung or pivoted at the top. The advantages of this style are as follows: The large pieces of rock to be crushed are received between the upper part of the jaws, where the motion is least and the purchase or lever- age greatest, so that they FIG. 1. are broken with the small- est possible expenditure of energy. The movement of the jaws is greatest at the discharge opening, thus affording a free and rapid discharge of the material crushed, and insuring a large capacity for the machine. The principal disadvantage is that the great variation in the discharge opening results in a considerable range in the size of the material delivered. This style of crusher has found a wide field for breaking down material TABLE or BLAKE CRUSHERS. 25 GO Approximate Prod- uct per Hour, Cubic Yards, to 2 Inches. Weight of Heaviest Piece. Total Weight. Extreme Dimensions. Proper Speed. Horsepower Required. Length. Breadth. Height. Inches. Lb. Lb. Ft. In. Ft. In. Ft. In. 8X1* 6X 2 10 X 4 10 X 7 15 X 9 15X10 20 X 6 20 X 10 12 X 30 15X30 Laboratory One Three Five Eight Nine Ten Ten 40 560 1,800 3,800 7,400 7,800 5,300 8,100 14,200 14,200 100 1,200 4,900 8,000 15,500 16,000 11,200 18,300 33,000 35,000 1 1 2 10 4 5 1 6 6 6 6 5 3 6 10 7 10 7 10 6 2 1 3 3 3 9 5 5 5 2 11 5 9 8 4 8 4 10 2 3 3 9 4 5 5 11 5 11 4 6 5 11 6 4 6 4 2;}0 L'.'.d LV>0 ]r!o j:>o ill) 1 4 6 8 - 15 15 15 20 30 30 Sixteen Twenty and preparing it for other crushers, or for breaking large quantities of any material where an approximate sizing is not essential. The Dodge crusher. Fig. 2, has a fixed jaw a and a movable jaw b, operated by a cam on the shaft g. The movable jaw is pivoted at the bottom, so that the minimum movement between the jaws is at the discharge opening. The Advantage of this is that the least movement occurs at the discharge opening, 420 ORE DRESSING AND PREPARATION OF COAL. and hence the product is of a fairly uniform size, so that the crusher maj be used as a rough sizing apparatus. The disadvantages are that the larg pieces of rock have to be crushed in the upper part of the space between the jaws, where the motion is greatest and the pur- chase or leverage least, thus re- quiring an excessive amount of power, especially when dealing with hard material. The move- ment of the jaw at the discharge opening is so much less than that above that there is danger of clogging or blocking the ma- chine, especially when working upon tough or sticky material. The capacity of the Dodge style of machine is less than that of the Blake. It is used largely as a secondary crusher, or for crushing comparatively small amounts of material where an approximately sized product is desired. THE DODGE CRUSHER. No. Size of Jaw Opening. Diameter of Pulleys. VidthofBelt Used. Horsepower Required. o. Tons per our, Nut Size. volutions per Minute. ight Complete. r*- E o> M o> Inches. Inches. Inches. 1 4X 6 20 4 2 to 4 itol 275 1,200 2 7X 9 24 5 4 to 8 Ito3 235 4,300 3 8X12 30 6 8 to 12 2 to 5 220 5,600 4 10X16 36 8 12 to 18 5 to 8 200 12,000 Roll -jaw crushers, Fig. 3, have a movable jaw that has a rocking or rolling motion, subjecting the material to a rolling and squeezing action instead of a direct squeeze. The advantages are that, owing to the peculiar motion of the movable jaw, the material is crushed with comparative ease, and that the product is approxi- mately sized. The disadvan- tages are that the discharge is so small that there is danger of blocking the machine, and the capacity is small when compared with the Blake crusher. The Sturtevant roll- jaw crusher and the Schranz rock breaker work on this prin- ciple. Gyratory Crushers. These crushers, Fig. 4, are all large capacity, continuous-action crushers, a is a ring or hopper against which the material is crushed by a conical head c, which fits on a shaft #, the bottom of which is placed in an eccentric bearing so that the amount of space between a and c varies as the head rotates. The material to be crushed is dumped into the receiv- ing hopper h, and the machine is thus automatically fed. FIG. 3. ROLLS. 421 The advantages of this style are that the large pieces of material are received at the top of the jaws, where the motion is least and the leverage or purchase greatest, thus reducing the work necessary in this heavy preliminary crushing. The relative move- ment between the crushing members is a maximum at the discharge opening, but the amount of this movement is so small that the product is approximately sized. The fact that the maximum movement is .at the point of discharge assures a free discharge. There is practically no shaking imparted to the building by gyratory crushers. Their capacity is very great, and with a large size, material may be dumped into the hopper h directly from the cars. For small capacity a gyratory crusher is more expensive than a jaw crusher. Frequently, where very great amounts of material are to be crushed, large gyra- tory crushers are used as secondary crush- ers after jaw crushers of the Blake pattern, the discharge from the jaw crushers ran- ging from 6" to 12" cubes, and that from the gyratory crushers from H" to 2i" cubes. (See table on page 422). ROLLS. Cracking Rolls. This is a general name applied to rolls having teeth, which are usually made separate and inserted. These rolls, Fig. 5, are employed for FIG. 4. breaking coal, phosphate rock, etc., the object being to break the material into angular pieces with the smallest possible production of very fine material. The principal field for cracking rolls is in the preparation of anthracite coal, and the exact style or design of the roll depends largely on the physical condition of the coal under treatment. In most cases, the rolls are constructed with an iron cylinder having steel teeth inserted, the size, spacing, and form of the teeth depending on the size and physical condition of the material to be broken. Cracking rolls vary from 12 to 48 in. in diameter and from 24 to 36 in. in face width. The teeth of the larger sizes are from 3 to 3i in. high, and of the smaller 1 in. or less. The average practice in the anthracite regions of Pennsylvania is to give the points of the teeth a speed of about 1,000 ft. per minute, FIG. 5. though the speed in different cases varies from 750 to 1,200 ft. per minute. One of the largest anthracite companies has a standard roll speed ot 97.5 R. P. M. for the main rolls and 124.5 R. P. M. for the pony rolls. The harder the coal, the faster the rolls can be run. If run slow and overcrowded, the rolls will make more culm than when driven at a proper speed. One advantage of comparatively fast driven rolls is that the higher speed has a tendency to free the rolls by throwing out, by centrifugal force, any material lodged between the 422 ORE DRESSING AND PREPARATION OF COAL. teeth. In one test it was found that less tine coal was produced at 800 ft. per minute, but that the rolls blocked at this speed and hence had to be driven 1,000ft. per minute. In one case a pair of main rolls 24 in. in diameter, 36 in. face, running g at 1,000 ft. per min- ute, handled 2,500 O tons of coal in 24 ^ hours. A pair of 19" X 24" main $ rolls run at 1,000 ft. o per minute handled w 300 tons mine run g in 10 hours. A well-known 5 maker of rolls for crushing bitumi- nous coal gives a H speed of 100 to 150 &, K. P. M., according to the output re- quired, for rolls 24 5 in. in diameter and 5 33 in. long. As a P-" rule, cracking rolls Q are never run up to S their full capacity, as is the case with crushing rolls. The form of the w teeth varies greatly, ft but, as a rule, the 3 larger rolls have straight pointed teeth of the spar- row-bill or s o m e o similar form, Fig. 6 jj a. The old curved, < or hawk-billed, teeth, Fig. 6 6, have g~ now gone almost # wholly out of use. g On small sized w rolls, rectangular ^ teeth with a height of equal to one side of g the square base are g frequently em- fc ployed, and these 8 may be cast in seg- M ments of manga- nese or chrome steel. Corrugated rolls have teeth or cor- rugations extend- ing their entire length. They were first introduced by Size Engine Recommended to Drive Breaker, Elevator, and Screen. S 1 i 3 ' 1 b a Granite, Ore. ~, Limestone. 551 I si 0) p^ Soft I s . Inches. .rtra m * . jo tftSuaT "S. 5s 8gSg383S 1 rHrHrH^rH^ g^ -auiBj^ oil J0 q;pIAV SSSSSS2E3S oj i i *j8ddojj S,o dox o; auiBij ^ rao^^oa uioj^j m^t^jj rHrHr-lr-t 'Xo^nj SUTATJ(J jo suoi^n[6A*8H . Dimensions of Driving Pulley. Inches. gj 1 ^^0000.^0000 i s ^MM^I o:* Suipjoooy '^UTH -ui f^ SuissBd '-qi; OOO'S jo suoj, ui 'jnoH J3d ^pBd^o 322232223 M ' Pounds. gllllSIISI "^sas^ss ^noqy 'pauiq -moo sSuiuado Sm ' suoisuamTa Inches. xxxxxxxxxx ^noqy 'suoisuaniT(i Inches. ^0(N^iOOOO^O(N XXXXXXXXXX azig go^co^o^oo ROLLS. 423 Mr. E. B. Coxe, at Drifton, Pa., but they have not come into general use owing to the fact that, while they break some coal fairly well, in most cases it has been found that a continuous edge causes too much disinte- gration along its length, while a point splits the coal into three or four pieces only, all the cracks radiating from the place where the point strikes, thus producing very much less culm. Another advantage possessed by the toothed rolls is that if anything hard passes through the corrugated roll and breaks out a piece of the corrugation, the entire roll is ruined, while, in the case of the toothed rolls, any one of the teeth may be replaced. Disintegrating rolls and pulverizers are sometimes used to reduce coking coal to the size of corn or rice before intro- ducing it into the ovens. One roll is driven at double the speed of the other, the slower roll acting as a feed-roll, and the other as a disintegrator. The slower roll is commonly driven at from 1.800 to 2,000 ft. per minute peripheral speed, and the faster roll at from 3,600 to 4,000 ft. per mi- nute. The teeth are always fine, rarely being over f in. high. In some cases, the inner roll is provided with a series of saw teeth from | in. to f in. high and having about f in. pitch, the individual teeth being set so as to form a slight spiral about the body of the roll. The other roll is provided with teeth having their greatest dimension in the direction of rotation, so that they tend to cross the teeth on the opposite roll. These teeth are also set so as to form a slight spiral, and thus prevent blocking. In other cases, the teeth on both rolls are set in the form of quite a steep spiral. Hammers. For the reduction of coal, crushers employing hammers have been used, Fig. 7. The crushing chamber is usually of a circular or barrel form, and the crushing is done by means of hammers pivoted about a central shaft. FIG. 6. These swing out by centrifugal force and strike blows upon the coal to be oken. When it is reduced sufficiently fine, it is discharged through bars brok or gratings at the lower portion of the machine. This style of machinery is usually employed in preparing coal for coke ovens, thus occupying the same field as the disintegrating rolls. A No. 3 pulverizer of this type will crush 50 to 75 tons per hour run of mine, down to i in., or it will crush 100 tons per hour of slack. Such a machine occupies about 8 sq. ft. of floor space and requires 25 to 30 H. P. to run it. Crushing Rolls. The prin- cipal representative of this type of machine is the ordi- nary Cornish roll having a fairly wide face and rather small diameter. The diam- eter of these rolls was kept down for a great many years on account of the fact that the chilled cast-iron shells could not be obtained in large sizes and were expen- sive and hard to handle. With the ad vent of the rolled- FIG. : steel shells, it became possible to employ larger diameters and higher speeds. Rolls of the Cornish type vary from 1" face and 9" diameter to 16" face and 42" diameter. The distinctive feature of the Cornish roll is a comparatively wide face compared with the diameter, and a rather slow peripheral speed. Many of the modern Cornish rolls are provided with rolled-steel shells, especially when employed for very fine crushing, owing to the fact that these shells are of a more uniform texture, work more evenly, can be worn much thinner before ' being discarded, and can be trued up with less difficulty than is the case when chilled iron is employed^ To guard against the bending of the roll 424 ORE DRESSING AND PREPARATION OF COAL. shaft or breaking of the machine in case any hard material (such as a pick or hammer) gets between the rolls, one roll is mounted in a movable bearing and kept in place by a compressed spring washer. This washer is composed of two plates between which are placed one or more steel springs. The plates are kept together by several small bolts, which are screwed up so as to compress the springs to a certain degree. Then the entire arrangement is employed as a washer on the rod that keeps the rolls together. Should the pressure exerted on the rolls exceed that already exerted in the spring, the plates would be brought nearer together and the roll allowed to move back and pass the hard substance, but at any pressure below this, the roll acts as if placed in a fixed bearing. Cracking, corrugated, and disintegrating rolls are usually provided with breaking pieces back of one of the rolls, so that in case any extra hard piece passes through the rolls, the breaking piece will give way, allowing the rolls to move back and thus prevent the bending of the shaft or breaking of the machine itself. Compressed spring washers have never come into general use in connection with this style of machinery. Amount Crushed. The amount of material that can pass between any pair of rolls is proportionate to the number of square feet of roll surface passing per minute; hence, the capacity may be increased by keeping the face width the same and in- creasing the speed, or the same capacity may be obtained by reducing the face and increasing the speed. According to Stutz (A. I. M. E. IX, page 464), if the distance between the contact points of the material with the rolls be t, Fig. 8, the dis- tance between the crushing face of the rolls w, the angle a, as shown in the figure, and R the radius of the roll, then p *~ w t w 2 vers. sin a ~~ 2(1 cos a)' According to Pernolet, the amount of material that may be crushed by a pair of rolls in a given time is equal to one-fourth or one-fifth of a band or layer whose length is the circumference of the roll multiplied by the number of revolutions; whose width is the length of the rolls, and whose thickness is equal to the space or distance between the rolls. Or, Q = , where d = diameter of rolls; = 3.14; n = number of revo- lutions in the given time: I = length, of rolls; iv = space between rolls: and = coefficient, to allow for the irregular feeding of the material and the space between the pieces. The Denver Engineering Works gives the following formulas for the capacity of crushing rolls: T = tons per hour; R = rev. per min.; S = mesh (inches). For 14" X IT' rolls. T = 7.725 RS. For 16" X 36" rolls, T = 11.775 RS. For 12" X 20" rolls, T = .327 R S. .Speeds. The pressure on the bearings necessary to crush ore depends directly on the face width, and hence if the capacity can be kept the same and the face width decreased, it is evident that there will be less pressure on the bearings and less loss in friction. The difficulty of keeping the bearings cool when crushing hard rock with the old Cornish rolls has led to the adoption of high-speed, narrow-faced rolls for certain classes of work. One objection to running the small diameter rolls fast is that the larger pieces of ore have a tendency to dance on the face of the rolls rather than to be crushed, while the bite is better when the speed is slower. The advantages of high-speed, narrow-faced rolls are: greater capacity for a given bearing pressure; less loss of power from friction; less dancing of the ore on the roll face, owing to the fact that the angle of approach between the surfaces of large rolls is more acute than with rolls of a small diameter. High-speed, large-diameter rolls will handle coarser material and hence make a greater range of reduction than small-diameter rolls. The disadvantage of high-speed rolls is that they tend to hammer and pulverize the ore, so that with very brittle minerals a high speed may be detrimental. In general, it may be stated that for crushing to any definite size with the lowest possible production of very fine material, rolls are the best form of ROLLS. 425 machinery on the market. For fine crushing of brittle material, quite slow speeds may give the best results. The accompanying table gives some facts in regard to the crushing-roll practice of several manufacturers, the data having been taken from their catalogues or other information furnished by them. CRUSHING ROLLS. Name. Size. Inches. Peripheral Speed in Ft. per Min. Spring Pres- sure in Lb. per In. of Face Width. Character of Rolls. Frazer & Chalmers... 24X8 36X16 600-1,500 4,000 for hard quartz. Cornish. Frazer & Chalmers... 44X5 56X8 2,200-2,300 Narrow face, high speed. Earle C.Bacon 1,000 Cornish. Sturtevant Mill Co. 16X3 27X5 3,000 Special cen- trifugal. E P A His Co 20X12 26X14 800 Cornish 30X14 36X14 E. P. Allis Co Colorado Iron Works 20X12 27X14 36X16 40X16 1,885 600 4,000 for hard rock. 4,800 for very hard rock. Narrow face, high speed. Cornish. Colorado Iron Works 36X6 42X6 54X8 2,100-2,800 Narrow face, high speed. Denver Engineering Works Co 16X10 to 350-100 3,500-4,500 Cornish. Gates Iron Works ... 42 X 16 9X4 26 X 15 36X15 470-850 2,266-3,333 Cornish. The Gates Iron Works has furnished the following formulas relating to crushing rolls, in which D = diameter of roll in inches; N = number of R. P. M.; S = maximum size of ore cube in inches fed to the rolls; S' = maximum size of cube for a given diameter of roll. It will be seen from the first of these formulas than N is an inverse function of S, which agrees with the results shown in the previous diagram. As a rule, it is best not to try to run rolls up to the maximum size that they will crush, but to feed smaller material to them. The Denver Engineering Works Company has furnished the diagram. Fig. 9, and formulas relating to rolls. This' diagram serves very well to illustrate the fact that small rolls do not grip or crush large pieces as well when running at comparatively high peripherial speeds as when running at slow speeds. In the case of the 10" X 16" roll, a difference of from V to \" cube size made a difference of 20 R. P. M. in order to obtain the 426 ORE DRESSING AND PREPARATION OF COAL. most effective crushing speed, and the difference between i" and " cube sizes made a difference almost as great. It will also be noticed that the larger diameters, as, for instance, the 42" roll, are not so greatly affected by this cause, owing to the fact that the effective or crushing angle between the rolls is much more acute than in the case of the smaller diameters. 'to/A . . . e of Ore Fed to ff FIG. 9. CRUSHING MILLS. Radial Roller Mills. In this type of mill, the crushing is performed on a ring or die by a series of heavy rolls pressing on it by gravity. In some cases, the rolls travel around on the die and in others the die travels in relation to the rolls. Fig. 10 represents one form of Chilian mill that is the leading type of this class. The peculiarity of the grinding action of the radial rolling mills is that it is not a pure crushing action, but a triturating or grinding action as well, owing to the fact that while the different portions of the face of the roll are all traveling at the same speed, the outer portions have to travel over a greater length of ring than the inner portions, so that there is only one line along which true crushing action occurs. Some manufacturers have made the crushing ring and the rollers both with coning faces, the vertices of both cones meeting at a common point. This has resulted in a true crushing action, but for some classes of work the triturating action is to be preferred, as, for instance, in the grinding of silver ores for the patio process of amalgamation. Centrifugal Roller Mills. In centrifugal roller mills, the crushing is accom- plished between rapidly moving rolls and the inside of a stationary die or ring. The Huntington mill, Fig. 11, is one of the principal representatives of this class of machinery. The rollers c are supported from bearings e and are carried rapidly around by means of the frame a and the shaft g. The ore is crushed against the ring cf. In order to prevent the accumulation CRUSHING MILLS. 427 of ore below the rollers, and to throw it out for crushing, scrapers / are pro- vided. The crushed ore discharges through screens, as shown in the illus- tration. There are many styles of this class of machinery having different numbers of rollers, varying from 1 up, and some machines have been intro- duced combining a portion of the action of radial and centrifugal machines, the faces of the die or ring being at an angle and the rollers being mounted in inclined bearings so that they tend to crowd out and down upon the ring. Centrifugal roller mills have found two espe- cial fields in concentration works, one for crushing clay or soft ores containing free gold, and the other for re- grinding middlings for fur- ther concentration. Rolls of this type are also extensively employed in grinding cement and phosphate rocks. Ball Mills. There are two types pf ball mills: (1) those in which the crushing is per- formed by balls traveling in a fixed path, and (2) those FIG. 10. in which the crushing is per- formed by a large mass of balls of various sizes rolling over one another. In the first type the balls travel in a fixed path, track, or race that may be either vertical or horizontal. Where it is vertical, the balls must be driven at such a rapid rate that their centrifugal force will keep them in contact with the crushing ring or track. This form may be likened to a bicycle ball bearing on a large scale, the crushing being accomplished between the balls and the race or track. The serious objec- tion to this class of ball mills is found in the uneven wear of both the balls and the race, so that the work soon becomes unevenly distributed, and also in the fact that the balls cannot be used after they have been worn to a slight extent. In the second class of machines the balls are introduced into a large barrel or chamber, where they roll over one another, the ore being crushed between the different balls and between the balls and the lin- ing of the chamber. In this style of machine the crushed material may be discharged through openings in the per- iphery or through openings in one end of the barrel. One great advantage with this style of mill is that the balls can be entirely worn out and it is only necessary to charge a sufficient number of new balls with the ore each day to make up for the wear of those in the mill. FIG. 11. STAMPS. Gravity stamps are especially well suited for material the valuable portion of which does t, as well as to operate, gives them a decided advantage over other crushers. Fig. 12 illustrates a 10-stamp battery of the gravity type. 428 ORE DRESSING AND PREPARATION OF COAL. Fig. 13 is a detail of the mortar stamp heads and dies. The mortar a is placed on a suitable foundation of timbers b and the ore crushed on dies d by the stamps s, which are secured by means of tapered joints to the heads or bosses h. The stems e are attached to the heads h and the whole lifted by the cams (shown in detail in Fig. 12). The cams operate under tappets on the stems, as shown in Fig. 12. As the cam operates under the edge of the tappet, it not only lifts the stamp, but gives a partial rotation, thus equalizing the wear on both the stamp and die. The ore is fed in at the back of the mortar and the crushed material discharged through the screen, as shown in Figs. 12 and 13. Usually a single screen at the front is employed, but sometimes two or more upon different sides of the mortar may be introduced. For treating free-milling gold ores in which the gold occurs in rather large grains free from iron pyrites, the California style of battery was developed, the charac- teristics of which are a small drop (4 in. to 6 in.), low discharge (4 in.), a heavy stamp (750 to 1,000 lb.), and a high speed or number of drops per min- ute (90 to 105). The advantage of this style is rapid crushing, but the majority of the gold had to be saved on apron plates outside the mortar. For working ores that contain large quantities of iron pyrites with the gold values occurring in the cleavage planes of the pyrites, the Gilpin County, Colo., style of battery was developed. This is characterized by a high drop (18 to 20 in.), a high discharge (14 in.), a light stamp (550 to 600 lb.), and a comparatively slow rate of drop (30 per minute). With this style of battery, most of the gold was obtained on amalgamated plates in the battery, but its use was accompanied by excessive sliming on FIG. 12. FIG. 13. account of the fact that the high discharge kept the material in the mortar for a long time, and subjected it to repeated treatment. Modern practice tends toward the use of rather heavy stamps (about 1,000 lb.), quick drop (90 to 105 per minute), and low discharge (4 to 6 in.). The advantages are that the capacity of the battery is very great and the sliming reduced to a minimum. If the ore contains sulphides carrying gold, they are separated by concentration upon vanners or bumping tables, and subsequently treated by chlorination or smelting. If the apron plates do not catch the major portion of the values, the tailings may be treated by the cyanide process. This last method is that employed at many large gold mines, especially those of the Transvaal in South Africa. Order of Drop. There is much diversity of practice in this respect. It is desirable to drop the stamps in such rotation as to insure an even distribu- tion of the pulp on the several dies. Adjacent stamps should not drop con- secutively, as this occasions accumulation of the pulp at one end of the mortar, in consequence of which the efficiency of the stamps at that end is reduced by having a decreased height of drop and a cushion that retards the pulverization of the ore. The stamps at the other end of the mortar have too little work, and are liable to " pound iron." The order of drop 1, 4, 2, 5, 3 STAMPS. 429 seems to best fulfil the requirements. It gives a good splash and satisfac- tory results in other respects. The order 1, 5, 2, 4, 3 is also extensively adopted. There are several other orders of drops in use, but the two just mentioned are generally preferred. In large mills, the standard drop is given as 1, 7, 3, 9, 5, 2, 8, 4, 10, 6, with 1, 8, 4, 10, 2, 7, 5, 9, 3, 6 as a close favorite; while 1, 5, 9, 7, 3, 2, 6, 10, 8, 4 and 1, 5, 9, 3, 7, 10, 6, 2, 8, 4 are used. Speed of Stamps. Heavy stamps and stamps having high drops should have correspondingly low speed. With 900- to 950-lb. stamps, having 6" to 1" drop, the speed should be from 85 to 95 drops per minute. With double- armed cams, the speed must not be great enough to bring the cam into collision with the falling tappet, i. e., the interval between the revolutions of the cam must be sufficient to give the tappet time to finish its drop. When the cam strikes the descending tappet, a shoe, boss, or tappet is often dislodged, and breakage is imminent. A fast drop produces a good splash, which is very desirable for battery amalgamation. Shoes and Dies. Shoes and dies are either of iron or steel. In most mills, remote from foundries where transportation is an important item in the cost of shoes and dies, steel shoes and dies have replaced those of iron. Chrome steel shoes and dies have been introduced and have proved superior. In some mills, steel shoes and iron dies are used. The iron dies wear more evenly with steel shoes than the steel dies do. The life is about 2 to 3 times that of iron shoes and dies, and the cost about twice as great as those of iron. The mixture of steel (from the old chrome steel shoes and dies) with iron produces shoes and dies that wear considerably longer than those of pure iron, and may be advantageously introduced where there is no other dispo- sition possible for the old steel,' because of want of local facilities for the utilization of this residue. In many districts, the old iron shoes and dies are sold to local foundries for from H to 2 cents per Ib. The weights of the shoes bear a certain relation to the weights of the tappets, stems, and bosses. Chrome steel shoes made for stamps of 850 to 950 Ib., weigh from 150 to 155 Ib., and measure about 9 in. in diameter by 7i to 8 in. long. The neck is from 4| to 5 in. long, with a taper to correspond to the socket of the boss or stamp head. Iron shoes are usually from 15 to 20 Ib. lighter than the above weights. The chrome steel dies weigh from 110 to 125 Ib., and measure (where shoes of the above dimensions are used) 9 in. in diameter by 4 to 4 in. in height, with a rectangular foot-plate 10i in. by 9^ in. by i in. thick. Iron shoes usually weigh from 20 to 25 Ib. less than the above weights for steel. Life of the Shoes and Dies. There are many conditions that affect the durability of shoes and dies, as, for instance, the hardness of the rock, the weight, speed, and height of drop of the stamp, the manner of feeding the ore, etc. Iron shoes of good quality last from 30 to 47 days. Old shoes wear usually down to H in. or 1 in. in thickness, and weigh about 25 or 40 Ib. Old dies usually wear down to about li in. in thickness, and weigh from 20 to 50 Ib. The consumption of iron or steel in shoes and dies depends on the character of the ore crushed. Other conditions being the same, it will depend on the coarseness of the stamping and the height of discharge. Dies wear less rapidly than the shoes, as they are protected by the thickness and the pulp, which covers them to the depth of from H to 3 in. But while the actual wear of dies is less than that of the shoes, the life of the dies is shorter than that of the shoes, owing to the fact that the shoes have several inches greater length of wearing part than the dies. The con- sumption of iron for shoes and dies per ton of ore crushed is, in California, from li to 3 Ib. To obtain the maximum crushing capacity of the battery, the dies must be kept as high (with reference to the lower edge of the screens) as is compatible with the safety of the screens and with successful amalgamation in the battery. To prevent the pounding of iron, it is necessary to preserve more or less uniformity in the level of the dies. Should one die in the battery project much above the others, little or no pulp would remain upon it. and the shoe would consequently drop upon the naked die. Cams, Stamp Heads, and Stems. Cams and stamp heads ought to last several years. They are usually broken through carelessness. The stems break at the socket of the stamp head. Stems are reversible; when broken, they may be swedged or planed down and additional lengths welded on when necessary. Tappets. When there is much grease on the tappet or cam or when the 430 ORE DRESSING AND PREPARATION OF COAL. tappets have so worn that the face of the cam strikes a grooved instead of a level face on a tappet, the rotary motion is greatly impaired. Tappets last for several years, from 4 to 5 years being their usual life. Sometimes they are broken by being too tightly keyed. When their faces are worn, they are planed down. They are reversible, so that when one face has been worn as far as possible, the other face is placed downwards. They are usually of steel, and weigh about 112 Ib. when 900-lb. stamps are used. Battery Water. The amount of water fed to the battery depends on the character of the ore and the size of the screen. Clayey arid highly sulphu- reted ores require the maximum amount of water. The amount of water used per ton of ore stamped varies from 1,000 to 2,400 gallons. The mean amount used per ton of ore stamped is about 1,800 gallons. From I to H miner's inches per battery should be provided. Tn winter, when the battery water is chilly, it should, when possible, be heated to tepidity, as this pro- motes amalgamation. A high temperature should be avoided, as it renders the quicksilver too lively. Duty of Stamps. The capacity of gravity stamps varies from a little over 1 ton per stamp for 24 hours to as high as 4 tons per stamp for 24 hours, depending on the quality of the ore. Usually, an average of from 1.7 to 2 tons per stamp for 24 hours in a combination mill would be good practice, while where the ore is crushed to a rather coarse screen and the tailings treated with the cyanide process, a larger capacity is usually obtained. The number of tons of ore crushed per stamp depends chiefly on the weight of the stamp, the number of drops per minute, the height of drop, the height of discharge, the size of the screens, the width of the mortar, and chiefly on the character of the ore. Hard ores and ores of a clayey nature (from the difficulty experienced in discharging the clayey pulp) decrease the duty of the stamps. About 2i tons per stamp in 24 hours is the average duty of the stamp in California. The discharging capacity of a mortar depends on the height and size of the discharge opening, the character of the screen, and the width of the mortar discharge, as will be illustrated from two well-known mills. The Homestake Mill uses an 850-lb. stamp dropped 9 in., 85 times per minute, developing 78,030.000 ft.-lb. in 24 hours, and crushing 4 tons of rock, or 1 ton for every 17,340,000 ft.-lb. developed. The Caledonia Mill uses an 850-lb. stamp, dropping 12 in., 74 times per minute, crushing 3.3 tons, of rock and developing 90,576,000 ft.-lb. in 24 hours, or 1 ton to every 24,447,272 ft.-lb. developed. Although developing more foot-pounds in 24 hours, and therefore seemingly more efficient, yet it crushes less rock than the former. The reasons for this are (1) that the rock is harder than that of the Homestake; (2) the width of mortar is 16 in. against 13! in.; and (3) the 2" recess for the 8" copper plate below the feed. On the other hand, the Caledonia has a lower discharge from the mortar, using 6 in. against 10 in. in the Homestake; but this advantage is again neutralized by a smaller screen, the Caledonia using 258 sq. in. against 376 sq. in. of the Homestake. Horsepower of Stamps. The H. P. of a stamp battery = No. of stamps Xwgt. of each stamp X No. of drops per min.x drop of each in in. 12 X 33,000 The weight of each stamp is equal to the sum of the weights of the stem, tappet, stamp head, and shoe. To the nominal H. P. add 25$ for friction of machinery in calculating driving H. P. Cost of Stamping. The cost of stamping varies from a little over $1.00 per ton up. The Montana Co., Limited, operating a 60-stamp combination mill, in 1888 treated 40,530 tons of ore at $1.13 per ton. In Australia, stamp- mill costs have been reported varying from $1.30 to $2.50 per ton where fairly favorable conditions for working could be obtained. Figures from other districts compare favorably with these, but it would be impossible to give any absolute rule by means of which the cost can be determined in advance, without an intimate knowledge of the character of the ore and the local conditions. Pneumatic Stamps. This is a name given to a form of large capacity power stamp, the head of which is connected to a piston in an air cylinder. The cylinder is raised and lowered by power, the air forming an elastic connection by means of which the stamp is operated. They are quite extensively employed in crushing tin ore, but have never come into general use for other purposes. The capacity is as high as 30 tons per 24 hours. SIZING AND CLASSIFYING APPARATUS. 431 Power Stamps. Various forms of stamps have been brought out at differ- ent times, intended to operate by power like a trip hammer, or in which the stamps were connected directly to the cranks operating them by means of spring joints. Nearly all of these forms have failed on account of exces- sive wear, small capacity, and the large amount of power consumed. Steam Stamps. The large capacity steam stamp, which was evolved in connection with the concentration of the Lake Superior copper ores, con- sists of a steam cylinder in which operates a piston, to the stem of which the stamp head is directly connected. Machines of this style are usually made very large and heavy, frequently extending through two or three stories of the mill, and having a capacity equivalent to from 60 to 100 ordi- nary gravity stamps. In most forms, live steam is admitted on top of the piston during the descent of the stamp, thus increasing the force of the blow. For lifting the stamp, the steam is throttled so that a lower pressure is employed. The discharge is usually through a coarse screen, f" to f" mesh not being uncommon. One interesting fact connected with the large steam stamps is that their heavy blows do not cause as excessive sliming as the lighter gravity stamps, and on this account this form of stamp has been introduced in some cases for crushing free-milling gold ores. For prospecting work, for testing properties, or for operating small prop- erties, a number of forms of portable or semiportable steam stamps have come out during the last few years. One of these (the Tremain) is illus- trated in Fig. 14. In this form, two pistons work in cylin- ders side by side and strike alternate blows in a common mortar. The steam is introduced at full boiler pressure on the lower side of the cylinder, which, owing to the large diameter of the piston rod, has a small area. This high pres- sure steam is then allowed to expand on to the top of the piston, thus urging it down with greater force than its own weight would. These steam stamps can be v run at a much higher speed than gravity stamps, and hence have a greater capacity. In the figure shown, three screens are employed, one in front and one at each end of the mortar. There are several other forms of portable steam stamps manufactured. They all have the advantage that for a small property they can be installed with much less trouble than any other form of crusher, owing to the fact that no steam engine is required and the steam necessary to drive them can usually be obtained from the boiler operating the hoisting engine, pumps, etc. Miscellaneous Forms of Crushers. Most crushers can be classed under one of the previous heads, but there are S9me forms that depend on the material itself to do the crushing. For instance, in the preparation of coal for coke ovens, there has been a combined crusher and separator invented that may be described as follows: A large horizontal drum or cylinder, provided with screen openings around its periphery, is mounted in a horizontal position. The coal to be separated is fed into one end and is caught by shelves or plates projecting radially into the cylinder. These lift the material to the upper side, from which it falls by gravity and strikes the bottom, thus crushing the softer parts. The sulphur and slate, being harder than the coal, are not crushed by the same height of fall, and hence, by a proper adjustment of the diameter of the cylinder, the coal may be crushed and discharged through the screen while the slate and sulphur will pass out at the opposite end of the cylinder. FIG. 14. SIZING AND CLASSIFYING APPARATUS. Stationary Screens, Grizzlies, Head-Bars, or Platform Bars. These are the various names given to an inclined screen employed for removing the fine material from the run of mine so that only the coarse portion will be passed to the crushers. At concentrating works, the term grizzly is usually employed, and a common form is shown in Fig. 15. This is composed of flat bars held apart by cast-iron washers through which the bar bolts are passed to hold the entire frame together. Grizzlies are usually placed at an angle of from 45 to 55, and ordinarily, for the head of a large concentrating works, they are from 3 to 6 ft. wide and from 8 to 12 ft. long, the amount of space between the bars depending on the size of the run-of-mine material and on its subsequent treatment. 432 ORE DRESSING AND PREPARATION OF COAL. FIG. 15. , , coal passing through %" screen. If a pea-coal screen is used, all coal passing over $", ", and f" would be pea coal, and that passin would be slack. In the anthracite coal breakers, the terms platform bars or head-bars are usually employed, and these bars are made of li" to 2" round iron placed at an inclination of 5 in. to 1 ft., the spacing depending on the size of coal it is desired to make in the breaker. At the present time, in accordance with an agreement between the oper- ators and the miners' officials, the standard size for a bituminous lump screen (the bars are called a screen) for Ohio, Pennsylvania, Indiana, and Illinois is 12 ft. long and 6 ft. wide over the screen surface. The screen consists of 6 bearing bars 4 in. by | in. of soft steel and 39 steel screen bars, Fig. 16, with li in. clear space between bars. In Iowa, the same sized bar is used, but the space be- tween the bars is If in. In the other Western and Southern States there is at present no standard. The standard nut-coal screen for Pennsyl- vania and Ohio is in. space, but in. is sometimes used and the nut screen is often varied to suit the special trade. At present very few pea screens are used, but if placed under a |" nut screen, the space is from | in. to f in. In the Pittsburg region of Pennsylvania, all coal passing over f" screen is called slack, while, on the Monongahela River, coal passing through l" screen is called slack and is used in stokers. Many companies are at present crushing their run-of-mine coal to make slack suitable for stokers. It is difficult to classify bituminous coal by sizes, but as nearly as possible the following seem to be the standard: Lump, all coal passing over l" screen; nut, all coal passing through l" openings and over \" openings; slack, all screen is used, all coal passing at passing through |", ", or f" Adjustable Bars. The top of the bar is cylindrical and projects beyond the web which supports it, so that any lump which passes through the upper part will fall freely without jamming. The two ends of the bar are V shaped and fit into similarly shaped grooves, so that the bars can be set at distances from each other varying with the sum of the width of the bases of the triangles, the usual opening being about 4 in. These bars are generally 4 ft. long, but they can be of any size. Finger bars are screen bars that are fixed at one end only, and the bars are narrower at the lower end than at the top, so that the spaces between them are wider at the bottom than at the top, thus giving less tendency for pieces of material to become wedged between the bars. Movable or oscillating bars are screen bars that are attached to eccentrics at their lower ends, the eccentrics of adjoining bars being placed 180 apart. This movement throws the material for- wards and the bars do not therefore require nearly the same inclination as fixed bars. Shaking screens have an advantage in that the entire area of the screen is available for sizing, and hence a greater capacity can be obtained from a given area of screening surface. They also occupy less vertical height than a revolv- ing screen. In coal breakers they are particularly applicable where the coal is wet and has a tendency to stick together. The principal disadvantage of the shaking screen is that the reciprocating motion imparts a vibration to the framing of the building. For anthracite coal, the screens usually have an angle or pitch of from in. to 2 in. per foot, the average being about in. per foot. These screens are run at from 90 to 280 shakes per minute, the average being about 200 shakes per minute, or 100 revolutions per minute for the cam-shaft. The throw of the eccentric or cam varies from 2 in. to 5 in. Similar screens are employed for sizing salt, but are usually placed at a much steeper incline and are frequently so hung that they have a combined rocking and swinging motion. Shaking screens are rarely employed in concentrating works on account of the fact that revolving screens can be hung in the upper part of the mill where they will not interfere with FIG. 16. SCREENS. 433 other machinery, and hence the greater space that they occupy is not objectionable while they do the sizing satisfactorily without imparting jar to the structure. The capacities of shaking screens operating on anthracite coal have been given as follows. The parties giving these figures advise the use of 140 R. P. M. for the cam-shaft. For broken and egg coal, i sq. ft. per ton for 10 hours. For stove and chestnut coal, i sq. ft. per ton for 10 hours. For pea and buckwheat coal, $ sq. ft. for 10 hours. For birdseye and rice, li sq. ft. per ton for 10 hours. For sizing bituminous coal, inclined shaking screens are extensively used in certain sections, particularly in the Middle Western States. These screens are given a shaking motion by means of cams and connecting-rods, which make from 60 to 100 strokes per minute, the speed varying acc9rding to the amount of moisture in the coal. The throw of the eccentric is about 6 in. These screens are 7 ft. wide and vary in length according to the conditions in the tipple, no standard having been adopted. The average inclination at which they are set is 14, though this angle varies under different conditions from 12 to 15. The capacity of these screens running under the conditions given above is given by one maker as 2,000 to 2,500 tons per day of 8 hours. In one test lasting 8 hours, 2,000 tons of coal were passed over screens having perforated plates of the following dimensions: 56 sq. ft. with " perforations for making slack. 56 sq. ft. with 1 j" perforations for making pea coal. 28 sq. ft. with 2" perforations for making nut coal. 28 sq. ft. with 4i" perforations for making egg coal. Another maker uses, for taking pea and dust from nut, and nut from lump, 50 to 60 sq. ft. of Surface for each size, and to handle 600 to 800 tons in 8 hours he uses a 4i" travel and 120 to 130 shakes per minute, with the screen at an inclination of 15. Size of Mesh. The following perforations have been adopted by two of the largest anthracite coal companies as the dimensions for the holes in shaking screens to produce sizes equivalent to those produced by revolving screens: MESH FOR SHAKING SCREENS. Kind of Coal. Lehigh Valley Coal Co. Phila. & Reading Coal & Iron Co. Kind of Coal. Round. Round. Square. Steamboat Lump 4*" 3|" w I $ 3i" 2- ff li" 1 5" 4" 2j" 2" | 1" i" Steamboat. Large broken. Small broken. Egg. Stove. Chestnut. Pea. Buckwheat. Rice. Broken Egg Stove Chestnut Pea Buckwheat Rice Revolving Screens, or Trommels. The screen is placed about the periphery of a cylinder or frustum of a cone. The material to be sized is introduced at one end; the small size passes through the screen, and the other size is discharged from the other end. If the form is cylindrical, it is necessary to place the supporting shaft on an incline so that the material will advance toward the discharge end. The inclination of the shaft deter- mines the rapidity with which the material will be carried through the screen. The advantage of the conical screen is that the shaft is horizontal and hence the bearings are simpler. This a very decided advantage in many mills where the machinery must of necessity be crowded into a minimum space and be hard to get at. Pentag9nal screens, or screens having some other number of flat sides, are sometimes employed. These are run at a very much more rapid rate than circular screens, it being intended that the material shall be thrown or dashed against the screen surfaces to break it or to loosen adhering clay 434 ORE DRESSING AND PREPARA TION OF COAL. or dirt. The shaft is sometimes hollow, and streams of water from this hollow shaft wash the material as it is being screened. Revolving screens are frequently jacketed, that is, two or more screens are placed concentrically about the same shaft, the inmost one being the coarsest, and each succeeding screen serving to make additional separations. This method reduces the space necessary for a given amount of sizing machinery. In other cases, a long cylindrical screen has a coarse mesh near its discharge end and finer mesh near the entrance end, thus making two or more through products as well as the overproduct. The disadvantage of jacketed screens is that the necessarily slow speed of the inmost screen reduces the capacity of the entire combination, so that if rapid work is essential, it is better to use fairly large-diameter screens placed one after the other in place of jacketed screens. Another disadvantage is that, to renew the inner jackets, it is often necessary to remove the outer ones. The disadvantages of having two or more sizes of wire cloth on one screen are that the fine-meshed screen near the head is worn out rapidly, as all the material both coarse and fine passes over it, while, when separate screens are employed, each screen has to deal only with its through or over sized product, all coarser material having been removed. Speed. The periphery of a revolving screen should travel about 200 ft. per minute. In the case of very fine material, screens are sometimes run faster than this. The following have been adopted as standard speeds for screens by one of the largest anthracite coal companies: SPEED OF SCREENS. Rev. per Minute. Rev. per Minute. Mud screens 8.87 Big screens 8.52 Counter mud screens .15.49 Pony screens 10.87 Cast-iron screens 11.25 Buckwheat screens 15.30 Duty of Anthracite Screens. The following table gives the number of square feet of screen surface required for a given duty in the case of revolving screens working upon anthracite coal: Egg coal, 1 ton per 1 sq. ft. per 10 hours. Stove coal. 1 ton per H sq. ft. per 10 hours. Chestnut coal, 1 ton per H sq. ft. per 10 hours. Pea coal, 1 ton per 2 sq. ft. per 10 hours. Buckwheat coal, 1 ton per 2J sq. ft. per 10 hours. Rice coal, 1 ton per 3| sq. ft. per 10 hours. Culm, 1 ton per 5 sq. ft. per 10 hours. These figures may be reduced from 20$ to 30# for very dry or wash coal. Revolving Screen Mesh for Anthracite. A standard mesh for revolving screens for sizing anthracite coal was adopted some years ago, but it is only approximately adhered to and a considerable variation from the standard is found throughout the anthracite region. The following are probably as nearly standard meshes for revolving screens for sizing anthracite coal as can be given: MESH FOR SIZING COAL. Culm passes through &" mesh. Birdseye passes over " mesh, and through VV' mesh. Buckwheat passes over |" mesh, and through " mesh. Pea passes over i" mesh, and through |" mesh. Chestnut passes over 3" mesh, and through If" mesh. Stove passes over If" mesh, and through 1" mesh. Egg passes over 2" mesh, and through 2" mesh. * Grate passes over 2" mesh, and out end of screen. * Special grate passes over 3" mesh, and out end of screen. * Special steamboat passes over 3" bars, and through 6" bars. Hydraulic Classifiers. The separation of materials by this class of machinery depends upon the law of equally falling bodies, which may be stated as follows: Bodies falling free in a fluid, fall at a speed proportional to their weight divided by the resistance. From this it will be seen that small masses of a heavy mineral will fall as rapidly as large masses of a light mineral, owing to the fact that the weight increases as the volume and the * These sizes and "lump" size are seldom made, and there is no uniformity whatever in the sizes called by these names. HYDRA ULIC CLASSIFIERS. 435 resistance only as the area, so that if a quantity of galena and quartz of various sizes were introduced into water, it would settle into approximate layers, each composed of relatively large pieces of quartz and relatively small pieces of galena. This same action would be true in the case of any FIG. 17. minerals differing in specific gravity. The principal representatives of the hydraulic classifying machines are the Spitzkasten and Spitzlutten. The Spitzkasten consists of a series of pyramidal boxes, one of which is shown in Fig. 17. The material enters the box at a, passes down under the diving board b, and discharges into the next box through the trough c. At the bottom of the box, water is introduced through the pipe d from the launder g in such quantity as to more than supply the opening or spigot e. The heavy particles of mineral settle against this rising stream of water into the elbow/, from which they are washed out through e. Each succeeding box is made larger than the preceding, and the rising current is so regulated that a different product will settle out in each. The Spitzlutten is a V-shaped box, inside of which is set another V having the same slope, the material flowing down between the two V's on one side and up and out on the other. The distance between the V's can be regulated, as can also the rising current of water, thus obtaining the separation desired. Many other forms of separators, all depending on this same principle, have been brought out, some having a conical form, some being arranged in the form of troughs, and others as boxes of various shapes. The Calumet classifier, Fig. 18, consists of a series of boxes or pockets in the bottom of a gradually widening trough. Wash water enters - .,,,,, i ,,. -.^\ , - through a pipe a and discharges directly against the discharge spigot d, which is however not large enough to carry all the water off directly, hence it twirls and eddies in the bottom of the box so that only the heaviest particles having weight enough to settle in this disturbed water a pass out through the spigot. A shield c reflects upward currents and confines the agitation to the bottom. The pulp flowing in boards s. The settling boxes employed for mills are really a form of hydraulic classi- fier. They are usually very large V-shaped boxes provided with a diving board similar to that shown at b in Fig. 17, but no current of water is 436 ORE DRESSING AND PREPARATION OF COAL. introduced. In some cases a small stream of the heavy muds or concen- trates is kept continually flowing from the bottom, while in others they are drawn off intermittently. One very important point to be observed in settling boxes is that the settling action depends on the arresting of the current, and with a given amount of floor space, very much more efficient settling can be obtained from two boxes placed side by side and having half the material pass through each than from two boxes placed in series, and that the width of the box is of vastly more importance than the length. The depth is also fairly important, and a diving board must always.be introduced to prevent surface currents. If the boxes are properly arranged, nearly all the solid material will be settled out of the water. The Jeffrey-Robinson coal washer, Fig. 19, which operates on the principle of the Spitzkasten, consists of a steel chamber B in the form of an inverted cone, inside of which are projecting arms and stir- ring plates C, C revolved by a driving gear A. The water supply enters at the bottom from the water pipe P through perforations M. The coal is introduced through a chute S and is kept in a continual state of agita- tion by the current of water, and being lighter than the impurities, it passes out through the overflow K onto the con- veyors E, F and through the chutes X, X, while the water and sludge drain through the hop- per into the sludge tank G, whence, if necessary, the same water can be again pumped by the pul- FIG. 19. soineter H back into the washer. (As mentioned elsewhere, it is poor practice to use this water over again when it is desired to decrease the percentage of sulphur in the washed product as greatly as possible. ) The heavy impurities sink to the bottom into the chamber J and when this is full the upper of the two valves shown is closed and the lower valve is opened to discharge the refuse. The following data in regard to one of these washers is given by Mr. J. J. Ormsbee in the Transactions of the A. I. M. E. These results were obtained at the Pratt Mines, Alabama, with a plant having a nominal capacity of 400 tons per day. By washing slack that passed between screen bars spaced f in. in the cleat, the washed coal contained 42$ less ash than the unwashed coal, the reduction in sulphur was 15$, while the volatile matter was increased 4$, and the fixed carbon 5$. With coal passing over f " perforations, the results were a reduction of 48$ in ash, 15$ in sulphur, and a gain of 5$ in volatile matter and 6$ fixed carbon. These results indicate that the washer is better adapted to large sizes than to fines. The amount of water used per ton of washed coal was 35.1 gallons and the cost was 2.25 cents per ton for washing 400 tons, itemized as follows: Labor at washer, $2.00; labor at boiler, fuel, etc., $4.00; repairs and supplies, $3.00; total, $9.00. Log Washer. For removing clay from ores or other material, the log washer illustrated in Fig. 20 has proved itself to be efficient. Either single or double logs are employed, the form shown being the double- log washer. The logs work over troughs which have a slight inclination, so that the water will flow from one end to the other. Water is introduced at the upper end and discharged at the lower end. The material to be washed is introduced near the lower end and is fed up against the water by spiral arms or plates fixed about the logs, as shown in the illustration. As the material is advanced, the clay or other sticky substance is broken up, washed away, and discharged at the lower end with the wash water. LOG AND TROUGH WASHERS. 437 FIG. 20. These washers have been extensively employed for cleaning iron ores occurring as rather hard masses in clay. There is no general standard size of these washers, but most of the double- log washers for both steel and wood logs are the same, except in length of logs, the washer box being 7 ft. 4 in. wide, 2 ft. deep at discharge end, and 4 ft. deep at receiving end. The length of logs varies from 20 to 30 ft. The logs are generally given an elevation of 1 in. in 1 ft., and sometimes H in. in 1 ft. The capacity of an ore washer depends very much on the quality of the material, avera- ging for one pair of logs from 100 tons per day, when the matrix is of a clayey nature, to 350 tons with loose sandy material. The capacity of a washer is based on the amount of material from the mines it will put through more than^the tonnage of clean ore, and this amount varies from 500 to 1,000 yd. per 10 hours. The amount of water used varies from 300 to 500 gal. per minute. The total expense for labor and fuel, including the water supply, varies from 5 cents to 25 cents per ton of ore, averaging possibly 10 cents per ton. The Scaife trough washer consists of a semicircular iron trough 2 ft. in diameter and 24 ft. long. Inside is a series of fixed dams or partitions that can be made higher or lower, as required, by means of plates. A shaft running the entire length of the trough and turning in babbitted journals carries a number of stirring arms or forks and is given a reciprocating motion by a connecting-rod attached to a driving pulley at its center. The co#l is fed with water at the upper end of the trough, and by the action of the flowing water and the agitation of the arms, the slate, pyrites, and other impurities settle at the bottom and are caught behind the dams, while the clean coal passes over the dams and out at the lower end of the trough. When the spaces behind the dams are filled, feeding is stopped and the refuse in the dams quickly dumped. This form of washer is particularly successful with coal mixed with fireclay. One washer handles from 75 to 100 tons of coal per day, and one man can attend to six washers. Each washer requires less than 1 H. P. to operate it. The larger the coal, the greater must be the slope and the quantity of water used. Jigs. This is a general term applied to that class of concentrating machines in which the separation of the mineral from the gangue takes place on a screen or bed of material and is effected by pulsating up-and- down currents of a fluid medium. There are a number of different methods in use for driving the pistons that cause the pulsations of the water in jigs. Some of these use plain eccentrics, giving the same time to both the up and the down strokes of the pistons, while others employ special arrangements of parts, which give a quick down stroke and a slow up stroke, thus allowing the water ample time to work its way back through the bed without any sucking action from the piston. This tends to make a better separation in some cases than the use of the plain eccentrics. Stationary Screen Jigs. This class is illustrated by Fig. 21, which shows a 3-compartment jig. The separation takes place on screens supported on wooden frames g, and is effected by moving the water in each compartment % so that it ascends through the screen, lifting the mineral and allowing it to settle again, thus giving the material an opportunity to arrange itself accord- ing to the law of equally falling particles. Each compartment is composed of two separate parts, one containing the screen on the support g and the other adjoining it and arranged so that the piston in it may impart the necessary pulsations to the water. These pistons are usually loose fitting and are operated by the eccentrics e on the shaft s. Jigs operating on coarse ore should be fed with approximately sized material, when the ore will accumu- late near the bottom on the screen arid the barren portion or gangue will 438 ORE DRESSING AND PREPARATION OF COAL. be carried over the discharge. Formerly, the concentrates were discharged trom jigs intermittently by digging out the tailings first, then the middlings, which are composed of pieces containing some ore and some gangue, and then the concentrates, but it has been found that the concentrates will flow over the screen like a liquid of comparatively heavy specific gravity, FIG. 21. Advantage has been taken of this fact in the design of several forms of jig discharges. The Heberle gate, Fig. 22, acts as follows: a is a U-shaped shield fastened against the inside of the jig and held in place by a band b, the ends of which are drawn down into the form of bolts and pass through the sides of the jig, where they are secured with suitable nuts. The shield a may be raised or lowered by loosening the band b. The discharge takes place through the open- ing / in the side of the jig, the size and position of the opening being regulated by slides c. The concentrates k rest on the screen e supported by a grating d, while the tailings i occupy a higher posi- tion. The shield a prevents the tailings from flowing out through the opening /, while the concentrates flow along the screen and rise to a height somewhat lower than the top of the tailings in the jig, when they are discharged through the opening / over the spout A, as shown at p. The tailings are usually discharged over the dam at the end of the jig, and in some cases a third discharge is provided of the Heberle-gate pattern and so arranged that the middlings will flow out through it and discharge separately from the tailings and the concentrates. In the case of jigs handling fine material, the material may be sorted by hydraulic classifiers and then introduced on to the jigs. In this class the mineral will be in the form of relatively small pieces, while the gangue will occur as relatively large pieces. Advantage may be taken of this fact by regulating the mesh of the jig screen so that the concentrates will pass through into the space below the screen, commonly called the hutch, while the tailings will pass over the tailing dam. In some cases the gate discharge is employed on the side to remove the middlings. The middlings are recrushed and treated on other machines. This form of concentration has been used very largely in connection with the Lake Superior copper ores, the values of which occur as metallic copper in a relatively light gangue, and also in concentrating tin ores that occur in the light gangue containing considerable mica. 22. THEORY OF JIGGING. 439 Theory of Jigging. By far the most exhaustive investigations on the theory of jigging carried on in America are those of Prof. Robert H. Richards, of the Massachusetts Institute of Technology, and the greater part of the following theoretical discussion is based on his several papers published in the Trans- actions of the American Institute of Mining Engineers. Four laws of jigging are given by the several authorities: (1) The law of equal settling particles, under free settling conditions; (2) the law of interstitial currents, or settling under hindered settling conditions; (3) the law of acceleration; (4) the law of suction. The first of these is the most important, but the others are elements that cannot be disregarded in connection with jigging. Equal Settling Particles. Rittinger gives the following formulas to repre- sent the relation between diameter of grains and rate of falling in water for irregularly shaped grains: V = 2.73|/D(S 1), for roundish grains; V = 2.44v / I>(5 1), for average grains; V = 2.37 1/ D(a 1), for long grains; V = 1.92 1/ D(6 1), for flat grains, in which V = velocity in meters per second; D = diameter of particles in meters, and 6 = specific gravity of the minerals. By means of these different formulas, the ratios of the diameters of different particles that will be equal settling in water can be computed. Professor Richards has not found these formulas to hold in all cases in practice, and, as the result of elaborate experiments, he gives the following table: EQUAL SETTLING FACTORS OR MULTIPLIERS. Table of equal settling factors or multipliers for obtaining the diameter of a quartz grain that will be equal settling under free settling conditions with the mineral specified. >> > O IB OQ Velocity in Inches per Second. CC 00 fc be-5 S-S- " -^ 33 1 2 3 4 5 6 7 8 9 Author's Multipliers. Anthracite Epidote Sphalerite Pyrrhotite Chalcocite Arsenopvrite ... Cassiterite Anitmonv Wolframite Galena 1.473 3.380 4.046 4.508 5.334 5.627 6.261 6.706 6.937 7.856 8.479 2.640 .500 1.57 .352 1.35 1.46 1.73 1.90 1.90 2.11 2.71 2.71 2.71 2.71 .225 1.05 1.05 1.29 1.47 1.57 1.79 2.00 1.83 1.83 2.00 .21? 1.13 1.17 1.48 1.62- 1.89 2.00 2.00 2.07 2.26 2.36 1.50 1.62 2.00 2.07- 2.42 2.73 2.73 2.86 3.00 3.00 1.61 1.64 2.22 2.28 2.56 2.93 2.93 3.04 3.42 3.20 1.56 1.68 2.26 2.4L 2.72 3.03 3.03 3.21 3.65 3.58 t 1.56 1.66 2.13 2.44 2.84 3.05 2.98 3.28 3.76 3.76 1.47 1.56 2.08 2.17 2.94 3.12 3.00 3.26 3.75 3.75 .288 1.45 1.85 2.14 2.64 2.82 3.32 3.48 3.64 4.01 4.56 Copper Quartz The significance of the above table is as follows: If a piece of anthracite of a certain size falls in water with a velocity of 4 in. per second, a piece of quartz 0.213 times the diameter of the anthracite will fall with the same velocity. If a piece of quartz of a certain size falls with a velocity of 7 in. per second, a piece of copper 3.58 times as large as the quartz will fall with the same velocity. Interstitial Currents, or Law of Settling Under Hindered Settling Conditions. If d equals the diameter of a falling particle, and D that of the tube in which it falls, the larger the fraction , the greater will be the retardation or loss 440 ORE DRESSING AND PREPARATION OF COAL. of velocity by the particle. When this fraction equals 1, the particle stops. If, in Fig. 23 (a), the larger circles represent particles of quartz and the smaller circles equal settling particles of galena, then if these mixed parti- cles are settling together or are held in suspension by a rising current of water, each particle may be considered to be falling in a tube, the walls of which consist of the surrounding particles. Substituting a circle in each case for the imaginary tube, we have / \ /x Fig. 23 (6) representing the condi- ( ) ( ) tions for galena and quartz, the K_ypV_y x ^ \ outer circle in each case represent- ing the imaginary tube. Evidently, d COO is much smaller for the galena /""""NO/^N > / D ( ) ( ) /fr, than for the quartz, and it will V / \_y therefore be much less impeded in fa) IT OQ its f? 11 tlian tne quartz; hence, the *JG. 2rf. particles of galena found adjacent to the particles of quartz .will be smaller than the ratio that the law of equal settling particles under free settling conditions would indicate. Application of this principle is found when a mass of grains is subjected to a rising current of sufficient force to rearrange the grains according to their settling power and the grains are said to be treated under hindered settling conditions, as on the bed of a jig. Interstitial factors, or multipliers for obtaining the diameter of the particle of quartz that under hindered settling conditions will be found adjacent to and in equilibrium with the particle of the mineral specified, are the following: Copper 8.598 Cassiterite 4.698 Pyrrhotite 2.808 Galena 5.842 Arsenopyrite ..3.737 Sphalerite 2.127 Wolframite... 5.155 Chalcocite 3.115 Epidote 1.628 Antimony ...4.897 Magnetite 2.808 Anthracite .1782 These signify that, after pulsion has done its work on a jig bed, for exam- ple, where quartz and anthracite are being jigged, the grains will be so arranged that the grains of quartz are .1782 times the diameter of the grains of anthracite that are adjacent to and in equilibrium with them. Acceleration. A particle of galena that is equal settling to the particle of quartz reaches its maximum velocity in perhaps ^ the time required by the quartz. The oft-repeated pulsations of a jig, therefore, give the galena par- ticles a decided advantage over the quartz, placing beside the quartz, when equilibrium is reached, a much smaller particle of galena than we should expect according to the law of equal settling particles. Suction acts to draw down through the screen small grains, mainly of the heavier mineral, which are distributed among large grains. It increases as the length of plunger stroke, with the difference in specific gravity of the two minerals, and with the diminishing of the thickness of the bed on the sieve, whether of the heavier mineral only or of both minerals. The law of suction seems to be that jigging is greatly hindered by strong suction where the two minerals are nearly of the saine size, the quickest and best work then being done with no suction; but when the two minerals differ much in size of particles, the quartz being the larger, strong suction is not only a great advantage, but may be necessary to get any separation at all. Experiments have indicated an approximate boundary between grains that are helped and those that are hindered by suction; namely, if the diameter of the quartz particles is equal to or greater than 3.52 times the diameter of the other mineral particles, then separation is helped by suction; if less, separation is hindered. This value 3.52 (obtained by dividing .0683 by .0195) is approximate only, and it will differ with the fracture of the quartz under consideration; if the quartz grains are much flattened, it will have a large value. Eccentric jigs invariably spend more time on pulsion than accelerated jigs. Is it not fair to conclude that the eccentric jigs are better adapted for treating sands that require the most pulsion? Such sands are the sized products from the trommel and the first spigot of the hydraulic classifier. On the other hand, may not the long-protracted mild suction of the acceler- ated jig be best adapted to the treatment of such products as require primary suction for their separation; for example, the second spigot and THEORY OF JIGGING. 441 the following spigots of the hydraulic classifier? This may be the reason that the Col lorn jig has found so great favor at Lake Superior and at Anaconda, where all the jigging is done on true hydraulic-separator products, except the first sieye of the first jig. We should, however, bear in mind that the somewhat harsh suction of the eccentric jig can be made milder by increasing the hydraulic water. This will diminish the harden- ing of the bed, but it cannot lengthen the time of suction, so as to secure the condition as presented in this particular by the accelerated jigs. Two extreme suggestions arise from a contemplation of the experiments we have carried on: (1) On closely sized products, an accelerated jig should be run backwards, to lengthen out the pulsion period, which is the only period that does any work; and (2) the accelerated jig should be run for- wards on the spigot products of the hydraulic separator, to increase the period of suction. In the way of the first suggestion, there are two difficulties, either of which may cancel the advantage: first, the violent downward motion of the quick return will tend to " blind up " the sieve; and, second, the same action will tend to pulverize a soft mineral like galena. Professor Richards summarizes his experiments in connection with jigging as follows: The two chief reactions of jigging are pulsion and suc- tion. The effect of pulsion depends on the laws of interstitial currents, or of equal settling particles, under hindered settling conditions. The chief function of pulsion is to save the larger grains of the heavier mineral, or the grains that settle faster and farther than the waste. The effect of suction depends on the interstitial factor of the minerals to be separated. If this factor is greater than 3.70, suction will be efficient and rapid. If the factor is less than 3.70, suction will be much hampered and hindered. The use of a long stroke will help to overcome this difficulty. The chief function of suction is to save the particles that are too small'to be saved by the law of interstitial currents, acting through the pulsion of the jig. For jigging mixed sizes, pulsion with full suction should be used. For jigging closely sized products, pulsion with a minimum of suction should be used. The degree of sizing needed as preparation for jigging, if perfect work is desired, depends on the interstitial factor of the minerals to be separated. If the factor is above 3.70 (assuming this value to be sufficiently proved), then sizing is simply a matter of convenience. The fine slimes should of course be removed; and if it is more convenient to send- egg size, nut size, pea size, and sand size, each to its own iig, the suitable screens should be provided for this purpose and a hydraulic separator for grading the finest sizes. But if, on the other hand, the factor is below 3.70, then the jigging of mixed sizes cannot give perfectly clean work, and the separation will be approximate only. To effect the most perfect separation, close sizing must be adopted, and the closer the sizes are to one another, the more rapid and perfect will the jigging be. There may be conditions where the jigging of mixed sizes of this class will be considered sufficiently satisfactory, as an expedient, under the circumstances. Removal of Sulphur From Coal. The object of washing coal is to remove the slate and pyrites, thus reducing the amount of ash and sulphur. Many forms of washers easily and cheaply reduce the slate from 2W in the coal to 8$ of ash in the coke, but it is much more difficult to reduce 4# of sulphur in the coal to 1$ or less of sulphur in the coke. Sulphur occurs in the coal in three forms, as hydrogen sulphide, calcium sulphate, and pyrite. The first is volatile and is removed in coking, the second cannot usually be removed by preliminary treatment, and it is the removal of the third form with which washing has to do. The presence of water in the coke ovens apparently assists the removal of the sulphur; but wet coals require a longer time for coking than dry, and, therefore, pyrite should be removed as far as practicable before charging the coal into the coke ovens. The pyrite in coal as it comes from the mine seems to be in particles even finer than those of the coal dust. This impalpable powder or flour pyrites floats in air or water. This being the case, the common practice of using the water over and over again in a washery cannot give the best results in the removal of sulphur, as some flour pyrites will be carried back each time and remain with the washed coal. Experiments made by Mr. C. C. Upham, of New York City, show that the critical size at which an almost complete division of the coal and pyrites takes place varies with coals from different districts and beds, and in laying out coal-washing plants, the proper fineness of crushing should be deter- mined beforehand by careful experiment. 442 ORE DRESSING AND PREPARATION OF COAL. Preparation of Anthracite. The method of preparing anthracite coal is clearly shown, graphically, by the diagram below. This consists in screen- ing the coal over bars and through revolving or over shaking screens, together with breaking it with rolls to produce the required market size. DIAGRAM SHOWING METHOD OP PREPARING ANTHRACITE COAL. The large lumps of slate and other impurities are separated by hand on the platform near the dump, while the smaller portions are picked out by auto- matic pickers or by hand by boys or old men seated along the chutes leading to the shipping pockets or bins. The smaller sizes are cleaned by jigging. HANDLING OF COAL. 443 HANDLING OF MATERIAL. Anthracite Coal. The following may be taken as average figures for the angle or grade of chutes for anthracite coal, to be used where the chutes are lined with sheet steel: For broken or egg coal, 2i in. per ft.; for stove or chestnut coal, 3 in. per ft.; for pea coal, 4i in. per ft.; for buckwheat coal, 6 in. per ft.; for rice coal, 7 in. per ft.; for culm, 8 in. per ft. If the coal is to start on the chute, 1 in. per ft. should be added to each of the above figures; while if the chutes are lined with manganese bronze in place of steel, the above figures can be reduced 1 in. per ft. for coal in motion, or would remain as in the table to start the coal. When the run of mine is to be handled, as in the main chute, at the head of the breaker, the angle should be not less than 5 in. per ft., or practically 22 from the hori- zontal. If chutes for hard coal are lined with glass, the angle can be reduced from 30$ to 50^, depending somewhat on the nature of the coal. In all cases, the flatter the coal, the steeper the angle must be, on account of the large friction surfaces exposed, compared with the weight of the piece. If chutes are lined with cast iron, the angle should be about the same as that employed for steel, though sometimes a slightly greater angle is allowed. The following table is printed through the courtesy of the Link-Belt Engineering Co., Philadelphia, Pa.: PITCH AT WHICH ANTHRACITE COAL WILL RUN, IN INCHES PER FOOT. Sheet Iron. Cast Iron. Glass. Glass. Kind of Coal. Start on. Con- tinue Start on. Start on. Con- tinue Start on. Con- tinue on. on. on. Dry. Wet. Broken slate . gi 41 -t 3 f 3 Dry egg slate Dry stove slate M 4| 4f ?f 3 3 Dry chestnut slate \ 5 4| 3} 3 1 Broken coal Egg coal 33 3 31 24 2| 1 2i 12 Stove coal 42 42 42 42 3 3 2* 21 2} 3 if Chestnut coal Pea coal 5* 52 3-L 3 Buckwheat No.l .... a 3| 3! 3i Buckwheat No.2... 32 31 32 Buckwheat No.3.... Buckwheat No.4.... 4f 41 If 41 41 ti Bituminous Coal When the run of mine is to be handled, the angle of the chutes should be from 35 to 45 from the horizontal, or from 8i in. to 12 in. per ft. If the coal is wet, the angle should always be steeper, and coarse coal will slide on a flatter angle than slack or fine coal. Ore, Rock, Etc. For coarse fairly dry ore, i. e., from 2 in. or 3 in. size up, chutes may have an angle of 45, or if the material is always to be in motion, the ore will sometimes slide on 40. For fine ore or run of mine, the chutes should have an angle of 50 from the horizontal or practically 14 in. vertical to 1 ft. horizontal. Flumes and Launders. Water flumes are given grades varying from 4 or 5 to 20 or 30 ft. per mile, depending on the surface of the ground and the amount of water to be carried. Practical results have demonstrated the fact that in ordinary ground the water should travel at the rate of from 180 to 200 ft. per minute. Where rather coarse stuff is to be carried through launders in a mill with a comparatively small amount of water, an angle of 2 in. per ft. should be used. With an excess of water, 1 in. per ft. will be ample. The spouting for vanners or launders from trommels carrying rather fine material should have a grade of about 2 in. per ft. In placer mining, the minimum grade 444 ORE DRESSING AND PREPARATION OF COAL. for the sluice should not be less than in. per ft., or about 4| in. per rod. Experiments made in river gravel have shown that with a grade of from 1 in 20 to 1 in 25, 60 cu. ft. per min. will wash 140 to 175 cu. yd. per day of 24 hours. No absolutely definite figures can be given on this subject, owing to the fact that the nature of the ore plays an important part, and while angular quartzose ore can be transported at a comparatively flat angle, it may be necessary to use quite a steep angle if the material is of a clayey nature or contains many large flat plates, exposing large friction surfaces when com- pared to the mass of the pieces. The following tables are printed through the courtesy of the Link-Belt Engineering Co., Philadelphia, Pa.: HORIZONTAL PRESSURE EXERTED BY BITUMINOUS COAL AGAINST VERTICAL RETAINING WALLS PER FOOT OF LENGTH. 99,9? *arto*^t*{ES^K Surface sloping { pfefsu^Towest ft. Angle of repose 6.37 d 2 6.37(2 d l) 10 d 2 10(2 d-1) 35 BITUMINOUS. Horizontal Surface. Sloping Surface. Horizontal Surface. Sloping Surface. a bm. be. .s b m. be. & O rO O> "*"* . &f . O)"*^ f 3! il '3 3 *-> iji itH ft 3g 2 to ' -^ M | 9 P g 1 || O 02 || P C M VI 0) O 02 H II K S p,c , : ;S PH p.0 1 6.4 6.4 10 10 26 4,305 325 6,760 510 2 25.0 19.0 40 30 27 4,641 338 7,290 530 3 57.0 32.0 90 50 28 4,993 350 7,840 550 4 102.0 45.0 160 70 29 5,358 363 8,410 570 5 159.0 57.0 250 90 30 5,733 376 9,000 590 6 229.0 70.0 360 110 31 6,122 389 9,610 610 7 312.0 83.0 490 130 32 6,523 401 10,240 630 8 407.0 96.0 640 150 33 6,935 414 10,890 650 9 516.0 108.0 810 170 34 7,362 427 11,560 670 10 637.0 121.0 1,000 190 35 7,778 440 12,250 690 11 770.0 134.0 1,210 210 36 8,253 452 12,960 710 12 917.0 146.0 1,440 230 37 8,754 465 13,690 730 13 1,076.0 159.0 1,690 250 38 9,193 478 14,440 750 14 1,248.0 172.0 1,960 270 39 9,682 490 15,210 770 15 1,433.0 185.0 2,250 290 40 10,192 503 16,000 790 16 1,630.0 197.0 2.560 310 41 10,669 516 16,810 810 17 1.840.0 210.0 2,890 330 42 11,236 529 17,640 830 18 2,063.0 223.0 3,240 350 43 11,797 541 18,490 850 19 2,298.0 236.0 3,610 370 44 12,331 554 19,360 870 20 2,548.0 248.0 4,000 390 45 12,968 567 20,250 890 21 2,809.0 261.0 4,410 410 46 13,478 580 21,160 910 22 3,083.0 274.0 4,840 430 47 14,100 592 22,090 930 23 3,369.0 287.0 5,290 450 48 14,679 605 23.040 950 24 3,669.0 299.0 5,760 470 49 15,275 618 24,010 970 25 3,981.0 312.0 6,250 490 50 15,925 631 25,000 990 Weight of coal = 47 Ib. per cu. ft. HANDLING OF COAL. 445 HORIZONTAL PRESSURE EXERTED BY ANTHRACITE COAL AGAINST VERTICAL RETAINING WALLS PER FOOT OF LENGTH. Surfacehorizontal Surface *fc Angle of repose st ft. ft. 9.78 d2 9.78(2 d 1) 14.22 <& 14.22(2 d 1) 27 ANTHRACITE. Horizontal Sloping Horizontal Sloping 1 Surface. Surface. -t-J Surface. Surface. a bm. be. .s bm. be. ^ * e -o r* sj 15 o rO -si gg ^o g | II II if t a) "O 02 w "02 02 Q) O ' & S ^ :_ Q) SH ^ P S ^ S ^ ^3 r S J.2 o In. Lb. Lb. Lb. per Min. Net Tons per Hr. is a : C 1 12X 9X11* 18* 11 1,100 33.0 '5,357 a a 14 X 9X11* 18 X 9X1U 22^ 27 a 1,250 1,650 37.5 49.5 5,357 5,357 X 24 X 9X11* 36 22 2,200 66.0 5,357 i 12 X 10 X 16} 18 X 10 X 16i 20 29 19 28i 1,380 2,072 41.4 62.2 5,357 5,357 i 24X10X16} 38 38 2,760 82.8 5,357 30 X 10 X 16} 46i 47| 3,450 103.5 5,357 a 18 X 12 X 16} 31 33 2,400 72.0 5,357 24 X 12 X 16} 40 44 3,200 96.0 5,357 30 X 12 X 16* 48 55 4,000 120.0 5,357 Buckets taken * full. Buckets continuous. 1 Ib. of coal = 34 cu. in. ELEVATING CAPACITIES OF MALLEABLE IRON BUCKETS. Table gives tons (2,000 Ib.) of pea coal per hour at 100 ft. per minute. Buckets. Capacities. Distance Between Buckets in In. Size. In. Wt. Lb. Cu. In. Lb. 8 10 12 14 16 18 20 22 24 2* X 4 0.75 15 0.48 2.16 1.73 1.44 1.23 1.08 3iX 5 1.50 31 0.97 4.36 3.49 2.91 2.49 2.18 1.94 4X6 2.00 51 1.57 7.06 5.65 4.71 4.04 3.53 3.14 2.83 4iX 7 2.56 75 2.33 10.38 8.39 6.99 5.99 5.19 4.66 4.19 3.81 5X8 3.56 102 3.15 11.34 9.45 8.10 7.09 6.30! 5.67 5.15 4.72 6 X10 5.47 185 5.73 17.19 14.73 12.88 11.4610.31 9.38 8.59 7 X12 8.97 287 8.90 22.88 20.02 17.80 16.02 14.56 13.35 7 X14 11.41 295 9.14 20.56' 18.28 16.45 14.95 13.71 10 X18 Weight of 1 cu. ft. of pea coal = 53.5 Ib. 32.3 cu. in., or .0187 cu. ft. = 1 Ib. CONVEYING CAPACITIES OF FLIGHTS AT 100 FT. PER MINUTE. (Tons of Pea Coal per Hour.) Horizontal. Inclined. of 10 20 30 Flight. In. Every 16 In. Every 18 In. Every 24 In. Lb.Coal per Flight. Every 24 In. Every 24 In. Everv 24 In. 4X 10 33.75 30 22.5 15 18.0 14.25 10.5 4X12 42.75 38 28.5 19 24.0 18.00 13.5 5X12 51.75 46 34.5 23 28.5 22.50 16.5 5X15 69.75 62 46.5 31 40.5 31.50 I 22.5 6X 18 80 60.0 40 49.5 40.50 31.5 8X18 120 90.0 60 72.0 57.00 48.0 8X 20 105.0 70 84.0 66.50 56.0 8X24 135.0 90 120.0 96.00 72.0 10 X 24 172.5 115 150.0 120.00 90.0 NOTE, These ratings are for continuous feed. 2,000 Ib, = 1 ton, HANDLING OF COAL. HORSEPOWER FOR BUCKET ELEVATORS. 447 N = number taken from table; H= height of elevator in feet; w == weight of material in one bucket: d = distance apart of buckets, in inches. Revolu- Diameter of Head-Wheels. Revolu- tions r s tions per per Minute. 22 In. 24 In. 26 In. 28 In. 30 In. 32 In. Minute. 10 .064 .070 .075 .080 .087 .093 10 12 .077 .083 .090 .097 .104 .111 12 14 .089 .096 .106 .114 .121 .130 14 16 .102 .111 .121 .130 .140 .148 16 18 .115 .125 .136 .146 .157 .167 18 20 .128 .139 .151 .162 .174 .186 20 22 .140 .153 .166 .179 .191 .204 22 24 .153 .167 .181 .195 .209 .223 24 26 .166 .181 .196 .211 .226 .242 26 28 .179 .195 .211 .227 .244 .260 28 30 .191 .209 .226 .244 .261 .279 30 32 .204 .223 .241 .260 .278 .297 32 34 .217 .237 .256 .276 .296 .316 34 36 .230 .251 .271 .292 .313 .334 36 38 .242 .265 .287 .309 .331 .353 38 40 .255 .279 .302 .325 .348 .372 40 COST OF UNLOADING COAL. Coal is generally unloaded from railroad cars into the h9ld of a vessel by some form of unloader, which usually raises the car bodily and dumps it directly into the hold of the vessel. In this way the cost of unloading has been reduced to a very small figure, and the speed of unloading greatly increased. The cost of unloading is given by the makers of the Brown hoist as varying from 2i cents per ton up to 4i cents per ton; deducting in each case 2 cents for trimming the coal in the vessel, the actual cost of loading varies from cent to 2i cents per ton, depending on the conditions. Along the Lakes it is customary to pay a premium of \ cent per ton to all connected with the toading, for all coal loaded in excess of 2,500 tons per day and 1,800 tons per night. The Brown hoist has a guaranteed capacity of at least 300 tons per hour, but this has been greatly exceeded in practice. The McMyler end dump has a record of 4.65 tons per minute, and the McMyler side dump of 8.41 tons per minute. These figures apply to the lake cities of the United States. (See " Mines and Minerals," May, 1898, for complete description of coal-unloading machines.) The C. W. Hunt Co., West New Brighton, New York, gives the following figures for handling coal along the Atlantic seaboard: The cost of shoveling coal by hand in the hold of the vessel into ordinary iron buckets is about 6 to 7 cents per ton of 2,000 lb.; the cost for iron ore, phosphate rock, or sand, about 10# less. The cost of shoveling coal and hoisting it out of vessel to the wharf with an ordinary hoist with manila rope is 12 to 13 cents per ton, so that the hoisting costs about the same as the shoveling. The cost for both shoveling and hoisting with a steam engine is 10 to 11 cents per ton. The cost when using a steam shovel or grab bucket for taking up coal out of the vessel varies greatly in different classes of vessels, but usually runs from about H to 5 cents per ton, averaging about 3 cents. After the coal is hoisted, it can be carried into storage with an automatic railway or other efficient plant, at a cost of about 1 to \\ cents per ton. In places where the distance is great, a cable railway or a conveyor can be used, which handles the material about as cheaply as for short distances, but the cost of the plant, is greatly increased. 448 BRIQUETING. The cost of stocking and unloading anthracite by the Dodge system is given by Mr. Piez, "Mines and Minerals," June, 1898, page 488, as follows: Year. Engine Service, Stocking and Lifting, per Ton. Cents. Office Expense, per Ton. Cents. Steam, Wages and Fuel, per Ton. Cents. Labor, Dumping and Lifting, per Ton. Cents. fed a S~S Id 0> ag Supplies, per Ton. Cents. Total, per Ton. Cents. 1895..- 1896 .87 .78 .29 .30 .97 .82 2.67 2.19 .78 90 .25 27 5.83 526 1897 69 32 62 1 88 97 16 4 64 BRIQUETING. Machines Employed. Fuel, fuel dust, and other products may be briqueted by a number of different styles of machines, but all these may be divided into two classes, briquet and eggette machines. The eggette machines have a pair of rollers, the faces of which are provided with semispherical or semi- ovoid openings. The material that is fed between these rolls crowds into the openings of the two rolls, thus forming small spheres. The material is mixed with a suitable bond before being fed to the rolls, and the eggettes are received on any suitable form of traveling belt or chute and removed for drying or storage. This style of machine has not been used to any great extent in this country. The briqueting machines all act more or less on the principle of the brick machine, having some kind of a die or mold into which the material is crowded. The material is either pressed as it is being fed into the mold or subsequently by some form of plunger. For some materials, common brick machines, such as are used in the manu- facture of building brick, are employed, while in others special forms are necessary. Briqueting of Fuel. Fuel briquets have not come into general use in the United States for two reasons: (1) on account of the great amount of cheap fuel available, which has prevented the utilization of culm, coal dust, etc.; and (2) on account of the lack of or high price of suitable bonding material. This latter condition is now being removed by the introduction of by-product coke ovens, from which supplies of coal tar can be obtained. Aside from peat and certain kinds of brown coal, and possibly some caking coals, it is neces- sary to employ a bond in the making of any fuel briquets. This is especially true in the case of anthracite coal The present tendency is to employ no inorganic bonding materials, as they increase the ash. The material to be briqueted should be as clean and free from dirt or slate as possible, and the particles should be of practically uniform size, the most satisfactory product being from coal crushed to about j in. cube size. The coal must be thor- oughly mixed with bonding material and then subjected to a heavy pressure. One advantage claimed for briquets is that they can be made of such a form as to occupy less space than the original fuel. The French navy has found it possible to store 10$ more briquets than coal in a given space, and also that the loss by breakage and pulverization is very much less. Under favor- able conditions/fuel can be briqueted for 20 cents per ton, and the following are some of the advantages claimed for these briquets: They are sound throughout and will not decrepitate while burning, thus reducing the loss by fine material working through the grates. The bond, if properly selected, renders the briquets practically waterproof, so that they are not injured if kept in storage, do not evolve combustible gases, nor ignite from spontaneous combustion. There is no fine material mixed with the briquets, and hence a more uniform fire can be maintained with them. Briqueting of Flue Oust Flue dust from iron blast furnaces has been suc- cessfully briqueted in a number of instances. One firm employs a common brick machine, making bricks 2 in. X 4i in. X 9 in. With this machine, they mix the flue dust with 3^ of lime and 3$ of cement, the lime acting as a flux in the furnace. These machines work with comparatively light pres- sure. When regular briqueting machines, producing round bricks and TREATMENT OF INJURED PERSONS. 449 employing high pressures are employed, no cement need be used, the flue dust being mixed with 4$ to 6$ lime. The flue dust is first carefully screened from hard lumps and tnen mixed warm with milk of lime in a mixer, after which it is put through the press, and the briquets are then placed in drying ovens and subjected to heat from the gases of a boiler or furnace plant, the temperature not to exceed 300 F. For moderate sized briquets, about 6 hours' drying is sufficient. Just before the briquets are quite dry, they are loaded into barrels and taken direct to the blast furnace, with as little handling as possible. The results have been very satisfactory com- pared with the ore replaced. The flue dust itself frequently contains 30$ to 40$ metallic iron and more or less carbonaceous matter. It is also stated that at a large furnace plant the cost of making and handling should not exceed $1 per ton. Another firm, figuring on a basis of 130 tons per 24 hours, and using 3$ lime in the solution, gave the following figures: 4 tons lime, $3.00 per ton $12.00 2 machine tenders (day and night), 12 hours, at $2.50 5.00 2 laborers (day and night), 12 hours, at $1.75 3.50 Oil and waste 2.00 Wear on machinery 1.50 Interest on cost of plant 1.00 $25.00 This is less than 20 cents per ton. This estimate does not take into con- sideration the cost of power, which would be about 35 H. P., nor does it take into consideration hauling of material to plant and removing of briquets. CUBIC FEET OCCUPIED BY 2,000 POUNDS OF VARIOUS COALS. (Link-Belt Engineering Co., Philadelphia, Pa.) Varieties. Broken. Egg. Stove. Chestnut. Pea. Lackawanna, anthracite 37.10 37.30 37.55 38.05 34.90 34.95 33.30 34.65 35.35 35.45 36.65 36.95 37.25 37.70 34.85 34.35 33.80 34.20 35.20 34.95 34.90 36.35 37.55 37.25 34.75 33.75 33.55 33.80 34.60 34.35 34.35 36.35 37.25 37.25 34.70 34.00 32.55 33.55 33.30 33.70 37.25 37.50 38.50 38.50 36.90 36.90 33.05 35.20 34.95 35.50 Garfield red ash, anthracite .. Lykens Valley, anthracite .... Shamokin, anthracite Plymouth red ash, anthracite. . Wilkes-Barre, anthracite Lehigh, anthracite Lorberry, anthracite Scranton anthracite Pittston, anthracite Cumberland, bituminous Clearfield, bituminous New River, bituminous 36.65 Pocahontas, bituminous 33.55 American cannel, bituminous 40.15 English cannel, bituminous- 34.00 41.50 42.30 TREATMENT OF INJURED PERSONS. The dangers to be feared in case of wounds, are: shock or collapse, loss of blood, and unnecessary suffering in the moving of the patient. In shock, the injured person lies pale, faint, and cold, sometimes insen- sible, with feeble pulse and superficial breathing. The cause of death in case pf a shock is arrest of heart action, produced by the suspension of the functions of the brain and spinal cord. In treatment, the two most import- ant parts are: (1) the position of the injured person; (2) the application of external warmth. The injured person should at once be placed in a recumbent position, his head resting on a plane lower than that of his trunk, legs, and feet. He should be well wrapped up and protected from the chilling influences of external air. When there is danger of immediate death, stimulants should be given; in all other conditions of shock, stimulants are injurious. Loss of Blood. In case of loss of blood, two conditions present themselves: (1) The bleeding is arrested spontaneously or otherwise, but the injured person presents all the symptoms of loss of blood; (2) the injured person is actually bleeding, and he is, or is not, suffering from loss of blood. In the first condition, life is threatened by anemia of brain and spinal cord, and all the efforts of treatment are to direct the flow of whatever 450 TREATMENT OF INJURED PERSONS. quantity of blood may still remain in the body to the vital centers in the brain and spinal cord. This is most efficiently done by placing the injured person in a recumbent position, with his head resting on a plane somewhat FIG. 1. lower than that of his trunk and legs. In graver cases, constricting bands should be applied to both arms, as near the shoulders as possible, and to both thighs, as near the abdomen as possible. This last maneuver directs the entire quantity of blood in the body to the suffering centers, the centers of life itself. Stimulants may be sparingly administered. If there is bleeding, do not try to stop it by binding up the wound. The current of blood to the part must be checked. To do this, find the artery; by its beating; lay a firm and even compress or pad (made of cloth or rags rolled up, or a round stone or piece of wood well wrapped) over the artery (Fig. 1) . Tie a handkerchief around the limb and compress; put a bit of stick through the handkerchief and twist the latter up until it is just tight enough to stop the bleed- ing; then put one end of the stick under the handkerchief, to prevent untwisting, as in Fig. 2. The artery in the thigh runs along the inner side of the muscle in front near the bone, as shown by dotted line in Fig. 3. A little above the knee it passes to the back of the bone. In injuries at or above the knee, apply the compress higher up. on the inner side of the thigh, at the point P, Fig. 3, with the knot on the outside of the thigh. When the leg is injured below the knee, apply the compress at the back of FIG. 3. the thigh, just above the knee, at P, Fig. 4, FIG. 4. and the knot in front, as in Figs. 1 and 2. The artery in the arm runs down the inner side of the large muscle in front, quite close to the bone, as shown by dotted line; low down it is further forwards, towards the bend of the elbow. It is most easily compressed a little above the middle, at P, Fig. 5. Care should be taken to examine the limb from time to time, and to lessen the compression if it becomes cold or purple; tighten up the handkerchief again if the bleeding begins afresh. To Transport a Wounded Person Comfortably. Make a soft and even bed for the injured part, of straw, folded blankets, quilts, or FIG. 5. FIG. 6. pillows, laid on a board with side pieces of board nailed on, when this can be done. If possible, let the patient be laid on a door, shutter, settee, or some firm support, properly covered. Have sufficient force to lift him steadily, and let those that bear him not keep step. Should any important arteries be opened, apply the handkerchief, as recommended. Secure the vessel by a surgeon's dressing forceps, or by a TREATMENT OF PERSONS OVERCOME BY GAS. 451 hook, then have a silk ligature put around the vessel, and tighten. Should the bleeding be from arterial vessels of small size, apply persulphate of iron, either in tincture or in powder, by wetting a piece of lint or sponge with the solution; then, after bleeding ceases, apply a compress against the parts, to sustain them during the application of the persulphate of iron, and to pre- vent further bleeding, should it occur. The persulphate of iron should be kept in or about all working places. Bleeding From Scalp Wounds. A pad or compress is placed immediately before the ear, over the region marked by a dotted line, Fig. 6. The com- press is firmly secured by a handkerchief. If this does not arrest bleeding, a similar compress on the opposite side should be applied. Should the bleed- ing issue from a wound of the posterior or back part of the head, a compress should be placed behind the ear, over the region marked by the dotted line, Fig. 6, and firmly secured by a handkerchief or bandage. TREATMENT OF PERSONS OVERCOME BY GAS. Miners are exposed to asphyxia when the circulation of the air is not suf- ficiently active, when the mine exhales a quantity of deleterious gas, when they imprudently penetrate into old and abandoned workings, and when there is an explosion. The symptoms of asphyxia are sudden cessation of the respiration, of the pulsations of the heart, and of the action of the senses; the countenance is swollen and marked with reddish spots, the eyes are protruded, the features are distorted, and the face is often livid, etc. The best and first remedy to employ, and in which the greatest confidence ought to be placed, is the renewal of the air necessary for respiration. Proceed as follows: 1. Promptly withdraw the asphyxiated person from the deleterious place and expose him to pure air. 2. Loosen the clothes round the neck and chest, and dash cold water in the face and on the chest. 3. Attempts should be made to irritate the mucous membrane with the feathered end of a quill, which should be gently moved in the nostrils of the insensible person, or to stimulate it with a bottle of volatile alkali placed under the nose. 4. Keep up the warmth of the body, and apply mustard plasters over the heart and around the ankles. 5. If these means fail to produce respiration, Doctor Sylvester's method of producing artificial respiration should be tried as follows: Place the patient on the back on a flat surface, inclined a little upwards from the feet; raise and support the head and shoulders on a small firm cushion or folded article of dress placed under the shoulder blades. Draw forwards the patient's tongue and keep it projecting beyond the lips; an elastic band over the tongue and under the cnin will answer this purpose, or a piece of string or tape may be tied around them, or by raising the lower jaw the teeth may be made to retain the tongue in that position. Remove all tight clothing from about the neck and chest, especially the suspenders. Then standing at the patient's head, grasp the arms just above the elbows, and draw the arms gently and steadily upwards above the head, and keep them stretched upwards for 2 seconds (by this means air is drawn into the lungs). Then turn down the patient's arms and press them gently and firmly for 2 seconds against the sides of the chest (by this means air is pressed out of the lungs). Repeat these measures alternately, deliberately, and per- severingly about 15 times in a minute, until a spontaneous effort to respire is perceived, immediately upon which cease to imitate the movements of breathing, and proceed to induce circulation and warmth. 6. To promote warmth and circulation, rub the limbs upwards with firm, grasping pressure and energy, using handkerchiefs, flannels, etc. Apply hot annels, bottles of hot water, heated bricks, etc. to the pit of the stomach, the arm pits, between the thighs, and to the soles of the feet. 7. On the restoration of life, a teaspoonful of warm water should be given, and then, if the power of swallowing has returned, small quantities of wine, warm brandy and water, or coffee should be administered. 8. These remedies should be promptly applied, and as death does not certainly appear for a long time, they ought only to be discontinued when it is clearly confirmed. Absence of the pulsation of the heart is not a sure sign of death, neither is the want of respiration. 452 COAL DEALER'S TABLE. COAL DEALERS' COMPUTING TABLE, FOR ASCERTAINING THE PRICE OF ANY NUMBER OF POUNDS, AT A GIVEN PRICE PER TON OF 2,000 POUNDS. Lb. 80.75 $1.00 $1.25 $1.50 $1.75 $2.00 $2.25' $2.50 $2.75 10 .01 .01 .01 .01 .01 .01 .01 .01 .01 20 .01 .01 .01 .02 .02 .02 .02 .03 .03 30 .01 .02 .02 .02 .03 .03 .03 .04 .04 40 .02 .02 .03 .03 .04 .04 .04 .05 .06 50 .02 .02 .03 .04 .04 .05 .06 .06 .07 60 .02 .03 .04 .05 .05 .06 .07 .08 .08 70 .03 .03 .04 .05 .06 .07 .08 .09 .10 80 .03 .04 .05 .06 .07 .08 .09 .10 .11 90 .03 .04 .06 .07 .08 .09 .10 .11 .12 100 .04 .05 .06 .08 .09 .10 .11 .13 .14 200 .08 .10 .13 .15 .17 .20 .23 .25 .28 300 .11 .15 .19 .23 .26 .30 .34 .38 .41 400 .15 .20 .25 .30 .35 .40 .45 .50 .55 500 .19 .25 .31 ' .38 .44 .50 .56 .63 .69 600 .23 .30 .37 .45 .53 .60 .68 .75 .83 700 .26 .35 .44 .53 .61 .70 .77 .88 . .96 800 .30 .40 .50 .60 .70 .80 .90 1.00 1.10 900 .34 .45 .56 .68 .79 .90 1.01 1.13 1.24 1,000 .38 .50 .63 .75 .88 1.00 1.13 1.25 1.38 1,100 .41 .55 .69 .83 .96 1.10 1.24 1.38 1.51 1,200 .45 .60 .75 .90 1.05 1.20 1.35 1.50 1.65 1,300 .49 .65 .81 .98 1.14 1.30 1.46 1.63 1.79 1,400 .52 .70 .88 1.05 1.22 1.40 1.58 1.75 1.93 1,500 .56 .75 .94 1.13 1.31 1.50 1.69 1.88 2.06 1,600 .60 .80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 1,700 .64 .85 1.06 1.28 1.49 1.70 1.91 2.13 2.34 1,800 .68 .90 1.13 1.35 1.58 1.80 2.03 2.25 2.48 1,900 .71 .95 1.19 1.43 1.66 1.90 2.14 2.38 2.61 Lb. $3.00 $3.25 $3.50 $3.75 $4.00 $4.25 $4.50 $4.75 $5.00 10 .02 .02 .02 .02 .02 .02 .03 .03 .03 20 .03 .03 .04 .04 .04 .05 .05 .05 .05 30 .05 .05 .05 .06 .06 .07 .07 .07 .08 40 .06 .07 .07 .08 .08 .09 .09 .10 .10 50 .08 .08 .09 .09 .10 .11 .12 .12 .13 60 .09 .10 .11 .11 .12 .13 .14 .15 .15 70 .11 .11 .12 .13 .14 .15 .16 .17- .18 80 .12 .13 .14 .15 .16 .17 .18 .19' .20 90 .14 .15 .16 .17 .18 .19 .20 .22 .23 100 .15 .16 .18 .19 .20 .22 .23 .24 .25 200 .30 .33 .35 .38 .40 .43 .45 .48 .50 300 .45 .49 .53 .56 .60 .64 .68 .72 .75 400 .60 .65 .70 .75 .80 .85 .90 .95 1.00 500 .75 .81 .88 .94 1.00 1.07 1.13 1.19 1.25 600 .90 .98 1.05 1.13 1.20 1.28 1.35 1.43 1.50 700 1.05 1.14 1.23 1.31 1.40 1.49 1.58 1.67 1.75 800 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 900 1.35 1.46 1.58 1.69 1.80 1.92 2.03 2.14 2.25 1,000 1.50 1.63 1.75 1.88 2.00 2.13 2.25 2.38 2.50 1,100 1.65 1.79 1.93 2.06 2.20 2.34 2.48 2.62 2.75 1,200 1.80 1.95 2.10 2.25 2.40 2.55 2.70 2.85 3.00 1,300 1.95 2.11 2.28 2.44 2.60 2.77 2.93 3.09 3.25 1,400 2.10 2.28 2.45 2.63 2.80 2.98 3.15 3.33 3.50 1,500 2.25 2.44 2.63 2.81 3.00 3.19 3.38 3.57 3.75 1,600 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00 1,700 2.55 2.76 2.98 3.19 3.40 3.62 3.83 4.04 4.25 1,800 2.70 2.93 3.15 3.38 3.60 3.83 4.05 4.28 4.50 1,900 2.85 3.09 3.33 3.56 3.80 4.04 4.28 4.52 4.75 NATURAL SINES AND COSINES. 453 TABLE OF NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. EXPLANATION. Given an angle, to find its sine, cosine, tangent, and cotangent: EXAMPLE. Find the sine, cosine, tangent, and cotangent of 37 24'. Look in the table of natural sines along the tops of the pages, and find 37. Glancing down the left-hand column marked ('), until 24 is found, find opposite this 24 in the column marked sine and headed 37, the number .60738; then .60738 = sin 37 24'. Similarly, find in the column marked cosine and headed 37, the number .79441, which corresponds to cos 37 24'. So, also, find in the column marked tangent and headed 37, and opposite 24', the number .76456; and in the column marked cotangent and headed 37, and opposite 24', the number 1.30795. In most of the tables published, the angles run only from to 45 at the heads of the columns; to find an angle greater than 45, look at the bottom of the page and glance upwards, using the extreme right-hand column to find minutes, which begin with at the bottom and run upwards, 1, 2, 3, etc., up to 60. EXAMPLE. Find the sine of 77 43'. Look along the bottom of the tables until the column marked sine and marked 77 is found. Glancing up the column of minutes on the right until 43' is found, find opposite 43' in the column marked sine at the bottom and marked 77, the number .97711; this is the sine of 77 43'. Similarly, the cosine, tangent, and cotangent may be found. To find the sine, cosine, tangent, or cotangent of an angle whose exact value is not given in the table: Rule. Find in the table the sine, cosine, tangent, or cotangent corresponding to the degrees and minutes of the angle. For the seconds, find the difference of the values of the sine, cosine, tangent, or cotangent taken from the table between which the seconds of the angle fall; multiply this difference by a fraction whose numerator is the number of seconds in the given angle and whose denominator is 60. If sine or tangent, add this correction to the value first found; if cosine or cotangent, subtract the correction. EXAMPLE. Find the sine, cosine, tangent, and cotangent of 56 43' 17". Sin 56 43' = .83597. Sin 56 44' = .83613. Since 56 43' 17" is greater than 56 43' and less than 56 44', the value of the sine of the angle lies between .83597 and .83613; the difference equals .83613 .83597 = .00016; multiplying this by the fraction $$, .00016 X U = -00005, nearly, which is to be added to .83597, the value first found, or .83597 + .00005 = .83602. Hence, sin 56 43' 17" = .83602. Cos 56 43' = .54878; cos 56 44' = .54854; the difference equals .54878 .54854 = .00024, and .00024 X 5 = .00007, nearly. Now, since the cosine is desired, we must subtract this correction from cos 56 43', or .54878; subtract- ing, .54878 - .00007 = .54871. Hence, cos 56 43' 17" = .54871. Given the sine, cosine, tangent, or cotangent, to find the angle corresponding: EXAMPLE. The sine of an angle is .47486; what is the angle? Consulting the table of natural sines, glance down the columns marked sine until .47486 is found, opposite 21' in the left-hand column and under the column headed 28. Therefore, the angle whose sine = .47486 is 28 21', or sin 28 21' = .47486. To find the angle corresponding to a given sine, cosine, tangent, or cotangent whose exact value is not contained in the table: Rule. -Find the difference of the two numbers in the table between which the given sine, cosine, tangent, or cotangent falls, and use the number of parts in this difference as the denominator of a fraction. 454 NATURAL SINES AND COSINES. Find the difference between the number belonging to the smaller angle and the given sine, cosine, tangent, or cotangent, and use the number of parts in the dif- ference just found as the numerator of the fraction mentioned above. Multiply this fraction by 60, and the result will be the number of seconds to be added to the smaller angle. EXAMPLE. Find the angle whose sine equals .57698. Looking in the table of natural sines, in the column marked sine, it is found between .57691 = sin 35 14' and .57715 = 35 15'. The difference between them is .57715 .57691 = .00024, or 24 parts. The difference between the sine of the smaller angle, or sin 35 14' = .57691, and the given sine, or .57698, is .57698 .57691 = .00007, or 7 parts. Then, 2 7 X 60 = 17.5", and the angle = 35 14' 17.5", or sin 35 14' 17.5" = .57698. The cosecant of an angle is equal to the reciprocal of its sine, and the secant is equal to the reciprocal of its cosine. Hence, to multiply a quantity by the cosecant, divide it by the sine; or, to divide it by the cosecant, multiply it by the sine. Similarly, to multiply a quantity by the secant of an angle, divide it by the cosine; or, to divide it by the secant, multiply it by the cosine. NATURAL SINES AND COSINES. 455 1 o 2 o 3 o 4 3 f r Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine .00000 1. .01745 .99985 .03490 .99939 .05234 .99863 .06976 .99756 60 1 .00029 .01774 .99984 .03519 .99938 .05263 .99861 .07005 .99754 59 .00058 .01803 .99984 .03548 .99937 .05292 .99860 .07034 .99752 58 .00087 .01832 .99983 .03577 .99936 .05321 .99858 .07063 .99750 57 .00116 .01862 .99983 .03606 .99935 .05350 .99857 .07092 .99748 56 .00145 .01891 .99982 .03635 .99934 .05379 .99855 .07121 .99746 55 .00175 .01920 .99982 .03664 .99933 .05408 .99854 .07150 .99744 54 .00204 .01949 .99981 .03693 .99932 .05437 .99852 .07179 .99742 53 8 .00233 .01978 ' .99980 .03723 .99931 .05466 .99851 .07208 .99740 52 9 .00262 .02007 .99980 .03752 .99930 .05495 .99849 .07237 .99738 51 10 .00291 .02036 .99979 .03781 .99929 .05524 .99847 .07266 .99736 50 11 .00320 .99999 .02065 .99979 .03810 .99927 .05553 .99846 .07295 .99734 49 12 .00349 .99999 .02094 .99978 .03839 .99926 .05582 .99844 .07324 .99731 48 13 .00378 .99999 .02123 .99977 .03868 .99925 .05611 .99842 .07353 .99729 47 14 .00407 .99999 .02152 .99977 .03897 .99924 .05640 .99841 .07382 .99727 46 15 .00436 .99999 .02181 .99976 .03926 .99923 .05669 .99839 .07411 .99725 45 16 .00465 .99999 .02211 .99976 .03955 .99922 .05698 99838 .07440 .99723 44 17 .00495 .99999 .02240 .99975 .03984 .99921 .05727 .99836 .07469 .99721 43 18 .00524 .02269 .99974 .04013 .99919 .05756 .99834 .07498 .99719 42 19 .00553 !99998 .02298 .99974 .04042 .99918 .05785 .99833 .07527 .99716 41 20 .00582 .99998 .02327 .99973 .04071 .99917 .05814 .99831 .07556 .99714 40 21 .00611 .99998 .02356 .99972 .04100 .99916 .05844 .99829 .07585 .99712 39 22 .00640 .99998 .02385 .99972 .04129 .99915 .05873 .99827 .07614 .99710 38 23 .00669 .99998 .02414 .99971 .04159 .99913 .05902 .99826 .07643 .99708 37 24 .00698 .99998 .02443 .99970 .04188 .99912 .05931 .99824 .07672 .99705 36 25 .00727 .99997 .02472 .99969 .04217 .99911 .05960 .99822 .07701 .99703 35 26 .00756 .99997 .02501 .99969 .04246 .99910 .05989 .99821 .07730 .99701 34 27 .00785 .99997 .02530 .99968 .04275 .99909 .06018 .99819 .07759 .99699 33 28 .00814 .99997 .02560 .99967 .04304 .99907 .06047 .99817 .07788 .99696 32 29 .00844 .02589 .99966 .04333 .99906 .06076 .99815 .07817 .99694 31 30 .00873 !99996 .02618 .99966 .04362 .99905 .06105 .99813 .07846 .99692 30 31 .00902 .99996 .02647 .99965 .04391 .99904 .06134 .99812 .07875 .99689 29 32 .00931 !99996 .02676 .99964 .04420 .99902 .06163 .99810 .07904 .99687 28 33 .00960 .99995 .02705 .99963 .04449 .99901 .06192 .99808 .07933 .99685 27 34 .00989 .99995 .02734 .99963 .04478 .99900 .06221 .99806 .07962 .99683 26 35 .01018 .99995 .02763 .99962 .04507 .99898 .06250 .99804 .07991 .99680 25 36 .01047 .99995 .02792 .99961 .04536 .99897 .06279 .99803 .08020 .99678 24 37 .01076 .99994 .02821 .99960 .04565 .99896 .06308 .99801 .08049 .99676 23 38 .01105 .99994 .02850 .99959 .04594 .99894 .06337 .99799 .08078 .99673 22 39 .01134 .99994 .02879 .99959 .04623 .99893 .06366 .99797 .08107 .99671 21 40 .01164 .99993 .02908 .99958 .04653 .99892 .06395 .99795 .08136 .99668 20 41 .01193 .99993 .02938 .99957 .04682 .99890 .06424 .99793 .08165 .99666 19 42 .01222 .99993 .02967 .99956 .04711 .99889 .06453 .99792 .08194 !99664 18 43 .01251 .99992 .02996 .99955 .04740 .99888 .06482 .99790 .08223 .99661 17 44 .01280 .99992 .03025 .99954 .04769 .99886 .06511 .99788 .08252 .99659 16 45 .01309 .99991 .03054 .99953 .04798 .99885 .06540 .99786 .08281 .99657 15 46 .01338 .99991 .03083 .99952 .04827 .99883 .06569 .99784 .08310 .99654 14 47 .01367 .99991 .03112 .99952 .04856 .99882 .06598 .99782 .08339 .99652 13 48 .01396 .99990 .03141 .99951 .04885 .99881 .06627 .99780 .08368 .99649 12 49 .01425 .99990 .03170 .99950 .04914 .99879 .06656 .99778 .08397 .99647 11 50 .01454 .99989 .03199 .99949 .04943 .99878 .06685 .99776 .08426 .99644 10 51 .01483 .99989 .03228 .99948 .04972 .99876 .06714 .99774 .08455 .99642 9 52 .01513 .99989 .03257 .99947 .05001 .99875 .06743 .99772 .08484 .99639 8 53 .01542 .99988 .03286 .99946 .05030 .99873 .06773 .99770 .08513 .99637 7 54 .01571 .99988 .03316 .99945 .05059 .99872 .06802 .99768 .08542 .99635 6 55 .01600 .99987 .03345 .99944 .05088 .99870 .06831 .99766 .08571 .99632 5 56 .01629 .99987 .03374 .99943 .05117 .99869 .06860 .99764 .08600 .99630 4 57 .01658 .99986 .03403 .99942 .05146 .99867 .06889 .08629 .99627 3 58 .01687 .99986 .03432 .99941 .05175 .99866 .06918 !99760 .08658 .99625 2 59 .01716 .99985 .03461 .99940 .05205 .99864 .06947 .99758 .08687 .99622 1 60 .01745 .99985 .03490 .99939 .05234 .99863 .06976 .99756 .08716 .99619 , Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine , 8 P & * 8' 1 8< ) 8 o .V.4 TVRAL SINES AND COSINES. > ( > o 3 < > Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine .08716 .99619 .10453 .99452 .12187 .99255 .13917 .99027 .15643 .98769 60 1 .08745 .99617 .10482 .99499 .12216 .99251 .13946 .99023 .15672 .98764 59 2 .08774 .99614 .10511 .99446 .12245 .99248 .13975 .99019 .15701 .98760 58 3 .08803 .99612 .10540 .99443 .12274 .99244 .14004 .99015 .15730 .98755 57 4 .08831 .99609 .10569 .99440 .12302 .99240 . 4033 .99011 .15758 .98751 56 5 .08860 .99607 .10597 .99437 .12331 .99237 . 4061 .99006 .15787 .98746 55 6 .08889 .99604 .10626 .99434 .12360 .99233 . 4090 .99002 .15816 .98741 54 7 .08918 .99602 .10655 .99431 .12389 .99230 . 4119 .98998 .15845 .98737 53 8 .08947 .99599 .10684 .99428 .12418 .99226 . 4148 .98994 .15873 .98732 52 9 .08976 .99596 .10713 .99424 .12447 .99222 . 4177 .98990 .15902 .98728 51 10 .09005 .99594 .10742 .99421 .12476 .99219 .14205 .98986 .15931 .98723 50 11 .09034 .99591 .10771 .99418 .12504 .99215 .14234 .98982 .15959 .98718 49 12 .09063 .99588 .10800 .99415 .12533 .99211 .14263 .98978 .15988 .98714 48 13 .09092 .99586 .10829 .99412 .12562 .99208 .14292 .98973 .16017 .98709 47 14 .09121 .99583 .10858 .99409 .12591 .99204 .14320 .98969 .16046 .98704 6 15 .09150 .99580 .10887 .99406 .12620 .99200 .14349 .98965 .16074 .98700 5 16 .09179 .99578 .10916 .99402 .12649 .99197 .14378 .98961 .16103 .98695 4 17 .09208 .99575 .10945 .99399 .12678 .99193 .14407 .98957 .16132 .98690 3 18 .09237 .99572 .10973 .99396 .12706 .99189 .14436 .98953 .16160 .98686 2 19 .09266 .99570 .11002 .99393 .12735 .99186 .14464 .98948 .16189 .98681 1 20 .09295 .99567 .11031 .99390 .12764 .99182 .14493 .98944 .16218 .98676 40 21 .09324 .99564 .11060 .99386 .12793 .99178 .14522 .98940 .16246 .98671 39 22 .09353 .99562 .11089 .99383 .12822 .99175 .14551 .98936 .16275 .98667 38 23 .09382 .99559 .11118 .99380 .12851 .99171 .14580 .98931 .16304 .98662 37 24 .09411 .99556 .11147 .99377 .12880 .99167 .14608 .98927 .16333 .98657 36 25 .09440 .99553 .11176 .99374 .12908 .99163 .14637 .98923 .16361 .98652 35 26 .09469 .99551 .11205 .99370 .12937 .99160 .14666 .98919 .16390 .98648 34 27 .09498 .99548 .11234 .99367 .12966 .99156 .14695 .98914 .16419 .98643 33 28 .09527 .99545 .11263 .99364 .12995 .99152 .14723 .98910 .16447 .98638 32 29 .09556 .99542 .11291 .99360 .13024 .99148 .14752 .98906 .16476 .98633 31 30 .09585 .99540 .11320 .99357 .13053 .99144 .14781 .98902 .16505 .98629 30 31 .09614 .99537 .11349 .99354 .13081 .99141 .14810 .98897 .16533 .98624 29 32 .09642 .99534 .11378 .99351 .13110 .99137 .14838 .98893 .16562 .98619 28 33 .09671 .99531 .11407 .99347 .13139 .99133 .14867 .98889 .16591 .98614 27 34 .09700 .99528 .11436 .99344 .13168 .99129 .14896 .98884 .16620 .98609 26 35 .09729 .99526 .11465 .99341 .13197 .99125 .14925 .98880 .16648 .98604 25 36 .09758 .99523 .11494 .99337 .13226 .99122 .14954 .98876 .16677 .98600 24 37 .09787 .99520 .11523 .99334 .13254 .99118 .14982 .98871 .16706 .98595 38 .09816 .99517 .11552 .99331 .13283 .99114 .15011 .98867 .16734 .98590 22 39 .09845 .99514 .11580 .99327 .13312 .99110 .15040 .98863 .16763 .98585 21 40 .09874 .99511 .11609 .99324 .13341 .99106 .15069 .98858 .16792 .98580 20 41 .09903 .99508 .11638 .99320 .13370 .99102 .15097 .98854 .16820 .99575 19 42 .09932 .99506 .11667 .99317 .13399 .99098 .15126 .98849 .16849 .98570 18 43 .09961 .99503 .11696 .99314 .13427 .99094 .15155 .98845 .16878 .98565 17 44 .09990 .99500 .11725 .99310 .13456 .99091 .15184 .98841 .16906 .98561 16 45 .10019 .99497 .11754 .99307 .13485 .99087 .15212 .98836 .16935 .98556 15 46 .10048 .99494 .11783 .99303 .13514 .99083 .15241 .98832 .16964 .98551 14 47 .10077 .99491 .11812 .99300 .13543 .99079 .15270 .98827 .16992 .98546 13 48 .10106 .99488 .11840 .99297 .13572 .99075 .15299 .98823 .17021 .98541 12 49 .10135 .99485 .11869 .99293 .13600 .99071 .15327 .98818 .17050 .98536 11 50 .10164 .99482 .11898 .99290 .13629 .99067 .15356 .98814 .17078 .98531 10 51 .10192 .99479 .11927 .99286 .13658 .99063 .15385 .98809 .17107 98526 9 52 .10221 .99476 .11956 .99283 .13687 .99059 .15414 .98805 .17136 98521 8 53 .10250 .99473 .11985 .99279 .13716 .99055 .15442 .98800 .17164 98516 7 54 .10279 .99470 .12014 .99276 .13744 .99051 .15471 .98796 .17193 98511 6 55 .10368 .99467 .12043 .99272 .13773 .99047 .15500 .98791 .17222 98506 5 56 .10337 .99464 .12071 .99269 .13802 .99043 .15529 .98787 .17250 98501 4 57 .10366 .99461 .12100 .99265 .13831 .99039 .15557 .98782 .17279 98496 3 58 .10395 .99458 .12129 .99262 .13860 .99035 .15586 .98778 .17308 98491 2 59 .10424 .99455 .12158 .99258 .13889 .99031 .15615 .98773 .17336 98486 1 60 .10453 .99452 .12187 .99255 .13917 .99027 .15643 .98769 .17365 98481 Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine i f 84 o 83 o 82 81 o 80 ( | NATURAL SINES AND COSINES. 457 1 1 1 ] 2 1 3 ] .4 Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine .17365 .98481 .19081 .98163 .20791 .97815 .22495 .97437 .24192 .97030 60 1 .17393 .98476 .19109 .98157 .20820 .97809 .22523 .97430 .24220 .97023 59 2 .17422 .98471 .19138 .98152 .20848 .97803 .22552 .97424 .24249 .97015 58 3 .17451 .98466 .19167 .98146 .20877 .97797 .22580 .97417 .24277 .97008 57 4 .17479 .98461 .19195 .98140 .20905 .97791 .22608 .97411 .24305 .97001 56 5 .17508 .98455 .19224 .98135 .20933 .97784 .22637 .97404 .24333 .96994 55 6 .17537 .98450 .19252 .98129 .20962 .97778 .22665 .97398 .24362 .96987 54 7 .17565 .98445 .19281 .98124 .20990 .97772 .22693 .97391 .24390 .96980 53 8 .17594 .98440 .19309 .98118 .21019 .97766 .22722 .97384 .24418 .96973 52 9 .17623 .98435 .19338 .98112 .21047 .97760 .22750 .97378 .24446 .96966 51 10 .17651 .98430 .19366 .98107 .21076 .97754 .22778 .97371 .24474 .96959 50 11 .17680 .98425 .19395 .98101 .21104 .97748 .22807 .97365 .24503 .96952 49 12 .17708 .98420 .19423 .98096 .21132 .97742 .22835 .97358 .24531 .96945 48 13 .17737 .98414 .19452 .98090 .21161 .97735 .22863 .97351 .24559 .96937 47 14 .17766 .98409 .19481 .98084 .21189 .97729 .22892 .97345 .24587 .96930 46 15 .17794 .98404 .19509 .98079 .21218 .97723 .22920 .97338 .24615 .96923 45 16 .17823 .98399 .19538 .98073 .21246 .97717 .22948 .97331 .24644 .96916 44 17 .17852 .98394 .19566 .98067 .21275 .97711 .22977 .97325 .24672 .96909 43 18 .17880 .98389 .19595 .98061 .21303 .97705 .23005 .97318 .24700 .96902 42 19 .17909 .98383 .19623 .98056 .21331 .97698 .23033 .97311 .24728 .96894 41 20 .17937 .98378 .19652 .98050 .21360 .97692 .23062 .97304 .24756 .96887 40 21 .17966 .98373 .19680 .98044 .21388 .97686 .23090 .97298 .24784 .96880 39 22 .17995 .98368 .19709 .98039 .21417 .97680 .23118 .97291 .24813 .96873 38 23 .18023 .98362 .19737 .98033 .21445 .97673 .23146 .97284 .24841 .96866 37 24 .18052 .98357 .19766 .98027 .21474 .97667 .23175 .97278 .24869 .96858 36 25 .18081 .98352 .19794 .98021 .21502 .97661 .23203 .97271 .24897 .96851 35 26 .18109 .98347 .19823 .98016 .21530 .97655 .23231 .97264 .24925 .96844 34 27 .18138 .98341 .19851 .98010 .21559 .97648 .23260 .97257 .24954 .96837 33 28 .18166 .98336 .19880 .98004 .21587 .97642 .23288 .97251 .24982 .96829 32 29 .18195 .98331 .19908 .97998 .21616 .97636 .23316 .97244 .25010 .96822 31 30 .18224 .98325 .19937 .97992 .21644 .97630 .23345 .97237 .25038 .96815 30 31 .18252 .98320 .19965 .97987 .21672 .97623 .23373 .97230 .25066 .96807 29 32 .18281 .98315 .19994 .97981 .21701 .97617 .23401 .97223 .25094 .96800 28 33 .18309 .98310 .20022 .97975 .21729 .97611 .23429 .97217 .25122 .96793 27 34 .18338 .98304 .20051 .97969 .21758 .97604 .23458 .97210 .25151 .96786 26 35 .18367 .98299 .20079 .97963 .21786 .97598 .23486 .97203 .25179 .96778 25 36 .18395 .98294 .20108 .97958 .21814 .97592 .23514 .97196 .25207 .96771 24 37 .18424 .98288 .20136 .97952 .21843 .97585 .23542 .97189 .25235 .96764 23 38 .18452 .98283 .20165 .97946 .21871 .97579 .23571 .97182 .25263 .96756 22 39 .18481 .98277 .20193 .97940 .21899 .97573 .23599 .97176 .25291 .96749 21 40 .18509 .98272 .20222 .97934 .21928 .97566 .23627 .97169 .25320 .96742 20 41 .18538 .98267 .20250 .97928 .21956 .97560 .23656 .97162 .25348 .96734 19 42 .18567 .98261 .20279 .97922 .21985 .97553 .23684 .97155 .25376 .96727 18 43 .18595 .98256 .20307 .97916 .22013 .97547 .23712 .97148 .25404 .96719 17 44 .18624 .98250 .20336 .97910 .22041 .97541 .23740 .97141 .25432 .96712 16 45 .18652 .98245 .20364 .97905 .22070 .97534 .23769 .97134 .25460 .96705 15 46 .18681 .98240 .20393 .97899 .22098 .97528 .23797 .97127 .25488 .96697 14 47 .18710 .98234 .20421 .97893 .22126 .97521 .23825 .97120 .25516 .96690 13 48 .18738 .98229 .20450 .97887 .22155 .97515 .23853 .97113 .25545 .96682 12 49 .18767 .98223 .20478 .97881 .22183 .97508 .23882 .97106 .25573 .96675 11 50 .18795 .98218 .20507 .97875 .22212 .97502 .23910 .97100 .25601 .96667 10 51 .18824 .98212 .20535 .97869 .22240 .97496 .23938 .97093 .25629 .96660 9 52 .18852 .98207 .20563 .97863 .22268 .97489 .23966 .97086 .25657 !96653 8 53 .18881 .98201 .20592 .97857 .22297 .97483 .23995 .97079 .25685 .96645 7 54 .18910 .98196 .20620 .97851 .22325 .97476 .24023 .97072 .25713 .96638 6 55 .18938 .98190 .20649 .97845 .22353 .97470 .24051 .97065 .25741 .96630 5 56 .18967 .98185 .20677 .97839 .22382 .97463 .24079 .97058 .25769 .96623 4 57 .18995 .98179 .20706 .97833 .22410 .97457 .24108 .97051 .25798 .96615 3 59 .19052 .98168 .20763 .97821 .22438 .22467 .97450 .97444 .24136 .24164 .97044 .97037 .25826 .25854 .96600 1 60 .19081 .98163 .20791 .97815 .22495 .97437 .24192 .97030 .25882 .96593 Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine 79 78 o 77 o 76 o 75 D t NATURAL SINES AND COSINES. It > 1( > r JO 1 ; 1< Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine .25882 .96593 .27564 .96126 .29237 .95630 .30902 .95106 .32557 .94552 60 1 .25910 .96585 .27592 .96118 .29265 .95622 .30929 .95097 .32584 .94542 59 2 .25938 .96578 .27620 .96110 .29293 .95613 .30957 .95088 .32612 .94533 58 3 .25966 .96570 .27648 .96102 .29321 .95605 .30985 .95079 .32639 .94523 57 4 .25994 .96562 .27676 .96094 .29348 .95596 .31012 .95070 .32667 .94514 56 5 .26022 .96555 .27704 .96086 .29376 .95588 .31040 .95061 .32694 .94504 55 6 .26050 .96547 .27731 .96078 .29404 .95579 .31068 .95052 .32722 .94495 54 7 .26079 .96540 .27759 .96070 .29432 .95571 .31095 .95043 .32749 .94485 53 8 .26107 .96532 .27787 .96062 .29460 .95562 .31123 .95033 .32777 .94476 52 9 .26135 .96524 .27815 .96054 .29487 .95554 .31151 .95024 .32804 .94466 51 10 .26163 .96517 .27843 .96046 .29515 .95545 .31178 .95015 .32832 .94457 50 11 .26191 .96509 .27871 .96037 .29543 .95536 .31206 .95006 .32859 .94447 49 12 .26219 .96502 .27899 .96029 .29571 .95528 .31233 .94997 .32887 .94438 8 13 .26247 .96494 .27927 .96021 .29599 .95519 .31261 .94988 .32914 .94428 7 14 .26275 .96486 .27955 .96013 .29626 .95511 .31289 .94979 .32942 .94418 6 15 .26303 .96479 .27983 .96005 .29654 .95502 .31316 .94970 .32969 .94409 5 16 .26331 .96471 .28011 .95997 .29682 .95493 .31344 .94961 .32997 .94399 4 17 .26359 .96463 .28039 .95989 .29710 .95485 .31372 .94952 .33024 .94390 3 18 .26387 .96456 .28067 .95981 .29737 .95476 .31399 .94943 .33051 .94380 2 19 .26415 .96448 .28095 .95972 .29765 .95467 .31427 .94933 .33079 .94370 1 20 .26443 .96440 .28123 .95964 .29793 .95459 .31454 .94924 .33106 .94361 21 .26471 .96433 .28150 .95956 .29821 .95450 .31482 .94915 .33134 .94351 39 22 .26500 .96425 .28178 .95948 .29849 .95441 .81510 .94906 .33161 .94342 38 23 .26528 .96417 .28206 .95940 .29876 .95433 .31537 .94897 .33189 .94332 37 24 .26556 .96410 .28234 .95931 .29904 .95424 .31565 .94888 .33216 .94322 36 25 .26584 .96402 .28262 .95923 .29932 .95415 .31593 .94878 .33244 .94313 35 26 .26612 .96394 .28290 .95915 .29960 .95407 .31620 .94869 .33271 .94303 34 27 .26640 .96386 .28318 .95907 .29987 .95398 .31648 .94860 .33298 .94293 33 28 .26668 .96379 .28346 .95898 .30015 .95389 .31675 .94851 .33326 .94284 32 29 .26696 .96371 .28374 .95890 .30043 .95380 .31703 .94842 .33353 .94274 31 30 .26724 .96363 28402 .95882 .30071 .95372 .31730 .94832 .33381 .94264 30 31 .26752 .96355 .28429 .95874 .30098 .95363 .31758 .94823 .33408 .94254 29 32 .26780 .96347 .28457 .95865 .30126 .95354 .31786 .94814 .33436 .94245 28 33 .26808 .96340 .28485 .95857 .30154 .95345 .31813 .94805 .33463 .94235 27 34 .26836 .96332 .28513 .95849 .30182 .95337 .31841 .94795 .33490 .94225 26 35 .26864 .96324 .28541 .95841 .30209 .95328 .31868 .94786 .33518 .94215 25 36 .26892 .96316 .28569 .95832 .30237 .95319 .31896 .94777 .33545 .94206 24 37 .26920 .96308 .28597 .95824 .30265 .95310 .31923 .94768 .33573 .94196 23 38 .26948 .96301 .28625 .95816 .30292 .95301 .31951 .94758 .33600 .94186 22 39 .26976 .96293 .28652 .95807 .30320 .95293 .31979 .94749 .33627 .94176 21 40 .27004 .96285 .28680 .95799 .30348 .95284 .32006 .94740 .33655 .94167 20 41 .27032 .96277 .28708 .95791 .30376 .95275 .32034 .94730 .33682 .94157 19 42 .27060 .96269 .28736 .95782 .30403 .95266 .32061 .94721 .33710 .94147 18 43 .27088 .96261 .28764 .95774 .30431 .95257 .32089 .94712 .33737 .94137 17 44 .27116 .96253 .28792 .95766 .30459 .95248 .32116 .94702 .33764 .94127 16 45 .27144 .96246 .28820 .95757 .30486 .95240 .32144 .94693 .33792 .94118 15 46 .27172 .96238 .28847 .95749 .30514 .95231 .32171 .94684 .33819 .94108 14 47 .27200 .96230 .28875 .95740 .30542 .95222 .32199 .94674 .33846 .94098 13 48 .27228 .96222 .28903 .95732 .30570 .95213 .32227 .94665 .33874 .94088 12 49 .27256 .96214 .28931 .95724 .30597 .95204 .32254 .94656 .33901 .94078 11 50 .27284 .96206 .28959 .95715 .30625 .95195 .32282 .94646 .33929 .94068 10 51 .27312 .96198 .28987 .95707 .30653 .95186 .32309 .94637 .33956 .94058 9 52 .27340 .96190 .29015 .95698 .30680 .95177 .32337 .94627 .33983 .94049 8 53 .27368 .96182 .29042 .95690 .30708 .95168 .32364 .94618 .34011 .94039 7 54 .27396 .96174 .29070 .95681 .30736 .95159 .32392 .94609 .34038 .94029 6 55 .27424 .96166 .29098 .95673 .30763 .95150 .32419 .94599 .34065 .94019 5 56 .27452 .96158 .29126 .95664 .30791 .95142 .32447 .94590 .34093 .94009 4 57 .27480 .96150 .29154 .95656 .30819 .95133 .32474 .94580 .34120 .93999 3 58 .27508 .96142 .29182 .95647 .30846 .95124 .32502 .94571 .34147 .93989 2 59 .27536 .96134 .29209 .95639 .30874 .95115 .32529 .94561 .34175 .93979 1 60 .27564 .96126 .29237 .95630 .30002 .95106 .32557 .94552 .34202 .93969 Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine / 7 40 7 3 7 2 T 1 7C NATURAL SINES AND COSINES. 459 20 21 22 23 24 Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine .34202 .93969 .35837 .93358 .37461 .92718 .39073 .92050 .40674 .91355 60 .34229 .93959 .35864 .93348 .37488 .92707 .39100 .92039 .40700 .91343 59 2 .34257 .93949 .35891 .93337 .37515 .92697 .39127 .92028 .40727 .91331 58 3 .34284 .93939 .35918 .93327 .37542 .92686 .39153 .92016 .40753 .91319 57 4 .34311 .93929 .35945 .93316 .37569 .92675 .39180 .92005 .40780 .91307 56 5 .34339 .93919 .35973 .93306 .37595 .92664 .39207 .91994 .40806 .91295 55 6 .34366 .93909 .36000 .93295 .37622 .92653 .39234 .91982 .40833 .91283 54 7 .34393 .93899 .36027 .93285 .37649 .92642 .39260 .91971 .40860 .91272 53 8 .34421 .93889 .36054 .93274 .37676 .92631 .39287 .91959 .40886 .91260 52 9 .34448 .93879 .36081 .93264 .37703 .92620 .39314 .91948 .40913 .91248 51 10 .34475 .93869 .36108 .93253 .37730 .92609 .39341 .91936 .40939 .91236 50 11 .34503 .93859 .36135 .93243 .37757 .92598 .39367 .91925 .40966 .91224 49 12 .34530 .93849 .36162 .93232 .37784 .92587 .39394 .91914 .40992 .91212 48 13 .34557 .93839 .36190 .93222 .37811 .92576 .39421 .91902 .41019 .91200 47 14 .34584 .93829 .36217 .93211 .37838 .92565 .39448 .91891 .41045 .91188 46 15 .34612 .93819 .36244 .93201 .37865 .92554 .39474 .91879 .41072 .91176 45 16 .34639 .93809 .36271 .93190 .37892 .92543 .39501 .91868 .41098 .91164 44 17 .34666 .93799 .36298 .93180 .37919 .92532 .39528 .91856 .41125 .91152 43 18 .34694 .93789 .36325 .93169 .37946 .92521 .39555 .91845 .41151 .91140 42 19 .34721 .93779 .36352 .93159 .37973 .92510 .39581 .91833 .41178 .91128 41 20 .34748 .93769 .36379 .93148 .37999 .92499 .39608 .91822 .41204 .91116 40 21 .34775 .93759 .36406 .93137 .38026 .92488 .39635 .91810 .41231 .91104 39 22 .34803 .93748 .36434 .93127 .38053 .92477 .39661 .91799 .41257 .91092 38 23 .34830 .93738 .36461 .93116 .38080 .92466 .39688 .91787 .41284 .91080 37 24 .34857 .93728 .36488 .93106 .38107 .92455 .39715 .91775 .41310 .91068 36 25 .34884 .93718 .36515 .93095 .38134 .92444 .39741 . .91764 .41337 .91056 35 26 .34912 .93708 .36542 .93084 .38161 .92432 .39768 .91752 .41363 .91044 34 27 .34939 .93698 .36569 .93074 .38188 .92421 .39795 .91741 .41390 .91032 33 28 .34966 .93688 .36596 .93063 .38215 .92410 .39822 .91729 .41416 .91020 32 29 .34993 .93677 .36623 .93052 .38241 .92399 .39848 .91718 .41443 .91008 31 30 .35021 .93667 .36650 .93042 .38268 .92388 .39875 .91706 .41469 .90996 30 31 .35048 .93657 .36677 .93031 .38295 .92377 .39902 .91694 .41496 .90984 29 32 .35075 .93647 .36704 .93020 .38322 .92366 .39928 .91683 .41522 .90972 28 33 .35102 .93637 .36731 .93010 .38349 .92355 .39955 .91671 .41549 .90960 27 34 .35130 .93626 .36758 .92999 .38376 .92343 .39982 .91660 .41575 .90948 26 35 .35157 .93616 .36785 .92988 .38403 .92332 .40008 .91648 .41602 .90936 25 36 .35184 .93606 .36812 .92978 .38430 .92321 .40035 .91636 .41628 .90924 24 37 .35211 .93596 .36839 .92967 .38456 .92310 .40062 .91625 .41655 .90911 23 38 .35239 .93585 .36867 .92956 .38483 .92299 .40088 .91613 .41681 .90899 22 39 .35266 .93575 .36894 .92945 .38510 .92287 .40115 .91601 .41707 .90887 21 40 .35293 .93565 .36921 .92935 .38537 .92276 .40141 .91590 .41734 .90875 20 41 .35320 .93555 .36948 .92924 .38564 .92265 .40168 .91578 .41760 .90863 19 42 .35347 .93544 .36975 .92913 .38591 .92254 .40195 .91566 .41787 .90851 18 43 .35375 .93534 .37002 .92902 .38617 .92243 .40221 .91555 .41813 .90839 17 44 .35402 .93524 .37029 .92892 .38644 .92231 .40248 .91543 .41840 .90826 16 45 .35429 .93514 .37056 .92881 .38671 .92220 .40275 .91531 .41866 .90814 15 46 .35456 .93502 .37083 .92870 .38698 .92209 .40301 .91519 .41892 .90802 14 47 .35484 .93493 .37110 .92859 .38725 .92198 .40328 .91508 .41919 .90790 13 48 .35511 .93483 .37137 .92849 .38752 .92186 .40355 .91496 .41945 .90778 12 49 .35538 .93472 .37164 .92838 .38778 .92175 .40381 .91484 .41972 .90766 11 50 .35565 .93462 .37191 .92827 .38805 .92164 .40408 .91472 .41998 .90753 10 51 .35592 .93452 .37218 .92816 .38832 .92152 .40434 .91461 .42024 .90741 9 52 .35619 .93441 .37245 .92805 .38859 .92141 .40461 .91449 .42051 .90729 8 53 .35647 .93431 .37272 .92794 .38886 .92130 .40488 .91437 .42077 .90717 7 54 .35674 .93420 .37299 .92784 .38912 .92119 .40514 .91425 .42104 .90704 6 55 .35701 .93410 .37326 .92773 .38939 .92107 .40541 .91414 .42130 .90692 5 56 .35728 .93400 .37353 .92762 .38966 .92096 .40567 .91402 .42156 .90680 4 57 .35755 .93389 .37380 .92751 .38993 .92085 .40594 .91390 .42183 .90668 3 58 .35782 .93379 .37407 .92740 .39020 .92073 .40621 .91378 .42209 .90655 2 59 .35810 .93368 .37434 .92729 .39046 .92062 .40647 .91366 .42235 .90643 1 60 .35837 .93358 .37461 .92718 .39073 .92050 .40674 .91355 .42262 .90631 Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine / 69 68 67 66 65 460 NATURAL SIXES AND COSINES. 2 5 2 6 2 7 2 H 2 9 Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine .42262 .90631 .43837 .89879 .45399 .89101 .46947 .88295 .48481 .87462 60 1 .42288 .90618 .43863 .89867 .45425 .89087 .46973 .88281 .48506 .87448 59 2 .42315 .90606 .43889 .89854 .45451 .89074 .46999 .88267 .48532 .87434 58 3 .42341 .90594 .43916 .89841 .45477 .89061 .47024 .88254 .48557 .87420 57 4 .42367 .90582 .43942 .89828 .45503 .89048 .47050 .88240 .48583 .87406 56 5 .42394 .90569 .43968 .89816 .45529 .89035 .47076 .88226 .48608 .87391 55 6 .42420 .90557 .43994 .89803 .45554 .89021 .47101 .88213 .48634 .87377 54 7 .42446 .90545 .44020 .89790 .45580 .89008 .47127 .88199 .48659 .87363 53 8 .42473 .90532 .44046 .89777 .45606 .88995 .47153 .88185 .48684 .87349 52 9 .42499 .90520 .44072 .89764 .45632 .88981 .47178 .88172 .48710 .87335 51 10 .42525 .90507 .44098 .89752 .45658 .88968 .47204 .88158 .48735 .87321 50 11 .42552 .90495 .44124 .89739 .45684 .88955 .47229 .88144 .48761 .87306 49 12 .42578 .90483 .44151 .89726 .45710 .88942 .47255 .88130 .48786 .87292 48 13 .42604 .90470 .44177 .89713 .45736 .88928 .47281 .88117 .48811 .87278 47 14 .42631 .90458 .44203 .89700 .45762 .88915 .47306 .88103 .48837 .87264 46 15 .42657 .90446 .44229 .89687 .45787 .88902 .47332 .88089 .48862 .87250 45 16 .42683 .90433 .44255 .89674 .45813 .88888 .47358 .88075 .48888 .87235 44 17 .42709 .90421 .44281 .89662 .45839 .88875 .47383 .88062 .48913 .87221 43 18 .42736 .90408 .44307 .89649 .45865 .88862 .47409 .88048 .48938 .87207 42 19 .42762 .90396 .44333 .89636 .45891 .88848 .47434 .88034 .48964 .87193 41 20 .42788 .90383 .44359 .89623 .45917 .88835 .47460 .88020 .48989 .87178 40 21 .42815 .90371 .44385 .89610 .45942 .88822 .47486 .88006 .49014 .87164 39 22 .42841 .90358 .44411 .89597 .45968 .88808 .47511 .87993 .49040 .87150 38 23 .42867 .90346 .44437 .89584 .45994 .88795 .47537 .87979 .49065 .87136 37 24 .42894 .90334 .44464 .89571 .46020 .88782 .47562 .87965 .49090 .87121 36 25 .42920 .90321 .44490 .89558 .46046 .88768 .47588 .87951 .49116 .87107 35 26 .42946 .90309 .44516 .89545 .46072 .88755 .47614 .87937 .49141 .87093 34 27 .42972 .90296 .44542 .89532 .46097 .88741 .47639 .87923 .49166 .87079 33 28 .42999 .90284 .44568 .89519 .46123 .88728 .47665 .87909 .49192 .87064 32 29 .43025 .90271 .44594 .89506 .46149 .88715 .47690 .87896 .49217 .87050 31 30 .43051 .90259 .44620 .89493 .46175 .88701 .47716 .87882 .49242 .87036 30 31 .43077 .90246 .44646 .89480 .46201 .88688 .47741 .87868 .49268 .87021 29 32 .43104 .90233 .44672 .89467 .46226 .88674 .47767 .87854 .49293 .87007 28 33 .43130 .90221 .44698 .89454 .46252 .88661 .47793 .87840 .49318 .86993 27 34 .43156 .90208 .44724 .89441 .46278 .88647 .47818 .87826 .49344 .86978 26 35 .43182 .90196 .44750 .89428 .46304 .88634 .47844 .87812 .49369 .86964 25 36 .43209 .90183 .44776 .89415 .46330 .88620 .47869 .87798 .49394 .86949 24 37 .43235 .90171 .44802 .89402 .46355 .88607 .47895 .87784 .49419 .86935 23 38 .43261 .90158 .44828 .89389 .46381 .88593 .47920 .87770 .49445 .86921 22 39 .43287 .90146 .44854 .89376 .46407 .88580 .47946 .87756 .49470 .86906 21 40 .43313 .90133 .44880 .89363 .46433 .88566 .47971 .87743 .49495 .86892 20 1 .43340 .90120 .44906 .89350 .46458 .88553 .47997 .87729 .49521 .86878 19 2 .43366 .90108 .44932 .89337 .46484 .88539 .48022 .87715 .49546 .86863 18 3 .43392 .90095 .44958 .89324 .46510 .88526 .48048 .87701 .49571 .86849 17 4 .43418 .90082 .44984 .89311 .46536 .88512 .48073 .87687 .49596 .86834 16 5 .43445 .90070 .45010 .89298 .46561 .88499 .48099 .87673 .49622 .86820 15 6 .43471 .90057 .45036 .89285 .46587 .88485 .48124 .87659 .49647 .86805 14 7 .43497 .90045 .45062 .89272 .46613 .88472 .48150 .87645 .49672 .86791 13 8 .43523 .90032 .45088 .89259 .46639 .88458 .48175 .87631 .49697 .86777 12 49 .43549 .90019 .45114 .89245 .46664 .88445 .48201 .87617 .49723 .86762 11 50 .43575 .90007 .45140 .89232 .46690 .88431 .48226 .87603 .49748 .86748 10 51 .43602 .89994 .45166 .89219 .46716 .88417 .48252 .87589 .49773 .86733 9 52 .43628 .89981 .45192 .89206 .46742 .88404 .48277 .87575 .49798 .86719 8 54 '.43680 ^89956 !45243 ^89180 .46767 .46793 .88390 .88377 J8328 .87546 .49849 .86690 6 55 .43706 .89943 .45269 .89167 .46819 .88363 .48354 .87532 .49874 .86675 5 56 .43733 .89930 .45295 .89153 .46844 .88349 .48379 .87518 .49899 .86661 4 57 .43759 .89918 .45321 .89140 .46870 .88336 .48405 .87504 .49924 .86646 3 58 .43785 .89905 .45347 .89127 .46896 .88322 .48430 .87490 .49950 .86632 2 59 .43811 .89892 .45373 .89114 .46921 .88308 .48456 .87476 .49975 .86617 1 60 .43837 .89879 .45399 .89101 .46947 .88295 .48481 .87462 .50000 .86603 Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine f 64 63 o 62 o 61 o 60 D / NATURAL SINES AND COSINES. 461 3( ) 3 L V )0 3 30 3- 1 / Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine | .50000 .86603 .51504 .85717 .52992 .84805 .54464 .83867 .55919 .82904 60 1 .50025 .86588 .51529 .85702 .53017 .84789 .54488 .83851 .55943 .82887 59 2 .50050 .86573 .51554 .85687 .53041 .84774 .54513 .83835 .55968 .82871 58 3 .50076 .86559 .51579 .85672 .53066 .84759 .54537 .83819 .55992 .82855 57 4 .50101 .86544 .51604 .85657 .53091 .84743 .54561 .83804 .56016 .82839 56 5 .50126 .86530 .51628 .85642 .53115 .84728 .54586 .83788 .56040 .82822 55 6 .50151 .86515 .51653 .85627 .53140 .84712 .54610 .83772 .56064 .82806 54 7 .50176 .86501 .51678 .85612 .53164 .84697 .54635 .83756 .56088 .82790 53 8 .50201 .86486 .51703 .85597 .53189 .84681 .54659 .83740 .56112 .82773 52 9 .50227 .86471 .51728 .85582 .53214 .84666 .54683 .83724 .56136 .82757 51 10 .50252 .86457 .51753 .85567 .53238 .84650 .54708 .83708 .56160 .82741 50 11 .50277 .86442 .51778 .85551 .53263 .84635 .54732 .83692 .56184 .82724 49 12 .50302 .86427 .51803 .85536 .53288 .84619 .54756 .83676 .56208 .82708 8 13 .50327 .86413 .51828 .85521 .53312 .84604 .54781 .83660 .56232 .82692 14 .50352 .86398 .51852 .85506 .53337 .84588 .54805 .83645 .56256 .82675 6 15 .50377 .86384 .51877 .85491 .53361 .84573 .54829 .83629 .56280 .82659 5 16 .50403 .86369 .51902 .85476 .53386 .84557 .54854 .83613 .56305 .82643 4 17 .50428 .86354 .51927 .85461 .53411 .84542 .54878 .83597 .56329 .82626 3 18 .50453 .86340 .51952 .85446 .53435 .84526 .54902 .83581 .56353 .82610 2 19 .50478 .86325 .51977 .85431 .53460 .84511 .54927 .83565 .56377 .82593 1 20 .50503 .86310 .52002 .85416 .53484 .84495 .54951 .83549 .56401 .82577 40 21 .50528 .86295 .52026 .85401 .53509 .84480 .54975 .83533 .56425 .82561 39- 22 .50553 .86281 .52051 .85385 .53534 .84464 .54999 .83517 .56449 .82544 38 23 .50578 .86266 .52076 .85370 .53558 .84448 .55024 .83501 .56473 .82528 37 24 .50603 .86251 .52101 .85355 .53583 .84433 .55048 .83485 .56497 .82511 36 25 .50628 .86237 .52126 .85340 .53607 .84417 .55072 .83469 .56521 .82495 35 26 .50654 .86222 .52151 .85325 .53632 .84402 .55097 .83453 .56545 .82478 34 27 .50679 .86207 .52175 .85310 .53656 .84386 .55121 .83437 .56569 .82462 33 28 .50704 .86192 .52200 .85294 .53681 .84370 .55145 .83421 .56593 .82446 32 29 .50729 .86178 .52225 .85279 .53705 .84355 .55169 .83405 .56617 .82429 31 30 .50754 .86163 .52250 .85264 .53730 .84339 .55194 .83389 .56641 .82413 30 31 .50779 .86148 .52275 .85249 .53754 .84324 .55218 .83373 .56665 .82396 29 32 .50804 .86133 .52299 .85234 .53779 .84308 .55242 .83356 .56689 .82380 28 33 .50829 .86119 .52324 .85218 .53804 .84292 .55266 .83340 .56713 .82363 27 34 .50854 .86104 .52349 .85203 .53828 .84277 .55291 .83324 .56736 .82347 26 35 .50879 .86089 .52374 .85188 .53853 .84261 .55315 .83308 .56760 .82330 25 36 .50904 .86074 .52399 .85173 .53877 .84245 .55339 .83292 .56784 .82314 24 37 .50929 .86059 .52423 .85157 .53902 .84230 .55363 .83276 .56808 .82297 23 38 .50954 .86045 .52448 .85142 .53926 .84214 .55388 .83260 .56832 .82281 22 39 .50979 .86030 .52473 .85127 .53951 .84198 .55412 .83244 .56856 .82264 21 40 .51004 .86015 .52498 .85112 .53975 .84182 .55436 .83228 .56880 .82248 20 41 .51029 .86000 .52522 .85096 .54000 .84167 .55460 .83212 .56904 .82231 19 42 .51054 .85985 .52547 !85081 .54024 .84151 .55484 .83195 .56928 .82214 18 43 .51079 .85970 .52572 .85066 .54049 .84135 .55509 .83179 .56952 .82198 17 44 .51104 .85956 .52597 .85051 .54073 .84120 .55533 .83163 .56976 .82181 16 45 .51129 .85941 .52621 .85035 .54097 .84104 .55557 .83147 .57000 .82165 15 46 .51154 .85926 .52646 .85020 .54122 .84088 .55581 .83131 .57024 .82148 14 47 .51179 .85911 .52671 .85005 .54146 .84072 .55605 .83115 .57047 .82132 13 48 .51204 .85896 .52696 .84989 .54171 .84057 .55630 .83098 .57071 .82115 12 49 .51229 .85881 .52720 .84974 .54195 .84041 .55654 .83082 .57095 .82098 11 50 .51254 .85866 .52745 .84959 .54220 .84025 .55678 .83066 .57119 .82082 10 51 .51279 .85851 .52770 .84943 .54244 .84009 .55702 .83050 .57143 .82065 9 52 .51304 .85836 .52794 .84928 .54269 .83994 .55726 .83034 .57167 .82048 8 53 .51329 .85821 .52819 .84913 .54293 .83978 .55750 .83017 .57191 .82032 7 54 .51354 .85806 .52844 .84897 .54317 .83962 .55775 .83001 .57215 .82015 6 55 .51379 .85792 .52869 .84882 .54342 .83946 .55799 .82985 .57238 .81999 5 56 .51404 .85777 .52893 .84866 .54366 .83930 .55823 .82969 .57262 .81982 4 57 .51429 .85762 .52918 .84851 .54391 .83915 .55847 .82953 .57286 .81965 3 58 .51454 .85747 .52943 .84836 .54415 .83899 .55871 .82936 .57310 .81949 2 59 .51479 .85732 .52967 .84820 .54440 .83883 .55895 .82920 .57334 .81932 1 60 .51504 .85717 .52992 .84805 .54464 .83867 .55919 .82904 .57358 .81915 Cosine Siue Cosine Sine Cosine Sine Cosine Sine Cosine Sine 5 o & * 57 o 5( > 5 462 NATURAL SINES AND COSINES. 1 35 36 37 38 39 Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine .57358 .81915 .58779 .80902 .60182 .79864 .61566 .78801 .62932 .77715 60 1 .57381 .81899 .58802 .80885 .60205 .79846 .61589 .78783 .62955 .77696 59 2 .57405 .81882 .58826 .80867 .60228 .79829 .61612 .78765 .62977 .77678 58 3 .57429 .81865 .58849 .80850 .60251 .79811 .61635 .78747 .63000 .77660 57 4 .57453 .81848 .58873 .80833 .60274 .79793 .61658 .78729 .63022 .77641 56 5 .57477 .81832 .58896 .80816 .60298 .79776 .61681 .78711 .63045 .77623 55 6 .57501 .81815 .58920 .80799 .60321 .79758 .61704 .78694 .63068 .77605 54 7 .57524 .81798 .58943 .80782 .60344 .79741 .61726 .78676 .63090 .77586 53 8 .57548 .81782 .58967 .80765 .60367 .79723 .61749 .78658 .63113 .77568 52 9 .57572 .81765 .58990 .80748 .60390 .79706 .61772 .78640 .63135 .77550 51 10 .57596 .81748 .59014 .80730 .60414 .79688 .61795 .78622 .63158 .77531 50 11 .57619 .81731 .59037 .80713 .60437 .79671 .61818 .78604 .63180 .77513 49 12 .57643 .81714 .59061 .80696 .60460 .79653 .61841 .78586 .63203 .77494 48 13 .57667 .81698 .59084 .80679 .60483 .79635 .61864 .78568 .63225 .77476 47 14 .57691 .81681 .59108 .80662 .60506 .79618 .61887 .78550 .63248 .77458 46 15 .57715 .81664 .59131 .80644 .60529 .79600 .61909 .78532 .63271 .77439 45 16 .57738 .81647 .59154 .80627 .60553 .79583 .61932 .78514 .63293 .77421 44 17 .57762 .81631 .59178 .80610 .60576 .79565 .61955 .78496 .63316 .77402 43 18 .57786 .81614 .59201 .80593 .60599 .79547 .61978 .78478 .63338 .77384 42 19 .57810 .81597 .59225 .80576 .60622 .79530 .62001 .78460 .63361 .77366 41 20 .57833 .81580 .59248 .80558 .60645 .79512 .62024 .78442 .63383 .77347 40 21 .57857 .81563 .59272 .80541 .60668 .79494 .62046 .78424 .63406 .77329 39 22 .57881 .81546 .59295 .80524 .60691 .79477 .62069 .78405 .63428 .77310 38 23 .57904 .81530 .59318 .80507 .60714 .79459 .62092 .78387 .63451 .77292 37 24 .57928 .81513 .59342 .80489 .60738 .79441 .62115 .78369 .63473 .77273 36 25 .57952 .81496 .59365 .80472 .60761 .79424 .62138 .78351 .63496 .77255 35 26 .57976 .81479 .59389 .80455 .60784 .79406 .62160 .78333 .63518 .77236 34 27 .57999 .81462 .59412 .80438 .60807 .79388 .62183 .78315 .63540 .77218 33 28 .58023 .81445 .59436 .80420 .60830 .79371 .62206 .78297 .63563 .77199 32 29 .58047 .81428 .59459 .80403 .60853 .79353 .62229 .78279 .63585 .77181 31 30 .58070 .81412 .59482 .80386 .60876 .79335 .62251 .78261 .63608 .77162 30 31 .58094 .81395 .59506 .80368 .60899 .79318 .62274 .78243 .63630 .77144* 29 32 .58118 .81378 .59529 .80351 .60922 .79300 .62297 .78225 .63653 .77125 28 33 .58141 .81361 .59552 .80334 .60945 .79282 .62320 .78206 .63675 .77107 27 34 .58165 .81344 .59576 .80316 .60968 .79264 .62342 .78188 .63698 .77088 26 35 .58189 .81327 .59599 .80299 .60991 .79247 .62365 .78170 .63720 .77070 25 36 .58212 .81310 .59622 .80282 .61015 .79229 .62388 .78152 .63742 .77051 24 37 .58236 .81293 .59646 .80264 .61038 .79211 .62411 .78134 .63765 .77033 23 38 .58260 .81276 .59669 .80247 .61061 .79193 .62433 .78116 .63787 .77014 22 39 .58283 .81259 .59693 .80230 .61084 .79176 .62456 .78098 .63810 .76996 21 40 .58307 .81242 .59716 .80212 .61107 .79158 .62479 .78079 .63832 .76977 20 41 .58330 .81225 .59739 .80195 .61130 .79140 .62502 .78061 .63854 .76959 19 42 .58354 .81208 .59763 .80178 .61153 .79122 .62524 .78043 .63877 .76940 18 43 .58378 .81191 .59786 .80160 .61176 .79105 .62547 .78025 .63899 .76921 17 44 .58401 .81174 .59809 .80143 .61199 .79087 .62570 .78007 .63922 .76903 16 45 .58425 .81157 .59832 .80125 .61222 .79069 .62592 .77988 .63944 .76884 15 46 .58449 .81140 .59856 .80108 .61245 .79051 .62615 .77970 .63966 .76866 14 47 .58472 .81123 .59879 .80091 .61268 .79033 .62638 .77952 .63989 .76847 13 48 .58496 .81106 .59902 .80073 .61291 .79016 .62660 .77934 .64011 .76828 12 49 .58519 .81089 .59926 .80056 .61314 .78998 .62683 .77916 .64033 .76810 11 50 .58543 .81072 .59949 .80038 .61337 .78980 .62706 .77897 .64056 .76791 10 51 .58567 .81055 .59972 .80021 .61360 .78962 .62728 .77879 .64078 .76772 9 52 .58590 .81038 .59995 .80003 .61383 .78944 .62751 .77861 .64100 .76754 8 53 .58614 .81021 .60019 .79986 .61406 .78926 .62774 .77843 .64123 .76735 7 54 .58637 .81004 .60042 .79968 .61429 .78908 .62796 .77824 .64145 .76717 6 55 .58661 .80978 .60065 .79951 .61451 .78891 .62819 .77806 .64167 .76698 5 56 .58684 .80970 .60089 .79934 .61474 .78873 .62842 .77788 .64190 .76679 4 57 .58708 .80953 .60112 .79916 .61497 .78855 .62864 .77769 .64212 .76661 3 58 .58731 .80936 .60135 .79899 .61520 .78837 .62887 .77751 .64234 .76642 2 59 .58755 .80919 .60158 .79881 .61543 .78819 .62909 .77733 .64256 .76623 60 .58779 .80902 .60182 .79864 .61566 .78801 .62932 .77715 .64279 .76604 Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine 54 53 52 51 50 NATURAL SINES AND COSINES. 4( ) 4] o )0 & 5 44 Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine .64279 .76604 .65606 .75471 .66913 .74314 .68200 .73135 .69466 .71934 60 1 .64301 .76586 .65628 .75452 .66935 .74295 .68221 .73116 .69487 .71914 59 2 .64323 .76567 .65650 .75433 .66956 .74276 .68242 .73096 .69508 .71894 58 3 .64346 .76548 .65672 .75414 .66978 .74256 .68264 .73076 .69529 .71873 57 4 .64368 .76530 .65694 .75395 .66999 .74237 .68285 .73056 .69549 .71853 56 5 .64390 .76511 .65716 .75375 .67021 .74217 .68306 .73036 .69570 .71833 55 6 .64412 .76492 .65738 .75356 .67043 .74198 .68327 .73016 .69591 .71813 54 .64435 .76473 .65759 .75337 .67064 .74178 .68349 .72996 .69612 .71792 53 8 .64457 .76455 .65781 .75318 .67086 .74159 .68370 .72976 .69633 .71772 52 9 .64479 .76436 .65803 .75299 .67107 .74139 .68391 .72957 .69654 .71752 51 10 .64501 .76417 .65825 .75280 .67129 .74120 .68412 .72937 .69675 .71732 50 11 .64524 .76398 .65847 .75261 .67151 .74100 .68434 .72917 .69696 .71711 49 12 .64546 .76380 .65869 .75241 .67172 .74080 .68455 .72897 .69717 .71691 48 13 .64568 .76361 .65891 .75222 .67194 .74061 .68476 .72877 .69737 .71671 47 14 .64590 .76342 .65913 .75203 .67215 .74041 .68497 .72857 .69758 .71650 46 15 .64612 .76323 .65935 .75184 .67237 .74022 .68518 .72837 .69779 .71630 45 16 .64635 .76304 .65956 .75165 .67258 .74002 .68539 .72817 .69800 .71610 44 17 .64657 .76286 .65978 .75146 .67280 .73983 .68561 .72797 .69821 .71590 43 18 .64679 .76267 .66000 .75126 .67301 .73963 .68582 .72777 .69842 .71569 42 19 .64701 .76248 .66022 .75107 .67323 .73944 .68603 .72757 .69862 .71549 41 20 .64723 .76229 .66044 .75088 .67344 .73924 .68624 .72737 .69883 .71529 40 21 .64746 .76210 .66066 .75069 .67366 .73904 .68645 .72717 .69904 .71508 39 22 .64768 .76192 .66088 .75050 .67387 .73885 .68666 .72697 .69925 .71488 38 23 .64790 .76173 .66109 .75030 .67409 .73865 .68688 .72677 .69946 .71468 37 24 .64812 .76154 .66131 .75011 .67430 .73846 .68709 .72657 .69966 .71447 36 25 .64834 .76135 .66153 .74992 .67452 .73826 .68730 .72637 .69987 .71427 35 26 .64856 .76116 .66175 .74973 .67473 .73806 .68751 .72617 .70008 .71407 34 27 .64878 .76097 .66197 .74953 .67495 .73787 .68772 .72597 .70029 .71386 33 28 .64901 .76078 .66218 .74934 .67516 .73767 .68793 .7*2577 .70049 .71366 32 29 .64923 .76059 .66240 .74915 .67538 .73747 .68814 .72557 .70070 .71345 31 30 .64945 .76041 .66262 .74896 .67559 .73728 .68835 .72537 .70091 .71325 30 31 .64967 .76022 .66284 .74876 .67580 .73708 .68857 .72517 .70112 .71305 29 .64989 .76003 .66306 .74857 .67602 .73688 .68878 .72497 .70132 .71284 28 33 .65011 .75984 .66327 .74838 .67623 .73669 .68899 .72477 .70153 .71264 27 34 .65033 .75965 .66349 .74818 .67645 .73649 .68920 .72457 .70174 .71243 26 35 .65055 .75946 .66371 .74799 .67666 .73629 .68941 .72437 .70195 .71223 25 36 .65077 .75927 .66393 .74780 .67688 .73610 .68962 .72417 .70215 .71203 24 37 .65100 .75908 .66414 .74760 .67709 .73590 .68983 .72397 .70236 .71182 23 '38 .65122 .75889 .66436 .74741 .67730 .73570 .69004 .72377 .70257 .71162 22 39 .65144 .75870 .66458 .74722 .67752 .73551 .69025 .72357 .70277 .71141 21 40 .65166 .75851 .66480 .74703 .67773 .73531 .69046 .72337 .70298 .71121 20 1 .65188 .75832 .66501 .74683 .67795 .73511 .69067 .72317 .70319 .71100 19 2 .65210 .75813 .66523 .74664 .67816 .73491 .69088 .72297 .70339 .71080 18 3 .65232 .75794 .66545 .74644 .67837 .73472 .69109 .72277 .70360 .71059 17 4 .65254 .75775 .66566 .74625 .67859 .73452 .69130 .72257 .70381 .71039 16 .65276 .75756 .66588 .74606 .67880 .73432 .69151 .72236 .70401 .71019 15 6 .65298 .75738 .66610 .74586 .67901 .73413 .69172 .72216 .70422 .70998 14 7 .65320 .75719 .66632 .74567 .67923 .73393 .69193 .72196 .70443 .70978 13 8 .65342 .75700 .66653 .74548 .67944 .73373 .69214 .72176 .70463 .70957 12 9 .65364 .75680 .66675 .74528 .67965 .73353 .69235 .72156 .70484 .70937 11 50 .65386 .75661 .66697 .74509 .67987 .73333 .69256 .72136 .70505 .70916 10 51 .65408 .75642 .66718 .74489 .68008 .73314 .69277 .72116 .70525 .70896 9 52 .65430 .75623 .66740 .74470 .68029 .73294 .69298 .72095 .70546 .70875 8 53 .65452 .75604 .66762 .74451 .68051 .73274 .69319 .72075 .70567 .70855 7 54 .65474 .75585 .66783 .74431 .68072 .73254 .69340 .72055 .70587 .70834 6 55 .65496 .75566 .66805 .74412 .68093 .73234 .69361 .72035 .70608 .70813 5 56 .65518 .75547 .66827 .74392 .68115 .73215 .69382 .72015 .70628 .70793 4 57 .65540 .75528 .66848 .74373 .68136 .73195 .69403 .71995 .70649 .70772 3 58 .65562 .75509 .66870 .74353 .68157 .73175 .69424 .71974 .70670 .70752 2 59 .65584 .75490 .66891 .74334 .68179 .73155 .69445 .71954 .70690 .70731 1 60 .65606 .75471 .66913 .74314 .68200 .73135 .69466 .71934 .70711 .70711 Cosine Sine Cosine Sine Cosine Sine Cosine Sine Cosine Sine 4 3 4J JP 4 1 4 5 4[ ) NATURAL TANGENTS AND COTANGENTS. 3 1 3 2 3 3 D 4 Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang .00000 Infln. .01746 57.2900 .03492 28.6363 .05241 19.0811 .06993 14.3007 60 1 .00029 3437.75 .01775 56.3506 .03521 28.3994 .05270 18.9755 .07022 14.2411 59 2 .00058 1718.87 .01804 55.4415 .03550 28.1664 .05299 18.8711 .07051 14.1821 58 3 .00087 1145.92 .01833 54.5613 .03579 27.9372 .05328 18.7678 .07080 14.1235 57 4 .00116 859.436 .01862 53.7086 .03609 27.7117 .05357 18.6656 .07110 14.0655 56 5 .00145 687.549 .01891 52.8821 .03638 27.4899 .05387 18.5645 .07139 14.0079 55 6 .00175 572.957 .01920 52.0807 .03667 27.2715 .05416 18.4645 .07168 13.9507 54 7' .00204 491.106 .01949 51.3032 .03696 27.0566 .05445 18.3655 .07197 13.8940 53 8 .00233 429.718 .01978 50.5485 .03725 26.8450 .05474 18.2677 .07227 13.8378 52 9 .00262 381.971 .02007 49.8157 .03754 26.6367 .05503 18.1708 .07256 13.7821 51 10 .00291 343.774 .02036 49.1039 .03783 26.4316 .05533 18.0750 .07285 13.7267 50 11 .00320 312.521 .02066 48.4121 .03812 26.2296 .05562 17.9802 .07314 13.6719 49 12 .00349 286.478 .02095 47.7395 .03842 26.0307 .05591 17.8863 .07344 13.6174 8 13 .00378 264.441 .02124 47.0853 .03871 25.8348 .05620 17.7934 .07373 13.5634 7 14 .00407 245.552 .02153 46.4489 .03900 25.6418 .05649 17.7015 .07402 13.5098 6 15 .00436 229.182 .02182 45.8294 .03929 25.4517 .05678 17.6106 .07431 13.4566 5 16 .00465 214.858 .02211 45.2261 .03958 25.2644 .05708 17.5205 .07461 13.4039 4 17 .00495 202.219 .02240 44.6386 .03987 25.0798 .05737 17.4314 .07490 13.3515 3 18 .00524 190.984 .02269 44.0661 .04016 24.8978 .05766 17.3432 .07519 13.2996 I 19 .00553 180.932 .02298 43.5081 .04046 24.7185 .05795 17.2558 .07548 13.2480 1 20 .00582 171.885 .02328 42.9641 .04075 24.5418 .05824 17.1693 .07578 13.1969 40 21 .00611 163.700 .02357 42.4335 .04104 24.3675 .05854 17.0837 .07607 13.1461 39 22 .00640 156.259 .02386 41.9158 .04133 24.1957 .05883 16.9990 .07636 13.0958 38 23 .00669 149.465 .02415 41.4106 .04162 24.0263 .05912 16.9150 .07665 13.0458 37 24 .00698 143.237 .02444 40.9174 .04191 23.8593 .05941 16.8319 .07695 12.9962 36 25 .00727 137.507 .02473 40.4358 .04220 23.6945 .05970 16.7496 .07724 12.9469 35 26 .00756 132.219 .02502 39.9655 .04250 23.5321 .05999 16.6681 .07753 12.8981 34 27 .00785 127.321 .02531 39.5059 .04279 23.3718 .06029 16.5874 .07782 12.8496 33 28 .00815 122.774 .025*60 39.0568 .04308 23.2137 .06058 16.5075 .07812 12.8014 32 29 .00844 118.540 .02589 38.6177 .04337 23.0577 .06087 16.4283 .07841 12.7536 31 30 .00873 114.589 .02619 38.1885 .04366 22.9038 .06116 16.3499 .07870 J2.7062 30 31 .00902 110.892 .02648 37.7686 .04395 22.7519 .06145 16.2722 .07899 12.6591 29 32 .00931 107.426 .02677 37.3579 .04424 22.6020 .06175 16.1952 .07929 12.6124 28 33 .00960 104.171 .02706 36.9560 .04454 22.4541 .06204 16.1190 .07958 12.5660 27 34 .00989 101.107 .02735 36.5627 .04483 22.3081 .06233 16.0435 .07987 12.5199 26 35 .01018 98.2179 .02764 36.1776 .04512 22.1640 .06262 15.9687 .08017 12.4742 25 36 .01047 95.4895 .02793 35.8006 .04541 22.0217 .06291 15.8945 .08046 12.4288 24 37 .01076 92.9085 .02822 35.4313 .04570 21.8813 .06321 15.8211 .08075 12.3838 23 38 .01105 90.4633 .02851 35.0695 .04599 21.7426 .06350 15.7483 .08104 12.3390 22 39 .01135 88.1436 .02881 34.7151 .04628 21.6056 .06379 15.6762 .08134 12.2946 21 40 .01164 85.9398 .02910 34.3678 .04658 21.4704 .06408 15.6048 .08163 12.2505 20 41 .01193 83.8*35 .02939 34.0273 .04687 21.3369 .06437 15.5340 .08192 12.2067 19 42 .01222 81.8470 .02968 33.6935 .04716 21.2049 .06467 15.4638 .08221 12.1632 18 43 .01251 79.9434 .02997 33.3662 .04745 21.0747 .06496 15.3943 .08251 12.1201 17 44 .01280 78.1263 .03026 33.0452 .04774 20.9460 .06525 15.3254 .08280 12.0772 16 45 .01309 76.3900 .03055 32.7303 .04803 20.8188 .06554 15.2571 .08309 12.0346 15 46 .01338 74.7292 .03084 32.4213 .04833 20.6932 .06584 15.1893 .08339 11.9923 14 47 .01367 73.1390 .03114 32.1181 .04862 20.5691 .06613 15.1222 .08368 11.9504 13 48 .01396 71.6151 .03143 31.8205 .04891 20.4465 .06642 15.0557 .08397 11.9087 12 49 .01425 70.1533 .03172 31.5284 .04920 20.3253 .06671 14.9898 .08427 11.8673 11 50 .01455 68.7501 .03201 31.2416 .04949 20.2056 .06700 14.9244 .08456 11.8262 10 51 .01484 67.4019 .03230 30.9599 .04978 20-.0872 .06730 14.8596 .08485 11.7853 9 52 .01513 66.1055 .03259 30.6833 .05007 19.9702 .06759 14.7954 .08514 11.7448 8 53 .01542 64.8580 .03288 30.4116 .05037 19.8546 .06788 14.7317 .08544 11.7045 7 54 .01571 63.6567 .03317 30.1446 .05066 19.7403 .06817 14.6685 .08573 11.6645 6 55 .01600 62.4992 .03346 29.8823 .05095 19.6273 .06847 14.6059 .08602 11.6248 5 56 .01629 61.3829 .03376 29.6245 .05124 19.5156 .06876 14.5438 .08632 11.5853 4 57 .01658 60.3058 .03405 29.3711 .05153 19.4051 .06905 14.4823 .08661 11.5461 3 58 .01687 59.2659 .03434 29.1220 .05182 19.2959 .06934 14.4212 .08690 11.5072 2 59 .01716 58.2612 .03463 28.8771 .05212 19.1879 .06963 14.3607 .08720 11.4685 1 60 .01746 57.2900 .03492 28.6363 .05241 19.0811 .06993 14.3007 .08749 11.4301 Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang / 8 9 8, 3 8 7 8 3 8 5 NATURAL TANGENTS AND COTANGENTS. 465 5 3 6 3 7 8 3 9 o Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang .08749 11.4301 .10510 9.51436 .12278 8.14435 .14054 7.11537 .15838 6.31375 60 1 .08778 11.3919 .10540 9.48781 .12308 8.12481 .14084 7.10038 .15868 6.30189 59 2 .08807 11.3540 .10569 9.46141 .12338 8.10536 .14113 7.08546 .15898 6.29007 58 3 .08837 11.3163 .10599 9.43515 .12367 8.08600 .14143 7.07059 .15928 6.27829 57 4 5 .08866 .08895 11.2789 11.2417 .10628 .10657 9^38307 .12426 8.04756 .14202 7.04105 .15958 .15988 6^25486 56 55 6 .08925 11.2048 .10687 9.35724 .12456 8.02848 .14232 7.02637 .16017 6.24321 54 7 .08954 11.1681 .10716 9.33155 .12485 8.00948 .14262 7.01174 .16047 6.23160 53 8 .08983 11.1316 .10746 9.30599 .12515 7.99058 .14291 6.99718 .16077 6.22003 52 9 .09013 11.0954 .10775 9.28058 .12544 7.97176 .14321 6.98268 .16107 6.20851 51 10 .09042 11.0594 .10805 9.25530 .12574 7.95302 .14351 6.96823 .16137 6.19703 50 11 .09071 11.0237 .10834 9.23016 .12603 7.93438 .14381 6.95385 .16167 6.18559 49 12 .09101 10.9882 .10863 9.20516 .12633 .91582 .14410 6.93952 .16196 6.17419 48 13 .09130 10.9529 .10893 9.18028 .12662 .89734 .14440 6.92525 .16226 6.16283 47 14 .09159 10.9178 .10922 9.15554 .12692 .87895 .14470 6.91104 .16256 6.15151 46 15 .09189 10.8829 .10952 9.13093 .12722 .86064 .14499 6.89688 .16286 6.14023 45 16 .09218 10.8483 .10981 9.10646 .12751 .84242 .14529 6.88278 .16316 6.12899 44 17 .09247 10.8139 .11011 9.08211 .12781 .82428 .14559 6.86874 .16346 6.11779 43 18 .09277 10.7797 .11040 9.05789 .12810 7.80622 .14588 6.85475 .16376 6.10664 42 19 .09306 10.7457 .11070 9.03379 .12840 7.78825 .14618 6.84082 .16405 6.09552 41 20 .09335 10.7119 .11099 9.00983 .12869 7.77035 .14648 6.82694 .16435 6.08444 40 21 .09365 10.6783 .11128 8.98598 .12899 7.75254 .14678 6.81812 .16465 6.07340 39 22 .09394 10.6450 .11158 8.96227 .12929 7.73480 .14707 6.79936 .16495 6.06240 38 23 .09423 10.6118 .11187 8.93867 .12958 7.71715 .14737 6.78564 .16525 6.05143 37 24 .09453 10.5789 .11217 8.91520 .12988 7.69957 .14767 6.77199 .16555 6.04051 36 25 .09482 10.5462 .11246 8.89185 .13017 7.68208 .14796 6.75838 .16585 6.02962 35 26 .09511 10.5136 .11276 8.86862 .13047 7.66466 .14826 6.74483 .16615 6.01878 34 27 .09541 10.4813 .11305 8.84551 .13076 7.64732 .14856 6.73133 .16645 6.00797 33 28 .09570 10.4491 .11335 8.82252 .13106 7.63005 .14886 6.71789 .16674 5.99720 32 29 .09600 10.4172 .11364 8.79964 .13136 7.61287 .14915 6.70450 .16704 5.98646 31 30 .09629 10.3854 .11394 8.77689 .13165 7.59575 .14945 6.69116 .16734 5.97576 30 31 .09658 10.3538 .11423 8.75425 .13195 7.57872 .14975 6.67787 .16764 5.96510 29 32 .09688 10.3224 .11452 8.73172 .13224 7.56176 .15005 6.66463 .16794 5.95448 28 33 .09717 10.2913 .11482 8.70931 .13254 7.54487 .15034 6.65144 .16824 5.94390 27 34 .09746 10.2602 .11511 8.68701 .13284 7.52806 .15064 6.63831 .16854 5.93335 26 35 .09776 10.2294 .11541 8 66482 .13313 7.51132 .15094 6.62523 .16884 5.92283 25 36 .09805 10.1988 .11570 8.64275 .13343 7.49465 .15124 6.61219 .16914 5.91236 24 37 .09834 10.1683 .11600 8.62078 .13372 7.47806 .15153 6.59921 .16944 5.90191 23 38 .09864 10.1381 .11629 8.59893 .13402 7.46154 .15183 6.58627 .16974 5.89151 22 39 .09893 10.1080 .11659 8.57718 .13432 7.44509 .15213 6.57339 .17004 5.88114 21 40 .09923 10.0780 .11688 8.55555 .13461 7.42871 .15243 6.56055 .17033 5.87080 20 1 .09952 10.0483 .11718 8.53402 .13491 7.41240 .15272 6.54777 .17063 5.86051 19 2 .09981 10.0187 .11747 8.51259 .13521 7.39616 .15302 6.53503 .17093 5.85024 18 3 .10011 9.98931 .11777 8.49128 .13550 7.37999 .15332 6.52234 .17123 5.84001 17 4 .10040 9.96007 .11806 8.47007 .13580 7.36389 .15362 6.50970 .17153 5.82982 16 5 .10069 9.93101 .11836 8.44896 .13609 7.34786 .15391 6.49710 .17183 5.81966 15 46 .10099 9.90211 .11865 8.42795 .13639 7.33190 .15421 6.48456 .17213 5.80953 14 47 .10128 9.87338 .11895 8.40705 .13669 7.31600 .15451 6.47206 .17243 5.79944 13 48 .10158 9.84482 .11924 8.38625 .13698 7.30018 .15481 6.45961 .17273 5.78938 12 49 .10187 9.81641 .11954 8.36555 .13728 7.28442 .15511 6.44720 .17303 5.77936 11 50 .10216 9.78817 .11983 8.34496 .13758 7.26873 .15540 6.43484 .17333 5.76937 10 51 .10246 9.76009 .12013 8.32446 .13787 7.25310 .15570 6.42253 .17363 5.75941 9 52 .10275 9.73217 .12042 8.30406 .13817 7.23754 .15600 6.41026 .17393 5.74949 8 53 .10305 9.70441 .12072 8.28376 .13846 7.22204 .15630 6.39804 .17423 5.73960 7 54 .10334 9.67680 .12101 8.26355 .13876 7.20661 .15660 6.38587 .17453 5.72974 6 55 .10363 9.64935 .12131 8.24345 .13906 7.19125 .15689 6.37374 .17483 5.71992 5 56 .10393 9.62205 .12160 8.22344 .13935 7.17594 .15719 6.36165 .17513 5.71013 4 57 .10422 9.59490 .12190 8.20352 .13965 7.16071 .15749 6.34961 .17543 5.70037 3 58 .10452 9.56791 .12219 8.18370 .13995 7.14553 .15779 6.33761 .17573 5.69064 2 59 .10481 9.54106 .12249 8.16398 .14024 7.13042 .15809 6.32566 .17603 5.68094 1 60 .10510 9.51436 .12278 8.14435 .14054 7.11537 .15838 6.31375 .17633 5.67128 Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang & 1 8, i 8 2 8] L 8 NATURAL TANGENTS AND COTANGENTS. 1( ) 1 L 1 i 1 3 1 40 Tang Cotang Tang Cotaug Tang Cotang Tang Cotang Tang Cotang .17633 5.67128 .19438 5.14455 .21256 4.70463 .23087 4.33148 .24933 4.01078 60 1 .17663 5.66165 .19468 5.13658 .21286 4.69791 .23117 4.32573 .24964 4.00582 59 2 .17693 5.65205 .19498 5.12862 .21316 4.69121 .23148 4.32001 .24995 4.00086 58 3 .17723 5.64248 .19529 5.120(59 .21347 4.68452 .23179 4.31430 .25026 3.99592 57 4 .17753 5.63295 .19559 5.11279 .21377 4.67786 .23209 4.30860 .25056 3.99099 56 5 .17783 5.62344 .19589 5.10490 .21408 4.67121 .23240 4.30291 .25087 3.98607 55 6 .17813 5.61397 .19619 5.09704 .21438 4.66458 .23271 4.29724 .25118 3.98117 54 7 .17843 5.60452 .19649 5.08921 .21469 4.65797 .23301 4.29159 .25149 3.97627 53 8 .17873 5.59511 .19680 5.08139 .21499 4.65138 .23332 4.28595 .25180 3.97139 52 9 .17903 5.58573 .19710 5.07360 .21529 4.64480 .23363 4.28032 .25211 3.96651 51 10 .17933 5.57638 .19740 5.06584 .21560 4.63825 .23393 4.27471 .25242 3.96165 50 11 .17963 5.56706 .19770 5.05809 .21590 4.63171 .23424 4.26911 .25273 3.95680 49 12 .17993 5.55777 .19801 5.05037 .21621 4.62518 .23455 4.26352 .25304 3.95196 48 13 .18023 5.54851 .19831 5.04267 .21651 4.61868 .23485 4.25795 .25335 3.94713 47 14 .18053 5.53927 .19861 5.03499 .21682 4.61219 .23516 4.25239 .25366 3.94232 46 15 .18083 5.53007 .19891 5.02734 .21712 4.60572 .23547 4.24685 .25397 3.93751 45 16 .18113 5.52090 .19921 5.01971 .21743 4.59927 .23578 4.24132 .25428 3.93271 44 17 .18143 5.51176 .19952 5.01210 .21773 4.59283 .23608 4.23580 .25459 3.92793 43 18 .18173 5.50264 .19982 5.00451 .21804 4.58641 .23639 4.23030 .25490 3.92316 42 19 .18203 5.49356 .20012 4.99695 .21834 4.58001 .23670 4.22481 .25521 3.91839 41 20 .18233 5.48451 .20042 4.98940 .21864 4.57363 .23700 4.21933 .25552 3.91364 40 21 .18263 5.47548 .20073 4.98188 .21895 4.56726 .23731 4.21387 .25583 3.90890 39 22 .18293 5.46648 .20103 4.97438 .21925 4.56091 .23762 4.20842 .25614 3.90417 38 23 .18323 5.45751 .20133 4.96690 .21956 4.55458 .23793 4.20298 .25645 3.89945 37 24 .18353 5.44857 .20164 4.95945 .21986 4.54826 .23823 4.19756 .25676 3.89474 36 25 .18384 5.43966 .20194 4.95201 .22017 4.54196 .23854 4.19215 .25707 3.89004 35 26 .18414 5.43077 .20224 4.94460 .22047 4.53568 .23885 4.18675 .25738 3.88536 34 27 .18444 5.42192 .20254 4.93721 .22078 4.52941 .23916 4.18137 .25769 3.88068 33 28 .18474 5.41309 .20285 4.92984 .22108 4.52316 .23946 4.17600 ,25800 3.87601 32 29 .18504 5.40429 .20315 4.92249 .22139 4.51693 .23977 4.17064 .25831 3.87136 31 30 .18534 5.39552 .20345 4.91516 .22169 4.51071 .24008 4.16530 .25862 3.86671 30 31 .18564 5.38677 .20376 4.90785 .22200 4.50451 .24039 4.15997 .25893 3.86208 29 32 .18594 5.37805 .20406 4.90056 .22231 4.49832 .24069 4.15465 .25924 3.85745 28 33 .18624 5.36936 .20436 4.89330 .22261 4.49215 .24100 4.14934 .25955 3.85284 27 34 .18654 5.36070 .20466 4.88605 .22292 4.48600 .24131 4.14405 .25986 3.84824 26 35 .18684 5.35206 .20497 4.87882 .22322 4. 7986 .24162 4.13877 .26017 3.84364 25 36 .18714 5.34345 .20527 4.87162 .22353 4. 7374 .24193 4.13350 .26048 3.83906 24 37 .18745 5.33487 .20557 4.86444 .22383 4. 6764 .24223 4.12825 .26079 3.83449 23 38 .18775 5.32631 .20588 4.85727 .22414 4.46155 .24254 4.12301 .26110 3.82992 22 39 .18805 5.31778 .20618 4.85013 .22444 4. 5548 .24285 4.11778 .26141 3.82537 21 40 .18835 5.30928 .20648 4.84300 .22475 4. 4942 .24316 4.11256 .26172 3.82083 20 41 .18865 5.30080 .20679 4.83590 .22505 4. 4338 .24347 4.10736 .26203 3.81630 19 42 .18895 5.29235 .20709 4.82882 .22536 4. 3735 .24377 4.10216 .26235 3.81177 18 43 .18925 5.28393 .20739 4.82175 .22567 4. 3134 .24408 4.09699 .26266 3.80726 17 44 .18955 5.27553 .20770 4.81471 .22597 4. 2534 .24439 4.09182 .26297 3.80276 16 45 .18986 5.26715 .20800 4.80769 .22628 4. 1936 .24470 4.08666 .26328 3.79827 15 46 .19016 5.25880 .20830 4.80068 .22658 4. 1340 .24501 4.08152 .26359 3.79378 14 47 .19046 5.25048 .20861 4.79370 .22689 4.40745 .24532 4.07639 .26390 3.78931 13 48 .19076 5.24218 .20891 4.78673 .22719 4.40152 .24562 4.07127 .26421 3.78485 12 49 50 .19106 .19136 5.23391 5.22566 .20921 .20952 4.77286 .22781 4.38969 .24624 4.06107 /26483 3^77595 10 51 .19166 5.21744 .20982 4.76595 .22811 4.38381 .24655 4.05599 .26515 3.77152 9 52 .19197 5.20925 .21013 4.75906 .22842 4.37793 .24686 4.05092 .26546 3.76709 8 53 .19227 5.20107 .21043 4.75219 .22872 4.37207 .24717 4.04586 .26577 3.76268 7 54 .19257 5.19293 .21073 4.74534 .22903 4.36623 .24747 4.04081 .26608 3.75828 6 55 .19287 5.18480 .21104 4.73851 .22934 4.36040 .24778 4.03578 .26639 3.75388 5 56 .19317 5.17671 .21134 4.73170 .22964 4.35459 .24809 4.03076 .26670 3.74950 4 57 .19347 5.16863 .21164 4.72490 .22995 4.34879 .24840 4.02574 .26701 3.74512 3 58 .19378 5.16058 .21195 4.71813 .23026 4.34300 .24871 4.02074 .26733 3.74075 2 59 .19408 5.15256 .21225 4.71137 .23056 4.33723 .24902 4.01576 .26764 3.73640 1 60 .19438 5.14455 .21256 4.70463 .23087 4.33148 .24933 4.01078 .26795 3.73205 Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang 7< ) 7 3 r 70 7( ) 7 ) t NATURAL TANGENTS AND COTANGENTS. 467 15 16 17 18 19 Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang .20795 3.73205 .28675 3.48741 .30573 3.27085 .32492 3.07768 .34433 2.90421 60 1 .26826 3.72771 .28706 3.48359 .30605 3.26745 .32524 3.07464 .34465 2.90147 59 2 26857 3.72338 .28738 3.47977 .30637 3.26406 .32556 3.07160 .34498 2.89873 58 3 .26888 3.71907 .28769 3.47596 .30669 3.26067 .32588 3.06857 .34530 2.89600 57 4 .26920 3.71476 .28800 3.47216 .30700 3.25729 .32621 3.06554 .34563 2.89327 56 5 .26951 3.71046 .28832 3.46837 .30732 3.25392 .32653 3.06252 .34596 2.89055 55 6 .26982 3.70616 .28864 3.46458 .30764 3.25055 .32685 3.05950 .34628 2.88783 54 7 .27013 3.70188 .28895 3.46080 .30796 3.24719 .32717 3.05649 .34661 2.88511 53 8 .27044 3.69761 .28927 3.45703 .30828 3.24383 .32749 3.05349 .34693 2.88240 52 9 .27076 3.69335 .28958 3.45327 .30860 3.24049 .32782 3.05049 .34726 2.87970 51 10 .27107 3.68909 .28990 3.44951 .30891 3.23714 .32814 3.04749 .34758 2.87700 50 11 .27138 3.68485 .29021 3.44576 .30923 3.23381 .32846 3.04450 .34791 2.87430 49 12 .27169 3.68061 .29053 3.44202 .30955 3.23048 .32878 3.04152 .34824 2.87161 48 13 .27201 3.67638 .29084 3.43829 .30987 3.22715 .32911 3.03854 .34856 2.86892 47 14 .27232 3.67217 .29116 3.43456 .31019 3.22384 .32943 3.03556 .34889 2.86624 46 15 .27263 3.66796 .29147 3.43084 .31051 3.22053 .32975 3.03260 .34922 2.86356 45 16 .27294 3.66376 .29179 3.42713 .31083 3.21722 .33007 3.02963 .34954 2.86089 44 17 .27326 3.65957 .29210 3.42343 .31115 3.21392 .33040 3.02667 .34987 2.85822 43 18 .27357 3.65538 .29242 3.41973 .31147 3.21063 .33072 3.02372 .35020 2.85555 42 19 .27388 3.65121 .29274 3.41604 .31178 3.20734 .33104 3.02077 .35052 2.85289 41 20 .27419 3.64705 .29305 3.41236 .31210 3.20406 .33136 3.01783 .35085 2.85023 40 21 .27451 3.64289 .29337 3.40869 .31242 3.20079 .33169 3.01489 .35118 2.84758 39 22 .27482 3.63874 .29368 3.40502 .31274 3.19752 .33201 3.01196 .35150 2.84494 38 23 .27513 3.63461 .29400 3.40136 .31306 3.19426 .33233 3.00903 .35183 2.84229 37 24 .27545 3.63048 .29432 3.39771 .31338 3.19100 .33266 3.00611 .35216 2.83965 36 25 .27576 3.62636 .29463 3.39406 .31370 3.18775 .33298 3.00319 .35248 2.83702 35 26 .27607 3.62224 .29495 3.39042 .31402 318451 .33330 3.00028 .35281 2.83439 34 27 .27638 3.61814 .29526 3.38679 .31434 3.18127 .33363 2.99738 .35314 2.83176 33 28 .27670 3.61405 .29558 3.38317 .31466 3.17804 .33395 2.99447 .35346 2.82914 32 29 .27701 3.60996 .29590 3.37955 .31498 3.17481 .33427 2.99158 .35379 2.82653 31 30 .27732 3.60588 .29621 3.37594 .31530 3.17159 .33460 2.98868 .35412 2.82391 30 31 .27764 3.60181 .29653 3.37234 .31562 3.16838 .33492 2.98580 .35445 2.82130 29 32 .27795 3.59775 .29685 3.36875 .31594 3.16517 .33524 2.98292 .35477 2.81870 28 33 .27826 3.59370 .29716 3.36516 .31626 3.16197 .33557 2.98004 .35510 2.81610 27 34 .27858 3.58966 .29748 3.36158 .31658 3.15877 .33589 2.97717 .35543 2.81350 26 35 .27889 3.58562 .29780 3.35800 .31690 3.15558 .33621 2.97430 .35576 2.81091 25 36 .27921 3.58160 .29811 3.35443 .31722 3.15240 .33654 2.97144 .35608 2.80833 24 37 .27952 3.57758 .29843 3.35087 .31754 3.14922 .33686 2.96858 .35641 2.80574 23 38 .27983 3.57357 .29875 3.34732 .31786 3 14605 .33718 2.96573 .35674 2.80316 22 39 .28015 3.56957 .29906 3.34377 .31818 3.14288 .33751 2.96288 .35707 2.80059 21 40 .28046 3.56557 .29938 3.34023 .31850 3.13972 .33783 2.96004 .35740 2.79802 20 41 .28077 3.56159 .29970 3.33670 .31882 3.13656 .33816 2.95721 .35772 2.79545 19 42 .28109 3.55761 .30001 3.33317 .31914 3.13341 .33848 2.95437 .35805 2.79289 18 43 .28140 3.55364 .30033 3.32965 .31946 3.13027 .33881 2.95155 .35838 2.79033 17 44 .28172 3.54968 .30065 3.32614 .31978 3.12713 .33913 2.94872 .35871 2.78778 16 45 .28203 3.54573 .30097 3.32264 .32010 1 3.12400 .33945 2.94591 .35904 2.78523 15 46 .28234 3.54179 .30128 3.31914 .32042 3.12087 .33978 2.94309 .35937 2.78269 14 47 .28266 3.53785 .30160 3.31565 .32074 3.11775 .34010 2.94028 .35969 2.78014 13 48 .28297 3.53393 .30192 3.31216 .32106 3.11464 .34043 2.93748 .36002 2.77761 12 49 .28329 3.53001 .30224 3.30868 .32139 3.11153 .34075 2.93468 .36035 2.77507 11 50 .28360 3.52609 .30255 3.30521 .32171 3.10842 .34108 2.93189 .36068 2.77254 10 51 .28391 3.52219 .30287 3.30174 .32203 3.10532 .34140 2.92910 .36101 2.77002 9 52 .28423 3.51829 .30319 3.29829 .32235 3.10223 .34173 2.92632 .36134 2.76750 8 53 .28454 3.51441 .30351 3.29483 .32267 3.09914 .34205 2.92354 .36167 2.76498 7 54 .28486 3.51053 .30382 3.29139 .32299 3.09606 .34238 2.92076 .36199 2.76247 6 55 .28517 3.50666 .30414 3.28795 .32331 3.09298 .34270 2.91799 .36232 2.75996 5 56 .28549 3.50279 .30446 3.28452 .32363 3.08991 .34303 2.91523 .36265 2.75746 4 57 .28580 3.49894 .30478 3.28109 .32396 3.08685 .34335 2.91246 .36298 2.75496 3 58 .28612 3.49509 .30509 3.27767 .32428 3.08379 .34368 2.90971 .36331 2.75246 2 59 .28643 3.49125 .30541 3.27426 .32460 3.08073 .34400 2.90696 .36364 2.74997 1 60 .28675 3.48741 .30573 3.27085 .32492 3.07768 .34433 2.90421 .36397 2.74748 Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang 74 73 72 71 70 468 NATURAL TANGENTS AND COTANGENTS. 20 o 21 o 25 p 2i 4 Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang .36397 2.74748 .38386 2.60509 .40403 2. 7509 .42447 2.35585 .44523 2.24604 60 1 .36430 2.74499 .38420 2.60283 .40436 2. 7302 .42482 2.35395 .44558 2.24428 59 2 .36463 2.74251 .38453 2.60057 .40470 2. 7095 .42516 2.35205 .44593 2.24252 58 3 .36496 2.74004 .38487 2.59831 .40504 2. 6888 .42551 2.35015 .44627 2.24077 57 4 .36529 2.73756 .38520 2.59606 .40538 2. 6682 .42585 2.34825 .44662 2.23902 56 5 .36562 2.73509 .38553 2.59381 .40572 2.46476 .42619 2.34636 .44697 2.23727 55 6 .36595 2.73263 .38587 2.59156 .40606 2.46270 .42654 2.34447 .44732 2.23553 54 7 .36628 2.73017 .38620 2.58932 .40640 2.46065 .42688 2.34258 .44767 2.23378 53 8 .36661 2.72771 .38654 2.58708 .40674 2.45860 .42722 2.34069 .44802 2.23204 52 9 .36694 2.72526 .38687 2.58484 .40707 2.45655 .42757 2.33881 .44837 2.23030 51 10 .36727 2.72281 .38721 2.58261 .40741 2.45451 .42791 2.33693 .44872 2.22857 50 11 .36760 2.72036 .38754 2.58038 .40775 2.45246 .42826 2.33505 .44907 2.22683 49 12 .36793 2.71792 .38787 2.57815 .40809 2.45043 .42860 2.33317 .44942 2.22510 48 13 .36826 2.71548 .38821 2.57593 .40843 2.44839 .42894 2.33130 .44977 2.22337 47 14 .36859 2.71305 .38854 2.57371 .40877 2.44636 .42929 2.32943 .45012 2.22164 46 15 .36892 2.71062 .38888 2.57150 .40911 2.44433 .42963 2.32756 .45047 2.21992 45 16 .36925 2.70819 .38921 2.56928 .40945 2.44230 .42998 2.32570 .45082 2.21819 44 17 .36958 2.70577 .38955 2.56707 .40979 2.44027 .43032 2.32383 .45117 2.21647 43 18 .36991 2.70335 .38988 2.56487 .41013 2.43825 .43067 2.32197 .45152 2.21475 42 19 .37024 2.70094 .39022 2.56266 .41047 2.43623 .43101 2.32012 .45187 2.21304 41 20 .37057 2.69853 .39055 2.56046 .41081 2.43422 .43136 2.31826 .45222 2.21132 40 21 .37090 2.69612 .39089 2.55827 .41115 2.43220 .43170 2.31641 .45257 2.20961 39 22 .37123 2.69371 .39122 2.55608 .41149 2.43019 43205 2.31456 .45292 2.20790 38 23 .37157 2.69131 .39156 2.55389 .41183 2.42819 .43230 2.31271 .45327 2.20619 37 24 .37190 2.68892 .39190 2.55170 .41217 2.42618 .43274 2.31086 .45362 2.20449 36 25 .37223 2.68653 .39223 2.54952 .41251 2.42418 .43308 2.30902 .45397 2.20278 35 26 .37256 2.68414 .39257 2.54734 .41285 2.42218 .43343 2.30718 .45432 2.20108 34 27 .37289 2.68175 .39290 2.54516 .41319 2.42019 .43378 2.30534 .45467 2.19938 33 28 .37322 2.67937 .39324 2.54299 .41353 2.41819 .43412 2.30351 .45502 2.19769 32 29 .37355 2.67700 .39357 2.54082 .41387 2.41620 .43447 2.30167 .45538 2.19599 31 30 .37388 2.67462 .39391 2.53865 .41421 2.41421 .43481 2.29984 .45573 2.19430 30 31 .37422 2.67225 .39425 2.53648 .41455 2.41223 .43516 2.29801 .45608 2.19261 29 32 .37455 2.66989 .39458 2.53432 .41490 2.41025 .43550 2.29619 .45643 2.19092 28 33 .37488 2.66752 .39492 2.53217 .41524 2.40827 .43585 2.29437 .45678 2.18923 27 34 .37521 2.66516 .39526 2.53001 .41558 2.40629 .43620 2.29254 .45713 2.18755 26 35 .37554 2.66281 .39559 2.52786 .41592 2.40432 .43654 2.29073 .45748 2.18587 25 36 .37588 2.66046 .39593 2.52571 .41626 2.40235 .43689 2.28891 .45784 2.18419 24 37 .37621 2.65811 .39626 2.52357 .41660 2.40038 .43724 2.28710 .45819 2.18251 23 38 .37654 2.65576 .39660 2.52142 .41694 2.39841 .43758 2.28528 .45854 2.18084 22 39 .37687 2.65342 .39694 2.51929 .41728 2.39645 .43793 2.28348 .45889 2.17916 21 40 .37720 2.65109 .39727 2.51715 .41763 2.39449 .43828 2.28167 .45924 2.17749 20 41 .37754 2.64875 .39761 2.51502 .41797 2.39253 .43862 2.27987 .45960 2.17582 19 42 .37787 2.64642 .39795 2.51289 .41831 2.39058 .43897 2.27806 .45995 2.17416 18 43 .37820 2.64410 .39829 2.51076 .41865 2.38863 .43932 2.27626 .46030 2.17249 17 44 .37853 2.64177 .39862 2.50864 .41899 2.38668 .43966 2.27447 .46065 2.17083 16 45 .37887 2.63945 .39896 2.50652 .41933 2.38473 .44001 2.27267 .46101 2.16917 15 46 .37920 2.63714 .39930 2.50440 .41968 2.38279 .44036 2.27088 .46136 2.16751 14 47 .37953 2.63483 .39963 2.50229 .42002 2.38084 .44071 2.26909 .46171 2.16585 13 48 .37986 2.63252 .39997 2.50018 .42036 2.37891 .44105 2.26730 .46206 2.16420 12 49 .38020 2.63021 .40031 2.49807 .42070 2.37697 .44140 2.26552 .46242 2.16255 11 50 .38053 2.62791 .40065 2.49597 .42105 2.37504 .44175 2.26374 .46277 2.16090 10 51 .38086 2.62561 .40098 2.49386 .42139 2.37311 .44210 2.26196 .46312 2.15925 9 52 .38120 2.62332 .40132 2.49177 .42173 2.37118 .44244 2.26018 .46348 2.15760 8 53 .38153 2.62103 .40166 2.48967 .42207 2.36925 .44279 2.25840 .46383 2.15596 7 54 .38186 2.61874 .40200 2.48758 .42242 2.36733 .44314 2.25663 .46418 2.15432 6 55 .38220 2.61646 .40234 2.48549 .42276 2.36541 .44349 2.25486 .46454 2.15268 5 56 .38253 2.61418 .40267 2.48340 .42310 2.36349 .44384 2.25309 .46489 2.15104 4 57 .38286 2.61190 .40301 2.48132 .42345 2.36158 .44418 2.25132 .46525 2.14940 3 58 .38320 2.60963 .40335 2.47924 .42379 2.35967 .44453 2.24956 .46560 2.14777 2 59 .38353 2.60736 .40369 2.47716 .42413 2.35776 .44488 2.24780 .46595 2.14614 1 60 .38386 2.60509 .40403 2.47509 .42447 2.35585 .44523 2.24604 .46631 2.14451 Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang f 6 3 6 8 6 7 6 5 6 5 NATURAL TANGENTS AND COTANGENTS. 469 25 26 27 28 29 Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang .46631 2.14451 .48773 2.05030 .50953 1.96261 .53171 1.88073 .55431 1.80405 60 1 .46666 2.14288 .48809 2.04879 .50989 1.96120 .53208 1.87941 .55469 1.80281 59 2 .46702 2.14125 .48845 2.04728 .51026 1.95979 .53246 1.87809 .55507 1.80158 58 3 .46737 2.13963 .48881 2.04577 .51063 1.95838 .53283 1.87677 .55545 1.80034 57 4 .46772 2.13801 .48917 2.04426 .51099 1.95698 .53320 1.87546 .55583 1.79911 56 5 .46808 2.13639 .48953 2.04276 .51136 1.95557 .53358 1.87415 .55621 1.79788 55 6 .46843 2.13477 .48989 2.04125 .51173 1.95417 .53395 1.87283 .55659 1.79665 54 7 .46879 2.13316 .49026 2.03975 .51209 1.95277 .53432 1.87152 .55697 1.79542 53 8 .46914 2.13154 .49062 2.03825 .51246 1.95137 .53470 1.87021 .55736 1.79419 52 9 .46950 2.12993 .49098 2.03675 .51283 1.94997 .53507 1.86891 .55774 1.79296 51 10 .46985 2.12832 .49134 2.03526 .51319 1.94858 .53545 1.86760 .55812 1.79174 50 11 .47021 2.12671 .49170 2.03376 .51356 1.94718 .53582 1.86630 .55850 1.79051 49 12 .47056 2.12511 .49206 2.03227 .51393 1.94579 .53620 1.86499 .55888 1.78929 48 13 .47092 2.12350 .49242 2.03078 .51430 1.94440 .53657 1.86369 .55926 1.78807 47 14 .47128 i 2.12190 .49278 2.02929 .51467 1.94301 .53694 1.86239 .55964 1.78685 46 15 .47163 | 2.12030 .49315 2.02780 .51503 1 .94162 .53732 1.86109 .56003 1.78563 45 16 .47199 2.11871 .49351 2.02631 .51540 | 1.94023 .53769 1.85979 .56041 1.78441 44 17 .47234 2.11711 .49387 2.02483 .51577 1 1.93885 .53807 1.85850 .56079 1.78319 43 18 .47270 2.11552 .49423 2.02335 .51614 1.93746 .53844 1.85720 .56117 1.78198 42 19 .47305 2.11392 .49459 2.02187 .51651 1.93608 .53882 1.85591 .56156 1.78077 41 20 .47341 2.11233 .49495 2.02039 .51688 1.93470 .53920 1.85462 .56194 1.77955 40 21 .47377 2.11075 .49532 2.01891 .51724 1.93332 .53957 1.85333 .56232 1.77834 39 22 .47412 2.10916 .49568 2.01743 .51761 1.93195 .53995 1.85204 .56270 1.77713 38 23 .47448 2.10758 .49604 2.015% .51798 1.93057 .54032 1.85075 .56309 1.77592 37 24 .47483 2.10600 .49640 2.01449 .51835 1.92920 .54070 1.84946 .56347 1.77471 36 25 .47519 2.10442 .49677 2.01302 .51872 1.92782 .54107 1.84818 .56385 1.77351 35 26 .47555 2.10284 .49713 2.01155 .51909 1.92645 .54145 1.84689 .56424 1.77230 34 27 .47590 2.10126 .49749 2.01008 .51946 1.92508 .54183 1.84561 .56462 1.77110 33 28 .47626 2.09969 .49786 2.00862 .51983 1.92371 .54220 1.84433 .56501 1.76990 32 29 .47662 2.09811 .49822 2.00715 .52020 1.92235 .54258 1.84305 .56539 1.76869 31 30 .47698 2.09654 .49858 2.00569 .52057 1.92098 .54296 1.84177 .56577 1.76749 30 31 .47733 2.09498 .49894 2.00423 .52094 1.91962 .54333 1.84049 .56616 1.76629 29 32 .47769 2.09341 .49931 2.00277 .52131 1.91826 .54371 1.83922 .56654 1.76510 28 33 .47805 2.09184 .49967 2.00131 .52168 1.91690 .54409 1.83794 .56693 1.76390 27 34 .47840 2.09028 .50004 1.99986 .52205 1.91554 .54446 1.83667 .56731 1.76271 26 35 .47876 2.08872 .50040 1.99841 .52242 1.91418 .54484 1.83540 .56769 1.76151 25 36 .47912 2.08716 .50076 1.99695 .52279 1.91282 .54522 1.83413 .56808 1.76032 24 37 .47948 2.08560 .50113 1.99550 .52316 1.91147 .54560 1.83286 .56846 1.75913 23 38 .47984 2.08405 .50149 1.99406 .52353 1.91012 .54597 1.83159 .56885 1.75794 22 39 .48019 2.08250 .50185 1.99261 .52390 1.90876 .54635 1.83033 .56923 1.75675 21 40 .48055 2.08094 .50222 1.99116 .52427 1.90741 .54673 1.82906 .56962 1.75556 20 41 .48091 2.07939 .50258 1.98972 .52464 1.90607 .54711 1.82780 .57000 1.75437 19 42 .48127 2.07785 .50295 1.98828 .52501 1.90472 .54748 1.82654 .57039 1.75319 18 43 .48163 2.07630 .50331 1.98684 .52538 1.90337 .54786 1.82528 .57078 1.75200 17 44 .48198 2.07476 .50368 1.98540 .52575 1.90203 .54824 1.82402 .57116 1.75082 16 45 .48234 2.07321 .50404 1.98396 .52613 1.90069 .54862 1.82276 .57155 1.74964 15 46 .48270 2.07167 .50441 1.98253 .52650 1.89935 .54900 1.82150 .57193 1.74846 14 47 .48306 2.07014 .50477 1.98110 .52687 1.89801 .54938 1.82025 .57232 1.74728 13 48 .48342 2.06860 .50514 1.97966 .52724 1.89667 .54975 1.81899 .57271 1.74610 12 49 .48378 2.06706 .50550 1.97823 .52761 1.89533 .55013 1.81774 .57309 1.74492 11 50 .48414 2.06553 .50587 1.97681 .52798 1.89400 .55051 1.81649 .57348 1.74375 10 51 .48450 2.06400 .50623 1.97538 .52836 1.89266 .55089 1.81524 .57386 1.74257 9 52 .48486 2.06247 .50660 1.97395 .52873 1.89133 .55127 1.81399 .57425 1.74140 8 53 .48521 2.06094 .50696 1.97253 .52910 1.89000 .55165 1.81274 .57464 1.74022 7 54 .48557 2.05942 .50733 1.97111 .52947 1.88867 .55203 1.81150 .57503 1.73905 6 55 .48593 2.05790 .50769 1.96969 .52985 1.88734 .55241 1.81025 .57541 1.73788 5 56 .48629 2,05637 .50806 1.96827 .53022 1.88602 .55279 1.80901 .57580 1.73671 4 57 .48665 2.05485 .50843 1 .96685 .53059 1.88469 .55317 1.80777 .57619 1.73555 3 58 .48701 2.05333 .50879 1.96544 .53096 1.88337 .55355 1.80653 .57657 1.73438 2 59 .48737 2.05182 .50916 1.96402 .53134 1.88205 .55393 1.80529 .57696 1.73321 1 60 .48773 2.05030 .50953 1.96261 .53171 1.88073 .55431 1.80405 .57735 1.73205 Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang 64 63 62 61 60 f NATURAL TANGENTS AND COTANGENTS. f 3( ) 3 i 3! 2 3 5 3 4 g g Cotang .57735 1.73205 .60086 1.66428 .62487 1.60033 .64941 1.53986 .67451 1.48256 60 1 .57774 1.73089 .60126 1.66318 .62527 1.59930 .64982 1.53888 .67493 1.48163 59 2 .57813 1.72973 .60165 1.66209 .62568 1.59826 .65024 1.53791 .67536 1.48070 58 3 .57851 1.72857 .60205 1.66099 .62608 1.59723 .65065 1.53693 .67578 1.47977 57 4 .57890 1.72741 .60245 1.65990 .62649 1.59620 .65106 1.53595 .67620 1.47885 56 5 .57929 1.72625 .60284 1.65881 .62689 1.59517 .65148 1.53497 .67663 1.47792 55 6 .57968 1.72509 .60324 1.65772 .62730 1.59414 .65189 1.53400 .67705 1.47699 54 7 .58007 1.72393 .60364 1.65663 .62770 1.59311 .65231 1.53302 .67748 1.47607 53 8 .58046 1.72278 .60403 1.65554 .62811 1.59208 .65272 1.53205 .67790 1.47514 52 9 .58085 1.72163 .60443 1.65445 .62852 1.59105 .65314 1.53107 .67832 1.47422 51 10 .58124 1.72047 .60483 1.65337 .62892 1.59002 .65355 1.53010 .67875 1.47330 50 11 .58162 1.71932 .60522 1.65228 .62933 1.58900 .65397 1.52913 .67917 1.47238 49 12 .58201 1.71817 .60562 1.65120 .62973 1.58797 .65438 1.52816 .67960 1.47146 48 13 .58240 1.71702 .60602 1.65011 .63014 1.58695 .65480 1.52719 .68002 1.47053 47 14 .58279 1.71588 .60642 1.64903 .63055 1.58593 .65521 1.52622 .68045 1.46962 46 15 .58318 1.71473 .60681 1.64795 .63095 1.58490 .65563 1.52525 .68088 1.46870 45 16 .58357 1.71358 .60721 1.64687 .63136 1.58388 .65604 1.52429 .68130 1.46778 44 17 .58396 1.71244 .60761 1.64579 .63177 1.58286 .65646 1.52332 .68173 1.46686 43 18 .58435 1.71129 .60801 1.64471 .63217 1.58184 .65688 1.52235 .68215 1.46595 42 19 .58474 1.71015 .60841 1.64363 .63258 1.58083 .65729 1.52139 .68258 1.46503 41 20 .58513 1.70901 .60881 1.64256 .63299 1.57981 .65771 1.52043 .68301 1.46411 40 21 .58552 1.70787 .60921 1.64148 .63340 1.57879 .65813 1.51946 .68343 1.46320 39 22 .58591 1.70673 .60960 1.64041 .63380 1.57778 .65854 1.51850 .68386 1.46229 38 23 .58631 1.70560 .61000 1.63934 .63421 1.57676 .65896 1.51754 .68429 1.46137 37 24 .58670 1.70446 .61040 1.63826 .63462 1.57575 .65938 1.51658 .68471 1.46046 36 25 .58709 1.70332 .61080 1.63719 .63503 1.57474 .65980 1.51562 .68514 1.45955 35 26 .58748 1.70219 .61120 1.63612 .63544 1.57372 .66021 1.51466 .68557 1.45864 34 27 .58787 1.70106 .61160 1.63505 .63584 1.57271 .66063 1.51370 .68600 1.45773 33 28 .58826 1.69992 .61200 1.63398 .63625 1.57170 .66105 1.51275 .68642 1.45682 32 29 .58865 1.69879 .61240 1.63292 .63666 1.57069 .66147 1.51179 .68685 1.45592 31 30 .58905 1.69766 .61280 1.63185 .63707 1.56969 .66189 1.51084 .68728 1.45501 30 31 .58944 1.69653 .61320 1.63079 .63748 1.56868 .66230 1.50988 .68771 1.45410 29 32 .58983 1.69541 .61360 1.62972 .63789 1.56767 .66272 1.50893 .68814 1.45320 28 33 .59022 1.69428 .61400 1.62866 .63830 1.56667 .66314 1.50797 .68857 1.45229 27 34 .59061 1.69316 .61440 1.62760 .63871 1.56566 .66356 1.50702 .68900 1.45139 26 35 .59101 1.69203 .61480 1.62654 .63912 1.56466 .66398 1.50607 .68942 1.45049 25 36 .59149 1.69091 .61520 1.62548 .63953 1.56366 .66440 1.50512 .68985 1.44958 24 37 .59179 1.68979 .61561 1.62442 .63994 1.56265 .66482 1.50417 .69028 1.44868 23 38 .59218 1.68866 .61601 1.62336 .64035 1.56165 .66524 1.50322 .69071 1.44778 22 39 .59258 1.68754 .61641 1.62230 .64076 1.56065 .66566 1.50228 .69114 1.44688 21 40 .59297 1.68643 .61681 1.62125 .64117 1.55966 .66608 1.50133 .69157 1.44598 20 41 .59336 1.68531 .61721 1.62019 .64158 1.55866 .66650 1.50038 .69200 1. 4508 19 42 .59376 1.68419 .61761 1.61914 .64199 1.55766 .66692 1.49944 .69243 1. 4418 18 3 .59415 1.68308 .61801 1.61808 .64240 1.55666 .66734 1.49849 .69286 1. 4329 17 4 .59454 1.68196 .61842 1.61703 .64281 1.55567 .66776 1.49755 .69329 1. 4239 16 5 .59494 1.68085 .61882 1.61598 .64322 1.55467 .66818 1.49661 .69372 1. 4149 15 6 .59533 1.67974 .61922 1.61493 .64363 1.55368 .66860 1.49566 .69416 1. 4060 14 7 .59573 1.67863 .61962 1.61388 .64404 1.55269 .66902 1.49472 .69459 1. 3970 13 8 .59612 1.67752 .62003 1.61283 .64446 1.55170 .66944 1 .49378 .69502 1. 3881 12 49 .59651 1.67641 .62043 1.61179 .64487 1.55071 .66986 1.49284 .69545 1. 3792 11 50 .59691 1.67530 .62083 1.61074 .64528 1.54972 .67028 1.49190 .69588 1. 3703 10 51 .59730 1.67419 .62124 1.60970 .64569 1.54873 .67071 1.49097 .69631 1.43614 9 52 .59770 1.67309 .62164 1.60865 .64610 1.54774 .67113 1.49003 .69675 1.43525 8 53 .5980J 1.67198 .62204 1.60761 .64652 1.54675 .67155 1.48909 .69718 1.43436 7 54 .59849 1.67088 .62245 1.60657 .64693 1.54576 .67197 1.48816 .69761 1.43347 6 55 .59888 1.66978 .62285 1.60553 .64734 1.54478 .67239 1.48722 .69804 .43258 5 56 .59928 1.66867 .62325 1.60449 .64775 1.54379 .67232 1.48629 .69847 .43169 4 57 .59967 1.66757 .62366 1.60345 .64817 1.54281 .67324 1.48536 .69891 .43080 3 58 .60007 1.66647 .62406 1.60241 .64858 1.54183 .67366 1.48442 .69934 .42992 2 59 .60046 1.66538 .62446 1.60137 .64899 1.54085 .67409 1.48349 .69977 .42903 1 60 .60086 1.66428 .62487 1.60033 .64941 1.53986 .67451 1.48256 .70021 .42815 Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang 5< ) n \ 57 o 5f 5, ) I NATURAL TANGENTS AND COTANGENTS. 471 35 o 36 37 o 38 o 3 9 Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang .70021 1.42815 .72654 1.37638 .75355 1.32704 .78129 1.27994 .80978 1.23490 60 1 .70064 1.42726 .72699 1.37554 .75401 1.32624 .78175 1.27917 .81027 1.23416 59 2 .70107 1.42638 .72743 1.37470 .75447 1.32544 .78222 1.27841 .81075 1.23343 58 3 .70151 1.42550 .72788 1.37386 .75492 1.32464 .78269 1.27764 .81123 1.23270 57 4 .70194 1.42462 .72832 1.37302 .75538 1.32384 .78316 1.27688 .81171 1.23196 56 5 .70238 1.42374 .72877 1.37218 .75584 1.32304 .78363 1.27611 .81220 1.23123 55 6 .70281 1.42286 .7291:1 1.37134 .75629 1.32224 .78410 1.27535 .81268 1.23050 54 7 .70325 1.42198 .72966 1.37050 .75675 1.32144 .78457 1.27458 .81316 1.22977 53 8 .70368 1.42110 .73010 1.36967 .75721 1.32064 .78504 1.27382 .81364 1.22904 52 9 .70412 1.42022 .73055 1.36883 .75767 1.31984 .78551 1.27306 .81413 1.22831 51 10 .70455 1.41934 .73100 1.36800 .75812 1.31904 .78598 1.27230 .81461 1.22758 50 11 .70499 1.41847 .73144 1.36716 .75858 1.31825 .78645 1.27153 .81510 1.22685 49 12 .70542 1.41759 .73189 1.36633 .75904 1.31745 .78692 1.27077 .81558 1.22612 48 13 .70586 1.41672 .73234 1.36549 .75950 1.31666 .78739 1.27001 .81606 1.22539 47 14 .70629 1.41584 .73278 1.36466 .75996 1.31586 .78786 1.26925 .81655 1.22467 46 15 .70673 1. 1497 .73323 1.36383 .76042 1.31507 .78834 1.26849 .81703 1.22394 45 16 .70717 1. 1409 .73368 1.36300 .76088 1.31427 .78881 1.26774 .81752 1.22321 44 17 .70760 1. 1322 .73413 1.36217 .76134 1.31348 .78928 1.26698 .81800 1.22249 43 18 .70804 1. 1235 .73457 1.36134 .76180 1.31269 .78975 1.26622 .81849 1.22176 42 19 .70848 1. 1148 .73502 1.36051 .76226 1.31190 .79022 1.26546 .81898 1.22104 41 20 .70891 1. 1061 .73547 1 35968 .76272 1.31110 .79070 1.26471 .81946 1.22031 40 21 .70935 1.40974 .73592 1.35885 .76318 1.31031 .79117 1.26395 .81995 1.21959 39 22 .70979 1.40887 .73637 1.35802 .76364 1.30952 .79164 1.26319 .82044 1.21886 38 23 .71023 1.40800 .73681 1.35719 .76410 1.30873 .79212 1.26244 .82092 1.21814 37 24 .71066 1.40714 .73726 1.35637 .76456 1.30795 .79259 1.26169 .82141 1.21742 36 25 .71110 1.40627 .73771 1.35554 .76502 1.30716 .79306 1.26093 .82190 1.21670 35 26 .71154 1.40540 .73816 1.35472 .76548 1.30637 .79354 1 .26018 .82238 1.21598 34 27 .71198 1.40454 .73861 1.35389 .76594 1.30558 .79401 1 .25943 .82287 1.21526 33 28 .71242 1.40367 .73906 1.35307 .76640 1.30480 .79449 1.25867 .82336 1.21454 32 29 .71285 1.40281 .73951 1.35224 .76686 1.30401 .79496 1.25792 .82385 1.21382 31 30 .71329 1.40195 .73996 1.35142 .76733 1.30323 .79544 1.25717 .82434 1.21310 30 31 .71373 1.40109 .74041 1.35060 .76779 1.30244 .79591 1.25642 .82483 1.21238 29 32 .71417 1.40022 .74086 1.34978 .76825 1.30166 .79639 1.25567 .82531 1.21166 28 33 .71461 1.39936 .74131 1.34896 .76871 1.30087 .79686 1.25492 .82580 1.21094 27 34 .71505 1.39850 .74176 1.34814 .76918 1.30009 .79734 1.25417 .82629 1.21023 26 35 .71549 1.39764 .74221 1.34732 .76964 1.29931 .79781 1.25343 .82678 1.20951 25 36 .71593 1.39679 .74267 1.34650 .77010 1.29853 .79829 1.25268 .82727 1.20879 24 37 .71637 1.39593 .74312 1.34568 .77057 1.29775 .79877 1.25193 .82776 1.20808 23 38 .71681 1.39507 .74357 1.34487 .77103 1.29696 .79924 1.25118 .82825 1.20736 22 39 .71725 1.39421 .74402 1 .34405 .77149 1.29618 .79972 1.25044 .82874 1.20665 21 40 .71769 1.39336 .74447 1.34323 .77196 1.29541 .80020 1.24969 .82923 1.20593 20 41 .71813 1.39250 .74492 1.34242 .77242 1.29463 .80067 1.24895 .82972 1.20522 19 42 .71857 1.39165 .74538 1.34160 .77289 1.29385 .80115 1.24820 .83022 1.20451 18 43 .71901 1.39079 .74583 1.34079 .77335 1.29307 .80163 1.24746 .83071 1.20379 17 44 .71946 1.38994 .74628 1.33998 .77382 1.29229 .80211 1.24672 .83120 1.20308 16 45 .71990 1.38909 .74674 1.33916 .77428 1.29152 .80258 1.24597 .83169 1.20237 15 46 .72034 1.38824 .74719 1.33835 .77475 1.29074 .80306 1.24523 .83218 1.20166 14 47 .72078 1.38738 .74764 1.33754 .77521 1.28997 .80354 1.24449 .83268 1.20095 13 48 .72122 1.38653 .74810 1.33673 .77568 1.28919 .80402 1.24375 .83317 1.20024 12 49 .72167 1.38568 .74855 1.33592 .77615 1.28842 .80450 1.24301 .83366 1.19953 11 50 .72211 1.38484 .74900 1.33511 .77661 1.28764 .80498 1.24227 .83415 1.19882 10 51 .72255 1.38399 .74946 1.33430 .77708 1.28687 .80546 1.24153 .83465 1.19811 9 52 .72299 1.38314 .74991 1.33349 .77754 1.28610 .80594 1.24079 .83514 1.19740 8 53 .72344 1.38229 .75037 1.33268 .77801 1.28533 .80642 1.24005 .83564 1.19669 7 54 .72388 1.38145 .75082 1.33187 .77848 1.28456 .80690 1.23931 .83613 1.19599 6 55 .72432 1.38060 .75128 1.33107 .77895 1.28379 .80738 1.23858 .83662 1.19528 5 56 .72477 1.37976 .75173 1.33026 .77941 1.28302 .80786 1.23784 .83712 1.19457 4 57 .72521 1.37891 .75219 1.32946 .77988 1.28225 .80834 1.23710 .83761 1.19387 3 58 .72565 1.37807 .75264 1.32865 .78035 1.28148 .80882 1.23637 .83811 1.19316 2 59 .72610 1.37722 .75310 1.32785 .78082 1.28071 .30930 1.23563 .83860 1.19246 1 60 .72654 1.37638 .75355 1.32704 .78129 1.27994 .80978 1.23490 .83910 1.19175 Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang 5 4 5 3 5 2 5 1 5 / NATURAL TANGENTS AND COTANGENTS. 4C 41 L 4$ >o 4J J 4 4 Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang .83910 1.19175 .86929 1.15037 .90040 1.11061 .93252 1.07237 .96569 1.03553 60 1 .83960 1.19105 .86980 1.14969 .90093 1.10996 .93306 1.07174 .96625 1.03493 59 2 .84009 1.19035 .87031 1.14902 .90146 1.10931 .93360 1.07112 .96681 1.03433 58 3 .84059 1.18964 .87082 1.14834 .90199 1.10867 .93415 1.07049 .96738 1.03372 57 4 .84108 1.18894 .87133 1.14767 .90251 1.10802 .93469 1.06987 .96794 1.03312 56 .84158 1.18824 .87184 1.14699 .90304 1.10737 .93524 1.06925 .96850 1.03252 55 6 .84208 1.18754 .87236 1.14632 .90357 1.10672 .93578 1.06862 .96907 1.03192 54 7 .84258 .18684 .87287 1.14565 .90410 1.10607 .93633 1.06800 .96963 1.03132 53 8 .84307 .18614 .87338 1.14498 .90463 1.10543 .93688 1.06738 .97020 1.03072 52 9 .84357 .18544 .87389 1.14430 .90516 1.10478 .93742 1.06676 .97076 1.03012 51 10 .84407 .18474 .87441 1.14363 .90569 1.10414 .93797 1.06613 .97133 1.02952 50 11 .84457 .18404 .87492 1.14296 .90621 1.10349 .93852 1.06551 .97189 1.02892 49 12 .84507 .18334 .87543 1.14229 .90674 1.10285 .93906 1.06489 .97246 1.02832 48 13 .84556 .18264 .87595 1.14162 .90727 1.10220 .93961 1.06427 .97302 1.02772 47 14 .84606 .18194 .87646 1.14095 .90781 1.10156 .94016 1.06365 .97359 1.02713 46 15 .84656 .18125 .87698 1.14028 .90834 1.10091 .94071 1.06303 .97416 1.02653 45 16 .84706 .18055 .87749 1.13961 .90887 1.10027 .94125 1.06241 .97472 1.02593 44 17 .84756 .17986 .87801 1.13894 .90940 1.09963 .94180 1.06179 .07529 1.02533 43 18 .84806 .17916 .87852 1.13828 .90993 1.09899 .94235 1.06117 .97586 1.02474 42 19 .84856 .17846 .87904 1.13761 .91046 1.09834 .94290 1.06056 .97643 1.02414 41 20 .84906 .17777 .87955 1.13694 .91099 1.09770 .94345 1.05994 .97700 1.02355 40 21 .84956 .17708 .88007 1.13627 .91153 1.09706 .94400 1.05932 .97756 1.02295 39 22 .85006 .17638 .88059 1.13561 .91206 1.09642 .94455 1.05870 .97813 1.02236 38 23 .85057 .17569 .88110 1.13494 .91259 1.09578 .94510 1.05809 .97870 1.02176 37 24 .85107 .17500 .88162 1.13428 .91313 1.09514 .94565 1.05747 .97927 1.02117 36 25 .85157 .17430 .88214 1.13361 .91366 1.09450 .94620 1.05685 .97984 1.02057 35 26 .85207 .17361 .88265 1.13295 .91419 1.09386 .94676 1.05624 .98041 1.01998 34 27 .85257 .17292 .88317 1.13228 .91473 1.09322 .94731 1.05562 .98098 1.01939 33 28 .85308 .17223 .88369 1.13162 .91526 1.09258 .94786 1.05501 .98155 1.01879 32 29 .85358 .17154 .88421 1.13096 .91580 1.09195 .94841 1.05439 .98213 1.01820 31 30 .85408 1.17085 .88473 1.13029 .91633 1.09131 .94896 1.05378 .98270 1.01761 30 31 .85458 1.17016 .88524 1.12963 .91687 1.09067 .94952 1.05317 .98327 1.01702 29 32 .85509 1.16947 .88576 1.12897 .91740 1.09003 .95007 1.05255 .98384 1.01642 28 33 .85559 1.16878 .88628 1.12831 .91794 1.08940 .95062 1.05194 .98441 1.01583 27 34 .85609 1.16809 .88680 1.12765 .91847 1.08876 .95118 1.05133 .98499 1.01524 26 35 .85660 1.16741 .88732 1.12699 .91901 1.08813 .95173 1.05072 .98556 1.01465 25 36 .85710 1.16672 .88784 1.12633 .91955 1.08749 .95229 1.05010 .98613 1.01406 24 37 .85761 1.16603 .88836 1.12567 .92008 1.08686 .95284 1.04949 .98671 1.01347 23 38 .85811 1.16535 .88888 1.12501 .92062 1.08622 .95340 1.04888 .98728 1.01288 22 39 .85862 1.16466 .88940 1.12435 .92116 1.08559 .95395 1.04827 .98786 1.01229 21 40 .85912 1.16398 .88992 1.12369 .92170 1.08496 .95451 1.04766 .98843 1.01170 20 41 .85963 1.16329 .89045 1.12303 .92224 1.08432 .95506 1.04705 .98901 1.01112 19 42 .86014 1.16261 .89097 1.12238 .92277 1.08369 .95562 1.04644 .98958 1.01053 18 43 .86064 1.16192 .89149 1.12172 .92331 1.08306 .95618 1.04583 .99016 1.00994 17 44 .86115 1.16124 .89201 1.12106 .92385 1.08243 .95673 1.04522 .99073 1.00935 16 45 .86166 1.16056 .89253 1.12041 .92439 1.08179 .95729 1.04461 .99131 1.00876 15 46 .86216 1.15987 .89306 1.11975 .92493 1.08116 .95785 1.04401 .99189 1.00818 14 47 .86267 1.15919 .89358 1.11909 .92547 1.08053 .95841 1.04340 .99247 1.00759 13 48 .86318 1.15851 .89410 1.11844 .92601 1.07990 .95897 1.04279 .99304 1.00701 12 49 .86368 1.15783 .89463 1.11778 .92655 1.07927 .95952 1.04218 .99362 1.00642 11 50 .86419 1.15715 .89515 1.11713 .92709 1.07864 .96008 1.04158 .99420 1.00583 10 51 .86470 1.15647 .89567 1.11648 .92763 1.07801 .96064 1.04097 .99478 1.00525 9 52 .86521 1.15579 .89620 1.11582 .92817 1.07738 .96120 1.04036 .99536 1.00467 8 53 .86572 1.15511 .89672 1.11517 .92872 1.07676 .96176 1.03976 .99594 1.00408 7 54 .86623 1.15443 .89725 1.11452 .92926 1.07613 .96232 1.03915 .99652 1.00350 6 55 .86674 1.15375 .89777 1.11387 .92980 1.07550 .96288 1.03855 .99710 1.00291 5 56 .86725 1.15308 .89830 1.11321 .93034 1.07487 .96344 1.03794 .99768 1.00233 4 57 .86776 1.15240 .89883 1.11256 .93088 1.07425 .96400 1.03734 .99826 1.00175 3 58 .86827 1.15172 .89935 1.11191 .93143 1.07362 .96457 1.03674 .99884 1.00116 2 59 .86878 1.15104 .89988 1.11126 .93197 1.07299 .96513 1.03613 .99942 1.00058 1 60 .86929 1.15037 .90040 1.11061 .93252 1.07237 .96569 1.03553 1.00000 1.00000 Cotang Tang Cotang Tang Cotang Tang Cotang Tang Cotang Tang f / 4< ) 4 3 4' P 4( ) 4 3 LOGARITHMIC TABLES. 473 LOGARITHMIC TABLES. For detailed directions as to the use of logarithms see page 22. To Find the Logarithmic Sine, Cosine, Tangent, or Cotangent of an Angle From to 45. In the table Logarithms of Trigonometric Functions, find the number of degrees at the top of the page, and the number of minutes in the left-hand column headed ('); opposite the latter, and under the proper head, find the desired logarithmic sine, cosine, tangent, or cotangent. To Find the Logarithmic Sine, Cosine, Tangent, or Cotangent of an Angle From 45 to 90. In the table Logarithms of Trigonometric Functions, find the number of degrees at the bottom of the page, and the number of minutes in the right-hand column headed ('); opposite the latter, and above the proper head, find the desired logarithmic sine, cosine, tangent, or cotangent. To Find the Logarithmic Functions for an Angle Containing Degrees, Minutes, and Seconds. Find the logarithm for the degrees and minutes in the manner given above, then from the column headed " d." take the number next below the logarithm thus found; under the heading "P. P.," find a column headed by this number, and find in this column the number opposite the given number of seconds; add it to the logarithm already found for the degrees and min- utes. If the exact number of seconds is not given under "P. P.," the proper values may be found by interpolating between the values given. Since the differences in the column headed "d." represent differences cor- responding to 60 minutes, the amount to be added after the logarithm of the degrees and minutes has been found may be obtained by multiplying the difference by the number of seconds, and dividing the result by 60. The columns headed "Cpl. S." and " Cpl. T." on pages 492-494 can be used to find logarithms of angles including seconds less than 3 and greater than 86. Reduce the degrees, minutes, and seconds to seconds, and use the following formulas, substituting for Cpl. S. and Cpl. T. the values given in the table, and for S. and T., the difference between 10 and Cpl. S. and Cpl. T. as given. For angles less than A, log sin a = log a" + S.; log tang a = log a" 4- T.; log cotg a = Cpl. log a" + Cpl. T. = Cpl. log tang a; log a" = log sin a + Cpl. S. = log tang a + Cpl. T. -= Cpl. log cotg a + Cpl. T. For angles greater than 86, log cos a = log (90 a)'' + S.; . = log (90- a)" + T.; log tang a = Cpl. log (90 a)" + Cpl. T. = Cpl. log COtg a; log (90 a)" = log COS a + Cpl. S. = log COtg a + Cpl. T. = Cpl. log tang a + Cpl. T. COMMON LOGARITHMS OF NUMBERS. No. Log. No. Log. No. Log. No. Log. No. Log. 00 20 30 103 40 60 206 60 77 815 80 90 309 i 00 000 21 32 222 41 61 278 61 78 533 81 90 849 2 30 103 22 34 242 42 62 325 62 79 239 82 91 381 3 47 712 23 36 173 43 63 347 63 79 934 83 91 908 4 60 206 24 38 021 44 64 345 64 80 618 84 92 428 5 69 897 25 39 794 45 65 321 65 81 291 85 92 942 6 77 815 26 41 497 46 66 276 66 81 954 86 93 450 7 84 510 27 43 136 47 67 210 67 82 607 87 93 952 8 90 309 28 44 716 48 68 124 68 83 251 88 94 448 9 95 424 29 46 240 49 69 020 69 83 885 89 94 939 10 00 000 30 47 712 50 69 897 70 84 510 90 95 424 11 04 139 31 49 136 51 70 757 71 85 126 91 95 904 12 07 918 32 50 515 52 71 600 72 85 733 92 96 379 13 11 394 33 51 851 53 72 428 73 86 332 93 96 848 14 14 613 34 53 148 54 73 239 74 86 923 94 97 313 15 17 609 35 54 407 55 74 036 75 87 506 95 97 772 16 20 412 36 55 630 56 74 819 76 88 081 % 98 227 17 23 045 37 56 820 57 75 587 77 88 649 97 98 677 18 25 527 38 57 978 58 76 343 78 89 209 98 99 123 19 27 875 39 59 106 59 77 085 79 89 763 99 99 564 20 30 103 40 60 206 60 77 815 80 90 309 100 00000 LOGARITHMS. N. L. 1 2 3 4 5 6 7 8 9 P.P. 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 ISO [X) 000 043 087 130 173 217 260 303 346 389 44 il 43| 42 432 860 1 284 703 2 119 531 938 03 342 743 475 903 326 745 160 572 979 383 782 518 945 368 787 202 612 *019 423 822 561 988 410 828 243 653 *060 463 862 604 *030 452 870 284 694 *100 503 902 647 *072 494 912 325 735 141 543 941 689 *115 536 953 366 776 *181 583 981 732 *157 578 995 407 816 *222 623 *021 775 *199 620 *036 449 857 *262 663 *060 817 *242 662 *078 490 898 *302 703 *100 2 3 4 5 (> 7 8 9 1 2 3 4 6 7 8 9 1 3 i 5 6 7 8 9 1 2 8 4 5 (i 7 8 9 1 2 3 4 5 6 7 8 9 8.8 13.2 17.6 22.0 26.4 30.8 35.2 39.6 41 4.1 8.2 12.3 16.4 20.5 24.6 28.7 32.8 36.9 38 3.8 7.6 11.4 15.2 19.0 22.8 26.6 80.4 34.2 35 3.5 7.0 10.5 14.0 17.5 21.0 24.5 28.0 31.5 32 3.2 6.4 9.6 12.8 16.0 19.2 22.4 25.6 28.8 8.6 12.9 17.2 21.5 25.8 30.1 34.4 38.7 40 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0 37 3.7 7.4 11.1 14.8 18.5 22.2 25.9 296 33.3 34 3.4 6.8 10.2 13.6 17.0 20.4 23.8 27.2 30.6 31 3.1 6.2 9.3 12.4 15.5 18.6 21.7 24.8 27.9 8.4 12.B 16.8 21.0 25.2 29.4 33.6 37.8 39 3.9 7.8 11.7 15.6 19.5 23.4 27.3 31.2 35.1 36 3.6 7.2 10.8 14.4 18.0 21.6 25.2 28.8 32.4 33 3.3 6.6 9.9 13.2 16.5 19.8 23.1 26.4 29.7 30 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 04 139 179 218 258 297 336 376 415 454 493 883 *269 652 *032 408 781 *151 518 882 532 922 05 308 690 06 070 446 819 07 188 555 571 961 346 729 108 483 856 225 591 610 999 385 767 145 521 893 262 628 650 *038 423 805 183 558 930 298 664 689 *077 461 843 221 595 967 335 700 727 *115 500 881 258 633 *004 372 737 766 *154 538 918 296 670 *041 408 773 805 *192 576 956 333 707 *078 445 809 844 *231 614 994 371 744 *115 482 846 918 954 990 *027 *063 *099 *135 *171 *207 *243 08 279 636 991 09 342 691 10 037 380 721 11 059 314 672 *026 377 726 072 415 755 093 350 707 *061 412 760 106 449 789 126 386 743 *096 447 795 140 483 823 160 422 778 *132 482 830 175 517 857 193 458 814 *167 517 864 209 551 890 227 493 849 *202 552 899 243 585 924 261 529 884 *237 587 934 278 619 958 294 628 565 920 *272 621 968 312 653 992 327 600 955 *307 656 *003 346 687 *025 361 394 428 461 793 123 450 775 098 418 735 *051 364 494 528 561 594 661 694 727 12 057 385 710 13 033 354 672 988 14 301 760 090 418 743 066 386 704 *019 333 826 156 483 808 130 450 767 *082 395 860 189 516 840 162 481 799 *114 426 893 222 548 872 194 513 830 *145 457 926 254 581 905 226 545 862 *176 489 959 287 613 937 258 577 893 *208 520 992 320 646 969 290 609 925 *239 551 *024 352 678 *001 322 640 956 *270 582 613 644 675 706 737 768 799 829 860 891 922 15 229 534 836 16 137 435 732 17 026 319 953 259 564 866 167 465 761 056 348 983 290 594 897 197 495 791 085 377 *014 320 625 927 227 524 820 114 406 *045 351 655 957 256 554 850 143 435 *076 381 685 987 286 584 879 173 464 *106 412 715 *017 316 613 909 202 493 *137 442 746 *047 346 643 938 231 522 *168 473 776 *077 376 673 967 260 551 *198 503 806 *107 406 702 997 289 580 609 638 667 696 725 754 782 811 840 869 N. L. 1 2 3 4 5 6 7 8 9 P.P. LOGARITHMS. 475 N. L.O 1 2 3 4 5 6 7 8 9 P.] ^ ISO 17 609 638 667 696 725 754 782 811 840 869 151 152 153 154 155 156 157 158 159 898 18 184 469 752 19 033 312 590 866 20 140 926 213 498 780 061 340 618 893 167 955 241 526 808 089 368 645 921 194 984 270 554 837 117 396 673 948 222 *013 298 583 865 145 424 700 976 249 *041 327 611 893 173 451 728 *003 276 *070 355 639 921 201 479 756 *030 303 *099 384 667 949 229 507 783 *058 330 *127 412 696 977 257 535 811 *085 358 *156 441 724 *005 285 562 838 *112 385 i 2 3 4 5 6 7 8 9 29 2.9 5.8 8.7 11.6 14.5 17.4 20.3 23.2 26.1 28 2.8 5. 8.4 11.2 14.0 16.8 19.6 22.4 25.2 160 412 439 466 493 520 548 575 602 629 656 161 162 163 164 165 166 167 168 169 683 952 21 219 484 748 22 Oil 272 531 789 710 978 245 511 775 037 298 557 814 737 *005 272 537 801 063 324 583 840 763 *032 299 564 827 089 350 608 866 790 *059 325 590 854 115 376 634 891 817 *085 352 617 880 141 401 660 917 844 *112 '378 643 906 167 427 686 943 871 *139 405 669 932 194 453 712 968 898 *165 431 696 958 220 479 737 994 925 *192 458 722 985 246 505 763 *019 1 2 3 4 5 6 7 8 9 27 2.7 5.4 8.1 10.8 13.5 16.2 18.9 21.6 24.3 26 2.6 5.2 7.8 10.4 13.0 15.6 18.2 20.8 23.4 170 23 045 070 096 121 147 172 198 223 249 274 171 172 173 174 175 176 177 178 179 300 553 805 24 055 304 551 797 25 042 285 325 578 830 080 329 576 822 066 310 350 603 855 105 353 601 846 091 334 376 629 880 130 378 625 871 115 358 401 654 905 155 403 650 895 139 382 426 679 930 180 428 674 920 164 406 452 704 955 204 452 699 944 188 431 477 729 980 229 477 724 969 212 455 502 754 *005 254 502 748 993 237 479 528 779 *030 279 527 773 *018 261 503 2 1 5 3 ' 4 1( 5 15 6 U 7 I' 8 2( 9 25 5 .5 .0 .5 .0 .5 .0 .5 .0 .5 180 527 551 575 600 624 648 672 696 720 744 181 182 183 184 185 186 187 188 189 768 26 007 245 482 717 951 27 184 416 646 792 031 269 505 741 975 207 439 669 816 055 293 529 764 998 231 462 692 840 079 316 553 788 *021 254 485 715 864 102 340 576 811 *045 277 508 738 888 126 364 600 834 *068 300 531 761 912 150 387 623 858 *091 323 554 784 935 174 411 647 881 *114 346 577 807 959 198 435 670 905 *138 370 600 830 983 221 458 694 928 *161 393 623 852 1 2 3 4 5 6 7 8 9 24 2.4 4.8 7.2 9.6 12.0 14.4 16.8 19.2 21.6 23 2.3 4.6 6.9 9.2 11.5 13.8 16.1 18.4 20.7 190 875 898 921 944 967 989 *012 *035 *058 *081 191 192 193 194 195 196 197 198 199 28 103 330 556 780 29 003 226 447 667 885 126 353 578 803 026 248 469 688 907 149 375 601 825 048 270 491 710 929 171 398 623 847 070 292 513 732 951 194 421 646 870 092 314 535 754 973 217 443 668 892 115 336 557 776 994 240 466 691 914 137 358 579 798 *016 262 488 713 937 159 380 601 820 *038 285 511 735 959 181 403 623 842 *060 307 533 758 981 203 425 645 863 *081 1 2 3 4 5 6 7 8 9 22 2.2 4.4 6.6 8.8 11.0 13.2 15.4 17.6 19.8 21 2.1 4.2 6.3 8.4 10.5 12.6 14.7 16.8 18.9 200 30 103 125 146 168 190 211 233 255 276 298 N. L.O 1 2 3 4 5 6 7 8 9 P.] > 47(5 LOGARITHMS. N. L.O 1 2 3 4 5 6 7 8 276 9 P.P. 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 30 103 125 146 168 190 211 233 255 298 2 1 2 2 4 3 fi 4 8 5 11 6 13 7 15 8 17 9 19 j 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 2 21 .2 2.1 .4 4.2 .6 6.3 .8 8.4 .0 10.5 .2 12.6 .4 14.7 .8 16.8 .8 18.9 20 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 19 1.9 3.8 5.7 7.6 9.5 11.4 13.3 15.2 17.1 18 1.8 3.6 5.4 7.2 9.0 10.8 12.6 14.4 16.2 . 17 1.7 34 5.1 6.8 8.5 10.2 11.9 13.6 15.3 320 535 750 963 31 175 387 597 - 806 32 015 341 557 771 984 197 408 618 827 035 363 578 792 *006 218 429 639 848 056 384 600 814 *027 239 450 660 869 077 284 406 621 835 *048 260 471 681 890 098 428 643 856 *069 281 492 702 911 118 449 664 878 *091 302 513 723 931 139 471 685 899 *112 323 534 744 952 160 492 707 920 *133 345 555 765 973 181 514 728 942 *154 366 576 785 994 201 222 243 263 305 325 346 366 387 408 428 634 838 33 041 244 445 646 846 34 044 449 654 858 062 264 465 666 866 064 469 675 879 082 284 486 686 885 084 490 695 899 102 304 506 706 905 104 510 715 919 122 325 526 726 925 124 531 736 940 143 345 546 746 945 143 552 756 60 163 365 566 766 965 163 572 777 980 183 385 586 786 985 183 593 797 *001 203 405 606 806 *005 203 613 818 *021 224 425 626 826 *025 223 242 262 282 301 321 341 361 380 400 420 439 635 830 35 025 218 411 603 793 984 459 655 850 044 238 430 622 813 *003 479 674 869 064 257 449 641 832 *021 498 694 889 083 276 468 660 851 *040 518 713 908 102 295 488 679 870 *059 537 733 928 122 315 507 698 889 *078 557 753 947 141 334 526 717 908 *097 577 772 967 160 353 545 736 927 *116 596 792 986 180 372 564 755 946 *135 616 811 *005 199 392 583 774 965 *154 36 173 192 211 229 248 267 286 305 324 342 361 549 736 922 37 107 291 475 658 840 380 568 754 940 125 310 493 676 858 399 586 773 959 144 328 511 694 876 418 605 791 977 162 346 530 712 894 436 624 810 996 181 365 548 731 912 455 642 829 *014 199 383 566 749 931 474 661 847 *033 218 401 585 767 949 493 680 866 *051 236 420 603 785 967 511 698 884 *070 254 438 621 803 985 530 717 903 *088 273 457 639 822 *003 38 021 039 057 075 093 112 130 148 166 184 202 382 561 739 917 39 094 270 445 620 220 399 578 757 934 111 287 463 637 238 417 596 775 952 129 305 480 655 256 435 614 792 970 146 322 498 672 274 453 632 810 987 164 340 515 690 863 4 292 471 650 828 *005 182 358 533 707 310 489 668 846 *023 199 375 550 724 328 507 686 863 *041 217 393 568 742 346 525 703 881 *058 235 410 585 759 364 543 721 899 *076 252 428 602 777 794 811 829 846 881 5 898 915 933 950 N. L.O 1 2 3 6 7 8 9 P.P. LOGARITHMS. N. L.O 1 2 3 4 5 6 7 8 9 P.P. 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 39 794 811 829 846 863 881 898 915 933 950 *123 295 466 637 807 976 *145 313 481 i 2 8 4 5 6 8 9 1 2 8 5 6 7 8 9 ] 2 8 4 6 8 1 3 4 6 7 8 9 2 4 5 6 8 9 18 1.8 3.6 5.4 7.2 9.0 10.8 12.6 14.4 16.2 17 1.7 3.4 5.1 6.8 8.5 10.2 11.9 13.6 15.3 16 1.6 3.2 4.8 6.4 8.0 9.6 11.2 12.8 14.4 15 1.5 3.0 4.5 6.0 9X) 10.5 12.0 13.5 14 1.4 2 8 4.2 5.6 7.0 8.4 9.8 11.2 12.6 967 40 140 312 483 654 824 993 41 162 330 985 157 329 500 671 841 *010 179 347 *002 175 346 518 688 858 *027 196 363 *019 192 364 535 705 875 *044 212 380 *037 209 381 552 722 892 *061 229 397 *054 226 398 569 739 909 *078 246 414 *071 243 415 586 756 926 *095 263 430 *088 261 432 603 773 943 *111 280 447 *106 278 449 620 790 960 *128 296 464 497 514 681 847 *012 177 341 504 667 830 991 531 547 714 880 *045 210 374 537 700 862 *024 564 581 597 614 631 797 963 *127 292 455 619 781 943 *104 647 664 830 996 42 160 325 488 651 813 975 697 863 *029 193 357 521 684 846 *008 731 896 *062 226 390 553 716 878 *040 747 913 *078 243 406 570 732 894 *056 764 929 *095 259 423 586 749 911 *072 233 780 946 *111 275 439 602 765 927 *088 814 979 *144 308 472 635 797 959 *120 43 136 152 169 185 201 217 249 265 281 297 457 616 775 933 44 091 248 404 560 313 473 632 791 949 107 264 420 576 329 489 648 807 965 122 279 436 592 345 505 664 823 981 138 295 451 607 361 521 680 838 996 154 311 467 623 778 377 537 696 854 *012 170 326 483 638 393 553 712 870 *028 185 342 498 654 409 569 727 886 *044 201 358 514 669 425 584 743 902 *059 217 373 529 685 441 600 759 917 *075 232 389 545 700 716 731 747 762 793 809 824 840 855 871 45 025 179 332 484 637 788 939 46 090 886 040 194 347 500 652 803 954 105 902 056 209 362 515 667 818 969 120 917 071 225 378 530 682 834 984 135 932 086 240 393 545 697 849 *000 150 948 102 255 408 561 712 864 *015 165 315 963 117 271 423 576 728 879 *030 180 979 133 286 439 591 743 894 *045 195 994 148 301 454 606 758 909 *060 210 *010 163 317 469 621 773 924 *075 225 240 255 270 285 300 330 345 359 374 389 538 687 835 982 47 129 276 422 567 404 553 702 850 997 144 290 436 582 419 568 716 864 *012 159 305 451 596 434 583 731 879 *026 173 319 465 611 449 598 746 894 *041 188 334 480 625 464 613 761 909 *056 202 349 494 640 479 627 776 923 *070 217 363 509 654 494 642 790 938 *085 232 378 524 669 509 657 805 953 *100 246 392 538 683 523 672 820 967 *114 261 407 553 698 712 727 741 756 770 784 799 813 828 842 N. L.O 1 2 3 4 5 6 7 8 9 P.P. 478 LOGARITHMS. N. L.O 1 2 3 4 5 6 7 8 9 P.P. 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 47 712 727 741 756 770 784 799 813 '828 842 15 1 1.5 2 3.0 3 4.5 4 6.0 5 7.5 6 9.0 7 10.5 8 12.0 9 13.5 14 1 1.4 2 2.8 3 4.2 4 5.6 5 7.0 6 8.4 7 9.8 8 11.2 9 j 12.6 13 1 1.3 2 2.6 3 3.9 4 52 6 7.8 7 9.1 8 10.4 9 11.7 12 1 1.2 2 2.4 3 3.6 4 4.8 5 6.0 6 7.2 7 8.4 8 9.6 9 10.8 857 48 001 144 287 430 572 714 855 996 871 015 159 302 444 586 728 869 *010 885 029 173 316 458 601 742 883 *024 900 044 187 330 473 615 756 897 *038 914 058 202 344 487 629 770 911 *052 929 073 216 359 501 643 785 926 *066 943 087 230 373 515 657 799 940 *080 220 958 101 244 387 530 671 813 954 *094 972 116 259 401 544 686 827 968 *108 986 130 273 416 558 700 841 982 *122 49 136 150 164 178 192 206 234 248 262 276 415 554 693 831 969 50 106 243 379 290 429 568 707 845 982 120 256 393 304 443 582 721 859 996 133 270 406 318 457 596 734 872 *010 147 284 420 332 471 610 748 886 *024 161 297 433 346 485 624 762 900 *037 174 311 447 360 499 638 776 914 *051 188 325 461 374 513 651 790 927 *065 202 338 474 388 527 665 803 941 *079 215 352 488 402 541 679 817 955 *092 229 365 501 515 529 542 556 569 583 596 610 623 637 772 907 *041 175 308 441 574 706 838 651 786 920 51 055 188 322 455 587 720 664 799 934' 068 202 335 468 601 733 678 813 947 081 215 348 481 614 746 691 826 961 095 228 362 495 627 759 705 840 974 108 242 375 508 640 772 718 853 987 121 255 388 521 654 786 732 866 *001 135 268 402 534 667 799 745 880 *014 148 282 415 548 680 812 759 893 *028 162 295 428 561 693 825 851 865 878 891 904 917 930 943 957 970 983 52 114 244 375 504 634 763 892 53 020 996 127 257 388 517 647 776 905 033 *009 140 270 401 530 660 789 917 046 *022 153 284 414 543 673 802 930 058 *035 166 297 427 556 686 815 943 071 *048 179 310 440 569 699 827 956 084 *061 192 323 453 582 711 840 969 097 *075 205 336 466 595 724 853 982 110 *088 218 349 479 608 737 866 994 122 *101 231 362 492 621 750 879 *007 135 148 161 173 186 199 212 224 237 250 263 275 403 529 656 782 908 54 033 158 283 288 415 542 668 794 920 045 170 295 301 428 555 681 807 933 058 183 307 314 441 567 694 820 945 070 195 320 326 453 580 706 832 958 083 208 332 339 466 593 719 845 970 095 220 345 352 479 605 732 857 983 108 233 357 364 491 618 744 870 995 120 245 370 377 504 631 757 882 *008 133 258 382 390 517 643 769 895 *020 145 270 394 407 419 432 444 456 469 481 494 506 518 N. L.O 1 2 3 4 5 6 7 8 9 P.P. LOGARITHMS. 479 N. L.O 1 2 3 4 5 6 7 8 9 P.P. 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 . 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 54 407 419 432 444 456 580 704 827 949 072 194 315 437 558 469 593 716 839 962 084 206 328 449 570 481 494 506 518 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 8 9 13 1.3 2.6 3.9 5.2 6.5 7.8 9.1 10.4 11.7 12 1.2 2.4 3.6 4.8 6.0 7.2 8.4 9.6 10.8 11 1 1 22 33 4 4 5 5 66 77 88 99 10 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 531 654 777 900 55 023 145 267 388 509 543 667 790 913 035 157 279 400 522 555 679 802 925 047 169 291 413 534 568 691 814 937 060 182 303 425 546 605 728 851 974 096 218 340 461 582 617 741 864 986 108 230 352 473 594 630 753 876 998 121 242 364 485 606 642 765 888 *011 133 255 376 497 618 630 642 654 775 895 *015 134 253 372 490 608 726 666 678 691 703 715 727 739 859 979 *098 217 336 455 573 691 808 751 871 991 56 110 229 348 467 585 703 763 883 *003 122 241 360 478 597 714 787 907 *027 146 265 384 502 620 738 799 919 *038 158 277 396 514 632 750 811 931 *050 170 289 407 526 644 761 823 943 *062 182 301 419 538 656 773 835 955 *074 194 312 431 549 667 785 847 967 *086 205 324 443 561 679 797 820 832 844 855 867 879 891 902 914 926 *043 159 276 392 507 623 738 852 967 937 57 054 171 287 403 519 634 749 864 949 066 183 299 415 530 646 761 875 961 078 194 310 426 542 657 772 887 *001 115 229 343 456 569 681 794 906 *017 972 089 206 322 438 553 669 784 898 984 101 217 334 449 565 680 795 910 996 113 229 345 461 576 692 807 921 *008 124 241 357 473 588 703 818 933 *019 136 252 368 484 600 715 830 944 *031 148 264 380 496 611 726 841 955 978 990 104 218 331 444 557 670 782 894 *006 *013 *024 *035 *047 *058 *070 *081 58 092 206 320 433 546 659 771 883 995 127 240 354 467 580 692 805 917 *028 138 252 365 478 591 704 816 928 *040 149 263 377 490 602 715 827 939 *051 161 274 388 501 614 726 838 950 *062 172 286 399 512 625 737 850 961 *073 184 297 410 524 636 749 861 973 *084 195 309 422 535 647 760 872 984 *095 59 106 118 129 140 251 362 472 583 693 802 912 *021 130 239 J51 262 373 483 594 704 813 923 *032 141 162 173 184 195 207 218 329 439 550 660 770 879 988 60 097 229 340 450 561 671 780 890 999 108 240 351 461 572 682 791 901 *010 119 273 384 494 605 715 824 934 *043 152 284 395 506 616 726 835 945 *054 163 295 406 517 627 737 846 956 *065 173 306 417 528 638 748 857 966 *076 184 318 428 539 649 759 868 977 *086 195 206 217 228 249 260 5 271 6 282 293 304 N. L.O 1 2 3 4 7 8 9 P.P. 480 LOGARITHMS. N. L 1 2 3 4 5 6 7 8 9 P .P. 400 60 206 217 228 239 249 260 271 282 293 304 401 402 403 404 405 406 407 408 409 314 423 531 638 746 853 959 61 066 172 325 433 541 649 756 863 970 077 183 336 444 552 660 767 874 981 087 194 347 455 563 670 778 885 991 098 204 358 466 574 681 788 895 *002 109 215 369 477 584 692 799 906 *013 119 225 379 487 595 703 810 917 *023 130 236 390 498 606 713 821 927 *034 140 247 401 509 617 724 831 938 *045 151 257 412 520 627 735 842 949 *055 162 268 i 2 II 1.1 2.2 410 278 289 300 310 321 331 342 352 363 374 4 4.4 411 412 413 414 415 416 417 418 419 384 490 595 700 805 909 62 014 118 221 395 500 606 711 815 920 024 128 232 405 511 616 721 826 930 034 138 242 416 521 627 731 836 941 045 149 252 426 532 637 742 847 951 055 159 263 437 542 648 752 857 962 066 170 273 448 553 658 763 868 972 076 180 284 458 563 669 773 878 982 086 190 294 469 574 679 784 888 993 097 201 304 479 584 690 794 899 *003 107 211 315 6 7 8 9 6.6 7.7 8.8 9.9 420 325 335 346 356 366 377 387 397 408 418 421 422 423 424 425 426 427 428 429 428 531 634 737 839 941 63 043 144 246 439 542 644 747 849 951 053 155 256 449 552 655 757 859 961 063 165 266 459 562 665 767 870 972 073 175 276 469 572 675 778 880 982 083 185 286 480 583 685 788 890 992 094 195 296 490 593 696 798 900 *002 104 205 306 500 603 706 808 910 *012 114 215 317 511 613 716 818 921 *022 124 225 327 521 624 726 829 931 *033 134 236 337 1 2 8 4 6 7 8 9 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 430 347 357 367 377 387 397 407 417 428 438 431 432 433 434 435 436 437 438 439 448 548 649 749 849 949 64 048 147 246 458 558 659 759 859 959 058 157 256 468 568 669 769 869 969 068 167 266 478 579 679 779 879 979 078 177 276 488 589 689 789 889 988 088 187 286 498 599 699 799 899 998 098 197 296 508 609 709 809 909 *008 108 207 306 518 619 719 819 919 *018 118 217 316 528 629 729 829 929 *028 128 227 326 538 639 739 839 939 *038 137 237 335 1 2 3 9 0.9 1.8 2.7 440 345 355 365 375 385 395 404 414 424 434 4.5 441 442 443 444 445 446 447 448 449 444 542 640 -738 836 933 65 031 128 225 454 552 650 748 846 943 040 137 234 464 562 660 758 856 953 050 147 244 473 572 670 768 865 963 060 157 254 483 582 680 777 875 972 070 167 263 493 591 689 787 885 982 079 176 273 503 601 699 797 895 992 089 186 283 513 611 709 807 904 *002 099 196 292 523 621 719 816 914 *011 108 205 302 532 631 729 826 924 *021 118 215 312 7 8 9 6.3 7.2 8.1 450 321 331 341 350 360 369 379 389 398 408 N. L.O 1 2 3 4 5 6 7 8 9 P .P. LOGARITHMS. 481 N. L.O 1 2 341 3 4 5 6 7 8 9 P.P. 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 65 321 331 350 360 369 379 389 398 408 i 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 9 0.9 1.8 2.7 3.6 4.5 5.4 6.3 8.1 8 0.8 1.6 2.4 4.0 4.8 5.6 6.4 7.2 418 514 610 706 801 896 992 66 087 181 427 523 619 715 811 906 *001 096 191 437 533 629 725 820 916 *011 106 200 447 543 639 734 830 925 *020 115 210 456 552 648 744 839 935 *030 124 219 466 562 658 753 849 944 *039 134 229 475 571 667 763 858 954 *049 143 238 485 581 677 772 868 963 *058 153 247 495 591 686 782 877 973 *068 162 257 504 600 696 792 887 982 *077 172 266 276 285 295 304 314 323 332 342 351 361 370 464 558 652 745 839 932 67 025 117 380 474 567 661 755 848 941 034 127 389 483 577 671 764 857 950 043 136 398 492 586 680 773 867 960 052 145 408 502 596 689 783 876 969 062 154 417 511 605 699 792 885 978 071 164 427 521 614 708 801 894 987 080 173 436 530 624 717 811 904 997 089 182 445 539 633 727 820 913 *006 099 191 455 549 642 736 829 922 *015 108 201 210 219 228 237 247 256 265 357 449 541 633 724 815 906 997 088 274 284 293 302 394 486 578 669 761 852 943 68 034 311 403 495 587 679 770 861 952 043 321 413 504 596 688 779 870 961 052 330 422 514 605 697 788 879 970 061 339 431 523 614 706 797 888 979 070 160 348 440 532 624 715 806 897 988 079 367 459 550 642 733 825 916 *006 097 376 468 560 651 742 834 925 *015 106 385 477 569 660 752 843 934 *024 115 124 133 142 151 169 178 187 196 205 215 305 395 485 574 664 753 842 931 224 314 404 494 583 673 762 851 940 233 323 413 502 592 681 771 860 949 242 332 422 511 601 690 780 869 958 251 341 431 520 610 699 789 878 966 055 260 350 440 529 619 708 797 886 975 269 359 449 538 628 717 806 895 984 278 368 458 547 637 726 815 904 993 287 377 467 556 646 735 824 913 *002 296 386 476 565 655 744 833 922 *011 69 020 028 037 046 064 073 082 090 099 108 197 285 373 461 548 636 723 810 117 205 294 381 469 557 644 732 819 126 214 302 390 478 566 653 740 827 135 223 311 399 487 574 662 749 836 144 232 320 408 496 583 671 758 845 152 241 329 417 504 592 679 767 854 161 249 338 425 513 601 688 775 862 170 258 346 434 522 609 697 784 871 179 267 355 443 531 618 705 793 880 188 276 364 452 539 627 714 801 888 975 897 906 914 923 932 940 949 958 966 N. L.O 1 2 3 4 5 6 7 8 9 P.P. 482 LOGARITHMS. N. L.O 1 2 3 4 5 6 7 8 9 P.P. 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 69 897 906 914 923 932 940 949 958 966 975 i 2 3 4 5 6 7 8 9 2 3 4 I 6 7 8 9 1 2 3 4 5 6 7 8 9 9 0.9 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 8 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 7 0.7 1.4 2.1 2.8 3.5 4.2 4.9 56 6.3 984 70 070 157 243 329 415 501 586 672 992 079 165 252 338 424 509 595 680 *001 088 174 260 346 432 518 603 689 *010 096 183 269 355 441 526 612 697 *018 105 191 278 364 449 535 621 706 791 *027 114 200 286 372 458 544 629 714 800 *036 122 209 295 381 467 552 638 723 808 *044 131 217 303 389 475 561 646 731 817 *053 140 226 312 398 484 569 655 740 *062 148 234 321 406 492 578 663 749 834 757 766 774 783 825 842 927 71 012 096 181 265 349 433 517 851 935 020 105 189 273 357 441 525 859 944 029 113 198 282 366 450 533 868 952 037 122 206 290 374 458 542 876 961 046 130 214 299 383 466 550 885 969 054 139 223 307 391 475 559 893 978 063 147 231 315 399 483 567 902 986 071 155 240 324 408 492 575 910 995 079 164 248 332 416 500 584 919 *003 088 172 257 341 425 508 592 600 609 617 625 634 642 650 659 667 675 684 767 850 933 72 016 099 181 263 346 692 775 858 941 024 107 189 272 354 700 784 867 950 032 115 198 280 362 709 792 875 958 041 123 206 288 370 452 717 800 883 966 049 132 214 296 378 460 725 809 892 975 057 140 222 304 387 734 817 900 983 066 148 230 313 395 742 825 908 991 074 156 239 321 403 750 834 917 999 082 165 247 329 411 759 842 925 *008 090 173 255 337 419 501 428 436 444 469 477 485 567 648 730 811 892 973 *054 135 215 493 509 591 673 754 835 916 997 73 078 159 518 599 681 762 843 925 *006 086 167 526 607 689 770 852 933 *014 094 175 534 616 697 779 860 941 *022 102 183 263 542 624 705 787 868 949 *080 111 191 272 550 632 713 795 876 957 *038 119 199 558 640 722 803 884 965 *046 127 207 575 656 738 819 900 981 *062 143 223 583 665 746 827 908 989 *070 151 231 312 392 472 552 632 711 791 870 949 *028 239 247 255 280 288 368 448 528 608 687 767 846 926 *005 296 304 384 464 544 624 703 783 862 941 *020 320 400 480 560 640 719 799 878 957 328 408 488 568 648 727 807 886 965 336 416 496 576 656 735 815 894 973 344 424 504 584 664 743 823 902 981 352 432 512 592 672 751 830 910 989 360 440 520 600 679 759 838 918 997 376 456 536 616 695 775 854 933 *013 74 036 044 052 060 068 076 084 092 099 107 N. L.O 1 2 3 4 5 6 7 8 9 PP. LOGARITHMS. 483 N. L.O 1 2 o 4 5 6 7 8 9 P.P. 550 74 036 044 052 060 068 076 084 092 099 107 551 552 553 554 555 556 557 558 559 115 194 273 351 429 507 586 663 741 123 202 280 359 437 515 593 671 749 131 210 288 367 445 523 601 679 757 139 218 296 374 453 531 609 687 764 147 225 304 382 461 539 617 695 772 155 233 312 390 468 547 624 702 780 162 241 320 398 476 554 632 710 788 170 249 327 406 484 562 640 718 796 178 257 335 414 492 570 648 726 803 186 265 343 421 500 578 656 733 811 560 819 827 834 842 850 858 865 873 881 889 g 561 562 563 564 565 566 567 568 569 896 974 75 051 128 205 282 358 435 511 904 981 059 136 213 289 366 442 519 912 989 066 143 220 297 374 450 526 920 997 074 151 228 305 381 458 534 927 *005 082 159 236 312 389 465 542 935 *012 089 166 243 320 397 473 549 943 *020 097 174 251 328 404 481 557 950 *028 105 182 259 335 412 488 565 958 *035 113 189 266 343 420 496 572 966 *043 120 197 274 351 427 504 580 1 0.8 2 1.6 3 2.4 4 3.2 5 4.0 6 4.8 7 5.6 8 6.4 9 7.2 570 587 595 603 610 618 626 633 641 648 656 571 572 573 574 575 576 577 578 579 664 740 815 891 967 76 042 118 193 268 671 747 823 899 974 050 125 200 275 679 755 831 906 982 057 133 208 283 686 762 838 914 989 065 140 215 290 694 770 846 921 997 072 148 223 298 702 778 853 929 *005 080 155 230 305 709 785 861 937 *012 087 163 238 313 717 793 868 944 *020 095 170 245 320 724 800 876 952 *027 103 178 253 328 732 808 884 959 *035 110 185 260 335 580 343 350 358 365 373 380 388 395 403 410 7 581 582 583 584 585 586 587 588 589 418 492 567 641 716 790 864 938 77 012 425 500 574 649 723 797 871 945 019 433 507 582 656 730 805 879 953 026 440 515 589 664 738 812 886 960 034 448 522 597 671 745 819 893 967 041 455 530 604 678 753 827 901 975 048 462 537 612 686 760 834 908 982 056 470 545 619 693 768 842 916 989 063 477 552 626 701 775 849 923 997 070 485 559 634 708 782 856 930 *004 078 1 0.7 2 1.4 3 2.1 4 2.8 5 3.5 6 4.2 7 4.9 8 ! 5.6 9 j 6.3 590 085 093 100 107 115 122 129 137 144 151 591 592 593 594 595 596 597 598 599 159 232 305 379 452 525 597 670 743 166 240 313 386 459 532 605 677 750 173 247 320 393 466 539 612 685 757 181 254 327 401 474 546 619 692 764 188 262 335 408 481 554 627 699 772 195 269 342 415 488 561 634 706 779 203 276 349 422 495 568 641 714 786 210 283 357 430 503 576 648 721 793 217 291 364 437 510 583 656 728 801 225 298 371 444 517 590 663 735 808 600 815 822 830 837 844 851 859 866 873 880 N L 1 2 3 4 5 6 7 8 9 P.P. 484 LOGARITHMS. N. L.O 1 2 3 4 5 6 7 8 9 r '.P. 600 77 815 822 830 837 844 851 859 866 873 880 601 602 603 604 605 606 607 608 609 887 960 78 032 104 176 247 319 390 462 895 967 039 111 183 254 326 398 469 902 974 046 118 190 262 333 405 476 909 981 053 125 197 269 340 412 483 916 988 061 132 204 276 347 419 490 924 996 068 140 211 283 355 426 497 931 *003 075 147 219 290 362 433 504 938 *010 082 154 226 297 369 440 512 945 *017 089 161 233 305 376 447 519 952 *025 097 168 240 312 383 455 526 i 2 8 0.8 1.6 610 533 540 547 554 561 569 576 583 590 597 4 3.2 611 612 613 614 615 616 617 618 619 604 675 746 817 888 958 79 029 099 169 611 682 753 824 895 965 036 106 176 618 . 689 760 831 902 972 043 113 183 625 696 767 838 909 979 050 120 190 633 704 774 845 916 986 057 127 197 640 711 781 852 923 993 064 134 204 647 718 789 859 930 *000 071 141 211 654 725 796 866 937 *007 078 148 218 661 732 803 873 944 *014 085 155 225 668 739 810 880 951 *021 092 162 232 6 8 9 4.8 5.6 6.4 620 239 246 253 260 267 274 281 288 295 302 621 622 623 624 625 626 627 628 629 309 379 449 518 588 657 727 796 865 316 386 456 525 595 664 734 803 872 323 393 463 532 602 671 741 810 879 330 400 470 539 609 678 748 817 886 337 407 477 546 616 685 754 824 893 344 414 484 553 623 692 761 831 900 351 421 491 560 630 699 768 837 906 358 428 498 567 637 706 775 844 913 365 435 505 574 644 713 782 851 920 372 442 511 581 650 720 789 858 927 1 2 3 4 5 I 8 9 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 630 934 941 948 955 962 969 975 982 989 996 631 632 633 634 635 636 637 638 639 80 003 072 140 209 277 346 414 482 550 010 079 147 216 284 353 421 489 557 017 085 154 223 291 359 428 496 564 024 092 161 229 298 366 434 502 570 030 099 168 236 305 373 441 509 577 037 106. 175 243 312 380 448 516 584 044 113 182 250 318 387 455 523 .591 051 120 188 257 325 393 462 530 598 058 127 195 264 332 400 468 536 604 065 134 202 271 339 407 475 543 611 1 2 3 6 0.6 1.2 1.8 640 618 625 632 638 645 652 659 665 672 679 5 3.0 641 642 643 644 645 646 647 648 649 686 754 821 889 956 81 023 090 158 224 693 760 828 895 963 030 097 164 231 699 767 835 902 969 037 104 171 238 706 774 841 909 976 043 111 178 245 713 781 848 916 983 050 117 184 251 720 787 855 922 990 057 124 191 258 726 794 862 929 996 064 131 198 265 733 801 868 936 *003 070 137 204 271 740 808 875 943 *010 077 144 211 278 747 814 882 949 *017 084 151 218 285 7 8 9 4.2 4.8 5.4 650 291 298 305 311 318 325 331 338 345 351 N. L.O 1 2 3 4 5 6 7 8 9 P, P. LOGARITHMS. 485 N. L.O 1 2 3 4 5 6 7 8 9 P.P. 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 81 291 298 305 311 318 385 451 518 584 651 717 783 849 915 325 331 398 465 531 598 664 730 796 862 928 338 345 351 7 1 0.7 2 1.4 3 2.1 4 2.8 5 3.5 6 4.2 7 4.9 8 5.6 9 6.3 6 1 0.6 2 1.2 3 1.8 4 2.4 5 3.0 6 3.6 7 4.2 8 4.8 9 5.4 358 425 491 558 624 690 757 823 889 365 431 498 564 631 697 763 829 895 371 438 505 571 637 704 770 836 902 378 445 511 578 644 710 776 842 908 391 458 525 591 657 723 790 856 921 405 471 538 604 671 737 803 869 935 411 478 544 611 677 743 809 875 941 418 485 551 617 684 750 816 882 948 954 961 968 033 099 164 230 295 360 426 491 556 974 040 105 171 236 302 367 432 497 562 981 046 112 178 243 308 373 439 504 569 987 053 119 184 249 315 380 445 510 575 994 060 125 191 256 321 387 452 517 582 *000 066 132 197 263 328 393 458 523 588 *007 *014 079 145 210 276 341 406 471 536 601 82 020 086 151 217 282 347 413 478 543 027 092 158 223 289 354 419 484 549 073 138 204 269 334 400 465 530 595 607 614 620 627 633 640 646 653 659 666 672 737 802 866 930 995 83 059 123 187 679 743 808 872 937 *001 065 129 193 685 750 814 879 943 *008 072 136 200 692 756 821 885 950 *014 078 142 206 698 763 827 892 956 *020 085 149 213 705 769 834 898 963 *027 091 155 219 283 711 776 840 905 969 *033 097 161 225 718 782 847 911 975 *040 104 168 232 724 789 853 918 982 *046 110 174 238 730 795 860 924 988 *052 117 181 245 251 257 264 270 276 289 296 302 308 315 378 442 506 569 632 696 759 822 321 385 448 512 575 639 702 765 828 327 391 455 518 582 645 708 771 835 334 398 461 525 588 651 715 778 841 340 404 467 531 594 658 721 784 847 347 410 474 537 601 664 727 790 853 353 417 480 544 607 670 734 797 860 359 423 487 550 613 677 740 803 866 366 429 493 556 620 683 746 809 872 372 436 499 563 626 689 753 816 879 885 891 897 904 967 029 092 155 217 280 342 404 466 528 910 916 923 929 935 998 061 123 186 248 311 373 435 497 942 948 84 Oil 073 136 198 261 323 386 448 954 017 080 142 205 267 330 392 454 960 023 086 148 211 273 336 398 460 973 036 098 161 223 286 348 410 473 535 979 042 105 167 230 292 354 417 479 985 048 111 173 236 298 361 423 485 992 055 117 180 242 305 367 429 491 *004 067 130 192 255 317 379 442 504 510 516 1 522 541 547 553 559 566 N. L.O 2 3 4 5 6 7 8 9 P.P. 480 LOGARITHMS. N. L.O 1 2 3 4 5 6 7 8 9 P P. 700 84 510 516. 522 528 535 541 547 553 559 566 701 702 703 704 705 706 707 708 709 572 634 696 757 819 880 942 85 003 065 578 640 702 763 825 887 948 009 071 584 646 708 770 831 893 954 016 077 590 652 714 776 837 899 960 022 083 597 658 720 782 844 905 967 028 089 603 665 726 788 850 911 973 034 095 609 671 733 794 856 917 979 040 101 615 677 739 800 862 924 985 046 107 621 683 745 807 868 930 991 052 114 628 689 751 813 874 936 997 058 120 i 2 7 0.7 1.4 710 126 132 138 144 150 156 163 169 175 181 4 2.8 711 712 713 714 715 716 717 718 719 187 248 309 370 431 491 552 612 673 193 254 315 376 437 497 558 618 679 199 260 321 382 443 503 564 625 685 205 266 327 388 449 509 570 631 691 211 272 333 394 455 516 576 637 697 217 278 339 400 461 522 582 643 703 224 285 345 406 467 528 588 649 709 230 291 352 412 473 534 594 655 715 236 297 358 418 479 540 600 661 721 242 303 364 425 485 546 606 667 727 8 9 4.2 4.9 5.6 6.3 720 733 739 745 751 757 763 769 775 781 788 721 722 723 724 725 726 727 728 729 794 854 914 974 86 034 094 153 213 273 800 860 920 980 040 100 159 219 279 806 866 926 986 046 106 165 225 285 812 872 932 992 052 112 171 231 291 818 878 938 998 058 118 177 237 297 824 884 944 *004 064 124 183 243 303 830 890 950 *010 070 130 189 249 308 836 896 956 *016 076 136 195 255 314 842 902 962 *022 082 141 201 261 320 848 908 968 *028 088 147 207 267 326 1 1 3 4 5 6 7 8 9 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 730 332 338 344 350 356 362 368 374 380 386 731 732 733 734 735 736 737 738 739 392 451 510 570 629 688 747 806 864 398 457 516 576 635 694 753 812 870 404 463 522 581 641 700 759 817 876 410 469 528 587 646 705 764 823 882 415 475 534 593 652 711 770 829 888 421 481 540 599 658 717 776 835 894 427 487 546 605 664 723 782 841, 900 433 493 552 611 670 729 788 847 906 439 499 558 617 676 735 794 853 911 445 504 564 623 682 741 800 859 917 2 3 5 0.5 1.0 1.5 740 923 929 935 941 947 953 958 964 970 976 5 2.5 741 742 743 744 745 746 747 748 749 982 87 040 099 157 216 274 332 390 448 988 046 105 163 221 280 338 396 454 994 052 111 169 227 286 344 402 460 999 058 116 175 233 291 349 408 466 *005 064 122 181 239 297 355 413 471 *011 070 128 186 245 303 361 419 477 *017 075 134 192 251 309 367 425 483 *023 081 140 198 256 315 373 431 489 *029 087 146 204 262 320 379 437 495 *035 093 151 210 268 326 384 442 500 7 8 9 3.5 4.0 45 750 506 512 518 523 529 535 541 547 552 558 N. L.O 1 2 3 4 5 6 7 8 9 P .P. LOGARITHMS. 487 N. L.O 1 2 3 4 5 6 7 8 9 P.P. 750 87 506 512 518 523 529 535 541 547 552 558 751 752 753 754 755 756 757 758 759 564 622 679 737 795 852 910 967 88 024 570 628 685 743 800 858 915 973 030 576 633 691 749 806 864 921 978 036 581 639 697 754 812 869 927 984 041 587 645 703 760 818 875 933 990 047 593 651 708 766 823 881 938 996 053 599 656 714 772 829 887 944 *001 058 604 662 720 777 835 892 950 *007 064 610 668 726 783 841 898 955 *013 070 616 674 731 789 846 904 961 *018 076 760 081 087 093 098 104 110 116 121 127 133 761 762 763 764 765 766 767 768 769 138 195 252 309 366 423 480 536 593 144 201 258 315 372 429 485 542 598 150 207 264 321 377 434 491 547 604 156 213 270 326 383 440 497 553 610 161 218 275 332 389 446 502 559 615 167 224 281 338 395 451 508 564 621 173 230 287 343 400 457 513 570 627 178 235 292 349 406 463 519 576 632 184 241 298 355 412 468 525 581 638 190 247 304 360 417 474 530 587 643 1 0.6 2 1.2 3 1.8 4 2.4 5 3.0 6 3.6 7 4.2 8 4.8 9 5.4 770 649 655 660 666 672 677 683 689 694 700 771 772 773 774 775 776 111 778 779 705 762 818 874 930 986 89 042 098 154 711 767 824 880 936 992 048 104 159 717 773 829 885 941 997 053 109 165 722 779 835 891 947 *003 059 115 170 728 784 840 897 953 *009 064 120 176 734 790 846 902 958 *014 070 126 182 739 795 852 908 964 *020 076 131 187 745 801 857 913 969 *025 081 137 193 750 807 863 919 975 *031 087 143 198 756 812 868 925 981 *037 092 148 204 780 209 215 221 226 232 237 243 248 254 260 5 781 782 783 784 785 786 787 788 789 265 321 376 432 487 542 597 653 708 271 326 382 437 492 548 603 658 713 276 332 387 443 498 553 609 664 719 282 337 393 448 504 559 614 669 724 287 343 398 454 509 564 620 675 730 293 348 404 459 515 570 625 680 735 298 354 409 465 520 575 631 686 741 304 360 415 470 526 581 636 691 746 310 365 421 476 531 586 642 697 752 315 371 426 481 537 592 647 702 757 1 ! 0.5 2 1.0 3 1.5 4 2.0 5 2.5 6 3.0 7 3.5 8 4.0 9 4.5 790 763 768 774 779 785 790 796 801 807 812 791 792 793 794 795 796 797 798 799 818 873 927 982 90 037 091 146 200 255 823 878 933 988 042 097 151 206 260 829 883 938 993 048 102 157 211 266 834 889 944 998 053 108 162 217 271 840 894 949 *004 059 113 168 222 276 845 900 955 *009 064 119 173 227 282 851 905 960 *015 069 124 179 233 287 856 911 966 *020 075 129 184 238 293 862 916 971 *026 080 135 189 244 298 867 922 977 *031 086 140 195 249 304 800 309 314 320 325 331 336 342 347 352 358 N. L.O 1 2 3 4 5 6 7 8 9 P.P. 488 LOGARITHMS. N. L.O 1 2 3 4 5 6 7 8 9 P.P. 800 90 309 314 320 325 331 336 342 347 352 358 801 802 803 804 805 806 807 808 809 363 417 472 526 580 634 687 741 795 369 423 477 531 585 639 693 747 800 374 428 482 536 590 644 698 752 806 380 434 488 542 596 650 703 757 811 385 439 493 547 601 655 709 763 816 390 445 499 553 607 660 714 768 822 396 450 504 558 612 666 720 773 827 401 455 509 563 617 671 725 779 832 407 461 515 569 623 677 730 784 838 412 466 520 574 628 682 736 789 843 810 849 854 859 865 870 875 881 886 891 897 811 812 813 814 815 816 817 818 819 902 956 91 009 062 116 169 222 275 328 907 961 014 068 121 174 228 281 334 913 966 020 073 126 180 233 286 339 918 972 025 078 132 185 238 291 344 924 977 030 084 137 190 243 297 350 929 982 036 089 142 196 249 302 355 934 988 041 094 148 201 254 307 360 940 993 046 100 153 206 259 312 365 945 998 052 105 158 212 265 318 371 950 *004 057 110 164 217 270 323 376 1 0.6 2 1.2 3 1.8 4 2.4 5 3.0 6 3.6 7 4.2 8 4.8 9 5.4 820 381 387 392 397 403 408 413 418 424 429 821 822 823 824 825 826 827 828 829 434 487 540 593 645 698 751 803 855 440 492 545 598 651 703 756 808 861 445 498 551 603 656 709 761 814 866 450 503 556 609 661 714 766 819 871 455 508 561 614 666 719 772 824 876 461 514 566 619 672 724 777 829 882 466 519 572 624 677 730 782 834 887 471 524 577 630 682 735 787 840 892 477 529 582 635 687 740 793 845 897 482 535 587 640 693 745 798 ' 850 903 830 908 913 918 924 929 934 939 944 950 955 5 831 832 833 834 835 836 837 838 839 960 92 012 065 117 169 221 273 324 376 965 018 070 122 174 226 278 330 381 971 023 075 127 179 231 283 335 387 976 028 080 132 184 236 288 340 392 981 033 085 137 189 241 293 345 397 986 038 091 143 195 247 298 350 402 991 044 096 148 200 252 304 355 407 997 049 101 153 205 257 309 361 412 *002 054 106 158 210 262 314 366 418 *007 059 111 163 215 267 319 371 423 1 0.5 2 1.0 3 1.5 4 2.0 5 2.5 6 3.0 7 3.5 8 4.0 9 4.5 840 428 433 438 443 449 454 459 464 469 474 841 842 843 844 845 846 847 848 849 480 531 583 634 586 737 788 840 891 485 536 588 639 691 742 793 845 896 490 542 593 645 696 747 799 850 901 495 547 598 650 701 752 804 855 906 500 552 603 655 706 758 809 860 911 505 557 609 660 711 763 814 865 916 511 562 614 665 716 768 819 870 921 516 567 619 670 722 773 824 875 927 521 572 624 675 727 778 829 881 932 526 578 629 681 732 783 834 886 937 850 942 947 952 957 962 967 973 978 983 988 N. L.O 1 2 3 4 5 6 7 8 9 P.P. LOGARITHMS. 489 N. L.O 1 2 3 4 5 6 7 8 9 P .P. 850 92 942 947 952 957 962 967 973 978 983 988 851 852 853 854 855 856 857 858 859 993 93 044 095 146 197 247 298 349 399 998 049 100 151 202 252 303 354 404 *003 054 105 156 207 258 308 359 409 *008 059 110 161 212 263 313 364 414 *013 064 115 166 217 268 318 369 420 *018 069 120 171 222 273 323 374 425 *024 075 125 176 227 278 328 379 430 *029 080 131 181 232 283 334 384 435 *034 085 136 186 237 288 339 389 440 *039 090 141 192 242 293 344 394 445 i 2 6 0.6 1.2 860 450 455 460 465 470 475 480 485 490 495 4 2.4 3 861 862 863 864 865 866 867 868 869 500 551 601 651 702 752 802 852 902 505 556 606 656 707 757 807 857 907 510 561 611 661 712 762 812 862 912 515 566 616 666 717 767 817 867 917 520 571 621 671 722 772 822 872 922 526 576 626 676 727 777 827 877 927 531 581 631 682 732 782 832 882 932 536 586 636 687 737 787 837 887 937 541 591 641 692 742 792 842 892 942 546 596 646 697 747 797 847 897 947 6 7 8 9 3.6 4.2 4.8 5.4 870 952 957 962 967 972 977 982 987 992 997 871 872 873 874 875 876 877 878 879 94 002 052 101 151 201 250 300 349 399 007 057 106 156 206 255 305 354 404 012 062 111 161 211 260 310 359 409 017 067 116 166 216 265 315 364 414 022 072 121 171 221 270 320 369 419 027 077 126 176 226 275 325 374 424 032 082 131 181 231 280 330 379 429 037 086 136 186 236 285 335 384 433 042 091 141 191 240 290 340 389 438 047 096 146 196 245 295 345 394 443 1 2 3 4 5 6 7 8 9 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 880 448 453 458 463 468 473 478 483 488 493 881 882 883 884 885 886 887 888 889 498 547 596 645 694 743 792 841 890 503 552 601 650 699 748 797 846 895 507 557 606 655 704 753 802 851 900 512 562 611 660 709 758 807 856 905 517 567 616 665 714 763 812 861 910 522 571 621 670 719 768 817 866 915 527 576 626 675 724 773 822 871 919 532 581 630 680 729 778 827 876 924 537 586 635 685 734 783 832 880 929 542 591 640 689 738 787 836 885 934 1 2 3 4 0.4 O.H 1.2 890 939 944 949 954 959 963 968 973 978 983 5 2.0 891 892 893 894 895 896 897 898 899 988 95 036 085 134 182 231 279 328 376 993 041 090 139 187 236 284 332 381 998 046 095 143 192 240 289 337 386 *002 051 100 148 197 245 294 342 390 *007 056 105 153 202 250 299 347 395 *012 061 109 158 207 255 303 352 400 *017 066 114 163 211 260 308 357 405 *022 071 119 168 216 265 313 361 410 *027 075 124 173 221 270 318 366 415 *032 080 129 177 226 274 323 371 419 7 8 9 '2.8 3.2 3.6 900 424 429 434 439 444 448 453 458 463 468 N. L.O 1 2 3 4 5 6 7 8 9 P P. LOGARITHMS. N. L.O 1 2 3 4 5 6 7 8 9 P.P. 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 95 424 429 477 525 574 622 670 718 766 813 861 434 439 444 448 453 458 463 468 5 1 0.5 2 1.0 3 1.5 4 2.0 5 2.5 6 3.0 7 3.5 8 4.0 9 4.5 4 1 0.4 2 0.8 3 1.2 4 1.6 5 2.0 6 2.4 7 2.8 8 3.2 9 3.6 472 521 569 617 665 713 761 809 856 482 530 578 626 674 722 770 818 866 487 535 583 631 679 727 775 823 871 492 540 588 636 684 732 780 828 875 497 545 593 641 689 737 785 832 880 501 550 598 646 694 742 789 837 885 506 554 602 650 698 746 794 842 890 511 559 607 655 703 751 799 847 895 516 564 612 660 708 756 804 852 899 904 909 914 918 923 928 933 938 942 947 952 999 96 047 095 142 190 237 284 332 957 *004 052 099 147 194 242 289 336 961 *009 057 104 152 199 246 294 341 966 *014 061 109 156 204 251 298 346 971 *019 066 114 161 209 256 303 350 976 *023 071 118 166 213 261 308 355 980 *028 076 123 171 218 265 313 360 985 *033 080 128 175 223 270 317 365 990 *038 085 133 180 227 275 322 369 995 *042 090 137 185 232 280 327 374 379 384 388 393 398 402 407 412 417 421 426 473 520 567 614 661 708 755 802 431 478 525 572 619 666 713 759 806 435 483 530 577 624 670 717 764 811 440 487 534 581 628 675 722 769 816 445 492 539 586 633 680 727 774 820 450 497 544 591 638 685 731 778 825 454 501 548 595 642 689 736 783 830 459 506 553 600 647 694 741 788 834 464 511 558 605 652 699 745 792 839 468 515 562 609 656 703 750 797 844 848 853 858 904 951 997 044 090 137 183 230 276 862 867 872 876 881 886 890 895 942 988 97 035 081 128 174 220 267 900 946 993 039 086 132 179 225 271 909 956 *002 049 095 142 188 234 280 914 960 *007 053 100 146 192 239 285 918 965 *011 058 104 151 197 243 290 923 970 *016 063 109 155 202 248 294 928 974 *021 067 114 160 206 253 299 932 979 *025 072 118 165 211 257 304 937 984 *030 077 123 169 216 262 308 313 317 364 410 456 502 548 594 640 685 731 322 327 331 336 340 387 433 479 525 571 617 663 708 754 345 350 354 359 405 451 497 543 589 635 681 727 368 414 460 506 552 598 644 690 736 373 419 465 511 557 603 649 695 740 377 424 470 516 562 607 653 699 745 382 428 474 520 566 612 658 704 749 391 437 483 529 575 621 667 713 759 396 442 488 534 580 626 672 717 763 400 447 493 539 585 630 676 722 768 772 777 782 786 791 795 800 804 809 813 N. L.O 1 2 3 4 5 6 7 8 9 P.P. LOGARITHMS. 491 N. L.O 1 2 3 786 4 791 5 6 7 8 9 P.P. 950 951 952 953 964 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 97 772 777 782 795 800 804 809 813 5 1 0.5 2 1.0 3 1.5 4 2.0 5 2.5 6 8.0 7 3.5 8 4.0 9 4.5 4 1 0.4 2 0.8 3 1.2 4 1.6 5 2.0 6 2.4 7 2.8 8 3.2 9 3.6 818 864 909 955 98 000 046 091 137 182 823 868 914 959 005 050 096 141 186 827 873 918 964 009 055 100 146 191 832 877 923 968 014 059 105 150 195 836 882 928 973 019 064 109 155 200 245 290 336 381 426 471 516 561 605 650 841 886 932 978 023 068 114 159 204 845 891 937 982 028 073 118 164 209 850 896 941 987 032 078 123 168 214 855 900 946 991 037 082 127 173 218 859 905 950 996 041 087 132 177 223 227 232 236 241 250 254 259 263 308 354 399 444 489 534 579 623 668 268 272 318 363 408 453 498 543 588 632 277 322 367 412 457 502 547 592 637 281 327 372 417 462 507 552 597 641 286 331 376 421 466 511 556 601 646 691 295 340 385 430 475 520 565 610 655 299 345 390 435 480 525 570 614 659 304 349 394 439 484 529 574 619 664 313 358 403 448 493 538 583 628 673 677 682 686 695 700 704 709 713 717 722 767 811 856 900 945 989 99 034 078 726 771 816 860 905 949 994 038 083 731 776 820 865 909 954 998 043 087 735 780 825 869 914 958 *003 047 092 740 784 829 874 918 963 *007 052 096 744 789 834 878 923 967 *012 056 100 749 793 838 883 927 972 *016 061 105 753 798 843 887 932 976 *021 065 109 758 802 847 892 936 981 *025 069 114 762 807 851 896 941 985 *029 074 118 123 127 131 136 140 145 149 154 158 162 .167 211 255 300 344 388 432 476 520 171 216 260 304 348 392 436 480 524 176 220 264 308 352 396 441 484 528 180 224 269 313 357 401 445 489 533 185 229 273 317 361 405 449 493 537 189 233 277 322 366 410 454 498 542 193 238 282 326 370 414 458 502 546 198 242 286 330 374 419 463 506 550 202 247 291 335 379 423 467 511 555 207 251 295 339 383 427 471 515 559 603 564 568 572 577 581 585 590 594 599 607 651 695 739 782 826 870 913 957 612 656 699 743 787 830 874 917 961 616 660 704 747 791 835 878 922 965 621 664 708 752 795 839 883 926 970 625 669 712 756 800 843 887 930 974 017 629 673 717 760 804 848 891 935 978 634 677 721 765 808 852 896 939 983 026 638 682 726 769 813 856 900 944 987 642 (WO 730 774 817 861 904 948 991 647 691 734 778 822 865 909 952 996 00 000 004 009 013 022 030 035 039 N. L.O 1 2 3 4 5 6 ' 7 8 9 P.P. 492 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. It t L. Sin. d. Cpl. S. Cpl. T. L.Tang. d.c. L.Cotg. L.Cos. o 60 120 180 240 1 2 3 4 6.46373 6.76476 6.94085 7.06579 30103 17609 12494 QfiQI 5.31443 5.31443 5.31443 5.31443 5.31443 5.31443 5.31443 5.31442 6.46373 6.76476 6.94085 7.06579 30103 17609 12494 Q/3Q-J 3.53627 3.23524 3.05915 2.93421 0.00000 0.00000 0.00000 0.00000 0.00000 60 59 58 57 56 300 360 420 480 540 5 6 7 8 9 7.16270 7.24188 7.30882 7.36682 7.41797 7918 6694 5800 5115 4576 5.31443 5.31443 5.31443 5.31443 5.31443 5.31442 5.31442 5.31442 5.31442 5.31442 7.16270 7.24188 7.30882 7.36682 7.41797 7918 6694 5800 5115 4576 2.83730 2.75812 2.69118 2.63318 2.58203 0.00000 0.00000 0.00000 0.00000 0.00000 55 54 53 52 51 600 , 660 720 780 840 10 11 12 13 14 7.46373 7.50512 7.54291 7.57767 7.60985 4139 3779 3476 3218 OQQ7 5.31443 5.31443 5.31443 5.31443 5.31443 5.31442 5.31442 5.31442 5.31442 5.31442 7.46373 7.50512 7.54291 7.57767 7.60986 4139 3779 3476 3219 2996 2.53627 2.49488 2.45709 2.42233 2.39014 0.00000 0.00000 0.00000 0.00000 0.00000 50 49 48 47 46 900 960 1020 1080 1140 15 16 17 18 19 7.63982 7.66784 7.69417 7.71900 7.74248 2802 2633 2483 2348 *>227 5.31443 5.31443 5.31443 5.31443 5.31443 5.31442 5.31442 5.31442 5.31442 5.31442 7.63982 7.66785 7.69418 7.71900 7.74248 2803 2633 2482 2348 2228 2.36018 2.33215 2.30582 2.28100 2.25752 0.00000 0.00000 9.99999 9.99999 9.99999 45 44 43 42 41 1200 1260 1320 1380 1440 20 21 22 23 24 7.76475 7.78594 7.80615 7.82545 7.84393 2119 2021 1930 1848 1 77^ 5.31443 5.31443 5.31443 5.31443 5.31443 5.31442 5.31442 5.31442 5.31442 5.31442 7.76476 7.78595 7.80615 7.82546 7.84394 2119 2020 1931 1848 1773 2.23524 2.21405 2.19385 2.17454 2.15606 9.99999 9.99999 9.99999 9.99999 9.99999 40 39 38 37 36 1500 1560 1620 1680 1740 25 26 27 28 29 7.86166 7.87870 7.89509 7.91088 7.92612 1704 1639 1579 1524 1472 5.31443 5.31443 5.31443 5.31443 5.31443 5.31442 5.31442 5.31442 5.31442 5.31441 7.86167 7.87871 7.89510 7.91089 7.92613 1704 1639 1579 1524 1473 2.13833 2.12129 2.10490 2.08911 2.07387 9.99999 9.99999 9.99999 9.99999 9.99998 86 34 33 32 31 1800 1860 1920 1980 2040 30 31 32 33 34 7.94084 7.95508 7.96887 7.98223 7.99520 1424 1379 1336 1297 1 9^0 5.31443 5.31443 5.31443 5.31443 5.31443 5.31441 5.31441 5.31441 5.31441 5.31441 7.94086 7.95510 7.96889 7.98225 7.99522 1424 1379 1336 1297 lOCQ 2.05914 2.04490 2.03111 2.01775 2.00478 9.99998 9.99998 9.99998 9.99998 9.99998 30 29 28 27 26 2100 2160 2220 2280 2340 35 36 37 38 39 8.00779 8.02002 8.03192 8.04350 8.05478 1223 1190 1158 1128 1100 5.31443 5.31443 5.31443 5.31443 5.31443 5.31441 5.31441 5.31441 5.31441 5.31441 8.00781 8.02004 8.03194 8.04353 8.05481 1223 1190 1159 1128 1100 1.99219 1.97996 1.96806 1.95647 1.94519 9.99998 9.99998 9.99997 9.99997 9.99997 25 24 23 22 21 2400 2460 2520 2580 2640 40 41 42 43 44 8.06578 8.07650 8.08696 8.09718 8.10717 1072 1046 1022 999 97fi 5.31443 5.31444 5.31444 5.31444 5.31444 5.31441 5.31440 5.31440 5.31440 5.31440 8.06581 8.07653 8.08700 8.09722 8.10720 1072 1047 1022 998 Q7fi 1.93419 1.92347 1.91300 1.90278 1.89280 9.99997 9.99997 9.99997 9.99997 9.99996 20 19 18 17 16 2700 2760 2820 2880 2940 45 46 47 48 49 8.11693 8.12647 8.13581 8.14495 8.15391 954 934 914 896 877 5.31444 5.31444 5.31444 5.31444 5.31444 5.31440 5.31440 5.31440 5.31440 5.31440 8.11696 8.12651 8.13585 8.14500 8.15395 955 934 915 895 878 1.88304 1.87349 1.86415 1.85500 1.84605 9.99996 9.99996 9.99996 9.99996 9.99996 15 14 13 12 11 3000 3060 3120 3180 3240 50 51 52 53 54 8.16268 8.17128 8.17971 8.18798 8.19610 860 843 827 812 797 5.31444 5.31444 5.31444 5.31444 5.31444 5.31439 5.31439 5.31439 5.31439 5.31439 8.16273 8.17133 8.17976 8.18804 8.19616 860 843 828 812 797 1.83727 1.82867 1.82024 1.81196 1.80384 9.99995 9.99995 9.99995 9.99995 9.99995 10 9 8 7 6 3300 3360 3420 3480 3540 55 56 57 58 59 8.20407 8.21189 8.21958 8.22713 8.23456 782 769 755 743 730 5.31444 5.31444 5.31445 5.31445 5.31445 5.31439 5.31439 5.31439 5.31438 5.31438 8.20413 8.21195 8.21964 8.22720 8.23462 782 769 756 742 730 1.79587 1.78805 1.78036 1.77280 1.76538 9.99994 9.99994 9.99994 9.99994 9.99994 5 4 3 2 1 3600 60 8.24186 5.31445 5.31438 8.24192 1.75808 9.99993 L. Cos. d. L. Cotg. d.c. L. Tang. L. Sin. ' 89 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. " ' L. Sin. d. Cpl. S. Cpl. T. L. Tang. d.c. L. Cotg. L. Cos. 3600 3660 3720 3780 3840 1 2 3 4 8.24186 8.24903 8.25609 8.26304 8.26988 717 706 695 684 673 5.31445 5.31445 5.31445 5.31445 5.31445 5.31438 5.31438 5.31438 5.31438 5.31437 8.24192 8.24910 8.25616 8.26312 8.26996 718 706 696 684 673 1.75808 1.75090 1.74384 1.73688 1.73004 9.99993 9.99993 9.99993 9.99993 9.99992 60 59 58 57 56 3900 3960 4020 4080 4140 5 6 7 8 9 8.27661 8.28324 8.28977 8.29621 8.30255 663 653 644 634 6'^4 5.31445 5.31445 5.31445 5.31445 5.31445 5.31437 5.31437 5.31437 5.31437 5.31437 8.27669 8.28332 8.28986 8.29629 8.30263 663 654 643 634 625 1.72331 1.71668 1.71014 1.70371 1.69737 9.99992 9.99992 9.99992 9.99992 9.99991 55 54 53 52 51 4200 4260 4320 4380 4440 10 11 12 13 14 8.30879 8.31495 8.32103 8.32702 8.33292 616 608 599 590 583 5.31446 5.31446 5.31446 5.31446 5.31446 5.31437 5.31436 5.31436 5.31436 5.31436 8.30888 8.31505 8.32112 8.32711 8.33302 617 607 599 591 584 1.69112 1.68495 1.67888 1.67289 1.66698 9.99991 9.99991 9.99990 9.99990 9.99990 50 49 48 47 46 4500 4560 4620 4680 4740 15 16 17 18 19 8.33875 8.34450 8.35018 8.35578 8.36131 575 568 560 553 547 5.31446 5.31446 531446 5.31446 5.31446 5.31436 5.31435 5.31435 5.31435 5.31435 8.33886 8.34461 8.35029 8.35590 8.36143 575 568 561 553 546 1.66114 1.65539 1.64971 1.64410 1.63857 9.99990 9.99989 9.99989 9.99989 9.99989 45 44 43 42 41 4800 4860 4920 4980 5040 20 21 22 23 24 8.36678 8.37217 8.37750 8.38276 8.38796 539 533 526 520 514 5.31446 5.31447 5.31447 5.31447 5.31447 5.31435 5.31434 5.31434 5.31434 5.31434 8.36689 8.37229 8.37762 8.38289 8.38809 540 533 527 520 514 1.63311 1.62771 1.62238 1.61711 1.61191 9.99988 9.99988 9.99988 9.99987 9.99987 40 39 38 37 36 5100 5160 5220 5280 5340 25 26 27 28 29 8.39310 8.39818 8.40320 8.40816 8.41307 508 502 496 491 485 5.31447 5.31447 5.31447 5.31447 5.31447 5.31434 5.31433 5.31433 5.31433 5.31433 8.39323 8.39832 8.40334 8.40830 8.41321 509 502 496 491 486 1.60677 1.60168 1.59666 1.59170 1.58679 9.99987 9.99986 9.99986 9.99986 9.99985 35 34 33 32 31 5400 5460 5520 5580 5640 30 31 32 33 34 8.41792 8.42272 8.42746 8.43216 8.43680 480 474 470 464 459 5.31447 5.31448 5.31448 5.31448 5.31448 5.31433 5.31432 5.31432 5.31432 5.31432 8.41807 8.42287 8.42762 8.43232 8.43696 480 475 470 464 460 1.58193 1.57713 1.57238 1.56768 1.56304 9.99985 9.99985 9.99984 9.99984 9.99984 30 29 28 27 26 5700 5760 5820 5880 5940 35 36 37 38 39 8.44139 8.44594 8.45044 8.45489 8.45930 455 450 445 441 436 5.31448 5.31448 5.31448 5.31448 5.31449 5.31431 5.31431 5.31431 5.31431 5.31431 8.44156 8.44611 8.45061 8.45507 8.45948 455 450 446 441 437 1.55844 1.55389 1.54939 1.54493 1.54052 9.99983 9.99983 9.99983 9.99982 9.99982 25 24 23 22 21 6000 6060 6120 6180 6240 40 41 42 43 44 8.46366 8.46799 8.47226 8.47650 8.48069 433 427 424 419 416 5.31449 5.31449 5.31449 5.31449 5.31449 5.31430 5.31430 5.31430 5.31430 5.31429 8.46385 8.46817 8.47245 8.47669 8.48089 432 428 424 420 416 1.53615 1.53183 1.52755 1.52331 1.51911 9.99982 9.99981 9.99981 9.99981 9.99980 20 19 18 17 16 6300 6360 6420 6480 6540 45 46 47 48 49 8.48485 8.48896 8.49304 8.49708 8.50108 411 408 404 400 396 5.31449 5.31449 5.31450 5.31450 5.31450 5.31429 5.31429 5.31428 5.31428 5.31428 8.48505 8.48917 8.49325 8.49729 8.50130 412 408 404 401 QQ7 1.51495 1.51083 1.50675 1.50271 1.49870 9.99980 9.99979 9.99979 9.99979 9.99978 15 14 13 12 11 6600 6660 6720 6780 6840 50 51 52 53 54 8.50504 8.50897 8.51287 8.51673 8.52055 393 390 386 382 379 5.31450 5.31450 5.31450 5.31450 5.31450 5.31428 5.31427 5.31427 5.31427 5.31427 8.50527 8.50920 8.51310 8.51696 8.52079 393 390 386 383 OCA 1.49473 1.49080 1.48690 1.48304 1.47921 9.99978 9.99977 9.99977 9.99977 9.99976 10 9 8 7 6 6900 6960 7020 7080 7140 55 56 57 58 59 8.52434 8.52810 8.53183 8.53552 8.53919 376 373 369 367 363 5.31451 5.31451 5.31451 5.31451 5.31451 5.31426 5.31426 5.31426 5.31425 5.31425 8.52459 8.52835 8.53208 8.53578 8.53945 376 373 370 367 363 1.47541 1.47165 1.46792 1.46422 1.46055 9.99976 9.99975 9.99975 9.99974 9.99974 5 4 3 2 1 7200 60 8.54282 5.31451 5.31425 8.54308 1.45692 9.99974 L. Cos. d. L. Cotg. d.c. L. Tang. L. Sin. ' 88 494 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 1' 1 2 3 4 L. Sin. d. Cpl. S. Cpl. T. L.Tang. d.c. L. Cotg. L. Cos. 60 59 58 57 56 7200 7260 7320 7380 7440 8.54282 8.54642 8.54999 8.55354 8.55705 360 357 355 351 349 346 343 341 337 336 332 330 328 325 323 320 318 316 313 311 309 307 305 302 301 298 296 294 293 290 288 287 284 283 281 279 277 276 274 272 270 269 267 266 263 263 260 259 258 256 254 253 252 250 249 247 246 244 243 242 5.31451 5.31451 5.31452 5.31452 5.31452 5.31425 5.31425 5.31424 5.31424 5.31424 8.54308 8.54669 8.55027 8.55382 8.55734 361 358 355 352 349 346 344 341 338 336 333 330 328 326 323 321 319 316 314 311 310 307 305 303 301 299 297 295 292 291 289 287 285 284 281 280 278 276 274 273 271 269 268 266 264 263 261 260 258 257 255 254 252 251 249 248 246 245 244 243 1.45692 1.45331 1.44973 1.44618 1.44266 9.99974 9.99973 9.99973 9.99972 9.99972 7500 7560 7620 7680 7740 5 6 7 8 9 10 11 12 13 14 8.56054 8.56400 8.56743 8.57084 8.57421 5.31452 5.31452 5.31452 5.31453 5.31453 5.31423 5.31423 5.31423 5.31422 5.31422 8.56083 8.56429 8.56773 8.57114 8.57452 1.43917 1.43571 1.43227 1.42886 1.42548 9.99971 9.99971 9.99970 9.99970 9.99969 55 54 53 52 51 7800 7860 7920 7980 8040 8.57757 8.58089 8.58419 8.58747 8.59072 5.31453 5.31453 5.31453 5.31453 5.31454 5.31422 5.31421 5.31421 5.31421 5.31421 8.57788 8.58121 8.58451 8.58779 8.59105 1.42212 1.41879 1.41549 1.41221 1.40895 9.99969 9.99968 9.99968 9.99967 9.99967 50 49 48 47 46 8100 8160 8220 8280 8340 15 16 17 18 19 8.59395 8.59715 8.60033 8.60349 8.60662 5.31454 5.31454 5.31454 5.31454 5.31454 5.31420 5.31420 5.31420 5.31419 5.31419 8.59428 8.59749 8.60068 8.60384 8.60698 1.40572 1.40251 1.39932 1.39616 1.39302 9.99967 9.99966 9.99966 9.99965 9.99964 45 44 43 42 41 8400 8460 8520 8580 8640 20 21 22 23 24 ~25~ 26 27 28 29 8.60973 8.61282 8.61589 8.61894 8.62196 5.31455 5.31455 5.31455 5.31455 5.31455 5.31418 5.31418 5.31418 5.31417 5.31417 8.61009 8.61319 8.61626 8.61931 8.62234 1.38991 1.38681 1.38374 1.38069 1.37766 9.99964 9.99963 9.99963 9.99962 9.99962 9.99961 9.99961 9.99960 9.99960 9.99959 40 39 38 37 36 35 34 33 32 31 8700 8760 8820 8880 8940 8.62497 8.62795 8.63091 8.63385 8.63678 5.31455 5.31456 5.31456 5.31456 5.31456 5.31417 5.31416 5.31416 5.31416 5.31415 8.62535 8.62834 8.63131 8.63426 8.63718 1.37465 1.37166 1.36869 1.36574 1.36282 9000 9060 9120 9180 9240 30 31 32 33 34 8.63968 8.64256 8.64543 8.64827 8.65110 5.31456 5.31456 5.31457 5.31457 5.31457 5.31415 5.31415 5.31414 5.31414 5.31413 8.64009 8.64298 8.64585 8.64870 8.65154 1.35991 1.35702 1.35415 1.35130 1.34846 9.99959 9.99958 9.99958 9.99957 9.99956 30 29 28 27 26 9300 9360 9420 9480 9540 35 36 37 38 39 8.65391 8.65670 8.65947 8.66223 8.66497 5.31457 5.31457 5.31458 5.31458 5.31458 5.31413 5.31413 5.31412 5.31412 5.31412 8.65435 8.65715 8.65993 8.66269 8.66543 1.34565 1.34285 1.34007 1.33731 1.33457 9.99956 9.99955 9.99955 9.99954 9.99954 25 24 23 22 21 9600 9660 9720 9780 9840 40 41 42 43 44 ^45" 46 47 48 49 8.66769 8.67039 8.67308 8.67575 8.67841 5.31458 5.31458 5.31459 5.31459 5.31459 5.31411 5.31411 5.31410 5.31410 5.31410 8.66816 8.67087 8.67356 8.67624 8.67890 1.33184 1.32913 1.32644 1.32376 1.32110 9.99953 9.99952 9.99952 9.99951 9.99951 20 19 18 17 16 9900 9960 10020 10080 10140 8.68104 8.68367 8.68627 8.68886 8.69144 5.31459 5.31459 5.31460 5.31460 5.31460 5.31409 5.31409 5.31408 5.31408 5.31408 8.68154 8.68417 8.68678 8.68938 8.69196 1.31846 1.31583 1.31322 1.31062 1.30804 9.99950 9.99949 9.99949 9.99948 9.99948 15 14 13 12 11 10200 10260 10320 10380 10440 50 51 52 53 54 8.69400 8.69654 8.69907 8.70159 8.70409 5.31460 5.31460 5.31461 5.31461 5.31461 5.31407 5.31407 5.31406 5.31406 5.31405 8.69453 8.69708 8.69962 8.70214 8.70465 1.30547 1.30292 1.30038 1.29786 1.29535 9.99947 9.99946 9.99946 9.99945 9.99944 10 9 8 7 6 10500 10560 10620 10680 10740 55 56 57 58 59 8.70658 8.70905 8.71151 8.71395 8.71638 5.31461 5.31461 5.31462 5.31462 5.31462 5.31405 5.31405 5.31404 5.31404 5.31403 8.70714 8.70962 8.71208 8.71453 8.71697 1.29286 1.29038 1.28792 1.28547 1.28303 9.99944 9.99943 9.99942 9.99942 9.99941 5 4 3 2 1 10800 60 8.71880 5.31462 5.31403 8.71940 1.28060 9.99940 L. Cos. d. L. Cotg. d.c.i L.Tang. L. Sin. 87 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 495 / L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. I >. P. 1 2 3 4 8.71880 8.72120 8.72359 8.72597 8.72834 240 239 238 237 235 8.71940 8.72181 8.72420 8.72659 8.72896 241 239 239 237 236 1.28060 1.27819 1.27580 1.27341 1.27104 9.99940 9.99940 9.99939 9.99938 9.99938 60 59 58 57 56 6 7 8 9 238 23.8 27.8 31.7 35.7 234 23.4 27.3 31.2 35.1 229 22.9 26.7 30.5 34.4 5 6 7 8 9 8.73069 8.73303 8.73535 8.73767 8.73997 234 232 232 230 99Q 8.73132 8.73366 8.73600 8.73832 8.74063 234 234 232 231 99Q 1.26868 1.26634 1.26400 1.26168 1.25937 9.99937 9.99936 9.99936 9.99935 9.99934 55 54 53 52 51 10 20 30 40 50 39.7 79.3 119.0 158.7 198.3 39.0 78.0 117.0 156.0 195.0 38.2 76.3 114.5 152.7 190.8 10 11 12 13 14 8.74226 8.74454 8.74680 8.74906 8.75130 228 226 226 224 223 8.74292 8.74521 8.74748 8.74974 8.75199 229 227 226 225 24 1.25708 1.25479 1.25252 1.25026 1.24801 9.99934 9.99933 9.99932 9.99932 9.99931 50 49 48 47 46 6 7 8 q 225 22.5 26.3 30.0 338 220 22.0 25.7 29.3 330 216 21.6 25.2 28.8 32.4 15 16 17 18 19 8.75353 8.75575 8.75795 8.76015 8.76234 222 220 220 219 217 8.75423 8.75645 8.75867 8.76087 8.76306 222 222 220 219 219 1.24577 1.24355 1.24133 1.23913 1.23694 9.99930 9.99929 9.99929 9.99928 9.99927 45 44 43 42 41 10 20 30 40 50 37.5 75.0 112.5 150.0 187.5 36.7 73.3 110.0 146.7 183.3 36.0 72.0 108.0 144.0 180.0 20 21 22 23 24 8.76451 8.76667 8.76883 8.77097 8.77310 216 216 214 213 212 8.76525 8.76742 8.76958 8.77173 8.77387 217 216 215 214 91 ^ 1.23475 1.23258 1.23042 1.22827 1.22613 9.99926 9.99926 9.99925 9.99924 9.99923 40 39 38 37 36 6 7 8 212 21.2 24.7 28.3 0-1 Q 208 20.8 24.3 27.7 q-| 204 20.4 23.8 27.2 OA 25 26 27 28 29 8.77522 8.77733 8.77943 8.78152 8.78360 211 210 209 208 208 8.77600 8.77811 8.78022 8.78232 8.78441 211 211 210 209 OAQ 1.22400 1.22189 1.21978 1.21768 1.21559 9.99923 9.99922 9.99921 9.99920 9.99920 35 34 33 32 31 10 20 30 40 50 35.3 70.7 106.0 141.3 176.7 34.7 69.3 104.0 138.7 1 173.3 34.0 68.0 102.0 136.0 170.0 30 31 32 33 34 8.78568 8.78774 8.78979 8.79183 8.79386 206 205 204 203 202 8.78649 8.78855 8.79061 8.79266 8.79470 206 206 205 204 203 1.21351 1.21145 1.20939 1.20734 1.20530 9.99919 9.99918 9.99917 9.99917 9.99916 30 29 28 27 26 6 7 8 201 20.1 23.5 26.8 197 19.7 23.0 26.3 193 19.3 22.5 25.7 35 36 37 38 39 8.79588 8.79789 8.79990 8.80189 8.80388 201 201 199 199 197 8.79673 8.79875 8.80076 8.80277 8.80476 202 201 201 199 198 1.20327 1.20125 1.19924 1.19723 1.19524 9.99915 9.99914 9.99913 9.99913 9.99912 25 24 23 22 21 9 10 20 30 40 50 30.2 33.5 67.0 100.5 134.0 167 5 29.6 32.8 65.7 98.5 131.3 164 2 29.0 32.2 64.3 96.5 128.7 160 8 40 41 42 43 44 8.80585 8.80782 8.80978 8.81173 8.81367 197 196 195 194 193 8.80674 8.80872 8.81068 8.81264 8.81459 198 196 196 195 194 1.19326 1.19128 1.18932 1.18736 1.18541 9.99911 9.99910 9.99909 9.99909 9.99908 20 19 18 17 16 6 7 8 189 18.9 22.1 25.2 185 18.5 21.6 24.7 181 18.1 21.1 24.1 45 46 47 48 49 8.81560 8.81752 8.81944 8.82134 8.82324 192 192 190 190 189 8.81653 8.81846 8.82038 8.82230 8.82420 193 192 192 190 190 1.18347 1.18154 1.17962 1.17770 1.17580 9.99907 9.99906 9.99905 9.99904 9.99904 15 14 13 12 11 9 10 20 30 40 CA. 28.4 31.5 63.0 94.5 126.0 1 ^7 ^ 27.8 30.8 61.7 92.5 123.3 154 2 27.2 30.2 60.3 90.5 120.7 150 8 50 51 52 53 54 8.82513 8.82701 8.82888 8.83075 8.83261 188 187 187 186 185 8.82610 8.82799 8.82987 8.83175 8.83361 189 188 188 186 186 1.17390 1.17201 1.17013 1.16825 1.16639 9.99903 9.99902 9.99901 9.99900 9.99899 10 9 8 7 6 6 7 8 4 0.4 0.5 0.5 3 2 0.3 0.2 0.4 0.2 0.4 0.3 1 0.1 0.1 0.1 55 56 57 58 59 8.83446 8.83630 8.83813 8.83996 8.84177 184 183 183 181 181 8.83547 8.83732 8.83916 8.84100 8.84282 185 184 184 182 189 1.16453 1.16268 1.16084 1.15000 1.15718 9.99898 9.99898 9.99897 9.99896 9.99895 5 4 3 2 1 9 10 20 30 40 0.6 0.7 1.3 2.0 2.7 0.5 0.3 0.5 0.3 1.0 0.7 1.5 1.0 2.0 1.3 0.2 0.2 0.3 0.5 0.7 60 8.84358 8.84464 1.15536 9.99894 50 3.3 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. / I '. P. 86 496 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. ' L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. I '. P. 1 2 3 4 8.84358 8.84539 8.84718 8.84897 8.85075 181 179 179 178 177 8.84464 8.84646 8.84826 8.85006 8.85185 182 180 180 179 178 1.15536 1.15354 1.15174 1.14994 1.14815 9.99894 9.99893 9.99892 9.99891 9.99891 60 59 58 57 56 6 7 8 9 181 18.1 21.1 24.1 27.2 179 17.9 20.9 23.9 26.9 177 17.7 20.7 23.6 26.6 5 6 7 8 9 8.85252 8.85429 8.85605 8.85780 8.85955 177 176 175 175 173 8.85363 8.85540 8.85717 8.85893 8.86069 177 177 176 176 174 1.14637 1.14460 1.14283 1.14107 1.13931 9.99890 9.99889 9.99888 9.99887 9.99886 55 54 53 52 51 10 20 30 40 50 30.2 60.3 90.5 120.7 150.8 29.8 59.7 89.5 119.3 149.2 29.5 59.0 88.5 118.0 147.5 10 11 12 13 14 8.86128 8.86301 8.86474 8.86645 8.86816 173 173 171 171 171 8.86243 8.86417 8.86591 8.86763 8.86935 174 174 172 172 171 1.13757 1.13583 1.13409 1.13237 1.13065 9.99885 9.99884 9.99883 9.99882 9.99881 50 49 48 47 46 6 7 8 9 175 17.5 20.4 23.3 263 173 17.3 20.2 23.1 260 171 17.1 20.0 22.8 25 7 15 16 17 18 19 8.86987 8.87156 8.87325 8.87494 8.87661 169 169 169 167 168 8.87106 8.87277 8.87447 8.87616 8.87785 171 170 169 169 168 1.12894 1.12723 1.12553 1.12384 1.12215 9.99880 9.99879 9 99879 9.99878 9.99877 45 44 43 42 41 10 20 30 40 50 29.2 58.3 87.5 116.7 145.8 28.8 57.7 86.5 115.3 144.2 28.5 57.0 85.5 114.0 142.5 20 21 22 23 24 8.87829 8.87995 8.88161 8.88326 8.88490 166 166 165 164 164 8.87953 8.88120 8.88287 8.88453 8.88618 167 167 166 165 165 1.12047 1.11880 1.11713 1.11547 1.11382 9.99876 9.99875 9.99874 9.99873 9.99872 40 39 38 37 36 6 7 8 9 168 16.8 19.6 22.4 25 2 166 16.6 19.4 22.1 24 9 164 16.4 19.1 21.9 24 6 25 26 27 28 29 8.88654 8.88817 8.88980 8.89142 8.89304 163 163 162 162 160 8.88783 8.88948 8.89111 8.89274 8.89437 165 163 163 163 161 1.11217 1.11052 1.10889 1.10726 1.10563 9.99871 9.99870 9.99869 9.99868 9.99867 35 34 33 32 31 10 20 30 40 50 28.0 56.0 84.0 112.0 140.0 27.7 55.3 83.0 110.7 138.3 27.3 54.7 82.0 109.3 136.7 30 31 32 33 34 8.89464 8.89625 8.89784 8.89943 8.90102 161 159 159 159 158 8.89598 8.89760 8.89920 8.90080 8.90240 162 160 160 160 159 1.10402 1.10240 1.10080 1.09920 1.09760 9.99866 9.99865 9.99864 9.99863 9.99862 30 29 28 27 26 6 7 8 162 16.2 18.9 21.6 C)A O 159 15.9 18.6 21.2 00 Q 157 15.7 18.3 20.9 35 36 37 38 39 8.90260 890417 8.90574 8.90730 8.90885 157 157 156 155 155 8.90399 8.90557 8.90715 8.90872 8.91029 158 158 157 157 156 1.09601 1.09443 1.09285 1.09128 1.08971 9.99861 9.99860 9.99859 9.99858 9.99857 25 24 23 22 21 10 20 30 40 50 27.0 54.0 81.0 108.0 135.0 26.5 53.0 79.5 106.0 132.5 26.2 52.3 78.5 104.7 130.8 40 41 42 43 44 8.91040 8.91195 8.91349 8.91502 8.91655 155 154 153 153 152 8.91185 8.91340 8.91495 8.91650 8.91803 155 155 155 153 154 1.08815 1.08660 1.08505 1.08350 1.08197 9.99856 9.99855 9.99854 9.99853 9.99852 20 19 18 17 16 6 7 8 155 15.5 18.1 20.7 153 15.3 17.9 20.4 151 15.1 17.6 20.1 45 46 47 48 49 8.91807 8.91959 8.92110 8.92261 8.92411 152 151 151 150 150 8.91957 8.92110 8.92262 8.92414 8.92565 153 152 152 151 151 1.08043 1.07890 1.07738 1.07586 1.07435 9.99851 9.99850 9.99848 9.99847 9.99846 15 14 13 12 11 9 10 20 30 40 50 23.3 25.8 51.7 77.5 103.3 129 2 23.0 25.5 51.0 76.5 102.0 127 5 22.7 25.2 50.3 75.5 100.7 125 8 50 51 52 53 54 8.92561 8.92710 8.92859 8.93007 8.93154 149 149 148 147 147 8.92716 8.92866 8.93016 8.93165 8.93313 150 150 149 148 149 1.07284 1.07134 1.06984 1.06835 1.06687 9.99845 9.99844 9.99843 9.99842 9.99841 10 9 8 7 6 6 7 8 149 14.9 17.4 19.9 147 14.7 17.2 19.6 1 0.1 0.1 0.1 55 56 57 58 59 8.93301 8.93448 8.93594 8.93740 8.93885 147 146 146 145 145 8.93462 3.93609 8.93756 8.93903 8.94049 147 147 147 146 146 1.06538 1.06391 1.06244 1.06097 1.05951 9.99840 9.99839 9.99838 9.99837 9.99836 5 4 3 2 1 9 10 20 30 40 crj 22.4 24.8 49.7 74.5 99.3 194. 9 22.1 24.5 49.0 73.5 98.0 199 ^ 0.2 0.2 0.3 0.5 0.7 A 8 60 8.94030 8.94195 1.05805 9.99834 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. / P . P. 85 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 497 / L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. ] 3 . P. 1 2 3 4 8.94030 8.94174 8.94317 8.94461 8.94603 144 143 144 142 143 8.94195 8.94340 8.94485 8.94630 8.94773 145 145 145 143 141 1.05805 1.05660 1.05515 1.05370 1.05227 9.99834 9.99833 9.99832 9.99831 9.99830 60 59 58 57 56 6 7 8 9 145 14.5 16.9 19.3 21.8 143 14.3 16.7 19.1 21.5 141 14.1 16.5 18.8 21.2 5 6 7 8 9 8.94746 8.94887 8.95029 8.95170 8.95310 141 142 141 140 140 8.94917 8.95060 8.95202 8.95344 8.95486 143 142 142 142 141 1.05083 1.04940 1.04798 1.04656 1.04514 9.99829 9.99828 9.99827 9.99825 9.99824 55 54 53 52 51 10 20 30 40 50 24.2 48.3 72.5 96.7 120.8 23.8 47.7 71.5 95.3 119.2 23.5 47.0 70.5 94.0 117.5 10 11 12 13 14 8.95450 8.95589 8.95728 8.95867 8.96005 139 139 139 138 -1OQ 8.95627 8.95767 8.95908 8.96047 8.96187 140 141 139 140 138 1.04373 1.04233 1.04092 1.03953 1.03813 9.99823 9.99822 9.99821 9.99820 9.99819 50 49 48 47 46 6 7 8 q 139 13.9 16.2 18.5 20 9 138 13.8 16.1 18.4 20 7 136 13.6 15.9 18.1 20 4 15 16 17 18 19 8.96143 8.962SO 8.96417 8.96553 8.96689 137 137 136 136 i^fi 8.96325 8.96464 8.96602 8.96739 8.96877 139 138 137 138 136 1.03675 1.03536 1.03398 1.03261 1.03123 9.99817 9.99816 9.99815 9.99814 9.99813 45 44 43 42 41 10 20 30 40 50 23.2 46.3 69.5 92.7 115.8 23.0 46.0 69.0 92.0 115.0 22.7 45.3 68.0 90.7 113.3 20 21 22 23 24 8.96825 8.96960 8.97095 8.97229 8.97363 135 135 134 134 133 8.97013 8.97150 8.97285 8.97421 8.97556 137 135 136 135 135 1.02987 1.02850 1.02715 1.02579 1.02444 9.99812 9.99810 9.99809 9.99808 9.99807 40 39 38 37 36 6 7 8 9 135 13.5 15.8 18.0 20 3 133 13.3 15.5 17.7 20 131 13.1 15.3 17.5 1Q 7 25 26 27 28 29 8.97496 8.97629 8.97762 8.97894 8.98026 133 133 132 132 131 8.97691 8.97825 8.97959 8.98092 8.98225 134 134 133 133 133 1.02309 1.02175 1.02041 1.01908 1.01775 9.99806 9.99804 9.99803 9.99802 9.99801 35 34 33 32 31 10 20 30 40 50 22.5 45.0 67.5 90.0 112.5 22.2 44.3 66.5 88.7 110.8 21.8 43.7 65.5 87.3 109.2 30 31 32 33 34 8.98157 8.98288 8.98419 8.98549 8.98679 131 131 130 130 129 8.98358 8.98490 8.98622 8.98753 8.98884 132 132 131 131 131 1.01642 1.01510 1.01378 1.01247 1.01116 9.99800 9.99798 9.99797 9.99796 9.99795 30 29 28 27 26 6 7 8 129 12.9 15.1 17.2 128 12.8 14.9 17.1 126 12.6 14.7 16.8 35 36 37 38 39 8.98808 8.98937 8.99066 8.99194 8.99322 129 129 128 128 128 8.99015 8.99145 8.99275 8.99405 8.99534 130 130 130 129 128 1.00985 1.00855 1.00725 1.00595 1.00466 9.99793 9.99792 9.99791 9.99790 9.99788 25 24 23 22 21 10 20 30 40 50 21.5 43.0 64.5 86.0 107.5 21.3 42.7 64.0 85.3 106.7 21.0 42.0 63.0 84.0 105.0 40 41 42 43 44 8.99450 8.99577 8.99704 8.99830 8.99956 127 127 126 126 126 8.99662 8.99791 8.99919 9.00046 9.00174 129 128 127 128 127 1.00338 1.00209 1.00081 0.99954 0.99826 9.99787 9.99786 9.99785 9.99783 9.99782 20 19 18 17 16 6 7 8 125 12.5 14.6 16.7 123 12.3 14.4 16.4 122 12.2 14.2 16.3 45 46 47 48 49 9.00082 9.00207 9.00332 9.00456 9.00581 125 125 124 125 123 9.00301 9.00427 9.00553 9.00679 9.00805 126 126 126 126 IOC 0.99699 0.99573 0.99447 0.99321 0.99195 9.99781 9.99780 9.99778 9.99777 9.99776 15 14 13 12 11 9 10 20 30 40 50 18.8 20.8 41.7 62.5 83.3 104 2 18.5 20.5 41.0 61.5 82.0 102 5 18.3 20.3 40.7 61.0 81.3 101 7 50 51 52 53 54 9.00704 9.00828 9.00951 9.01074 9.01196 124 123 123 122 9.00930 9.01055 9.01179 9.01303 9.01427 125 124 124 124 1 9Q 0.99070 0.98945 0.98821 0.98697 0.98573 9.99775 9.99773 9.99772 9.99771 9.99769 10 9 8 7 6 6 7 8 121 12.1 14.1 16.1 120 12.0 14.0 16.0 1 0.1 0.1 0.1 55 56 57 58 59 9.01318 9.01440 9.01561 9.01682 9.01803 122 121 121 121 1 9 9.01550 9.01673 9.01796 9.01918 9.02040 123 123 122 122 122 0.98450 0.98327 0.98204 0.98082 0.97960 9.99768 9.99767 9.99765 9.99764 9.99763 5 4 3 2 1 9 10 20 30 40 CA 18.2 20.2 40.3 60.5 80.7 inn s 18.0 20.0 40.0 60.0 SO.O 100 0.2 0.2 0.3 0.5 0.7 8 60 9.01923 9.02162 0.97838 9.99761 L. Cos. d. L. Cotgr. d.c. L.Tang. L. Sin. ' P . p. 84 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 6 / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. P . P. 1 2 3 4 9.01923 9.02043 9.02163 9.02283 9.02402 120 120 120 119 118 9.02162 9.02283 9.02404 9.02525 9.02645 121 121 121 120 121 0.97838 0.97717 0.97596 0.97475 0.97355 9.99761 9.99760 9.99759 9.99757 9.99756 60 59 58 57 56 6 7 8 9 121 12.1 14.1 16.1 18 2 120 12.0 14.0 16.0 18 119 11.9 13.9 15.9 17 9 5 6 7 8 9 9.02520 9.02639 9.02757 9.02874 9.02992 119 118 117 118 117 9.02766 9.02885 9.03005 9.03124 9.03242 119 120 119 118 11Q 0.97234 0.97115 0.96995 0.96876 0.96758 9.99755 9.99753 9.99752 9.99751 9.99749 55 54 53 52 51 10 20 30 40 50 1 20.2 40.3 60.5 80.7 00.8 20.0 40.0 60.0 80.0 100.0 19.8 39.7 59.5 79.3 99.2 10 11 12 13 14 9.03109 9.03226 9.03342 9.03458 9.03574 117 116 116 116 116 9.03361 9.03479 9.03597 9.03714 9.03832 118 118 117 118 116 0.96639 0.96521 0.96403 0.96286 0.96168 9.99748 9.99747 9.99745 9.99744 9.99742 50 49 48 47 46 6 7 8 A 118 11.8 13.8 15.7 17 7 117 11.7 13.7 15.6 17 R 116 11.6 13.5 15.5 174. 15 16 17 18 19 9.03690 9.03805 9.03920 9.04034 9.04149 115 115 114 115 113 9.03948 9.04065 9.04181 9.04297 9.04413 117 116 116 116 1 -I K 0.96052 0.95935 0.95819 0.95703 0.95587 9.99741 9.99740 9.99738 9.99737 9.99736 45 44 43 42 41 10 20 30 40 50 19.7 39.3 59.0 78.7 98.3 19.5 39.0 58.5 78.0 97.5 19.3 38.7 58.0 77.3 96.7 20 21 22 23 24 9.04262 9.04376 9.04490 9.04603 9.04715 114 114 113 112 9.04528 9.04643 9.04758 9.04873 9.04987 115 115 115 114 0.95472 0.95357 0.95242 0.95127 0.95013 9.99734 9.99733 9.99731 9.99730 9.99728 40 39 38 37 36 6 7 8 115 11.5 13.4 15.3 114 11.4 13.3 15.2 113 11.3 13.2 15.1 25 26 27 28 29 9.04828 9.04940 9.05052 9.05164 9.05275 112 112 112 111 111 9.05101 9.05214 9.05328 9.05441 9.05553 113 114 113 112 0.94899 0.94786 0.94672 0.94559 0.94447 9.99727 9.99726 9.99724 9.99723 9.99721 35 34 33 32 31 9 10 20 30 40 50 17.3 19.2 38.3 57.5 76.7 95 g 17.1 19.0 38.0 57.0 76.0 95 17.0 18.8 37.7 56.5 75.3 94 2 30 31 32 33 34 9.05386 9.05497 9.05607 9.05717 9.05827 111 110 110 110 110 9.05666 9.05778 9.05890 9.06002 9.06113 112 112 112 111 0.94334 0.94222 0.94110 0.93998 0.93887 9.99720 9.99718 9.99717 9.99716 9.99714 30 29 28 27 26 6 7 8 112 11.2 13.1 14.9 III 11.1 13.0 14.8 110 11.0 12.8 14.7 35 36 37 38 39 9.05937 9.06046 9.06155 9.06264 9.06372 109 109 109 108 I AQ 9.06224 9.06335 9.06445 9.06556 9.06666 111 110 111 110 ino 0.93776 0.93665 0.93555 0.93444 0.93334 9.99713 9.99711 9.99710 9.99708 9.99707 25 24 23 22 21 9 10 20 30 40 KA 16.8 18.7 37.3 56.0 74.7 AO q 16.7 18.5 37.0 55.5 74.0 Q9 ^ 16.5 18.3 36.7 55.0 73.3 Q1 7 40 41 42 43 44 9.06481 9.06589 9.06696 9.06804 9.06911 108 107 108 107 107 9.06775 9.06885 9.06994 9.07103 9.07211 110 109 109 108 -I AQ 0.93225 0.93115 0.93006 0.92897 0.92789 9.99705 9.99704 9.99702 9.99701 9.99699 20 19 18 17 16 6 7 8 109 10.9 12.7 14.5 108 10.8 12.6 14.4 107 10.7 12.5 14.3 45 46 47 48 49 9.07018 9.07124 9.07231 9.07337 9.07442 106 107 106 105 infi 9.07320 9.07428 9.07536 9.07643 9.07751 108 108 107 108 1(Y7 0.92680 0.92572 0.92464 0.92357 0.92249 9.99698 9.99696 9.99695 9.99693 9.99692 15 14 13 12 11 9 10 20 30 40 16.4 18.2 36.3 54.5 72.7 16.2 18.0 36.0 54.0 72.0 16.1 17.8 35.7 53.5 71.3 50 51 52 53 54 9.0/548 9.07653 9.07758 9.07863 9.07968 105 105 105 105 -\f\A 9.07858 9.07964 9.08071 9.08177 9.08283 106 107 106 106 infi 0.92142 0.92036 0.91929 0.91823 0.91717 9.99690 9.99689 9.99687 9.99686 9.99684 10 9 8 7 6 50 6 7 8 90.8 IOC 10.6 12.4 14.1 90.0 105 10.5 12.3 14.0 89.2 104 10.4 12.1 13.9 55 56 57 58 59 9.08072 9.08176 9.08280 9.08383 9.08486 104 104 103 103 -i no 9.08389 9.08495 9.08600 9.08705 9.08810 106 105 105 105 104 0.91611 0.91505 0.91400 0.91295 0.91190 9.99683 9.99681 9.99680 9.99678 9.99677 5 4 3 2 1 9 10 20 30 40 15.9 17.7 35.3 53.0 70.7 15.8 17.5 35.0 52.5 70.0 15.6 17.3 34.7 52.0 69.3 60 9.08589 9.08914 0.91086 9.99675 50 88.3 87.5 86.7 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. / P . P. R3 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 499 t L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. P P. 1 2 3 4 9.08589 9.08692 9.08795 9.08897 9.08999 103 103 102 102 109 9.08914 9.09019 9.09123 9.09227 9.09330 105 104 104 103 104 0.91086 0.90981 0.90877 0.90773 0.90670 9.99675 9.99674 9.99672 9.99670 9.99669 60 59 58 57 56 6 7 8 9 10 11 11 14 In 5 .5 .3 .0 8 104 10.4 12.1 13.9 15 6 103 10.3 12.0 13.7 15 5 5 6 7 8 9 9.09101 9.09202 9.09304 9.09405 9.09506 101 102 101 101 inn 9.09434 9.09537 9.09640 9.09742 9.09845 103 103 102 103 102 0.90566 0.90463 0.90360 0.90258 0.90155 9.99667 9.99666 9.99664 9.99663 9.99661 55 54 53 52 51 10 20 30 40 50 17 3;3 51 70 87 .5 .0 .5 .0 .5 17.3 34.7 52.0 69.3 86.7 17.2 34.3 51.5 68.7 85.8 10 11 12 13 14 9.09606 9.09707 9.09807 9.09907 9.10006 101 100 100 99 inn 9.09947 9.10049 9.10150 9.10252 9.10353 102 101 102 101 101 0.90053 0.89951 0.89850 0.89748 0.89647 9.99659 9.99658 9.99656 9.99655 9.99653 50 49 48 47 46 6 7 8 10 1C 11 l: 2 .2 .9 .6 101 10.1 11.8 13.5 100 10.0 11.7 13.3 15 16 17 18 19 9.10106 9.10205 9.10304 9.10402 9.10501 99 99 98 99 98 9.10454 9.10555 9.10656 9.10756 9.10856 101 101 100 100 100 0.89546 0.89445 0.89344 0.89244 0.89144 9.99651 9.99650 9.99648 9.99647 9.99645 45 44 43 42 41 10 20 30 40 50 17 3J 51 6J- 8? .0 .0 .0 .0 16.8 33.7 50.5 67.3 84.2 16.7 33.3 50.0 66.7 83.3 20 21 22 23 24 9.10599 9.10697 9.10795 9.10893 9.10990 98 98 98 97 97 9.10956 9.11056 9.11155 9.11254 9.11353 100 99 99 99 99 0.89044 0.88944 0.88845 0.88746 0.88647 9.99643 9.99642 9.99640 9.99638 9.99637 40 39 38 37 36 6 7 8 9 9 11 13 9 9 .9 9 .6 11 .2 13 8 .8 .4 .1 25 26 27 28 29 9.11087 9.11184 9.11281 9.11377 9.11474 97 97 96 97 9.11452 9.11551 9.11649 9.11747 9.11845 99 98 98 98 0.88548 0.88449 0.88351 0.88253 0.88155 9.99635 9.99633 9.99632 9.99630 9.99629 35 34 33 32 31 ] i t 10 .0 if) 1C 8:5 40 6(1 V-) .5 16 .0 32 .5 49 .0 65 5 81 .3 .7 .0 .3 7 30 31 32 33 34 9.11570 9.11666 9.11761 9.11857 9.11952 96 95 96 95 QC 9.11943 9.12040 9.12138 9.12235 9.12332 97 98 97 97 0.88057 0.87960 0.87862 0.87765 0.87668 9.99627 9.99625 9.99624 9.99622 9.99620 30 29 28 27 26 6 7 8 9 ! 11 11 7 .7 .3 .9 96 9.6 11.2 12.8 95 9.5 11.1 12.7 35 36 37 38 39 9.12047 9.12142 9.12236 9.12331 9.12425 95 94 95 94 94 9.12428 9.12525 9.12621 9.12717 9.12813 97 96 96 96 96 0.87572 0.87475 0.87379 0.87283 0.87187 9.99618 9.99617 9.99615 9.99613 9.99612 25 24 23 22 21 9 10 20 30 40 50 14 1 31 4<^ 6-1 W( .6 .2 .3 .5 .7 g 14.4 16.0 32.0 48.0 64.0 80 14.3 15.8 31.7 47.5 63.3 79 2 40 41 42 43 44 46 47 48 49 9.12519 9.12612 9.12706 9.12799 9.12892 9.12985 9.13078 9.13171 9.13263 9.13355 93 94 93 93 93 93 93 92 92 92 9.12909 9.13004 9.13099 9.13194 9.13289 9.13384 9.13478 9.13573 9.13667 9.13761 95 95 95 95 95 94 95 94 94 93 0.87091 0.86996 0.86901 0.86806 0.86711 "086616 0.86522 0.86427 0.86333 0.86239 9.99610 9.99608 9 f 99607 9.99605 9.99603 9.99601 9.99600 9.99598 9.99596 9.99595 20 19 18 17 16 15 14 13 12 11 6 7 8 9 10 20 30 40 9 ] 11 H 1-1 1| 31 47 61 4 .4 .0 .5 .1 .7 .3 .0 .7 93 9.3 10.9 12.4 14.0 15.5 31.0 46.5 62.0 92 9.2 10.7 12.3 13.8 15.3 30.7 46.0 61.3 50 51 52 53 54 9.13447 9.13539 9.13630 9.13722 9.13813 92 91 92 91 91 9.13854 9.13948 9.14041 9.14134 9.14227 94 93 93 93 no 0.86146 0.86052 0.85959 0.85866 0.85773 9.99593 9.99591 9.99589 9.99588 9.99586 10 9 8 7 6 6 7 8 1 1 91 U J.6 >1 90 9.0 10.5 12.0 2 0.2 02 0.3 55 56 57 58 59 9.13904 9.13994 9.14085 9.14175 9.14266 90 91 90 91 90 9.14320 9.14412 9.14504 9.14597 9.14688 92 92 93 91 92 0.85680 0.&5588 0.85496 0.85403 0.85312 9.99584 9.99582 9.99581 9.99579 9.99577 5 4 3 2 1 9 10 20 30 40 1 1 a 4 6 r.7 VJ ).7 13.5 15.0 30.0 45.0 60.0 0.3 0.3 0.7 1.0 1.3 60 9.14356 9.14780 0.8522C 9.99575 50 / j.8 ! 75.0 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. ' P . P. 82 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 8 ' L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. P P 1 2 3 4 9.14356 9.14445 9.14535 9.14624 9.14714 89 90 89 90 OQ 9.14780 9.14872 9.14963 9.15054 9.15145 92 91 91 91 Q1 0.85220 0.85128 0.85037 0.84946 0.84855 9.99575 9.99574 9.99572 9.99570 9.99568 60 59 58 57 56 6 7 8 g i 1( li 1' 2 K2 ).7 >.3 > J j 1C Y< Y- II .1 .6 .1 7 90 9.0 10.5 12.0 13 5 5 6 7 8 9 9.14803 9.14891 9.14980 9.15069 9.15157 88 89 89 88 QO 9.15236 9.15327 9.15417 9.15508 9.15598 91 90 91 90 QO 0.84764 0.84673 0.84583 0.84492 0.84402 9.99566 9.99565 9.99563 9.99561 9.99559 55 54 53 52 51 10 20 30 40 50 If 3( 4( 61 7( >.3 ).7 >.o .3 >.7 U 3C 4t 6C 7c .2 .3 .5 .7 .8 15.0 30.0 45.0 60.0 75.0 10 11 12 13 14 9.15245 9.15333 6.15421 9.15508 9.15596 88 88 87 88 07 9.15688 9.15777 9.15867 9.15956 9.16046 89 90 89 90 on 0.84312 0.84223 0.84133 0.84044 0.83954 9.99557 9.99556 9.99554 9.99552 9.99550 50 49 48 47 46 6 7 8 8 8 10 n i } 9 .9 .4 .9 i 8 8 10 11 -iq 8 .8 .3 .7 9 15 16 17 18 19 9.15683 9.15770 9.15857 9.15944 9.16030 87 87 87 86 Off 9.16135 9.16224 9.16312 9.16401 9.16489 89 88 89 88 00 0.83865 0.83776 0.83688 0.83599 0.83511 9.99548 9.99546 9.99545 9.99543 9.99541 45 44 43 42 41 ] J t f >0 50 to rf) 14 29 44 59 74 8 7 5 3 2 14 29 44 58 73 .7 3 .0 .7 3 20 21 22 23 24 9.16116 9.16203 9.16289 9.16374 9.16460 87 86 85 86 oc 9.16577 9.16665 9.16753 9.16841 9.16928 88 88 88 87 00 0.83423 0.83335 0.83247 0.83159 0.83072 9.99539 9.99537 9.99535 9.99533 9.99532 40 39 38 37 36 6 7 8 8 8 10 11 7 7 2 6 8 8 10 11 B 6 5 25 26 27 28 29 9.16545 9.16631 9.16716 9.16801 9.16886 86 85 85 85 QA 9.17016 9.17103 9.17190 9.17277 9.17363 87 87 87 86 07 0.82984 0.82897 0.82810 0.82723 0.82637 9.99530 9.99528 9.99526 9.99524 9.99522 35 34 33 32 31 J 5 '. 4 F o 14 29 43 58 7'> 5 5 ^ 14 28 43 57 71 3 7 3 7 30 31 32 33 34 9.16970 9.17055 9.17139 9.17223 9.17307 85 84 84 84 84 9.17450 9.17536 9.17622 9.17708 9.17794 86 86 86 86 Q 0.82550 0.82464 0.82378 0.82292 0.82206 9.99520 9.99518 9.99517 9.99515 9.99513 30 29 28 27 26 6 7 8 8 8 9 11 5 9 3 8 8 9 11 t 4 8 2 35 36 37 38 39 9.17391 9.17474 9.17558 9.17641 9.17724 83 84 83 83 oq 9.17880 9.17965 9.18051 9.18136 9.18221 85 86 85 85 QC 0.82120 0.82035 0.81949 0.81864 0.81779 9.99511 9.99509 9.99507 9.99505 9.99503 25 24 23 22 21 jl C 4 i 9 (J 12 14 28 42 56 '"O 8 2 3 5 7 8 12 14 28 42 56 70 6 O 40 41 42 43 44 9.17807 9.17890 9.17973 9.18055 9.18137 83 83 82 82 OO 9.18306 9.18391 9.18475 9.18560 9.18644 85 84 85 84 QA 0.81694 0.81609 0.81525 0.81440 0.81356 9.99501 9.99499 9.99497 9.99495 9.99494 20 19 18 17 16 6 7 8 8 8 9 11 3 3 7 1 8 8 9 10 I 2 6 9 45 46 47 48 49 9.18220 9.18302 9.18383 9.18465 9.18547 82 81 82 82 o-i 9.18728 9.18812 9.18896 9.18979 9.19063 84- 84 83 84 00 0.81272 0.81188 0.81104 0.81021 0.80937 9.99492 9.99490 9.99488 9.99486 9.99484 15 14 13 12 11 1 2 3 4 9 12 13 27 41 55 5 8 7 5 3 12 13 27 41 54 3 7 3 7 50 51 52 53 54 9.18628 9.18709 9.18790 9.18871 9.18952 81 81 81 81 81 9.19146 9.19229 9.19312 9.19395 9.19478 83 83 83 83 oq 0.80854 0.80771 0.80688 0.80605 0.80522 9.99482 9.99480 9.99478 9.99476 9.99474 10 9 8 7 6 6 7 8 >0 1 1 ( 1( }| U ).5 ).8 * i 1( *.o ).3 ).7 2 0.2 0.2 0.3 55 56 57 58 59 9.19033 9.19113 9.19193 9.19273 9.19353 80 80 80 80 80 9.19561 9.19643 9.19725 9.19807 9.19889 82 82 82 82 QO 0.80439 0.80357 0.80275 0.80193 0.80111 9.99472 9.99470 9.99468 9.99466 9.99464 5 4 3 2 1 9 10 20 30 40 11 i: 2 4( f> 2.2 5.5 -.0 ),5 1.0 11 11 2( 4( 5r 5.0 5.3 >.7 ).0 5.3 0.3 0.3 0.7 1.0 1.3 60 9.19433 9.19971 0.80029 9.99462 50 b .5 ht >. / 1.7 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. ' P P 81 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 9 ' L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. P. P 1 2 3 4 9.19433 9.19513 9.19592 9.19672 9.19751 80 79 80 79 7Q 9.19971 9.20053 9.20134 9.20216 9.20297 82 81 82 81 fti 0.80029 0.79947 0.79866 0.79784 0.79703 9.99462 9.99460 9.99458 9.99456 9.99454 60 59 58 57 56 8 6 i 7 < 8 1C 9 IS 2 .2 .6 .9 g 8 8 S 1C v 1 .1 .5 .8 2 80 8.0 9.3 10.7 12 5 6 7 8 9 9.19830 9.19909 9.19988 9.20067 9.20145 79 79 79 78 78 9.20378 9.20459 9.20540 9.20621 9.20701 81 81 81 80 Q-l 0.79622 0.79541 0.79460 0.79379 0.79299 9.99452 9.99450 9.99448 9.99446 9.99444 55 54 53 52 51 10 Yi 20 27 30 4] 40 54 50 & .7 .3 .0 .7 .3 13 27 4C 54 67 .5 .0 .5 .0 .5 13.3 26.7 40.0 53.3 66.7 10 11 12 13 14 9.20223 9.20302 9.20380 9.20458 9.20535 79 78 78 77 78 9.20782 9.20862 9.20942 9.21022 9.21102 80 80 80 80 Of) 0.79218 0.79138 0.79058 0.78978 0.78898 9.99442 9.99440 9.99438 9.99436 9.99434 50 49 48 47 46 6 7 8 Q 7 7 9 10 11 3 9 2 5 o 7 7 8 10 8 .8 .1 .4 7 15 16 17 18 19 9.20613 9.20691 9.20768 9.20845 9.20922 78 77 77 77 77 9.21182 9.21261 9.21341 9.21420 9.21499 79 80 79 79 0.78818 0.78739 0.78659 0.78580 0.78501 9.99432 9.99429 9.99427 9.99425 9.99423 45 44 43 42 41 10 20 30 40 50 13 26 39 52 f>5 2 3 5 7 8 13 21 3fl 52 fir .0 .0 .0 .0 .0 20 21 22 23 24 9.20999 9.21076 9.21153 9.21229 9.21306 77 77 76 77 7fi 9.21578 9.21657 9.21736 9.21814 9.21893 79 79 78 79 0.78422 0.78343 0.78264 0.78186 0.78107 9.99421 9.99419 9.99417 9.99415 9.99413 40 39 38 37 36 6 7 8 7 7 9 10 7 7 3 7 7 g 10 6 .6 .9 .1 25 26 27 28 29 9.21382 9.21458 9.21534 9.21610 9.21685 76 76 76 75 76 9.21971 9.22049 9.22127 9.22205 9.22283 78 78 78 78 0.78029 0.77951 0.77873 0.77795 0.77717 9.99411 9.99409 9.99407 9.99404 9.99402 35 34 33 32 31 9 10 20 30 40 50 11 12 25 38 51 61 6 8 7 5 3 11 11 25 38 50 6 .4 .7 .3 .0 .7 3 30 31 32 33 34 9.21761 9.21836 9.21912 9.21987 9.22062 75 76 75 75 75 9.22361 9.22438 9.22516 9.22593 9.22670 77 78 77 77 0.77639 0.77562 0.77484 0.77407 0.77330 9.99400 9.99398 9.99396 9.99394 9.99392 30 29 28 27 26 6 7 8 7 7 8 10 5 5 8 7 7 8 S 4 .4 .6 .9 35 36 37 38 39 9.22137 9.22211 9.22286 9.22361 9.22435 74 75 75 74 74 9.22747 9.22824 9.22901 9.22977 9.23054 77 77 76 77 7ft 0.77253 0.77176 0.77099 0.77023 0.76946 9.99390 9.99388 9.99385 9.99383 9.99381 25 24 23 22 21 9 10 20 30 40 crv ii 12 25 37 50 r~) 3 5 5 ,- 11 12 24 37 4Q n .1 .3 .7 .0 .3 7 40 41 42 43 44 9.22509 9.22583 9.22657 9.22731 9.22805 74 74 74 74 73 9.23130 9.23206 9.23283 9.23359 9.23435 76 77 76 76 7^ 0.76870 0.76794 0.76717 0.76641 0.76565 9.99379 9.99377 9.99375 9.99372 9.99370 20 19 18 17 16 6 7 8 7 7 8 9 3 3 5 7 7 7 g 8 2 .2 .4 .6 45 46 47 48 49 9.22878 9.22952 9.23025 9.23098 9.23171 74 73 73 73 73 9.23510 9.23586 9.23661 9.23737 9.23812 76 75 76 75 IJK. 0.76490 0.76414 0.76339 0.76263 0.76188 9.99368 9.99366 9.99364 9.99362 9.99359 15 14 13 12 11 9 10 20 30 40 11 12 24 3(5 48 2 3 5 7 1C 12 24 3t 48 .8 .0 .0 .0 .0 50 51 52 53 54 9.23244 9.23317 9.23390 9.23462 9.23535 73 73 72 73 72 9.23887 9.23962 9.24037 9.24112 9.24186 75 75 75 74 rjK. 0.76113 0.76038 0.75963 0.75888 0.75814 9.99357 9.99355 9.99353 9.99351 9.99348 10 9 8 7 6 6 7 8 71 7.1 8.3 95 .3 .4 .4 0.2 0.2 0.3 55 56 57 58 59 9.23607 9.23679 9.23752 9.23823 9.23895 72 73 71 72 72 9.24261 9.24335 9.24410 9.24484 9.24558 74 75 74 74 74 0.75739 0.75665 0.75590 0.75516 0.75442 9.99346 9.99344 9.99342 9.99340 9.99337 5 4 3 2 1 9 1 10 1 20 2 30 8 40 4 0.7 1.8 3.7 5.5 7.3 1 1 2 .5 .5 .0 .5 .0 0.3 0.3 0.7 1.0 1.3 60 9.23967 9.24632 0.75368 9.99335 50 5 9.2 2 .a 1.7 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. ' P. P 80 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 10 / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. P. P 1 2 3 4 9.23967 9.24039 9.24110 9.24181 9.24253 72 71 71 72 71 9.24632 9.24706 9.24779 9.24853 9.24926 74 73 74 73 74 0.75368 0.75294 0.75221 0.75147 0.75074 9.99335 9.99333 9.99331 9.99328 9.99326 60 59 58 57 56 6 7 8 9 74 7.4 8.6 9.9 11 1 73 7.3 8.5 9.7 11 5 6 7 8 9 9.24324 9.24395 9.24466 9.24536 9.24607 71 71 70 71 7ft 9.25000 9.25073 9.25146 9.25219 9.25292 73 73 73 73 73 0.75000 0.74927 0.74854 0.74781 0.74708 9.99324 9.99322 9.99319 9.99317 9.99315 55 54 53 52 51 10 20 30 40 50 12.3 24.7 37.0 49.3 61.7 12.2 24.3 36.5 48.7 60.8 10 11 12 13 14 9.24677 9.24748 9.24818 9.24888 9.24958 71 70 70 70 '70 9.25365 9.25437 9.25510 9.25582 9.25655 72 73 72 73 72 0.74635 0.74563 0.74490 0.74418 0.74345 9.99313 9.99310 9.99308 9.99306 9.99304 50 49 48 47 46 6 7 8 g 72 7.2 8.4 9.6 10 8 71 7.1 8.3 9.5 10 7 15 16 17 18 19 9.25028 9.25098 9.25168 9.25237 9.25307 70 70 69 70 69 9.25727 9.25799 9.25871 9.25943 9.26015 72 72 72 72 71 0.74273 0.74201 0.74129 0.74057 0.73985 9.99301 9.99299 9.99297 9.99294 9.99292 45 44 43 42 41 10 20 30 40 50 12.0 24.0 36.0 48.0 60.0 11.8 23.7 35.5 47.3 59.2 20 21 22 23 24 9.25376 9.25445 9.25514 9.25583 9.25652 69 69 69 69 69 9.26086 9.26158 9.26229 9.26301 9.26372 72 71 72 71 71 0.73914 0.73842 0.73771 0.73699 0.73628 9.99290 9.99288 9.99285 9.99283 9.99281 40 39 38 37 36 6 7 8 70 7.0 8.2 9.3 69 6.9 8.1 9.2 25 26 27 28 29 9.25721 9.25790 9.25858 9.25927 9.25995 69 68 69 68 Q 9.26443 9.26514 9.26585 9.26655 9.26726 71 71 70 71 71 0.73557 0.73486 0.73415 0.73345 0.73274 9.99278 9.99276 9.99274 9.99271 9.99269 35 34 33 32 31 10 20 30 40 50 11.7 23.3 35.0 46.7 58 3 11.5 23.0 34.5 46.0 57 5 30 31 32 33 34 9.26063 9.26131 9.26199 9.26267 9.26335 68 68 68 68 9.26797 9.26867 9.26937 9.27008 9.27078 70 70 71 70 7fl 0.73203 0.73133 0.73063 0.72992 0.72922 9.99267 9.99264 9.99262 9.99260 9.99257 30 29 28 27 26 6 7 8 68 6.8 7.9 9.1 67 6.7 7.8 8.9 35 36 37 38 39 9.26403 9.26470 9.26538 9.26605 9.26672 67 68 67 67 67 9.27148 9.27218 9.27288 9.27357 9.27427 70 70 69 70 an 0.72852 0.72782 0.72712 0.72643 0.72573 9.99255 9.99252 9.99250 9.99248 9.99245 25 24 23 22 21 9 10 20 30 40 50 10.2 11.3 22.7 34.0 45.3 56 7 10.1 11.2 22.3 33.5 44.7 55 8 40 41 42 43 44 9.26739 9.26806 9.26873 9.26940 9.27007 67 67 67 67 66 9.27496 9.27566 9.27635 9.27704 9.27773 70 69 69 69 fQ 0.72504 0.72434 0.72365 0.72296 0.72227 9.99243 9.99241 9.99238 9.99236 9.99233 20 19 18 17 16 6 7 8 66 6.6 7.7 8.8 65 6.5 7.6 8.7 45 46 47 48 49 9.27073 9.27140 9.27206 9.27273 9.27339 67 66 67 66 66 9.27842 9.27911 9.27980 9.28049 9.28117 69 69 69 68 69 0.72158 0.72089 0.72020 0.71951 0.71883 9.99231 9.99229 9.99226 9.99224 9.99221 15 14 13 12 11 9 10 20 30 40 9.9 11.0 22.0 33.0 44.0 9.8 10.8 21.7 32.5 43.3 50 51 52 53 54 9.27405 9.27471 9.27537 9.27602 9.27668 66 66 65 66 66 9.28186 9.28254 9.28323 9.28391 9.28459 68 69 68 68 CQ 0.71814 0.71746 0.71677 0.71609 0.71541 9.99219 9.99217 9.99214 9.99212 9.99209 10 9 8 7 6 6 7 8 3 0.3 0.4 0.4 2 0.2 0.2 0.3 55 56 57 58 59 9.27734 9.27799 9.27864 9.27930 9.27995 65 65 66 65 cc 9.28527 9.28595 9.2S662 9.28730 9.28798 68 67 68 68 f\7 0.71473 0.71405 0.71338 0.71270 0.71202 9.99207 9.99204 9.99202 9.99200 9.99197 5 4 3 2 1 9 10 10 30 40 0.5 0.5 1.0 1.5 2.0 0.3 0.3 0.7 1.0 1.3 60 9.28060 9.28865 0.71135 9.99195 50 2.5 1.7 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. ' P. P 79 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 11 ' L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. P. P 1 3 4 9.28060 9.28125 9.28190 9.28254 9.28319 65 65 64 65 65 9.28865 9.28933. 9.29000' 9.29067 9.29134 68 67 67 67 67 0.71135 0.71067 0.71000 0.70933 0.70866 9.99195 9.99192 9.99190 9.99187 9.99185 60 59 58 57 56 6 7 8 9 68 6.8 7.9 9.1 10 2 67 6.7 7.8 8.9 10 1 5 6 7 8 9 9.28384 9.28448 9.28512 9.28577 9.28641 64 64 65 64 CA 9.29201 9.29268 9.29335 9.29402 9.29468 67 67 67 66 67 0.70799 0.70732 0.70665 0.70598 0.70532 9.99182 9.99180 9.99177 9.99175 9.99172 55 54 53 52 51 10 20 30 40 50 11.3 22.7 34.0 45.3 56.7 11.2 22.3 33.5 44.7 55.8 to 11 12 13 14 9.28705 9.28769 9.28833 9.28896 9.28960 64 64 63 64 CA 9.29535 9.29601 9.29668 9.29734 9.29800 66 67 66 66 66 0.70465 0.70399 0.70332 0.70266 0.70200 9.99170 9.99167 9.99165 9.99162 9.99160 50 49 48 47 46 6 7 8 66 6.6 7.7 8.8 65 6.5 7.6 8.7 15 16 17 18 19 9.29024 9.29087 9.29150 9.29214 9.29277 63 63 64 63 63 9.29866 9.29932 9.29998 9.30064 9.30130 66 66 66 66 65 0.70134 0.70068 0.70002 0.69936 0.69870 9.99157 9.99155 9.99152 9.99150 9.99147 45 44 43 42 41 10 20 30 40 50 11.0 22.0 33.0 44.0 55.0 10.8 21.7 32.5 43.3 54.2 20 21 22 23 24 9.29340 9.29403 9.29466 9.29529 9.29591 63 63 63 62 63 9.30195 9.30261 9.30326 9.30391- 9.30457 66 65 65 66 65 0.69805 0.69739 0.69674 0.69609 0.69543 9.99145 9.99142 9.99140 9.99137 9.99135 40 39 38 37 36 6 7 8 64 6.4 7.5 8.5 63 6.3 7.4 8.4 25 26 27 28 29 30 31 32 33 34 ~35~ 36 37 38 39 9.29654 9.29716 9.29779 9.29841 9.29903 "9^29966^ 9.30028 9.30090 9.30151 9.30213 1K30275 9.30336 9.30398 9.30459 9.30521 62 63 62 62 63 62 62 61 62 62 61 62 61 62 fii 9.30522 9.30587 9.30652 9.30717 9.30782 9.30846" 9.30911 9.30975 9.31040 9.31104 T3li68" 9.31233 9.31297 9.31361 9.31425 65 65 65 65 64 65 64 65 64 64 65 64 64 64 CA 0.69478 0.69413 0.69348 0.69283 0.69218 0.69154 0.69089 0.69025 0.68960 0.68896 0.68832 0.68767 0.68703 0.68639 0.68575 9.99132 9.99130 9.99127 9.99124 9.99122 9.99119 9.99117 9.99114 9.99112 9.99109 9.99106 9.99104 9.99101 9.99099 9.99096 35 34 33 32 31 ~30~ 29 28 27 26 ~25~ 24 23 22 21 9 10 20 30 40 50 6 7 8 9 10 20 30 40 9.6 10.7 21.3 32.0 42.7 53.3 62 6.2 7.2 8.3 9.3 10.3 20.7 31.0 41.3 9.5 10.5 21.0 31.5 42.0 52.5 61 6.1 7.1 8.1 9.2 10.2 20.3 30.5 40.7 40 41 42 43 44 9.30582 9.30643 9.30704 9.30765 9.30826 61 61 61 61 fii 9.31489 9.31552 9.31616 9.31679 9.31743 63 64 63 64 fiS 0.68511 0.68448 0.68384 0.68321 0.68257 9.99093 9.99091 9.99088 9.99086 9.99083 20 19 18 17 16 6 7 8 60 6.0 7.0 8.0 59 5.9 6.9 7.9 45 46 47 48 49 9.30887 9.30947 9.31008 9.31068 9.31129 60 61 60 61 fin 9.31806 9.31870 9.31933 9.31996 9.32059 64 63 63 63 63 0.68194 0.68130 0.68067 0.68004 0.67941 9.99080 9.99078 9.99075 9.99072 9.99070 15 14 13 12 11 9 10 20 30 40 9.0 10.0 20.0 30.0 40.0 8.9 9.8 19.7 29.5 39.3 50 51 52 53 54 9.31189 9.31250 9.31310 9.31370 9.31430 61 60 60 60 60 9.32122 9.32185 9.32248 9.32311 9.32378 63 63 63 62 : AQ 0.67878 0.67815 0.67752 0.67689 0.67627 9.99067 9.99064 9.99062 9.99059 9.99056 10 9 8 7 6 50 6 7 8 50.0 3 0.3 0.4 0.4 2 0.2 0.2 0.3 55 56 57 58 59 9.31490 9.31549 9.31609 9.31669 9.31728 59 60 60 59 60 9.32436 9.32498 9.32561 9.32623 9.32685 62 63 62 62 62 0.67564 0.67502 0.67439 0.67377 0.67315 9.99054 9.99051 9.99048 9.99046 9.99043 5 4 3 2 1 9 10 20 30 40 0.5 0.5 1.0 1.5 2.0 0.3 0.3 0.7 1.0 1.3 60 9.31788 9.32747 0.67253 9.99040 50 2.5 1.7 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. ' P.P. 78 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 12 1 L. Sin. d. L.Tang. d. o. L. Cotg. L. Cos. P.P 1 2 3 4 9.31788 9.31847 9.31907 9.31966 9.32025 59 60 59 59 KQ 9.32747 9.32810 9.32872 9.32933 9.32995 63 62 61 62 62 0.67253 0.67190 0.67128 0.67067 0.67005 9.99040 9.99038 9.99035 9.99032 9.99030 60 59 58 57 56 6 7 8 g 63 6.3 7.4 8.4 9 5 62 6.2 7.2 8.3 9 3 5 6 7 8 9 9.32084 9.32143 9.32202 9.32261 9.32319 59 59 59 58 rq 9.33057 9.33119 9.33180 9.33242 9.33303 62 61 62 61 62 0.66943 0.66881 0.66820 0.66758 0.66697 9.99027 9.99024 9.99022 9.99019 9.99016 55 54 53 52 51 10 20 30 40 50 10.5 21.0 31.5 42.0 52.5 10.3 20.7 31.0 41.3 51.7 10 11 12 13 14 9.32378 9.32437 9.32495 9.32553 9.32612 59 58 58 59 CO 9.33365 9.33426 9.33487 9.33548 9.33609 61 61 61 61 61 0.66635 0.66574 0.66513 0.66452 0.66391 9.99013 9.99011 9.99008 9.99005 9.99002 50 49 48 47 46 6 7 8 61 6.1 7.1 8.1 60 6.0 7.0 8.0 15 16 17 18 19 9.32670 9.32728 9.32786 9.32844 9.32902 58 58 58 58 CO 9.33670 9.33731 9.33792 9.33853 9.33913 61 61 61 60 61 0.66330 0.66269 0.66208 0.66147 0.66087 9.99000 9.98997 9.98994 9.98991 9.98989 45 44 43 42 41 10 20 30 40 50 10.2 20.3 30.5 40.7 50.8 10.0 20.0 30.0 40.0 50.0 20 21 22 23 24 9.32960 9.33018 9.33075 9.33133 9.33190 58 57 58 57 CO 9.33974 9.34034 9.34095 9.34155 9.34215 60 61 60 60 61 0.66026 0.65966 0.65905 0.65845 0.65785 9.98986 9.98983 9.98980 9.98978 9.98975 40 39 38 37 36 6 I 7 ( 8 ' 9 >.9 >.9 r .9 25 26 27 28 29 9.33248 9.33305 9.33362 9.33420 9.33477 57 57 58 57 57 9.34276 9.34336 9.34396 9.34456 9.34516 60 60 60 60 60 0.65724 0.65664 0.65604 0.65544 0.65484 9.98972 9.98969 9.98967 9.98964 9.98961 35 34 33 32 31 9 J 10 \ 20 \\ 30 2< 40 3< 50 4* 5.9 ).8 ).7 ).5 ).3 )2 30 31 32 33 34 9.33534 9.33591 9.33647 9.33704 9.33761 57 56 57 57 C7 9.34576 9.34635 9.34695 9.34755 9.34814 59 60 60 59 60 0.65424 0.65365 0.65305 0.65245 0.65186 9.98958 9.98955 9.98953 9.98950 9.98947 30 29 28 27 26 6 7 8 58 5.8 6.8 7.7 57 5.7 6.7 7.6 35 36 37 38 39 9.33818 9.33874 9.33931 9.33987 9.34043 56 57 56 56 57 9.34874 9.34933 9.34992 9.35051 9.35111 59 59 59 60 59 0.65126 0.65067 0.65008 0.64949 0.64889 9.98944 9.98941 9.98938 9.98936 9.98933 25 24 23 22 21 9 10 20 30 40 50 8.7 9.7 19.3 29.0 38.7 48 3 8.6 9.5 19.0 28.5 38.0 47 5 40 41 42 43 44 9.34100 9.34156 9.34212 9.34268 9.34324 56 56 56 56 56 9.35170 9.35229 9.35288 9.35347 9.35405 59 59 59 58 59 0.64830 0.64771 0.64712 0.64653 0.64595 9.98930 9.98927 9.98924 9.98921 9.98919 20 19 18 17 16 6 7 8 56 5.6 6.5 7.5 55 5.5 6.4 7.3 45 46 47 48 49 9.34380 9.34436 9.34491 9.34547 9.34602 56 55 56 55 KC 9.35464 9.35523 9.35581 9.35640 9.35698 59 58 59 58 crj 0.64536 0.64477 0.64419 0.64360 0.64302 9.98916 9.98913 9.98910 9.98907 9.98904 15 14 13 12 11 9 10 20 30 40 8.4 9.3 18.7 28.0 37.3 8.3 9.2 18.3 27.5 36.7 50 51 52 53 54 9.34658 9.34713 9.34769 9.34824 9.34879 55 56 55 55 55 9.35757 9.35815 9.35873 9.35931 9.35989 58 58 58 58 58 0.64243 0.64185 0.64127 0.64069 0.64011 9.98901 9.98898 9.98896 9.98893 9.98890 10 9 8 7 6 50 6 7 8 46.7 0.3 0.4 0.4 45.8 2 0.2 0.2 0.3 55 56 57 58 59 9.34934 9.34989 9.35044 9.35099 9.35154 55 55 55 55 55 9.36047 9.36105 9.36163 9.36221 9.36279 58 58 58 58 57 0.63953 0.63895 0.63837 0.63779 0.63721 9.98887 9.98884 9.98881 9.98878 9.98875 5 4 3 2 1 9 10 20 30 40 0.5 0.5 1.0 1.5 2.0 0.3 0.3 0.7 1.0 1.3 60 9.35209 9.36336 0.63664 9.98872 50 2.5 1.7 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. ' P.P 77 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, 13 505 ' L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. P. P 1 2 3 4 9.35209 9.35263 9.35318 9.35373 9.35427 54 55 55 54 KA 9.36336 9.36394 9.36452 9.36509 9.36566 58 58 57 57 CO 0.63664 0.63606 0.63548 0.63491 0.63434 9.98872 9.98869 9.98867 9.98864 9.98861 60 59 58 57 56 6 7 8 9 58 5.8 6.8 7.7 8 7 57 5.7 6.7 7.6 8 6 5 6 7 8 9 9.35481 9.35536 9.35590 9.35644 9.35698 55 54 54 54 f^A 9.36624 9.36681 9.36738 9.36795 9.36852 57 57 57 57 K7 0.63376 0.63319 0.63262 0.63205 0.63148 9.98858 9.98855 9.98852 9.98849 9.98846 55 54 53 52 51 10 20 30 40 50 9.7 19.3 29.0 38.7 48.3 9.5 19.0 28.5 38.0 47.5 10 11 12 13 14 9.35752 9.35806 9.35860 9.35914 9.35968 54 54 54 54 54 9.36909 9.36966 9.37023 9.37080 9.37137 57 57 57 57 FU; 0.63091 0.63034 0.62977 0.62920 0.62863 9.98843 9.98840 9.98837 9.98834 9.98831 50 49 48 47 46 6 7 8 g 56 5.6 6.5 7.5 8 4 55 5.5 6.4 7.3 Q q 15 16 17 18 19 9.36022 9.36075 9.36129 9.36182 9.36236 53 54 53 54 53 9.37193 9.37250 9.37306 9.37363 9.37419 57 56 57 56 K7 0.62807 0.62750 0.62694 0.62637 0.62581 9.98828 9.98825 9.98822 9.98819 9.98816 45 44 43 42 41 10 20 30 40 50 9.3 18.7 28.0 37.3 46.7 9.2 18.3 27.5 36.7 45.8 20 21 22 23 24 9.36289 9.36342 9.36395 9.36449 9.36502 53 53 54 53 53 9.37476 9.37532 9.37588 9.37644 9.37700 56 56 56 56 KC 0.62524 0.62468 0.62412 0.62356 0.62300 9.98813 9.98810 9.98807 9.98804 9.98801 40 39 38 37 36 5 6 7 ( 8 'J 4 .4 .3 .2 25 26 27 28 29 9.36555 9.36608 9.36660 9.36713 9.36766 53 52 53 53 53 9.37756 9.37812 9.37868 9.37924 9.37980 56 56 56 56 EK 0.62244 0.62188 0.62132 0.62076 0.62020 9.98798 9.98795 9.98792 9.98789 9.98786 35 34 33 32 31 10 < 20 1* 30 2' 40 3( 30 4 ).0 5.0 r .O >.o > 30 31 32 33 34 9.36819 9.36871 9.36924 9.36976 9.37028 52 53 52 52 53 9.38035 9.38091 9.38147 9.38202 9.38257 56 56 55 55 ^A 0.61965 0.61909 0.61853 0.61798 0.61743 9.98783 9.98780 9.98777 9.98774 9.98771 30 29 28 27 26 6 7 8 53 5.3 6.2 7.1 52 5.2 6.1 6.9 35 36 37 38 39 9.37081 9.37133 9.37185 9.37237 9.37289 52 52 52 52 52 9.38313 9.38368 9.38423 9.38479 9.38534 55 55 56 55 KK 0.61687 0.61632 0.61577 0.61521 0.61466 9.98768 9.98765 9.98762 9.98759 9.98756 25 24 23 22 21 9 10 20 30 40 50 8.0 8.8 17.7 26.5 35.3 44 ** 7.8 8.7 17.3 26.0 34.7 43 3 40 41 42 43 44 9.37341 9.37393 9.37445 9.37497 9.37549 52 52 52 52 51 9.38589 9.38644 9.38699 9.38754 9.38808 55 55 55 54 55 0.61411 0.61356 0.61301 0.61246 0.61192 9.98753 9.98750 9.98746 9.98743 9.98740 20 19 18 17 16 6 7 8 51 5.1 6.0 6.8 4 0.4 0.5 0.5 45 46 47 48 49 9.37600 9.37652 9.37703 9.37755 9.37806 52 51 52 51 52 9.38863 9.38918 9.38972 9.39027 9.39082 55 54 55 55 54 0.61137 0.61082 0.61028 0.60973 0.60918 9.98737 9.98734 9.98731 9.98728 9.98725 15 14 13 12 11 9 10 20 30 40 7.7 8.5 17.0 25.5 34.0 0.6 0.7 1.3 2.0 2.7 o q 50 51 52 53 54 9.37858 9.37909 9.37960 9.38011 9.38062 51 51 51 51 51 9.39136 9.39190 9.39245 9.39299 9.39353 54 55 54 54 CiA 0.60864 0.60810 0.60755 0.60701 0.60647 9.98722 9.98719 9.98715 9.98712 9.98709 10 9 8 7 6 6 7 8 0.3 0.4 0.4 2 0.2 0.2 0.3 55 56 57 58 59 9.38113 9.38164 9.38215 9.38266 9.38317 51 51 51 51 51 9.39407 9.39461 9.39515 9.39569 9.39623 54 54 54 54 54 0.60593 0.60539 0.60485 0.60431 0.60377 9.98706 9.98703 9.98700 9.98697 9.98694 5 4 3 2 1 9 10 20 30 40 0.5 0.5 1.0 1.5 2.0 0.3 0.3 0.7 1.0 1.3 60 9.38368 9.39677 0.60323 9.98690 50 2.5 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. ' P. P 76 50B LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 14 ' L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P.P. 1 2 3 4 9.38368 9.38418 9.38469 9.38519 9.38570 50 51 50 51 50 50 51 50 50 50 50 50 50 50 50 49 50 50 49 50 49 49 50 49 49 49 49 49 49 49 49 49 48 49 48 49 48 49 48 49 48 48 48 48 48 48 48 48 48 47 48 48 47 48 47 48 47 47 47 48 9.39677 9.39731 9.39785 9.39838 9.39892 54 54 53 54 53 54 53 54 53 53 54 53 53 53 53 53 53 52 53 53 53 52 53 52 53 52 52 52 53 52 52 52 52 52 52 52 51 52 52 51 52 51 52 51 51 52 51 51 51 51 51 51 51 51 51 51 50 51 51 50 0.60323 0.60269 0.60215 0.60162 0.60108 9.98690 9.98687 9.98684 9.98681 9.98678 3 3 3 3 3 4 3 3 3 3 3 4 3 3 3 3 4 3 3 3 4 3 3 3 4 3 3 3 4 3 3 3 4 3 3 4 3 3 3 4 3 3 4 3 3 4 3 3 4 3 3 4 3 3 4 3 3 4 3 4 60 59 58 57 56 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 54 5.4 6.3 7.2 8.1 9.0 18.0 27.0 36.0 45.0 52 5.2 6.1 6.9 7.8 8.7 17.3 26.0 34.7 43.3 50 5.0 5.8 6.7 7.5 8.3 16.7 25.0 33.3 41.7 48 4.8 5.6 6.4 7.2 8.0 16.0 24.0 32.0 40.0 4 0.4 0.5 0.5 0.6 0.7 1.3 2.0 2.7 3.3 53 5.3 6.2 7.1 8.0 8.8 17.7 26.5 35.3 44.2 51 5.1 6.0 6.8 7.7 8.5 17.0 25.5 34.0 42.5 49 4.9 5.7 6.5 7.4 8.2 16.3 24.5 32.7 40.8 47 4.7 5.5 6.3 7.1 7.8 15.7 23.5 31.3 39.2 3 0.3 0.4 0.4 0.5 0.5. 1.0 1.5 2.0 2.5 5 6 7 8 9 9.38620 9.38670 9.38721 9.38771 9.38821 9.39945 9.39999 9.40052 9.40106 9.40159 0.60055 0.60001 0.59948 0.59894 0.59841 9.98675 9.98671 9.98668 9.98665 9.98662 55 54 53 52 51 10 11 12 13 14 9.38871 9.38921 9.38971 9.39021 9.39071 9.39121 9.39170 9.39220 9.39270 9.39319 9.40212 9.40266 9.40319 9.40372 9.40425 0.59788 0.59734 0.59681 0.59628 0.59575 9.98659 9.98&56 9.98652 9.98649 9.98646 50 49 48 47 46 45 44 43 42 41 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 ^0~ 31 32 33 34 9.40478 9.40531 9.40584 9.40636 9.40689 9.40742 9.40795 9.40847 9.40900 9.40952 0.59522 0.59469 0.59416 0.59364 0.59311 9.98643 9.98640 9.98636 9.98633 9.98630 9.39369 9.39418 9.39467 9.39517 9.39566 0.59258 0.59205 0.59153 0.59100 0.59048 9.98627 9.98623 9.98620 9.98617 9.98614 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 9.39615 9.39664 9.39713 9.39762 9.39811 9.39860 9.39909 9.39958 9.40006 9.40055 9.40103 9.40152 9.40200 9.40249 9.40297 9.41005 9.41057 9.41109 9.41161 9.41214 9.41266 9.41318 9.41370 9.41422 9.41474 0.58995 0.58943 0.58891 0.58839 0.58786 0.58734 0.58682 0.58630 0.58578 0.58526 9.98610 9.98607 9.98604 9.98601 9.98597 9.98594 9.98591 9.98588 9.98584 9.98581 35 36 37 38 39 9.41526 9.41578 9.41629 9.41681 9.41733 9.41784 9.41836 9.41887 9.41939 9.41990 0.58474 0.58422 0.58371 0.58319 0.58267 9.98578 9.98574 9.98571 9.98568 9.98565 25 24 23 22 21 40 41 42 43 44 9.40346 9.40394 9.40442 9.40490 9.40538 0.58216 0.58164 0.58113 0.58061 0.58010 9.98561 9.98558 9.98555 9.98551 9.98548 20 19 18 17 16 45 46 47 48 49 9.40586 9.40634 9.40682 9.40730 9.40778 9.42041 9.42093 9.42144 9.42195 9.42246 0.57959 0.57907 0.57856 0.57805 0.57754 9.98545 9.98541 9.98538 9.98535 9.98531 15 14 13 12 11 10 9 8 7 6 50 51 52 53 54 9.40825 9.40873 9.40921 9.40968 9.41016 9.42297 9.42348 9.42399 9.42450 9.42501 0.57708 0.57652 0.57601 0.57550 0.57499 9.98528 9.98525 9.98521 9.98518 9.98515 55 56 57 58 59 9.41063 9.41111 9.41158 9.41205 9.41252 9.42552 9.42603 9.42653 9.42704 9.42755 9.42805 0.57448 0.57397 0.57347 0.57296 0.57245 9.98511 9.98508 9.98505 9.98501 9.98498 5 4 3 2 1 60 9.41300 0.57195 9.98494 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. ' P.P. 75 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 15 507 ; L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P. 1* 1 2 3 4 9.41300 9.41347 9.41394 9.41441 9.41488 47 47 47 47 d.7 9.42805 9.42856 9.42906 9.42957 9.43007 51 50 51 50 50 0.57195 0.57144 0.57094 0.57043 0.56993 9.9.8494 9.98491 9.98488 9.98484 9.98481 3 3 4 3 4 60 59 58 57 56 6 7 51 5.1 60 50 5.0 5.8 5 6 7 8 9 10 11 12 13 14 9.41535 9.41582 9.41628 9.41675 9.41722 9.41768 9.41815 9.41861 9.41908 9.41954 47 46 47 47 46 47 46 47 46 47 9.43057 9.43108 9.43158 9.43208 9.43258 9.43308 9.43358 9.43408 9.43458 9.43508 51 50 50 50 50 50 50 50 50 50 0.56943 0.56892 0.56842 0.56792 0.56742 0.56692 0.56642 0.56592 0.56542 0.56492 9.98477 9.98474 9.98471 9.98467 9.98464 9.98460 9.98457 9.98453 9.98450 9.98447 3 3 4 3 4 3 4 3 3 4 55 54 53 52 51 50 49 48 47 46 8 9 10 20 30 40 50 6.8 7.7 8.5 17.0 25.5 34.0 42.5 49 6.7 7.5 8.3 16.7 25.0 33.3 41.7 48 15 16 17 18 19 9.42001 9.42047 9.42093 9.42140 9.42186 46 46 47 46 46 9.43558 9.43607 9.43657 9.43707 9.43756 49 50 50 49 50 0.56442 0.56393 0.56343 0.56293 0.56244 9.98443 9.98440 9.98436 9.98433 9.98429 3 4 3 4 3 45 44 43 42 41 6 7 8 9 10 4.9 5.7 6.5 7.4 8.2 4.8 5.6 6.4 7.2 8.0 20 21 22 23 24 9.42232 9.42278 9.42324 9.42370 9.42416 46 46 46 46 AK. 9.43806 9.43855 9.43905 9.43954 9.44004 49 50 49 50 An 0.56194 0.56145 0.56095 0.56046 0.55996 9.98426 9.98422 9.98419 9.98415 9.98412 4 3 4 3 3 40 39 38 37 36 20 30 40 50 16.3 24.5 32.7 40.8 16.0 24.0 32.0 40.0 25 26 27 28 29 9.42461 9.42507 9.42553 9.42599 9.42644 46 46 46 45 A.R 9.44053 9.44102 9.44151 9.44201 9.44250 49 49 50 49 49 0.55947 0.55898 0.55849 0.55799 0.55750 9.98409 9.98405 9.98402 9.98398 9.98395 4 3 4 3 4 35 34 33 32 31 6 7 8 47 4.7 5.5 6.3 46 4.6 5.4 6.1 30 31 32 33 34 9.42690 9.42735 9.42781 9.42826 9.42872 45 46 45 46 45 9.44299 9.44348 9.44397 9.44446 9.44495 49 49 49 49 49 0.55701 0.55652 0.55603 0.55554 0.55505 9.98391 9.98388 9.98384 9.98381 9.98377 3 4 3 4 4 30 29 28 27 26 10 20 30 40 50 7.8 15.7 23.5 31.3 39.2 7.7 15.3 23.0 30.7 38.3 35 36 37 38 39 9.42917 9.42962 9.43008 9.43053 9.43098 45 46 45 45 45 9.44544 9.44592 9.44641 9.44690 9.44738 48 49 49 48 49 0.55456 0.55408 0.55359 0.55310 0.55262 9.98373 9.98370 9.98366 9.98363 9.98359 3 4 3 4 g 25 24 23 22 21 6 7 45 4.5 5 3 44 4.4 5 1 40 41 42 43 44 9.43143 9.43188 9.43233 9.43278 9.43323 45 45 45 45 44 9.44787 9.44836 9.44884 9.44933 9.44981 49 48 49 48 48 0.55213 0.55164 0.55116 0.55067 0.55019 9.98356 9.98352 9.98349 9.98345 9.98342 4 3 4 3 4 20 19 18 17 16 8 9 10 20 30 6.0 6.8 7.5 15.0 22.5 5.9 6.6 7.3 14.7 22.0 45 46 47 48 49 9.43367 9.43412 9.43457 9.43502 9.43546 45 45 45 44 45 9.45029 9.45078 9.45126 9.45174 9.45222 49 48 48 48 J.Q 0.54971 0.54922 0.54874 0.54826 0.54778 9.98338 9.98334 9.98331 9.98327 9.98324 4 3 4 3 A 15 14 13 11 40 50 30.0 37.5 4 29.3 36.7 3 50 51 52 53 54 9.43591 9.43635 9.43680 9.43724 9.43769 44 45 44 45 44 9.45271 9.45319 9.45367 9.45415 9.45463 48 48 48 48 48 0.54729 0.54681 0.54633 0.54585 0.54537 9.98320 9.98317 9.98313 9.98309 9.98306 3 4 4 3 4 10 9 8 7 6 6 7 8 9 10 0.4 0.5 0.5 0.6 0.7 0.3 0.4 0.4 0.5 0.5 55 56 57 58 59 9.43813 9.43857 9.43901 9.43946 9.43990 44 44 45 44 11 9.45511 9.45559 9.45606 9.45654 9.45702 48 47 48 48 48 0.54489 0.54441 0.54394 0.54346 0.54298 9.98302 9.98299 9.98295 9.98291 9.98288 3 4 4 3 4 5 4 3 2 1 20 30 40 50 1.3 2.0 2.7 3.3 1.0 1.5 2.0 2.5 60 9.44034 9.45750 0.54250 9.98284 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. ' P. P. 74 508 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 16 ' L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. d. P. P 1 2 3 4 9.44034 9.44078 9.44122 9.44166 9.44210 44 44 44 44 Aft 9.45750 9.45797 9.45845 9.45892 9.45940 47 48 47 48 0.54250 0.54203 0.54155 0.54108 0.54060 9.98284 9.98281 9.98277 9.98273 9.98270 3 4 4 3 60 59 58 57 56 6 7 48 4.8 5 6 47 4.7 5 5 5 6 7 8 9 9.44253 9.44297 9.44341 9.44385 9.44428 44 44 44 43 A A 9.45987 9.46035 9.46082 9.46130 9.46177 48 47 48 47 0.54013 0.53965 0.53918 0.53870 0.53823 9.98266 9.98262 9.98259 9.98255 9.98251 4 3 4 4 3 55 54 53 52 51 8 9 10 20 30 6.4 7.2 8.0 16.0 24.0 6.3 7.1 7.8 15.7 23.5 10 11 12 13 14 15 16 17 18 19 9.44472 9.44516 9.44559 9.44602 9.44646 9.44689 9.44733 9.44776 9.44819 9.44862 44 43 43 44 43 44 43 43 43 AO 9.46224 9.46271 9.46319 9.46366 9.46413 9.46460 9.46507 9.46554 9.46601 9.46648 47 48 47 47 47 47 47 47 47 0.53776 0.53729 0.53681 0.53634 0.53587 0.53540 0.53493 0.53446 0.53399 0.53352 9.98248 9.98244 9.98240 9.98237 9.98233 9.98229 9.98226 9.98222 9.98218 9.98215 4 4 3 4 4 3 4 4 3 A 50 49 48 47 46 ~45~ 44 43 42 41 40 50 6 7 8 9 10 32.0 40.0 46 4.6 5.4 6.1 6.9 7.7 31.3 39.2 45 4.5 5.3 6.0 6.8 7.5 20 21 22 23 24 9.44905 9.44948 9.44992 9.45035 9.45077 43 44 43 42 A'l 9.46694 9.46741 9.46788 9.46835 9.46881 47 47 47 46 An 0.53306 0.53259 0.53212 0.53165 0.53119 9.98211 9.98207 9.98204 9.98200 9.98196 4 3 4 4 4 40 39 38 37 36 20 30 40 50 15.3 23.0 30.7 38.3 15.0 22.5 30.0 37.5 25 26 27 28 29 9.45120 9.45163 9.45206 9.45249 9.45292 43 43 43 43 9.46928 9.46975 9.47021 9.47068 9.47114 47 46 47 46 0.53072 0.53025 0.52979 0.52932 0.52886 9.98192 9.98189 9.98185 9.98181 9.98177 3 4 4 4 35 34 33 32 31 6 7 8 44 4.4 5.1 5.9 43 4.3 5.0 5.7 30 31 32 33 34 9.45334 9.45377 9.45419 9.45462 9.45504 43 42 43 42 Aft 9.47160 9.47207 9.47253 9.47299 9.47346 47 46 46 47 AR 0.52840 0.52793 0.52747 0.52701 0.52654 9.98174 9.98170 9.98166 9.98162 9.98159 4 4 4 3 A. 30 29 28 27 26 9 10 20 30 40 50 6.6 7.3 14.7 22.0 29.3 367 6.5 7.2 14.3 21.5 28.7 358 35 36 37 38 39 9.45547 9.45589 9.45632 9.45674 9.45716 42 43 42 42 42 9.47392 9.47438 9.47484 9.47530 9.47576 46 46 46 46 AR 0.52608 0.52562 0.52516 0.52470 0.52424 9.98155 9.98151 9.98147 9.98144 9.98140 4 4 3 4 A. 25 24 23 22 21 6 7 42 4.2 4 9 41 4.1 4 8 40 41 42 43 44 9.45758 9.45801 9.45843 9.45885 9.45927 43 42 42 42 An 9.47622 9.47668 9,47714 9.47760 9.47806 46 46 46 46 AR 0.52378 0.52332 0.52286 0.52240 0.52194 9.98136 9.98132 9.98129 9.98125 9.98121 4 3 4 4 4 20 19 18 17 16 8 9 10 20 30 5.6 6.3 7.0 14.0 21.0 5.5 6.2 6.8 13.7 20.5 45 46 47 48 49 9.45969 9.46011 9.46053 9.46095 9.46136 42 42 42 41 42 9.47852 9.47897 9.47943 9.47989 9.48035 45 46 46 46 AK. 0.52148 0.52103 0.52057 0.52011 0.51965 9.98117 9.98113 9.98110 9.98106 9.98102 4 3 4 4 4. 15 14 13 12 11 40 50 28.0 35.0 4 27.3 34.2 3 50 51 52 53 54 9.46178 9.46220 9.46262 9.46303 9.46345 42 42 41 42 41 9.48080 9.48126 9.48171 9.48217 9.48262 46 45 46 45 4A 0.51920 0.51874 0.51829 0.51783 0.51738 9.98098 9.98094 9.98090 9.98087 9.98083 4 4 3 4 4 10 9 8 7 6 6 7 8 9 10 0.4 0.5 0.5 0.6 0.7 0.3 0.4 0.4 0.5 0.5 55 56 57 58 59 9.46386 9.46428 9.46469 9.46511 9.46552 42 41 42 41 An 9.48307 8.48353 9.48398 9.48443 9.48489 46 45 45 46 xc 0.51693 0.51647 0.51602 0.51557 0.51511 9.98079 9.98075 9.98071 9.98067 9.98063 4 4 4 4 g 5 4 3 2 1 20 30 40 50 1.3 2.0 2.7 3.3 1.0 1.5 2.0 2.5 60 9.46594 9.48534 0.51466 9.98060 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. 1 P.P. 73 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 17 509 L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P.P. 9.46594 9.48534 0.51466 9.98060 60 1 9.46635 41 9.48579 45 0.51421 9.98056 4 59 2 9.46676 41 9.48624 45 0.51376 9.98052 4 58 3 9.46717 41 9.48669 45 0.51331 9.98048 4 57 40 44 4 9.46758 41 9.48714 45 Ati 0.51286 9.98044 4 56 6 7 4.5 5 3 4.4 5 1 5 9.46800 42 9.48759 4O 0.51241 "9798040" 4 55 8 6^0 5.9 6 9.46841 41 9.48804 45 0.51196 9.98036 4 54 9 6.8 6.6 7 9.46882 41 9.48849 45 0.51151 9.98032 4 53 10 7.5 7.3 8 9.46923 41 9.48894 45 0.51106 9.98029 3 52 20 15.0 14.7 9 9.46964 41 41 9.48939 45 45 0.51061 9.98025 4 A 51 30 22.5 22.0 10 9.47005 9.48984 0.51016 9.98021 50 40 30.0 29.3 11 9.47045 40 9.49029 45 0.50971 9.98017 4 49 50 37.5 36.7 12 9.47086 41 9.49073 44 0.50927 9.98013 4 48 13 9.47127 41 9.49118 45 0.50882 9.98009 4 47 14 9.47168 41 41 9.49163 45 44 0.50837 9.98005 4 4 46 43 15 9.47209 9.49207 0.50793 9.98001 45 6 4.3 16 9.47249 40 9,49252 45 0.50748 9.97997 4 44 7 5.0 17 9.47290 41 9.49296 44 0.50704 9.97993 4 43 8 5.7 18 9.47330 40 9.49341 45 0.50659 9.97989 4 42 9 6.5 19 9.47371 41 40 9.49385 44 45 0.50615 9.97986 3 A 41 10 7.2 20 1U7411 9.49430 0.50570 9.97982 40 20 14.3 21 9.47452 41 9.49474 44 0.50526 9.97978 4 39 30 21.5 22 9.47492 40 9.49519 45 0.50481 9.97974 4 38 40 28.7 23 9.47533 41 9.49563 44 0.50437 9.97970 4 37 50 35.8 24 9.47573 40 9.49607 44 0.50393 9.97966 4 36 40 45 4 25 9.47613 9.49652 0.50348 9.97962 35 26 9.47654 41 9.49696 44 0.50304 9.97958 4 34 42 41 27 9.47694 40 9.49740 44 0.50260 9.97954 4 33 6 4.2 4.1 28 9.47734 40 9.49784 44 0.50216 9.97950 4 32 7 4.9 4.8 29 9.47774 40 40 9.49828 44 44 0.50172 9.97946 4 A 31 8 5.6 5.5 30 31 32 33 34 9.47814 9.47854 9.47894 9.47934 9.47974 40 40 40 40 40 9.49872 9.49916 9.49960 9.50004 9.50048 44 44 44 44 44 0.50128 0.50084 0.50040 0.49996 0.49952 9.97942 9.97938 9.97934 9.97930 9.97926 4 4 4 4 A 30 29 28 27 26 9 10 20 30 40 50 6.3 7.0 14.0 21.0 28.0 35.0 6.2 6.8 13.7 20.5 27.3 34.2 35 9.48014 9.50092 0.49908 9.97922 25 36 9.48054 40 9.50136 44 0.49864 9.97918 4 24 37 9.48094 40 9.50180 44 0.49820 9.97914 4 23 38 9.48133 39 9.50223 43 0.49777 9.97910 4 22 4U 39 39 9.48173 40 An 9.50267 44 44 0.49733 9.97906 4 A 21 6 4.0 4.7 3.9 4 e 40 9.48213 *i\) 9.50311 0.49689 9.97902 20 8 5i3 5^2 41 9.48252 39 9.50355 44 0.49645 9.97898 4 19 9 6.0 5.9 42 9.48292 40 9.50398 43 0.49602 9.97894 4 18 10 6.7 6.5 43 9.48332 40 9.50442 44 0.49558 9.97890 4 17 20 13.3 13.0 44 9.48371 39 40 9.50485 43 44 0.49515 9.97886 4 A 16 30 20.0 19.5 ~45~ 9.48411 9.50529 0.49471 9.97882 15 40 26.7 26.0 46 9.48450 39 9.50572 43 0.49428 9.97878 4 14 50 33.3 32.5 47 9.48490 40 9.50616 44 0.49384 9.97874 4 13 48 9.48529 39 9.50659 43 0.49341 9.97870 4 12 49 9.48568 39 39 9.50703 44 43 0.49297 9.97866 4 5 11 543 ^oT 9.48607 9.50746 0.49254 9.97861 10 6 0.5 0.4 0.3 51 9.48647 40 9.50789 43 0.49211 9.97857 4 9 7 0.6 0.5 0.4 52 9.48686 39 9.50833 44 0.49167 9.97853 4 8 8 0.7 0.5 0.4 53 9.48725 39 9.50876 43 0.49124 9.97849 4 7 9 0.8 0.6 0.5 54 9.48764 39 9.50919 43 0.49081 9.97845 4 6 10 0.8 0.7 0.5 ^35~ 56 57 58 9.48803" 9.48842 9.48881 9.48920 39 39 39 39 9.50962 9.51005 9.51048 9.51092 43 43 43 44 0.49038 0.48995 0.48952 0.48908 9.97841 9.97837 9.97833 9.97829 4 4 4 4 5 4 3 2 20 30 40 50 1.7 1.3 1.0 2.5 2.0 1.5 3.3 2.7 2.0 i.2 3.3 2.5 59 9.48959 39 39 9.51135 43 43 0.48865 9.97825 4 4 1 60 9.48998 9.51178 0.48822 9.97821 "IT L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. "~dT ' P.P. 72 510 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 18 1 2 3 4 T 6 8 9 10 11 12 13 14 L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P.P. 9.48998 9.49037 9.49076 9.49115 9.49153 9.49192 9.49231 9.49269 9.49308 9.49347 9.49385 9.49424 9.49462 9.49500 9.49539 39 39 39 38 39 39 38 39 39 38 39 38 38 39 38 38 39 38 38 38 38 38 38 38 38 38 38 38 38 38 37 38 38 37 38 38 37 38 37 37 38 37 37 38 37 37 37 37 37 38 37 37 37 36 37 37 37 37 36 37 9.51178 9.51221 9.51264 9.51306 9.51349 9.51392 9.51435 9.51478 9.51520 9.51563 9.51606 9.51648 9.51691 9.51734 9.51776 43 43 42 43 43 43 43 42 43 43 42 43 43 42 43 42 42 43 42 43 42 42 42 43 42 42 42 42 42 42 42 42 42 42 41 42 42 42 42 41 42 41 42 42 41 42 41 41 42 41 42 41 41 41 42 41 41 41 41 41 0.48822 0.48779 0.48736 0.48694 0.48651 ~04860 0.48565 0.48522 0.48480 0.48437 0.48394 0.48352 0.48309 0.48266 0.48224 9.97821 9.97817 9.97812 9.97808 9.97804 9.97800" 9.97796 9.97792 9.97788 9.97784 9.97779 9.97775 9.97771 9.97767 9.97763 4 5 4 4 4 4 4 4 4 5 4 4 4 4 4 5 4 4 4 4 4 5 4 4 4 4 5 4 4 4 5 4 4 4 5 4 4 4 5 4 4 4 5 4 4 4 5 4 4 5 4 4 5 4 4 5 4 4 5 4 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 6 7 8 9 10 20 30 40 50 1 2 3 4 5 6 7 8 * 9 , 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 43 4.3 5.0 5.7 6.5 7.2 14.3 21.5 28.7 35.8 4 6 4 7 4 8 5 9 6 6 13 20 27 34 39 3.9 4.6 5.2 5.9 6.5 13.0 19.5 26.0 32.5 37 3.7 4.3 4.9 5.6 6.2 12.3 18.5 24.7 30.8 0.5 0.6 0.7 0.8 0.8 1.7 2.5 3.3 4.2 42 4.2 4.9 5.6 6.3 7.0 14.0 21.0 28.0 35.0 1 1 8 5 2 8 7. 5 3 2 38 3.8 4.4 5.1 5.7 6.3 12.7 19.0 25.3 31.7 36 3.6 4.2 4.8 5.4 6.0 12.0 18.0 24.0 30.0 4 0.4 0.5 0.5 0.6 0.7 1.3 2.0 2.7 3.3 15 16 17 18 19 9.49577 9.49615 9.49654 9.49692 9.49730 9.51819 9.51861 9.51903 9.51946 9.51988 0.48181 0.48139 0.48097 0.48054 0.48012 9.97759 9.97754 9.97750 9.97746 9.97742 45 44 43 42 41 20 21 22 23 24 25 26 27 28 29 9.49768 9.49806 9.49844 9.49882 9.49920 9.49958 9.49996 9.50034 9.50072 9.50110 9.52031 9.52073 9.52115 9.52157 9.52200 "9^52242 9.52284 9.52326 9.52368 9.52410 0.47969 0.47927 0.47885 0.47843 0.47800 0.47758 0.47716 0.47674 0.47632 0.47590 9.97738 9.97734 9.97729 9.97725 9.97721 " 9.97717 9.97713 9.97708 9.97704 9.97700 40 39 38 37 36 35 34 33 32 31 ^r 29 28 27 26 30 31 32 33 34 9.50148 9.50185 9.50223 9.50261 9.50298 9.52452 9.52494 9.52536 9.52578 9.52620 0.47548 0.47506 0.47464 0.47422 0.47380 9.97696 9.97691 9.97687 9.97683 9.97679 35 36 37 38 39 9.50336 9.50374 9.50411 9.50449 9.50486 9.52661 9.52703 9.52745 9.52787 9.52829 0.47339 0.47297 0.47255 0.47213 0.47171 9.97674 9.97670 9.97666 9.97662 9.97657 25 24 23 22 21 40 41 42 43 44 45 46 47 48 49 9.50523 9.50561 9-50598 9.50635 9.50673 9.50710 9.50747 9.50784 9.50821 9.50858 9.52870 9.52912 9.52953 9.52995 9.53037 0.47130 0.47088 0.47047 0.47005 0.46963 9.97653 9.97649 9.97645 9.97640 9.97636 20 19 18 17 16 9.53078 9.53120 9.53161 9.53202 9.53244 9.53285 9.53327 9.53368 9.53409 9.53450 0.46922 0.46880 0.46839 0.46798 0.46756 9.97632 9.97628 9.97623 9.97619 9.97615 15 14 13 12 11 50 51 52 53 54 9.50896 9.50933 9.50970 9.51007 9.51043 0.46715 0.46673 0.46632 0.46591 0.46550 0.46508 0.46467 0.46426 0.46385 0.46344 9.97610 9.97606 9.97602 9.97597 9.97593 10 9 8 7 6 55 56 57 58 59 9.51080 9.51117 9.51154 9.51191 9.51227 9.53492 9.53533 9.53574 9.53615 9.53656 9.97589 9.97584 9.97580 9.97576 9.97571 5 4 3 2 1 60 9.51264 9.53697 L. Cotg. 0.46303 9.97567 L. Cos. d. d. o. L.Tang. L. Sin. d. ' P.P. 71 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 19 511 / L. Sin. d. L.Tang. d. c. |L. Cotg. L. Cos. d. 60 59 58 57 56 6 7 8 9 10 20 30 40 50 >: ; ii !i ? 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 P.P. 1 2 3 4 9.51264 9.51301 9.51338 9.51374 9.51411 37 37 36 37 36 37 36 37 36 36 37 36 36 36 37 36 36 36 36 36 36 36 36 36 36 36 35 36 36 36 35 36 35 36 35 36 35 36 35 36 35 35 36 35 35 35 35 35 35 35 36 34 35 35 35 35 35 35 34 35 9.53697 9.53738 9.53779 9.53820 9.53861 41 41 41 41 41 41 41 41 40 41 41 40 41 41 40 41 40 41 40 41 40 41 40 40 41 40 40 41 40 40 40 40 40 40 40 40 40 40 40 40 40 40 39 40 40 40 39 40 40 39 40 39 40 39 40 39 40 39 39 40 0.46303 0.46262 0.46221 0.46180 0.46139 9.97567 9.97563 9.97558 9.97554 9.97550 9.97545 9.97541 9.97536 9.97532 9.97528 9.97523 9.97519 9.97515 9 97510 9.97506 4 5 4 4 5 4 5 4 4 5 4 4 5 4 5 4 5 4 4 5 4 5 4 5 4 4 5 4 5 4 5 4 \ 5 4 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 41 4.1 4.8 5.5 6.2 6.8 13.7 20.5 27.3 34.2 3 6 3 7 4 8 5 9 5 LO 6 20 13 50 19 tO 26 JO 32 37 3.7 4.3 4.9 5.6 6.2 12.3 18.5 24.7 30.8 35 3.5 4.1 4.7 5.3 5.8 11.7 17.5 23.3 29.2 5 0.5 0.6 0.7 0.8 0.8 11.7 2.5 3.3 4.2 40 4.0 4.7 5.3 6.0 6.7 13.3 20.0 26.7 33.3 9 .9 .6 2 !9 .5 .0 .5 .0 .5 36 3.6 4.2 4.8 5.4 6.0 12.0 18.0 24.0 30.0 34 3.4 4.0 4.5 5.1 5.7 11.3 17.0 22.7 28.3 4 0.4 0.5 0.5 0.6 0.7 1.3 2.0 2.7 3.3 5 6 7 8 9 10 11 12 13 14 9.51447 9.51484 9.51520 9.51557 9.51593 9.51629 9.51666 9.51702 9.51738 9.51774 9.53902 9.53943 9.53984 9.54025 9.54065 9.54106 9.54147 9.54187 9.54228 9.54269 0.46098 0.46057 0.46016 0.45975 0.45935 0.45894 0.45853 0.45813 0.45772 0.45731 55 54 53 52 51 50 49 48 47 46 ~45~ 44 43 42 41 To~ 39 38 37 36 35 34 33 32 31 15 16 17 18 19 20 21 22 23 24 9.51811 9.51847 9.51883 9.51919 9.51955 9.51991 9.52027 9.52063 9.52099 9.52135 9.54309 9.54350 9.54390 9.54431 9.54471 9.54512 9.54552 9.54593 9.54633 9.54673 0.45691 0.45650 0.45610 0.45569 0.45529 0.45488 0.45448 0.45407 0.45367 0.45327 9.97501 9.97497 9.97492 9.97488 9.97484 9.97479 9.97475 9.97470 9.97466 9.97461 25 26 27 28 29 9.52171 9.52207 9.52242 9.52278 9.52314 9.54714 9.54754 9.54794 9.54835 9.54875 0.45286 0.45246 0.45206 0.45165 0.45125 9.97457 9.97453 9.97448 9.97444 9.97439 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 9.52350 9.52385 9.52421 9.52456 9.52492 9.54915 9.54955 9.54995 9.55035 9.55075 0.45085 0.45045 0.45005 0.44965 0.44925 9.97435 9.97430 9.97426 9.97421 9.97417 9.97412 9.97408 9.97403 9.97399 9.97394 9.97390 9.97385 9.97381 9.97376 9.97372 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 9.52527 9.52563 9.52598 9.52634 9.52669 9.55115 9.55155 9.55195 955235 9.55275 0.44885 0.44845 0.44805 0.44765 0.44725 9.52705 9.52740 9.52775 9.52811 9.52846 9.55315 9.55355 9.55395 9.55434 9.55474 0.44685 0.44645 0.44605 0.44566 0.44526 45 46 47 48 49 50 51 52 53 54 9.52881 9.52916 9.52951 9.52986 9.53021 9.55514 9.55554 9.55593 9.55633 9.55673 0.44486 0.44446 0.44407 0.44367 0.44327 9.97367 9.97363 9.97358 9.97353 9.97349 15 14 13 12 11 9.53056 9.53092 9.53126 9.53161 9.53196 9.53231 9.53266 9.53301 9.53336 9.53370 9.55712 9.55752 9.55791 9.55831 9.55870 0.44288 0.44248 0.44209 0.44169 0.44130 9.97344 9.97340 9.97335 9.97331 9.97326 10 9 8 7 6 55 56 57 58 59 9.55910 9.55949 9.55989 9.56028 9.56067 0.44090 0.44051 0.44011 0.43972 0.43933 9.97322 9.97317 9.97312 9.97308 9.97303 5 4 3 2 1 60 9.53405 9.56107 0.43893 9.97299 L. Cos. d. L. Cotg. <1. c. L.Tang. L. Sin. d. ' P.P. 70 512 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 20 ' L. Sin. d. L.Tang d.c. L. Cotg L. Cos. d. P.I 1 2 3 4 9.53405 9.53440 9.53475 9.53509 9.53544 35 35 34 35 34 9.56107 9.56146 9.56185 9.56224 9.56264 39 39 39 40 39 0.43893 0.43854 0.43815 0.43776 0.43736 9.97299 9.97294 9.97289 9.97285 9.97280 5 5 4 5 60 59 58 57 56 6 y 40 4.0 A 17 39 3.9 A f( 5 6 7 8 9 9.53578 9.53613 9.53647 9.53682 9.53716 35 34 35 34 35 9.56303 9.56342 9.56381 9.56420 9.56459 39 39 39 39 qq 0.43697 0.43658 0.43619 0.43580 0.43541 9.97276 9.97271 9.97266 9.97262 9.97257 5 5 4 5 55 54 53 52 51 8 9 10 20 30 5.3 6.0 6.7 13.3 ?oo 5.2 5.9 6.5 13.0 19.5 10 11 12 13 14 9.53751 9.53785 9.53819 9.53854 9.53888 34 34 35 34 34 9.56498 9.56537 9.56576 9.56615 9.56654 39 39 39 39 39 0.43502 0.43463 0.43424 0.43385 0.43346 9.97252 9.97248 9.97243 9.97238 9.97234 4 5 5 4 50 49 48 47 46 40 50 26.7 33.3 38 26.0 32.5 37 15 16 17 18 19 9.53922 9.53957 9.53991 9.54025 9.54059 35 34 34 34 34 9.56693 9.56732 9.56771 9.56810 9.56849 39 39 39 39 qo 0.43307 0.43268 0.43229 0.43190 0.43151 9.97229 9.97224 9.97220 9.97215 9.97210 5 4 5 5 45 44 43 42 41 6 7 8 9 10 3.8 4.4 5.1 5.7 6.3 3.7 4.3 4.9 5.6 6.2 20 21 22 23 24 9.54093 954127 9.54161 9.54195 9.54229 34 34 34 34 34 9.56887 9.56926 9.56965 9.57004 9.57042 39 39 39 38 qq 0.43113 0.43074 0.43035 0.42996 0.42958 9.97206 9.97201 9.97196 9.97192 9.97187 5 5 4 5 40 39 38 37 36 20 30 40 50 12.7 19.0 25.3 31.7 12.3 18.5 24.7 30.8 25 26 27 28 29 9.54263 9.54297 9.54331 9.54365 9.54399 34 34 34 34 34 9.57081 9.57120 9.57158 9.57197 9.57235 39 38 39 38 qq 0.42919 0.42880 0.42842 0.42803 0.42765 9.97182 9.97178 9.97173 9.97168 9.97163 4 5 5 5 35 34 33 32 31 3 6 3 7 4 8 4 .5 .1 .7 30 31 32 33 34 9.54433 9.54466 9.54500 9.54534 9.54567 33 34 34 33 CM 9.57274 9.57312 9.57351 9.57389 9.57428 38 39 38 39 qo 0.42726 0.42688 0.42649 0.42611 0.42572 9.97159 9.97154 9.97149 9.97145 9.97140 5 5 4 5 30 29 28 27 26 ] i 1 9 5 LO 5 JO 11 50 17 10 23 >0 29 .3 .8 .7 .5 .3 2 35 36 37 38 39 9.54601 9.54635 9.54668 9.54702 9.54735 34 33 34 33 34 9.57466 9.57504 9.57543 9.57581 9.57619 38 39 38 38 qq 0.42534 0.42496 0.42457 0.42419 0.42381 9.97135 9.97130 9.97126 9.9712] 9.97116 5 4 5 5 25 24 23 22 21 6 34 3.4 A ft 33 3.3 q Q 40 41 42 43 44 9.54769 9.54802 9.54836 9.54869 9.54903 33 34 33 34 qq 9.57658 9.57696 9.57734 9.57772 9.57810 38 38 38 38 qq 0.42342 0.42304 0.42266 0.42228 0.42190 9.97111 9.97107 9.97102 9.97097 9.97092 4 5 5 5 20 19 18 17 16 8 9 10 20 30 4.5 5.1 5.7 11.3 170 4.4 5.0 5.5 11.0 16.5 45 46 47 48 49 9.54936 9.54969 9.55003 9.55036 9.55069 33 34 33 33 qq 9.57849 9.57887 9.57925 9.57963 9.58001 38 38 38 38 0.42151 0.42113 0.42075 0.42037 0.41999 9.97087 9.97083 9.97078 9.97073 9.97068 4 5 5 5 15 14 13 12 11 40 50 22.7 28.3 5 22.0 27.5 4 50 51 52 53 54 9.55102 9.55136 9.55169 9.55202 9.55235 34 33 33 33 33 9.58039 9.58077 9.58115 9.58153 9.58191 38 38 38 0.41961 0.41923 0.41885 0.41847 0.41809 9.97063 9.97059 9.97054 9.97049 9.97044 4 5 5 5 10 9 8 7 6 6 7 8 9 10 0.5 0.6 0.7 0.8 0.8 0.4 0.5 0.5 0.6 0.7 55 56 57 58 59 9.55268 9.55301 9.55334 9.55367 9.55400 33 33 33 33 33 9.58229 9.58267 9.58304 9.58342 9.58380 38 37 38 38 38 0.41771 0.41733 0.41696 0.41658 0.41620 9.97039 9.97035 9.97030 9.97025 9.97020 4 5 5 5 5 4 3 2 1 20 30 40 50 1.7 2.5 3.3 4.2 1.3 2.0 2.7 3.3 60 9.55433 9.58418 0.41582 9.97015 .. L. Cos. d. L. Cotg. d.c. ,.Tang. L. Sin. d. ' P. P. LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 21 513 ' L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. d. P. P 1 2 3 4 9.55433 9.55466 9.55499 9.55532 9.55564 33 33 33 32 qo 9.58418 9.58455 9.58493 9.58531 9.58569 37 38 38 38 37 0.41582 0.41545 0.41507 0.41469 0.41431 9.97015 9.97010 9.97005 9.97001 9.96996 5 5 4 5 60 59 58 57 56 6 7 38 3.8 4 4 37 3.7 4 3 5 6 7 8 9 10 11 12 13 14 9.55597 9.55630 9.55663 9.55695 9.55728 9.55761 9.55793 9.55826 9.55858 9.55891 33 33 32 33 33 32 33 32 33 32 9.58606 9.58644 9.58681 9.58719 9.58757 9.58794 9.58832 9.58869 9.58907 9.58944 38 37 38 38 37 38 37 38 37 37 0.41394 0.41356 0.41319 0.41281 0.41243 0.41206 0.41168 0.41131 0.41093 0.41056 9.96991 9.96986 9.96981 9.96976 9.96971 9.96966 9.96962 9.96957 9.96952 9.96947 5 5 5 5 5 4 5 5 5 5 55 54 53 52 51 50 49 48 47 46 8 9 10 20 30 40 50 5.1 5.7 6.3 12.7 19.0 25.3 31.7 36 4.9 5.6 6.2 12.3 18.5 24.7 30.8 33 15 16 17 18 19 9.55923 9.55956 9.55988 9.56021 9.56053 33 32 33 32 qo 9.58981 9.59019 9.59056 9.59094 9.59131 38 37 38 37 q7 0.41019 0.40981 0.40944 0.40906 0.40869 9.96942 9.96937 9.96932 9.96927 9.96922 5 5 5 5 45 44 43 42 41 6 7 . 8 9 10 3.6 4.2 4.8 5.4 6.0 3.3 3.9 4.4 5.0 5.5 20 21 22 23 24 25 26 27 28 29 9.56085 9.56 118 9.56150 9.56182 9.56215 "9^56247 9.56279 9.56311 9.56343 9.56375 33 32 32 33 32 32 32 32 32 qq 9.59168 9.59205 9.59243 9.59280 9.59317 9.59354 9.59391 9.59429 9.59466 9.59503 37 38 37 37 37 37 38 37 37 07 0.40832 0.40795 0.40757 0.40720 0.40683 0.40646 0.40609 0.40571 0.40534 0.40497 9.96917 9.96912 9.96907 9.96903 9.96898 9.96893 9.96888 9.96883 9.96878 9.96873 5 5 4 5 5 5 5 5 5 40 39 38 37 36 35 34 33 32 31 20 30 40 50 12.0 18.0 24.0 30.0 3 6 3 7 3 8 4 11.0 16.5 22.0 27.5 2 .2 .7 .3 30 31 32 33 34 9.56408 9.56440 9.56472 9.56504 9.56536 32 32 32 32 32 9.59540 9.59577 9.59614 9.59651 9.59688 37 37 37 37 37 0.40460 0.40423 0.40386 0.40349 0.40312 9.96868 9.96863 9.96858 9.96853 9.96848 5 5 5 5 5 30 29 28 27 26 ] < t 9 4 .0 5 >0 10 10 16 M) 21 >0 26 .8 .3 .7 .0 .3 7 35 36 37 38 39 9.56568 9.56599 9.56631 9.56663 9.56695 31 32 32 32 32 9.59725 9.59762 9.59799 9.59835 9.59872 37 37 36 37 37 0.40275 0.40238 0.40201 0.40165 0.40128 9.96843 9.96838 9.96833 9.96828 9.96823 5 5 5 5 25 24 23 22 21 6 31 3.1 6 0.6 n 7 40 41 42 43 44 9.56727 9.56759 9.56790 9.56822 9.56854 32 31 32 32 32 9.59909 9.59946 9.59983 9.60019 9.60056 ,37 37 36 37 37 0.40091 0.40054 0.40017 0.39981 0.39944 9.96818 9.96813 9.96808 9.96803 9.96798 5 5 5 5 20 19 18 17 16 8 9 10 20 30 4.1 4.7 5.2 10.3 155 0.8 0.9 1.0 2.0 3.0 45 46 47 48 49 9.56886 9.56917 9.56949 9.56980 9.57012 31 32 31 32 32 9.60093 9.60130 9.60166 9.60203 9.60240 37 36 37 37 36 0.39907 0.39870 0.39834 0.39797 0.39760 9.96793 9.96788 9.96783 9.96778 9.96772 5 5 5 6 K 15 14 13 12. 11 40 50 20.7 25.8 5 4.0 5.0 4 50 51 52 53 54 9.57044 9.57075 9.57107 9.57138 9.57169 31 32 31 31 32 9.60276 9.60313 9.60349 9.60386 9.60422 37 36 37 36 37 0.39724 0.39687 0.39651 0.39614 0.39578 9.96767 9.96762 9.96757 9.96752 9.96747 5 5 5 5 10 9 8 7 6 6 7 8 9 10 0.5 0.6 0.7 0.8 0.8 0.4 0.5 0.5 0.6 0.7 55 56 57 58 59 9.57201 9.57232 9.57264 9.57295 9.57326 31 32 31 31 32 9.60459 9.60495 9.60532 9.60568 9.60605 36 37 36 37 q** 0.39541 0.39505 0.39468 0.39432 0.39395 9.96742 9.96737 9.96732 9.96727 9.96722 5 5 5 5 5 4 3 1 20 30 40 50 1.7 2.5 3.8 4.2 1.3 2.0 2.7 3.3 60 9.57358 9.60641 0.39359 9.96717 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. ' P.P. 68 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 22 t L. Sin. d. L.Tang. d. e. L. Cotg. L. Cos. d. P.P. 1 2 3 4 9.57358 9.57389 9.57420 9.57451 9.57482 31 31 31 31 qo 9.60641 9.60677 9.6U714 9.60750 9.60786 36 37 36 36 37 0.39359 0.39323 0.39286 0.39250 0.39214 9.96717 9.96711 9.96706 9.96701 9.96696 6 5 5 5 60 59 58 57 56 6 37 3.7 4 3 36 3.6 4 2 5 6 7 8 9 10 11 12 13 14 9.57514 9.57545 9.57576 9.57607 9.57638 9.57669 9.57700 9.57731 9.57762 9.57793 31 31 31 31 31 31 31 31 31 9.60823 9.60859 9.60895 9.60931 9.60967 9.61004 9.61040 9.61076 9.61112 9.61148 36 36 36 36 37 36 36 36 36 36 0.39177 0.39141 0.39105 0.39069 0.39033 0.38996 0.38960 0.38924 0.38888 0.38852 9.96691 9.96686 9.96681 9.96676 9.96670 9.96665 9.96660 9.96655 9.96650 9.96645 5 5 5 6 5 5 5 5 5 55 54 53 52 51 50 49 48 47 46 8 9 10 20 30 40 50 4.9 5.6 6.2 12.3 18.5 24.7 30.8 3 4.8 5.4 6.0 12.0 18.0 24.0 30.0 5 15 16 17 18 19 9.57824 9.57855 9.57885 9.57916 9.57947 31 30 31 31 q-l 9.61184 9.61220 9.61256 9.61292 9.61328 36 '. 36 36 36 36 0.38816 0.38780 0.38744 0.38708 0.38672 9.96640 9.96634 9.96629 9.96624 9.96619 6 5 5 5 45 44 43 42 41 ] 6 3 7 4 8 4 9 5 .0 5 .5 .1 .7 .3 .8 20 21 22 23 24 9.57978 9.58008 9.58039 9.58070 9.58101 30 31 31 31 qrv 9.61364 9.61400 9.61436 9.61472 9.61508 36 36 36 36 36 0.38636 0.38600 0.38564 0.38528 0.38492 9.96614 9.96608 9.96603 9.96598 9.96593 6 5 5 5 5 40 39 38 37 36 1 i i JO 11 50 17 10 23 >0 29 !5 .3 2 25 26 27 28 29 9.58131 9.58162 9.58192 9.58223 9.58253 31 30 31 30* q-i 9.61544 9.61579 9.61615 9.61651 9.61687 35 36 36 36 35 0.38456 0.38421 0.38385 0.38349 0.38313 9.96588 9.96582 9.96577 9.96572 9.96567 6 5 5 5 5 35 34 33 32 31 6 7 8 32 3.2 3.7 4.3 31 3.1 3.6 4.1 30 31 32 33 34 9.58284 9.58314 9.58345 9.58375 9.58406 30 31 30 31 30 9.61722 9.61758 9.61794 9.61830 9.61865 36 36 36 35 36 0.38278 0.38242 0.38206 0.38170 0.38135 9.96562 9.96556 9.96551 9.96546 9.96541 6 5 5 5 g 30 29 28 27 26 10 20 30 40 50 5.3 10.7 16.0 21.3 26.7 5.2 10.3 15.5 20.7 25.8 35 36 37 38 39 9.58436 9.58467 9.58497 9.58527 9.58557 31 30 30 30 q-i 9.61901 9.61936 9.61972 9.62008 9.62043 35 36 36 35 36 0.38099 0.38064 0.38028 0.37992 0.37957 9.96535 9.96530 9.96525 9.96520 9.96514 5 5 5 6 5 25 24 23 22 21 6 7 30 3.0 3 5 29 2.9 3 4 40 41 42 43 44 45 46 47 48 49 9.58588 9.58618 9.58648 9.58678 9.58709 9.58739 9.58769 9.58799 9.58829 9.58859 30 30 30 31 30 30 30 30 30' 30 9.62079 9.62114 9.62150 9.62185 9.62221 9.62256 9.62292 9.62327 9.62362 9.62398 35 36 35 36 35 36 35 35 36 35 0.37921 0.37886 0.37850 0.37815 0.37779 0.37744 0.37708 0.37673 0.37638 0.37602 9.96509 9.96504 9.96498 9.96493 9.96488 9.96483 9.96477 9.96472 9.96467 9.96461 5 6 5 5 5 6 5 5 6 5 20 ]9 18 17 16 15 14 13 12 11 8 9 10 20 30 40 50 4.0 4.5 5.0 10.0 15.0 20.0 25.0 6 3.9 4.4 4.8 9.7 14.5 19.3 24.2 5 50 51 52 53 54 9.58889 9.58919 9.58949 9.58979 9.59009 30 30 30 30 30 9.62433 9.62468 9.62504 9.62539 9.62574 35 36 35 35 qp: 0.37567 0.37532 0.37496 0.37461 0.37426 9.96456 9.96451 9.96445 9.96440 9.96435 5 6 5 5 g 10 9 8 7 6 6 7 8 9 10 1 0.6 0.7 0.8 0.9 1.0 0.5 0.6 0.7 0.8 0.8 55 56 57 58 59 9.59039 9.59069 9.59098 9.59128 9.59158 30 29 30 30 Of\ 9.62609 9.62645 9.62680 9.62715 9.62750 36 35 35 35 qfc 0.37391 0.37355 0.37320 0.37285 0.37250 9.96429 9.96424 9.96419 9.96413 9.96408 5 5 6 5 5 5 4 3 2 1 20 30 40 50 2.0 3.0 4.0 5.0 1.7 2.5 3.3 4.2 60 9.59188 9.62785 0.37215 9.96403 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. ' P. P 67 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 23 515 t L. Sin.'. d. L.Tang. d.c. L.Cotg. L. Cos. d. P. P 1 2 3 4 ~5~ 6 7 8 9 ItT 11 12 13 14 9.59188 9.59218 9.59247 9.59277 9.59307 9.59336 9.59366 9.59396 9.59425 9.59455 9.59484 9.59514, 9.59543 9.59573 9.59602 30 29 30 30 29 30 30 29 30 29 30 29 30 29 30 9.62785 9.62820 9.62855 9.62890 9.62926 9.62961 9.62996 9.63031 9.63066 9.63101 9.63135 9.63170 9.63205 9.63240 9.63275 35 35 35 36 35 35 35 35 35 34 35 35 35 35 35 0.37215 0.37180 0.37145 0.37110 0.37074 0.37039 0.37004 0.36969 0.36934 0.36899 0.36865 0.36830 0.36795 0.36760 0.36725 9.96403 9.96397 9.96392 9.96387 9.96381 9.96376 9.96370 9.96365 9.96360 9.96354 9.96349 9.96343 9.96338 9.96333 9.96327 6 5 5 6 5 6 5 5 6 5 6 5 5 6 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 6 7 8 9 10 20 30 40 50 36 3.6 4.2 4.8 5.4 6.0 L2.0 18.0 24.0 30.0 3 35 3.5 4.1 4.7 5.3 5.8 11.7 17.5 23.3 29.2 4 15 '16 17 18 19 9.59632 9.59661 9.59690 9.59720 9.59749 29 29 30 29 9Q 9.63310 9.63345 9.63379 9.63414 9.63449 35 34 35 35 OF; 0.36690 0.36655 0.36621 0.36586 0.36551 9.96322 9.96316 9.96311 9.96305 9.96300 6 5 6 5 45 44 43 42 41 e I < 1C > 3 4 \ 4 I 5 I 5 .4 .0 .5 .1 .7 20 21 22 23 24 9.59778 9.59808 9.59837 9.59866 9.59895 30 29 29 29 29 9.63484 9.63519 9.63553 9.63588 9.63623 35 34 35 35 34 0.36-516 0.36481 0.36447 0.36412 0.36377 9.96294 9.96289 9.96284 9.96278 9.96273. 5 5 6 5 g 40 39 38 37 36 ; 2( 3( 4( 5C > 11 > 17 22 28 .3 .0 .7 .3 25 26 27 28 29 9.59924 9.59954 9.59983 9.60012 9.60041 30 29 29 29 29 9.63657 9.63692 9.63726 9.63761 9.63796 35 34 35 35 QJ. 0.36343 0.36308 0.36274 0.36239 0.36204 9.96267 9.96262 9.96256 9.96251 9.96245 5 6 5 6 35 34- 33 32 31 6 7 8 30 3.0 3.5 4.0 29 2.9 3.4 3.9 30 31 32 33 34 ~35~ 36 37 38 39 9.60070 9.60099 9.60128 9.60157 9.60186 1M5021JT 9.60244 9.60273 9.60302 9.60331 29 29 29 29 29 29 29 29' 29 28 9.63830 9.63865 9.63899 9.63934 9.63968 9.64003 9.64037 9.64072 9.64106 9.64140 35 34 35 34 35 34 35 34 34 or 0.36170 0.36135 0.36101 0-36066 0.36032 0.35997 0.35963 0.35928 0.35894 0.35860 9.96240 9.96234 9.96229 9.96223 9.96218 9.96212 9.96207 9.96201 9.96196 9.96190 6 5 6 5 6 5 6 5 6 30 29 28 27 26 25 24 23 22 21 9 10 20 30 40 50 ! 6 j 4.5 5.0 LO.O L5.0 20.0 25.0 2 2 rq 4.4 4.8 9.7 14.5 ]9.3 24.2 8 .8 Q 40 41 42 43 44 9.60359 9.60388 9.60417 9.60446 9.60474 29 29 29 28 29 9.64175 9.64209 9.64243 9.64278 9.64312 34 34 35 34 04. 0.35825 0.35791 0.35757 0.35722 0.35688 9.96185 9.96179 9.96174 9.96168 9.96162 6 5 6 6 20 19 18 17 16 i 1C 2C 3d 3 4 4 9 14 7 2 .7 3 .0 45 46 47 48 49 9.60503 9.60532 9.60561 9.60589 9.60618 29 29 28 29 28 9.64346 9.64381 9.64415 9.64449 9.64483 35 34 34 34 34 0.35654 0.35619 0.35585 0.35551 0.35517 9.96157 9.96151 9.96146 9.96140 9.96135 6 5 6 5 g 15 14 13 12 11 4C 5C 18 23 6 7 3 5 50 51 52 53 54 9.60646 9.60675 9.60704 9.60732 9.60761 29 29 28 29 28 9.64517 9.64552 9.64586 9.64620 9.64654 35 34 34 34 rtA 0.35483 0.35448 0.35414 0.35380 0.35346 9.96129 9.96123 9.96118 9.96112 9.96107 6 5 6 5 10 9 8 7 6 6 7 8 | 9 1 10 j 0.6 0.7 0.8 0.9 1.0 0.5 0.6 0.7 0.8 0.8 55 56 57 58 59 9.60789 9.60818 9.60846 9.60875 9.60903 29 28 29 28 28 9.64688 9.64722 9.64756 9.64790 9.64824 34 34 34 34 CtA 0.35312 0.35278 0.35244 0.35210 0.35176 9.96101 9.96095 9.96090 9.96084 9.96079 6 5 6 5 5 4 3 .2 1 20 30 40 50 2.0 3.0 4.0 5.0 1.7 2.5 3.3 4.2 60 9.60931 9.64858 0.35142 9.96073 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. ' ] t 1 . P. 66 516 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 24 L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. d. P .P. 1 2 3 4 9.60931 9.60960 9.60988 9.61016 9.61045 29 28 28 29 28 9.64858 9.64892 9.64926 9.64960 9.64994 34 34 34 34 34 0.35142 0.35108 0.35074 0.35040 0.35006 9.96073 9.96067 9.96062 9.96056 9.96050 6 5 6 6 60 59 58 57 56 3 6 { 7 L 4 33 J.4 3.3 10 39 5 6 7 8 9 9.61073 9.61101 9.61129 9.61158 9.61186 28 28 29 28 OQ 9.65028 9.65062 9.65096 9.65130 9.65164 34 34 34 34 33 0.34972 0.34938 0.34904 0.34870 0.34836 9.96045 9.96039 9.96034 9.96028 9.96022 6 5 6 6 55 54 53 52 51 8 < 9 { 10 I 20 11 30 1' L5 4.4 ).l 5.0 ).7 5.5 L.3 11.0 r.O 16.5 10 11 12 13 14 9.61214 9.61242 9.61270 9.61298 9.61326 28 28 28 28 28 9.65197 9.65231 9.65265 9.65299 9.65333 34 34 34 34 33 0.34803 0.34769 0.34735 0.34701 0.34667 9.96017 9.96011 9.96005 9.96000 9.95994 6 6 5 6 50 49 48 47 46 40 % 50 2* 1.7 22.0 S.3 27.5 29 15 16 17 18 19 9.61354 9.61382 9.61411 9.61438 9.61466 28 29 27 28 28 9.65366 9.65400 9.65434 9.65467 9.65501 34 34 33 34 34 0.34634 0.34600 0.34566 0.34533 0.34499 9.95988 9.95982 9.95977 9.95971 9.95965 6 5 6 6 K 45 44 43 42 41 6 7 8 9 10 2.9 3.4 3.9 4.4 4.8 20 21 22 23 24 9.61494 9.61522 9.61550 9.61578 9.61606 28 28 28 28 28 9.65535 9.65568 9.65602 9.65636 9.65669 33 34 34 33 34 0.34465 0.34432 0.34398 0.34364 0.34331 9.95960 9.95954 9.95948 9.95942 9.95937 6 6 6 5 40 39 38 37 36 20 30 40 50 9.7 14.5 19.3 24.2 25 26 27 28 29 9.61634 9.61662 9.61689 9.61717 9.61745 28 27 28 28 28 9.65703 9.65736 9.65770 9.65803 9.65837 33 34 33 34 33 0.34297 0.34264 0.34230 0.34197 0.34163 9.95931 9.95925 9.95920 9.95914 9.95908 6 5 6 6 35 34 '33 32 31 6 7 8 28 2.8 3.3 3.7 30 31 32 33 34 9.61773 9.61800 9.61828 9.61856 9.61883 27 28 28 27 28 9.65870 9.65904 9.65937 9.65971 9.66004 34 33 34 33 34 0.34130 0.34096 0.34063 0.34029 0.33996 9.95902 9.95897 9.95891 9.95885 9.95879 5 6 6 6 30 29 28 27 26 10 20 30 40 50 4.2 4.7 9.3 14.0 18.7 23 3 35 36 37 38 39 9.61911 9.61939 9.61966 9.61994 9.62021 28 27 28 27 28 9.66038 9.66071 9.66104 9.66138 9.66171 33 33 34 33 qq 0.33962 0.33929 0.33896 0.33862 0.33829 9.95873 9.95868 9.95862 9.95856 9.95850 5 6 6 6 25 24 23 22 21 6 7 27 2.7 q 9 40 41 42 43 44 9.62049 9.62076 9.62104 9.62131 9.62159 27 28 27 28 27 9.66204 9.66238 9.66271 9.66304 9.66337 34 33 33 33 34 0.33796 0.33762 0.33729 0.33696 0.33663 9.95844 9.95839 9.95833 9.95827 9.95821 5 6 6 6 20 19 18 17 16 8 9 10 20 30 3.6 4.1 4.5 9.0 13.5 45 46 47 48 49 9.62186 9.62214 9.62241 9.62268 9.62296 28 27 27 28 27 9.66371 9.66404 9.66437 9.66470 9.66503 33 33 33 33 f>A 0.33629 0.33596 0.33563 0.33530 0.33497 9.95815 9.95810 9.95804 9.95798 9.95792 5 6 6 6 15 14 13 12 11 40 50 18.0 22.5 6 5 50 51 52 53 54 9.62323 9.62350 9.62377 9.62405 9.62432 27 27 28 27 27 9.66537 9.66570 9.66603 9.66636 9.66669 33 33 33 33 qq 0.33463 0.33430 0.33397 0.33364 0.33331 9.95786 9.95780 9.95775 9.95769 9.95763 6 5 6 6 10 9 8 7 6 6 C 7 C 8 C 9 C 10 1 .6 0.5 .7 0.6 .8 0.7 .9 0.8 .0 0.8 55 56 57 58 59 9.62459 9.62486 9.62513 9.62541 9.62568 27 27 28 27 27 9.66702 9.66735 9.66768 9.66801 9.66834 33 33 33 33 qq 0.33298 0.33265 0.33232 0.33199 0.33166 9.95757 9.95751 9.95745 9.95739 9.95733 6 6 6 6 5 4 3 2 1 20 2 30 3 40 4 50 5 .0 1.7 .0 2.5 .0 3.3 .0 4.2 60 9.62595 9.66867 0.33133 9.95728 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. 1 P P. 65 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 25 517 / L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. d. P. P 1 2 3 4 9.62595 9.62622 9.62649 9.62676 9.62703 27 27 27 27 97 9.66867 9.66900 9.66933 9.66966 9.66999 33 33 33 33 qo 0.33133 0.33100 0.33067 0.33034 0.33001 9.95728 9.95722 9.95716 9.95710 9.95704 6 6 6 6 60 59 58 57 56 3 6 3 7 3 3 .3 32 3.2 3 7 5 6 7 8 9 9.62730 9.62757 9.62784 9.62811 9.62838 27 27 27 27 97 9.67032 9.67065 9.67098 9.67131 9.67163 33 33 33 32 33 0.32968 0.32935 0.32902 0.32869 0.32837 9.95698 9.95692 9.95686 9.95680 9.95674 6 6 6 6 55 54 53 52 51 8 4 9 5 10 5 20 11 30 16 .4 .0 ,5 .0 .5 4.3 4.8 5.3 10.7 16.0 10 11 12 13 14 9.62865 9.62892 9.62918 9.62945 9.62972 27 26 27 27 97 9.67196 9.67229 9.67262 9.67295 9.67327 33 33 33 32 33 0.32804 0.32771 0.32738 0.32705 0.32673 9.95668 9.95663 9.95657 9.95651 9.95645 5 6 6 6 50 49 48 47 46 40 22 50 27 .0 .5 ? 21.3 26.7 7 15 16 17 18 19 20 21 22 23 24 9.62999 9.63026 9.63052 9.63079 9.63106 9.63133 9.63159 9.63186 9.63213 9.63239 27 26 27 27 27 26 27 27 26 27 9.67360 9.67393 9.67426 9.67458 9.67491 9.67524 9.67556 9.67589 9.67622 9.67654 33 33 32 33 33 32 33 33 32 33 0.32640 0.32607 0.32574 0.32542 0.32509 0.32476 0.32444 0.32411 0.32378 0.32346 9.95639 9.95633 9.95627 9.95621 9.95615 9.95609 9.95603 9.95597 9.95591 9.95585 6 6 6 6 6 6 6 6 6 g 45 44 43 42 41 lo~ 39 38 37 36 6 7 8 9 10 20 30 40 50 2 3 3 4 4 S 13 If 22 .7 .2 .6 .1 .5 .0 .5 .0 .5 25 26 27 28 29 9.63266 9.63292 9.63319 9.63345 9.63372 26 27 26 27 26 9.67687 9.67719 9.67752 9.67785 9.67817 32 33 33 32 33 0.32313 0.32281 0.32248 0.32215 0.32183 9.95579 9.95573 9.95567 9.95561 9.95555 6 6 6 6 35 34 33 32 31 6 7 8 2 '2 3 S 6 .6 .0 .5 30 31 32 33 34 9.63398 9.63425 9.63451 9.63478 9.63504 27 26 27 26 27 9.67850 9.67882 9.67915 9.67947 9.67980 32 33 32 33 32 0.32150 0.32118 0.32085 0.32053 0.32020 9.95549 9.95543 9.95537 9.95531 9.95525 6 6 6 6 30 29 28 27 26 9 10 20 30 40 50 a 4 13 17 1 .9 .3 .7 .0 .3 7 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 9.63531 9.63557 9.63583 9.63610 9.63636 9.63662 9.63689 9.63715 9.63741 9.63767 9.63794 9.63820 9.63846 9.63872 9.63898 26 26 27 26 26 27 26 26 26 27 26 26 26 26 26 9.68012 9.68044 9.68077 9.68109 9.68142 9.68174 9.68206 9.68239 9.68271 9.68303 9.68336 9.68368 9.68400 9.68432 9.68465 32 33 32 33 32 32 33 32 32 33 32 32 32 33 32 0.31988 0.31956 0.31923 0.31891 0.31858 0.31826 0.31794 0.31761 0.31729 0.31697 0.3T66T 0.31632 0.31600 0.31568 0.31535 9.95519 9.95513 9.95507 9.95500 9.95494 9.95488 9.95482 9.95476 9.95470 9.95464 9.95458 9.95452 9.95446 9.95440 9.95434 6 6 7 6 6 6 6 6 6 6 6 6 6 6 25 24 23 22 21 I(T 19 18 17 16 15 14 13 12 11 6 7 8 9 10 20 30 40 50 1 1 2 3 4 5 6 r 7 8 9 1 2 3 5 7 8 5 50 51 52 53 54 9.63924 9.63950 9.63976 9.64002 9.64028 26 26 26 26 26 9.68497 9.68529 9.68561 9.68593 9.68626 32 32 32 33 32 0.31503 0.31471 0.31439 0.31407 0.31374 9.95427 9.95421 9.95415 9.95409 9.95403 6 6 6 6 g 10 9 8 7 6 6 7 8 9 10 1 . .7 .8 .9 .0 0.5 0.6 0.7 0.8 0.8 55 56 57 58 59 9.64054 9.64080 9.64106 9.64132 9.64158 26 26 26 26 26 9.68658 9.68690 9.68722 9.68754 9.68786 32 32 32 32 32 0.31342 0.31310 0.31278 0.31246 0.31214 9.95397 9.95391 9.95384 9.95378 9.95372 6 7 6 6 g 5 4 3 2 1 20 2 30 3 40 4 50 5 .0 .0 .0 .0 1.7 2.5 3.3 4.2 60 9.64184 9.68818 0.31182 9.95366 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. ' P. P 64 518 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 26 / L. Sin. d. L.Tang. d.c. L. Cotg L. Cos. d. P . P 1 2 3 4 9.64 184 9.64210 9.64236 9.64262 9.64288 26 26 26 26 25 9.68818 9.68850 9.68882 9.68914 9.68946 32 32 32 32. 32 0.31182 0.31150 0.31118 0.31086 0.31054 9.95366 9.95360 9.95354 9.95348 9.95341 6 6 6 m 60 59 58 57 56 6 7 3 '< 2 5.2 5 7 31 3.1 3 6 5 6 7 8 9 9.64313 9.64339 9.64365 9.64391 9.64417 26 26 26 26 9F1 9.68978 9.69010 9.69042 9.69074 9.69106 32 32 32 32' 09 0.31022 0.30990 0.30958 0.30926 0.30894 9.95335 9.95329 9.95323 9.95317 9.95310 6 6 .6 55 54 53 52 51 8 9 10 20 80 L M . \ 1( If 1.3 1.8 ).7 4.1 4.7 5.2 10.3 15.5 10 11 12 13 14 9.64442 9.64468 9.64494 9.64519 9.64545 26 26 25 26 26 9.69138 9.69170 9.69202 9.69234 9.69266 32 32 32 32 09 0.30862 0.30830 0.30798 0.30766 0.30734 9.95304 9.95298 9.95292 9.95286 9.95279 6 6 6 7 50 49 48 47 46 40 50 21 2( .3 >.7 ? 20.7 25,8 6 15 16 17 18 19 9.64571 9.64596 9.64622 9.64647 9.64673 25 26 25 26 25 9.69298 9.69329 9.69361 9.69393 9.69425 31 32 32 32 09 0.30702 0.30671 0.30639 0.30607 0.30575 9.95273 9.95267 9.95261 9.95254 9.95248 6 6 7 6 45 44 43 42 41 1 6 7 8 9 2 3 3 3 4 .6 .0 .5 .9 .3 20 21 22 23 24 9.64698 9.64724 9.64749 9.64775 9.64800 26 25 26 25 26 9.69457 9.69488 9.69520 9.69552 9.69584 31 32 32 32 q-i 0.30543 0.30512 0.30480 0.30448 0.30416 9.95242 9.95236 9.95229 9.95223 9.95217 6 6 6 40 39 38 37 36 j 4 , $ I H 1 8 13 17 21 !o .3 .7 25 26 27 28 29 9.64826 9.64851 9.64877 9.64902 9.64927 25 26 25 25 26 9.69615 9.69647 9.69679 9.69710 9.69742 32 32 31 32 32 0.30385 0.30353 0.30321 0.30290 0.30258 9.95211 9.95204 9.95198 9.95192 9,95185 7 6 6 7 Q 35 34 33 32 31 6 7 .8 2 2 2 3 5 .5 .9 .3 30 31 32 33 34 9.64953 9.64978 9.65003 9.65029 9.65054 25 25 26 25 9^ 9.69774 9.69805 9.69837 9.69868 9.69900 31 31 32 09 0.30226 0.30195 0.30163 0.30132 0.30100 9.95179 9.95173 9.95167 9.95160 9.95154 6 6 7 6 30 29 28 27 26 1 : 'P J 4 [ o 4 8 12 ie 4) .8 .2 .3 .5 .7 8 35 36 37 38 39 9.65079 9.65104 9.65130 9.65155 9.65180 25 26 25 25 25 9.69932 9.69963 9.69995 9.70026 9.70058 31 32 31 32 qi 0.30068 0.30037 0.30005 0.29974 0.29942 9.95148 9.95141 9.95135 9.95129 9.95122 7 6 6 7 25 24 23 22 21 6 2 2 4 .4 40 41 42 43 44 9.65205 9.65230 9.65255 9.65281 9.65306 25 25 26 25 25 9.70089 9.70121 9.70152 9.70184 9.70215 32 31 32 31 32 0.29911 0.29879 0.29848 0.29816 0.29785 9.95116 9.95110 9.95103 9.95097 9.95090 6 7 6 7 20 19 18 17 16 1 2 j 8 9 3 3 4 8 12 .2 .6 .0 .0 .0 45 46 47 48 49 9.65331 9.65356 9.65381 9.65406 9.65431 25 25 25 25 25 9.70247 9.70278 9.70309 9.70341 9.70372 31 31 32 31 09 0.29753 0.29722 0.29691 0.29659 0.29628 9.95084 9.95078 9.95071 9.95065 9.95059 6 7 6 6 15 14 13 12 11 4 : I 16 20 7 .0 .0 6 50 51 52 53 54 9.65456 9.65481 9.65506 9.65531 9.65556 25 25 25 25 24 9.70404 9.70435 9.70466 9.70498 9.70529 31 31 32 31 31 0.29596 0.29565 0.29534 0.29502 0.29471 9.95052 9.95046: 9.95039 9.95033 9.95027 6 7 6 6 7 10 9 8 ' 7 6 6 7 8 9 10 C C C 1 1 .7 .8 .9 .1 .2 0.6 0.7 0.8 0.9 1.0 55 56 57 58 59 9.65580 9.65605 9.65630 9.65655 9.65680 25 25 25 25 25 9.70560 9.70592 9.70623 9.70654 9.70685 32 31 31 31 32 0.29440 0.29408 0.29377 0.29346 0.29315 9.95020 9.95014 9.95007 9.95001 9.94995 S 7 6 6 5 4 3 2 1 20 30 40 50 2 3 4 5 .3 .5 .7 .8 2.0 3.0 4.0 5.0 60 9.65705 9.70717 0.29283 9.94988 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. 1 P P. LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 27 519 / L. Sin. ; d. L.Tang. d. c. L. Cotg. L. Cos. d. P.P. 1 2 3 4 9.65705 9.65729 9.65754 9.65779 9.65804 24 25 25 25 24 25 25 24 25 25 24 25 24 25 25 24 25 24 25 24 24 25 24 25 24 24 25 24 24 25 24 24 24 24 25 24 24 24 24 24 24 25 24 24 24 24 24 24 24 23 24 24 24 24 24 24 24 23 24 24 9.70717 9.70748 9.70779 9.70810 9.70841 31 31 31 31 32 31 31 31 31 31 31 31 31 32 31 31 31 31 31 31 31 31 30 31 31 31 31 31 31 31 31 30 31 31 31 31 30 31 31 30 31 31 31 30 31 31 30 31 30 31 31 30 31 30 31 30 31 30 31 30 0.29283 0.29252 0.29221 0.29190 0.29159 9.94988 9.94982 9.94975 9.94969 9.94962 6 7 6 7 6 7 6 7 6 7 6 6 7 6 7 6 7 7 6 7 6 7 6 7 6 7 6' 7 ' 7 6 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 7 .7 60 59 58 57 56 6 7 8 9 10 20 30 40 50 1 1 S 4 E 6 7 8 9 10 20 30 40 50 1 i 7 8 9 10 20 30 40 50 32 3.2 3.7 4.3 4.8 5.3 10.7 16.0 21.3 26.7 3 6 3 7 3 8 4 9 4 5 10 15 20 25 25 2.5 2.9 3.3 3.8 4.2 8.3 12.5 16.7 20.8 2 6 2 7 2 8 3 9 3 LO 3 >0 7 K) 11 10 15 K) IS 7 0.7 0.8 0.9 1.1 1.2 2.3 3.5 4.7 5.8 31 3.1 3.6 4.1 4.7 5.2 10.3 15.5 20.7 25.8 D 5 .0 .5 .0 .0 .0 .0 .0 24 2.4 2.8 3.6 4.0 8.0 12.0 16.0 20.0 3 .3 .7 .1 .5 .8 .7 .5 .3 .2 6 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 5.0 5 6 7 8 9 9.65828 9.65853 9.65878 9.65902 9.65927 9.65952 9.65976 9.66001 9.66025 9.66050 9.70873 9.70904 9.70935 9.70966 9.70997 0.29127 0.29096 0.29065 0.29034 0.29003 9.94956 9.94949 9.94943 9.94936 9.94930 , 55 54 53 52 51 10 11 12 13 14 9.71028 9.71059 9.71090 9.71121 9.71153 0.28972 0.28941 0.28910 0.28879 0.28847 9.94923 9.94917 9.94911 9.94904 9.94898 50 49 48 47 46 15 16 17 18 19 9.66075 9.66099 9.66124 9.66148 9.66173 9.71184 9.71215 9.71246 9.71277 9.71308 0.28816 0.28785 0.28754 0.28723 0.28692 9.94891 9.94885 9.94878 9.94871 9.94865 45 44 43 42 41 20 21 22 23 24 9.66197 9.66221 9.66246 9.66270 9.66295 9.71339 9.71370 9.71401 9.71431 9.71462 0.28661 0.28630 0.28599 0.28569 0.28538 9.94858 9.94852 9.94845 9.94839 9.94832 40 39 38 37 36 25 26 27 28 29 9.66319 9.66343 9.66368 9.66392 9.66416 9.71493 9.71524 9.71555 9.71586 9.71617 0.28507 0.28476 0.28445 0/28414 0.28383 9.94826 9.94819 9.94813 9.94806 9.94799 35 34 33 32 31 30 31 32 33 34 9.66441 9.66465 9.66489 9.66513 9.66537 9.71648 9.71679 9.71709 9.71740 9.71771 0.28352 0.28321 0.28291 0.28260 0.28229 9.94793 9.94786 9.94780 9.94773 9.94767 30 29 28 27 26 35 36 37 38 39 9.66562 9.66586 9.66610 9.66634 9.66658 9.71802 9.71833 9.71863 9.71894 9.71925 0.28198 0.28167 0.28137 0.28106 0.28075 9.94760 9.94753 9.94747 9.94740 9.94734 25 24 23 22 21 40 41 42 43 44 9.66682 9.66706 9.66731 9.66755 9.66779 9.71955 9.71986 9.72017 9.72048 9.72078 0.28045 0.28014 0.27983 0.27952 0.27922 9.94727 9.94720 9.94714 9.94707 9.94700 20 19 18 17 16 45 46 47 48 49 9.66803 9.66827 9.66851 9.66875 9.66899 9.72109 9.72140 9.72170 9.72201 9.72231 0.27891 0.27860 0.27830 0.27799 0.27769 9.94694 9.94687 9.94680 9.94674 9.94667 15 14 13 12 11 50 51 52 53 54 55 56 57 58 59 9.66922 9.66946 9.66970 9.66994 9.67018 9.72262 9.72293 9.72323 9.72354 9.72384 0.27738 0.27707 0.27677 0.27646 0.27616 9.94660 9.94654 9.94647 9.94640 9.94634 10 9 8 7 6 9.67042 9.67066 9.67090 9.67113 9.67137 9.72415 9.72445 9.72476 9.72506 9.72537 0.27585 0.27555 0.27524 0.27494 0.27463 9.94627 9.94620 9.94614 9.94607 9.94600 5 4 3 2 1 60 9.97161 9.72567 0.27433 9.94593 L. Cos. d. L. Cotg.l d. c. L.Tang L. Sin, d. / P.P. 62 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 28 ' L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. | d. P.P. 1 2 3 4 9.67161 9.67185 9.67208 9.67232 9.67256 24 23 24 24 24 9.72567 9.72598 9.72628 9.72659 9.72689 31 30 31 30 31 0.27433 0.27402 0.27372 0.27341 0.27311 9.94593 9.94587 9.94580 9.94573 9.94567 6 7 7 6 w 60 59 58 57 56 6 7 31 3.1 3 6 30 3.0 35 5 6 7 8 9 9.67280 9.67303 9.67327 9.67350 9.67374 23 24 23 24 24 9.72720 9.72750 9.72780 9.72811 9.72841 30 30 31 30 31 0.27280 0.27250 0.27220 0.27189 0.27159 9.94560 9.94553 9.94546 9.94540 9.94533 7 7 6 7 55 54 53 52 51 8 9 10 20 30 4.1 4.7 5.2 10.3 15.5 4.0 4.5 5.0 10.0 15.0 10 11 12 13 14 9.67398 9.67421 9.67445 9.67468 9.67492 23 24 23 24 90 9.72872 9.72902 9.72932 9.72963 9.72993 30 30 31 30 OA 0.27128 0.27098 0.27068 0.27037 0.27007 9.94526 9.94519 9.94513 9.94506 9.94499 7 6 7 7 50 49 48 47 46 40 50 20.7 25.8 ? 20.0 25.0 9 15 16 17 18 19 9.67515 9.67539 9.67562 9.67586 9.67609 24 23 24 23 24 9.73023 9.73054 9.73084 9.73114 9.73144 31 30 30 30 31 0.26977 0.26946 0.26916 0.26886 0.26856 9.94492 9.94485 9.94479 9.94472 9.94465 7 6 7 7 7 45 44 43 42 41 1 6 2 7 3 8 3 9 4 4 9 4 9 .4 8 20 21 22 23 24 9.67633 9.67656 9.67680 9.67703 9.67726 23 24 23 23 24 9.73175 9.73205 9.73235 9.73265 9.73295 30 30 30 30 31 0.26825 0.26795 0.26765 0.26735 0.26705 9.94458 9.94451 9.94445 9.94438 9.94431 7 6 7 7 7 40 39 38 37 36 2 \ ( 1 9 14 19 24 .7 .5 .3 .2 25 26 27 28 29 9.67750 9.67773 9.67796 9.67820 9.'67843 23 23 24 23 23 9.73326 9.73356 9.73386 9.73416 9.73446 30 30 30 30 30 0.26674 0.26644 0.26614 0.26584 0.26554 9.94424 9.94417 9.94410 9.94404 9.94397 7 7 6 7 7 35 34 33 32 31 6 7 8 24 2.4 2.8 3.2 23 2.3 2.7 3.1 q C 30 31 32 33 34 9.67866 9.67890 9.67913 9.67936 9.67959 24 23 23 23 23 9.73476 9.73507 9.73537 9.73567 9.73597 31 30 30 30 30 0.26524 0.26493 0.26463 0.26433 0.26403 9.94390 9.94383 9.94376 9.94369 9.94362 7 7 7 7 7 30 29 28 27 26 10 20 30 40 50 4.0 8.0 12.0 16.0 ?00 3.8 7.7 11.5 15.3 19.2 35 36 37 38 39 9.67982 9.68006 9.68029 9.68052 9.68075 24 23 23 23 23 9.73627 9.73657 9.73687 9.73717 9.73747 30 30 30 30 30 0.26373 0.26343 0.26313 0.26283 0.26253 9.94355 9.94349 9.94342 9.94335 9.94328 6 7 7 7 7 25 24 23 22 21 2 6 - 2 7 2 2 .2 (j 40 41 42 43 44 9.68098 9.68121 9.68144 9.68167 9.68190 23 23 23 23 23 9.73777 9.73807 9.73837 9.73867 9.73897 30 30 30 30 30 0.26223 0.26193 0.26163 0.26133 0.26103 9.94321 9.94314 9.94307 9.94300 9.94293 7 7 7 7 7 20 19 18 17 16 1 8 2 9 3 3 >0 7 50 11 .9 .3 .7 .3 .0 45 46 47 48 49 9.68213 9.68237 9.68260 9.68283 9.68305 24 23 23 22 23 9.73927 9.73957 9.73987 9.74017 9.74047 30 30 30 30 30 0.26073 0.26043 0.26013 0.25983 0.25953 9.94286 9.94279 9.94273 9.94266 9.94259 7 6 7 7 7 15 14 13 12 11 t \ N 10 14 >0 1 7 .7 .3 6 50 51 52 53 54 9.68328 9.68351 9.68374 9.68397 9.68420 23 23 23 23 23 9.74077 9.74107 9.74137 9.74166 9.74196 30 30 29 30 30 0.25923 0.25893 0.25863 0.25834 0.25804 9.94252 9.94245 9.94238 9.94231 9.94224 7 7 7 7 7 10 9 8 7 6 6 7 8 9 10 ! 0.7 0.8 0.9 1.1 1.2 0.6 0.7 0.8 0.9 1.0 55 56 57 58 59 9.68443 9.68466 9.68489 9.68512 9.68534 23 23 23 22 23 9.74226 9.74256 9.74286 9.74316 9.74345 30 30 30 29 30 0.25774 0.25744 0.25714 0.25684 0.25655 9.94217 9.94210 9.94203 9.94196 9.94189 7 7 7 7 7 5 4 3 2 1 20 30 40 50 2.3 3.5 4.7 5.8 2.0 3.0 4.0 5.0 60 9.68557 9.74375 0.25625 9.94182 L. Cos. d. L. Cotg d.c. L.Tang L. Sin. d. ' P. P LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 29 521 ' L. Sin. d. L.Tang. d. e. J,. Cotg. L. Cos. d. V P .P. 1 2 3 4 9.68557 9.68580 9.68603 9.68625 9.68648 23 23 22 23 23 9.74375 9.74405 9.74435 9.74465 9.74494 30 30 30 29 30 0.25625 0.25595 0.25565 0.25535 0.25506 9.94182 9.94175 9.94168 9.94161 9.94154 7 7 7 7 7 60 59 58 57 56 6 7 30 3.0 35 5 6 7 8 9 9.68671 9.68694 9.68716 9.68739 9.68762 23 22 23 23 99 9.74524 9.74554 9.74583 9.74613 9.74643 30 29 30 30 on 0.25476 0.25446 0.25417 0.25387 0.25357 9.94147 9.94140 9.94133 9.94126 9.94119 7 7 7 7 7 55 54 53 52 51 8 9 10 20 30 4.0 4.5 5.0 10.0 15.0 10 11 12 13 14 9.68784 9.68807 9.68829 9.68852 9.68875 23 22 23 23 99 9.74673 9.74702 9.74732 9.74762 9.74791 29 30 30 29 30 0.25327 0.25298 0.25268 0.25238 0.25209 9.94112 9.94105 9.94098 9.94090 9.94083 7 7 8 7 7 50 49 48 47 46 40 50 20.0 25.0 29 15 16 17 18 19 9.68897 9.68920 9.68942 9.68965 9.68987 23 22 23 22 90 9.74821 9.74851 9.74880 9.74910 9.74939 30 29 30 29 on 0.25179 0.25149 0.25120 0.25090 0.25061 9.94076 9.94069 9.94062 9.94055 9.94048 7 7 7 7 7 45 44 43 42 41 6 7 8 9 10 2.9 3.4 3.9 4.4 4.8 20 21 22 23 24 9.69010 9.69032 9.69055 9.69077 9.69100 22 23 22 23 22 9.74969 9.74998 9.75028 9.75058 9.75087 29 30 30 29 30 0.25031 0.25002 0.24972 0.24942 0.24913 9.94041 9.94034 9.94027 9.94020 9.94012 7 7 7 8 7 40 39 38 37 36 20 30 40 50 9.7 14.5 19.3 24.2 25- 26 27 28 29 9.69122 9.69144 9.69167 9.69189 9.69212 22 23 22 23 22 9.75117 9.75146 9.75176 9.75205 9.75235 29 30 29 30 29 0.24883 0.24854 0.24824 0.24795 0.24765 9.94005 9.93998 9.93991 9.93984 9.93977 7 7 7 7 7 35 34 33 32 31 6 7 8 23 2.3 2.7 3.1 30 31 32 33 34 9.69234 9.69256 9.69279 9.69301 9.69323 22 23 22 22 22 9.75264 9.75294 9.75323 9.75353 9.75382 30 29 30 29 29 0.24736 0.24706 0.24677 0.24647 0.24618 9.93970 9.93963 9.93955 9.93948 9.93941 7 8 7- 7 7 30 29 28 27 26 10 20 30 40 50 3.8 7.7 11.5 15.3 19.2 35 36 37 38 39 9.69345 9.69368 9.69390 9.69412 9.69434 23 22 22 22 22 9.75411 9.75441 9.75470 9.75500 9.75529 30 29 30 29 29 0.24589 0.24559 0.24530 0.24500 0.24471 9.93934 9.93927 9.93920 9.93912 9.93905 7 7 8 7 7 25 24 23 22 21 6 7 22 2.2 f) a 40 41 42 43 44 9.69456 9.69479 9.69501 9.69523 9.69545 23 22 22 22 22 9.75558 9.75588 9.75617 9.75647 9.75676 30 29 30 29 29 0.24442 0.24412 0.24383 0.24353 0.24324 9.93898 9.93891 9.93884 9.93876 9.93869 7 7 8 7 7 20 19 18 17 16 8 9 10 20 30 2.9 3.3 3.7 7.3 11.0 45 46 47 48 49 9.69567 9.69589 9.69611 9.69633 9.69655 22 22 22 22 22 9.75705 9.75735 9.75764 9.75793 9.75822 30 29 29 29 30 0.24295 0.24265 0.24236 0.24207 0.24178 9.93862 9.93855 9.93847 993840 9.93833 7 8 7 7 7 15 14 13 12 11 40 50 14.7 18.3 8 7 50 51 52 53 54 9.69677 9.69699 9.69721 9.69743 9.69765 22 22 22 22 22 9.75852 9.75881 9.75910 9.75939 9.75969 29 29 29 30 29 0.24148 0.24119 0.24090 0.24061 0.24031 9.93826 9.93819 9.93811 9.93804 9.93797 7 8 * 7 7 3 10 9 8 7 6 6 ( 7 C 8 1 9 1 10 1 .8 0.7 .9 0.8 .1 0.9 .2 1.1 .3 1.2 55 56 57 58 59 9.69787 9.69809 9.69831 9.69853 9.69875 22 22 22 22 22 9.75998 9.76027 9.76056 9.76086 9.76115 29 29 30 29 9Q 0.24002 0.23973 0.23944 0.23914 0.23885 9.93789 9.93782 9.93775 9.93768 9.93760 7 7 7 8 5 4 3 2 1 20 i 30 4 40 50 6 .7 2.3 .0 3.5 .3 4.7 .7 5.8 60 9.69897 9.76144 0.23856 9.93753 L. Cos. d. L. Cotg. d. e. L.Tang. L. Sin. d. ' P .P. 6O 522 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 30 / L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. d. P P 1 2 3 4 9.69897 9.69919 9.69941 9.69963 9.69984 22 22 22 21 22 9.76144 9.76173 9.76202 9.76231 9.76261 29 29 29 30 29 0.23856 0.23827 0.23798 0.23769 0.23739 9.93753 9.93746 9.93738 9.93731 9.93724 7 8 7 7 fj 60 59 58 57 56 3 6 3 7 3 .0 5 29 2.9 3 4 5 6 7 8 9 9.70006 9.70028 9.70050 9.70072 9.70093 22 22 22 21 22 9.76290 9.76319 9.76348 9.76377 9.76406 29 29 29 29 29 0.23710 0.23681 0.23652 0.23623 0.23594 9.93717 9.93709 9.93702 9.93695 9.93687 8 7 7 8 55 54 53 52 51 8 4 9 4 10 5 20 10 30 15 .0 .5 .0 .0 .0 3.9 4.4 4.8 9.7 14.5 10 11 12 13 14 9.70115 9.70137 9.70159 9.70180 9.70202 22 22 21 22 22 9.76435 9.76464 9.76493 9.76522 9.76551 29 29 29 29 29 0.23565 0.23536 0.23507 0.23478 '0.23449 9.93680 9.93673 9.93665 9.93658 9.93650 7 8 7 8 17 50 49 48 47 46 40 20 50 25 .0 .0 ? 19.3 24.2 8 15 16 17 18 19 9.70224 9.70245 9.70267 9.70288 9.70310 21 22 21 22 22 9.76580 9.76609 9.76639 9.76668 9.76697 29 30 29 29 OQ 0.23420 0.23391 0.23361 0.23332 0.23303 9.93643 9.93636 9.93628 9.93621 9.93614 7 8 7 7 45 44 43 42 41 6 7 8 9 10 2 3 3 4 4 .8 , .3 .7 .2 .7 20 21 22 23 24 9.70332 9.70353 9.70375 9.70396 9.70418 21 22 21 22 21 9.76725 9.76754 9.76783 9.76812 9.76841 29 29 29 29 29 0.23275 0.23246 0.23217 0.23188 0.23159 9.93606 9.93599 9.93591 9.93584 9.93577 7' 8 7 7 Q 40 39 38 37 36 20 30 40 50 9 14 18 23 ,3 .0 .7 .3 25 26 27 28 29 9.70439 9.70461 9.70482 9.70504 9.70525 22 21 22 21 22 9.76870 9.76899 9.76928 9.76957 9.76986 29- 29 29 29 29 0.23130 0.23101 0.23072 0.23043 0.23014 9.93569 9.93562 9.93554 9.93547 9.93539 7 8 7 8 35 34 33 32 31 6 7 8 2 2 2 2 2 .2 .6 .9 30 31 32 33 34 9.70547 9.70568 9.70590 9.70611 9.70633 21 22 21 22 21 9.77015 9.77044 9.77073 9.77101 9.77130 29 29 28 29 29 0.22985 0.22956 0.22927 0.22899 0.22870 9.93532 9.93525 9.93517 9.93510 9.93502 7 8 7 8 30 29 28 27 26 9 10 20 30 40 50 3 3 7 11 14 1 .3 .7 .3 .0 .7 .3 35 36 37 38 39 9.70654 9.70675 9.70697 9.70718 9.70739 21 22 21 21 22 9.77159 9.77188 9.77217 9.77246 9.77274 29 29 29 28 29 0.22841 0.22812 0.22783 0.22754 0.22726 9.93495 9.93487 9.93480 9.93470 9.93465 8 7 8 7 25 24 23 22 21 6 7 2 2 1 .1 40 41 42 43 44 9.70761 9.70782 9.70803 9.70824 9.70846 21 21 21 22 21 9.77303 9.77332 9.77361 9.77390 9.77418 29 29 29 28 29 0.22697 0.22668 0.22639 0.22610 0.22582 9.93457 9.93450 9.93442 9.93435 9.93427 7 8 7 8 7 20 19 18 17 16 8 9 10 20 30 2 3 3 7 1C '.8 .2 .5 .0 .5 45 46 47 48 49 9.70867 9.70888 9.70909 9.70931 9.70952 21 21 22 21 21 9.77447 9.77476 9.77505 9.77533 9.77562 29 29 28 29 29 0.22553 0.22524 0.22495 0.22467 0.22438 9.93420 9:93412 9.93405 9.93397 9.93390 8 7 8 7 g 15 14 13 12 11 40 50 14 17 ft .0 .5 7 50 51 52 53 54 9.70973 9.70994 9.71015 9.71036 9.71058 21 21 21 22 21 9.77591 9.77619 9.77648 9.77677 9.77706 28 29 29 29 28 0.22409 0.22381 0.22352 0.22323 0.22294 9.93382 9.'93375 9.93367 9.93360 9.93352 7 8 7 8 g 10 9 8 7 6 6 ( 7 ( 8 ] 9 ] 10 ] .8 .9 .1 2 !s 0.7 0.8 0.9 1.1 1.2 55 56 57 58 59 9.71079 9.71100 9.71121 9.71142 9.71163 21 21 21 21 21 9.77734 9.77763 9.77791 9.77820 9.77849 29 28 29 29 OQ 0.22266 0.22237 0.22209 0.22180 0.22151 9.93344 9.93337 9.93329 9.93322 9.93314 7 8 7 8 y 5 4 3 2 1 20 5 30 4 40 i 50 e .7 .0 .3 .7 2.3 3.5 4.7 5.8 60 9.71184 9.77877 0.22123 .9:93307 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. ' P .P 59 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 31 523 / L. Bin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P. P. 1 2 3 4 9.71184 9.71205 9.71226 9.71247 9.71268 21 21 21 21 91 9.77877 9.77906 9.77935 9.77963 9.77992 29 29 28 29 28 0.22123 0.22094 0.22065 0.22037 0.22008 9.93307 9.93299 9.93291 9.93284 9.93276 8 8 7. 8 60 59 58 57 56 6 7 29 2.9 3 4 5 6 7 8 9 9.71289 9.71310 9.71331 9.71352 9.71373 21 21 21 21 20 9.78020 9.78049 9.78077 9.78106 9.78135 29 28 29 29 28 0.21980 0.21951 0.21923 0.21894 0.21865 9.93269 9.93261 9.93253 9.93246 9.93238 8 8 7 8 8^ 55 54 53 52 51 8 9 10 20 30 3.9 4.4 4.8 9.7 14.5 10 11 12 13 14 9.71393 9.71414 9.71435 9.71456 9.71477 21 21 21 21 21 9.78163 9.78192 9.78220 9.78249 9.78277 29 28 29 28 29 0.21837 0.21808 0.21780 0.21751 0.21723 9.93230 9.93223 9.93215 9.93207 9.93200 7 ' 8 8 7 50 49 48 47 46 40 50 19.3 24.2 28 15 16 17 18 19 9.71498 9.71519 9.71539 9.71560 9.71581 21 20 21 21 21 9.78306 9.78334 9.78363 9.78391 9.78419 28 29 28 28 29 0.21694 0.21666 0.21637 0.21609 0.21581 9.93192 9.93184 9.93177 9.93169 9.93161 8 7 8 8 45 44 43 42 41 6 7 8 9 10 2.8 3.3 3.7 4.2 4.7 20 21 22 23 24 9.71602 9.71622 9.71643 9.71664 9.71685 20 21 21 21 9ft 9.78448 9.78476 9.78505 9.78533 9.78562 28 29 28 29 00 0.21552 0.21524 0.21495 0.21467 0.21438 9.93154 9.93146 9.93138 9.93131 9.93123 8 8 7 8 40 39 38 37 36 20 30 40 50 9.3 14.0 18.7 23.3 25 26 27 28 29 9.71705 9.71726 9.71747 9.71767 9.71788 21 21 20 21 21 9.78590 9.78618 9.78647 9.78675 9.78704 28 ( 28 29 28 29 28 0.21410 0.21382 0.21353 0.21325 0.21296 9.93115 9.93108 9.93100 9.93092 9.93084 7 8 8 8 35 34 33 32 31 6 7 8 21 2.1 2.5 2.8 30 31 32 33 34 9.71809 9.71829 9.71850 9.71870 9.71891 20 21 20 21 20 9.78732 9.78760 9.78789 9.78817 9.78845 28 29 28 28 29 0.21268 0.21240 0.21211 0.21183 0.21155 9.93077 9.93069 9.93061 9.93053 9.93046 8 8 8 7 30 29 28 27 26 9 10 20 30 40 50 3.2 3.5 7.0 10.5 14.0 17 5 35 36 37 38 39 9.71911 9.71932 9.71952 9.71973 9.71994 21 20 21 21 20 9.78874 9.78902 9.78930 9.78959 9.78987 28 28 29 28 28 0.21126 0.21098 0.21070 0.21041 0.21013 9.93038 9.93030 9.93022 9.93014 9.93007 8 8 8 7 g 25 24 23 22 21 6 7 20 2.0 2 3 40 41 42 43 44 9.72014 9.72034 9.72055 9.72075 9.72096 20 21 20 21 20 9.79015 9.79043 9.79072 9.79100 9.79128 28 29 28 28 28 0.20985 0.20957 0.20928 0.20900 0.20872 9.92999 9.92991 9.92983 9.92976 9.92968 8 8 7 8 g 20 19 18 17 16 8 9 10 20 30 2.7 3.0 3.3 6.7 10.0 45 46 47 48 49 9.72116 9.72137 9.72157 9.72177 9.72198 21 20 20 21 20 9.79156 9.79185 9.79213 9.79241 9.79269 29 28 28 28 28 0.20844 0.20815 0.20787 0.20759 0.20731 9.92960 9.92952 9.92944 9.92936 9.92929 8 8 8 7 15 14 13 12 11 40 50 13.3 16.7 B 7 50 51 52 53 54 9.72218 9.72238 9.72259 9.72279 9.72299 20 21 20 20 21 9.79297 9.79326 9.79354 9.79382 9.79410 29 28 28 28 28 0.20703 0.20674 0.20646 0.20618 0.20590 9.92921 9.92913 9.92905 9.92897 9.92889 8 8 8 8 g 10 9 8 7 6 6 7 8 1 9 1 10 1 .8 0.7 .9 0.8 .1 0.9 .2 LI .3 1.2 55 56 57 58 59 9.72320 9.72340 9.72360 9.72381 9.72401 20 20 21 20 20 9.79438 9.79466 9.79495 9.79523 9.79551 28 29 28 28 28 0.20562 0.20534 0.20505 0.20477 0.20449 9.92881 9.92874 9.92866 9.92858 9.92850 7 8 8 8 Q 5 4 3 2 .1 20 2 30 4 40 5 50 6 .7 2.3 .0 3.5 .3 4.7 .7 5.8 60 9.72421 9.79579 0.20421 9.92842 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. ' P P. 58 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 32 1 2 3 4 .5 6 7 8 9 L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. d. P. r 9 .9 .4 .9 .4 .8 .7 .5 .3 .2 J 1 1 2 1 5 8 2 5 5 5 1 1 2 2 ') 3 ( S 12 15 3 0. 1. 1. 1. 2 4 5 6. 9.72421 9.72441 9.72461 9.72482 9.72502 20 20 21 20 20 20 20 20 20 20 21 20 20 20 20 20 20 20 20 20 20 20 20 19 20 20 20 20 20 20 19 20 20 20 20 19 20 20 20 19 20 20 19 20 20 19 20 20 19 20 19 20 19 20 19 20 19 20 19 20 9.79579 9.79607 9.79635 9.79663 9.79691 28 28 28 28 28 28 29 28 28 28 28 28 28 28 28 28 28 28 28 28 28 27 28 28 28 28 28 28 28 28 28 27 28 28 28 28 28 28 27 28 28 28 28 27 28 28 28 27 28 28 28 27 28 28 27 28 28 27 28 28 0.20421 0.20393 0.20365 0.20337 0.20309 9.92842 9.92834 9.92826 9.92818 9.92810 8 8 8 8 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 8 8 8 8 8 8 8 8 9 8 8 8 8 8 8 9 8 8 8 8 8 9 8 60 59 58 57 56 6 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 2 2 3 3 4 4 9 14 19 24 6 7 8 9 10 20 30 40 50 2 i 2 2 2 3 3 7 10 14 17 6 7 8 9 10 20 30 40 50 9 0.9 1.1 1.2 1.4 1.5 3.0 4.5 6.0 7.5 28 2.8 3.3 3.7 4.2 4.7 9.3 14.0 18.7 23.3 >7 2.7 i.2 S.6 1.1 1.5 ).0 5.5 3.0 2.5 20 2.0 2.3 2.7 3.0 3.3 6.7 10.0 13.3 16.7 3 .9 .2 .5 .9 .2 .3 .5 .7 .8 7 8 0.7 9 0.8 1 0.9 2 1.1 3 1.2 7 2.3 3.5 3 4.7 7 5.8 9.72522 9.72542 9.72562 9.72582 9.72602 9.79719 9.79747 9.79776 9.79804 9.79832 0.20281 0.20253 0.20224 0.20196 0.20168 9.92803 9.92795 9.92787 9.92779 9.92771 55 54 53 52 51 10 11 12 13 14 9.72622 9.72643 9.72663 9.72683 9.72703 9.79860 9.79888 9.79916 9.79944 9.79972 0.20140 0.20112 0.20084 0.20056 0.20028 9.92763 9.92755 9.92747 9.92739 9.92731 50 49 48 47 46 15 16 17 18 19 20 21 22 23 24 9.72723 9.72743 9.72763 9.72783 9.72803 9.80000 9.80028 9.80056 9.80084 9.80112 0.20000 0.19972 0.19944 0.19916 0.19888 9.92723 9.92715 9.92707 9.92699 9.92691 45 44 43 42 41 9.72823 9.72843 9.72863 9.72883 9.72902 9.80140 9.80168 9.80195 9.80223 9.80251 0.19860 0.19832 0.19805 0.19777 0.19749 9.92683 9.92675 9.92667 9.92659 9.92651 40 39 38 37 36 35" 34 33 32 31 25 26 27 28 29 9.72922 9.72942 9.72962 9.72982 9.73002 9.80279 9.80307 9.80335 9.80363 9.80391 0.19721 0.19693 0.19665 0.19637 0.19609 9.92643 9.92635 9.92627 9.92619 9.92611 30 31 32 33 34 9.73022 9.73041 9.73061 9.73081 9.73101 9.80419 9.80447 9.80474 9.80502 9.80530 0.19581 0.19553 0.19526 0.19498 0.19470 9.92603 9.92595 9.92587 9.92579 9.92571 30 29 28 27 26 35 36 37 38 39 9.73121 9.73140 9.73160 9.73180 9.73200 9.80558 9.80586 9.80614 9.80642 9.80669 0.19442 0.19414 0.19386 0.19358 0.19331 9.92563 9.92555 9.92546 9.92538 9.92530 25 24 23 22 21 40 41 42 43 44 9.73219 9.73239 9.73259 9.73278 9.73298 9.80697 9.80725 9.80753 9.80781 9.80808 0.19303 0.19275 0.19247 0.19219 0.19192 9.92522 9.92514 9.92506 9.92498 9.92490 20 19 18 17 16 45 46 47 48 49 9.73318 9.73337 9.73357 9.73377 9.73396 9.80836 9.80864 9.80892 9.80919 9.80947 0.19164 0.19136 0.19108 0.19081 0.19053 9.92482 9.92473 9.92465 9.92457 9.92449 15 14 13 12 11 50 51 52 53 54 9.73416 9.73435 9.73455 9.73474 9.73494 9.80975 9.81003 9.81030 9.81058 9.81086 0.19025 0.18997 0.18970 0.18942 0.18914 9.92441 9.92433 9.92425 9.92416 9.92408 10 9 8 7 6 5 4 3 2 1 55 56 57 58 59 9.73513 9.73533 9.73552 9.73572 9.73591 9.81113 9.81141 9.81169 9.81196 9.81224 0.18887 0.18859 0.18831 0.18804 0.18776 9.92400 9.92392 9.92384 9.92376 9.92367 60 9.73611 9.81252 0.18748 9.92359 L.Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. ' P.P. LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 33 525 > L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P .P 1 2 3 4 9.73611 9.73630 9.73650 9.73669 9.73689 19 20 19 20 1Q 9.81252 9.81279 9.81307 9.81335 9.81362 27 28 28 27. 28 0.18748 0.18721 0.18693 0.18665 0.18638 9.92359 9.92351 9.92343 9.92335 9.92326 8 8 8 9 g 60 59 58 57 56 6 7 2 8* > 9 27 2.7 32 5 6 7 8 9 9.73708 9.73727 9.73747 9.73766 9.73785 19 20 19 19 20 9.81390 9.81418 9.81445 9.81473 9.81500 28 27 28 27 00 0.18610 0.18582 0.18555 0.18527 0.18500 9.92318 9.92310 9.92302 9.92293 9.92285 8 8 9 8 g 55 54 53 52 51 8 9 10 20 30 ^ * 1 14 L2 L7 .0 3.6 4.1 4.5 9.0 13.5 10 11 12 13 14 9.73805 9.73824 9.73843 9.73863 9.73882 19 19 20 19 19 9.81528 9.81556 9.81583 9.81611 9.81638 28 27 28 27 28 0.18472 0.18444 0.18417 0.18389 0.18362 9.92277 9.92269 9.92260 9.92252 9.92244 8 9 8 8 50 49 48 47 46 40 50 1> 2', .7 .3 ? 18.0 22.5 15 16 17 18 19 9.73901 9.73921 9.73940 9.73959 9.73978 20 19 19 19 19 9.81666 9.81693 9.81721 9.81748 9.81776 27 28 27 28 27 0.18334 0.18307 0.18279 0.18252 0.18224 9.92235 9.92227 9.92219 9.92211 9.92202 8 8 8 9 g 45 44 43 42 41 ] 6 7 8 9 2 2 2 3 1 .0 .3 .7 .0 .3 20 21 22 23 24 9.73997 9.74017 9.74036 9.74055 9.74074 20 19 19 19 19 9.81803 9.81831 9.81858 9.81886 9.81913 28 27 28 27 28 0.18197 0.18169 0.18142 0.18114 0.18087 9.92194 9.92186 9.92177 9.92169 9.92161 8 9 8 8 9 40 39 38 37 36 2 S - 4 \ ( 10 13 If .7 .0 .3 .7 25 26 27 28 29 9.74093 9.74113 9.74132 9.74151 9.74170 20 19 19 19 19 9.81941 9.81968 9.81996 9.82023 9.82051 27 28 27 28 27 0.18059 0.18032 0.18004 0.17977 0.17949 9.92152 9.92144 9.92136 9.92127 9.92119 8 8 9 8 g 35 34 33 32 31 6 7 8 1 1 2 2 9 .9 .2 .5 30 31 32 33 34 9.74189 9.74208 9.74227 9.74246 9.74265 19 19 19 19 19 9.82078 9.82106 9.82133 9.82161 9.82188 28 27 28 27 27 0.17922 0.17894 0.17867 0.17839 0.17812 9.92111 9.92102 9.92094 9.92086 9.92077 9 8 8 9 30 29 28 27 26 1 2 3 4 5 I) 8 6 9 12 ^~^ .2 .3 .5 .7 8 35 36 37 38 39 9.74284 9.74303 9.74322 9.74341 9.74360 19 19 19 19 19 9.82215 9.82243 9.82270 9.82298 9.82325 28 27 28 27 27 0.17785 0.17757 0.17730 0.17702 0.17675 9.92069 9.92060 9.92052 9.92044 9.92035 9 8 8 9 g 25 24 23 22 21 6 *j \ i I .8 T 40 41 42 43 44 9.74379 9.74398 9.74417 9.74436 9.74455 19 19 19 19 19 9.82352 9.82380 9.82407 9.82435 9.82462 28 27 28 27 27 0.17648 0.17620 0.17593 0.17565 0.17538 9.92027 9.92018 9.92010 9.92002 9.91993 9 8 8 9 g 20 19 18 17 16 1 2 3 8 9 o 2 3 6 9 .4 .7 .0 .0 .0 45 46 47 48 49 9.74474 9.74493 9.74512 9.74531 9.74549 19 19 19 18 19 9.82489 9.82517 9.82544 9.82571 9.82599 28 27 27 28 97 0.17511 0.17483 0.17456 0.17429 0.17401 9.91985 9.91976 9.91968 9.91959 9.91951 9 8 9 8 9 15 14 13 12 11 4 5 12 15 q .0 .0 8 50 51 52 53 54 9.74568 9.74587 9.74606 9.74625 9.74644 19 19 19 19 18 9.82626 9.82653 9.82681 9.82708 9.82735 27 28 27 27 97 0.17374 0.17347 0.17319 0.17292 0.17265 9.91942 9.91934 9.91925 9.91917 9.91908 8 9 8 9 g 10 9 8 7 6 6 7 8 9 10 1 1 1 1 .9 .1 .2 A .5 0.8 0.9 1.1 1.2 1.3 55 56 57 58 59 9.74662 9.74681 9.74700 9.74719 9.74737 19 19 19 18 19 9.82762 9.82790 9.82817 9.82844 9.82871 28 27 27 27 no 0.17238 0.17210 0.17183 0.17156 0.17129 9.91900 9.91891 9.91883 9.91874 9.91866 9 8 9 8 9 5 4 3 2 1 20 30 40 50 g 4 6 7 ,0 .5 .0 .5 2.7 4.0 5.3 6.7 60 9.74756 9.82899 0.17101 9.91857 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. ' P P. 56 526 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 34 ' L. Sin. d. L.Tang d. c. L. Cotg L. Cos. . d. 1 \ I 1 2 3 4 9.74756 9.74775 9.74794 9.74812 9.74831 19 19 18 19 19 9.82899 9.82926 9.82953 9.82980 9.83008 27 27 27 ,28 97 0.17101 0.17074 0.17047 0.17020 0.16992 9.91857 9.91849 9.91840 9.91832 9.91823 8 9 8 9 60 59 58 57 56 6 7 IB 2.8 r> o 27 2.7 q o 5 6 7 8 9 9.74850 9.74868 9.74887 9.74906 9.74924 18 19 19 18 19 9.83035 9.83062 9.83089 9.83117 9.83144 27 27 28 27 27 0.16965 0.16938 0.16911 0.16883 0.16856 9.91815 9.91806 9.91798 9.91789 9.91781 9 8 9 8 55 54 53 52 51 8 9 10 20 30 1 3.7 4.2 4.7 9.3 4.0 3.6 4.1 4.5 9.0 13.5 10 11 12 13 14 9.74943 9.74961 9.74980 9.74999 9.75017 18 19 19 18 19 9.83171 9.83198 9.83225 9.83252 9.83280 27 27 27 28 27 0.16829 0.16802 0.16775 0.16748 0.16720 9.91772 9.91763 9.91755 9.91746 9.91738 9 8 9 8 50 49 48 47 46 40 50 1 2 3.7 3.3 ? 18.0 22.5 6 15 16 17 18 19 9.75036 9.75054 9.75073 9.75091 9.75110 18 if 18 19 18 9.83307 9.83334 9.83361 9.83388 9.83415 27 27 27 27 27 0.16693 0.16666 0.16639 0.16612 0.16585 9.91729 9.91720 9.91712 9.91703 9.91695 9 8 9 8 45 44 43 42 41 ] <; 7 8 9 i 3 a 3 4 .6 .0 .5 .9 .3 20 21 22 23 24 9.75128 9.75147 9.75165 9.75184 9.75202 19 18 19 18 19 9.83442 9.83470 9.83497 9.83524 9.83551 28 27 27 27 97 0.16558 046530 0.16503 0.16476 0.16449 9.91686 9.91677 9.91669 9.91660 9.91651 9 8 9 9 40 39 38 37 36 r< r\ - ; \ 5 * 13 17 21 .7 .0 .3 .7 25 26 27 28 29 9.75221 9.75239 9.75258 9.75276 9.75294 18 19 18 18 19 9.83578 9.83605 9.83632 9.83659 9.83686 27 27 27 27 27 0.16422 0.16395 0.16368 0.16341 0.16314 9.91643 9.91634 9.91625 9.91617 9.91608 , 9 9 8 9 35 34 33 32 31 fi 7 8 1 1 2 o 9 .9 .2 .5 30 31 32 33 34 9.75313 9.75331 9.75350 9.75368 9.75386 18 19 18 18 19 9.83713 9.83740 9.83768 9.83795 9.83822 27 28 27 27 27 0.16287 0.16260 0.16232 0.16205 0.16178 9.91599 9.91591 9.91582 9.91573 9.91565 8 9 9 8 30 29 28 27 26 1 '2 3 4 5 9 2 3 6 9 12 li .9 2 !a .5 .7 g as 36 37 38 39 9.75405 9.75423 9.75441 9.75459 9.75478 18 18 18 19 18 9.83849 9.83876 9.83903 9.83930 9.83957 27 27 27 27 27 0.16151 0.16124 0.16097 0.16070 0.16043 9.91556. 9.91547 9.91538 9.91530 9.91521 9 9 8 9 25 24 23 22 21 6 1 1 5 8 40 41 .42 43 44 9.75496 9.75514 9.75533 9.75551 9.75569 18 19 18 18 18 9.83984 9.84011 9.84038 9.84065 9.84092 27 27 27 27 27 0.16016 0.15989 0.15962 0.15935 0.15908 9.91512 9.91504 9.91495 9.91486 9.91477 8 9 9 9 g 20 19 18 17 16 1 2 3 8 9 ) ) 2 3 6 9 4 7 45 46 47 48 49 9.75587 9.75605 9.75624 9.75642 9.75660 18 , 19 18 18 18 9.84119 9.84146 9.84173 9.84200 9.84227 27 27 27 27 27 0.15881 0.15854 0.15827 0.15800 0.15773 9.91469 9.91460 9.91451 9.91442 9.91433 9 9 9 9 g 15 14 13 12 11 4 5 D 12 15 g 3 50 51 52 53 54 9.75678 9.75696 9.75714 9.75733 ' 9.75751 18 18 19 18 18 9.84254 9.84280 9.84307 9.84334 9.84361 26 27 27 27 27 0.15746 0.15720 0.15693 0.15666 0.15639 9.91425 9.91416 9.91407 9.91398 9.91389 9 9 9 9. g 10 9 8 7 6 6 7 8 9 10 1 1 1 1 .9 .1 .2 .4 .5 0.8 0.9 1.1 1.2 1.3 55 56 57 58 59 9.75769 9.75787 9.75805 9.75823 9.75841 18 18 18 9.84388 9.84415 9.84442 9.84469 9.84496 27 27 27 27 27 0.15612 0.15585 0.15558 0.15531 0.15504 9.91381 9.91372 9.91363 9.91354 9.91345 9 9 9 9 5 4 3 (2 1 20 30 40 50 3 4 6 7 .0 5 5 2.7 4.0 5.3 6.7 60 9.75859 9.84523 0.15477 9.91336 L. Cos. d. L. Cote. d. c. L.Tang. L/. Sin. d. 1 P. P. 55 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 35 527 / L. Sin. d. L.Tang. d. c. 'L. Cotg. L. Cos. d. F .P. 1 2 3 4 9.75859 9.75877 9.75895 9.75913 9.75931 18 18 18 18 10 9.84523 9.84550 9.84576 9.84603 9.84630 27 26 27 27 97 0.15477 0.15450 0.15424 0.15397 0.15370 9.91336 9.91328 9.91319 9.91310 9.91301 8 9 9 9 60 59 58 57 56 6 7 2 r - 7 26 5.7 2.6 2 30 5 6 7 8 9 9.75949 9.75967 9.75985 9.76003 9.76021 18 18 18 18 -1 Q 9.84657 9.84684 9.84711 9.84738 9.84764 27 27 27 26 27 0.15343 0.15316 0.15289 0.15262 0.15236 9.91292 9.91283 9.91274 9.91266 9.91257 9 9 8 9 55 54 53 52 51 8 9 10 20 30 c 4 4 S 1? .6 3.5 .1 3.9 .5 4.3 * .0 8.7 .5 13.0 10 11 12 13 14 9.76039 9.76057 , 9.76075 9.76093 9.76111 18 18 18 18 18 9.84791 9.84818 9.84845 9.84872 9.84899 27 27 27 27 26 0.15209 0.15182 0.15155 0.15128 0.15101 9.91248 9.91239 9.91230 9.91221 9.91212 9 9 9 9 50 49 48 47 46 40 50 1? 22 .0 17.3 .5 21.7 18 15 16 17 18 19 9.76129 9.76146 9.76164 9.76182 9.76200 17 18 18 18 18 9.84925 9.84952 9.84979 9.85006 9.85033 27 27 27 27 26 0.15075 0.15048 0.15021 0.14994 0.14967 9.91203 9.91194 9.91185 9.91176 9.91167 9 9 9 9 45 44 43 42 41 ] 6 7 8 9 1.8 2.1 2.4 2.7 3.0 20 21 22 23 24 9.76218 9.76236 9.76253 9.76271 9.76289 18 17 18 18 18 9.85059 9.85086 9.85113 9.85140 9.85166 27 27 27 26 27 0.14941 0.14914 0.14887 0.14860 0.14834 9.91158 9.91149 9.91141 9.91132 9.91123 9 8 9 9 40 39 38 37 36 9 1 i \ 6.0 9.0 12.0 15.0 2o 26 27 28 29 9.76307 9.76324 9.76342 9.76360 9.76378 17 18 18 18 17 9.85193 9.85220 9.85247 9.85273 9.85300 27 27 26 27 27 0.14807 0.14780 0.14753 0.14727 0.14700 9.91114 9.91105 9.91096 9.91087 9.91078 9 9 9 9 35 34 33 32 31 6 7 8 17 1.7 2.0 2.3 30 31 32 33 34 9.76395 9.76413 9.76431 9.76448 9.76466 18 18 17 18 18 9.85327 9.85354 9.85380 9.85407 9.85434 27 26 27 27 26 0.14673 0.14646 0.14620 0.14593 0.14566 9.91069 9.91060 9.91051 9.91042 9.91033 9 9 9 9 10 30 29 28 27 26 : '\ il 4 fjj o 2.6 2.8 5.7 8.5 11.3 14 2 35 36 37 38 39 9.76484 9.76501 9.76519 9.76537 9.76554 17 18 18 17 18 9.85460 9.85487 9.85514 9.85540 9.85567 27 27 26 27 27 0.14540 0.14513 0.14486 0.14460 0.14433 9.91023 9.91014 9.91005 9.90996 9.90987 9 9 9 9 25 24 23 22 21 <; 7 10 1.0 1 2 40 41 42 43 44 9.76572 9.76590 9.76607 9.76625 9.76642 18 17 18 17 18 9.85594 9.85620 9.85647 9.85674 9.85700 26 27 27 26 27 0.14406 0.14380 0.14353 0.14326 0.14300 9.90978 9.90969 9.90960 9.90951 9.90942 9 9 9 9 (, 20 19 18 17 16 8 9 10 20 iO 1.3 1.5 1.7 3.3 5.0 45 46 47 48 49 9.76660 9.76677 9.76695 9.76712 9.76730 17 18 17 18 17 9.85727 9.85754 9.85780 9.85807 9.85834 27 26 27 27 26 0.14273 0.14246 0.14220 0.14193 0.14166 9.90933 9.90924 9.90915 9.90906 9.90896 9 9 9 10 9 15 14 13 12 11 40 >0 6.7 8.3 9 8 50 51 52 53 54 9.76747 9.76765 9.76782 9.76800 9.76817 18 17 18 17 18 9.85860 9.85887 9.85913 9.85940 9.85967 27 26 27 27 0.14140 0.14113 0.14087 0.14060 0.14033 9.90887 9.90878 9.90869 9.90860 9.90851 9 9 9 9 9 10 9 8 7 6 6 7 8 9 10 1 1 1 1 .9 0.8 .1 0.9 .2 1.1 .4 1.2 .5 1.3 55 56 57 58 59 9.76835 9.76852 9.76870 9.76887 9.76904 17 18 17 17 18 9.85993 9.86020 9.86046 9.86073 9.86100 27 26 27 27 OR 0.14007 0.13980 0.13954 0.13927 0.13900 9.90842 9.90832 9.90823 9.90814 9.90805 10 9 9 9 5 4 3 2 1 20 30 40 50 3 4 6 7 .0 2.7 .5 4.0 .0 5.3 .5 6.7 60 9.76922 9.86126 0.13874 9.90796 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. ' P P. 54 528 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 36 ' L. Sin. d. L.TangJ d. c. |L. Cotg L. Cos d. P.P. 1 2 3 4 9.76922 9.76939 9.76957 9.76974 9.76991 17 18 17 17 18 17 17 18 17 17 17 18 17 17 17 18 17 17 17 18 17 17 17 17 17 17 17 18 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 16 17 17 17 17 17 17 16 17 17 17 17 16 9.86126 9.86153 9.86179 9.86206 9.86232 27 26 27 26 27 26 27 26 27 27 26 ' 27 26 27 26 27 26 26 27 26 27 26 27 26 27 26 27 26 26 27 26 27 26 27 26 26 27 26 26 27 26 27 26 26 27 26 26 27 26 26 27 26 26 27 26 26 27 26 26 26 0.13874 0.13847 0.13821 0.13794 0.13768 9.90796 9.90787 9.90777 9.90768 9.90759 c 10 g 9 g 9 10 9 9 9 10 9 9 9 10 9 9 9 10 9 9 10 9 9 9 10 9 9 10 9 9 10 9 10 9 9 10 9 9 10 9 10 9 10 60 59 58 57 56 6 7 , 8 ; 9 < 10 < 20 < 30 K 40 If 50 2 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 1 6 1 7 1 8 1 9 1 10 1 20 3. 30 5. 40 6. 50 8. !7 26 2.7 2.6 5.2 3.0 5.6 3.5 U 3.9 L5 4.3 ).0 8.7 5.5 13.0 $.0 17.3 1.5 21.7 18 1.8 2.1 2.4 2.7 3.0 6.0 9.0 12.0 15.0 17 1.7 2.0 2.3 2.6 2.8 5.7 8.5 11.3 14.2 16 1.6 1.9 2.1 2.4 2.7 5.3 8.0 10.7 13.3 9 0.9 2 1.1 3 1.2 5 1.4 7 1.5 3 3.0 4.5 7 6.0 3 7.5 5 6 * 7 8 9 9.77009 9.77026 9.77043 9.77061 9.77078 9.86259 9.86285 9.86312 9.86338 9.86365 0.13741 0.13715 0.13688 0.13662 0.13635 9.90750 9.90741 9.90731 9.90722 9.90713 55 54 53 52 51 10 11 12 13 14 9.77095 9.77112 9.77130 9.77147 9.77164 9.86392 9.86418 9.86445 9.86471 9.86498 9.86524 9.86551 9.86577 9.86603 9.86630 0.13608 0.13582 0.13555 0.13529 0.13502 9.90704 9.90694 9.90685 9.90676 9.90667 50 49 48 47 46 15 16 17 18 19 9.77181 9.77199 9.77216 9.77233 9.77250 0.13476 0.13449 0.13423 0.13397 0.13370 9.90657 9.90648 9.90639 9.90630 9.90620 45 44 43 42 41 20 21 22 23 24 25 26 27 28 29 9.77268 9.77285 9.77302 9.77319 9.77336 9.86656 9.86683 9.86709 9.86736 9.86762 0.13344 0.13317 0.13291 0.13264 0.13238 9.90611 9.90602 9.90592 9.90583 9.90574 40 39 38 37 36 35 34 33 32 31 9.77353 9.77370 9.77387 9.77405 9.77422 9.86789 9.86815 9.86842 9.86868 9.86894 0.13211 0.13185 0.13158 0.13132 0.13106 9.90565 9.90555 9.90546 9.90537 9.90527 30 31 32 33 34 9.77439 9.77456 9.77473 9.77490 9.77507 9.86921 9.86947 9.86974 9.87000 9.87027 0.13079 0.13053 0.13026 0.13000 0.12973 9.90518 9.90509 9.90499 9.90490 9.90480 30 29 28 27 26 35 36 37 38 39 9.77524 9.77541 9.77558 9.77575 9.77592 9.87053 9.87079 9.87106 9.87132 9.87158 9.87185 9.87211 9.*87264 9.87290 0.12947 0.12921 0.12894 0.12868 0.12842 9.90471 9.90462 9.90452 9.90443 9.90434 25 24 23 22 21 40 41 42 43 44 45 46 47 48 49 9.77609 9.77626 9.77643 9.77660 9.77677 0.12815 0.12789 0.12762 0.12736 0.12710 9.90424 9.90415 9.90405 9.90396 9.90386 20 19 18 17 16 9.77694 9.77711 9.77728 9.77744 9.77761 9.87317 9.87343 9.87369 9.87396 9.87422 0.12683 0.12657 0.12631 0.12604 0.12578 9.90377 9.90368 9.90358 9.90349 9.90339 9 10 9 10 9 10 9 10 9 10 9 10 9 10 9 15 14 13 12 11 50 51 52 53 54 9.77778 9.77795 9.77812 9.77829 9.77846 9.87448 9.87475 9.87501 9.87527 9.87554 0.12552 0.12525 0.12499 0.12473 0.12446 9.90330 9.90320 9.90311 9.90301 9.90292 10 9 8 7 6 55 56 57 58 59 9.77862 9.77879 9.77896 9.77913 9.77930 9.87580 9.87606 9.87633 9.87659 9.87685 0.12420 0.12394 0.12367 0.12341 0.12315 9.90282 9.90273 9.90263 9.90254 9.90244 5 4 3 2 1 60 9.77946 9.87711 0.12289 9.90235 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin d. P.P. 53 Q LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 37 529 / L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. d. p P. 1 2 3 4 9.77946 9.77963 9.77980 9.77997 9.78013 17 17 17 16 17 9.87711 9.87738 9.87764 9.87790 9.87817 27 26 26 27 26 0.12289 0.12262 0.12236 0.12210 0.12183 9.90235 9.90225 9.90216 9.90206 9.90197 10 9 10 9 10 60 59 58 57 56 6 7 27 2.7 32 5 6 7 8 9 9.78030 9.78047 9.78063 9.78080 9.78097 17 16 17 17 -I C 9.87843 9.87869 9.87895 9.87922 9.87948 26 26 27 26 26 0.12157 0.12131 0.12105 0.12078 0.12052 9.90187 9.90178 9.90168 9.90159 9.90149 9 10 9 10 10 55 54 53 52 51 8 9 10 20 30 3.6 4.1 4.5 9.0 13.5 10 11 12 13 14 9.78113 9.78130 9.78147 9.78163 9.78180 17 17 16 17 1 7 9.87974 9.88000 9.88027 9.88053 9.88079 26 27 26 26 26 0.12026 0.12000 0.11973 0.11947 0.11921 9.90139 9.90130 9.90120 9.90111 9.90101 9 10 9 10 10 50 49 48 47 46 40 50 18.0 22.5 26 15 16 17 18 19 9.78197 9.78213 9.78230 9.78246 9.78263 16 17 16 17 -17 9.88105 9.88131 9.88158 9.88184 9.88210 26 27 26 26 26 0.11895 0.11869 0.11842 0.11816 0.11790 9.90091 9.90082 9.90072 9.90063 9.90053 9 10 9 10 10 45 44 43 42 41 6 7 8 9 10 2.6 3.0 3.5 3.9 4.3 20 21 22 23 24 9.78280 9.78296 9.78313 9.78329 9.78346 16 17 16 17 16 9.88236 9.88262 9.88289 9.88315 9.88341 26 27 26 26 26 0.11764 0.11738 0.11711 0.11685 0.11659 9.90043 9.90034 9.90024 9.90014 9.90005 9 10 10 9 10 40 39 38 37 36 20 30 40 50 8.7 13.0 17.3 21.7 25 26 27 28 29 9.78362 9.78379 9.78395 9.78412 9.78428 17 16 17 16 9.88367 9.88393 9.88420 9.88446 9.88472 26 27 26 26 26 0.11633 0.11607 0.11580 0.11554 0.11528 9.89995 9.89985 9.89976 9.89966 9.89956 10 9 10 10 g 35 34 33 32 31 6 7 8 17 1.7 2.0 2.3 30 31 32 33 34 9.78445 9.78461 9.78478 9.78494 9.78510 16 17 16 16 17 9.88498 9.88524 9.88550 9.88577 9.88603 26 26 27 26 26 0.11502 0.11476 0.11450 0.11423 0.11397 9.89947 9.89937 9.89927 9.89918 9.89908 10 10 9 10 10 30 29 28 27 26 10 20 30 40 50 2.8 5.7 8.5 11.3 14.2 35 36 37 38 39 9.78527 9.78543 9.78560 9.78576 9.78592 16 17 16 16 9.88629 9.88655 9.88681 9.88707 9.88733 26 26 26 26 26 0.11371 0.11345 0.11319 0.11293 0.11267 9.89898 9.89888 9.89879 9.89869 9.89859 10 9 10 10 in 25 24 23 22 21 6 7 16 1.6 1 9 40 41 42 43 44 9.78609 9.78625 9.78642 9.78658 9.78674 16 17 16 16 9.88759 9.88786 9.88812 .9.88838 9.88864 27 26 26 26 26 0.11241 0.11214 0.11188 0.11162 0.11136 9.89849 9.89840 9.89830 9.89820 9.89810 9 10 10 10 20 19 18 17 16 8 9 10 20 30 2.1 2.4 2.7 5.3 8.0 45 46 47 48 49 9.78691 9.78707 9.78723 9.78739 9.78756 16 16 16 17 16 9.88890 9.88916 9.88942 9.88968 9.88994 26 26 26 26 26 0.11110 0.11084 0.11058 0.11032 0.11006 9.89801 9.89791 9.89781 9.89771 9.89761 10 10 10 10 Q 15 14 13 12 11 40 50 | 10.7 13.3 9 50 51 52 53 54 9.78772 9.78788 9.78805 9.78821 9.78837 16 17 16 16 i fi 9.89020 9.89046 9.89073 9.89099 9.89125 26 27 26 26 26 0.10980 0.10954 0.10927 0.10901 0.10875 9.89752 9.89742 9.89732 9.89722 9.89712 10 10 10 10 in 10 9 8 7 6 6 1 7 1 8 1 9 1 10 1 .0 0.9 .2 1.1 .3 1.2 .5 1.4 .7 1.5 55 56 57 58 59 9.78853 9.78869 9.78886 9.78902 9.78918 16 17 16 16 16 9.89151 9.89177 9.89203 9.89229 9.89255 26 26 26 26 26 0.10849 0.10823 0.10797 0.10771 0.10745 9.89702 9.89693 9.89683 9.89673 9.89663 9 10 10 10 10 5 4 3 2 1 20 3 30 5 40 6 50 8 .3 3.0 .0 4.5 .7 6.0 .3 7.5 60 9.78934 9.89281 0.10719 9.89653 L. Cos. d. L. Cotg d.c. L.Tang. L. Sin. d. ' P .P. 52 530 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 38 / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P . 1 1 2 3 4 9.78934 9.78950 9.78967 9.78983 9.78999 16 17 16 16 i fi 9.89281 9.89307 9.89333 9.89359 9.89385 26 26 26 26 Ofi 0.10719 0.10693 0.10667 0.10641 0.10615 9.89653 9.89643 9.89633 9.89624 9.89614 10 10 9 10 60 59 58 57 56 6 2 2 6 .6 25 2.5 5 6 7 8 9 9.79015 9.79031 9.79047 9.79063 9.79079 16 16 16 16 16 9.89411 9.89437 9.89463 9.89489 9.89515 26 26 26 26 O? 0.10589 0.10563 0.10537 0.10511 0.10485 9.89604 9.89594 9.89584 9.89574 9.89564 10 10 10 10 in 55 54 53 52 51 8 9 10 20 30 3 3 4 8 13 .5 .9 .3 .7 3.3 3.8 4.2 8.3 12.5 10 11 12 13 14 9.79095 9.79111 9.79128 9.79144 9.79160 16 17 16 16 16 9.89541 9.89567 9.89593 9.89619 9.89645 26 26 26 26 26 0.10459 0.10433 0.10407 0.10381 0.10355 9.89554 9.89544 9.89534 9.89524 9.89514 10 IP 10 10 in 50 49 48 47 46 40 50 17 21 .3 .7 16.7 20.8 7 15 16 17 18 19 9.79176 9.79192 9.79208 9.79224 9.79240 16 16 16 16 i fi 9.89671 9.89697 9.89723 9.89749 9.89775 26 26 26 26 9fi 0.10329 0.10303 0.10277 0.10251 0.10225 9.89504 9.89495 9.89485 9.89475 9.89465 9 10 10 10 in 45 44 43 42 41 6 7 8 9 10 1 i L.7 >.o 5.3 J.6 }.8 20 21 22 23 24 9.79256 9.79272 9.79288 9.79304 9.79319 16 16 16 15 16 9.89801 9.89827 9.89853 9.89879 9.89905 26 26 26 26 9fi 0.10199 0.10173 0.10147 0.10121 0.10095 9.89455 9.89445 9.89435 9.89425 9.89415 10 10 10 10 in 40 39 38 37 36 20 iO 10 50 i \ 11 1^ ).7 5.5 L.3 L2 25 26 '27 28 29 9.79335 9.79351 9.79367 9.79383 9.79399 16 16 16 16 16 9.89931 9.89957 9.89983 9.90009 9.90035 26 26 26 26 26 0.10069 0.10043 0.10017 0.09991 0.09965 9.89405 9.89395 9.89385 9.89375 9.89364 10 10 10 11 in 35 34 33 32 31 6 7 8 1 1 I 2 3 6 9 1 15 1.5 1.8 2.0 30 31 32 33 34 9.79415 9.79431 9.79447 9.79463 9.79478 16 16 16 15 16 9.90061 9.90086 9.90112 9.90138 9.90164 25 26 26 26 26 0.09939 0.09914 0.09888 0.09862 0.09836 9.89354 9.89344 9.89334 9.89324 9.89314 10 10 10 10 10 30 29 28 27 26 9 10 20 30 40 50 '2 2 5 8 10 VI 4 7 3 7 3 2.3 2.5 5.0 7.5 10.0 l' ) 5 35 36 37 38 39 9.79494 9.79510 9.79526 9.79542 9.79558 16 16 16 16 i ^ 9.90190 9.90216 9.90242 9.90268 9.90294 26 26 26 26 ')& 0.09810 0.09781 0.09758 0.09732 0.09706 9.89304 9.89294 9.89284 9.89274 9.89264 10 10 10 10 in 25 24 23 22 21 6 1 1 1 1 40 41 42 43 44 9.79573 9.79589 9.79605 9.79621 9.79636 16 16 16 15 16 9.90320 9.90346 9.90371 9.90397 9.90423 26 25 26 26 9fi 0.09680 0.09654 0.09629 0.09603 0.09577 9.89254 9.89244 9.89233 9.89223 9.89213 10 11 10 10 in 20 19 18 17 16 8 9 10 20 JO 1 1 1 8 5 5 7 8 7 5 45 46 47 48 49 9.79652 9.79668 9.79684 9.79699 9.79715 16 16 15 16 i fi 9.90449 9.90475 9.90501 9.90527 9.90553 26 26 26 26 QC 0.09551 0.09525 0.09499 0.09473 0.09447 9.89203 9.89193 9.89183 9.89173 9.89162 10 10 10 11 in 15 14 13 12 11 40 ->() 1 7 9 o 3 2 g 50 51 52 53 54 9.79731 9.79746 9.79762 9.79778 9.79793 15 16 16 15 16 9.90578 9.90604 9.90630 9.90656 9.90682 26 26 26 26 26 0.09422 0.09396 0.09370 0.09344 0.09318 9.89152 9.89142 9.89132 9.89122 9.89112 10 10 10 10 ^ 10 9 8 7 6 6 7 8 9 10 1 1 1 1 1 2 3 5 7 0.9 1.1 1.2 1.4 1.5 55 56 57 58 59 9.79809 9.79825 9.79840 9.79856 9.79872 16 15 16 16 15 9.90708 9.90734 9.90759 9.90785 9.90811 26 25 26 26 9fi 0.09292 0.09266 0.09241 0.09215 0.09189 9.89101 9.89091 9.89081 9.89071 9.89060 10 10 10 11 10 5 4 3 2 1 20 30 40 50 8 5 6 8 9 7 3 3.0 4.5 6.0 7.5 60 9.79887 9.90837 0.09163 9.89050 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. ' P. p 51 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 39 / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P. P. 1 2 3 4 9.79887 9.79903 9.79918 9.79934 9.79950 16 15 16 16 15 16 15 16 15 16 15 16 15 16 15 16 15 15 16 15 16 15 16 15 15 16 15 15 16 15 15 16 15 15 16 15 15 15 16 15 15 15 16 15 15 15 15 15 16 15 15 15 15 15 15 15 16 15 15 15 9.90837 9.90863 9.90889 9.90914 9.90940 26 26 25 26 26 26 26 25 26 26 26 26 25 26 26 26 26 25 26 26 26 25 26 26 26 25 26 26 26 25 26 26 26 25 26 26 26 25 26 26 25 26 26 26 25 26 26 25 26 26 25 26 26 25 26 26 25 26 26 25 0.09163 0.09137 0.09111 0.09086 0.09060 9.89050 9.89040 9.89030 9.89020 9.89009 10 10 10 11 10 10 11 10 10 10 11 10 10 11 10 10 11 10 10 11 10 10 11 10 10 11 10 11 10 10 11 10 11 10 11 10 10 11 10 11 10 11 10 11 10 11 10 11 10 11 10 11 11 10 11 10 11 10 11 11 "dT 60 59 58 57 56 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 7 8 9 10 20 30 40 50 6 1 7 1 8 1 9 1 10 1 20 3 30 5 40 7 50 9 26 2.6 3.0 3.5 3.9 4.3 8.7 13.0 17.3 21.7 25 2.5 2.9 3.3 3.8 4.2 8.3 12.5 16.7 20.8 16 1.6 1.9 2.1 2.4 ' 2.7 5.3 8.0 10.7 13.3 15 1.5 1.8 2.0 2.3 2.5 5.0 7.5 10.0 12.5 1 10 1 1.0 3 1.2 5 1.3 7 1.5 8 1.7 7 3.3 5 5.0 3 6.7 2 8.3 P. 5 6 7 8 9 9.79965 9.79981 9.79996 9.80012 9.80027 9.90966 9.90992 9.91018 9.91043 9.91069 0.09034 0.09008 0.08982 0.08957 0.08931 0.08905 0.08879 0.08853 0.08828 0.08802 9.88999 9.88989 9.88978 9.88968 9.88958 9.88948 9.88937 9.88927 9.88917 9.88906 55 54 53 52 51 10 11 12 13 14 9.80043 9.80058 9.80074 9.80089 9.80105 9.91095 9.91121 9.91147 9.91172 9.91198 50 49 48 47 46 15 16 17 18 19 9.80120 9.80136 9.80151 9.80166 9.80182 9.91224 9.91250 9.91276 9.91301 9.91327 0.08776 0.08750 0.08724 0.08699 0.08673 9.88896 9.88886 9.88875 9.88865 9.88855 45 44 43 42 41 20 21 22 23 24 9.80197 9.80213 9.80228 9.80244 9.80259 9.91353 9.91379 9.91404 9.91430 9.91456 0.08647 0.08621 0.08596 0.08570 0.08544 9.88844 9.88834 9.88824 9.88813 9.88803 40 39 38 37 36 25 26 27 28 29 9.80274 9.80290 9.80305 9.80320 9.80336 9.91482 9.91507 9.91533 9.91559 9.91585 0.08518 0.08493 0.08467 0.08441 0.08415 9.88793 9.88782 9.88772 9.88761 9.88751 35 34 33 32 31 30 31 32 33 34 9.80351 9.80366 9.80382 9.80397 9.80412 9.91610 9.91636 9.91662 9.91688 9.91713 0.08390 0.08364 0.08338 0.08312 0.08287 9.88741 9.88730 9.88720 9.88709 9.88699 30 29 28 27 26 25 24 23 22 21 35 36 37 38 39 40 41 42 43 44 ~W 46 47 48 49 9.80428 9.80443 9.80458 9.80473 9.80489 9.91739 9.91765 9.91791 9.91816 9.91842 0.08261 0.08235 0.08209 0.08184 0.08158 9.88688 9.88678 9.88668 9.88657 9.88647 9.80504 9.80519 9.80534 9.80550 9.80565 9.91868 9.91893 9.91919 9.91945 9.91971 0.08132 0.08107 0.08081 0.08055 0.08029 9.88636 9.88626 9.88615 9.88605 9.88594 20 19 18 17 16 9.80580 9.80595 9.80610 9.80625 9.80641 9.91996 9.92022 9.92048 9.92073 9.92099 0.08004 0.07978 0.07952 0.07927 0.07901 9.88584 9.88573 9.88563 9.88552 9.88542 15 14 13 12 11 50 51 52 53 54 9.80656 9.80671 9.80686 9.80701 9.80716 9.92125 9.92150 9.92176 9.92202 9.92227 0.07875 0.07850 0.07824 0.07798 0.07773 0.07747 0.07721 0.07696 0.07670 0.07644 9.88531 9.88521 9.88510 9.88499 9.88489 1C88478 9.88468 9.88457 9.88447 9.88436 10 9 8 7 6 5 4 3 2 1 55 56 57 58 59 60 9.80731 9.80746 9.80762 9.80777 9.80792 9.92253 9.92279 9.92304 9.92330 9.92356 9.80807 9.92381 0.07619 9.88425 L. Cos. d. L. Cotg.l d. c. L.Tang. L. Sin. ' P 50 532 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 40 ' L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P P. 1 2 3 4 9.80807 9.80822 9.80837 9.80852 9.80867 15 15 15 15 15 9.92381 9.92407 9.92433 9.92458 9.92484 26 26 25 26 26 0.07619 0.07593 0.07567 0.07542 0.07516 9.88425 9.88415 9.88404 9.88394 9.88383 10 11 10 11 jl 60 59 58 57 56 6 7 26 2.6 3 5 6 7 8 9 9.80882 9.80897 9.80912 9.80927 9.80942 15 15 15 15 i f\ 9.92510 9.92535 9.92561 9.92587 9.92612 25 26 26 25 26 0.07490 0.07465 0.07439 0.07413 0.07388 9.88372 9.88362 9.88351 9.88340 9.88330 10 11 11 10 55 54 53 52 51 8 9 10 20 30 3.5 3.9 4.3 8.7 13.0 10 11 12 13 14 9.80957 9.80972 9.80987 9.81002 9.81017 15 15 15 15 IF: 9.92638 9.92663 9.92689 9.92715 9.92740 25 26 26 25 26 0.07362 0.07337 0.07311 0.07285 0.07260 9.88319 9.88308 9.88298 9.88287 9.88276 11 10 11 11 10 50 49 48 47 46 40 50 17.3 21.7 25 15 16 17 18 19 9.81032 9.81047 9.81061 9.81076 9.81091 15 14 15 15 i ^ 9.92766 9.92792 9.92817 9.92843 9.92868 26 26 25 f)a 0.07234 0.07208 0.07183 0.07157 0.07132 9.88266 9.88255 9.88244 9.88234 9.88223 11 11 10 11 45 44 43 42 41 6 7 8 9 10 2.5 2.9 3.3 3.8 4.2 20 21 22 23 24 9.81106 9.81121 9.81136 9.81151 9.81166 15 15 15 15 9.92894 9.92920 9.92945 9.92971 9.92996 26 25 26 25 26 0.07106 0.07080 0.07055 0.07029 0.07004 9.88212 9.88201 9.88191 9.88180 9.88169 11 10 11 11 11 40 39 38 37 36 20 30 40 50 8.3 12.5 16.7 20.8 25 26 27 28 29 9.81180 9.81195 9.81210 9.81225 9.81240 15 15 15 15 14 9.93022 9.93048 9.93073 9.93099 9.93124 26 25 26 25 26 0.06978 0.06952 0.06927 0.06901 0.06876 9.88158 9.88148 9.88137 9.88126 9.88115 10 11 11 11 10 35 34 33 32 31 6 7 8 15 1.5 1.8 2.0 30 31 32 33 34 9.81254 9.81269 9.81284 9.81299 9.81314 15 15 15 15 1 A 9.93150 9.93175 9.93201 9.93227 9.93252 25 26 26 25 .)( 0.06850 0.06825 0.06799 0.06773 0.06748 9.88105 9.88094 9.88083 9.88072 9.88061 11 11 11 11 in 30 29 28 27 26 10 20 30 40 50 2.5 5.0 7.5 10.0 12 5 35 36 37 38 39 9.81328 9.81343 9.81358 9.81372 9.81387 15 15 14 15 IK 9.93278 9.93303 9.93329 9.93354 9.93380 25 26 25 26 9fi 0.06722 0.06697 0.06671 0.06646 0.06620 9.88051 9.88040 9.88029 9.88018 9.88007 11 11 11 11 i ^ 25 24 23 22 21 - 6 7 14 1.4 1 6 40 41 42 43 44 9.81402 9.81417 9.81431 9.81446 9.81461 15 14 15 15 14 9.93406 9.93431 9.93457 9.93482 9.93508 25 26 25 26 25 0.06594 0.06569 0.06543 0.06518 0.06492 9.87996 9.87985 9.87975 9.87964 9.87953 11 10 11 11 n 20 19 18 17 16 8 9 10 20 30 1.9 2.1 2.3 4.7 7.0 45 46 47 48 49 9.81475 9.81490 9.81505 9.81519 9.81534 15 15 14 15 15 9.93533 9.93559 9.93584 9.93610 9.93636 26 25 26 26 OR 0.06467 0.06441 0.06416 0.06390 0.06364 9.87942 9.87931 9.87920 9.87909 9.87898 11 11 11 11 ]_]_ 15 14 13 12 11 40 50 | 9.3 11.7 1 10 50 51 52 53 54 9.81549 9.81563 9.81578 9.81592 9.81607 14 15 14 15 15 9.93661 9.93687 9.93712 9.93738 9.93763 26 25 26 25 26 0.06339 0.06313 0.06288 0.06262 0.06237 9.87887 9.87877 9.87866 9.87855 9.87844 10 11 11 11 ]_]_ 10 9 8 7 6 6 1 7 1 8 1 9 1 10 1 1 1.0 3 1.2 5 1.3 7 1.5 8 1.7 55 56 57 58 59 9.81622 9.81636 9.81651 9.81665 9.81680 14 15 14 15 14 9.93789 9.93814 9.93840 9.93865 9.93891 25 26 25 26 25 0.06211 0.06186 0.06160 0.06135 0.06109 9.87833 9.87822 9.87811 9.87800 9.87789 11 11 11 11 ]_]_ 5 4 3 2 1 20 3 30 5 40 7 50 9 7 3.3 5 5.0 3 6.7 2 8.3 60 9.81694 9.93916 0.06084 9.87778 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. ' P P. LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 41 533 ' L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P . P. 1 2 3 4 9.81694 9.81709 9.81723 9.81738 9.81752 15 14 15 14 15 9.93916 9.93942 9.93967 9.93993 9.94018 26 25 26 25 26 0.06084 0.06058 0.06033 0.06007 0.05982 9.87778 9.87767 9.87756 9.87745 9.87734 11 11 11 11 11 60 59 58 57 56 6 7 26 2.6 3 5 6 7 8 9 9.81767 9.81781 9.81796 9.81810 9.81825 14 15 14 15 u. 9.94044 9.94069 9.94095 9.94120 9.94146 25 26 25 26 OK 0.05956 0.05931 0.05905 0.05880 0.05854 9.87723 9.87712 9.87701 9.87690 9.87679 11 11 11 11 55 54 53 52 51 8 9 10 20 30 3.5 3.9 4.3 8.7 13.0 10 11 12 13 14 9.81839 9.81854 9.81868 9.81882 9.81897 15 14 14 15 14 9.94171 9.94197 9.94222 9.94248 9.94273 26 25 26 25 26 0.05829 0.05803 0.05778 0.05752 0.05727 9.87668 9.87657 9.87646 9.87635 9.87624 11 11 11 11 11 50 49 48 47 46 40 50 17.3 21.7 25 15 16 17 18 19 9.81911 9.81926 9.81940 9.81955 9.81969 15 14 15 14 9.94299 9.94324 9.94350 9.94375 9.94401 25 26 25 26 oc 0.05701 0.05676 0.05650 0.05625 0.65599 9.87613 9.87601 9.87590 9.87579 9.87568 12 11 11 11 45 44 43 42 41 6 7 8 9 10 2.5 2.9 3.3 3.8 4.2 20 21 22 23 24 9.81983 9.81998 9.82012 9.82026 9.82041 15 14 14 15 14 9.94426 9.94452 9.94477 9.94503 9.94528 26 25 26 25 26 0.05574 0.05548 0.05523 0.05497 0.05472 9.87557 9.87546 9.87535 9.87524 9.87513 11 11 11 11 12 40 39 38 37 36 20 30 40 50 8.3 12.5 16.7 20.8 25 26 27 28 29 9.82055 9.82069 9.82084 9.82098 9.82112 14 15 14 14 14 9.94554 9.94579 9.94604 9.94630 9.94655 25 25 26 25 26 0.05446 0.05421 0.05396 0.05370 0.05345 9.87501 9.87490 9.87479 9.87468 9.87457 11 11 11 11 11 35 34 33 32 31 6 7 8 15 1.5 1.8 2.0 30 31 32 33 34 9.82126 9.82141 9.82155 9.82169 9.82184 15 14 14 15 14 9.94681 9.94706 9.94732 5.94757 9.94783 25 26 25 26 25 0.05319 0.05294 0.05268 0.05243 0.05217 9.87446 9.87434 9.87423 9.87412 9.87401 12 11 11 11 11 30 29 28 27 26 10 20 30 40 50 2.5 5.0 7.5 10.0 12.5 35 36 37 38 39 9.82198 9.82212 9.82226 9.82240 9.82255 14 14 14 15 14 9.94808 9.94834 9.94859 9.94884 9.94910 26 25 25 26 25 0.05192 0.05166 0.05141 0.05116 0.05090 9.87390 9.87378 9.87367 9.87356 9.87345 12 11 11 11 U 25 24 23 22 21 6 7 14 1.4 1 6 40 41 42 43 44 9.82269 9.82283 9.82297 9.82311 9.82326 14 14 14 15 14 9.94935 9.94961 9.94986 9.95012 9.95037 26 25 26 25 25 0.05065 0.05039 0.05014 0.04988 0.04963 9.87334 9.87322 9.87311 9.87300 9.87288 12 11 11 12 U 20 19 18 17 16 8 9 10 20 30 1.9 2.1 2.3 4.7 7.0 45 46 47 48 49 9.82340 9.82354 9.82368 9.82382 9.82396 14 14 14 14 14 9.95062 9.95088 9.95113 9.95139 9.95164 26 25 26 25 26 0.04938 0.04912 0.04887 0.04861 0.04836 9.87277 9.87266 9.87255 9.87243 9.87232 11 11 12 11 11 15 14 13 12 11 40 50 9.3 11.7 2 II 50 51 52 53 54 9.82410 9.82424 9.82439 9.82453 9.82467 14 15 14 14 14 9.95190 9.95215 9.95240 9.95266 9.95291 25 25 26 25 26 0.04810 0.04785 0.04760 0.04734 0.04709 9.87221 9.87209 9.87198 9.87187 9.87175 12 11 11 12 11 10 9 8 7 6 6 1 7 ] 8 1 9 3 10 5 .2 1.1 .4 1.3 .6 1.5 .8 1.7 .0 1.8 55 56 57 58 59 9.82481 9.82495 9.82509 9.82523 9.82537 14 14 14 14 14 9.95317 9.95342 9.95368 9.95393 9.95418 25 26 25 25 26 0.04683 0.04658 0.04632 0.04607 0.04582 9.87164 9.87153 9.87141 9.87130 9.87119 11 12 11 11 19 5 4 3 2 1 20 4 30 ( 40 I 50 1C .0 3.7 .0 5.5 .0 7.3 .0 9.2 60 9.82551 9.95444 0.04556 9.87107 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. ' P. 48 534 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 42 / L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. d. P . P. 1 2 3 4 9.82551 9.82565 9.82579 9.82593 9.82607 14 14 14 14 9.95444 9.95469 9.95495 9.95520 9.95545 25 26 25 25 26 0.04556 0.04531 0.04505 0.04480 0.04455 9.87107 9.87096 9.87085 9.87073 9.87062 11 11 12 11 19 60 59 58 57 56 6 7 26 2.6 3 5 6 7 8 9 9.82621 9.82635 9.82649 9.82663 9.82677 14 14 14 14 14 9.95571 9.95596 9.95622 9.95647 9.95672 25 26 25 25 26 0.04429 0.04404 0.04378 0.04353 0.04328 9.87050 9.87039 9.87028 9.87016 9.87005 11 11 12 11 12 55 54 53 52 51 8 9 10 20 30 3.5 3.9 4.3 8.7 13.0 10 11 12 13 14 9.82691 9.82705 9.8C719 9.82733 9.82747 14 14 14 14 14 9.95698 9.95723 9.95748 9.95774 9.95799 25 25 26 25 26 0.04302 0.04277 0.04252 0.04226 0.04201 9.86993 9.86982 9.86970 9.86959 9.86947 11 12 11 12 11 50 49 48 47 46 40 50 17.3 21.7 25 15 16 17 18 19 9.82761 9.82775 9.82788 9.82802 9.82816 14 13 14 14 14 9.95825 9.95850 9.95875 9.95901 9.95926 25 25 26 25 26 0.04175 0.04150 0.04125 0.04099 0.04074 9.86936 9.86924 9.86913 9.86902 9.86890 12 11 11 12 45 44 43 42 41 6 7 8 9 10 2.5 2.9 3.3 3.8 4.2 20 21 22 23 24 9.82830 9.82844 9.82858 9.82872 9.82885 14 14 14 13 14 9.95952 9.95977 9.96002 9.96028 9.96053 25 25 26 25 25 0.04048 0.04023 0.03998 0.03972 0.03947 9.86879 9.86867 9.86855 9.86844 9.86832 12 12 11 12 11 40 39 38 37 36 20 30 40 50 8.3 12.5 16.7 20.8 25 26 27 28 29 9.82899 9.82913 9.82927 9.82941 9.82955 14 14 14 14 13 9.96078 9.96104 9.96129 9.96155 9.96180 26 25 26 25 25 0.03922 0.03896 0.03871 0.03845 0.03820 9.86821 9.86809 9.86798 9.86786 9.86775 12 11 12 11 12 35 34 33 32 31 6 7 8 14 1.4 1.6 1.9 30 31 32 33 34 9.82968 9.82982 9.82996 9.83010 9.83023 14 14 14 13 14 9.96205 9.96231 9.96256 9.96281 9.96307 26 25 25 26 25 0.03795 0.03769 0.03744 0.03719 0.03693 9.86763 9.86752 9.86740 9.86728 9.86717 11 12 12 11 19 30 29 28 27 26 10 20 30 40 50 2.3 4.7 7.0 9.3 11 7 35 36 37 38 39 9.83037 9.83051 9.83065 9.83078 9.83092 14 14 13 14 14 9.96332 9.96357 9.96383 9.96408 9.96433 25 26 25 25 26 0.03668 0.03643 0.03617 0.03592 0.03567 9.86705 9.86694 9.86682 9.86670 9.86659 11 12 12 11 19 25 24 23 22 21 6 13 1.3 1 5 40 41 42 43 44 9.83106 9.83120 9.83133 9.83147 9.83161 14 13 14 14 13 9.96459 9.96484 9.96510 9.96535 9.96560 25 26 25 25 26 0.03541 0.03516 0.03490 0.03465 0.03440 9.86647 9.86635 9.86624 9.86612 9.86600 12 11 12 12 20 19 18 17 16 8 9 10 20 30 1.7 2.0 2.2 4.3 6.5 45 46 47 48 49 9.83174 9.83188 9.83202 9.83215 9.83229 14 14 13 14 13 9.96586 9.96611 9.96636 9.96662 9.96687 25 25 26 25 25 0.03414 0.03389 0.03364 0.03338 0.03313 9.86589 9.86577 9.86565 9.86554 9.86542 12 12 11 12 19 15 14 13 12 11 40 50 8.7 10.8 2 II 50 51 52 53 54 9.83242 9.83256 9.83270 9.83283 9.83297 14 14 13 14 13 9.96712 9.96738 9.96763 9.96788 9.96814 26 25 25 26 25 0.03288 0.03262 0.03237 0.03212 0.03186 9.86530 9.86518 9.86507 9.86495 9.86483 12 11 12 12 10 9 8 7 6 6 7 8 9 10 1.2 1.1 L.4 1.3 L.6 1.5 L.8 1.7 2.0 1.8 55 56 57 58 59 9.83310 9.83324 9.83338 9.83351 9.83365 14 14 13 14 13 9.96839 9.96864 9.96890 9.96915 9.96940 25 26 25 25 26 0.03161 0.03136 0.03110 0.03085 0.03060 9.86472 9.86460 9.86448 9.86436 9.86425 12 12 12 11 12 5 4 3 2 1 20 ' 30 40 50 1 1.0 3.7 3.0 5.5 S.O 7.3 3.0 9.2 60 9.83378 9.96966 0.03034 9.86413 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. 1 P P. LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 43 535 / L. Sin. d. L.Tang. d.c. L. Cotg. L. Cos. d. P P. 1 2 3 4 9.83378 9.83392 9.83405 9.83419 9.83432 14 13 14 13 14 9.96966 9.96991 9.97016 9.97042 9.97067 25 25 26 25 25 0.03034 0.03009 0.02984 0.02958 0.02933 9.86413 9.86401 9.86389 9.86377 9.86366 12 12 12 11 12 60 59 58 57 56 6 7 26 2.6 3 5 6 7 8 9 9.83446 9.83459 9.83473 9.83486 9.83500 13 14 13 14 iq 9.97092 9.97118 9.97143 9.97168 9.97193 26 25 25 25 f)O 0.02908 0.02882 0.02857 0.02832 0.02807 9.86354 9.86342 9.86330 9.86318 9.86306 12 12 12 12 j i 55 54 53 52 51 8 9 10 20 30 3.5 3.9 4.3 8.7 13.0 10 11 12 13 14 9.83513 9.83527 9.83540 9.83554 9.83567 14 13 14 13 -1 A 9.97219 9.97244 9.97269 9.97295 9.97320 25 25 26 25 or: 0.02781 0.02756 0.02731 0.02705 0.02680 9.86295 9.86283 9.86271 9.86259 9.86247 12 12 12 12 12 50 49 48 47 46 40 50 17.3 21.7 25 15 16 17 18 19 9.83581 9.83594 9.83608 9.83621 9.83634 13 14 13 13 14 9.97345 9.97371 9.97396 9.97421 9.97447 26 25 25 26 op: 0.02655 0.02629 0.02604 0.02579 0.02553 9.86235 9.86223 9.86211 9.86200 9.86188 12 12 11 12 12 45 44 43 42 41 6 7 8 9 10 2.5 2.9 3.3 3.8 4.2 20 21 22 23 24 9.83648 9.83661 9.83674 9.83688 9.83701 13 13 14 13 14 9.97472 9.97497 9.97523 9.97548 9.97573 25 26 25 25 OK 0.02528 0.02503 0.02477 0.02452 0.02427 9.86176 9.86164 9.86152 9.86140 9.86128 12 12 12 12 12 40 39 38 37 36 20 30 40 50 8.3 12.5 16.7 20.8 25 26 27 28 29 9.83715 9.83728 9.83741 9.83755 9.83768 13 13 14 13 13 9.97598 9.97624 9.97649 9.97674 9.97700 26 25 25 26 25 0.02402 0.02376 0.02351 0.02326 0.02300 9.86116 9.86104 9.86092 9.86080 9.86068 12 12 12 12 12 35 34 33 32 31 6 7 8 14 1.4 1.6 1.9 30 31 32 33 34 35 36 37 38 39 9.83781 9.83795 9.83808 9.83821 9.83834 "9783848 9.83861 9.83874 9.83887 9.83901 14 13 13 13 14 13 13 13 14 -10 9.97725 9.97750 9.97776 9.97801 9.97826 9.97851 9.97877 9.97902 9.97927 9.97953 25 26 25 25 25 26 25 25 26 9r 0.02275 0.02250 0.02224 0.02199 0.02174 0.02149 0.02123 0.02098 0.02073 0.02047 9.86056 9.86044 9.86032 9.86020 9.86008 9.85996 9.85984 9.85972 9.85960 9.85948 12 12 12 12 12 12 12 12 12 19 30 29 28 27 26 ~25~ 24 23 22 21 10 20 30 40 50 6 n 2.3 4.7 7.0 9.3 11.7 13 1.3 1x 40 41 42 43 44 9.83914 9.83927 9.83940 9.83954 9.83967 13 13 14 13 13 9.97978 9.98003 9.98029 9.98054 9.98079 25 26 25 25 25 0.02022 0.01997 0.01971 0.01946 0.01921 9.85936 9.85924 9.85912 9.85900 9.85888 12 12 12 12 12 20 19 18 17 16 8 9 10 20 30 1.7 2.0 2.2 4.3 6.5 45 46 47 48 49 9.83980 9.83993 9.84006 9.84020 9.84033 13 13 14 13 -ID 9.98104 9.98130 9.98155 9.98180 9.98206 26 25 25 26 oc 0.01896 0.01870 0.01845 0.01820 0.01794 9.85876 9.85864 9.85851 9.85839 9.85827 12 13 12 12 19 15 14 13 12 11 40 50 8.7 10.8 2 II 50 51 52 53 54 9.84046 9.84059 9.84072 9.84085 9.84098 13 13 13 13 14 9.98231 9.98256 9.98281 9.98307 9.98332 25 25 26 25 oc 0.01769 0.01744 0.01719 0.01693 0.01668 9.85815 9.85803 9.85791 9.85779 9.85766 12 12 12 13 12 10 9 8 6 6 7 8 9 10 1.2 1.1 1.4 1.3 1.6 1.5 1.8 1.7 2.0 1.8 55 56 57 58 59 9.84112 9.84125 9.84138 9.84151 9.84164 13 13 13 13 13 9.98357 9.98383 9.98408 9.98433 9.98458 26 25 25 25 9fi 0.01643 0.01617 0.01592 0.01567 0.01542 9.85754 9.85742 9.85730 9.85718 9.85706 12 12 12 12 13 5 4 3 2 1 20 30 40 50 1 4.0 3.7 6.0 5.5 8.0 7.3 0.0 9.2 60 9.84177 9.98484 0.01516 9.85693 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. ' P .P. 46 536 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P .P. 1 2 3 4 9.84177 9.84190 9.84203 9.84216 9.84229 13 13 13 13 iq 9.98484 9.98509 9.98534 9.98560 9.98585 25 25 26 25 OK 0.01516 0.01491 0.01466 0.01440 0.01415 9.85693 9.85681 9.85669 9.85657 9.85645 12 12 12 12 -iq 60 59 58 57 56 6 7 26 2.6 3 5 6 7 8 9 9.84242 9.84255 9.84269 9.84282 9.84295 13 14 13 13 iq 9.98610 9.98635 9.98661 9.98686 9.98711 25 26 25 25 9fi 0.01390 0.01365 0.01339 0.01314 0.01289 9.85632 9.85620 9.85608 9.85596 9.85583 12 12 12 13 19 55 54 53 52 51 8 9 10 20 30 3.5 3.9 4.3 8.7 13.0 10 11 12 13 14 9.84308 9.84321 9.84334 9.84347 9.84360 13 13 13 13 13 9.98737 9.98762 9.98787 9.98812 9.98838 25 25 25 26 25 0.01263 0.01238 0.01213 0.01188 0.01162 9.85571 9.85559 9.85547 9.85534 9.85522 12 12 13 12 12 50 49 48 47 46 40 50 17.3 21.7 25 15 16 17 18 19 9.84373 9.84385 9.84398 9.84411 9.84424 12 13 13 13 13 9.98863 9.98888 9.98913 9.98939 9.98964 25 25 26 25 25 0.01137 0.01112 0.01087 0.01061 0.01036 9.85510 9.85497 9.85485 9.85473 9.85460 13 12 12 13 12 45 44 43 42 41 6 7 8 9 10 2.5 2.9 3.3 3.8 4.2 20 21 22 23 24 9.84437 9.84450 9.84463 9.84476 9.84489 13 13 13 13 13 9.98989 9.99015 9.99040 9.99065 9.99090 26 25 25 25 26 0.01011 0.00985 0.00960 0.00935 0.00910 9.85448 9.85436 9.85423 9.85411 9.85399 12 13 12 12 13 40 39 38 37 36 20 30 40 50 8.3 12.5 16.7 20.8 25 26 27 28 29 9.84502 9.84515 9.84528 9.84540 9.84553 13 13 12 13 -iq 9.99116 9.99141 9.99166 9.99191 9.99217 25 25 25 26 oc 0.00884 0.00859 0.00834 0.00809 0.00783 9.85386 9.85374 9.85361 9.85349 9.85337 12 13 12 12 13 35 34 33 32 31 6 7 8 14 1.4 1.6 1.9 30 31 32 33 34 9.84566 9.84579 9.84592 9.84605 9.84618 13 13 13 13 19 9.99242 9.99267 9.99293 9.99318 9.99343 25 26 25 25 f)K. 0.00758 0.00733 0.00707 0.00682 0.00657 9.85324 9.85312 9.85299 9.85287 9.85274 12 13 12 13 12 30 29 28 27 26 9 10 20 30 40 50 2.3 4.7 7.0 9.3 11.7 35 36 37 38 39 9.84630 9.84643 9.84656 9.84669 9.84682 13 13 13 13 12 9.99368 9.99394 9.99419 9.99444 9.99469 26 25 25 25 26 0.00632 0.00606 0.00581 0.00556 0.00531 9.85262 9.85250 9.85237 9.85225 9.85212 12 13 12 13 12 25 24 23 22 21 6 7 13 1.3 1 5 40 41 42 43 44 9.84694 9.84707 9.84720 9.84733 9.84745 13 13 13 12 iq 9.99495 9.99520 9.99545 9.99570 9.99596 25 25 25 26 25 0.00505 0.00480 0.00455 0.00430 0.00404 9.85200 9.85187 9.85175 9.85162 9.85150 13 12 13 12 13 20 19 18 17 16 8 9 10 20 30 1.7 2.0 2.2 4.3 6.5 45 46 47 48 49 9.84758 9.84771 9.84784 9.84796 9.84809 13 13 12 13 iq 9.99621 9.99646 9.99672 9.99697 9.99722 25 26 25 25 OK 0.00379 0.00354 0.00328 0.00303 0.00278 9.85137 9.85125 9.85112 9.85100 9.85087 12 13 12 13 13 15 14 13 12 11 40 50 8.7 10.8 12 50, 51 52 53 54 9.84822 9.84835 9.84847 9.84860 9.84873 13 12 13 13 12 9.99747 9.99773 9.99798 9.99823 9.99848 26 25 25 25 26 0.00253 0.00227 0.00202 0.00177 0.00152 9.85074 9.85062 9.85049 9.85037 9.85024 12 13 12 13 12 10 9 8 7 6 6 7 8 9 10 1.2 1.4 1.6 1.8 2.0 55 56 57 58 59 9.84885 9.84898 9.84911 9.84923 9.84936 13 13 12 13 13 9.99874 9.99899 9.99924 9.99949 9.99975 25 25 25 26 25 0.00126 0.00101 0.00076 0.00051 0.00025 9.85012 9.84999 9.84986 9.84974 9.84961 13 13 12 13 12 5 4 3 2 1 20 30 40 50 4.0 6.0 8.0 10.0 60 9.84949 0.00000 0.00000 9.84949 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. ' P P. 4.5 TRAVERSE TABLES. 537 ' TRAVERSE TABLES. To use the tables, find the number of degrees in the left-hand column if the angle be less than 45, and in the right-hand column if greater than 45. The numbers on the same line running across the page are the latitudes and departures for that angle and for the respective distances, 1, 2, 3, 4, 5, 6, 7, 8, 9, which appear at the top and bottom of the pages. Thus, if the bearing of a line be 10 and the distance 4, the latitude will be 3.939 and the departure 0.695; with the same bearing, and the distance 8, the latitude will be 7.878 and the departure 1.389. The latitude and departure for 80 is 10 times the latitude and departure for 8, and is found by moving the decimal point one place to the right; that for 500 is 100 times the latitude and departure for 5, and is found by moving the decimal point two places to the right and so on. By moving the decimal point one, two, or more places to the right, the latitude and departure may be found for any multiple of any number given in the table. In finding the latitude and departure for any number such as 453, the number is resolved into three numbers, viz.: 400, 50, 3, and the latitude and departure for each taken from the table and then added together. We thus obtain the following: Rule. Write down the latitude and departure, neglecting the decimal points, for the first figure of the given distance; write under them the latitude and depar- ture for the second figure, setting them one place farther to the right; under these, place the latitude and departure for the third figure, setting them one place still farther to the right, and so continue until all the figures of the given distance have been used; add these latitudes and departures, and point off on the right of their sums a number of decimal places equal to the number of decimal places to which the tables being used are carried; the resulting numbers will be the latitude and departure of the given distance in feet, links, chains, or whatever unit of measure- ment is adopted. EXAMPLE. A bearing is 16 and the distance 725 ft.: what is the latitude and departure? Distances. Latitudes. Departures. 700 6729 1929 20 1923 0551 5 4806 1378 725 6 9 6.9 3 6 1 9 9.7 8 8 Taking the nearest whole numbers and rejecting the decimals, we find the latitude and departure to be 697 and 200. When a occurs in the given number, the next figure must be set two places to the right as in the following example: The bearing is 22 and the distance 907 ft ; required, the latitude and departure. Distances. Latitudes. Departures. 900 8345 3371 7 6490 2622 907 8 4 0.9 9 3 3 9.7 2 2 Here the place of both in the distance column and in the latitude and departure columns is occupied by a dash . Rejecting the decimals, the latitude is 841 ft. and the departure 340 ft. When the bearing is more than 45, the names of the columns must be read from the bottom of the page. The latitude of any bearing, as 60, is the departure of its complement, 30; and the departure of any bearing, as 30, is the latitude of its complement, 60. Where the bearings are given in smaller fractions of degrees than is found in the table, the latitudes and departures can be found by inter- polation. LATITUDES AND DEPARTURES. B 1 2 3 4 5 c | Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 00 i 1.000 0.000 2.000 0.000 3.000 0.000 4.000 0.000 5.000 90 0* 1.000 0.004 2.000 0.009 3.000 0.013 4.000 0.017 5.000 89* 0* 1.000 0.009 2.000 0.017 3.000 0.026 4.000 0.035 5.000 89i 0* 1.000 0.013 2.000 0.026 3.000 0.039 4.000 0.052 5.000 89i 1 1.000 0.017 2.000 0.035 3.000 0.052 3.999 0.070 4.999 89 H 1.000 0.022 2.000 0.044 2.999 0.065 3.999 0.087 4.999 88* If 1.000 0.026 1.999 0.052 2.999 0.079 3.999 0.105 4.998 88i i* 1.000 0.031 1.999 0.061 2.999 0.092 3.998 0.122 4.998 88i 2 0.999 0.035 1.999 0.070 2.998 0.105 3.998 0.140 4.997 88 2i 0.999 0.039 1.998 0.079 2.998 0.118 3.997 0.157 4.996 87* 24 0.999 0.044 1.998 0.087 2.997 0.131 3.996 0.174 4.995 87 2f 0.999 0.048 1.998 0.096 2.997 0.144 3.995 0.192 4.994 87i 3 0.999 0.052 1.997 0.105 2.996 0.157 3.995 0.209 4.993 87 84 0.998 0.057 1.997 0.113 2.995 0.170 3.994 0.227 4.992 86* 8* 0.998 0.061 1.996 0.122 2.994 0.183 3.993 0.244 4.991 86i 3* 0.998 0.065 1.996 0.131 2.994 0.196 3.991 0.262 4.989 86i 4 0.998 0.070 1.995 0.140 2.993 0.209 3.990 0.279 4.988 86 4| 0.997 0.074 1.995 0.148 2.992 0.222 3.989 0.296 4.986 85* i* 0.997 0.078 1.994 0.157 2.991 0.235 3.988 0.314 4.985 85i 4* 0.997 0.083 1.993 0.166 2.990 0.248 3.986 0.331 4.983 85i 5 0.996 0.087 1.992 0.174 2.989 0.261 3.985 0.349 4.981 85 5 0.996 0.092 1.992 0.183 2.987 0.275 3.983 0.366 4.979 84* 5 0.995 0.096 1.991 0.192 2.986 0.288 3.982 0.383 4.977 84^ 5* 0.995 0.100 1.990 0.200 2.985 0.301 3.980 0.401 4.975 84| 6 0.995 0.105 1.989 0.209 2.984 0.314 3.978 0.418 4.973 84 6i 0.994 0.109 1.988 0.218 2.982 0.327 3.976 0.435 4.970 83* 6ft 0.994 0.113 1.987 0.226 2.981 0.340 3.974 0.453 4.968 83i 0.993 0.118 1.986 0.235 2.979 0.353 3.972 0.470 4.965 83i- 7 0.993 0.122 1.985 0.244 2.978 0.366 3.970 0.487 4.963 83 7i 0.992 0.126 1.984 0.252 2.976 0.379 3.968 0.505 4.960 82* 7i 0.991 0.131 1.983 0.261 2.974 0.392 3.966 0.522 4.957 82i 7* 0.991 0.135 1.982 0.270 2.973 0.405 3.963 0.539 4.954 82J 8 0.990 0.139 1.981 0.278 2.971 0.418 3.961 0.557 4.951 82 8i 0.990 0.143 1.979 0.287 2.969 0.430 3.959 0.574 4.948 81* 84 0.989 0.148 1.978 0.296 2.967 0.443 a 956 0.591 4.945 8H 8* 0.988 0.152 1.977 0.304 2.965 0.456 3.953 0.608 4.942 8H 9 0.988 0.156 1.975 0.313 2.963 0.469 3.951 0.626 4.938 81 9i 0.987 0.161 1.974 0.321 2.961 0.482 3.948 0.643 4.935 80* 9i 0.986 0.165 1.973 0.330 2.959 0.495 3.945 0.660 4.931 80i 9| 0.986 0.169 1.971 0.339 2.957 0.508 3.942 0.677 4.928 80i 10 0.985 0.174 1.970 0.347 2.954 0.521 3.939 0.695 4.924 80 w 0.984 0.178 1.968 0.356 2.952 0.534 3.936 0.712 4.920 79* 104 0.983 0.182 1.967 0.364 2.950 0.547 3.933 0.729 4.916 79i 101 0.982 0.187 1.965 0.373 2.947 0.560 3.930 0.746 4.912 m 11 0.982 0.191 1.963 0.382 2.945 0.572 3.927 0.763 4.908 79 1U 0.981 0.195 1.962 0.390 2.942 0.585 3.923 0.780 4.904 78* 114 0.980 0.199 1.960 0.399 2.940 0.598 3.920 0.797 4.900 78i 1U 0.979 0.204 1.958 0.407 2.937 0.611 3.916 0.815 4.895 78i 12 0.978 0.208 1.956 0.416 2.934 0.624 3.913 0.832 4.891 78 12i 0.977 0.212 1.954 0.424 2.932 0.637 3.909 0.849 4.886 77* 12ft 0.976 0.216 1.953 0.433 2.929 0.649 3.905 0.866 4.881 77i 121 0.975 0.221 1.951 0.441 2.926 0.662 3.901 0.883 4.877 77i 13 0.974 0.225 1.949 0.450 2.923 0.675 3.897 0.900 4.872 77 ba Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. ti c. 00 1 2 3 4 5 CO LA TITUDES AND DEPARTURES. 539 ifj 5 6 7 8 9 OJB I 00 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 0.000 6.000 0.000 7.000 0.000 8.000 0.000 9.000 0.000 90 Oi 0.022 6.000 0.026 7.000 0.031 8.000 0.035 9.000 0.039 89* 0.044 6.000 0.052 7.000 0.061 8.000 0.070 9.000 0.079 89 0* 0.065 5.999 0.079 6.999 0.092 7.999 0.105 8.999 0.118 89i 1 0.087 5.999 0.105 6.999 0.122 7.999 0.140 8.999 0.157 89 H 0.109 5.999 0.131 6.998 0.153 7.998 0.175 8.998 0.196 88* U 0.131 5.998 0.157 6.998 0.183 7.997 0.209 8.997 0.236 88? l* 0.153 5.997 0.183 6.997 0.214 7.996 0.244 8.996 0.275 ggi 2 0.174 5.996 0.209 6.996 0.244 7.995 0.279 8.995 0.314 88 Stt 0.196 5.995 0.236 6.995 0.275 7.994 0.314 8.993 0.353 87* 2i 0.218 5.994 0.262 6.993 0.305 7.992 0.349 8.991 0.393 87i 2* 0.240 5.993 0.288 6.992 0.336 7.991 0.384 8.990 0.432 87 3 0.262 5.992 0.314 6.990 0.366 7.989 0.419 8.988 0.471 87 3i 0.283 5.990 0.340 6.989 0.397 7.987 0.454 8.986 0.510 86* si 0.305 5.989 0.366 6.987 0.427 7.985 0.488 8.983 0.549 86i 3* 0.327 5.987 0.392 6.985 0.458 7.983 0.523 8.981 0.589 sei- 4 0.349 5.985 0.419 6.983 0.488 7.981 0.558 8.978 0.628 se 4i 0.371 5.984 0.445 6.981 0.519 7.978 0.593 8.975 0.667 85* 4 0.392 5.982 0.471 6.978 0.549 7.975 0.628 8.972 0.706 85 4* 0.414 5.979 0.497 6.976 0.580 7.973 0.662 8.969 0.745 85i 5 0.436 5.977 0.523 6.973 0.610 7.970 0.697 8.966 1 0.784 85 0.458 5.975 0.549 6.971 0.641 7.966 0.732 8.962 0.824 84* fit 0.479 5.972 0.575 6.968 0.671 7.963 0.767 8.959 0.863 84i 0.501 5.970 0.601 6.965 0.701 7.960 0.802 8.955 0.902 84i 6 0.523 5.967 0.627 6.962 0.732 7.956 0.836 8.951 0.941 84 it 0.544 5.964 0.653 6.958 0.762 7.952 0.871 8.947 0.980 83* 4 0.566 5.961 0.679 6.955 0.792 7.949 0.906 8.942 1.019 83i 6* 0.588 5.958 0.705 6.951 0.823 7.945 0.940 8.938 1.058 83i 7 0.609 5.955 0.731 6.948 0.853 7.940 0.975 8.933 1.097 83 7i 0.631 5.952 0.757 6.944 0.883 7.936 1.010 8.928 1.136 82* 0.653 5.949 0.783 6.940 0.914 7.932 1.044 8.923 1.175 82i 7* 0.674 5.945 0.809 6.936 0.944 7.927 1.079 8.918 1.214 82i 8 0.696 5.942 0.835 6.932 0.974 7.922 1.113 8.912 1.253 82 M 0.717 5.938 0.861 6.928 1.004 7.917 1.148 8.907 1.291 81* 3 0.739 5.934 0.887 6.923 1.035 7.912 1.182 8.901 1.330 814 8* 0.761 5.930 0.913 6.919 1.065 7.907 1.217 8.895 1.369 8H 9 0.782 5.926 0.939 6.914 1.095 7.902 1.251 8.889 1.408 81 0.804 5.922 0.964 6.909 1.125 7.896 1.286 8.883 1.447 80* 9 0.825 5.918 0.990 6.904 1.155 7.890 1.320 8.877 1.485 m 9* 0.847 5.913 1.016 6.899 1.185 7.884 1.355 8.870 1.524 80i 10 0.868 5.909 1.042 6.894 1.216 7.878 1.389 8.863 1.563 80 10i 0.890 5.904 1.068 6.888 1.246 7.872 1.424 8.856 1.601 79* 10| 0.911 5.900 1.093 6.883 1.276 7.866 1.458 8.849 1.640 79 10* 0.933 5.895 1.119 6.877 1.306 7.860 1.492 8.842 1.679 79i 11 0.954 5.890 1.145 6.871 1.336 7.853 1.526 8.835 1.717 79 Hi 0.975 5.885 1.171 6.866 1.366 7.846 1.561 8.827 1.756 78* 1H 0.997 5.880 1.196 6.859 1.396 7.839 1.595 8.819 1.794 78i 111 1.018 5.874 1.222 6.853 1.425 7.832 1.629 8.811 1.833 78i 12 1.040 5.869 1.247 6.847 1.455 7.825 1.663 8.803 1.871 78 12i 1.061 5.863 1.273 6.841 1.485 7.818 1.697 8.795 1.910 77* 124 1.082 5.858 1.299 6.834 1.515 7.810 1.732 8.787 1.948 77i 12* 1.103 5.852 1.324 6.827 1.545 7.803 1.766 8.778 1.986 77i 13 1.125 5.846 1.350 6.821 1.575 7.795 1.800 8.769 2.025 77 t* Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. bi _e= 5 6 7 8 9 540 LATITUDES AND DEPARTURES. bi> 1 2 3 4 5 ab c V 00 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. I CO 13 0.974 0.225 1.949 0.450 2.923 0.675 3.897 0.900 4.872 77 18* 0.973 0.229 1.947 0.458 2.920 0.688 3.894 0.917 4.867 76* IB* 0.972 0.233 1.945 0.467 2.917 0.700 3.889 0.934 4.862 76i 13* 0.971 0.238 1.943 0.475 2.914 0.713 3.885 0.951 4.857 76i 14 0.970 0.242 1.941 0.484 2.911 0.726 3.881 0.968 4.851 76 14* 0.969 0.246 1.938 0.492 2.908 0.738 3.877 0.985 4.846 75* 14* 0.968 0.250 1.936 0.501 2.904 0.751 3.873 1.002 4.841 75i 14* 0.967 0.255 1.934 0.509 2.901 0.764 3.868 1.018 4.835 75i 15 0.966 0,259 1.932 0.518 2.898 0.776 3.864 1.035 4.830 75 15i 0.965 0.263 1.930 0.526 2.894 0.789 3.859 1.052 4.824 74* 15i 0.964 0.267 1.927 0.534 2.891 0.802 3.855 1.069 4.818 74i 15f 0.962 0.271 1.925 0.543 2.887 0.814 3.850 1.086 4.812 74| 16 0.961 0.276 1.923 0.551 2.884 0.827 3.845 1.103 4.806 74 16* 0.960 0.280 1.920 0.560 2.880 0.839 3.840 1.119 4.800 73* 16* 0.959 0.284 1.918 0.568 2.876 0.852 3.835 1.136 4.794 73i 16| 0.958 0.288 1.915 0.576 2.873 0.865 3.830 1.153 4.788 73i 17 0.956 0.292 1.913 0.585 2.869 0.877 3.825 1.169 4.782 73 m 0.955 0.297 1.910 0.593 2.865 0.890 3.820 1.186 4.775 72* in 0.954 0.301 1.907 0.601 2.861 0.902 3.815 1.203 4.769 72i 17* 0.952 0.305 1.905 0.610 2.857 0.915 3.810 1.220 4.762 72i 18 0.951 0.309 1.902 0.618 2.853 0.927 3.804 1.236 4.755 72 18* 0.950 0.313 1.899 0.626 2.849 0.939 3.799 1.253 4.748 71* 18* 0.948 0.317 1.897 0.635 2.845 0.952 3.793 1.269 4.742 7H 18* 0.947 0.321 1.894 0.643 2.841 0.964 3.788 1.286 4.735 71i 19 0.946 0.326 1.891 0.651 2.837 0.977 3.782 1.302 4.728 71 19* 0.944 0.330 1.888 0.659 2.832 0.989 3.776 1.319 4.720 70* W 0.943 0.334 1.885 0.668 2.828 1.001 3.771 1.335 4.713 70i 19* 0.941 0.338 1.882 0.676 2.824 1.014 3.765 1.352 4.706 70 20 0.940 0.342 1.879 0.684 2.819 1.026 3.759 1.368 4.698 70 20* 0.938 0.346 1.876 0.692 2.815 1.038 3.753 1.384 4.691 69* 20i 0.937 0.350 1.873 0.700 2.810 1.051 3.747 1.401 4.683 69i 20* 0.935 0.354 1.870 0.709 2.805 1.063 3.741 1.417 4.676 69i 21 0.934 0.358 1.867 0.717 2.801 1.075 3.734 1.433 4.668 69 2H 0.932 0.362 1.864 0.725 2.796 1.087 3.728 1.450 4.660 68* 2H 0.930 0.367 1.861 0.733 2.791 1.100 3.722 1.466 4.652 68i 21* 0.929 0.371 1.858 0.741 2.786 1.112 3.715 1.482 4.644 68i 22 0.927 0.375 1.854 0.749 2.782 1.124 3.709 1.498 4.636 68 22i 0.926 0.379 1.851 0.757 2.777 1.136 3.702 1.515 4.628 67* 22* 0.924 0.383 1.848 0.765 2.772 1.148 3.696 1.531 4.619 67i 22* 0.922 0.387 1.844 0.773 2.767 1.160 3.689 1.547 4.611 67i 23 0.921 0.391 1.841 0.781 2.762 1.172 3.682 1.563 4.603 67 23 0.919 0.395 1.838 0.789 2.756 1.184 3.675 1.579 4.594 66* 23 0.917 0.399 1.834 0.797 2.751 1.196 3.668 1.595 4.585 66J- 23* 0.915 0.403 1.831 0.805 2.746 1.208 3.661 1.611 4.577 66i 24. 0.914 0.407 1.827 0.813 2.741 1.220 3.654 1.627 4.568 66 24i 0.912 0.411 1.824 0.821 2.735 1.232 3.647 1.643 4.559 65* 24 0.910 0.415 1.820 0.829 2.730 1.244 3.640 1.659 4.550 65i 24* 0.908 0.419 1.816 0.837 2.724 1.256 3.633 1.675 4.541 65i 25 0.906 0.423 1.813 0.845 2.719 1.268 3.625 1.690 4.532 65 25i 0.904 0.427 1.809 0.853 2.713 1.280 3.618 1.706 4.522 64* 25* 0.903 0.431 1.805 0.861 2.708 1.292 3.610 1.722 4.513 64i 25* 0.901 0.434 1.801 0.869 2.702 1.303 3.603 1.738 4.503 64i 26 0.899 0.438 1,798 0.877 2.696 1.315 3.595 1.753 4.494 64 bo c 'Z Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. bo CD 1 2 3 4 5 1 LATITUDES AND DEPARTURES. 541 bib 5 6 7 8 9 bo c I 00 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. CO CD 13 1.125. 5.846 1.350 6.821 1.575 7.795 1.800 8.769 2.025 77 13i 1.146 5.840 1.375 6.814 1.604 7.787 1.834 8.760 2.063 76* 13i 1.167 5.834 1.401 6.807 1.634 7.779 1.868 8.751 2.101 76i 13* 1.188 5.828 1.426 6.799 1.664 7.771 1.902 8.742 2.139 76i 14 1.210 5.822 1.452 6.792 1.693 7.762 1.935 8.733 2.177 76 14i 1.231 5.815 1.477 6.785 1.723 7.754 1.969 8.723 2.215 75* i4 1.252 5.809 1.502 6.777 1.753 7.745 2.003 8.713 2.253 75i 14| 1.273 5.802 1.528 6.769 1.782 7.736 2.037 8.703 2.291 75i 15 1.294 5.796 1.553 6.761 1.812 7.727 2.071 8.693 2.329 75 15i 1.315 5.789 1.578 6.754 1.841 7.718 2.104 8.683 2.367 74* 15i 1.336 5.782 1.603 6.745 1.871 7.709 2.138 8.673 2.405 74i m 1.357 5.775 1.629 6.737 1.900 7.700 2.172 8.662 2.443 74| 16 1.378 5.768 1.654 6.729 1.929 7.690 2.205 8.651 2.481 74 16i 1.399 5.760 1.679 6.720 1.959 7.680 2.239 8.640 2.518 73* m 1.420 5.753 1.704 6.712 1.988 7.671 2.272 8.629 2.556 73i 16* 1.441 5.745 1.729 6.703 2.017 7.661 2.306 8.618 2.594 73| 17 1.462 5.738 1.754 6.694 2.047 7.650 2.339 8.607 2.631 73 17i 1.483 5.730 1.779 6.685 2.076 7.640 2.372 8.595 2.669 72* 17i 1.504 5.722 1.804 6.676 2.105 7.630 2.406 8.583 2.706 72i 17* 1.524 5.714 1.829 6.667 2.134 7.619 2.439 8.572 2.744 72i 18 1.545 5.706 1.854 6.657 2.163 7.608 2.472 8.560 2.781 72 18* 1.566 5.698 1.879 6.648 2.192 7.598 2.505. 8.547 2.818 71* IB* 1.587 5.690 1.904 6.638 2.221 7.587 2.538 8.535 2.856 71* 18* 1.607 5.682 1.929 6.629 2.250 7.575 2.572 8.522 2.893 71* 19 1.628 5.673 1.953 6.619 2.279 7.564 2.605 8.510 2.930 71 19i 1.648 5.665 1.978 6.609 2.308 7.553 2.638 8.497 2.967 70* 191 1.669 5.656 2.003 6.598 2.337 7.541 2.670 8.484 3.004 70i 19* 1.690 5.647 2.028 6.588 2.365 7.529 2.703 8.471 3.041 70i 20 1.710 5.638 2.052 6.578 2.394 7.518 2.736 8.457 3.078 70 20i 1.731 5.629 2.077 6.567 2.423 7.506 2.769 8.444 3.115 69* 20i 1.751 5.620 2.101 6.557 2.451 7.493 2.802 8.430 3.152 69i 20* 1.771 5.611 2.126 6.546 2.480 7.481 2.834 8.416 3.189 69i 21 1.792 5.601 2.150 6.535 2.509 7.469 2.867 8.402 3.225 69 21i 1.812 5.592 2.175 6.524 2.537 7.456 2.900 8.388 3.262 68* a* 1.833 5.582 2.199 6.513 2.566 7.443 2.932 8.374 3.299 68i 21* 1.853 5.573 2.223 6.502 2.594 7.430 2.964 8.359 3.335 68i 22 1.873 5.563 2.248 6.490 2.622 7.417 2.997 8.345 3.371 68 22i 1.893 5.553 2.272 6.479 2.651 7.404 3.029 8.330 3.408 67* 22i 1.913 5.543 2.296 6.467 2.679 7.391 3.061 8.315 3.444 67i 22* 1.934 5.533 2.320 6.455 2.707 7.378 3.094 8.300 3.480 67i 23 1.954 5.523 2.344 6.444 2.735 7.364 3.126 8.285 3.517 67 23i 1.974 5.513 2.368 6.432 2.763 7.350 3.158 8.269 3.553 66* 23i 1.994 5.502 2.392 6.419 2.791 7.336 3.190 8.254 3.589 66| 23* 2.014 5.492 2.416 6.407 2.819 7.322 3.222 8.238 3.625 66i 24 2.034 5.481 2.440 6.395 2.847 7.308 3.254 8.222 3.661 66 24i 2.054 5.471 2.464 6.382 2.875 7.294 3.286 8.206 3.696 65* 24i 2.073 5.460 2.488 6.370 2.903 7.280 3.318 8.190 3.732 65i 24* 2.093 5.449 2.512 6.357 2.931 7.265 3.349 8.173 3.768 65i 25 2.113 5.438 2.536 6.344 2.958 7.250 3.381 8.157 3.804 65 25i 2.133 5.427 2.559 6.331 2.986 7.236 3.413 8.140 3.839 64* 25 2.153 5.416 2.583 6.318 3.014 7.221 3.444 8.123 3.875 64 25* 2.172 5.404 2.607 6.305 3.041 7.206 3.476 8.106 3.910 64| 26 2.192 5.393 2.630 6.292 3.069 7.190 3.507 8.089 3.945 64 bib c Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. b0 s 5 6 7 8 9 to CO 542 LATITUDES AND DEPARTURES. 00 c 1 2 : \ i I 5 .E I CD Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 26 0.899 0.438 1.798 0.877 2.696 1.315 3.595, 1.753 4.494 64 26 0.897 0.442 1.794 0.885 2.691 1.327 3.587 1.769 4.484 63* 26 0.895 0.446 1.790 0.892 2.685 1.339 3.580 1.785 4.475 63i 26* 0.893 0.450 1.786 0.900 2.679 1.350 3.572 1.800 4.465 63i 27 0.891 0.454 1.782 0.908 2.673 1.362 3.564 1.816 4.455 63 27i 0.889 0.458 1.778 0.916 2.667 1.374 3.556 1.831 4.445 62* 27i 0.887 0.462 1.774 0.923 2.661 1.385 3.548 1.847 4.435 62i 27* 0.885 0.466 1.770 0.931 2.655 1.397 3.540 1.862 4.425 62| 28 0.883 0.469 1.766 0.939 2.649 1.408 3.532 1.878 4.415 62 28i 0.881 0.473 1.762 0.947 2.643 1.420 3.524 1.893 4.404 61* 28i 0.879 0.477 1.758 0.954 2.636 1.431 3.515 1.909 4.394 6H 28* 0.877 0.481 1.753 0.962 2.630 1.443 3.507 1.924 4.384 61i 29 0.875 0.485 1.749 0.970 2.624 1.454 3.498 1.939 4.373 61 29i 0.872 0.489 1.745 0.977 2.617 1.466 3.490 1.954 4.362 60* 29i 0.870 0.492 1.741 0.985 2.611 1.477 3.481 1.970 4.352 60 a L 29* 0.868 0.496 1.736 0.992 2.605 1.489 3.473 1.985 4.341 60i 30 0.866 0.500 1.732 1.000 2.598 1.500 3.464 2.000 4.330 60 30i 0.864 0.504 1.728 1.008 2.592 1.511 3.455 2.015 4.319 59* 30i 0.862 0.508 1.723 1.015 2.585 1.523 3.447 2.030 4.308 59i 30* 0.859 0.511 1.719 1.023 2.578 1.534 3.438 2.045 4.297 59| 31 0.857 0.515 1.714 1.030 2.572 1.545 3.429 2.060 4.286 59 3H 0.855 0.519 1.710 1.038 2.565 1.556 3.420 2.075 4.275 58* 31* 0.853 0.522 1.705 1.045 2.558 1.567 3.411 2.090 4.263 58i 31* 0.850 0.526 1.701 1.052 2.551 1.579 3.401 2.105 4.252 58i 32 0.848 0.530 1.696 1.060 2.544 1.590 3.392 2.120 4.240 58 32i 0.846 0.534 1.691 1.067 2.537 1.601 3.383 2.134 4.229 57* 32 0.843 0.537 1.687 1.075 2.530 1.612 3.374 2.149 4.217 57i 32* 0.841 0.541 1.682 1.082 2.523 1.623 3.364 2.164 4.205 57i 33 0.839 0.545 1.677 1.089 2.516 1.634 3.355 2.179 4.193 57 33i 0.836 0.548 1.673 1.097 2.509 1.645 3.345 2.193 4.181 56* 33i 0.834 0.552 1.668 1.104 2.502 1.656 3.336 2.208 4.169 56i 33* 0.831 0.556 1.663 1.111 2.494 1.667 3.326 2.222 4.157 56i 34 0.829 0.559 1.658 1.118 2.487 1.678 3.316 2.237 4.145 56 34i 0.827 0.563 1.653 1.126 2.480 1.688 3.306 2.251 4.133 55* 34i 0.824 0.566 1.648 1.133 2.472 1.699 3.297 2.266 4.121 55 34* 0.822 0.570 1.643 1.140 2.465 1.710 3.287 2.280 4.108 55i 35 0.819 0.574 1.638 1.147 2.457 1.721 3.277 2.294 4.096 55 35i 0.817 0.577 1.633 1.154 2.450 1.731 3.267 2.309 4.083 54* 35i 0.814 0.581 1.628 1.161 2.442 1.742 3.257 2.323 4.071 54^ 35* 0.812 0.584 1.623 1.168 2.435 1.753 3.246 2.337 4.058 54i 36 0.809 0.588 1.618 1.176 2.427 1.763 3.236 2.351 4.045 54 36i 0.806 0.591 1.613 1.183 2.419 1.774 3.226 2.365 4.032 53* 36i 0.804 0.595 1.608 1.190 2.412 1.784 3.215 2.379 4.019 53i 36* 0.801 0.598 1.603 1.197 2.404 1.795 3.205 2.393 4.006 53* 37 0.799 0.602 1.597 1.204 2.396 1.805 3.195 2.407 3.993 53 37i 0.796 0.605 1.592 1.211 2388 1.816 3.184 2.421 3.980 52* 37i 0.793 0.609 1.587 1.218 2.380 1.826 3.173 2.435 3.967 52i 37* 0.791 0.612 1.581 1.224 2.372 1.837 3.163 2.449 3.953 52i 38 0.788 0.616 1.576 1.231 2.364 1.847 3.152 2.463 3.940 52 38i 0.785 0.619 1.571 1.238 2.356 1.857 3.141 2.476 3.927 51* 38i 0.783 0.623 1.565 1.245 2.348 1.868 3.130 2.490 3.913 5H 38* 0.780 0.626 1.560 1.252 2.340 1.878 3.120 2.504 3.899 5H 39 0.777 0.629 1.554 1.259 2.331 1.888 3.109 2.517 3.886 51 tZ c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. .S 00 1 I J t * 5 1 LATITUDES AND DEPARTURES. 543 b0 c 5 6 7 8 9 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 26 2.192 5.393 2.630 6.292 3.069 7.190 3.507 8.089 3.945 64 26i 2.211 5.381 2.654 6.278 3.096 7.175 3.538 8.072 3.981 63* 261 2.231 5.370 2.677 6.265 3.123 7.160 3.570 8.054 4.016 631 26* 2.250 5.358 2.701 6.251 3.151 7.144 3.601 8.037 4.051 63i 27 2.270 5.346 2.724 6.237 3.178 7.128 3.632 8.019 4.086 63 27i 2.289 5.334 2.747 6.223 3.205 7.112 3.663 8.001 4.121 62* 271 2.309 5.322 2.770 6.209 3.232 7.096 3.694 7.983 4.156 621 27* 2.328 5.310 2.794 6.195 3.259 7.080 3.725 7.965 4.190 62i 28 2.347 5.298 2.817 6.181 3.286 7.064 3.756 7.947 4.225 62 28i 2.367 5.285 2.840 6.166 3.313 7.047 3.787 7.928 4.260 61* 281 2.386 5.273 2.863 6.152 3.340 7.031 3.817 7.909 4.294 611 28* 2.405 5.260 2.886 6.137 3.367 7.014 3.848 7.891 4.329 6H 29 2.424 5.248 2.909 6.122 3.394 6.997 3.878 7.872 4.363 61 29i 2.443 5.235 2.932 6.107 3.420 6.980 3.909 7.852 4.398 60* 291 2.462 5.222 2.955 6.093 3.447 6.963 3.939 7.833 4.432 601 29* 2.481 5.209 2.977 6.077 3.474 6.946 3.970 7.814 4.466 60i 30 2.500 5.196 3.000 6.062 3.500 6.928 4.000 7.794 4.500 60 30 2.519 5.183 3.023 6.047 3.526 6.911 4.030 7.775 4.534 59* 301 2.538 5.170 3.045 6.031 3.553 6.893 4.060 7.755 4.568 30* 2.556 5.156 3.068 6.016 3.579 6.875 4.090 7.735 4.602 59-J- 31 2.575 5.143 3.090 6.000 3.605 6.857 4.120 7.715 4.635 59 3H 2.594 5.129 3.113 5.984 3.631 6.839 4.150 7.694 4.669 58* 311 2.612 5.116 3.135 5.968 3.657 6.821 4.180 7.674 4.702 581 31* 2.631 5.102 3.157 5.952 3.683 6.803 4.210 7.653 4.736 58| 32 2.650 5.088 3.180 5.936 3.709 6.784 4.239 7.632 4.769 58 32i 2.668 5.074 3.202 5.920 3.735 6.766 4.269 7.612 4.802 57* 321 2.686 5.060 3.224 5.904 3.761 6.747 4.298 7.591 4.836 571 32* 2.705 5.046 3.246 5.887 3.787 6.728 4.328 7.569 4.869 57i- 33 2.723 5.032 3.268 5.871 3.812 6.709 4.357 7.548 4.902 57 33i 2.741 5.018 3.290 5.854 3.838 6.690 4.386 7.527 4.935 56* 331 2.760 5.003 3.312 5.837 3.864 6.671 4.416 7.505 4.967 561 33* 2.778 4.989 3.333 5.820 3.889 6.652 4.445 7.483 5.000 56i 34 2.796 4.974 3.355 5.803 3.914 6.632 4.474 7.461 5.033 56 34i 2.814 4.960 3.377 5.786 3.940 6.613 4.502 7.439 5.065 55* 341 2.832 4.945 3.398 5.769 3.965 6.593 4.531 7.417 5.098 551 34* 2.850 4.930 3.420 5.752 3.990 6.573 4.560 7.395 5.130 55i 35 2.868 4.915 3.441 5.734 4.015 6.553 4.589 7.372 5.162 55 35i 2.886 4.900 3.463 5.716 4.040 6.533 4.617 7.350 5.194 54* 351 2.904 4.885 3.484 5.699 4.065 6.513 4.646 7.327 5.226 541 35* 2.921 4.869 3.505 5.681 4.090 6.493 4.674 7.304 5.258 54i 36 2.939 4.854 3.527 5.663 4.115 6.472 4.702 7.281 5.290 54 36i 2.957 4.839 3.548 5.645 4.139 6.452 4.730 7.258 5.322 53* 361 2.974 4.823 3.569 5.627 4.164 6.431 4.759 7.235 5.353 36* 2.992 4.808 3.590 5.609 4.188 6.410 4.787 7.211 5.385 53 37 3.009 4.792 3.611 5.590 4.213 6.389 4.815 7.188 5.416 53 37* 3.026 4.776 3.632 5.572 4.237 6.368 4.842 7.164 5.448 52* 371 3.044 4.760 3.653 5.554 4.261 6.347 4.870 7.140 5.479 521 37* 3.061 4.744 3.673 5.535 4.286 6.326 4.898 7.116 5.510 52| 38 3.078 4.728 3.694 5.516 4.310 6.304 4.925 7.092 5.541 52 38i 3.095 4.712 3.715 5.497 4.334 6.283 4.953 7.068 5.572 51* 381 3.113 4.696 3.735 5.478 4.358 6.261 4.980 7.043 5.603 511 38* 3.130 4.679 3.756 5.459 4.381 6.239 5.007 7.019 5.633 5ll 39 3.147 4.663 3.776 5.440 4.405 6.217 5.035 6.994 5.664 51 g Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. c co CD 5 6 7 8 9 CO 544 LATITUDES AND DEPARTURES. u> 1 2 3 4 5 M 00 39 3.147 4.663 3.776 5.440 4.405 6.217 5.035 6.994 5.664 51 39i 3.164 4.646 3.796 5.421 4.429 6.195 5.062 6.970 5.694 50? 39i 3.180 4.630 3.816 5.401 4.453 6.173 5.089 6.945 5.725 50 39| 3.197 4.613 3.837 5.382 4.476 6.151 5.116 6.920 5.755 50i 40 3.214 4.596 3.857 5.362 4.500 6.128 5.142 6.894 5.785 50 40i 3.231 4.579 3.877 5.343 4.523 6.106 5.169 6.869 5.815 49? 40i 3.247 4.562 3.897 5.323 4.546 6.083 5.196 6.844 5.845 49i 40? 3.264 4.545 3.917 5.303 4.569 6.061 5.222 6.818 5.875 49i 4,0 3.280 4.528 3.936 5.283 4.592 6.038 5.248 6.792 5.905 49 4H 3.297 4.511 3.956 5.263 4.615 6.015 5.275 6.767 5.934 48? 41* 3.313 4.494 3.976 5.243 4.638 5.992 5.301 6.741 5.964 48i 41? 3.329 4.476 3.995 5.222 4.661 5.968 5.327 6.715 5.993 48i 42 3.346 4.459 4.015 5.202 4.684 5.945 5.353 6.688 6.022 48 42i 3.362 4.441 4.034 5.182 4.707 5.922 5.379 6.662 6.051 47? 42| 3.378 4.424 4.054 5.161 4.729 5.898 5.405 6.635 6.080 47i 42? 3.394 4.406 4.073 5.140 4.752 5.875 5.430 6.609 6.109 47i 43 3.410 4.388 4.092 5.119 4.774 5.851 5.456 6.582 6.138 47 43| 3.426 4.370 4.111 5.099 4.796 5.827 5.481 6.555 6.167 46? 43i 3.442 4.352 4.130 5.078 4.818 5.803 5.507 6.528 6.195 46i 43? 3.458 4.334 4.149 5.057 4.841 5.779 5.532 6.501 6.224 46i 44 3.473 4.316 4.168 5.035 4.863 5.755 5.557 6.474 6.252 46 44i 3.489 4.298 4.187 5.014 4.885 5.730 5.582 6.447 6.280 45? 44i 3.505 4.280 4.206 4.993 4.906 5.706 5.607 6.419 6.308 45i 44? 3.520 4.261 4.224 4.971 4.928 5.681 5.632 6.392 6.336 45i 45 3.536 4.243 4.243 4.950 4.950 5.657 5.657 6.364 6.364 45 Bear- ing. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Bear- ing. CIRCUMFERENCES, AND AREAS. 545 SQUARES, CUBES, SQUARE AND CUBE ROOTS, CIRCUMFERENCES, AND AREAS. No. Square. Cube. Sq. Root Cu. Root Reciprocal. Circum. Area. 1 1 1 1.0000 1.0000 .100000000 3.1416 0.7854 2 4 8 1.4142 1.2599 .500000000 6.2832 3.1416 3 9 27 1.7321 1.4422 .333333333 9.4248 7.0686 4 16 64 2.0000 1.5874 .250000000 12.5664 12.5664 5 25 125 2.2361 1.7100 .200000000 15.7080 19.635 6 36 216 2.4495 1.8171 .166666667 18.850 28.274 7 49 343 2.6458 1.9129 .142857143 21.991 38.485 8 64 512 2.8284 2.0000 .125000000 25.133 50.266 9 81 729 3.0000 2.0801 .111111111 28.274 63.617 10 100 1,000 3.1623 2.1544 .100000000 31.416 78.540 11 121 1,331 3.3166 2.2240 .090909091 34.558 95.033 12 144 1,728 3.4641 2.2894 .083333333 37,699 113.10 13 169 2,197 3.6056 2.3513 .076923077 40.841 132.73 14 196 2,744 3.7417 2.4101 .071428571 43.982 153.94 15 225 3,375 3.8730 2.4662 .066666667 47.124 176.71 16 256 4,096 4.0000 2.5198 .062500000 50.265 201.06 17 289 4,913 4.1231 2.5713 .058823529 53.407 226.98 18 324 5,832 4.2426 2.6207 .055555556 56.549 254.47 19 361 6,859 4.3589 2.6684 .052631579 59.690 283.53 20 400 8,000 4.4721 2.7144 .050000000 62.832 314.16 21 441 9,261 4.5826 2.7589 .047619048 65.973 346.36 22 484 10,648 4.6904 2.8020 .045454545 69.115 380.13 23 529 12,167 4.7958 2.8439 .043478261 72.257 415.48 24 576 13,824 4.8990 2.8845 .041666667 75.398 452.39 25 625 15,625 5.0000 2.9240 .040000000 78.540 490.87 26 676 17,576 5.0990 2.9625 .038461538 81.681 530.93 27 729 19,683 5.1962 3.0000 .037037037 84.823 572.56 28 784 21,952 5.2915 3.0366 .035714286 87.965 615.75 29 841 24,389 5.3852 3.0723 .034482759 91.106 660.52 30 900 27,000 5.4772 3.1072 .033333333 94.248 706.86 31 961 29,791 5.5678 3.1414 .032258065 97.389 754.77 32 1,024 32,768 5.6569 3.1748 .031250000 100.53 804.25 33 1,089 35,937 5.7446 3.2075 .030303030 103.67 855.30 34 1,156 39,304 5.8310 3.2396 .029411765 106.81 907.92 35 1,225 42,875 5.9161 3.2717 .028571429 109.96 962.11 36 1,296 46,656 6.0000 3.3019 .027777778 113.10 1,017.88 37 1,369 50,653 6.0828 3.3322 .027027027 116.24 1,075.21 38 1,444 54,872 6.1644 3.3620 .026315789 119.38 1,134.11 39 1,521 59,319 6.2450 3.3912 .025641026 122.52 1,194.59 40 1,600 64,000 6.3246 3.4200 .025000000 125.66 1,256.64 41 1,681 68,921 6.4031 3.4482 .024390244 128.81 1,320.25 42 1,764 74,088 6.4807 3.4760 .023809524 131.95 1,385.44 43 1,849 79,507 6.5574 3.5034 .023255814 135.09 1,452.20 44 1,936 85,184 6.6332 3.5303 .022727273 138.23 1,520.53 45 2,025 91,125 6.7082 3.5569 .022222222 141.37 1,590.43 46 2,116 97,336 6.7823 3.5830 .021739130 144.51 1,661.90 47 2,209 103,823 6.8557 3.6088 .021276600 147.65 1,734.94 48 2,304 110,592 6.9282 3.6342 .020833333 150.80 1,809.56 49 2,401 117,649 7.0000 3.6593 .020408163 153.94 1,885.74 50 2,500 125,000 7.0711 3.6840 .020000000 157.08 1,963.50 51 2,601 132,651 7.1414 3.7084 .019607843 160.22 2,042.82 52 2,704 140,608 7.2111 3.7325 .019230769 163.36 2,123.72 53 2,809 148,877 7.2801 3.7563 .018867925 66.50 2,206.18 54 2,916 157,464 7.3485 3.7798 .018518519 69.65 2,290.22 55 3,025 166,375 7.4162 3.8030 .018181818 72.79 2,375.83 546 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. i Sq. Root Cu. Root Reciprocal. Circum. Area. 56 3,136 175,616 7.4833 3.8259 .017857143 175.93 2,463.01 57 3,249 185,193 7.5498 3.8485 .017543860 179.07 2,551.76 58 3,364 195,112 7.6158 3.8709 .017241379 182.21 2,642.08 59 3,481 205,379 7.6811 3.8930 .016949153 185.35 2,733.97 60 3,600 216,000 7.7460 3.9149 .016666667 188.50 2,827.43 61 3,721 226,981 7.8102 3.9365 .016393443 191.64 2,922.47 62 3,844 238,328 7.8740 3.9579 .016129032 194.78 3,019.07 63 3,969 250,047 7.9373 3.9791 .015873016 197.92 3,117.25 64 4,096 262,144 8.0000 4.0000 .015625000 201.06 3,216.99 65 4,225 274,625 8.0623 4.0207 .015384615 204.20 3,318.31 66 4,356 287,496 8.1240 4.0412 .015151515 207.34 3,421.19 67 4,489 300,763 8.1854 4.0615 .014925373 210.49 3,525.65 68 4,624 314,432 8.2462 4.0817 .014705882 213.63 3,631.68 69 4,761 328,509 8.3066 4.1016 .014492754 216.77 3,739.28 70 4,900 343,000 8.3666 4.1213 .014285714 219.91 3,848.45 71 5,041 357,911 8.4261 4.1408 .014084517 223.05 3,959.19 72 5,184 373,248 8.4853 4.1602 .013888889 226.19 4,071.50 73 5,329 389,017 8.5440 4.1793 .013698630 229.34 4,185.39 74 5,476 405,224 8.6023 4.1983 .013513514 232.48 4,300.84 75 5,625 421,875 8.6603 4.2172 .013333333 235.62 4,417.86 76 5,776 438,976 8.7178 4.2358 .013157895 238.76 4,536.46 77 5,929 456,533 8.7750 4.2543 .012987013 241.90 4,656.63 78 6,084 474,552 8.8318 4.2727 .012820513 245.04 4,778.36 79 6,241 493,039 8.8882 4.2908 .012658228 248.19 4,901.67 80 6,400 512,000 8.9443 4.3089 .012500000 251.33 5,026.55 81 6,561 531,441 9.0000 4.3267 .012345679 254.47 5,153.00 82 6,724 551,368 9.0554 4.3445 .012195122 257.61 5.281.02 83 6,889 571,787 9.1104 4.3621 .012048193 260.75 5,410.61 84 7,056 592,704 9.1652 4.3795 .011904762 263.89 5,541.77 85 7,225 614,125 9.2195 4.3968 .011764706 267.04 5,674.50 86 7,396 636,056 9.2736 4.4140 .011627907 270.18 5,808.80 87 7,569 658,503 9.3274 4.4310 .0114942-53 273.32 5,944.68 88 7,744 681,472 9.3808 4.4480 .011363636 276.46 6,082.12 89 7,921 704,969 9.4340 4.4647 .011235955 279.60 6,221.14 90 8,100 729,000 9.4868 4.4814 .011111111 282.74 6,361.73 91 8,281 753,571 9.5394 4.4979 .010989011 285.88 6,503.88 92 8,464 778,688 9.5917 4.5144 .010869565 289.03 6,647.61 93 8,649 804,357 9.6437 4.5307 .010752688 292.17 6,792.91 94 8,836 830,584 9.6954 4.5468 .010638298 295.31 6,939.78 95 9,025 857,375 9.7468 4.5629 .010526316 298.45 7,088.22 96 9,216 884,736 9.7980 4.5789 .410416667 301.59 7,238.23 97 9,409 912,673 9.8489 4.5947 .010309278 304.73 7,389.81 98 9,604 941,192 9.8995 4.6104 .010204082 307.88 7,542.96 99 9,801 970,299 9.9499 4.6261 .010101010 311.02 7,697.69 100 10,000 1,000,000 10.0000 4.6416 .010000000 314.16 7,853.98 101 10,201 1,030,301 10.0499 4.6570 .009900990 317.30 8,011.85 102 10,404 1,061,208 10.0995 4.6723 .009803922 320.44 8,171.28 103 10,609 1,092,727 10.1489 4.6875 .009708738 323.58 8,332.29 104 10,816 1,124,864 10.1980 4.7027 .009615385 326.73 8,494.87 105 11,025 1,157,625 10.2470 4.7177 .009523810 329.87 8,659.01 106 11,236 1,191,016 10.2956 4.7326 .009433962 333.01 8,824.73 107 11,449 1,225,043 10.3441 4.7475 .009345794 336.15 8,992.02 108 11,664 1,259,712 10.3923 4.7622 .009259259 339.29 9,160.88 109 11,881 1,295,029 10.4403 4.7769 .009174312 342.43 9,331.32 110 12,100 1,331,000 10.4881 4.7914 .009090909 345.58 9,503.32 111 12,321 1,367,631 10.5357 4.8059 .009009009 348.72 9,676.89 112 12,544 1,404,928 10.5830 4.8203 .008928571 351.86 9.&52.03 113 12,769 1,442,897 10.6301 4.8346 .008849558 355.00 10,028.75 114 12,996 1,481,544 10.6771 4.8488 .008771930 358.14 10,207.03 115 13,225 1,520,875 10.7238 4.8629 .008695652 361.28 10,386.89 116 13,456 1,560,896 10.7703 4.8770 .008020690 364.42 10,568.32 117 13,689 1,601,613 10.8167 4.8910 .008547009 367.57 10,751.32 118 13,924 1,643,032 ! 10.8628 4.9049 .008474576 370.71 10,935.88 CIRCUMFERENCES, AND AREAS. 547 No. Square. Cube. Sq. Root Cu. Root. Reciprocal. Circum. Area. 119 14,161 1,685,159 10.9087 4.9187 .008403361 373.85 11,122.02 120 14,400 1,728,000 10.9545 4.9324 .008333333 376.99 11,309.73 121 14,641 1,771,561 11.0000 4.9461 .008264463 380.13 11,499.01 122 14,834 1,815,848 11.0454 4.9597 .008196721 383.27 11,689.87 123 15,129 1,860,867 11.0905 4.9732 .008130081 386.42 11,882.29 124 15,376 1,906,624 11.1355 4.9866 .008064516 389.56 12,076.28 125 15,625 1,953,125 11.1803 5.0000 .008000000 392.70 12,271.85 126 15,876 2,000,376 11.2250 5.0133 .007936508 395.84 12,468.98 127 16,129 2,048,383 11.2694 5.0265 .007874016 398.98 12,667.69 128 16,384 2,097,152 11.3137 5.0397 .007812500 402.12 12,867.96 129 16,641 2,146,689 11.3578 i 5.0528 .007751938 405.27 13,069.81 130 16,900 2,197,000 11.4018 1 5.0658 .007692308 408.41 13,273.23 131 17,161 2,248,091 11.4455 5.0788 .007633588 ! 411.55 13,478.22 132 17,424 2,299,968 11.4891 5.0916 .007575758 i 414.69 13,684.78 133 17,689 2,352,637 11.5326 5.1045 .007518797 417.83 13,892.91 134 17,956 2,406,104 11.5758 5.1172 .007462687 420.97 14,102.61 135 18,225 2,460,375 11.6190 5.1299 .007407407 424.12 14,313.88 136 18,496 2,515,456 11.6619 5.1426 .007352941 427.26 14,526.72 137 18,769 2,571,353 11.7047 5.1551 .007299270 430.40 14,741.14 138 19,044 2,628,072 11.7473 51676 .007246377 433.54 14,957.12 139 19,321 2,685,619 11.7898 5.1801 .007194245 436.68 15,174.68 140 19,600 2,744,000 11.8322 5.1925 .007142857 439.82 15,393.80 141 19,881 2,803,221 11.8743 5.2048 .007092199 442.96 15,614.50 142 20,164 2,863,288 11.9164 5.2171 .007042254 446.11 15,836.77 143 20,449 2,924,207 11.9583 5.2293 .006993007 449.25 16,060.61 144 20,736 2,985,984 12.0000 5.2415 .006944444 452.39 16,286.02 145 21,025 3,048,625 12.0416 5.2536 .006896552 455.53 16,513.00 146 21,316 3,112,136 12.0830 5.2656 .006849315 458.67 16,741.55 147 21,609 3,176,523 12.1244 5.2776 .006802721 461.81 16,971.67 148 21,904 3,241,792 12.1655 5.2896 .006756757 464.96 17,203.36 149 22,201 3,307,949 12.2066 5.3015 .006711409 468.10 17,436.62 150 22,500 3,375,000 12.2474 5.3133 .006666667 471.24 17,671.46 151 22,801 3,442,951 12.2882 5.3251 .006622517 474.38 17,907.86 152 23,104 3,511,008 12.3288 5.3368 .006578947 477.52 18,145.84 153 23,409 3,581,577 12.3693 5.3485 .006535948 480.66 18,385.39 154 23,716 3,652,264 12.4097 5.3601 .006493506 483.81 18,626.50 155 24,025 3,723,875 12.4499 5.3717 .006451613 486.95 18,869.19 156 24,336 3,796,416 12.4900 5.3832 .006410256 490.09 19.113.45 157 24,649 3,869,893 12.5300 5.3947 .006369427 493.23 19,359.28 158 24,964 3,944,312 12.5698 5.4061 .006329114 496.37 19,606.68 159 25,281 4,019,679 12.6095 5.4175 .006289308 499.51 19,855.65 160 25,600 4,096,000 12.6491 5.4288 .006250000 502.65 20,106.19 161 25,921 4,173,281 12.6886 5.4401 .006211180 505.80 20,358.31 162 26,244 4,251,528 12.7279 5.4514 .006172840 508.94 20,611.99 163 26,569 4,330,747 12.7671 5.4626 .006134969 512.08 20,867.24 164 26,896 4,410,944 12.8062 5.4737 .006097561 515.22 21,124.07 165 27,225 4,492,125 12.8452 5.4848 .006060606 518.36 21,382.46 166 27,556 4,574,296 12.8841 5.4959 .006024096 521.50 21,642.43 167 27,889 4,657,463 12.9228 5.5069 .005988024 524.65 21,903.97 168 28,224 4,741.632 12.9615 5.5178 .005952381 527.79 22,167.08 169 28,561 4,826,809 13.0000 5.5288 .005917160 530.93 22,431.76 170 28,900 4,913,000 13.9384 5.5397 .005882353 534.07 22,698.01 171 29,241 5,000,211 13.0767 5.5505 .005847953 537.21 22,965.83 172 28,584 5,088,448 13.1149 5.5613 .005813953 540.35 23,235.22 173 29,929 5,177,717 13.1529 5.5721 .005780347 543.50 23,506.18 174 30,276 5,268,024 13.1909 5.5828 .005747126 546.64 23,778.71 175 30,625 5,359,375 13.2288 5.5934 .005714286 549.78 24,052.82 176 30,976 5,451,776 13.2665 5.6041 .005681818 552.92 24,328.49 177 31,329 5,545,233 13.3041 5.6147 .005649718 556.06 24,605.74 178 31,684 5,639,752 13.3417 5.6252 .005617978 559.20 24,884.56 179 32,041 5,735,339 13.3791 5.6357 .005586592 562.35 25,164.94 180 32,400 5,832,000 13.4164 5.6462 .005555556 565.49 25,446.90 181 32,761 5,929,741 13.4536 5.6567 .005524862 568.63 25,730.43 1 548 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. c.,.. Sq. Root. Cu.Root. Reciprocal. Circum. Area. 182 33,124 6,028,568 13.4907 5.6671 .005494505 571.77 26,015.53 183 33,489 6,128,487 13.5277 5.6774 .005464481 574.91 26,302.20 184 33,856 6,229,504 13.5647 5.6877 .005434783 578.05 26,590.44 185 34,225 6,331,625 13.6015 5.6980 .005405405 581.19 26,880.25 186 34,596 6,434,856 13.6382 5.7083 .005376344 584.34 27,171.63 187 34,969 6,539,203 13.6748 5.7185 .005347594 587.48 27,464.59 188 35,344 6,644,672 13.7113 5.7287 .005319149 590.62 27,759.11 189 35,721 6,751,269 13.7477 5.7388 .005291005 593.76 28,055.21 190 36,100 6,859,000 13.7840 5.7489 .005263158 596.90 28,352.87 191 36,481 6,967,871 13.8203 5.7590 .005235602 600.04 28,652.11 192 36,864 7,077,888 13.8564 5.7690 .005208333 603.19 28,952.92 193 37,249 7,189,017 13.8924 5.7790 .005181347 606.33 29,255.30 194 37,636 7,301,384 13.9284 5.7890 .005154639 609.47 29,559.25 195 38,025 7,414,875 13.9642 5.7989 .005128205 612.61 29,864.77 196 38,416 7,529,536 14.0000 5.8088 .005102041 615.75 30,171.86 197 38,809 7,645,373 14.0357 5.8186 .005076142 618.89 30,480.52 198 39,204 7,762,392 14.0712 5.8285 .005050505 622.04 30,790.75 199 39,601 7,880,599 14.1067 5.8383 .005025126 625.18 31,102.55 200 40,000 8,000,000 14.1421 5.8480 .005000000 628.32 31,415.93 201 40,401 8,120,601 14.1774 5.8578 .004975124 631.46 31,730.87 202 40,804 8,242,408 14.2127 5.8675 .004950495 634.60 32,047.39 203 41,209 8,365,427 14.2478 5.8771 .004926108 637.74 32,365.47 204 41,616 8,489,664 14.2829 5.8868 .004901961 640.88 32,685.13 205 42,025 8,615,125 14.3178 5.8964 .004878049 644.03 33,006.36 206 42,436 8,741,816 14.3527 5.9059 .004854369 647.17 33,329.16 207 42,849 8,869,743 14.3875 5.9155 .004830918 650.31 33,653.53 208 43,264 8,998,912 14.4222 5.9250 .004807692 653.45 33,979.47 209 43,681 9,129,329 14.4568 5.9345 .004784689 656.59 34,306.98 210 44,100 9,261,000 14.4914 5.9439 .004761905 659.73 34,636.06 211 44,521 9,393,931 14.5258 5.9533 .004739336 662.88 34,966.71 212 44,944 9,528.128 14.5602 5.9627 .004716981 666.02 35,298.94 213 45,369 9,663,597 14.5945 5.9721 .004694836 669.16 35,632.73 214 45,796 9,800,344 14.6287 5.9814 .004672897 672.30 35,968.09 215 46,225 9,938,375 14.6629 5.9907 .004651163 675.44 36,305.03 216 46,656 10,077,696 14.6969 6.0000 .004629630 678.58 36,643.54 217 47,089 10,218,313 14.7309 G.0092 .004608295 681.73 36,983.61 218 47,524 10,360,232 14.7648 6.0185 .004587156 684.87 37,325.26 219 47,961 10,503,459 14.7986 610277 .004566210 688.01 37,668.48 220 48,400 10,648,000 14.8324 6.0368 .004545455 691.15 38,013.27 221 48,841 10,793,861 14.8661 6.0459 .004524887 694.29 38,359.63 222 49,284 10,941,048 14.8997 6.0550 .004504505 697.43 38,707.56 223 49,729 11,089,567 14.9332 6.0641 .004484305 700.58 39,057.07 224 50,176 11,239,424 14.9666 6.0732 .004464286 703.72 39,408.14 225 50,625 11,390,625 15.0000 6.0822 .004444444 706.86 39,760.78 226 51,076 11,543,176 15.0333 6.0912 .004424779 710.00 40,115.00 227 51,529 11,697,083 15.0665 6.1002 .004405286 713.14 40,470.78 228 51,984 11,852,352 15.0997 6.1091 .004385965 716.28 40,828.14 229 52,441 12,008,989 15.1327 6.1180 .004366812 719.42 41,187.07 230 52,900 12,167,000 15.1658 6.1269 .004347826 722.57 41,547.56 231 53,361 12,326,391 15.1987 6.1358 .004329004 725.71 41,909.63 232 53,824 12,487,168 15.2315 6.1446 .004310345 728.85 42,273.27 233 54.289 12,649,337 15.2643 6.1534 .004291845 731.99 42,638.48 234 54,756 12,812,904 15.2971 6.1622 .004273504 735.13 43,005.26 235 55,225 12,977,875 15.3297 6.1710 .004255319 738.27 43,373.61 236 55,696 13,144.256 15.3623 6.1797 .004237288 741.42 43,743.54 237 56,169 13,312,053 15.3948 6.1885 .004219409 744.56 44,115.03 238 56,644 13,481,272 15.4272 6.1672 .004201681 747.70 44,488.09 239 57,121 13,651,919 15.4596 6.2058 .004184100 750.84 44,862.73 240 57,600 13,824,000 15.4919 6.2145 .004166667 753.98 45,238.93 241 58,081 13,997,521 15.5242 6.2231 .004149378 757.12 45,616.71 242 58,564 14,172.488 15.5563 6.2317 .004132231 760.27 45,996.06 243 59,049 14,348,907 15.5885 8.2403 .004115226 763.41 46,376.98 244 59,536 14,526,784 15.6205 6.2488 .004098361 766.55 46,759.47 CIRCUMFERENCES, AND AREAS. 549 N 0. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 245 60,025 14,706,125 15.6525 6.2573 .004081633 769.69 47,143.52 246 60.516 14,886,936 15.6844 6.2658 .004065041 772.83 47,529.16 247 61,009 15,069,223 15.7162 6.2743 .004048583 775.97 47,916.36 248 61,504 15,252,992 15.7480 6.2828 .004032258 779.11 48,305.13 249 62,001 15,438,249 15.7797 6.2912 .004016064 782.26 48,695.47 250 62,500 15,625,000 15.8114 6.2996 .004000000 785.40 49,087.39 251 63,001 15,813,251 15.8430 6.3080 .003984064 788.54 49,480.87 252 63,504 16,003,008 15.8745 6.3164 .003968254 791.68 49,875.92 253 64,009 16,194,277 15.9060 6.3247 .003952569 794.82 50,272.55 254 64,516 16,387,064 15.9374 6.3330 .003937008 797.96 50,670.75 255 65,025 16,581,375 15.9687 6.3413 .003921569 801.11 51,070.52 256 65,536 16,777,216 16.0000 6.3496 .003906250 804.25 51,471.85 257 66,049 16,974,593 16.0312 6.3579 .003891051 807.39 51,874.76 258 66,564 17,173,512 16.0624 6.3661 .003875969 810.53 52,279.24 259 67,081 17,373,979 16.0935 6.3743 .003861004 813.67 52,685.29 260 67,600 17,576,000 16.1245 6.3825 .003846154 816.81 53,092.92 261 68,121 17,779,581 16.1555 6.3907 .003831418 819.96 53,502.11 262 68,644 17,984,728 16.1864 6.3988 .003816794 823.10 53,912.87 263 69,169 18,191,447 16.2173 6.4070 .003802281 826.24 54,325.21 264 69,696 18,399,744 16.2481 6.4151 .003787879 829.38 54,739.11 265 70,225 18,609,625 16.2788 6.4232 .003773585 832.52 55,154.59 266 70,756 18,821,096 16.3095 6.4312 .003759398 835.66 55,571.63 267 71,289 19,034,163 16.3401 6.4393 .003745318 838.81 55,990.25 268 71,824 19,248,832 16.3707 6.4473 .003731343 841.95 56,410.44 269 72,361 19,465,109 16.4012 6.4553 .003717472 845.09 56,832.20 270 72,900 19,683,000 16.4317 6.4633 .003703704 848.23 57,255.53 271 73,441 19,902,511 16.4621 6.4713 .003690037 851.37 57,680.43 272 73,984 20,123,643 16.4924 6.4792 .003676471 854.51 58,106.90 273 74,529 20,346,417 16.5227 6.4872 .003663004 857.65 58,534.94 274 75,076 20,570,824 16.5529 6.4951 .003649635 860.80 58,964.55 275 75,625 20,796,875 16.5831 6.5030 .003636364 863.94 59,395.74 276 76,176 21,024,576 16.6132 6.5108 .003623188 867.08 59,828.49 277 76,729 21,253,933 16.6433 6.5187 .003610108 870.22 60,262.82 278 77,284 21,484,952 16.6783 6.5265 .003597122 873.36 60,698.71 279 77,841 21,717,639 16.7033 6.5343 .003584229 876.50 61,136.18 280 78,400 21,952,000 16.7332 6.5421 .003571429 879.65 61,575.22 281 78,961 22,188,041 16.7631 6.5499 .003558719 882.79 62,015.82 282 79,524 22,425,768 16.7929 6.5577 .003546099 885.93 62,458.00 283 80,089 22,665,187 16.8226 6.5654 .003533569 889.07 62,901.75 284 80,656 , 22,906,304 16.8523 6.5731 .003522127 892.21 63,347.07 285 81,225 23,149,125 16.8819 6.5808 .003508772 895.35 63,793.97 286 81,796 23,393,656 16.9115 6.5885 .003496503 898.50 64,242.43 287 82,369 23,639,903 16.9411 6.5962 .003484321 901.64 64,692.46 288 82,944 23,887,872 16.9706 6.6039 .003472222 904.78 65,144.07 289 83,521 24,137,569 17.0000 6.6115 .003460208 907.92 65,597.24 290 84,100 24,389,000 17.0294 6.6191 .003448276 911.06 66,051.99 291 84,681 24,642,171 17.0587 6.6267 .003436426 914.20 66,508.30 292 85,264 24,897,088 17.0880 6.6343 .003424658 917.35 66,966.19 293 85,849 25,153,757 17.1172 6.6419 .003412969 920.49 67,425.65 294 86,436 25,412,184 17.1464 6.6494 .003401361 923.63 67,886.68 295 87,025 25,672,375 17.1756 6.6569 .003389831 926.77 68,349.28 296 87,616 25,934,836 17.2047 6.6644 .003378378 929.91 68,813.45 297 88,209 26,198,073 17.2337 6.6719 .003367003 933.05 69,279.19 298 88,804 26,463,592 17.2627 6.6794 .003355705 936.19 69,746.50 299 89,401 26,730,899 17.2916 6.6869 .003344482 939.34 70,215.38 300 90,000 27,000,000 17.3205 6.6943 .003333333 942.48 70,685.83 301 90,601 27,270,901 17.3494 6.7018 .003322259 945.62 71,157.86 302 91,204 27,543,608 17.3781 6.7092 .003311258 948.76 71,631.45 303 91,809 27,818,127 17.4069 6.7166 .003301330 951.90 72,106.62 304 92,416 28,094,464 17.4356 6.7240 .003289474 955.04 72,583.36 305 93,025 28,372,625 17.4642 6.7313 .003278689 958.19 73,061.66 306 93,636 28,652,616 17.4929 6.7387 .003267974 961.33 73,541.54 307 94,249 28,934,443 17.5214 6.7460 .003257329 964.47 74,022.99 SQUARES, CUBES, SQUARE AND CUBE ROOTS, *. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 308 94,864 29,218,112 17.5499 6.7533 .003246753 967.61 74,506.01 309 95,481 29,503,629 17.5784 6.7606 .003236246 970.75 74,990.60 310 96,100 29,791,000 17.6068 6.7679 .003225806 973.89 75,476.76 311 96,721 30,080,231 17.6352 6.7752 .003215434 977.04 75,964.50 312 97,344 30,371,328 17.6635 6.7824 .003205128 980.18 76,453.80 313 97,969 30,664,297 17.6918 6.7897 .003194888 983.32 76,944.67 314 98,596 30,959,144 17.7200 6.7969 .003184713 986.46 77,437.12 315 99,225 31,255,875 17.7482 6.8041 .003174603 989.60 77,931.13 316 99,856 31,554,496 17.7764 6.8113 .003164557 992.74 78,426.72 317 100,489 31,855,013 17.8045 6.8185 .003154574 995.88 78,923.88 318 101,124 32,157,432 17.8326 6.8256 .003144654 999.03 79,422.60 319 101,761 32,461,759 17.8606 6.8328 .003134796 1,002.17 79,922.90 320 102,400 32,768,000 17.8885 6.8399 .003125000 1,005.31 80,424.77 321 103,041 33,076,161 17.9165 6.8470 .003115265 1,008.45 80,928.21 322 103,684 33,386,248 17.9444 6.8541 .003105590 1,011.59 81,433.22 323 104,329 33,698,267 17.9722 6.8612 .003095975 1,014.73 81,939.80 324 104,976 34,012,224 18.0000 6.8683 .003086420 1,017.88 82,447.96 325 105,625 34,328,125 18.0278 6.8753 .003076923 1,021.02 82,957.68 326 106,276 34,645,976 18.0555 6.8824 .003067485 1,024.16 83,468.98 327 106,929 34,965,783 18.0831 6.8894 .003058104 1,027.30 83,981.84 328 107,584 35,287,552 18.1108 6.8964 .003048780 1,030.44 84,496.28 329 108,241 35,611,289 18.1384 6.9034 .003039514 1,033.58 85,012.28 330 108,900 35,937,000 18.1659 6.9104 .003030303 1,036.73 85,529.86 331 109,561 36,264,691 18.1934 6.9174 .003021148 1,039.87 86,049.01 332 110,224 36,594,368 18.2209 6.9244 .003012048 1,043.01 86,569.73 333 110,889 36,926,037 18.2483 6.9313 .003003003 1,046.15 87,092.02 334 111,556 37,259,704 18.2757 6.9382 .002994012 1,049.29 87,615.88 335 112,225 37,595,375 18.3030 6.9451 .002985075 1,052.43 88,141.31 336 112,896 37,933,056 18.3303 6.9521 .002976190 1,055.58 88,668.31 337 113,569 38,272,753 18.3576 6.9589 .002967359 1,058.72 89,196.88 338 114,244 38,614,472 18.3848 6.9658 .002958580 1,061.86 89,727.03 339 114,921 38,958,219 18.4120 6.9727 .002949853 1,065.00 90,258.74 340 115,600 39,304,000 18.4391 6.9795 .002941176 1,068.14 90,792.03 341 116,281 39,651,821 18.4662 6.9864 .002932551 1,071.28 91,326.88 342 116,964 40,001,688 18.4932 6.9932 .002923977 1,074.42 91,863.31 343 117,649 40,353,607 18.5203 7.0000 .002915452 1,077.57 92,401.31 344 118,336 40,707,584 18.5472 7.0068 .002906977 1,080.71 92,940.88 345 119,025 41,063,625 18.5742 7.0136 .002898551 1,083.85 93,482.02 346 119,716 41,421,736 18.6011 7.0203 .002890173 1,086.99 94,024.73 347 120,409 41,781,923 18.6279 7.0271 .002881844 1,090.13 94,569.01 348 121,104 42,144,192 18.6548 7.0338 .002873563 1,095.27 95,114.86 349 121,801 42,508,549 18.6815 7.0406 .002865330 1,096.42 95,662.28 350 122,500 42,875,000 18.7083 7.0473 .002857143 1,099.56 96,211.28 351 123,201 43,243,551 18.7350 7.0540 .002849003 1,102.70 96,761.84 352 123,904 43,614,208 18.7617 7.0607 .002840909 1,105.84 97,313.97 353 124,609 43,986,977 18.7883 7.0674 .002832861 1,108.98 97,867.68 354 125,316 44,361,864 18.8149 7.0740 .002824859 1,112.12 98,422.96 355 126,025 44,738,875 18.8414 7.0807 .002816901 1,115.27 98,979.80 356 126,736 45,118,016 18.8680 7.0873 .002808989 1,118.41 99,538.22 357 127,449 45,499,293 18.8944 7.0940 .002801120 1,121.55 100,098.21 358 128,164 45,882,712 18.9209 7.1006 .002793296 1,124.69 100,659.77 359 128,881 46,268,279 18.9473 7.1072 .002785515 1,127.83 101,222.90 360 129,600 46,656,000 18.9737 7.1138 .002777778 1,130.97 101,787.60 361 130,321 47,045,881 19.0000 7.1204 .002770083 1,134.11 102,353.87 362 131,044 47,437,928 19.0263 7.1269 .002762431 1,137.26 102,921.72 363 131,769 47,832,147 19.0526 7.1335 .002754821 1,140.40 103,491.13 364 132,496 48,228,544 19.0788 7.1400 .002747253 1,143.54 104,062.12 365 133,225 48,627,125 19.1050 7.1466 .002739726 1,146.68 j 104,634.67 366 133,956 49,027,896 19.1311 7.1531 .002732240 1,149.82 105,208.80 367 134,689 49,430,863 19.1572 7.1596 .002724796 1,152.96 105,784.49 368 135,424 49,&36,032 19.1833 7.1661 .002717391 1,156.11 j!06,361.76 369 136,161 50,243,409 19.2094 7.1726 .002710027 1,159.25 106,940.60 370 136,900 50,653,000 19.2354 7.1791 .002702703 1,162.39 107,521.01 CIRCUMFERENCES, AND AREAS. 551 Xo. Square. 1 Cube. Sq. Root. Cu. Root.; Reciprocal. Circum. Area. i j 371 137,641 51,064,811 19.2614 7.1855 .002695418 1,165.53 108,102.99 372 138,384 ' 51,478,848 19.2873 7.1920 .002688172 1,168.67 108,686.54 373 139,329 51,895,117 19.3132 7.1984 .002680965 1,171.81 109,271.66 374 139,876 52.313,624 19.3391 7.2048 .002673797 1,174.96 109,858.35 375 140,625 52,734,375 19.3649 7.2112 .002666667 1,178.10 110,446.62 376 141,376 53,157,376 19.3907 7.2177 .002659574 1,181.24 111,036.45 377 142,129 53,582,633 19.4165 7.2240 .002652520 1,184.38 111,627.86 378 142,884 54,010,152 19.4422 7.2304 .002645503 1,187.52 112,220.83 379 143,641 54,439,939 19.4679 7.2368 .002638521 1,190.66 112,815.38 380 144,400 54,872,000 19.4936 7.2432 .002631579 1,193.81 113,411.49 381 145,161 55,306,341 19.5192 7.2495 .002624672 1,196.95 114,009.18 382 145,924 55,742,968 19.5448 7.2558 .002617801 1,200.09 i 114, 608.44 383 146,689 56,181,887 19.5704 7.2622 .002610966 1,203.23 115,209.27 384 147,456 56,623,104 19.5959 7.2685 .002604167 1,206.37 115,811.67 385 148,225 57,066,625 19.6214 7.2748 .002597403 1,209.51 116,415.64 386 148,996 57,512,456 19.6469 7.2811 .002590674 1,212.65 117,021.18 387 149,769 57,960,603 19.6723 7.2874 .002583979 1,215.80 117,628.30 388 150,544 58,411,072 19.6977 7.2936 .002577320 1,218.94 118,236.98 389 151,321 58,863,869 19.7231 7.2999 .002570694 1,222.08 118,847.24 390 152,100 59,319,000 19.7484 7.3061 .002564103 1,225.22 119,459.06 391 152,881 59,776,471 19.7737 7.3124 .002557545 1,228.36 120,072.46 392 153,664 60,236,288 19.7990 7.3186 .002551020 1,231.50 120,687.42 393 154,449 60,698,457 19.8242 7.3248 .002544529 1,234.65 121,303.96 394 155,236 61,162,984 19.8494 7.3310 .002538071 1,237.79 121,922.07 395 156,025 61,629,875 19.8746 7.3372 .002531646 1,240.93 122,541.75 396 156,816 62,099,136 19.8997 7.3434 .002525253 1,244.07 123,163.00 397 157,609 62,570,773 19.9249 7.3496 .002518892 1,247.21 123,785.82 398 158,404 63,044,792 19.9499 7.3558 .002512563 1,250.35 124,410.21 399 159,201 63,521,199 19.9750 7.3619 .002506266 1,253.50 125,036.17 400 160,000 64,000,000 20.0000 7.3681 .002500000 1,256.64 125,663.71 401 160,801 64,481,201 20.0250 7.3742 .002493766 1,259.78 126,292.81 402 161,604 64,964,808 20.0499 7.3803 .002487562 1,262.92 126,923.48 403 162,409 65,450,827 20.0749 7.3864 .002481390 1,266.06 127,555.73 404 163,216 65,939,264 20.0998 7.3925 .002475248 1,269.20 128,189.55 405 164,025 66,430,125 20.1246 7.3986 .002469136 1,272.35 128.824.93 406 164,836 66,923,416 20.1494 7.4047 .002463054 1,275.49 I129I461.89 407 165,649 67,419,143 20.1742 7.4108 .002457002 1,278.63 1130,100.42 408 166,464 67,917.312 20.1990 7.4169 .002450980 1,281.77 130,740.52 409 167,281 68,417,929 20.2237 7.4229 .002444988 1,284.91 131,382.19 410 168,100 68,921,000 20.2485 7.4290 .002439024 1,288.05 132,025.43 411 168,921 69,426,531 20.2731 7.4350 .002433090 1,291.19 132,670.24 412 169,744 69,934.528 20.2978 7.4410 .002427184 1,294.34 133,316.63 413 170,569 70,444,997 20.3224 7.4470 .002421308 1,297.48 133,964.58 414 171,396 70,957,944 20.3470 7.4530 .002415459 1,300.62 134,614.10 415 172,225 71,473,375 20.3715 7.4590 .002409639 1,303.76 135,265.20 416 173,056 71,991,296 20.3961 7.4650 .002406846 1,306.90 135,917.86 417 173,889 72,511,713 20.4206 7.4710 .002398082 1,310.04 136,572.10 418 174,724 73,034,632 20.4450 7.4770 .002392344 1,313.19 137,227.91 419 175,561 73,560,059 20.4695 7.4829 .002386635 1,316.33 137,885.29 420 176,400 74,088,000 20.4939 7.4889 .002380952 1,319.47 138,544.24 421 177,241 74,618,461 20.5183 7.4948 .002375297 1,322.61 139,204.76 422 178,084 75,151,448 20.5426 7.5007 .002369668 1,325.75 139,866.85 423 178,929 75,686,967 20.5670 7.5067 .002364066 1,328.89 140,530.51 424 179,776 76,225,024 20.5913 7.5126 .002358491 1,332.04 141,195.74 425 180,625 76,765,625 20.6155 7.5185 .002352941 1,335.18 141,862.54 426 181,476 77,308,776 20.6398 7.5244 .002347418 1,338.32 142,530.92 427 182,329 77,854,483 20.6640 7.5302 .002341920 1,341.46 143,200.86 428 183,184 78,402,752 20.6882 7.5361 .002336449 1,344.60 143,872.38 429 184,041 78,953,589 20.7123 7.5420 .002331002 1,347.74 144,545.46 430 184,900 79,507,000 20.7364 7.5478 .002325581 1,350.88 145,220.12 431 185,761 80,062,991 20.7605 7.5537 .002320186 1,354.03 145.896.35 432 186,624 80,621,568 20.7846 7.5595 .002314815 1,357.17 146,574.15 433 187,489 81,182,737 20.8087 7.5654 .002309469 1,360.31 147,253.52 1 ( SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 434 188,356 81,746,504 20.8327 7.5712 .002304147 1,363.45 147,934.46 435 189,225 82,312,875 20.8567 7.5770 .002298851 1,366.59 148,616.97 436 190,096 82,881,856 20.8806 7.5828 .002293578 1,369.73 149,301.05 437 190,969 83,453,453 20.9045 7.5886 .002288330 1,372.88 149,986.70 438 191,844 84,027,672 20.9284 7.5944 .002283105 1,376.02 150,673.93 439 192,721 84,604,519 20.9523 7.6001 .002277904 1,379.16 151,362.72 440 193,600 85,184,000 20.9762 7.6059 .002272727 1,382.30 152,053.08 441 194,481 85,766,121 21.0000 7.6117 .002267574 1,385.44 152,745.02 442 195,364 86,350,888 21.0238 7.6174 .002262443 1,388.58 153,438.53 443 196,249 86,938,307 21.0476 7.6232 .002257336 1,391.73 154,133.60 444 197,136 87,528,384 21.0713 7.6289 .002252252 1,394.87 154,830.25 445 198,025 88,121,125 21.0950 7.6346 .002247191 1,398.01 155,528.47 446 198,916 88,716,536 21.1187 7.6403 .002242152 1,401.15 156,228.26 447 199,809 89,314,623 21.1424 7.6460 .002237136 1,404.29 156,929.62 448 200,704 89,915,392 21.1660 7.6517 .002232143 1,407.43 157,632.55 449 201,601 90,518,849 21.1896 7.6574 .002227171 1,410.58 158,337.06 450 202,500 91,125,000 21.2132 7.6631 .002222222 1,413.72 159,043.13 451 203,401 91,733,851 21.2368 7.6688 .002217295 1,416.86 159,750.77 452 204,304 92,345,408 21.2603 7.6744 .002212389 1,420.00 160,459.99 453 205,209 92,959,677 21.2838 7.6801 .002207506 1,423.14 161,170.77 454 206,116 93,576,664 21.3073 7.6857 .002202643 1,426.28 161,883.13 455 207,025 94,196,375 21.3307 7.6914 .002197802 1,429.42 162,597.05 456 207,936 94,818,816 21.3542 7.6970 .002192982 1,432.57 163,312.55 457 208,849 95,443,993 21.3776 7.7026 .002188184 1,435.71 164,029.62 458 209,764 96,071,912 21.4009 7.7082 .002183406 1,438.85 164,748.26 459 210,681 96,702,579 21.4243 7.7188 .002178649 1,441.99 165,468.47 460 211,600 97,336,000 21.4476 7.7194 .002173913 1,445.13 166,190.25 461 212,521 97,972,181 21.4709 7.7250 .002169197 1,448.27 166,913.60 462 213,444 98,611,128 21.4942 7.7306 .002164502 1,451.42 167,638.53 463 214,369 99,252,847 21.5174 7.7362 .002159827 1,454.56 168,365.02 464 215,296 99,897,344 21.5407 7.7418 .002155172 1,457.70 169,093.08 465 216,225 100,544,625 21.5639 7.7473 .002150538 1,460.84 169,822.72 466 217,156 101,194,696 21.5870 7.7529 .002145923 1,463.98 170,553.92 467 218,089 101,847,563 21.6102 7.7584 .002141328 1,467.12 171,286.70 468 219,024 102,503,232 21.6333 7.7639 .002136752 1,470.27 172,021.05 469 219,961 103,161,709 21.6564 7.7695 .002132196 1,473.41 172,756.97 470 220,900 103,823,000 21.6795 7.7750 .002127660 1,476.55 173,494.45 471 221,841 104,487,111 21.7025 7.7805 .002123142 1,479.69 174,233.51 472 222,784 105,154,048 21.7256 7.7860 .002118644 1,482.83 174,974.14 473 223,729 105,823,817 21.7486 7.7915 .002114165 1,485.97 175,716.35 474 224,676 106,496,424 21.7715 7.7970 .002109705 1,489.11 176,460.12 475 225,625 107,171,875 21.7945 7.8025 .002105263 1,492.26 177,205.46 476 226,576 107,850,176 21.8174 7.8079 .002100840 1,495.40 177,952.37 477 227,529 108,531,333 21.8403 7.8134 .002096486 1,498.54 178,700.86 478 228,484 109,215,352 21.8632 7.8188 .002092050 1,501.68 179,450.91 479 229,441 109,902,239 21.8861 7.8243 .002087683 1,504.82 180,202.54 480 230,400 110,592,000 21.9089 7.8297 .002083333 1,507.96 180,955.74 481 231,361 111,284,641 21.9317 7.8352 .002079002 1,511.11 181,710.50 482 232,324 111,980,168 21.9545 7.8406 .002074689 1,514.25 182,466.84 483 233,289 112,678,587 21.9775 7.8460 .002070393 1.517.39 183,224.75 484 234,256 113,379,904 22.0000 7.8514 .002066116 1,520.53 183,984.23 485 235,225 114,084,125 22.0227 7.8568 .002061856 1,523.67 184,745.28 486 236,196 114,791,256 22.0454 7.8622 .002057613 1,526.81 185,507.90 487 237,169 115,501,303 22.0681 7.8676 .002053388 1,529.96 186,272.10 488 238,144 116,214,272 22.0907 7.8730 .002049180 1,533.10 187,037.86 489 239,121 116,930,169 22.1133 7.8784 .002044990 1,536.24 187,805.19 490 240,100 117,649,000 22.1359 7.8837 .002040816 1,539.38 188,574.10 491 241,081 118,370,771 22.1585 7.8891 .002036660 1,542.52 189,344.57 492 242,064 119,095,488 22.1811 7.8944 .002032520 1,545.66 190,116.62 493 243,049 119,823,157 22.2036 7.8998 .002028398 1,548.81 190,890.24 494 244,036 120,553,784 22.2261 7.9051 .002024291 1,551.95 191,665.43 495 245,025 121,287,375 22.2486 7.9105 .002020292 1,555.09 192,442.18 496 246,016 122,023,936 22.2711 7.9158 .002016129 1,558.23 193,220.51 CIRCUMFERENCES, AND AREAS. 553 No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 497 247,009 122,763,473 22.2935 7.9211 .002012072 1,561.37 194,000.41 498 248,004 123,505,992 22.3159 7.9264 .002008032 1,564.51 194,781.89 499 249,001 124,251,499 22.3383 7.9317 .002004008 1,567.65 195,564.93 500 250,000 125,000,000 22.3607 7.9370 .002000000 1,570.80 196,349.54 501 251,001 125,751,501 22.3830 7.9423 .001996008 1,573.94 197,135.72 502 252,004 126,506,008 22.4054 7.9476 .001992032 1,577.08 197,923.48 503 253,009 127,263,527 22.4277 7.9528 .001988072 1,580.22 198,712.80 504 254,016 128,024,064 22.4499 7.9581 .001984127 1,583.36 199,503.70 505 255.025 128,787,625 22.4722 7.9634 .001980198 1,586.50 200,296.17 506 256,036 129,554,216 22.4944 7.9686 .001976285 1,589.65 201,090.20 507 257,049 130,323,843 22.5167 7.9739 .001972387 1,592.79 201,885.81 508 258,064 131,096,512 22.5389 7.9791 .001968504 1,595.93 202,682.99 509 259,081 131,872,229 22.5610 7.9843 .001964637 1,599.07 203,481.74 510 260,100 132,651,000 22.5832 7.9895 .001960785 1,602.21 204,282.06 511 261,121 133,432,831 22.6053 7.9948 .001956947 1,605.35 205,083.95 512 262,144 134,217,728 22.6274 8.0000 .001953125 1,608.50 205,887.42 513 263,169 135,005,697 22.6495 8.0052 .001949318 1,611.64 206,692.45 514 264.196 135,796,744 22.6716 8.0104 .001945525 1,614.78 207,499.05 515 265,225 136,590,875 22.6936 8.0156 .001941748 1,617.92 208,307.23 516 266,256 137,388,096 22.7156 8.0208 .001937984 1,621.06 209,116.97 517 267,289 138,188,413 22.7376 8.0260 .001934236 1,624.20 209,928.29 518 268,324 138,991,832 22.7596 8.0311 .001930502 1,627.34 210,741.18 519 269,361 139,798,359 22.7816 8.0363 .001926782 1,630.49 211,555.63 520 270,400 140,608,000 22.8035 8.0415 .001923077 1,633.63 212,371.66 521 271,411 141,420,761 22.8254 8.0466 .001919386 1,636.77 213,189.26 522 272,484 142,236,648 22.8473 8.0517 .001915709 1,639.91 214,008.43 523 273,529 143,055,667 22.8692 8.0569 .001912046 1,643.05 214,829.17 524 274,576 143,877,824 22.8910 8.0620 .001908397 1,646.19 215,651.49 525 275,625 144,703,125 22.9129 8.0671 .001904762 1,649.34 216,475.37 526 276,676 145,531,576 22.9347 8.0723 .001901141 1,652.48 217,300.82 527 277,729 146,363,183 22.9565 8.0774 .001897533 1,655.62 218,127.85 528 278,784 147,197,952 22.9783 8.0825 .001893939 1,658.76 218,956.44 529 279.841 148,035,889 23.0000 8.0876 .001890359 1,661.90 219,786.61 530 280,900 148,877,001 23.0217 8.0927 .001886792 1,665.04 220,618.34 531 281,961 149,721,291 23.0434 8.0978 .001883239 1,668.19 221,451.65 532 283,024 150,568,768 23.0651 8.1028 .001879699 1,671.33 222,286.53 533 284,089 151,419,437 23.0868 8.1079 .001876173 1,674.47 223,122.98 534 285,156 152,273,304 23.1084 8.1130 .001872659 1,677.61 223,961.00 535 286,225 153,130,375 23.1301 8.1180 .001869159 1,680.75 224,800.59 536 287,296 153,990,656 23.1517 8.1231 .001865672 1,683.89 225,641.75 537 288,369 154,854,153 23.1733 8.1281 .001862197 1,687.04 226,484.48 538 289,444 155,720,872 23.1948 8.1332 .001858736 1,690.18 227,328.79 539 290,521 156,590,819 23.2164 8.1382 .001855288 1,693.32 228,174.66 540 291,600 157,464,000 23.2379 8.1433 .001851852 1,696.46 229,022.10 541 292,681 158,340,421 23.2594 8.1483 .001848429 1,699.60 229,871.12 542 293,764 159,220,088 23.2809 8.1533 .001845018 1,702.74 230,721.71 543 294,849 160,103,007 23.3024 8.15&3 .001841621 1,705.88 231,573.86 544 295,936 160,989,184 23.3238 8.1633 .001838235 1,709.03 232,427.59 545 297,025 161,878,625 23.3452 8.1683 .001834862 1,712.17 233,282.89 546; 298,116 162,771,336 23.3666 8.1733 .001831502 1,715.31 234,139.76 547 299,209 163,667,323 23.3880 8.1783 .001828154 1,718.45 234,998.20 548 300,304 164,566,592 23.4094 8.1833 .001824818 1,721.59 235,858.21 549 301,401 165,469,149 23.4307 8.1882 .001821494 1,724.73 236,719.79 550 302,500 166,375,000 23.4521 8.1932 .001818182 1,727.88 237,582.94 551 303,601 167,284,151 23.4734 8.1982 .001814882 1,731.02 238,447.67 552 304,704 168,196,608 23.4947 8.2031 .001811594 1,734.16 239,313.96 553 305,809 169,112,377 23.5160 8.2081 .001808318 1,737.30 240,181.83 554 306,916 170,031,464 23.5372 8.2130 .001805054 1,740.44 241,051.26 555 308,025 170,953,875 23.5584 8.2180 .001801802 1,743.58 241,922.27 556 309,136 171,879,616 23.5797 8.2229 .001798561 1,746.73 242,794.85 557 310,249 172,808,693 23.6008 8.2278 .001795332 1,749.87 243,668.99 558 311,364 173,741,112 23.6220 8.2327 .001792115 1,753.01 244,544.71 559 312,481 174,676,879 23.6432 8.2377 .001788909 1,756.15 245,422.00 554 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq. Root . Cu. Roo Reciprocal. Circum Area. 560 313,600 175,616,000 23.6643 8.2426 .001785714 1,759.29 246,300.86 561 314,721 176,558,481 23.6854 8.2475 .001782531 1,762.43 247,181.30 562 315,844 177,504,328 23.7065 8.2524 .001779359 1,765.58 248,063.30 563 316,969 178,453,547 23.7276 8.2573 .001776199 1,768.72 248,946.87 564 318,096 179,406,144 | 23.7487 8.2621 .001773050 1,771.86 249,832.01 565 319,225 180,362,125 23.7697 8.2670 .001769912 1,775.00 i250,718.73 566 320,356 181,321,496 23.7908 8.2719 .001766784 1,778.14 251,607.01 567 321,489 182,284,263 23.8118 8.2768 .001763668 1,781.28 252,496.87 568 322,624 183,250,432 23.8328 8.2816 .001760563 1,784.42 253,388.30 569 323,761 184,220,009 23.8537 8.2865 .001757469 1,787.57 254,281.29 570 324,900 185,193,000 23.8747 8.2913 .001754386 1,790.71 255,175.86 571 326,041 186,169,411 23.8956 8.2962 .001751313 1,793.85 256,072.00 572 327,184 187,149,248 23.9165 8.3010 .001748252 1,796.99 256,969.71 573 328,329 188,132,517 23,9374 8.3059 .001745201 1,800.13 257,868.99 574 329,476 189,119,224 23.9583 8.3107 .001742164 1,803.27 258,769.85 575 330,625 190,109,375 23.9792 8.3155 .001739130 1,806.42 259,672.27 576 331,776 191,102.976 24.0000 8.3203 .001736111 ,809.56 260,576.26 577 332,929 192,100,033 24.0208 8.3251 .001733102 1,812.70 261,481.83 578 334,084 193,100,552 24.0416 8.3300 .001730104 1,815.84 262,388.96 579 335,241 194,104,539 24.0624 8.3348 .001727116 1,818.98 263,297.67 580 336,400 195,112,000 24.0832 8.3396 .001724138 1,822.12 264,207.94 581 337,561 196,122,941 24.1039 8.3443 .001721170 1,825.27 265,119.79 582 338,724 197,137,368 24.1247 8.3491 .001718213 1,828.41 266,033.21 583 339,889 198,155,287 24.1454 8.3539 .001715266 1,831.55 266,948.20 584 341,056 199,176,704 24.1661 8.3587 .001712329 1,834.69 267,864.76 585 342,225 200,201,625 24.1868 8.3634 .001709402 1,837.83 268,782.89 586 343,396 201,230,056 24.2074 8.3682 .001706485 1,840.97 269,702.59 587 344,569 202,262,003 24.2281 8.3730 .001703578 1,844.11 270,623.86 588 345,744 203,297,472 24.2487 8.3777 .001700680 1,847.26 271,546.70 589 346,921 ' 204,336,469 24.2693 8.3825 .001697793 1,850.40 272,471.12 590 348,100 205,379,000 24.2899 8.3872 .001694915 1,853.54 273,397.10 591 349,281 206,425,071 24.3105 8.3919 .001692047 1,856.68 274,324.66 592 350,464 207,474,688 24.3311 8.3967 .001689189 1,859.82 275,253.78 593 351,649 208,527,857 24.3516 8.4014 .001686341 1,862.96 276,184.48 594 352,836 209,584,584 24.3721 8.4061 .001683502 1,866.11 277,116.75 595 354,025 210,644,875 24.3926 8.4108 .001680672 1,869.25 278,050.58 596 355,216 211,708,736 24.4131 8.4155 .001677852 1,872.39 278,985.99 597 356,409 212,776,173 24.4336 8.4202 .001675042 1,875.53 i279.922.97 598 357,604 213,847,192 24.4540 8.4249 001672241 1,878.67 280,861.52 599 358,801 214,921,799 24.4745 8.4296 001669449 1,881.81 281,801.65 600 360,000 216,000,000 24.4949 8.4343 001666667 1,884.96 282,743.34 601 361,201 217,081,801 24.5153 8.4390 001663894 1,888.10 283,686.60 602 362,404 218,167,208 24.5357 8.4437 001661130 1,891.24 284,631.44 603 363,609 219,256,227 24.5561 8.4484 001658375 1,894.38 285,577.84 604 364,816 220,348,864 24.5764 8.4530 001655629 1,897.52 286,525.82 605 366,025 221,445,125 24.5968 8.4577 001652893 1,900.66 287,475.36 606 367,236 222,545,016 24.6171 8.4623 001650165 1,903.81 288,426.48 607 368,449 223,648,543 24.6374 8.4670 001647446 1,906.95 289,379.17 608 369,664 224,755,712 24.6577 8.4716 001644737 1,910.09 290,333.43 609 370,881 225,866,529 24.6779 8.4763 001642036 1,913.23 i 291,289.26 610 372,100 226,981,000 24.6982 8.4809 001639344 1,916.37 292,246.66 611 373,321 228,099,131 24.7184 8.4856 001636661 1,919.51 293,205.63 612 374,544 229,220,928 24.7386 8.4902 001633987 1,922.65 294,166.17 613 375,769 230,346,397 24.7588 8.4948 001631321 1,925.80 295,128.28 614 376,996 231,475,544 24.7790 8.4994 001628664 L,928.94 296,091.97 615 378,225 232,608,375 24.7992 8.5040 001626016 1,932.08 i 297,057.22 616 379,456 233,744,896 24.8193 8.5086 001623377 1,935.22 298,024.05 617 380,689 234,885,113 24.8395 8.5132 001620746 L,938.36 1 >98, 992.44 618 619 381,924 383,161 236,029,032 237,176,659 24.8596 24.8797 8.5178 8.5224 001618123 001615509 1,941.50 299,962.41 L,944.65 300,933.95 620 384,400 238,328,000 24.8998 8.5270 001612903 L,947.79 301,907.05 621 385,641 239,483,061 24.9199 8.5316 001610306 L,950.93 J 502,881.73 622 386,884 240,641,848 24.9399 8.5362 001607717 L,954.07 [ 503,857.98 CIRCUMFERENCES, AND AREAS. ,,. Square. Cube. Sq. Root Cu. Root Reciprocal. Circum. Area. 623 388,129 241,804,367 24.9600 8.5408 .001605136 1,957.21 304,835.80 624 389,376 242,970,624 24.9800 8.5453 .001602564 1,960.35 305,815.20 625 390,625 244,140,625 25.0000 8.5499 .001600000 1,963.50 306,796.16 626 391,876 245,314,376 25.0200 8.5544 .001597444 1,966.64 307,778.69 627 393,129 246,491,883 25.0400 8.5589 .001594896 1,969.78 308,762.79 628 394,384 247,673,152 25.0599 8.5635 .001592357 1,972.92 309,748.47 629 395,641 248,858,189 25.0799 8.5681 .001589825 1,976.06 310,735.71 630 396,900 250,047,000 25.0998 8.5726 .001587302 1,979.20 311,724.53 631 398,161 251,239,591 25.1197 8.5772 .001584786 1,982.35 312,714.92 632 399,424 252,435,968 25.1396 8.5817 .001582278 1,985.49 313,706.88 633 400,689 253,636,137 25.1595 8.5862 .001579779 1,988.63 314,700.40 634 401,956 254,840,104 25.1794 8.5907 .001577287 1,991.77 315,695.50 635 403,225 256,047,875 25.1992 8.5952 .001574803 1,994.91 316,692.17 636 404,496 257,259,456 25.2190 8.5997 .001572327 1,998.05 317,690.42 637 405,769 258,474,853 25.2389 8.6043 .001569859 2,001.19 318,690.23 638 407,044 259,694,072 25.2587 8.6088 .001567398 2,004.34 319,691.61 639 408,321 260,917,119 25.2784 8.6132 .001564945 2,007.48 320,694.56 640 409,600 262,144,000 25.2982 8.6177 .001562500 2,010.62 321,699.09 641 410,881 263,374,721 25.3180 8.6222 .001560062 2,013.76 322.705.18 642 412,164 264,609,288 25.3377 8.6267 .001557632 2,016.90 323,712.85 643 413,449 265,847,707 25.3574 8.6312 .001555210 2,020.04 324,722.09 644 414,736 267,089,984 25.3772 8.6357 .001552795 2,023.19 325,732.89 645 416,125 268,336,125 25.3969 8.6401 .001550388 2,026.33 326,745.27 646 417,316 269,585,136 25.4165 8.6446 .001547988 2,029.47 327,759.22 647 418,609 270,840,023 25.4362 8.6490 .001545595 2,032.61 328,774.74 648 419,904 272,097,792 25.4558 8.6535 .001543210 2,035.75 329,791.83 649 421,201 273,359,449 25.4755 8.6579 .001540832 2,038.89 330,810.49 650 422,500 274,625,000 25.4951 8.6624 .001538462 2,042.04 331,830.72 651 423,801 275,894,451 25.5147 8.6668 .001536098 2,045.18 332,852.53 652 425,104 277,167,808 25.5343 8.6713 .001533742 2,048.32 333,875.90 653 426,409 278,445,077 25.5539 8.6757 .001531394 2,051.46 334,900.85 654 427,716 279,726,264 25.5734 8.6801 .001529052 2,054.60 335,927.36 655 429,025 281,011,375 25.5930 8.6845 .001526718 2,057.74 336,955.45 656 430,336 282,300,416 25.6125 8.6890 .001524390 2,060.88 337,985.10 657 431,639 283,593,393 25.6320 8.6934 .001522070 2,064.03 339,016.33 658 432,964 284,890,312 25.6515 8.6978 .001519751 2,067.17 340,049.13 659 434,281 286,191,179 25.6710 8.7022 .001517451 2,070.31 341,083.50 660 435,600 287,496,000 25.6905 8.7066 .001515152 2,073.45 342,119.44 661 436,921 288,804,781 25.7099 8.7110 .001512859 2,076.59 343,156.95 662 438,244 290,117,528 25.7294 8.7154 .001510574 2,079.73 344,196.03 663 439,569 291,434.247 25.7488 8.7198 .001508296 2,082.88 345,236.69 664 440,896 292,754,944 25.7682 8.7241 .001506024 2,086.02 346,278.91 665 442,225 294,079,625 25.7876 8.7285 .001503759 2,089.16 347,322.70 666 443,556 295,408,296 25.8070 8.7329 .001501502 2,092.30 348,368.07 667 444,899 296,740,963 25.8263 8.7373 .001499250 2,095.44 349,415.00 668 446,224 298,077,632 25.8457 8.7416 .001497006 2,098.58 350,463.51 669 447,561 299,418,309 25.8650 8.7460 .001494768 2,101.73 351,513.59 670 448,900 300,763,000 25.8844 8.7503 .001492537 2,104.87 352,565.24 671 450,241 302,111,711 25.9037 8.7547 .001490313 2,108.01 353,618.45 672 451,584 303,464,448 25.9230 8.7590 .001488095 2,111.15 354,673.24 673 452,929 304,821,217 25.9422 8.7634 .001485884 2,114.29 355,729.60 674 454,276 306,182,024 25.9615 8.7677 .001483680 2,117.43 356,787.54 675 455,625 307,546,875 25.9808 8.7721 .001481481 2,120.58 357,847.04 676 456,976 308.915,776 26.0000 8.7764 .001479290 2,123.72 358,908.11 677 458,329 310,288,733 26.0192 8.7807 .001477105 2,126.86 359,970.75 678 459,684 311,665,752 26.0384 8.7850 .001474926 2,130.00 361,034.97 679 461,041 313,046,839 26.0576 8.7893 .001472754 2,133.14 362,100.75 680 462,400 314,432.000 26.0768 8.7937 .001470588 2,136.28 363,168.11 681 463,761 315.821,241 26.0960 8.7980 .001468429 2,139.42 364,237.04 682 465,124 317,214,568 26.1151 8.8023 .001466276 2,142.57 365,307.54 683 466,489 318,611,987 26.1343 8.8066 .001464129 2,145.71 366,379.60 684 467,856 320,013,504 26.1534 8.8109 .001461988 2,148.85 367,453.24 685 469,225 321,419,125 26.1725 8.8152 .001459854 2,151.99 368,528.45 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq. Root. Cu. Root Reciprocal. Circum. - Area. 686 470,596 322,828,856 26.1916 8.8194 .001457726 2,155.13 369,605.23 687 471,969 324,242,703 26.2107 8.8237 .001455604 2,158.27 370,683.59 688 473,344 325,660,672 26.2298 8.82SO .001453488 2,161.42 371,763.51 689 474,721 327,082,769 26.2488 8.8323 .001451379 2,164.56 372,845.00 690 476,100 328,509,000 26.2679 8.8366 .001449275 2,167.70 373,928.07 691 477,481 329,939,371 26.2869 8.8408 .001447178 2,170.84 375,012.70 692 478,864 331,373,888 26.3059 8.8451 .001445087 2,173.98 376,098.91 693 480,249 332,812,557 26.3249 8.8493 .001443001 2,177.12 377,186.68 694 481,636 334,255,384 26.3439 8.8536 .001440922 2,180.27 378,276.03 695 483,025 335,702,375 26.3629 8.8578 .001438849 2,183.41 379,366.95 696 484,416 337,153,536 26.3818 8.8621 .001436782 2,186.55 380,459.44 697 485,809 338,608,873 26.4008 8.8663 .001434720 2,189.69 381,553.50 698 487,204 340,068,392 26.4197 8.8706 .001432665 2,192.83 382,649.13 699 488,601 341,532,099 26.4386 8.8748 .001430615 2,195.97 383,746.33 700 490,000 343,000,000 26.4575 8.8790 .001428571 2,199.11 384,845.10 701 491,401 344,472,101 26.4764 8.8833 .001426534 2,202.26 385,945.44 702 492,804 345,948,408 26.4953 8.8875 .001424501 2,205.40 387,047.36 703 494,209 347,428,927 26.5141 8.8917 .001422475 2,208.54 388,150.84 704 495,616 348,913,664 26.5330 8.8959 .001420455 2,211.68 389,255.90 705 497,025 350,402,625 26.5518 8.9001 .001418440 2,214.82 390,362.52 706 498,436 351,895,816 26.5707 8.9043 .001416431 2,217.96 391,470.72 707 499,849 353,393,243 26.5895 8.9085 .001414427 2,221.11 392,580.49 708 501,264 354,894,912 26.6083 8.9127 .001412429 2,224.25 393,691.82 709 502,681 356,400,829 26.6271 8.9169 .001410437 2,227.39 394,804.73 710 504,100 357,911,000 26.6458 8.9211 .001408451 2,230.53 395,919.21 711 505,521 359,425,431 26.6646 8.9253 .001406470 2,233.67 397,035.26 712 506,944 360,944,128 26.6833 8.9295 .001404494 2,236.81 398,152.89 713 508,369 362,467,097 26.7021 8.9337 .001402525 2,239.96 399,272.08 714 509,796 363,994,344 26.7208 8.9378 .001400560 2,243.10 400,392.84 715 511,225 365,525,875 26.7395 8.9420 .001398601 2,246.24 401,515.18 716 512,656 367,061,696 26.7582 8.9462 .001396648 2,249.38 402,639.08 717 514,089 368,601,813 26.7769 8.9503 .001394700 2,252.52 403,764.56 718 515,524 370,146,232 26.7955 8.9545 .001392758 2,255.66 404,891.60 719 516,961 371,694,959 26.8142 8.9587 .001390821 2,258.81 406,020.22 720 518,400 373,248,000 26.8328 8.9628 .001388889 2,261.95 407,150.41 721 519,841 374,805,361 26.8514 8.9670 .001386963 2,265.09 408,282.17 722 521,284 376,367,048 26.8701 8.9711 .001385042 2,268.23 409,415.50 723 522,729 377,933,067 26.8887 8.9752 .001383126 2,271.37 410,550.40 724 524,176 379,503,424 26.9072 8.9794 .001381215 2,274.51 411,686.87 725 525,625 381,078,125 26.9258 8.9835 .001379310 2,277.65 412,824.91 726 527.076 382,657,176 26.9444 8.9876 .001377410 2,280.80 413,964.52 727 528,529 384,240,583 26.9629 8.9918 .001375516 2,283.94 415,105.71 728 529,984 385,828,352 26.9815 8.9959 .001373626 2,287.08 416,248.46 729 531,441 387,420,489 27.0000 9.0000 .001371742 2,290.22 417,392.79 730 532,900 389,017,000 27.0185 9.0041 .001369863 2,293.36 418,538.68 731 534,361 390,617,891 27.0370 9.0082 .001367989 2,296.50 419,686.15 732 535,824 392,223,168 27.0555 9.0123 .001366120 2,299.65 420,835.19 733 537,289 393,832,837 27.0740 9.0164 .001364256 2,302.79 421,985.79 734 538,756 395,446,904 27.0924 9.0205 .001362398 2,305.93 423,137.97 735 540,225 397,065,375 27.1109 9.0246 .001360544 2,309.07 424,291.72 736 541,696 398,688,256 27.1293 9.0287 .001358696 2,312.21 425,447.04 737 543,169 400,315,553 27.1477 9.0328 .001356852 2,315.35 426,603.94 738 544,644 401,947,272 27.1662 9.0369 .001355014 2,318.50 427,762.40 739 546,121 403,583,419 27.1846 9.0410 .001353180 2,321.64 428,922.43 740 547,600 405,224,000 27.2029 9.0450 .001351351 2,324.78 430,084.03 741 549,801 406,869,021 27.2213 9.0491 .001349528 2,327.92 431,247.21 742 550,564 408,518,488 27.2397 9.0532 .001347709 2,331.06 432,411.95 743 552,049 410,172,407 27.2580 9.0572 .001345895 2,334.20 433,578.27 744 553,536 411,830,784 27.2764 9.0613 .001344086 2,337.34 434,746.16 745 555,025 413,493,625 27.2947 9.0654 .001342282 2,340.49 435,915.62 746 556,516 415,160,936 27.3130 9.0694 .001340483 2,343.63 437,086.64 747 558,009 416,832,723 27.3313 9.0735 .001338688 2,346.77 438,259.24 748 559,504 418,508,992 27.3496 9.0775 .001336898 2,349.91 439,433.41 CIRCUMFERENCES, AND AREAS. No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 749 561,001 420,189,749 27.3679 9.0816 .001335113 2,353.05 440,609.16 750 562,500 421,875,000 27.3861 9.0856 .001333333 2,356.19 441,786.47 751 564,001 423,564,751 27.4044 9.0896 .001331558 2,359.34 442,965.35 752 565,504 425,259,008 27.4226 9.0937 .001329787 2,362.48 444,145.80 753 567,009 426,957,777 27.4408 9.0977 .001328021 2,365.62 445,327.83 754 568,516 428,661,064 27.4591 9.1017 .001326260 2,368.76 446,511.42 755 570,025 430,368,875 27.4773 9.1057 .001324503 2,371.90 447,696.59 756 571,536 432,081,216 27.4955 9.1098 .001322751 2,375.04 448,883.32 757 573,049 433,798,093 27.5136 9.1138 .001321004 2,378.19 450,071.63 758 574,564 435,519,512 27.5318 9.1178 .001319261 2,381.33 451,261.51 759 576,081 437,245,479 27.5500 9.1218 .001317523 2,384.47 452,452.96 760 577,600 438,976,000 27.5681 9.1258 .001315789 2,387.61 453,645.98 761 579,121 440,711,081 27.5862 9.1298 .001314060 2,390.75 454,840.57 762 580,644 442,450,728 27.6043 9.1338 .001312336 2,393.89 456,036.73 763 582,169 444,194,947 27.6225 9.1378 .001310616 2,397.04 457,234.46 764 583,696 445,943,744 27.6405 9.1418 .001308901 2,400.18 458,433.77 765 585,225 447,697,125 27.6586 9.1458 .001307190 2,403.32 459,634.64 766 586,756 449,455,096 27.6767 9.1498 .001305483 2,406.46 460,837.08 767 588,289 451,217,663 27.6948 9.1537 .001303781 2,409.60 462,041.10 768 589,824 452,984,832 27.7128 9.1577 .001302083 2,412.74 463,246.69 769 591,361 454,756,609 27.7308 9.1617 .001300390 2,415.88 464,453.84 770 592,900 456,533,000 27.7489 9.1657 .001298701 2,419.03 465,662.57 771 594,441 458,314,011 27.7669 9.1696 .001297017 2,422.17 466,872.87 772 595,984 460,099,648 27.7849 9.1736 .001295337 2,425.31 468,084.74 773 597,529 461,889,917 27.8029 9.1775 .001293661 2,428.45 469,298.18 774 599,076 463,684,824 27.8209 9.1815 .001291990 2,431.59 470,513.19 775 600,625 465,484,375 27.8388 9.1855 .001290323 2,434.73 471,729.77 776 602,176 467,288,576 27.8568 9.1894 .001288660 2,437.88 472,947.92 777 603,729 469,097,433 27.8747 9.1933 .001287001 2,441.02 474,167.65 778 605,284 470,910,952 27.8927 9.1973 .001285347 2,444.16 475,388.94 779 606,841 472,729,139 27.9106 9.2012 .001283697 2,447.30 476,611.81 780 608,400 474,552,000 27.9285 9.2052 .001282051 2,450.44 477,836.24 781 609,961 476,379,541 27.9464 9.2091 .001280410 2,453.58 479,062.25 782 611,524 478,211,768 27.9643 9.2130 .001278772 2,456.73 480,289.83 783 613,089 480,048,687 27.9821 9.2170 .001277139 2,459.87 481,518.97 784 614,656 481,890,304 28.0000 9.2209 .001275510 2,463.01 482,749.69 785 616,225 483,736,625 28.0179 9.2248 .001273885 2,466.15 483,981.98 786 617,796 485,587,656 28.0357 9.2287 .001272265 2,469.29 485,215.84 787 619,369 487,443,403 28.0535 9.2326 .001270648 2,472.43 486,451.28 788 620,944 489,303,872 28.0713 9.2365 .001269036 2,475.58 487,688.28 789 622,521 491,169,069 28.0891 9.2404 .001267427 2,478.72 488,926.85 790 624,100 493,039,000 28.1069 9.2443 .001265823 2,481.86 490,166.99 791 625,681 494,913,671 28.1247 9.2482 .001264223 2,485.00 491,408.71 792 627,624 496,793,088 28.1425 9.2521 .001262626 2,488.14 492,651.99 793 628,849 498,677,257 28.1603 9.2560 .001261034 2,491.28 493,896.85 794 630,436 500,566,184 28.1780 9.2599 .001259446 2,494.42 495,143.28 795 632,025 502,459,875 28.1957 9.2638 .001257862 2,497.57 496,391.27 796 633,616 504,358,336 28.2135 9.2677 .001256281 2,500.71 497,640.84 797 635,209 506,261,573 28.2312 9.2716 .001254705 2,503.85 498,891.98 798 636,804 508,169,592 28.2489 9.2754 .001253133 2,506.99 500,144.69 799 638,401 510,082,399 28.2666 9.2793 .001251364 2,510.13 501,398.97 800 640,000 512,000,000 28.2843 9.2832 .001250000 2,513.27 502,654.82 801 641,601 513,922,401 28.3019 9.2870 .001248439 2,516.42 503,912.25 802 643,204 515,849,608 28.3196 9.2909 .001246883 2,519.56 505,171.24 803 644,809 517,781,627 28.3373 9.2948 .001245330 2,522.70 506,431.80 804 646,416 519,718,464 28.3549 9.2986 .001243781 2,525.84 507,693.94 805 648,025 521,660,125 28.3725 9.3025 .001242236 2,528.98 508,957.64 806 649,636 523,606,616 28.3901 9.3063 .001240695 2,532.12 510,222.92 807 651,249 525,557,943 28.4077 9.3102 .001239157 2,535.27 511,489.77 808 652,864 527,514,112 28.4253 9.3140 .001237624 2,538.41 512,758.19 809 654,481 529,475,129 28.4429 9.3179 .001236094 2,541.55 514,028.18 810 656,100 531,441,000 28.4605 9.3217 .001234568 2,544.69 515,299.74 811 657,721 533,411,731 28.4781 9.3255 .001233046 2,547.83 516,572.87 558 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq. Root Cu. Root Reciprocal. Circum. Area. 812 659,344 535,387,328 28.4956 9.3294 .001231527 2,550.97 517,847.57 813 660,969 537,367,797 28.5132 9.3332 .001230012 2,554.11 519,123.84 814 662,596 539,353,144 28.5307 9.3370 .001228501 2,557.26 520,401.68 815 664,225 541,343,375 28.5482 9.3408 .001226994 2,560.40 521,681.10 816 665,856 543,338,496 28.5657 9.3447 .001225490 2,563.54 522,962.08 817 667,489 545,338,513 28.5832 9.3485 .001223990 2,566.68 524,244.63 818 669,124 547,343,432 28.6007 9.3523 .001222494 2,569.82 525,528.76 819 670,761 549,353,259 28.6182 9.3561 .001221001 2,572.96 526,814.46 820 672,400 551,368,000 28.6356 9.3599 .001219512 2,576.11 528,101.73 821 674,041 553,387,661 28.6531 9.3637 .001218027 2,579.25 529,390.56 822 675,584 555,412,248 28.6705 9.3675 .001216545 2,582.39 530,680.97 823 677,329 557,441,767 28.6880 9.3713 .001215067 2,585.53 531,972.95 824 678,976 559,476,224 28.7054 9.3751 .001213592 2,588.67 533,266.50 825 680,625 561,515,625 28.7228 9.3789 .001212121 2,591.81 534,561.62 826 682,276 563,559,976 28.7402 9.3827 .001210654 2,594.96 535,858.32 827 683,929 565,609,283 28.7576 9.3865 .001209190 2,598.10 537,156.58 828 685,584 567,663,552 28.7750 93902 .001207729 2,601.24 538,456.41 829 687,241 569,722,789 28.7924 9.3940 .001206273 2,604.38 539,757.82 830 688,900 571,787,000 28.8097 9.3978 .001204819 2,607.52 541,060.79 831 690,561 573,856,191 28.8271 9.4016 .001203369 2,610.66 542,365.34 832 692,224 575,930,368 28.8444 9.4053 .001201923 2,613.81 543,671.46 833 693,889 578,009,537 28.8617 9.4091 .001200480 2,616.95 544,979.15 834 695,556 580,093,704 28.8791 9.4129 .001199041 2,620.09 546,288.40 835 697,225 582,182,875 28.8964 9.4166 .001197605 2,623.23 547,599.23 836 698,896 584,277,056 28.9137 9.4204 .001196172 2,626.37 548,911.63 837 700,569 586,376,253 28.9310 9.4241 .001194743 2,629.51 550,225.61 838 702,244 588,480,472 28.9482 9.4279 .001193317 2,632.65 551,541.15 839 703,921 590,589,719 28.9655 9.4316 .001191895 2,635.80 552,858.26 840 705,600 592,704,000 28.9828 9.4354 .001190476 2,638.94 554,176.94 841 707,281 594,823,321 29.0000 9.4391 .001189061 2,642.08 555,497.20 842 708,964 596,947,688 29.0172 9.4429 .001187648 2,645.22 556,819.02 843 710,649 599,077,107 29.0345 9.4466 .001186240 2,648.36 558,142.42 844 712,336 601,211,584 29.0517 9.4503 .001184834 2,651.50 559,467.39 845 714,025 603,351,125 29.0689 9.4541 .001183432 2,654.65 560,793.92 846 715,716 605,495,736 29.0861 9.4578 .001182033 2,657.79 562,122.03 847 717,409 607,645,423 29.1033 9.4615 .001180638 2,660.93 563,451.71 848 719,104 609,800,192 29.1204 9.4652 .001179245 2,664.07 564,782.96 849 720,801 611,960,049 29.1376 9.4690 .001177856 2,667.21 566,115.78 850 722,500 614,125,000 29.1548 9.4727 .001176471 2,670.35 567,450.17 851 724,201 616,295,051 29.1719 9.4764 .001175088 2,673.50 568,786.14 852 725,904 618,470,208 29.1890 9.4801 .001173709 2,676.64 570,123.67 853 727,609 620,650,477 29.2062 9.4838 .001172333 2,679.78 571,462.77 854 729,316 622,835,864 29.2233 - 9.4875 .001170960 2,682.92 572,803.45 855 731,025 625,026,375 29.2404 9.4912 .001169591 2,686.06 574,145.69 856 732,736 627,222,016 29.2575 9.4949 .001168224 2,689.20 575,489.51 857 734,449 629,422,793 29.2746 9.4986 .001166861 2,692.34 576,834.90 858 736,164 631,628,712 29.2916 9.5023 .001165501 2,695.49 578,181.85 859 737,881 633,839,779 29.3087 9.5060 .001164144 2,698.63 579,530.38 860 739,600 636,056,000 29.3258 9.5097 .001162791 2,701.77 580,880.48 861 741,321 638,277,381 29.3428 9.5135 .001161440 2,704.91 582,232.15 862 743,044 640,503,928 29.3598 9.5171 .001160093 2,708.05 583,585.39 863 744,769 642,735,647 29.3769 9.5207 .001158749 2,711.19 584,940.20 864 746,496 644,972,544 29.3939 9.5244 .001157407 2.714.34 586,296.59 865 748,225 647,214,625 29.4109 9.5281 .001156069 2,717.48 587,654.54 866 749,956 649,461,896 29.4279 9.5317 .001154734 2,720.62 589,014,07 867 751,689 651,714,363 29.4449 9.5354 .001153403 2,723.76 590,375.16 868 753,424 653,972,032 29.4618 9.5391 .001152074 2,726.90 591,737.83 869 755,161 656,234,909 29.4788 9.5427 .001150748 2,730.04 593,102.06 870 756,900 658,503,000 29.4958 9.5464 .001149425 2,733.19 594,467.87 871 758,641 660,776,311 29.5127 9.5501 .001148106 2,736.33 595,835.25 872 760,384 663,054,848 29.5296 9.5537 .001146789 2,739.47 597,204.20 873 762,129 665,338,617 29.5466 9.5574 .001145475 2,742.61 598,574.72 874 763,876 667,627,624 29.5635 9.5610 .001144165 2,745.75 599,946.81 CIRCUMFERENCES, AND AREAS. No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 875 765,625 669,921,875 29.5804 9.5647 .001142857 2,748.89 601,320.47 876 767,376 672,221,376 29.5973 9.5683 .001141553 2,752.04 602,695.70 877 769,129 674,526,133 29.6142 9.5719 .001140251 2,755.18 604,072.50 878 770,884 676,836,152 29.6311 9.5756 .001138952 2,758.32 605,450.88 879 772,641 679,151,439 29.6479 9.5792 .001137656 2,761.46 606,830.82 880 774,400 681,472,000 29.6648 9.5828 .001136364 2,764.60 608,212.34 881 776,161 683,797,841 29.6816 9.5865 .001135074 2,767.74 609,595.42 882 777,924 686,128,968 29.6985 9.5901 .001133787 2,770.88 610,980.08 883 779,689 688,465,387 29.7153 9.5937 .001132503 2,774.03 612,366.31 884 781,456 690,807,104 29.7321 9.5973 .001131222 2,777.17 613,754.11 885 783,225 693,154,125 29.7489 9.6010 .001129944 2,780.31 615,143.48 886 784,996 695,506,456 29.7658 9.6046 .001128668 2,783.45 616,534.42 887 786,769 697,864,103 29.7825 9.6082 .001127396 2,786.59 617,926.93 888 788,544 700,227,072 29.7993 9.6118 .001126126 2,789.73 6^.9,321.01 889 790,321 702,595,369 29.8161 9.6154 .001124859 2,792.88 620,716.66 890 792,100 704,969,000 29.8329 9.6190 .001123596 2,796.02 622,113.89 891 793,881 707,347,971 29.8496 9.6226 .001122334 2,799.16 623,512.68 892 795,664 707,932,288 29.8664 9.6262 .001121076 2,802.30 624,913.04 893 797,449 712,121,957 29.8831 9.6298 .001119821 2,805.44 626,314.98 894 799,236 714,516,984 29.8998 9.6334 .001118568 2,808.58 627,718.49 895 801,025 716,917,375 29.9166 9.6370 .001117818 2,811.73 629,123.56 896 802,816 719,323,136 29.9333 9.6406 .001116071 2,814.87 630,530.21 897 804,609 721,734,273 29.9500 9.6442 .001114827 2,818.01 631,938.43 898 806,404 724,150,792 29.9666 9.6477 .001113586 2,821.15 633,348.22 899 808,201 726,572,699 29.9833 9.6513 .001112347 2,824.29 634,759.58 900 810,000 729,000,000 30.0000 9.6549 .001111111 2,827.43 636,172.51 901 811,801 731,432,701 30.0167 9.6585 .001109878 2,830.58 637,587.01 902 813,604 733,870,808 30.0333 9.6620 .001108647 2,833.72 639,003.09 903 815,409 736,314,327 30.0500 9.6656 .001107420 2,836.86 640,420.73 904 817,216 738,763,264 30.0666 9.6692 .001106195 2,840.00 641,839.95 905 819,025 741,217,625 30.0832 9.6727 .001104972 2,843.14 643,260.73 906 820,836 743,677,416 30.0998 9.6763 .001103753 2,846.28 644,683.09 907 822,649 746,142,643 30.1164 9.6799 .001102536 2,849.42 646,107.01 908 824,464 748,613,312 30.1330 9.6834 .001101322 2,852.57 647,532.51 909 826,281 751,089,429 30.1496 9.6870 .001100110 2,855.71 648,959.58 910 828,100 753,571,000 30.1662 9.6905 .001098901 2,858.85 650,388.22 911 829,921 756,058,031 30.1828 9.6941 .001091695 2,861.99 651,818.43 912 831,744 758,550,825 30.1993 9.6976 .001096491 2,865.13 653,250.21 913 833,569 761,048,497 30.2159 9.7012 .001095290 2,868.27 654,683.56 914 835,396 763,551,944 30.2324 9.7047 .001094092 2,871.42 656,118.48 915 837,225 766,060,875 30.2490 9.7082 .001092896 2,874.56 657,554.98 916 839,056 768,575,296 30.2655 9.7118 .001091703 2,877.70 658,993.04 917 840,889 771,095,213 30.2820 9.7153 .001090513 2,880.84 660,432.68 918 842,724 773,620,632 30.2985 9.7188 .001089325 2,883.98 661,873.88 919 844,561 776,151,559 30.3150 9.7224 .001088139 2.887.12 663,316.66 920 846,400 778,688,000 30.3315 9.7259 .001086957 2,890.27 664,761.01 921 848,241 781,229,961 30.3480 9.7294 .001085776 2,893.41 666,206.92 922 850,084 783.777,448 30.3645 9.7329 .001084599 2,896.55 667,654.41 923 851,929 7861330,467 30.3809 9.7364 .001083423 2,899.69 669,103.47 924 853,776 788,889,024 - 30.3974 9.7400 .001082251 2,902.83 670,554.10 925 855,625 791,453,125 30.4138 9.7435 .001081081 2,905.97 672,006.30 926 857,476 794,022,776 30.4302 9.7470 .001079914 2,909.11 673,460.08 927 859,329 796,597,983 30.4467 9.7505 .001078749 2,912.26 674,915.42 928 861,184 799,178,752 30.4631 9.7540 .001077586 2,915.40 676,372.33 929 863,041 801,765,089 30.4795 9.7575 .001076426 2,918.54 677,830.82 930 864.900 804,357,000 30.4959 9.7610 .001075269 2,921.68 679,290.87 931 866,761 806,954,491 30.5123 9.7645 .001074114 2,924.82 680,752.50 932 868,624 809,557,568 30.5287 9.7680 .001072961 2,927.96 682,215.69 933 870,489 812,166,237 30.5450 9.7715 .001071811 2,931.11 683,680.46 934 872,356 814,780,504 30.5614 9.7750 .001070664 2,934.25 685,146.80 935 874,225 817,400,375 30.5778 9.7785 .001069519 2,937.39 686,614.71 936 876,096 820,025,856 30.5941 9.7829 .001068376 2,940.53 688,084.19 937 877,969 822,656.953 30.6105 9.7854 .001067236 2,943.67 689,555.24 560 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 938 879,844 825,293,672 30.6268 9.7889 .001066098 2,946.81 691,027.86 939 881,721 827,936,019 30.6431 9.7924 .001064963 2,949.96 692,502.05 940 883,600 830,584,000 30.6594 9.7959 .001063830 2,953.10 693,977.82 941 885,481 833,237,621 30.6757 9.7993 .001062699 2,956.24 695,455.15 942 887,364 835,896,888 30.6920 9.8028 .001061571 2,959.38 696,934.06 943 889,249 838,561,807 30.7083 9.8063 .001060445 2,962.52 698,414.53 944 891,136 841,232,384 30.7246 9.8097 .001059322 2,965.66 699,896.58 945 893,025 843,908,625 30.7409 9.8132 .001058201 2,968.81 701,380.19 946 894,916 846,590,536 30.7571 9.8167 .001057082 2,971.95 702,865.38 947 896,808 849,278,123 30.7734 9.8201 .001055966 2,975.09 704,352.14 948 898,704 851,971,392 30.7896 9.8236 .001054852 2,978.23 705,840.47 949 900,601 854,670,349 30.8058 9.8270 .001053741 2,981.37 707,330.37 950 902,500 857,375,000 30.8221 9.8305 .001052632 2,984.51 708,821.84 951 904,401 860,085,351 30.8383 9.8339 .001051525 2,987.65 710,314.88 952 '906,304 862,801,408 30.8545 9.8374 .001050420 2,990.80 711,809.50 953 908,209 865,523,177 30.8707 9.8408 .001049318 2,993.94 713,305.68 954 910,116 868,250,664 30.8869 9.8443 .001048218 2,997.08 714,803.43 955 912,025 870,983,875 30.9031 9.8477 .001047120 3,000.22 716,302.76 956 913,936 873,722,816 30.9192 9.8511 .001046025 3,003.36 717,803.66 957 915,849 876,467,493 30.9354 9.8546 .001044932 3,006.50 719,306.12 958 917,764 879,217,912 30.9516 9.8580 .001043841 3,009.65 720,810.16 959 919,681 881,974,079 30.9677 9.8614 .001042753 3,012.79 722,315.77 960 921,600 884,736,000 30.9839 9.8648 .001041667 3,015.93 723,822.95 961 923,521 887,503,681 31.0000 9.8683 .001040583 3,019.07 725,331.70 962 925,444 890,277,128 31.0161 9.8717 .001039501 3,022.21 726,842.02 963 927,369 893,056,347 31.0322 9.8751 .001038422 3,025.35 728,353.91 964 929,296 895,841,344 31.0483 9.8785 .001037344 3,028.50 729,867.37 965 931,225 898,632,125 31.0644 9.8819 .001036269 3,031.64 731,382.40 966 933,156 901,428,696 31.0805 9.8854 .001035197 3,034.78 732,899.01 967 935,089 904,231,063 31.0966 9.8888 .001034126 3,037.92 734,417.18 968 937,024 907,039,232 31.1127 9.8922 .001033058 3,041.06 735,936.93 969 938,961 909,853,209 31.1288 9.8956 .001031992 3,044.20 737,458.24 970 940,900 912,673,000 31.1448 9.8990 .001030928 3,047.34 738,981.13 971 942,841 915,498,611 31.1609 9.9024 .001029866 3,050.49 740,505.59 972 944,784 918,330,048 31.1769 9.9058 .001028807 3,053.63 742,031.62 973 946,729 921,167,317 31.1929 9.9092 .001027749 3,056.77 743,559.22 974 948,676 924,010,424 31.2090 9.9126 .001026694 3,059.91 745,088.39 975 950,625 926,859,375 31.2250 9.9160 .001025641 3,063.05 746,619.13 976 952,576 929,714,176 31.2410 9.9194 .001024590 3,066.19 748,151.44 977 954,529 932,574,833 31.2570 9.9228 .001023541 3,069.34 749,685.32 978 956,484 935,441,352 31.2730 9.9261 .001022495 3,072.48 751,220.78 979 958,441 938,313,739 31.2890 9.9295 .001021450 3,075.62 752,757.80 980 960,400 941,192,000 31.3050 9.9329 .001020408 3.078.76 754,296.40 981 962,361 944,076,141 31.3209 9.9363 .001019168 3,081.90 755,836.56 982 964,324 946,966,168 31.3369 9.9396 .001018330 3,085.04 757,378.30 983 966,289 949,862,087 31.3528 9.9430 .001017294 3,088.19 758,921.61 984 968,256 952,763,904 31.3688 9.9464 .001016260 3,091.33 760,466.48 985 970,225 955,671,625 31.3847 9.9497 .001015228 3,094.47 762,012.93 986 972,196 958,585,256 31.4006 9.9531 .001014199 3,097.61 763,560.95 987 974,169 961,504,803 31.4166 9.9565 .001013171 3,100.75 765,110.54 988 976,144 964,430,272 31.4325 9.9598 .001012146 3,103.89 766,661.70 989 978,121 967,361,669 31.4484 9.9632 .001011122 3,107.04 768,214.44 990 980,100 970,299,000 31.4643 9.9666 .001010101 3,110.18 769,768.74 991 982,081 973,242,271 31.4802 9.9699 .001009082 3,113.32 771,324.61 992 984,064 976,191,488 31.4960 9.9733 .001008065 3,116.46 772,882.06 993 986,049 979,146,657 31.5119 9.9766 .001007049 3,119.60 774,441.07 994 988,036 982,107,784 31.5278 9.9800 .001006036 3,122.74 776,001.66 995 990,025 985,074,875 31.5436 9.9833 .001005025 3,125.88 777,563.82 996 992,016 988,047,936 31.5595 9.9866 .001004016 3,129.03 779,127.54 997 994,009 991,026,973 31.5753 9.9900 .001003009 3,132.17 780,692.84 998 996,004 994,011,992 31.5911 9.9933 .001002004 3,135.31 782,259.71 999 998,001 997,002,999 31.6070 9.9967 .001001001 3,138.45 783,828.15 1000 1,000,000 1,000,000,000 31.6228 10.0000 .001000000 3,141.59 785,398.16 CIRCUMFERENCES AND AREAS OF CIRCLES. CIRCUMFERENCES AND AREAS OF CIRCLES FROM 1-64 TO 100. Diam. Circum. Area. Diam. Circum. Area. i Diam. Circum. Area. B 1 ! .0491 .0002 6 18.8496 1 28.2744 131 41.2335 135.297 .0982 j .0008 61 19.2423 29.4648 is! 41.6262 137.887 A .1963 .0031 e! 19.6350 30.6797 42.0189 140.501 * .3927 .0123 6f 20.0277 31.9191 13ft 42.4116 143.139 .5890 j .0276 6ft 20.4204 33.1831 42.8043 145.802 5 .7854 .0491 20.8131 34.4717 13! 43.1970 148.490 T 6 g .9817 .0767 62 21.2058 35.7848 131 43.5897 151.202 I 1.1781 .1104 61 21.5985 37.1224 14 43.9824 153.938 I ? B 1.3744 .1503 7 21.9912 38.4846 141 44.3751 156.700 ^ 1.5708 .1963 71 22.3839 39.8713 14! 44.7678 159.485 A 1.7671 .2485 7i 22.7766 41.2826 141 45.1605 162.296 i 1.9635 .3068 7| 23.1693 42.7184 14| 45.5532 165.130 2.1598 .3712 7* 23.5620 44.1787 45.9459 167.990 2.3562 .4418 7* ! 23.9547 45.6636 14* 46.3386 170.874 H 2.5525 .5185 72 i 24.3474 47.1731 141 46.7313 173.782 2.7489 .6013 71 ! 24.7401 48.7071 15 47.1240 176.715 it 2.9452 .6903 8 25.1328 50.2656 151 47.5167 179.673 1 3.1416 .7854 81 25.5255 51.8487 15+ 47.9094 182.655 11 3.5343 .9940 8i 25.9182 53.4563 15| 48.3021 185.661 3.9270 1.2272 8f 26.3109 55.0884 15ft 48.6948 188.692 if 4.3197 1.4849 8ft 26.7036 56.7451 151 49.0875 191.748 a 4.7124 1.7671 8| 27.0963 58.4264 152 49.4802 194.828 it 5.1051 2.0739 82 27.4890 60.1322 151 49.8729 197.933 5.4978 2.4053 81 27.8817 61.8625 16 50.2656 201.062 11 5.8905 2.7612 9 28.2744 63.6174 161 50.6583 204.216 2 6.2832 3.1416 91 j 28.6671 65.3968 16* 51.0510 207.395 21 6.6759 3.5466 9i 29.0598 67.2008 16| 51.4437 210.598 2i 7.0686 3.9761 9f 29.4525 69.0293 iel 51.8364 213.825 2 f 7.4613 4.4301 91 29.8452 70.8823 16* 52.2291 217.077 7.8540 4.9087 91 30.2379 72.7599 162 52.6218 220.354 2| 8.2467 5.4119 92 30.6306 74.6621 161 53.0145 223.655 22 8.6394 5.9396 91 31.0233 76.589 17 53.4072 226.981 21 9.0321 6.4918 10 31.4160 78.540 171 53.7999 230.331 3 9.4248 7.0686 101 31.8087 80.516 54.1926 233.706 s 9.8175 | 7.6699 32.2014 82.516 17* 54.5853 237.105 10.2102 8.2958 io| 32.5941 84.541 17ft 54.9780 240.529 3| 10.6029 8.9462 10! 32.9868 86.590 17* 55.3707 243.977 3ft 10.9956 9.6211 10f 33.3795 88.664 172 55.7634 247.450 11.3883 10.3206 102 33.7722 90.763 171 56.1561 250.948 32 11.7810 11.0447 101 34.1649 92.886 18 56.5488 254.470 31 12.1737 11.7933 11 34.5576 95.033 181 56.9415 258.016 4 12.5664 12.5664 HI 34.9503 97.205 18 1 57.3342 261.587 41 12.9591 13.3641 111 35.3430 99.402 18| 57.7269 265.183 4i 13.3518 ! 14.1863 HI 35.7357 101.623 58.1196 268.803 4| 13.7445 ! 15.0330 lift 36.1284 103.869 18} 58.5123 272.448 14.1372 15.9043 HI 36.5211 106.139 182 58.9050 276.117 14.5299 16.8002 112 36.9138 108.434 181 59.2977 279.811 42 14.9226 17.7206 111 37.3065 110.754* 19 1 59.6904 283.529 41 15.3153 18.6555 12 37.6992 113.098 60.0831 287.272 5 15.7080 19.6350 121 38.0919 115.466 19| 60.4758 291.040 5ft 16.1007 20.6290 12$ 38.4846 117.859 19f 60.8685 294.832 5i 16.4934 21.6476 12* 38.8773 120.277 19ft 61.2612 298.648 61 16.8861 22.6907 39.2700 122.719 19| 61.6539 302.489 51 17.2788 23.7583 12f 39.6627 125.185 192 62.0466 306.355 5| 17.6715 24.8505 122 40.0554 127.677 191 62.4393 310.245 52 i 18.0642 25.9673 121 40.4481 130.192 20 62.8320 314.160 51 ! 18.4569 27.1086 13 40.8408 132.733 201 63.2247 318.099 562 CIRCUMFERENCES A\I> A UK AS OF Diam. Circum. Area. 1 >i;i m Circum Area. Diam. Circum Area. 20i 63.6174 322.063 28i 88.3575 621.264 36 113.098 1,017.878 20f 64.0101 326.051 28j 88.7502 626.798 36i 113.490 1,024.960 20* 64.4028 330.064 28f 89.1429 632.357 36i 113.883 1,032.0(55 20| 64.7955 334.102 28* 89.5356 637.941 36& 114.276 1,039.195 20? 65.1882 338.164 28| 89.9283 643.549 36* 114.668 1,046.349 201 65.5809 342.250 28? 90.3210 649.182 36* 115.061 1,053.528 21 65.9736 346.361 281 90.7137 654.840 36? 115.454 1,060.732 21i 66.3663 350.497 29 91.1064 660.521 361 115.846 1,067.960 2l| 66.7590 354.657 29J 91.4991 666.228 37 116.239 1,075.213 W 67.1517 358.842 29* 91.8918 671.959 371 116.632 1,082.490 21* 67.5444 363.051 29| 92.2845 677.714 m 117.025 1,089.792 2H 67.9371 367.285 29* 92.6772 683.494 37* 117.417 1,097.118 21? 68.3298 371.543 29| 93.0699 689.299 37* 117.810 1,104.469 21f 68.7225 375.826 29? 93.4626 695.128 37| 118.203 1,111.844 22 69.1152 380.134 291 93.8553 700.982 37? 118.595 1,119.244 22i 69.5079 384.466 30 94.2480 706.860 37* 118.988 1,126.669 22} 69.9006 388.822 30 94.6407 712.763 38 119.381 1,134.118 22f 70.2933 393.203 30* 95.0334 718.690 38i 119.773 1,141.591 22} 70.6860 397.609 30| 95.4261 724.642 38i 120.166 1,149.089 22} 71.0787 402.038 30* 95.8188 730.618 m 120.559 1,156.612 22? 71.4714 406.494 30| 96.2115 736.619 38* 120.952 1,164.159 22^ 71.8641 410.973 30? 96.6042 742.645 38| 121.344 1,171.731 23 72.2568 415.477 301 96.9969 748.695 38? 121.737 1,179.327 23* 72.6495 420.004 31 97.3896 754.769 381 122.130 1,186.948 231 73.0422 424.558 311 97.7823 760.869 39 122.522 1,194.593 23f 73.4349 429.135 3lJ 98.1750 766.992 39i 122.915 1,202.263 23* 73.8276 433.737 81* 98.5677 773.140 39i 123.308 1,209.958 23| 74.2203 438.364 81* 98.9604 779.313 39& 123.700 1,217.677 231 74.6130 443.015 31| 99.3531 785.510 39} 124.093 1,225.420 231 75.0057 447.690 31? 99.7458 791.732 39& 124.486 1,233.188 24 75.3984 452.390 311 100.1385 797.979 39? 124.879 1,240.981 24i 75.7911 457.115 32 100.5312 804.250 39J 125.271 1,248.798 24* 76.1838 461.864 32J 100.9239 810.545 40 125.664 1,256.640 24* 76.5765 466.638 32| 101.3166 816.865 40i 126.057 1,264.510 24* 76.9692 471.436 32| 101.7093 823.210 40* 126.449 1,272.400 24$ 77.3619 476.259 32* 102.1020 829.579 40* 126.842 1,280.310 24? 77.7546 481.107 321 102.4947 835.972 40* 127.235 1,288.250 24| 78.1473 485.979 32? 102.8874 842.391 40| 127.627 1,296.220 25 78.5400 490.875 321 103.280 8.18.833 40? 128.020 1,304.210 251 78.9327 495.796 33 103.673 855.301 401 128.413 1,31-2.220 25i 79.3254 500.742 33i 104.065 861.792 41 128.806 1,320.260 25* 79.7181 505.712 as! 104.458 868.309 4U 129.198 1,328.320 25* 80.1108 510.706 33| 104.851 874.850 41i 129.591 1 ,336.410 25| 80.5035 515.726 33* 105.244 881.415 41* 129.984 1,344.520 25? 80.8962 520.769 m 105.636 888.005 41* 130.376 1,352.660 251 81.2889 525.838 33? 106.029 894.620 41* 130.769 1,360.820 26 81.6816 530.9: ;o 331 106.422 901.259 41? 131.162 1,369.000 26f 82.0743 536.048 34 106.814 907.922 411 131.554 1,377.210 261- 82.4670 541.190 34* 107.207 914.611 42 131.947 1,385.450 26| 82.8597 546.356 34* 107.600 921.823 42i 132.340 1,393.700 Si* 83.2524 551.547 34t 107.992 92S.OU1 42] 132.733 1,401.990 26| 83.6451 556.763 34* 108.385 934.822 42| 133.125 1,110.300 26? 84.0378 562.003 344 108.778 941.609 42* 133.518 I,118.(i30 261 84.4305 567.267 34? 109.171 948.420 42* 1:53.911 1,426.990 27 84.8232 572.557 341 109.563 955.255 42? 134.303 1,435.370 27* 85.2159 577.870 35 109.950 962.115 421 i3i.<;9<; 1,443.770 27* 85.6086 583.209 35* 110.349 969.000 43 135.089 1,452.200 27| 86.0013 588.571 35! 110.741 975.909 43i 135.481 1,460.660 27* 86.3940 593.959 35J 111.134 982.842 43j 135.874 1,469.140 27| 86.7867 599.371 35* 111.527 989.800 43g 136.267 1,477.640 27? 87.1794 604.807 35| 111.919 996.783 43* 136.660 1,486.170 27{- 87.5721 610.268 35? 112.312 1,003.790 43| 137.052 1,494.730 28 87.9648 616.754 35| 112.705 1,010.822 4I| 137.445 1,503.300 CIRCUMFERENCES AND AREAS OF CIRCLES. Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. Area. 43* 137.838 1,511.910 511 162.578 2,103.35 59$ 187.318 2,792.21 44 138.230 1,520.530 51| 162.970 2,113.52 59? 187.711 2,803.93 44^ 138.623 1,529.190 52 163.363 2,123.72 59* 188.103 2,815.67 44| 139.016 1,537.860 52i 163.756 2,133.94 60 188.496 2,827.44 44! 139.408 1,546.56 52j 164.149 2,144.19 60i 188.889 2,839.23 44* 139.801 1,555.29 52f 164.541 2,154.46 60i 189.281 2,851.05 44| 140.194 1,564.04 52* 164.934 2,164.76 60f 189.674 2,862.89 44| 140.587 1,572.81 52| 165.327 2,175.08 60* 190.067 2,874.76 44* 140.979 1,581.61 52? 165.719 2,185.42 60* 190.459 2,886.65 45 141.372 1,590.43 52* 166.112 2,195.79 60? 190.852 2,898.57 45 141.765 1,599.28 53 166.505 2,206.19 60* 191.245 2,910.51 46* 142.157 1,608.16 531 166.897 2,216.61 61 191.638 2,922.47 45! 142.550 1,617.05 53j 167.290 2,227.05 6H 192.030 2,934.46 46* 142.943 1,625.97 53* 167.683 2,237.52 6lJ 192.423 2,946.48 45| 143.335 1,634.92 53* 168.076 2,248.01 61| 192.816 2,958.52 45? 143.728 1,643.89 53| 168.468 2,258.53 61* 193.208 2,970.58 45* 144.121 1,652.89 53$ 168.861 2,269.07 61| 193.601 2,982.67 46 144.514 1,661.91 53* 169.254 2,279.64 61? 193.994 2,994.78 46i 144.906 1,670.95 54 169.646 2,290.23 61* 194.386 3,006.92 46| 145.299 1,680.02 54i 170.039 2,300.84 62 194.779 3,019.08 46! 145.692 1,689.11 Ml 170.432 2,311.48 62i 195.172 3,031.26 46k 146.084 1,698.23 54f 170.824 2,322.15 62J 195.565 3,043.47 46| 146.477 1,707.37 54* 171.217 2,332.83 62f 195.957 3,055.71 463 146.870 1,716.54 54| 171.610 2,343.55 62* 196.350 3,067.97 46* 147.262 1,725.73 54* 172.003 2,354.29 62| 196.743 3,080.25 47 147.655 1,734.95 54* 172.395 2,365.05 62? 197.135 3,092.56 47 i 148.048 1,744.19 55 172.788 2,375.83 62* 197.528 3,104.89 4?! 148.441 1,753.45 55i 173.181 2,386.65 63 197.921 3,117.25 47| 148.833 1,762.74 55j 173.573 2,397.48 631 198.313 3,129.64 47i 149.226 1,772.06 55 j 173.966 2,408.34 63j 198.706 3,142.04 47| 149.619 1,781.40 55* 174.359 2,419.23 63| 199.099 3,154.47 47? 150.011 1,790.76 55| 174.751 2,430.14 63* 199.492 3,166.93 47* 150.404 1,800.15 55? 175.144 2,441.07 63| 199.884 3,179.41 48 150.797 1,809.56 55* 175.537 2,452.03 63? 200.277 3,191.91 48i 151.189 1,819.00 56 175.930 2,463.01 63* 200.670 3,204.44 48i 151.582 1,828.46 56i 176.322 2,474.02 64 201.062 3,217.00 48f 151.975 1,837.95 56j 176.715 2,485.05 641 201.455 3,229.58 48* 152.368 1,847.46 56f 177.108 2,496.11 64j 201.848 3,242.18 48| 152.760 1,856.99 56* 177.500 2,507.19 64$ 202.240 3,254.81 48| 153.153 1,866.55 56| 177.893 2,518.30 64* 202.633 3,267.46 48| 153.546 1,876.14 56? 178.286 2,529.43 64| 203.026 3,280.14 49 153.938 1,885.75 56* 178.678 2,540.58 64? 203.419 3,292.84 49i 154.331 1,895.38 57 179.071 2,551.76 64* 203.811 3,305.56 49j 154.724 1,905.04 57| 179.464 2,562.97 65 204.204 3,318.31 49i 155.116 1,914.72 57* 179.857 2,574.20 65i 204.597 3,331.09 494 155.509 1,924.43 57f 180.249 2,585.45 65* 204.989 3,343.89 49| 155.902 1,934.16 57* 180.642 2,596.73 65! 205.382 3,356.71 49? 156.295 1,943.91 57| 181.035 2,608.03 65* 205.775 3,369.56 49* 156.687 1,953.69 57? 181.427 2,619.36 654 206.167 3,382.44 50 157.080 1,963.50 57* 181.820 2,630.71 65? 206.560 3,395.33 50f 157.473 1,973.33 58 182.213 2,642.09 65* 206 953 3,408.26 50| 157.865 1,983.18 58i 182.605 2.653.49 66 207.346 3,421.20 601 158.258 1,993.06 58j 182.998 2'664.91 66i 207.738 3,434.17 50 158.651 2,002.97 58! 183.391 2,676.36 66| 208.131 3,447.17 50| 159.043 2,012.89 58* 183.784 2,687.84 66| 208.524 3,460.19 50? 159.436 2,022.85 58| 184.176 2,699.33 66* 208.916 3,473.24 50| 159.829 2,032.82 58? 184.569 2,710.86 66| 209.309 3,486.30 51 160.222 2,042.83 58* 184.962 2,722.41 66? 209.702 3,499.40 51i 160.614 2,052.85 59 185.354 2,733.98 66* 210.094 3,512.52 51| 161.007 2,062.90 59i 185.747 2,745.57 67 210.487 3,525.66 51! 161.400 2,072.98 59i 186.140 2,757.20 67i 210.880 3,538.83 511 161.792 2,083.08 59| 186.532 2,768.84 67i 211.273 3,552.02 51| 162.185 2.093.20 59i 186.925 2,780.51 67! 211.665 3,565.24 564 CIRCUMFERENCES AND AREAS OF CIRCLES. Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. Area. 671 212.058 3,578.48 75| 236.798 4,462.16 831 261.538 5,443.26 67f 212.451 3,591.74 751 237.191 4,476.98 83| 261.931 5,459.62 67* 212.843 3,605.04 75| 237.583 4,491.81 83i 262.324 5,476.01 671 213.236 3,618.35 75* 237.976 4,506.67 83 262.716 5,492.41 68 213.629 3,631.69 751 238.369 4,521.56 83* 263.109 5,508.84 681 214.021 3,645.05 76 238.762 4,536.47 831 263.502 5,525.30 681 214.414 3,658.44 761 239.154 4,551.41 84 263.894 5,541.78 68f. 214.807 3,671.86 76i 239.547 4,566.36 841 264.287 5,558.29 681 215.200 3,685.29 76J 239.940 4,581.35 84-i- 264.680 5,574.82 68| 215.592 3,698.76 761 240.332 4,596.36 84| 265.072 5,591.37 68* 215.985 3,712.24 76$ 240.725 4,611.39 841 265.465 5,607.95 68^ 216.378 3,725.75 76* 241.118 4,626.45 84| 265.858 5,624.56 69 216.770 3,739.29 761 241.510 4,641.53 84* 266.251 5,641.18 691 217.163 3,752.85 77 241.903 4,656.64 841 266.643 5,657.84 69i 217.556 3,766.43 771 242.296 4,671.77 85 267.036 5,674.51 69| 217.948 3,780.04 771 242.689 4,686.92 851 267.429 5,691.22 691 218.341 3,793.68 77f 243.081 4,702.10 85| 267.821 5,707.94 69| 218.734 3,807.34 771 243.474 4,717.31 85f 268.214 5,724.69 69* 219.127 3,821.02 77| 243.867 4,732.54 851 268.607 5,741.47 69| 219.519 3,834.73 772 244.259 4,747.79 85| 268.999 5,758.27 70 219.912 3,848.46 771 244.652 4,763.07 85* 269.392 5,775.10 701 220.305 3,862.22 78 245.045 4,778.37 -851 269.785 5,791.94 701 220.697 3,876.00 781 245.437 4,793.70 86 270.178 5,808.82 70| 221.090 3,889.80 781 245.830 4,809.05 86| 270.570 5,825.72 701 221.483 3,903.63 78| 246.223 4,824.43 86j 270.963 5,842,64 70| 221.875 3,917.49 781 246.616 4,839.83 86} 271.356 5,859.59 70* 222.268 3,931.37 78| 247.008 4,855.26 861 271.748 5,876.56 70^ 222.661 3,945.27 78* 247.401 4,870.71 86 272.141 5,893.55 71 223.054 3,959.20 781 247.794 4,886.18 86* 272.534 5,910.58 7H 223.446 3,973.15 79 248.186 4,901.68 86-1 272.926 5,927.62 7H 223.839 3,987.13 791 248.579 4,917.21 87 273.319 5,944.69 Til 224.232 4,001.13 791 248.972 4,932.75 871 273.712 5,961.79 711 224.624 4,015.16 79| 249.364 4,948.33 87| 274.105 5,978.91 71| 225.017 4,029.21 791 249.757 4,963.92 87f 274.497 5,996.05 71* 225.410 4,043.29 79| 250.150 4,979.55 871 274.890 6,013.22 711 225.802 4,057.39 79* 250.543 4,995.19 871 275.283 6,030.41 72 226.195 4,071.51 791 250.935 5,010.86 87* 275.675 6,047.63 721 226.588 4,085.66 80 251.328 5,026.56 871 276.068 6,064.87 721 226.981 4,099.84 801 251.721 5,042.28 88 276.461 6,082.14 72 227.373 4,114.04 '80i 252.113 5,058.03 881 276.853 6,099.43 721 227.766 4,128.26 80| 252.506 5,073.79 881 277.246 6,116.74 72| 228.159 4,142.51 801 252.899 5,089.59 88| 277.629 6,134.08 72* 228.551 4,156.78 80| 253.291 5,105.41 881 278.032 6,151.45 721 228.944 4,171.08 80* 253.684 5,121.25 m 278.424 6,168.84 73 229.337 4,185.40 801 254.077 5,137.12 88* 278.817 6,186.25 73} 229.729 4,199.74 81 254.470 5,153.01 881 279.210 6,203.69 73i 230.122 4,214.11 811 254.862 5,168.93 89 279.602 6,221.15 73f 230.515 4,228.51 8H 255.255 5,184.87 891 279.995 6,238.64 731 230.908 4,242.93 81f 255.648 5,200.83 891 280.388 6,256.15 73| 231.300 4,257.37 811 256.040 5,216.82 89| 280.780 6,273.69 73* 231.693 4,271.84 811 256.433 5,232.84 891 281.173 6,291.25 73f 232.086 4,286.33 81* 256.826 5,248.88 89| 281.566 6,308.84 74 232.478 4,300.85 811 257.218 5,264.94 89* 281.959 6,326.45 741 232.871 4,315.39 82 257.611 5,281.03 891 282.351 6,344.08 74i 233.264 4,329.96 821 258.004 5,297.14 90 282.744 6,361.74 74| 233.656 4,344.55 82i 258.397 5,313.28 901 283.137 6,379.42 741 234.049 4,359.17 82i 258.789 5,329.44 90i 283.529 6,397.13 74| 234.442 4,373.81 821 259.182 5,345.63 90| 283.922 6,414.86 74* 234.835 4,388.47 821 259.575 5,361.84 901 284.315 6,432.62 741 235.227 4,403.16 82* 259.967 5,378.08 90| 284.707 6,450.40 75 235.620 4,417.87 821 260.360 5,394.34 90* 285.100 6,468.21 751 236.013 4,432.61 83 250.753 5,410.62 901 285.493 6,486.04 75 236.405 4.447.38 831 261.145 5,426.93 91 285.886 6,503.90 CIRCUMFERENCES AND AREAS OF CIRCLES. 565 Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. Area. 91} 286.278 6,521.78 94} 295.703 6,958.26 97} 305.128 7,408.89 9l| 286.671 6,539.68 94* 296.096 6,976.76 97} 305.521 7,427.97 91f 287.064 6,557.61 94f 296.488 6,995.28 97* 305.913 7,447.08 91} 287.456 6,575.56 94} 296.881 7,013.82 97} 306.306 7,466.21 91| 287.849 6,593.54 94| 297.274 7,032.39 97| 306.699 7,485.37 91* 288.242 6,611.55 94* 297.667 7,050.98 97* 307.091 7,504.55 ail 288.634 6,629.57 941 298.059 7,069.59 97} 307.484 7,523.75 92 289.027 6,647.63 95 298.452 7,088.24 98 307.877 7,542.98 92} 289.420 6,665.70 95} 298.845 7,106.90 98} 308.270 7,562.24 92i 289.813 6,683.80 95} 299.237 7,125.59 98} 308.662 7,581.52 92f 290.205 6,701.93 95* 299.630 7,144.31 98| 309.055 7,600.82 92} 290.598 6,720.08 95} 300.023 7,163.04 98} 309.448 7,620.15 92| 290.991 6,738.25 95| 300.415 7,181.81 98* 309.840 7,639.50 92| 291.383 6,756.45 95* 300.808 7,200.60 98* 310.233 7,658.88 921 291.776 6,774.68 951 301.201 7,219.41 98} 310.626 7,678.28 93 1 292.169 6,792.92 96 301.594 7,238.25 99 311.018 7,697.71 292.562 6,811.20 96} 301.986 7,257.11 99} 311.411 7,717.16 93- 292.954 6,829.49 96} 302.379 7,275.99 99} 311.804 7,736.63 93| 293.347 6,847.82 96f 302.772 7,294.91 99| 312.196 7,756.13 93} 293.740 6,866.16 96} 303.164 7,313.84 99} 312.589 7,775.66 93* 294.132 6,884.53 96* 303.557 7,332.80 99| 312.982 7,795.21 93* 294.525 6,902.93 96* 303.950 7,351.79 99* 313.375 7,814.78 931 294.918 6,921.35 961 304.342 7,370.79 99} 313.767 7,834.38 94 295.310 6,939.79 97 304.735 7,389.83 100 314.160 7,854.00 The preceding table may be used to determine the diameter when the circumference or area is known. Thus, the diameter of a circle having an area of 7,200 sq. in. is approximately 95* in. A GLOSSARY OF MINING TERMS. The present glossary is a combination of glossaries of mining terms con- tained in the following works: Coal and Metal Miners' Pocketbook, Fifth Edition; Raymond's Glossary of Mining and Metallurgical Terms; Powers' Pocketbook for Miners and Metallurgists; Locke's Miners' Pocketbook; Vol. AC, Second Pennsylvania Geological Survey; Ilhseng's Manual of Mining; Chism's Encyclopedia of Mexican Mining Law; a Glossary of Terms as Used in Coal Mining, by W. S. Gresley; llth Annual Report of the State Mine Inspector of Missouri; Bullman's Colliery Working and Management; Reynolds' Handbook of Mining Laws; Report of the Mine Inspector of Tennessee for 1897; Smithsonian Report for 1886; together with a large num- ber of words which have been added from various stray sources. It is impossible to quote the authority for each definition, as many of the defini- tions are combinations from a number of authors. Where such different definitions have given distinctly different meanings, each one has been included, but where there has been expressed merely a slight shade of difference, the definition agreeing most closely with current American practice has been taken, or else modified to suit such practice. The foreign words selected are those with which an American is most likely to come in contact, and this portion of the glossary is, of course, not exhaustive. For the large number of purely local terms used in the several coal fields of Great Britain, the reader is referred to Mr. Gresley's glossary. 56(i ABA GLOSSARY. GLOSSARY. Abattis (Leicester). Cross-packing of branches or rough wood, used to keep roads open for ventilation. Abra (Spanish). Fissure in a lode, unfilled or only partially filled. Abronziado (Spanish). Copper sulphides. Absolute Pressure. The pressure reckoned from a vacuum. Absolute Temperature. The temperature reckoned from the absolute zero, 459.2 F. or 273 C. Accompt (Cornish). Settling day or place. Achicar (Mexican). To diminish the quantity of water in any gallery or working, generally by carrying it out in buckets or in leather bags. Achicadores. Laborers employed for said purpose. Achichinques. Same as Achicadores. Also applied to hangers-on about police courts, etc. Such people as are generally called strikers in the United States. Acreage Rent (English). Royalty or rent for working minerals. Adarme (Mexican). A weight for gold, about 1.8 grams. Addlings (North of England). Earnings. Ademador (Spanish). Mine carpenter, or timberman. Ademar (Spanish). To timber. Adit. A nearly horizontal passage from the surface, by which a mine is entered and unwatered with just sufficient slope to insure drainage. In the United States, an adit driven across the measures is usually called a tunnel, though the latter, strictly speaking, passes entirely through a hill, and is open at both ends. Adobe. Sun-dried brick. Adventurers. Original prospectors. Adverse. To oppose the granting of a patent to mining claim. Adze. A curved cutting instrument for dressing timber. Aerage (French). Ventilation. Aerometers. The air pistons of a Struve ventilator. Aerophore. The name given to an apparatus that will enable a man to enter places in mines filled with explosive or other deadly gases, with safety. Afinar (Mexican). Refining gold and silver. Afterdamp. The gaseous mixture resulting from an explosion of firedamp. Agent. The manager of a mining property. Agitator A. mechanical stirrer used in pan amalgamation. Ahondar (Spanish). To sink. Air. The current of atmospheric air circulating through and ventilating the workings of a mine. Air .Box. Wooden tubes used to convey air for ventilating headings or sinkings or other local ventilation. Air Compartment. An air-tight portion of any shaft, winze, rise, or level, used for improving ventilation. Air-Course. See Airway. Air Crossing. A bridge that carries one air-course over another. Air Cushion. A spring caused by confined air. Air Door. A door for the regulation of currents of air through the workings of a mine. Air-End Way (Locke). Ventilation levels run parallel with main level. Air Furnace. A reverberatory furnace in which to smelt lead. Air Gates (Locke). (1) Underground roadways, used principally for venti- lating purposes. (2) An air regulator. Air Head (Staff ) . yentilation ways. Air Heading. An airway. Air Hole (Powers). A hole drilled in advance to improve ventilation by communication with other workings or the surface. Airless End. The extremity of a stall in longwall workings in which there is no current of air, or circulation of ventilation, but which is kept pure by diffusion and by the ingress and egress of cars, men, etc. AIR GLOSSARY. AQU 567 Air Level A. level or airway of former workings made use of in subsequent deeper mining operations for ventilating purposes. Air Oven. A heated chamber for drying samples of ore, etc. . Air Pipe. A pipe made of canvas or metal, or a wooden box used in con- veying air to the workmen, or for rock drills or air locomotives. Air-Shaft. A shaft or pit used expressly for ventilation. Air Slit (Yorks). A short head between other air heads. Air Sollar.A brattice carried beneath the tram rails or road bed in a head- ing or gangway. Air Stack. A stack or chimney built over a shaft for ventilation. Airway. Any passage through which air is carried. Aitch Piece. Parts of a pump in which the valves are fixed. Albanil (Spanish). Mason. Albayalde (Spanish). White lead. Alberti Furnace. A continuous reverberatory for mercury ores. Alcam (Wales). Tin. Alive (Cornish). Productive. Alloy. A homogeneous mixture of two or more metals by fusion. Alluvial Gold. Gold, found associated with water-worn material. Alluvium. Gravel, sand, and mud deposited by streams. Almadeneta (Spanish). Stamp head. Almagre (Spanish). Red ocher. Alternating Motion. Up and down, or backward and forward motion. Alto ( Mexican). The hanging wall of a vein. See Eespaldos. Aludel (Spanish). Earthen condenser for mercury. Amalgam. An alloy of quicksilver with some other metal. Amalgamation. Absorption of gold and, silver by mercury. Amalgamator. One that amalgamates gold and silver ores. Amygdaloidal. Almond-shaped. Analysis. The determination of the original elements and the proportions of each in a substance. Anemometer. An instrument used for measuring the velocity of a ventilating current. Angle Beam. A two-limbed beam used for turning angles in shafts, etc. Anhydrous. Without water in its composition. Anneal. To toughen metals, glass, etc. by first heating and then cooling very slowly. Anthracite. A* variety of coal containing a small percentage of volatile matter. Anticline. A flexure or fold in which the rocks on the opposite sides of the fold dip away from each other, like the two legs of the letter A. The inclination on one side may be much greater than on the opposite side. An anticlinal is said to be overturned when the rocks on both sides dip in the same direction. Anticlinal Axis. The ridge of a saddle in a mineral vein, or the line along the summit of a vein, from which the vein dips in opposite directions. Anticlinal Flexure; Anticlinal Fold. An anticline. Antiguos, Los (Mexican). The Spanish or Indian miners of colonial times. . Antimony Star. The metal antimony when crystallized, showing fern-like, markings on the surface. Aparadores (Mexican). Persons that re wash or rework tailings from silver mills. Apare/jo (Mexican). A pack saddle. Any rough-and-ready apparatus for moving and adjusting heavy timbers, etc. Aperos (Mexican). All kinds of mining supplies in general. Aperador. A storekeeper. Apex. The landing point at the top of a slope or inclined plane, the knuckle; also, the top of an anticlinal. In the U. S. Revised Statutes, the end or edge of a vein nearest the surface. A pique (Mexican). Perpendicular. Apolvillados (Spanish). Superior ores. Apron (English). (1) A covering of timber, stone, or metal, to protect a sur- face against the action of water flowing over it. (2) A hinged extension to a loading chute. Aprons. Stamp-battery copper plates. Aqua Fortis. Nitric acid. Aqua Regia.A mixture of hydrochloric acid and nitric acid. Aqueduct. An artificial elevated way for carrying water. 568 ARA GLOSSARY. Azo Arajo ( Mexican ).-^See Hatajo. Arch (Cornish). Portion of lode left standing to support hanging wall, or .because too poor. Arcfiean. An early period of geological time. Arching. Brickwork or stonework forming the roof of any underground roadway. Arenaceous. Sandy; rocks are arenaceous when they contain a considerable percentage of sand. Arends Tap. An inverted siphon for drawing molten lead from a crucible or furnace. Arenillas (Spanish). Refuse earth. Argentiferous. Silver-bearing. Argillaceous. Clayey; rocks are argillaceous when they contain a consid- erable percentage of clay, or have some of the characteristics of clay. ArgoL Crude tartar deposited from wine. Arian (Wales). Silver. Arm. The inclined leg of a set of timber. Arrage (North England). Sharp corner. Arrastre. A circular trough in which drags are pulled round by being con- nected with a central revolving shaft by an arm and chain. Used for grinding and amalgamating ores. Arrastre de cuchara, spoon arrastre; de marca, large arrastre; de mula, mule-power arrastre. Arrastrar (Mexican). To drag along the ground. Arrastrar el Agua. To almost completely exhaust the water in a sump or working. Arroba (Mexican). 25 Ib. Artesian Well. An artificial channel of escape, made by a bore hole, for a subterranean stream, subject to hydrostatic pressure. Ascensional Ventilation. The arrangement of the ventilating currents in such a manner that the air shall continuously rise until reaching the bottom of the upcast shaft. Particularly applicable to steep seams. AsMar. A facing of cut stone applied to a backing of nibble or rough masonry or brickwork. Aspirail (French). Opening for ventilation. Assay. The determination of the quality and quantity" of any particular substance in a mineral. Assayer. One who performs assays. Assessment Work. The annual work necessary to hold a mining claim. Astel. Overhead boarding in a gallery. Astyllen (Cornish). Small dam in an adit; partition between ore and deads on grass. Atacador (Mexican). A tamping bar or tamping stick. Atecas (Mexican). Same as Achicadores, etc. Atierres (Spanish). Refuse rock or dirt inside a mine. Attle (Cornish). Refuse rock. Attle (Addle). The waste of a mine. Attrition. The act of wearing away by friction. Auger Stem. The iron rod or bar to which the bit is attached in rope drilling. Auget. Priming tube. Aur (Wales). Gold. Auriferous. Gold-bearing. Ausscharen (German). Junction of lodes. Auszimmern ( German) .Timber! ng. Average Produce (Cornish). Percentage of fine copper in ore. Average Standard (Cornish). Price of pure copper in ore. Aviador (Spanish). One who provides the capital to work a mine. Avio. Money furnished to the proprietors of a mine to work the mine, by another person, the Aviador. Avio Contract. A contract between two parties for working a mine by which one of the parties, the aviador, furnishes the money to the proprietors for working the mine. Axis. An imaginary line passing through a body that may be supposed to revolve around it. Azimuth. The azimuth of a body is that arc of the horizon that is included between the meridian circle at the given place and a vertical plane passing through the body. It is always measured from due north around to the right. Azogue (Spanish). Mercury. Azogueria. Amalgamating works. Azoguero. Amalgamator. The person in charge of a patio works. Azogues. Free milling ores. Azoic. The age of rocks that were formed before animal life existed. BAC GLOSSARY. BAN 569 Back. (1) A plane or cleavage in coal, etc., having frequently a smooth parting and some sooty coal included in it. (2) The inner end of a heading or gangway. (3) To throw back into the gob or waste the small slack, dirt, etc. (4) To roll large coals out of a waste for loading into cars. Back Balance. A self-acting incline in the mine, where a balance car and a carriage in which the mine car is placed are used. The loaded car upon the carriage will hoist the balance car, and the balance car will hoist the carriage and empty car. Backbye Work. Work done between the shaft and the working face, in contradistinction to face work, or work done at the face. Back Casing. A wall or lining of dry bricks used in sinking through drift deposits, the permanent walling being built up within it. The use of timber cribs and planking serves the same purpose. Back End (England). The last portion of a jud. Backing. (I) The rough masonry of a wall faced with finer work. (2) Earth deposited behind a retaining wall, etc. (3) Timbers let into notches in the rock across the top of a level. Backing Deals. Deal boards or planking placed at the back of curbs for supporting the sides of a shaft that is liable to run. Back Joint. Joint plane more or less parallel to the strike of the cleavage, and frequently vertical. Backlash. (1) Backward suction of air-currents produced after an explosion of firedamp. (2) Reentry of air into a fan. Back of Ore. The ore between two levels which has to be worked from the lower level. Back Pressure. The loss, expressed in pounds per square inch, due to getting the steam out of the cylinder after it has done its work. Back Shift. Afternoon shift. Back Skin (North of England). A leather jacket for wet workings. Backstay. A wrought-iron forked bar attached to the back of cars when ascending an inclined plane, which throws them off the rails if the rope or coupling breaks. Baff Ends. Long wooden edges for adjusting linings in sinking shafts dur- ing the operation of fixing the lining. Baffle. To brush out firedamp. Bait. Provisions. Bajo (Mexican). The footwall of a vein. See Respaldo. Bal (Cornish). A mine. Balance. (I) The counterpoise or weights attached to the drum of a winding engine, to assist the engine in lifting the load out of a shaft bottom and in helping it to slacken speed when the cage reaches the surface. It consists often of a bunch of heavy chains suspended in a shallow shaft, the chains resting on the shaft bottom as unwound off the balance drum attached to the main shaft of the engine. (2) Scales used in chemical analysis and assaying. Balance Bob. A large beam or lever attached to the main rods of a Cornish pumping engine, carrying on its outer end a counterpoise. Balance Box. A large box placed on one end of a balance bob and filled with old iron, rock, etc. to counterbalance the weight of pump rods. Balance Brow. An inclined plane in steep seams on which a platform on wheels travels and carries the cars of coal. Balance Car. A small weighted truck mounted upon a short inclined track, and carrying a sheave around which the rope of an endless haulage system passes as it winds off the drum. Balance Pit. A pit or shaft in which a balance rises or falls. Balanzon (Mexican). The balance bob of a Cornish pump. Balk. (1) A more or less sudden thinning out of a seam of coal. (2) Irregu- lar-shaped masses of stone intruding into a coal seam, or bulgings out of the stone roof into the seam. (3) A bar of timber supporting the roof of a mine, or for carrying any heavy load. Balland (Derbyshire). Pulverulent lead ore. Ballast. Broken stone, gravel, sand, etc. used for keeping railroad ties steady. Bancos (Spanish). Horses in a vein or cross-courses. Band. A seam or thin stratum of stone or other refuse in a seam of coal. Bank (1) The top of the shaft, or out of the shaft. (2) The surface around the mouth of a shaft. (3) To manipulate coals, etc. on the bank. (4) The whole or sometimes only one side or one end of a working place underground. (5) A large heap of mineral on the surface. 570 BAN GLOSSARY. BAS Bank Chain. A chain that includes the bank of a river or creek. Bank Claim (Australian). Mining right on bank of stream. Banket. Auriferous conglomerate of South Africa. Bank Head. The upper end of an inclined plane, next to the engine or drum, made nearly level. Bank Eight (Australian). Right to divert water to bank claim. Banksman. The man in attendance at the top of the shaft, superintending the work of banking. Bankwork.A. system of working coal in South Yorkshire. Bank to Bank. A. shift. Bannocking. See Kirving. Bano (Spanish). Excess of mercury used in torta. Bar. A. length of timber placed horizontally for supporting the roof. In some cases, bars of wrought iron, about 3 in. X 1 in. X 5 ft. are used. Bar Diggings. (I) River placers subject to overflow. (2) Auriferous claims on shallow streams. Bargain. Portion of mine worked by a gang on contract. Barilla (Spanish). Grains of native copper disseminated through ores. Baring. See Stripping. Barmaster (Derbyshire) Mine manager, agent, and engineer. Bar Mining. The mining of river bars, usually between low and high water, although the stream is sometimes deflected and the bar worked below water level. Barney A. small car, used on inclined planes and slopes to push the mine car up the slope. Barney Pit. A pit at the bottom of a slope or plane into which the barney runs to allow the mine car to pass over it. Barra (Mexican). (1) A bar, as of gold, silver, iron, steel, etc. (2) A cer- tain share in a mine. The ancient Spanish laws, from time immemorial, considered a mine as divided into 24 parts, and each part was called a "barra." Barra Viuda, or Aviada (Mexican). These are "barras " or shares that par- ticipate in the profits, but not in the expenses, of mining concerns. Their share of the expenses is paid by the other shares. Non-assessable shares. Barranca (Mexican). A ravine, a gulch. What is improperly called in the United States a canyon or canon. Barrel Amalgamation. Amalgamating ores in revolving barrels. Barrel Work. (1) Native copper that can be hand-sorted ready for smelt- ing. (2) Barrel amalgamation. Barrena (Mexican). A hand drill for opening holes in rocks for blasting purposes. Barrenarse (Mexican). When two mines or two workings (as a shaft or winze, or a gallery) communicate with each other. Barren Ground. Strata, unproductive of seams of coal, etc. of a workable thickness. Barreno (Mexican) .(1) A drill hole for blasting purposes. In mechanics, any bored hole. (2) A communication between two mines or two workings. Barretero (Mexican). A miner of the first class: one that knows how to point his holes, drill, and blast, or work with a gad. Barrier Pillar. A solid block or rib of coal, etc., left unwprked between two collieries or mines for security against accidents arising from influx of water. Barrier System. The method of working a colliery by pillar and stall, where solid ribs or barriers of coal are left in between a set or series of working places. Barrow. (1) A box with two handles at one end and a wheel at the other. (2) Heap of waste stuff raised from a mine; a dump. Bar Timbering. A. system of supporting a tunnel roof by long top bars, while the whole lower tunnel core is taken out, leaving an open space for the masons to run up the arching. Under certain conditions, the bars are withdrawn after the masonry is completed, otherwise they are bricked in and not drawn. Base Bullion. Lead combined with precious metals. Base Metal. Metal not classed with the precious metals, gold, silver, plat- inum, etc., that are not easily oxidized. Basin. (I) A coal field having some resemblance in form to a basin. (2) The synclinal axis of a seam of coal or stratum of rock. Basket A. measure of weight = 2 cwt. BAS GLOSSARY. BEN 571 Basque. Crucible or furnace lining. Bass (Derbyshire). Indurated clay. Basset. Outcrop of a lode or stratum. Bastard. A particularly hard massive rock or boulder. Batch. An assorted parcel of ore, sometimes called doles, when divided into equal quantities. Batea.A shallow wooden bowl used for washing out gold, etc. Bait (English). (1) A highly bituminous shale found in the coal measures. (2) Hardened clay, but not fireclay. Same as Bend and Bind. Batten A. piece of thin board less than 12 in. in width. Batter. The inclination of a face of masonry or of any inclined portion of a frame or metal structure. Battery. (I) A structure built to keep coal from sliding down a chute or breast. (2) An embankment or platform on which miners work. (3) A set of stamps. Bay. An open space for waste between two packs in a longwall working. See Board. Bay of Biscay Country. (Geological). See Crab Holes. Beach Combing. Working the sands on a beach for gold, tin, or platinum. Beans (North of England). All coal that will pass through about i" screen. Bean Shot Copper granulated by pouring into hot water. Bear. A deposit of iron at the bottom of a furnace. Bear; to Bear In. Underholding or undermining; driving in at the top or at the side of a working. Bearers. Pieces of timber 3 or 4 ft. longer than the breadth of a shaft, which are fixed into the solid rock at the sides at certain intervals apart; used as foundations for sets of timber. Bearing. (I) The course by a compass. (2) The span or length in the clear between the points of support of a beam, etc. (3) The points of support of a beam, shaft, axle, etc. Bearing Door. A door placed for the purpose of directing and regulating the amount of ventilation passing through an entire district of a mine. Bearing In. The depth or distance under of the undercut or holing. Bearing-up Pulley. A pulley wheel fixed in a frame and arranged to tighten up or take up the slack rope in endless-rope haulage. Bearing-up Stop. A partition of brattice or plank that serves to conduct air to a face. Beat (Cornish). To cut away a lode. Beataway. Working hard ground by means of wedges and sledge hammers. Bed. (1) The level surface of a rock upon which a curb or crib is laid. (2) A stratum of coal, ironstone, clay, etc. Bed Claim (Australian). A claim that includes the bed of a river or creek. Bede. Miners' pickax. Bedplate. A large plate of iron used as a foundation for an engine. Bed Rock. The solid rock underlying the soil, drift, or alluvial deposits. Before- Breast. Rock or vein, which still lies ahead. Belgian Zinc Furnace. A furnace for the production of zinc, in which the calcined ore is distilled in tubular retorts. Bell. Overhanging rock or slate, of a bell-like form, disconnected from the main roof. Belland.A form of lead poisoning to which lead miners are subject. Belly. A swelling mass of ore in a lode. Ben, Benhayl (Cornish). Productive. The productive portion of a tin stream. Bench. (l) A natural terrace marking the outcrop of any stratum. (2) A stratum of coal forming a portion of the vein. Bench Diggings. River placers not subject to overflow. Benching. To break up with wedges the bottom coals when the holing is done in the middle of the seam. Benching Up (North of England). Working on top of coal. Bench Mark. A mark cut in a tree or rock whose elevation is known. Used by surveyors for reference in determining elevations. Bench Working. The system of working one or more seams or beds of mineral by open working or stripping, in stages or steps. Bend (Derbyshire). Indurated clay. Beneficiar (Mexican). To treat ores for the purpose of extracting the metallic contents. 572 BEN GLOSSARY. BLO Beneficio (Mexican). Any metallurgical process. Benheyl (Cornish). Flowing tin stream. Bessemer Steel. Steel made by the Bessemer process. Beton (English). Concrete of hydraulic cement with broken stone, bricks, gravel, etc. Bevel. The slope formed by trimming away on edge. Bevel Gear. A gear-whe^el whose teeth are inclined to the axis of the wheel. Biche. A hollow-ended tool for recovering boring rods. Billy Boy. A boy who attends a Billy Playfair. Billy Playfair. A. mechanical contrivance for weighing coal, consisting of an iron trough with a sort of hopper bottom, into which all the small coal passing through the screen is conducted and weighed off and emptied from time to time. Bin. A box with cover, used for tools, stones, ore, etc. Bind, or Binder. Indurated argillaceous shales or clay, very commonly forming the roof of a coal seam and frequently containing clay iron- stone. See Batt. Binding. Hiring men. Bing (North of England). 8 cwt. of ore. Bing Hole (Derbyshire). An ore shoot. Bing Ore (Derbyshire). Lead ore in lumps. Bing Tale (North of England). Ore given to the miner for his labor. Bit A. piece of steel placed in the cutting edge of a drill or point of a pick. Blackband Carbonaceous ironstone in beds, mingled with coaly matter sufficient for its own calcination. Black Batt, or Black Stone. Black carbonaceous shale. Black Copper. Impure smelted copper. Blackdamp Carbonic-acid gas. Black Diamonds. Coal. Black Ends. Refuse coke. Black Flux. Charcoal and potassium carbonate. Black Jack. (1) Properly speaking, dark varieties of zinc blende, but many miners apply it to any black mineral. (2) Crude black oil used to oil mine cars. Black Lead. Graphite. Black Ore (English). Partly decomposed pyrites containing copper. Black Sand. Dark minerals found with alluvial gold. Black Stone. A carbonaceous shale. Black Tin. Dressed cassiterite; oxide of tin. Blanch. (1) A piece of ore found isolated in the hard rock. (2) Lead ore mixed with other minerals. Blanched Copper. Copper alloyed with arsenic. Blanket Strake (Australian). Sloping tables or sluices lined with baize, for catching gold. Blanket Tables. Inclined planes covered with blankets, to catch the heavier minerals passing over them. Blast. (1) The sudden rush of fire, gas, and dust of an explosion through the workings and roadways of a mine. (2) To cut or bring down coal, rocks, etc. by the explosion of gunpowder, dynamite, etc. Blasting Barrel. A small pipe used for blasting in wet or gaseous places. Blast Pipe. A pipe for supplying air to furnaces. Blende. Sulphide of zinc; sphalerite. Blick (Germany). Iridescence on gold and silver at end of cupeling. Blind Coal. Coal altered by the heat of a trap dike. Blind Creek. (1) A creek in which water flows only in very wet weather. (2) (Australasian) Dry watercourse. Blind Drift. A horizontal passage in the mine not yet connected with the other workings. Blind Joint. Obscure bedding plane. Blind Lead, or Blind Lode. A vein having no visible outcrop. Blind Level. (1) An incomplete level. (2) A drainage level. Blind Shaft, or Blind Pit. A shaft not coming to the surface. Bloat. A hammer swelled at the eye. Block Claim (Australian). A square mining claim. Block Coal. Coal that breaks in large rectangular lumps. Blocking Out. (1) Working deep leads in blocks; somewhat like horizontal stoping. (2) (Australian) Washing gold gravel in sections. Block Reefs. Reefs showing frequent contractions longitudinally. BLO GLOSSARY. BON 573 Block Tin. Cast tin. Bloomary.A forge for making wrought iron. Blossom. The decomposed outcrop, float, surface stain, or any indicating traces of a coal bed or mineral deposit. Blossom Rock. (I) Colored veinstone detached from an outcrop. (2) The rock detached from a vein, but which has not been transported. Blow. (1) To blast with gunpowder, etc. (2) A dam or stopping is said to blow when gas escapes through it. Blower. (1) A sudden emission or outburst of gas in a mine. (2) Any emission of gas from a coal seam similar to that from an ordinary gas burner. (3) A type of centrifugal fan used largely to force air into furnaces. (4) A blowdown ventilating fan. Blow Fan. A. small centrifugal fan used to force air through canvas pipes or wooden boxes to the workmen. Blowdown Fan. A force fan. Blow In. To commence a smelting process. Blown-Out Shot. A shot that has blown out the tamping, but not broken the coal or rock. Blow Off. To let off excess of steam from a boiler. Blow Out. (1) To finish a smelting campaign. (2) A blown-out shot. (3) The decomposed mineral exposure of a vein. Blowpipe. An instrument for creating a blast whereby the heat of a flame or lamp can be better utilized. Blue Billy. Residue of copper pyrites after roasting with salt. Blue Cap. The blue halo of ignited gas (firedamp and air) on the top of the flame in a safety lamp, in an explosive mixture. Blue Elvan (Cornish). Greenstone. Blue John. Fluorspar. Blue Lead. A blue-stained stratum of gravel of great extent and richness. Blue Metal. A local term for shale possessing a bluish color. Blue Peach (Cornish). A slate-blue fine-grained schorl. Bluestone.(l] Sulphate of copper. (2) Lapis lazuli. (3) Basalt. (4) Maryland, a gray gneiss; in Ohio, a gray sandstone; in the District of Columbia, a mica schist; in New York, a blue-gray sandstone; in Pennsylvania, a blue-gray sandstone. (5) A popular term among stone men not suf- ficiently definite to be of value. Bluff. Blunt. Board. A wide heading usually from 3 to 5 yd. wide. Board-and-Pillar. A system of working coal where the first stage of exca- vation is accomplished with the roof sustained by pillars of coal left between the breasts; often called Breast-and-Pillar. Bob. An oscillating bell-crank, or lever, through which the motion of an engine is transmitted to the pump rods in an engine or pumping pit. There are j. bobs, L bobs, and V bobs. Boca or Boca Mina (Mexican). Mouth or mine mouth. This is the name applied to the principal or first opening of a mine, or to the one where the miners are accustomed to descend. Bochorno (Mexican). Excessive heat, with want of ventilation, so that the lights go out. See Vapores. Body.(l] An ore body, or pocket of mineral deposit. (2) The thickness of a lubricating oil or other liquid; also the measure of that thickness expressed in the number of seconds in which a given quantity of the oil at a given temperature flows through a given aperture. Bog Iron Ore. Loose earthy brown hematite recently formed in swampy ground. Boleo (Mexican). A dump pile for waste rock. Boliche (Spanish). Concentrating bowl. Bollos (Spanish). Triangular blocks of amalgam. Bolsa (Spanish). Small bunch of ore. Bonanza. An aggregation of rich ore in a mine. Bond. (I) The arrangement of blocks of stone or brickwork to form a firm structure by a judicious overlapping of each other so as to break joint. (2) An agreement for hiring men. Bone. Slaty coal or carbonaceous shale found in coal seams. Bone Ash. Burnt bones pulverized and sifted. Bonnet. (I) The overhead cover of a cage. (2) A cover for the gauze of a safety lamp. (3) A cap piece for an upright timber. Bonney (Cornish). An isolated body of ore. 574 BON GLOSSARY. BRE Bonze. Undressed lead ore. Booming. Ground sluicing on a large scale by emptying the contents of a reservoir at once on material collected below, thus removing boulders. Bord (English). A narrow breast. Bord-and-Pillar (English). See Pillar-and- Breast. Bord Room. The space excavated in driving a bord. The term is used in connection with the "ridding" of the fallen stone in old bords when driving roads across them in pillar working: thus, " ridding across the old bord room." Bord Ways Course. The direction at right angles to the main cleavage planes. In some mining districts, it is termed "on face." Bore. To drill. Bore Hole. A hole made with a drill, auger, or other tools, in coal, rock, or other material. Borrasca (Mexican). The reverse of bonanza. When the mine has a vein, but no ore, it is said to be " en borrasca." Bort. Amorphous dark diamond. Bosh. The plane in a blast furnace where the greatest diameter is reached. Boss (English). (1) An increase of the diameter at any part of the shaft. (2) A person in charge of a piece of work. Botas (Mexican). Buckets made of an entire ox skin, to take out water. Botryoidal. Grape-like in appearance. Bottle Jack (English). An appliance for lifting heavy weights. Bottom. (I) The landing at the bottom of the shaft or slope. (2) The lowest point of mining operations. (3) The floor, bottom rock, or stratum underlying a coal bed. (4) In alluvial, the bed rock or reef. Bottomer, Bottomman.The person that loads the cages at the pit bottom and gives the signal to bank. Bottom Joint. Joint or bedding plane, horizontal or nearly so. Bottom Lift. (I) The deepest column of a pump. (2) The lowest or deepest lift or level of a mine. Bottom Pillars. Large pillars left around the bottom of a shaft. Bottoms. Impure copper alloy below the matte in smelting. Boulders. Loose rounded masses of stone detached from the parent rock. Bounds (Cornish). A tract of tin ground. Bout (Derbyshire). Twenty-four dishes of lead ore. Bow, The handle of a kibble. Bowk. An iron barrel or tub used for hoisting rock and other debris when sinking a shaft. Bowke (Staffordshire). A small wooden box for hauling ironstone under- ground. Bowl Metal. The impure antimony obtained from doubling. Bowse (Derbyshire). Lead ore as cut from the lode. Box. (I) A 12' to 14' section of a sluice. (2) A mine car. Box Bill. Tool for recovering boring rods. Boxing. A method of securing shafts solely by slabs and wooden pegs. Brace. (1) An inclined beam, bar, or strut for sustaining compression or tension. See Tie-Brace, Sway-Brace. (2) A platform at the top of u shaft on which miners stand to work the tackle. (3) (Cornish) Building at pit mouth. Brace Heads. Wooden handles or bars for raising and rotating the rods when boring a deep hole. Braize. Charcoal dust. Brake Save. Hand jigger. Brances.lron pyrites in coal. Branch. Small vein shooting off from main lode. Brashy. Short and tender. Brasque.A mixture of clay and coke or charcoal used for furnace bottoms. Brass. (1) Iron pyrites in coal. (2) An alloy of copper and zinc. Brasses (English). Fitting of brass in plumriier blocks, etc., for diminishing the friction of revolving journals that rest upon them. Brat. A thin bed of coal mixed with pyrites or limestone. Brattice. A lining or partition. Brattice Cloth. Ducking or canvas used for making a brattice. Brazzil (North of England). Iron pyrites in coal. Breaker. In anthracite mining, the structure in which the coal is broken, sized, and cleaned for market. Known also as Coal Breaker, Breaker Boy. A boy who works in a coal breaker. BRE GLOSSARY. BUL 575 Breakstaff. The lever for blowing a blacksmiths' bellows, or for working bore rods up and down. Breakthrough. A. narrow passage cut through a pillar connecting rooms. Breast. (1) A stall, board, or room in which coal is mined. (2) The face or wall of a quarry is sometimes called by this name. Breast-and-Pillar.A system of working coal by boards or rooms with pillars of coal between them. Breasting Ore. The ore taken from the face or end of the tunnel. Breast Wall (English). A wall built to prevent the falling of a vertical face cut into the natural soil. Breccia. A rock composed of angular fragments cemented together. Breeding Fire. See Gob Fire. Breese.Fine slack. Breeze. Small coke, probably same as braize or braise. Brettis (Derbyshire). A timber crib filled with slack. Bridge. (1) A platform on wheels running on rails for covering the mouth of a shaft or slope. (2) A track or platform passing over an inclined haulage way and which can be raised out of the way of ascending and descending cars. (3) An air crossing. Bridle Chains. Short chains by which a cage, car, or gunboat is attached to a winding rope; of use in case the rope pulls out of its socket. Briquets. Fuel made of slack or culm and pressed into brick form. Broaching Bit A tool for reopening a bore hole that has been partially closed by swelling of the walls. Brob.A spike to prevent timber slipping. Broil (Cornish). Traces of a vein in loose matter. Broken. A district of coal pillars in process of removal, so called in contra- distinction to the first working of a seam by bord-and-wall, or working in the "whole." See Whole Working. Broken Coal. Anthracite coal that will pass through a mesh or bars 3i to 4| in., and over a mesh 2f in. square. (See page 434.) Bronce (Mexican). In mining, copper or iron pyrites. Brooch (Cornish). Mixed ores. Brooching. Smoothing. Brood (Cornish). Heavy waste from tin and copper ores. Brow. An underground roadway leading to a working place driven either to the rise or to the dip. Brown Coal. Lignite. A fuel classed between peat and bituminous coal. Brown Spar. Dolomite containing carbonate of iron. Brownstone.(l) Decomposed iron pyrites. (2) Brown sandstone. Browse. Imperfectly smelted ore mixed with cinder and clay. Brujula (Mexican). A surveyors' (or marine) magnetic compass. Brush. (I) To mix air with the gas in a mine working by swinging a jacket, etc., which creates a current. (2) To "brush" the roof of an airway, is to take down some of the roof slate, to increase the height or headroom. Bryle (Cornish). Traces of a vein in loose matter. Bucket. (1) An iron or wooden receptacle for hoisting ore, or for raising rock in shaft sinking. (2) The top valve or clack of a pump. Bucket Pump. A lifting pump, consisting of buckets fastened to an endless belt or chain. BuckefSword.A wrought-iron rod to which the pump bucket is attached. Bucket Tree. The pipe between the working barrel and the wind bore. Bucking. Breaking down ore with a very broad hammer, ready for jigging. Bucking Hammer. An iron disk, provided with a handle, used for breaking up minerals by hand. Buck Quartz. Hard non-auriferous quartz. Buck Staff. Uprights for bracing reverberatory furnaces together. Buckwheat. Anthracite coal that will pass through a mesh \ in. and over a mesh | in. Buddie. An inclined table, circular or oblong, on which ore is concentrated. Buddling. Washing. Buggy. A small mine car. Bug Hole A small cavity usually lined with crystals. Building. A built-up block or pillar of stone or coal to support the roof. Buitron (Spanish). A silver furnace of peculiar form. Bulkhead (I) A tight partition or stopping. (2) The end of a flume carry- ing water for hydraulicking. 576 BUL GLOSSARY. CAL Bulldog. A refractory furnace lining of calcined mill cinder, containing iron and silica. Bull Engine. A single, direct-acting pumping engine, the pump rods form- ing a continuation of the piston rod. Butter Shot. A second shot put in close to, and to do the work not done by, a blown-out shot, loose powder being used. Bull. An iron rod used in ramming clay to line a shot hole. Bulling. Lining a shot hole with clay. Bullion. Uncoined gold and silver. Butt Pump. A single-acting pumping engine in which the steam cylinder is placed over the shaft or slope and the pump rods are attached directly to the piston rod. The steam enters below the piston and raises the pump rods; the water is pumped on the down stroke by the weight of the rods. Butt Pup. A worthless claim. Bull Wheel. A wheel on which the rope carrying the boring rod is coiled when boring by steam machinery. Bully. A miners' hammer. Bumping Table. A concentrating table with a jolting motion. Bunch. A small rich deposit of ore. Bunding. A staging in a level for carrying debris. Bunkers. Steam coal consumed on board ship. Bunney. A nest of ore not lying in a regular vein. Bunions. Timbers placed horizontally across a shaft or slope to carry the cage guides, pump rods, column pipe, etc. ; also, to strengthen the shaft timbering. Burden. (1) Earth overlying a bed of useful mineral. (2) The proportion of ore and flux to fuel in the charge of a blast furnace. Burr. Solid rock. Burrow. Refuse heap. Buscones (Spanish). Prospectors, fossickers, tribute workers. Bush. To line a circular hole with a ring of metal, to prevent the hole from wearing out. Butt. (1) Coal surface exposed at right angles to the face; the "ends" of the coal. (2) The butt of a slate quarry is where the overlying rock comes in contact with an inclined stratum of slate rock. Butt Entry. A gallery driven at right angles with the butt joint (see page 285). Butterfly Valve. A circular valve that revolves on an axis passing through its center. Butt Heading. See Butt Entry. Button. The globule of metal, the result of an assay. Button Balance. A small very delicate balance used for weighing assay buttons. Batty. A partner in a contract for driving or mining; a comrade, crony. Sometimes called " Buddy." By Level. A side level driven for some unusual but necessary purpose. Cab. The side parts of a lode, nearest the walls, which are generally hard and deficient of ore. Caballo (Mexican). A " horse " or mass of barren rock in a vein. Cabezuela (Spanish). Rich gold and silver concentrates. Cabin. (1) A miner's house. (2) A small room in the mine for the use of the officials. Cable Drilling. Rope drilling. Cage. A platform on which mine cars are raised to the surface. Cage Guides. Vertical rods of pine, iron, or steel, or wire rope, fixed in a shaft, between which cages run, and whereby they are prevented from striking one another, or against any portion of the shaft. Cager. The person that puts the cars on the cage at the bottom of the shaft. Cage Seat. Scaffolding, sometimes fitted with strong springs, to take off the shock, and on which the cage drops when reaching the pit bottom. Cage Sheets. Short props or catches on which cages stand during caging or changing cars. Caking Coal.Co&l that agglomerates on the grate. Cat. Wolfram. Gala (Spanish). Prospecting pit. Calcareous. Containing lime. Calcine. -To heat a substance; not sufficiently to melt it, but enough to drive off the volatile contents. CAL GLOSSARY. CAU 577 Calcining Furnace. A furnace used for roasting ore in order to drive off certain impurities. Caliche ( Spanish ) .Feldspar. California Pump. A rude pump made of a wooden box through which an endless belt with floats circulates; used for pumping water from shallow ground. Catty s (Cornish). Stratified rocks traversed by lodes. Cam. (I) A curved arm attached to a revolving shaft for raising stamps. (2) Carbonate of lime a'nd fluorspar, found on the joints of lodes. Camino (Mexican). Any gallery, winze, or shaft, inside of a mine used for general transit. Campaign. The length of time a furnace remains in blast. Canada (Mexican). See Barranca. Canch, or Caunche.(l) A thickness of stone required to be removed to make height or to improve the gradient of a road. If above a seam, it is termed a "top canch"; if below, a "bottom canch." (2) A trend with sloping sides and very narrow bottom. Cancha (Spanish). Space for drying slimes. Cand (Cornish). Fluorspar. Cank (Derbyshire). Whinstone. Canker. The ocherous sediment in coal-pit waters. Cannel Coal. See Classification of Coals (page 170). Canon (Mexican). A level, drift, or gallery within a mine. Canon de Guia.A drift along the vein. Cants (English). The pieces forming the ends of buckets of a waterwheel. Cap. (I) A piece of plank placed on top of a prop. See, also, Collar. (2) The pale bluish elongation of the flame of a lamp caused by the presence of gas. CapeUina (Mexican). An old-style retort for retorting silver amalgam. Caple (Cornish). Hard rock lining tin lodes. Cap Rock. The upper rock that covers the bed rock. Capstan. A vertical axle used for heavy hoisting, and worked by horizontal arms or bars. Captain. Cornish name for manager or boss of a mine. Car. Any car used for the conveyance of coal along the gangways or haulage roads of a mine. Carat. A weight nearly equal to 4 grains. Carbon. A combustible elementary substance forming the largest compo- nent part of coal. Carbona. (1) A rich bunch of ore in the country rock connected with the. lode by a mere thread of mineral. (2) (Cornish) An irregular deposit of tin ore. Carbonaceous. Coaly, containing carbon or coal. Carbonate. Carbonic acid combined with a base. Carbonates. Lead ore. The oxide and carbonic-acid compounds of lead; also applied to lead sulphate. Carboniferous. Containing or carrying coal. Carga (Mexican). A charge. A mule load, generally of 300 pounds, but variable in different parts of Mexico. Carriage. See Cage and Slope Cage. Cartridge. Paper or waterproof cylindrical case filled with gunpowder, forming the charge for blasting. Cascajo (Mexican). Gravel. Case. A fissure admitting water into a mine. Case-Harden.To convert the outer surface of wrought iron into steel by heating it while in contact with charcoal. Casing. Tubing inserted in a bore hole to keep out water or to protect the sides from collapsing. Cast Iron. Pig iron that contains carbon (up to 5$), silicon, sulphur, phos- phorus, etc. Cata (Spanish). A mine denounced but not worked. Catches. (1) Iron levers or props at the top and bottom of a shaft. (2) Stops fitted on a cage to prevent cars from running off. Catch Pit. A reservoir for saving tailings from reduction works. Cauf (North of England). A coal bucket or basket. Cauldron Bottoms. The fossil remains or the " casts " of the trunks of sigil- laria that have remained vertical above or below the seam. Caulk. To fill seams or joints with something to prevent leaking. 578 CAU GLOSSARY. CHO Gaunter, or Gaunter Lode (Cornish). A vein running obliquely across the regular veins of the district. Cave, or Cave In. A caving-in of the roof strata of a mine, sometimes extend- ing to the surface. Cavils. Lots drawn by the hewers each quarter year to determine their working places. Gawk. Baryta sulphate. x Cazeador (Spanish). Amalgamator. Cazo (Mexican). A vessel for hot amalgamation'. Any large copper or iron vessel. Cebar (Mexican). (1) To melt rich ores, or lead bullion, etc. in a smelting furnace. (2) To add small quantities of material, from time to time, to the melted mass within a furnace. (3) Generally, to feed any kind of metallurgical machinery or process. .Cement. (1) Auriferous gravel consolidated together. (2) A finely divided metal obtained by precipitation. (3) A binding material. Cementation. The process of converting wrought iron into steel by heating it in contact with charcoal, or of treating cast iron in a bed of hema- tite ore. Cendrada (Mexican). The cupel bottom of a furnace. Cendradilla (Mexican). A small reverberaiory furnace for smelting rich silver ores in a rough way. Also called Galeme. Center. A temporary support, serving at the same time as a guide to the masons, placed under an arch during the progress of its construction. Centrifugal Force. A force drawing away from the center. Centripetal Force. A force drawing toward the center. CH 4 . Marsh gas (see page 348). Chain. A measure 66 or 100 ft. long, divided into 100 links. Chain-Brow Way. An underground inclined plane worked on the endless- chain system of haulage. Chain Pillar. A pillar left to protect the gangway and air-course, and run- ning parallel to these passages. Chain Road. An underground wagonway worked on the endless-chain system of haulage. Chair. Sometimes applied to keeps. Chamber. See Breast. Charco (Mexican). A pool of water. Charge. (1) The amount of powder or other explosive used in one blast or shot. (2) The amount of flux used in assaying. (3) The material fed into a furnace at one time. Charquear (Mexican). To dip out water from pools within the mine, throwing it into gutters or pipes that will conduct it to the shaft. Chats. (1) The gravel-like tailings derived from the concentration of ores. (2) A low-grade ore, often too poor to handle; the refuse from concen- tration works. (3) (North of England) Small pieces of stone with ore. Check- Battery. A battery to close the lower part of a chute, acting as a check to the flow of coal and as an air stopping. Checker Coal. Anthracite coal that seems to be made up of rectangular grains. Check- Weighman.A man appointed and paid by the miners to check the weighing of the coal at the surface. Cheek. Wall. Chert. A silicious rock, often the gangue of lead and zinc. Chestnut Coal. Anthracite coal that will pass through a mesh If in. square and over a mesh in. square (see page 434). Chiflon (Mexican). A narrow drift directed obliquely downwards. Any pipe from which issues water or air under pressure, or at high velocity. Chile Bars. Bars of impure copper, weighing about 200 lb., imported from Chile, corresponding to the Welsh blister copper, containing 98$ Cu. Chilian Mill. A roller mill for crushing ore. Chill Hardening. Giving a greater hardness to the outside of cast iron by pouring it into iron molds, which causes the skin of the casting to cool rapidly. Chimney. (I) An ore shoot. (2) A furnace or air stack. Chinese Pump. Like a California pump, but made entirely of wood. Chock. A square pillar for supporting the roof, constructed of prop timber laid up in alternate cross-layers, in log-cabin style, the center being filled with waste. CHO GLOSSARY. COF 579 Chokedamp.See Blackdamp. Churn Drill. A. long iron bar with a cutting end of steel, used in quarrying, and worked by raising and letting it tall. When worked by blows of a hammer or sledge, it is called a " jumper." Chute (also spelled Shute).(l) A narrow inclined passage in a mine, down which coal or ore is either pushed or slides by gravity. (2) The load- ing chute of a tipple. Chuza (Spanish). A catch basin for mercury. Cielo (Mexican.) A ceiling. Trabajar de Cielo. Overhead sloping. Cinnabar. Mercury and sulphur. Clack. A valve that is opened and closed by the force of the water. Clack Door. The opening into the valve chamber to facilitate repairs and renewals without unseating the pump or breaking the connections. Clack Piece. The casting forming the valve chamber. Clack Seal. The receptacle for the valve to rest on. Claggy (North of England). When coal is tightly joined to the roof. Claim. A portion of ground staked out and held by virtue of a miner's right. Clanny.A type of safety lamp invented by Dr. Clanny. Clastic. Constituted of rocks or minerals that are fragments derived from other rocks. Clay Course. A clay seam or gouge found at the sides of some veins. Claying Bar. For. molding clay in a wet bore hole. Clay Band. Argillaceous iron ore; common in many coal measures. Clean- Up. Collecting the product of a period of work with battery or sluice. Clearance. (1) The distance between the piston at the end of its stroke and the end of the cylinder. (2) The volume or -entire space filled with steam at end of a stroke including the space between piston and cylinder head, and the steam ducts to the valve seat. Cleat. (I) Vertical cleavage of coal seams, irrespective of dip or strike. (2) A small piece of wood nailed to two planks to keep them together, or nailed to any structure to make a support for something else. Cleavage. The property of splitting more readily in some directions than in others. Clinometer. An instrument used to measure the angle of dip. Clod. Soft and tough shale or slate forming the roof or floor of a coal seam. Closed Season. When placers cannot be worked. Clunch (English). Under clay, fireclay. Clutch. An arrangement at the end of separate shafts by means of which they catch into each other, so that both can revolve together. Coal Breaker. See Breaker. Coal Cutter. A machine for holing or undercutting coal. Coal Dust. Very finely powdered coal suspended in the airways of a mine. Coal Measures Strata, of coal with the attendant rocks. Coal Pipes (North of England). Very thin irregular coal beds. Coal Road. An underground roadway or heading in coal. Coal Smut. See Blossom. Coaly Rashings.Soft dark shale, in small pieces, containing much carbona- ceous matter. Coarse ( Goose] . When lode stuff is not rich, the ore being only thinly dis- seminated throughout it. Coarse Metal. In copper smelting, the compound containing the copper concentrated in it after the first smelting to get rid of the bulk of the gangue in the ore. Coaster. One that picks ore from the dump. Cob (Cornish). To break up ore for sorting. Cobbing Hammer. A short double-ended hammer for breaking minerals to sizes. Cobre. Cuban copper ores. Cockermeg, or Cockers. Timber used to hold coal face while it is being undercut. Cockle (Cornish). Black tourmaline, often mistaken for tin. Cod (North of England). The bearing of an axle. Cofer (Derbyshire). To calk a shaft by ramming clay behind the lining. Coffer. Mortar box of a battery. Coffer Dam. An enclosure built in the water, and then pumped dry, so as to permit masonry or other work to be carried on inside of it. Coffin (Cornish). An old pit. 580 COG GLOSSARY. COR Cog. A. chock. Cohete (Mexican). A rocket; applied to a blast within a mine or outside. Coil Drag A. tool for picking pebbles, etc. from drill holes. Coke. The fixed carbon and ash of coal sintered together. Colas (Spanish). Tailings from a stamp mill or any wet process. Collar. (1) A flat ring surrounding anything closely. (2) Collar of a shaft is the first wood frame of a shaft. (3) The bar or crosspiece of a framing in entry timbering. Colliery. The whole plant, including the mine and all adjuncts. Colliery Warnings (English). Telegraphic messages sent from signal-service stations to the principal colliery centers to warn managers of mines when sudden falls of the barometer occur. Colorados (Spanish). Decomposed ores stained with iron. Colores (Mexican). Metal-stained ground or rocks. Colrake.A shovel for stirring lead ores while washing. Color. Minute traces or individual specks of gold. Column, or Column Pipe. The pipe conveying the drainage water from the mine to the surface. Comer (Mexican). To eat. Comerse los Pilares.To take out the last vestiges of mineral from the sides and rock pillars of a mine. ConchoidaL Shell-like, such as the curved fracture of flint. Concrete. Artificial stone, formed by mixing broken stone, gravel, etc. with lime, cement, tar, or other binder. When hydraulic cement is used instead of lime, the mixture is called beton (English). Concretion. A. cemented aggregation of one or more kinds of minerals around a nucleus. Conduit. (1) A covered waterway. (2) An airway. Conduit Hole. A flat hole drilled for blasting up a thin piece in the bottom of a level. Conductors (English). See Guides. Conformable. Strata are conformable when they lie one over the other with the same dip. Conglomerate. The rock formation underlying the Coal Measures; a rock containing or consisting of pebbles, or of fragments of other rocks cemented together; English Pudding Rock or millstone grit. Conical Drum. The rope roll or drum of a winding engine, constructed in the form of two truncated cones placed back to back, the outer ends being usually the smaller in diameter. Consumido (Mexican). The amount of mercury that disappears by chem- ical combination during the treatment of ore by any amalgamation process. Contact. Union of different formations. Contact Load or Vein. A vein lying between two differently constituted rocks. Contour. (I) The line that bounds the figure of an object. (2) In survey- ing, a contour line is a line every point of which is at an equal elevation. Contramina (Mexican). Countermine. Any communication between two or more mines. Also, a tunnel communicating with a shaft. Cope (Derbyshire). Lead mining on contract. Cope, or Coup. An exchange of working places between hewers. Copelilla ( Spanish ) .Zinc-blende. Copella (Spanish). Dry amalgam. Copper Plate A sheet of copper that, when coated with mercury, is used in amalgamation. Corbond. An irregular mass from a lode. Cord. A cord weighs about 8 tons. Cores. Cylinder-shaped pieces of rock produced by the diamond-drill system of boring. Corf. A mine wagon or tub. Cornish Pumps. A single-acting pump, in which the motion is transmitted through a walking beam; in other respects similar to a Bull Pump. Coro-Coro (South American). Grains of native copper mixed with pyrite, chalcopyrite, mispickel, etc. Cortar Pillar (Mexican). To form a rock support or pillar within a mine, at the opening of a cross-cut or elsewhere. Cortar Sogas (Mexican). Literally, to cut the ropes. To abandon the mine, taking away everything useful or movable. Corve. A mining wagon or tub. Cos GLOSSARY. ORO 581 Costean (Cornish). To prospect a lode by sinking pits on its supposed course. Costeaning. Trenching for a lode. Cost Book (Cornish). Mining accounts. Cotton Rock. (I) Decomposed chert. (2) A variety of earthy limestone. Coulee. (I) A solified stream or sheet of lava extending down a volcano, often forming a ridge or spur. (2) A deep gulch or water channel, usually dry. Counter. (I) A cross-vein. (2) (English) An apparatus for recording the number of strokes made by the Cornish pumping engine. (3) A second- ary haulageway in a coal mine. Counterchute.A chute down which coal is dumped to a lower level or gangway. Counter gangway. A level or gangway driven at a higher level than the main one. Country. The formation traversed by a lode. Country Rock. The main rock of the region through which the veins cut, or that surrounding the veins. Course. The direction of a line in regard to the points of compass. Coursing or Coursing the Air. Conducting it through the different portions of a mine by means of doors, stoppings, and brattices. Cow. A self-acting brake. Coyoting. Irregular mining by small pits. Crab. A variety of windlass or capstan consisting of a short shaft or axle, either horizontal or vertical, which serves as a rope drum for raising weights; it may be worked by a winch or handspikes. Crab Holes. Roles often met with in the bed rock of alluvial. Also depres- sions on the surface owing to unequal disintegration of the underlying rock. Cradle. A box with a sieve mounted on rockers for washing auriferous alluvial. Cradle Dump. A rocking tipple for dumping cars. See Dump. Cramp (English). (1) A short bar of metal having its two ends bent down- wards at right angles for insertion into two adjoining pieces of stone, wood, etc. to hold them together. (2) A pillar left for support in a mine. Cranch. Part of a vein left by previous workers. Crane (English). A hoisting machine consisting of a revolving vertical post or stalk, a projecting jib, and a stay for sustaining the outer end of the jib; these dp not change their relative positions as they do in a derrick. There is also a rope drum with winding rope, etc. Creaze (Cornish). (1) Tin ore collected in the middle of the buddle. (2) The middle of a buddle. Creep. The gradual upheaval of the floor or sagging of the roof of mine workings due to the weighting action of the roof and a tender floor. Creston (Mexican). The outcrop or apex of a vein or mineral deposit. Crevice. A fissure. Crevicing. Picking out the gold caught in cracks and crevices in the rocks over which it has been washed. Criadero (Mexican). (1) A mineral deposit of irregular form, not vein-like. (2) A chamber in a vein filled with ore of more or less richness. (3) Any mineral deposit. This latter is the more modern sense, and the word is so used in the mining laws at present in force in Mexico. Crib. (1) A structure composed of horizontal timbers laid on one another, or a framework built like a log cabin. See Chock. (2) A miner's lunch- eon. (3) See Curb. Cribbing. Close timbering, as the lining of a shaft, or the construction of cribs of timber, or timber and earth or rock to support a roof. Cribble. A sieve. Crisol (Mexican). A crucible of any kind. Crop. See Outcrop. Crop Fall. A caving in of the surface at or near the outcrop of a bed of coal. Cropping Coal. The leaving of a small thickness of coal at the bottom of the seam in a working place, usually in order to keep back water. The coal so left is termed " Cropper Coal." Croppings. Portions of a vein as seen exposed at the surface. Cropping Out. Appearing at the surface; outcropping. Cross- Course. A vein lying more or less at right angles to the regular vein of the district. 582 CRO GLOSSART. DEB Crosscut. (I) A tunnel driven through or across the measures from one seam to another. (2) A small passageway driven at right angles to the main gangway to connect it with a parallel gangway or air-course. Crosses and Holes (Derbyshire). Made in the ground by the discoverer of a lode to temporarily secure possession. Cross-Heading. A passage driven for ventilation from the airway to the gang- way, or from one breast through the pillar to the adjoining working. Cross- Heading, or Cross-Gateway. A road kept through goaf and cutting off' the gateways at right angles or diagonally. Cross-HoleSee Crosscut (2). Cross- Latches. See Latches. Cross-Spur. A vein of quartz that crosses the reef. Cross- Vein. An. intersecting vein. Crouan (Cornish). Granite. Crowbar. A strong iron bar with a slightly curved and flattened end. Crowfoot. A tool for drawing broken boring rods. Crown Tree. A piece of timber set on props to support the roof. Crucero (Mexican). A crosscut for ventilation to get around a horse, or to prospect for the vein. Crucible. (I) The bottom of a cupola furnace in which the molten materials collect. (2) Pots for smelting assays in. Crush. See Squeeze, Thrust. Crusher. A machine used for crushing ores and rock. Crushing. Reduction of mineral in size by machinery. Crystal. A solid of definite geometrical form, which mineral (or sometimes organic) matter has assumed. Culm. Anthracite-coal dirt. Culm Bank, or Culm Dump. Heaps of culm now generally kept separate from the rock and slate dumps. Cuna (Mexican). Literally, a wedge. A short drill or picker generally known in the United States as a "gad." Cupel. A cup made of bone ash for absorbing litharge. Curb. (1 ) A timber frame intended as a support or foundation for the lining of a shaft. (2) The heavy frame or sill at the top of a shaft. Curbing. The wooden lining of a shaft. Cut. (1) To strike or reach a vein. (2) To excavate in the side of a hill. Cutter. A term employed in speaking of any coal-cutting or rock-cutting machines; the men operating them, or the men engaged in underholing by pick or drill. Cutting Down. To cut down a shaft is to increase its sectional area. Dam. A timber bulkhead, or a masonry or brick stopping built to prevent the water in old workings from flooding other workings, or to confine the water in a mine flooded to drown out a mine fire. Damp. Mine gases and gaseous mixtures are called damps. See also After- damp, Blackdamp, Firedamp, Stinkdamp. Dan (North of England). A truck without wheels. Danger Board. See Fireboard. Dant (North of England). Soft inferior coal. Datum Water Level. The level at which water is first struck in a shaft sunk on a reef or gutter. Davy. A safety lamp invented by Sir Humphrey Davy. Day. Light seen at the top of a shaft. Day Fall See Crop Fall. * Day Shift. The relay of men working in the daytime. Dead. The air of a mine is said to be dead or heavy when it contains car- bonic-acid gas, or when the ventilation is sluggish. Dead. (I) Unproductive. (2) Un ventilated. Dead Men's Graves (Australian). Grave-like mounds in the basalt under- lying auriferous gravels. Dead Quartz. (Quartz carrying 110 mineral. Dead Riches. Lead carrying much bullion. Dead Roast. To completely drive off all volatile substances. Deads. Waste or rubbish from a mine. Dead Work. Exploratory or prospecting work that is not directly productive. Brushing roof, lifting bottom, cleaning up falls, blowing rock, etc. Dean (Cornish). The end of a level. n's. Fragments from any kind of disintegration. DEE GLOSSARY. DIP 583 Deep (English). " To the deep," toward the lower portion of a mine; hence, the lower workings. Delta. A triangularly shaped piece of alluvial land at the mouth of the river. Demasia (Mexican). A piece of unoccupied ground between two mining concessions. Denudation. The laying bare by water or other agency. Denuncio (Mexican). Denouncement. The act of applying for a mining concession under the old mining laws. Deposit. (I) Irregular ore bodies not veins. (2) A bed or any sedimentary formation. Deputy (English). (1) A man who fixes and withdraws the timber sup- porting the roof of a mine, and attends to the safety of the roof and sides, builds stoppings, puts up bratticing, and looks after the safety of the hewers, etc. (2) An underground official who sees to the general safety of a certain number of stalls or of a district, but does not set the timber himself, although he has to see that it is properly and suffi- ciently done. (3) (American) A deputy sheriff. Derrick. (I) A crane in which the rope of chain forming the stay can be let out or hauled in at pleasure, thus altering the inclination of the jib. (2) The structure erected to sink a drill hole and the framework above shafts are sometimes called by this name. Derrumbe, or Derrumbamineto (Mexican). The caving in of the whole or a portion of a mine. Desayuador (Spanish). A water pipe or drain. Desague (Mexican). Drainage of a mine by any means. Descargar (Mexican). Literally, "to unload." Descargar un Homo. To tear down a furnace. Descubridora (Mexican). The first mine opened in a new district or on a new mineral deposit. Desecho (Spanish). Foul red mercury. Desfrute (Mexican). Taking out ore. Obras de Desfrute.Stopes, etc. Desmontar (Mexican). Literally, to clear away underbrush. In mining, to take away useless and barren rocks; to remove rubbish. Desmontes (Spanish). Poor ores. Despensa ( Mexican^. (1) A pantry or storeroom. (2) A secure room to lock up rich ore. Despoblado (Spanish). Ore with much gangue. Despoblar (Mexican). To suspend work in a mine. Dessue (Cornish). To cut away the ground beside a thin vein so as to remove the latter whole. Destajo (Mexican). (1) A contract to do any kind of work in or about a mine or elsewhere for a fixed price. (2) Piece work, as distinguished from time work. Destajero.A contractor for piece work. Detaching Hook. A. self-acting mechanical contrivance for setting free a winding rope from a cage when the latter is raised beyond a certain point in the head-gear; the rope being released, the cage remains suspended in the frame. Devil's Dice. Cubes of limonite, pseudomorphs after pyrites. Diagonal Joints. Joints diagonal to the strike of the cleavage. Dial (English). An instrument similar to a surveyor's compass, with vernier attached. Dialing. Surveying. Die. The bottom iron block of a battery, or grinding pan on which the shoe acts. Digging. Mining operations in coal or other minerals. Diggings. Vf here gold and other, minerals are dug out from shallow alluvials. Dike. See also Dyke. Ditties, or Ginneys. Short self-acting inclines where one or two tubs at a time are run. DiUueing (Cornish). Dressing tin slimes in a fine sieve. Dip (1) To slope downwards. (2) The inclination of strata with a hori- zontal plane. (3) The lower workings of a mine. Dip Joint. Vertical joints about parallel to the direction of the cleavage dip. Dippa (Cornish). A small catch-water pit. ^-'^ping Needle. A magnetic needle suspended in a vertical plane; for locating iron deposits. 584 DIR GLOSSAR}'. DRE Dirt- Fault. A confusion in a seam of coal, the top and bottom of the seam being well denned, but the body of the vein being soft and dirty. Dish (Cornish). An ore measure; in lead mines, a trough 28 in. long, 4 in. deep, and 6 in. broad; sometimes 1 gallon, sometimes 14 to 16 pints. Disintegration. Separation by mechanical means, not by decomposition. Ditch. (I) The drainage gutter in a mine. (2) A drainage gutter on the surface. (3) An open conveyor of water for hydraulic or irrigation purposes. Divide. The top of a ridge, hill, or mountain. Dividing Slate. A stratum of slate separating two benches of coal. See Parting. Divining, or Dowsing, Rod. A. small forked hazel twig that, when held loosely in the hands, is supposed to dip downwards when passing over water or metallic minerals. Dizzue (Cornish). See Dessue. Dog. (l) An iron bar, spiked at the ends, with which timbers are held together or steadied. (2) A short heavy iron bar, used as a drag behind a car or trip of cars when ascending a slope to prevent their running back down the slope in case of accident. See Drag. Dog Hole. A little opening from one place in a mine to another, smaller than a breakthrough. Dog Iron. A short bar of iron with both ends pointed and bent down so as to hold together two pieces of wood into which the points are driven. Or one end may be bent down and pointed, while the other is formed into an eye, so that if the point be driven into a log, the other end may be used to haul on. Dotes. Small piles of assorted or concentrated ore. Dotty. (1) A machine for breaking up minerals, being a rough pestle and mortar, the former being attached to a spring pole by a rope. (2) A tool used to sharpen drills. Dolly Tub (Cornish). A tub in which ore is washed, being agitated by a dolly or perforated boards. Donk (North of England). Soft mineral found in cross-veins. Donkey Engine (English). (1) A small steam engine attached to a large one, and fed from the same boiler; used for pumping water into the boiler. (2) A small steam engine. Door Piece (English). The portion of a lift of pumps in which the clack or valve is situated. Doors. Wooden doors in underground roads or airways to deflect the air- current. Door Tender. A boy whose duty it is to open and close a mine door before and after the passage of a train of mine cars. Dope. An absorbent for holding a thick liquid. The material that absorbs the nitroglycerine in explosives. Double Shift. When there are two sets of men at work, one set relieving the other. Double Tape Fuse. Fuse of superior quality, or having a heavier and stronger covering. Double Timber. Two props with a bar placed across the tops of them to sup- port the roof and sides. Downcast The opening through which the fresh air is drawn or forced into the mine; the intake. Dradge (Cornish). (1) Inferior ore separated from the prill. (2) Pulverized refuse. Draftage.A deduction made from the gross weight of ore when transported, to allow for loss. Drag. (I) The frictional resistance offered to a current of air in a mine. (2) See Dog. Draw. (1) To " draw " the pillars; robbing the pillars after the breasts are exhausted. (2) An effect of creep upon the pillars of a mine. Draw a Charge. To take a charge from a furnace. Drawlift.A pump that receives its water by suction and will not force it above its head. Draw-Hole. ATI aperture in a battery through which the coal is drawn. Drawing an Entry. Removing the last of the coal from an entry. Drawn. The condition in which an entry or room is left after all the coal has been removed. See Robbed. Dresser (Staffordshire). A large coal pick. DUE GLOSSARY. Ecu! 585 Dressing. Preparing 1 poor or mixed ores mechanically for metallurgical operations. Dressinq Floors. The floors or places where ores are dressed. Drift. (1) A horizontal passage underground. A drift follows the vein, as distinguished from a crosscut, which intersects it, or a level or gallery, which may do either. (2) In coal mining, a gangway above water level, drive'n from the surface in the seam. (3) Unstratified diluvium. Drifting. Winning pay dirt from the ground by means of drives. Drill. An instrument used in boring holes. Drive (Drift). A horizontal passage in a lode. Drive. To cut an opening through strata. Driving. Excavating horizontal passages, in contradistinction to sinking or raising. Di-iving on Line. Keeping a heading or breast accurately on a given course by means of a compass or transit. Dropper. (1) A spur dropping into the lode. (2) A feeder. (3) A branch leaving the vein on the footwall side. (4) Water dropping from the roof. Drop Shaft. A monkey shaft down which earth and other matter are lowered oy means of a drop (i. e., a kind of pulley with break attached); the empty bucket is brought up as the full one is lowered. Druggon (Staffordshire). A vessel for carrying fresh water into a mine. Drum. The cylinder or pulley on which' the winding ropes are coiled or wound. Drum Rings. Cast-iron rings with projections to which are bolted the laggings forming the surface for the ropes to lap on. Drummy. Sounding loose, open, shaky, or dangerous when tested. Druse. A hollow cavity lined with small crystals. Dry Amalgamation. Treating ores with hot, dry mercury. Dry Diggings. Placers never subject to overflow. Dry Ore. Argentiferous ores that do not contain enough lead for smelting purposes. Duck Machine. An arrangement of two boxes, one working within the other, for forcing air into mines. Duelas (Mexican). Staves of a barrel or cask, etc. Dumb'd. Choked, of a sieve or grating. Dumb Drift. A short tunnel or passage connecting the main return airways of a mine with the upcast shaft some distance above the furnace, in order to prevent the return air laden with mine gases from passing through or over the ventilating furnace. Dump. (I) A pile or heap of ore, coal, culm, slate, or rock. (2) The tipple by which the cars are dumped. (3) To unload a car by tipping it up. (4) The pile of mullock as discharged from a mine. Dumper. A car so constructed that the body may be revolved to dump the material in front or on either side of the track. Durn (Cornish). A timber frame. Durr (German). Barren ground. Dust See Coal Dust. Dust Gold. Pieces under 2 to 3 dwt. Duty. The unit of measure of the work of a pumping engine expressed in foot-pounds of work obtained from a bushel, or 100 lb., or other unit of fuel. Dyke, or Dike. (1) A wall of igneous rock passing through strata, with or without accompanying dislocation of the strata. (2) A fissure filled with igneous matter. (3) Barren rock. Dzhu (Cornish). See Dessue. Ear. The inlet or intake of a fan. Echadero (Mexican). A level place near a mine where ore is cleaned, piled, weighed, and loaded on mules or other conveyance. Also called patio of the mine. Echado (Mexican). The dip of the vein. Edge Coals (English). Highly inclined seams of coal, or those having a dip greater than 30. Efflorescence. An incrustation by a secondary mineral, due to loss of water of crystallization. . Efydd (Wales). Copper. Egg Coal Anth . racite coal that will pass through a 22" square mesh and over a 2" square mesh (see page 434). 586 ELB GLOSSARY. FAL Elbow. A sharp bend, as in a lode or pipe. Electric Blast. Instantaneous blasting of rock by means of electricity. Elevator Pump An endless band with buckets attached, running over two drums for draining shallow ground. Elvan.A Cornish name applied to most dike rocks of that county, irre- spective of the mineral constitution, but in the present day restricted to quartz porphyries. Emborrascarse (Mexican). To go barren by the vein terminating or pinching out, etc. Empties. Empty mine or railroad cars. Encino (Mexican). Live oak. End Joint (End Cleat). A joint or cleat in a seam about at right angles to the principal or face cleats. Endless Chain. A system of haulage or pumping by the moving of an endless chain. Endless Hope. A system of haulage same as endless chain, except that a wire rope is used instead of chain. End, or End- On. Working a seam of coal at right angles to the principal or face cleats. Engine Plane. An incline up which loaded cars are drawn by a rope operated by an engine located at the top or bottom of the incline. The empty cars descend by gravity, pulling the rope after them. Engineer. (I) One who has charge of the surveying or machinery about a mine. (2) One who runs an engine. Ensayes (Mexican). Assays. Entibar (Mexican). To timber a mine or any part thereof. Entry. A main haulage road, gangway, or airway. An underground passage used for haulage or ventilation, or as a man way. Entry Stumps. Pillars of coal left in the mouths of abandoned rooms to support the road, entry, or gangway till the entry pillars are drawn. Erosion. The wearing away of rocks by rains, etc. Escaleras (Mexican). Ladders, generally made of notched sticks. Escarpment. A nearly vertical natural face of rock or soil. Escoria (Mexican). Slag or cinders. Escorial. Slag pile. Escomficador (Mexican). A scorifier, in assaying. Espejuelo (Mexican). A mineral gangue, with a faintly reflecting surface. Espeton (Mexican). The tapping bar of a smelting furnace. Estano (Spanish). Tin. Estrujon (Mexican). A second collection of amalgam, generally very pasty. Exploder. A chemical employed for the instantaneous explosion of powder. Exploitation. The working of a mine, and similar undertakings; the exami- nation instituted for that purpose. Exploration. Development. Explosion. Sudden ignition of a body of firedamp. Eye (English). (1) A circular hole in a bar for receiving a pin and for other purposes. (2) The eye of a shaft is the very beginning of a pit. (3) The eye of a fan is the central or intake opening. p ace ._(l) The place at which the material is actually being worked, either in a breast or heading or in longwall. (2) The end of a drift or tunnel. .Pace-On. When the face of the breast or entry is parallel to the face cleats of the seam (see page 285). Face Wall A wall built to sustain a face cut into the natural earth, in distinction to a retaining wall, which supports earth deposited behind it. Faenas (Mexican). Dead work, in the way of development. Fahlband (German). A course impregnated with metallic sulphides. Faiscador (Spanish). A gold washer. Fall. (I) A mass of roof or side which has fallen in any part of a mine. (2) To blast or wedge down coal. False Bedding. Irregular lamination, wherein the laminae, though for short distances parallel to each other, are oblique to the general strati- fication of the mass at varying angles and directions. False Bottom. 0) A movable bottom in some apparatus. (2) A stratum on which pay dirt lies, but which has other layers below it. False Cleavage. A secondary slip cleavage superinduced on slaty cleavage. False Set. A temporary set of timber used until work is far enough advanced to put in a permanent set. FAM 'GLOSSARY. FLA T>87 Famp (North of England). Thin beds of soft tough shale. Fan. A machine for creating a circulation of air in a mine. Fan Drift. A short tunnel or conduit leading from the top of the air-shaft to the fan. Fanega (Mexican). A Spanish measure of about 21 bushels. Fang (Derbyshire). An air-course. Fascines (English). Bunches of twigs and small branches for forming foundations on soft ground. Fast. (1) A road driven in a seam with the solid coal at each side. " Fast at an end," or " fast at one side," implies that one side is solid coal and the other open to the goaf or some previous excavation. (2) Bed rock. Fast End. An end of a breast of coal that requires cutting. Fat Coals. Those containing volatile oily matters. Fathom (English). 6 ft, Fault. A fracture or disturbance of the strata breaking the continuity of the formation. Feather. A slightly projecting narrow rib lengthwise on a shaft, arranged to catch into a corresponding groove in anything that surrounds and slides along the shaft. Feather Edge. (I) A passage from false to true bottom. (2) The thin end of a wedge-shaped piece of rock or coal. Feather Ore. Sulphide of lead and antimony. Feed. Forward motion imparted to the cutters or drills of rock-drilling or coal-cutting machinery, either hand or automatic. Feeder. (1) A runner of water. (2) A small blower of gas. Feigh (North of England). Ore refuse. Fencing. Fencing in a claim is to make a drive round the boundaries of an alluvial claim, to prevent wash dirt from being worked out by adjoining claim holders. Fend-Off (English) . A sort of bell-crank for turning a pump rod past the angle of a crooked shaft. Fierros (Mexican). Iron matte. Fiery. Containing explosive gas. Fines. Very small material produced in breaking up large lumps. Fire. (1) A miners' term for firedamp. (2) To blast with gunpowder or other explosive. (3) A word shouted by miners to warn one another when a shot is fired. Fire-Bars (English) .The iron bars of a grate on which the fuel rests. Fireboard.A piece of board with the word fire painted upon it and sus- pended to a prop, etc., in the workings, to caution men not to take a naked light beyond it, or to pass it without the consent of the foreman or his assistants. Fire Boss. An underground official who examines the mine for gas and inspects safety lamps taken into the mine. Fireclay. Any clay that will withstand a great heat without vitrifying. Firedamp. (I) A mixture of light carburetted hydrogen (Cff 4 ) and air in explosive proportions; often applied to CH alone or to any explosive mixture of mine gases. Fireman. See Fire Boss. Fire-Setting. The process of exposing very hard rock to intense heat, ren- dering it thereby easier for breaking down. First Working. See Whole Working. Firsts. The best ore picked from a mine. Fish. To join two beams, rails, etc. together by long pieces at their sides. Fissure. An extensive crack. Fissure Vein. Any mineralized crevice in the rock of very great depth. Flags. Broad flat stones for paving. Flagstone. Any kind of a stone that separates naturally into thin tabular plates suitable for pavements and curbing. Especially applicable to sandstone and schists. Flang (Cornish). A double-pointed pick. Flange (English). A projecting ledge or rim. Flat. (1) A district or set of workings separated by faults, old workings, or barriers of solid coal. (2) The siding or station laid with two or more lines of railway, to which the putters bring the full cars from the work- ing face, and where they get the empty cars to take back. (3) The area of working places, from which coal is brought to the same station, is also called "flat." 588 FI,A GLOSSARY. FitR Flat Rod. A horizontal rod for conveying power to a distance. Flats. Narrow decomposed parts of limestones that are mineralized. Flat Sheet. Sheet-iron flooring at. landings and in the plats, chambers, and junctions of drives, to facilitate the turning and management of trucks. Flat Watt (Cornish). Foot-wall. Flintshire Furnace. A kind of reverberatory furnace used for smelting lead ores. Float Broken and transported particles or boulders of vein matter. Float Gold. Gold in thin scales, which floats on water. Float Ore. A term applied by miners to ore found loose in the clay or soil. Float Stones. Loose boulders from lodes lying on or near the surface. Flood Gate (English). A gate to let off excess of water in flood or other times. Floor. (I) The stratum of rock upon which a seam of coal immediately lies. (2) That part of a mine upon which you walk or upon which the road bed is laid. Floram (Cornish). Very fine tin. Flour Gold. The finest alluvial gold. Flouring. Mercury reduced to fine globules that are easily contaminated and will not amalgamate. Flucan.A soft, greasy, clayey substance found in the joints of veins. Fluke. A rod for cleaning out drill holes. Flume. An artificial watercourse. Fluming Lifting a river out of its bed with wooden launders or pipes, in order to get at the bed for working. Flush. (1) To clean out a line of pipes, gutters, etc. by letting in a sudden rush of water. (2) The splitting of the edges of stone under pressure. (3) Forming an even continuous line or surface. (4) To fill a mine with fine material. Fluthwerk (German). River prospecting. Flux. Iron ore, limestone, and sand, which are added in various propor- tions to the charge in a furnace to make the gangue melt up and flow off easily. Fodder (North of England). 21 cwt. of lead. Following Stone. Roof stone that falls on the removal of the seam. Foot (Cornish). 2 gallons, or 60 lb., black tin. Foot-Hole. Holes cut in the sides of shafts or winzes to enable miners to ascend and descend. Foot-Piece. (1) A wedge of wood or part of a slab placed on the foot-wall against which a stull piece is jammed. (2) A piece of wood placed on the floor of a drive to support a leg or prop of timber. Foot- Wall. The lower boundary of a lode. Footway. Ladders in mines. Force Fan. See Slowdown Fan. Force Piece. Diagonal timbering to secure the ground. Force Pump. A pump that forces water above its valves. Forebay. Penstock. The reservoir from which water passes directly to a water wheel. Forepoling. Driving the poles over the timbers so that their ends project beyond the last set of timber, so as to protect the miner from roof falls; used also in quicksand or other loose material. Forewinning. The first working of a seam in distinction from pillar drawing. Fork. (1) A deep receptacle in the rock, to enable a pump to extract the bottom water. A pump is said to be " going in fork " when the water is so low that air is sucked through the windbore. (2) (Cornish) Bottom of sump. (3) (Derbyshire) Prop for soft ground. Formation. A series of strata that belong to a single geological age. Fossickers (Australian). Grubbers for gold in the beach sand. Fossicking. Overhauling old workings and refuse heaps for gold. Fossil. Organic remains or impressions of them found in mineral matter. Fother (North of England). j chaldron. Frame. A table composed of boards, slightly inclined, over which water runs to wash off waste from sluice tin. Frame Set. The legs and cap or collar arranged so as to support a passage mined out of the rock or lode; also called Framing. Free. Coal is said to be " free " when it is loose and easily mined, or when it will "run" without mining. Free Milling. Ores requiring no roasting or chemical treatment. FRE GLOSSARY. GOB 58i) Free Miner. Licensed miner. Fresno (Mexican). An ash tree. Fronton (Mexican). Any working face. Fuelle (Mexican). A bellows. Furnace. A large coal fire at or near the bottom of an upcast shaft, for pro- ducing a current of air for ventilating the mine. Furnace Shaft. The upcast shaft in furnace ventilation. Fuse. (I) A hollow tube tilled with an explosive mixture for igniting car- tridges. <2) To melt. Gabarro (Mexican). Ore in large pieces, from egg size up. Gad. A small steel wedge used for loosening jointy ground. Gal (Cornish). Hard gossan. Galapago (Mexican). A turtle-shaped pig of lead. Gale. A grant of mining ground. Galemador (Spanish). A silver furnace. Galerne (Mexican). A reverberatory furnace. See Cendradilla. Galera (Mexican). A shed; any long or large room; a storehouse. Galiage. Royalty . Gallery. A horizontal passage. Gattos (Mexican). Rich specimens of silver or gold ore, particularly those that show native silver or gold. Gallows Frame. The frame supporting a pulley over which the hoisting rope passes to the engine. Gambucino (Mexican). A prospector for gold placers or ores. Gang. A set of miners, a "shift." Gangue. Waste material from lodes. Gangway. The main haulage road or level. Ganister. A hard, compact, extremely silicious fireclay. Garabata (Mexican). A curved iron bar used in copper smelting. Gas. See Firedamp. Any firedamp mixture in a mine is called gas. Gas Coal. Bituminous coal containing a large percentage of gas. Gash Vein. A wedge-shaped vein. Gasket. A band or ring of any material put between the flanges of pipes before bolting, to make them water-tight or steam-tight. Gatches (Cornish). Final sludge from tin dressing. Gate. An underground road connecting a stall or breast with a main road. Gateway. (I) A road kept through goaf in longwall working. (2) A gang- way having ventilating doors. Gauge Door. A wooden door fixed in an airway for regulating the supply of ventilation necessary for a certain district or number of men. Gauge Pressure. The pressure shown by an ordinary steam gauge. It is the pressure above that of the atmosphere. Gears, or Pair of Gears. (I) Two props and a plank, the plank being sup- ported by the props at either end. (2) The teeth of a gear-wheel or pinion. Geodes. Large nodules of stone with a hollow in the center. Geordie.A safety lamp invented by George Stephenson. Geyser. Natural fountain of hot water and steam. Gib. (I) A short prop of timber by which coal is supported while being holed or undercut. (2) A piece of metal often used in the same hole with a wedge-shaped key for holding pieces together. Ginneys. See Ditties. Gin, or Horse Gin. A vertical drum and framework by which the minerals and dirt are raised from a shallow pit. Giraffe. A mechanical appliance for receiving and tipping a car full of ore or waste rock when it arrives at the surface. Girdle. A thin bed or band of stone. A roof is described as a post roof with metal girdles, or a metal roof with post girdles, according as the post or the metal predominates. Glist (Cornish). Micaceous iron ore. Goaf, or Goave. That part of a mine from which the coal has been worked away, and the space more or less filled up with waste. Gob. (1) Another word for Goaf. (2) To leave coal and other minerals that are not marketable in the mine. (3) To stow or pack any useless underground roadway with rubbish. Gob Fire. Spontaneous combustion underground of fine coal and slack in the gob. 590 GOB GLOSSARY. GUT Gobbing Up. Filling with waste. Gob Road. A roadway in a mine carried through the goaf. Going Headways, or Going Bord.A headway or bord laid with rails, and used for conveying the coal tubs to and from the face. Golpeador (Mexican). A striker, in hand drilling. Gossan. A spongy ferruginous oxide, left after the soluble substances have been dissolved out of a lode. Goths (Staffordshire). Sudden burstings of coal from the face, owing to tension caused by unequal pressure. Gouge. The layer of clay, or decomposed rock, that lies along the wall or walls of a vein. It is not always valueless. Grade. The amount of fall or inclination in ditches, flumes, roads, etc. Grain. An obscure vertical cleavage usually more or lees parallel to the end or dip joints. Granza (Mexican). Metallic minerals from the size of rice to that of hens' eggs. Gmsa (Mexican). Literally, grease. Slags. Grass. The surface of the ground. Grassero (Spanish). Slag heap. Grate Coal. See Broken Coal. Grating. A perforated iron sheet or wire gauze placed in front of reducing machinery. Gravel. Water- worn stones about the size of marbles. Gray Metal. Shale of a grayish color. Graywacke.A compact gray sandstone frequently found in Paleozoic formations. Greenstone. A general term employed to designate green-colored igneous rocks, as diorite, dolerite, diabase, gabbro, etc. Grena (Spanish). Undressed ore. Greta (Mexican). Impure litharge formed in a reverberatory furnace. Griddle. A coarse sieve used for sifting ores, clay, etc. Grizzly. A grating to throw out large stones from hydraulic gold sluices. Ground Rent. Rent paid for surface occupied by the plant, etc. of a colliery. Groundsill. A log laid on the floor of a drive on which the legs of a set of timber rest. Ground Sluicing. Washing alluvial, loosened by pick and shovel, in trenches cut out of the bed rock, using bars of rock as natural riffles. Used in shallow placers, hill claims, bank claims, and stream diggings. Grout (English). Thin mortar poured into the interstices between stones and bricks. Grove (Derbyshire). A mine. Grub Stake. The mining outfit or supplies furnished to a prospector on con- dition of sharing in his finds. Grueso (Mexican). Lump ore. Grundy. Granulated pig iron. Guag (Cornish). Worked-out ground. Gualdria (Mexican). A long and stout beam, generally sustaining other beams or some heavy weight. Guano. A brown, gray, or white, light powdery deposit, consisting mainly of the excrement of sea fowl in rainless tracts, or of bats in caves. Guarda Raya (Mexican). A landmark; a monument. Guardas (Mexican). The country seat immediately enclosing any metal- liferous vein or deposit. Gubbin. Ironstone. Guia (Mexican). Indications where to cut a pay streak or to find a vein. Guides. See Cage Guides. Guija ( Spanish ) .Quartz. Guijo (Mexican). A pointed pivot, upon which turns the upright center piece of an arrastre, of a door, etc. Gunboat. A self-dumping car, holding from 5 to 8 tons of coal, used upon inclined planes or slopes. They are filled by emptying the mine cars into them at the foot of the slope. Gunnies (Cornish). 3 ft. Ourt (Cornish). Water runnel from dressing floor. Gutter. (I) A small water-draining channel. (2) The lowest part of a lead that contains the most highly auriferous dirt. HAC GLOSSARY. HEA 591 Hacienda de Beneficio (Mexican). In mining, a metallurgical works; any metallurgical works, usually an amalgamation works. Hacienda de Fundicion (Mexican). A smelting works. Hacienda de Maquila (Mexican). A custom mill. Hade. The inclination of a vein or fault, taking the vertical as zero. Haiarn (Wales). Iron. Half Course. (1) At an angle of 45 from general or previous course. (2) Half on the level and half on the dip. Half Set. One leg piece and a cap. Halvans. Gangue containing a little ore. Hammer-and- Plate. A signaling apparatus. Hand Barrow. A long box with handles at each end. Hand Dog. A kind of spanner or wrench for screwing up and disconnecting the joints of boring rods at the surface. Handspike. A wooden lever for working a capstan or windlass. Handwhip. An apparatus used in shallow alluvial workings, consisting of an upright, at the top of which is balanced a long sapling; at the thick end of the sapling, a bag of earth is fastened to counterbalance the bucket of dirt to be raised at the other end. Hanger-On.The man that runs the loaded cars on to the cages and gives the signal to hoist. See Cager. Hanging Spear Rod. Wooden pump rods adjustable by screws, etc. by which a sinking set of pumps is suspended in a shaft. Hanging Wall. In metalliferous mining, the stratum lying geologically directly above a bed or vein. Hardhead. Residue from tin refining; contains much iron and arsenic. Harrow. Somewhat like an agricultural harrow; it is fixed to the pole of a puddling machine and dragged around to break up and mix the aurifer- ous clays with water. Hatajo (Mexican). A drove of pack mules. Hat Rollers. Cast-iron or steel rollers shaped like a hat, revolving on a vertical pin, for guiding inclined haulage ropes around curves. Hatter. A miner working by himself on his own account. Haulage Clip. Levers, jaws, wedges, etc. by ivhich cars, singly or in trains, are connected to the hauling ropes. Hauling. The drawing or conveying of the product of the mine from the working places to the bottom of the hoisting shaft, or slope. Haunches. The parts of an arch from the keystone to the skew back. Hazle (North of England). Sandstone mixed with shale- Head. (1) Pressure of water in pounds per square inch. (2) Any subter- ranean passage driven in solid coal. (3) That part of a face nearest the roof. Head, or Sluice Head (Australia and New Zealand). A supply of 1 cu. ft. of water per second, regardless of the head, pressure, or size of orifice. Head-Block. (I) A stop at the head of a slope or shaft to stop cars from going down the shaft or slope. (2) A cap piece. Headboard. A wedge of wood placed against the hanging wall, and against which one end of the stull piece is jammed. Header. (I) A rock that heads off or delays progress. (2) A blast hole at or above the head. (3) A stone or brick laid lengthwise at right angles to the face of the masonry. (4) The Stanley Header is an entry boring machine that bores the entire section of the entry in one operation. Head-Gear. The pulley frame erected over a shaft. Head-House. When the head-frame is housed in, the structure is known by this name. Heading. (1) A continuous passage for air or for use as a manway; a gang- way or entry. (2) A connecting passage between two rooms, breasts, or other working places. Head-Piece. A cap; a collar. Headrace. An aqueduct for bringing a supply of water on to the ground. Headstocks. Gallows frame; head-frame. Headways (1) A road; usually 9 ft. wide, in a direction parallel to the main-cleavage planes of the coal seams, which direction is called "headways course." and is generally about north and south in the Newcastle coal field. It is termed "on end'^in other districts. (2) Cross-headings. Heave. The shifting of rocks, seams, or lodes on the face of a cross-course, etc. 592 HEA GLOSSARY. HYD Heaving. The rising of the thill (or floor) of a seam where the coal has been removed. Hechado (Spanish). Dip. Heel of Coal. A small body of coal left under a larger body as a support. Heel of a Shot. In blasting, the front of a shot, or the face of the shot farthest from the charge. Heep Stead (English). The entire surface plant of a colliery. Helper. A miner's assistant, who works under the direction of the miner. Helve. A handle. Hewer. A collier that cuts coal; a digger. High Reef. The bed rock or reef is frequently found to rise more abruptly on one side of a gutter than on the other, and this abrupt reef is termed a high reef. Hijuelas (Mexican). Literally, little children. A small-sized torta made up as a sort of assay on a large scale, with from 1 to 5 kilograms of argentif- erous mud. Hill Diggings. Placers on hills. Hilo (Spanish). A thin metalliferous vein. Hitch. (1) A fault or dislocation of less throw than the thickness of the seam in which it occurs. (2) Step cut in the rock or lode for holding stay-beams, beams, or timber, etc. for various purposes. Hoarding. A temporary close fence of boards placed around a work in progress. Hogback. A roll occurring in the floor and not in the roof, the coal being cut out or nearly so, for a distance. Hoister.A machine used in hoisting the product. It may be operated by steampower or horsepower. Hole. (1) To undercut a seam of coal by hand or machine. (2) A bore hole. (3) To make a communication from one part of a mine to another. Holing. (I) The portion of the seam or underclay removed from beneath the coal before it is broken down. (2) A short passage connecting two roads. (3) See Kirving. Holing Through. Driving a passage through to make connection with another part of the same workings, or with those in an adjacent mine. Hood. See Bonnet. Hopper. A coal pocket; a funnel-shaped feeding trough. Horn. A piece of bullock's horn about 8 in. in length, cut boat-shaped, for concentrating by water on a small scale. Horn Coal.Co&l worked partly end-on and partly face-on. Horn Silver. Chloride of silver. Horse Gin. A gearing for winding by horsepower. Horsepower. The power that will raise 33,000 Ib. 1 ft. high per minute. Horse, or Horsebacks. (1) Natural channels cut or washed away by water in a coal seam, and tilled up with shale and sandstone. Sometimes a bank or ridge of foreign matter in a coal seam. (2) A mass of country rock lying within a vein or bed. (3) Any irregularity cutting out a portion of the vein. See Dirt Fault and Rock Fault. Horse Whim. A vertical drum worked by a horse, for hauling or hoisting. Called also Horse Gin. Hose. A strong flexible pipe made of leather, canvas, rubber, etc., and used for the conveyance of water, steam, or air under pressure to any partic- ular point. H Piece. The portion of a column pipe containing the valves of the pump. Hueco (Mexican). See Demasia. Hulk (Cornish). To pick out the soft portions of a lode. Hundido (Mexican). See Derrumbe. Hungry. Worthless looking. Hurdy Gurdy.A waterwheel that receives motion from the force of traveling water. Hushing. Prospecting by laying ground bare by sudden discharges of pent-up water. Hutch (Cornish). (1) An ore-washing box. (2) (English) A mine car. Hydraulic Cement. A mixture of lime, magnesia, alumina, and silica that solidifies beneath water. Hydraulickiny. Working auriferous gravel beds by hydraulic power. Hydrocarbons. Compounds of hydrogen and carbon. IGN GLOSSARY. JIG 593 Igneous Rocks. Those that have been in a more or less fused state. Inbye. In a direction inward toward the face of the workings, or away from the entrance. Incline. bnort for inclined plane. Any inclined heading or slope road or track having a general inclination or grade in one direction. Incorporo (Mexican). The act of adding and mixing the mercury and other ingredients in and to the metalliferous mud for the patio process of amalgamation. Incorporadero. Place where the incorporo is effected. Indicator. (1) A mechanical contrivance attached to winding, hauling, or other machinery, which shows the position of the cages in the shaft or the cars on an incline during its journey or run. (2) An apparatus for showing the presence of firedamp in mines, the temperature of goaves, the speed of a ventilator, pressure of steam, air, or water, etc. Indicator Card, or Diagram. A diagram showing the variation of steam pressure in the cylinder of an engine during an entire stroke or revo- lution. Indoor Catches. Strong beams in Cornish pumping-engine houses to catch the beam in case of a smash, thus preventing damage to the engine itself. In-fork. When a pump continues working after water has receded below the holes of the wind bore. Ingot. A lump of cast metal. In Place. A vein or deposit in its original position. Insalmoro (Mexican). The addition of salt to the torta or mud heap. Inset. The entrance to a mine at the bottom, or part way down a shaft where the cages are loaded. Inside Slope. A slope on which coal is raised from a lower to a higher gangway. Inspector. A government official whose duties are to enforce the laws regu- lating the working of mines. Instrofce. The right to take coal from a royalty to the surface by a shaft in an adjoining royalty. A rent is usually charged for this privilege. Intake. (1) The passage through which the fresh air is drawn or forced in a mine, commencing at the bottom of a downcast shaft, or the mouth of a slope. (2) The fresh air passing into a colliery. Inversion. Such a change in the dip of a vein or seam as makes the foot- wall or floor the upper and the hanging wall or roof the lower of the two. Irestone (Cornish). Any hard tough stone. Iron Hat. Decomposed ferruginous mineral capping a lode. Iron Man. A coal-cutting machine. Jaboncillo (Mexican). Decomposed talcose rock or hardened clay, generally found in a vein, and sometimes indicating the proximity of a rich strike. Jacal (Mexican). See Xacal. Jack. A lantern-shaped case made of tin, in which safety lamps are carried in strong currents of air. Jacket. (1) An extra surface covering, as a steam jacket. (2) A water- jacket is a furnace having double iron walls, between which water circulates. Jack-Lamp. A. Davy lamp, with the addition of a glass cylinder outside the gauze. Jacotinga (Brazilian). Ferruginous ores associated with gold. Jales ( Spanish ) .Tailings. Jales-Jalsontles (Mexican). Rich tailings or middlings from concentration or amalgamation. Jars. In rope drilling, two long links which take up the shock of impact when the falling tools strike the bottom of the hole. Jenkin. A road cut in a pillar of coal in a bordways direction, that is, at right angles to the main-cleavage planes. Jig. (1) A self-acting incline. (2) A machine for separating ores or minerals from worthless rock by means of their difference in specific gravity; also called Jigger or Washer. Jigger. (I) A kind of coupling hook for connecting cars on an incline. (2) An allowance of liquor sometimes issued to workmen (almost obsolete). (3) See Jig. Ji(jfjinrj. Separating heavy from light particles by agitation in water. 594 Joe GLOSSARY. LAG Jockey. A self-acting apparatus carried on the front truck of a set for re- leasing it from the hauling rope. Joggle. A joint of trusses or sets of timber for receiving pressure at right angles, or nearly so. Joints. (1) Divisional planes that divide the rock in a quarry into natural blocks. There are usually two or three nearly parallel series, called by quarrymen end joints, back joints, and bottom joints, according to their position. (2) In coal seams, the less pronounced cleats or vertical cleavages in the coal. The shorter cleats, about at right angles to the face cleats and the bedding plane of the coal. Jud. (1) A portion of the working face loosened by " kirving " underneath, and "nicking" up one side. The operation of kirving and nicking is spoken of as "making a jud." (2) The term jud is also applied to a working place, usually 6 to 8 yd. wide, driven in a pillar of coal. When a jud has been driven the distance required, the timber and rails are removed, and this is termed " drawing a jud." Judge (Derbyshire and North of England). A measuring staff. Jugglers, or Jugulars. Timbers set obliquely against the rib in a breast, to form a triangular passage to be used as a manway, airway, or chute. Jump. An upthrow or a downthrow fault. Jumper. A hand drill used in boring holes in rock for blasting. Kann (Cornish). Fluorspar. Kazen (Cornish). A sieve. Keckle-Meckle. Poorest lead ore. Keeker. An official that superintends the screening and cleaning of the coal. Keel Wedge. A long iron wedge for driving over the top of a pick hilt. Keeps, or Keps. Wings, catches, or rests to hold the cage at rest when it reaches any landing. Keeve.A large wooden tub used for the final concentration of tin oxide. Kenner. Time for quitting work. Kerf. The undercut made to assist the breaking of the coal. Kerned (Cornish). Pyrites hardened by exposure. Kerve (North of England). In coal mining, to cut under. Kevil (Derbyshire). Calcspar found in lead veins. Key. (1) An iron bar of suitable size and taper for filling the key ways of shaft and pulley so as to keep both together. (2) A kind of spanner used in deep boring by hand. Kibble. See Bowk. Often made with a bow or handle, and carrying over a ton of debris. Kickup. An apparatus for emptying trucks. Kieve. Tossing tub. Killas (Cornish). Clay slate. Kiln. A. chamber built of stone or brick, or sunk in the ground, for burning minerals in. Kind. (1) Tender, soft, easy. (2) Likely looking stone. Kind-Chaudron. A system of sinking shafts through water-bearing strata. Kirving (North of England). The cutting made beneath the coal seam. Kist. The wooden box or chest in which the deputy keeps his tools. The chest is always placed at the flat or lamp station, and this spot is often referred to by the expression " at the kist." Kit. Any workman's necessary outfit, as tools, etc. Kitty. A squib made of a straw tube filled with powder. Knee Piece. A bent piece of piping. Knocker. A lever that strikes on a plate of iron at the mouth of a shaft, by means of which miners below can signal to those on the top. Knocker Line. The signal line extending down the shaft from the knocker. Koepe System. A system of hoisting without using drums, the rope being endless and passing over pulleys instead of around a drum. Labor (Mexican). Mine workings in general. Specifically, a stope or any other place where ore is being taken out. Ladderway, Ladder Road. The particular shaft, or compartment of a shaft, used for ladders. Lagging. (I) Small round timbers, slabs, or plank, driven in behind the legs and over the collar, to prevent pieces of the sides or roof from falling through. (2) Long pieces of timber closely fitted together and fastened to the drum rings to form a surface for the rope to wind on. LAM GLOSSARY. LID 595 Lamas (Spanish). (1) Slimes. (2) Argentiferous mud treated by amalga- mation. Lamer o (Mexican). Place of deposit for lamas. Laminse Sheets not naturally separated, but which may be forced apart. Lampazo (Mexican). A sort of broom formed of green branches on the end of a long stick, to dampen the flame in a reverberatory furnace. Lamp Men. Cleaners, repairers, and those having charge of the safety lamps at a colliery. Lamp Stations. Certain fixed stations in a mine at which safety lamps are allowed to be opened and relighted by men appointed for that purpose, or beyond which, on no pretense, is a naked light allowed to be taken. Lander. The man that receives a load of ore at the mouth of a shaft. Lander's Crook. A hook or tongs for upsetting the bucket of hoisted rock. Landing. (I) A level stage for loading or unloading a cage or skip. (2) The top or bottom of a slope, shaft, or inclined plane. Land Sale. The sale of coal loaded into carts or wagons for local consump- tion. Land-Sale Collieries. Those selling the entire product for local consumption, and shipping none by rail or water. Lap. One coil of rope on a drum or pulley. Lappior (Cornish). An ore dresser. Large. The largest lumps of coal sent to the surface, or all coal that is hand picked or does not pass over screens; also, the large coal that passes over screens. Larry. (I) A car to which an endless rope is attached, fixed at the inside end of the road, forming part of the appliance for taking up slack rope. See Balance Car. (2) See Barney. (3) A car with a hopper bottom and adjustable chutes for feeding coke ovens. (4) A hopper-shaped car for charging coke ovens. Latches. (1) A synonym of switch. Applied to the split rail and hinged switches. (2) Hinged switch points, or short pieces of rail that form rail crossings. Lateral. From the side. Lath. A plank laid over a framed center or used in poling. Launder. Water trough. Laundry Box. The box at the surface receiving the water pumped up from below. Lava. A common term for all rock matter that has flowed from a volcano or fissure. Lavadero (Mexican). A washer. A tank with a stirring arrangement to loosen up the argentiferous mud from the patio, and dilute the same with water, so that the silver amalgam may have a chance to precipitate. An agitator. Lazadores (Mexican). Men formerly employed in recruiting Indians for work in the mines by the gentle persuasion of a lasso. Lazy Back (Staffordshire). A coal stack, or pile of coal. Leaching. To dissolve out by some liquid. Lead (pronounced leed).(l) Ledge (America); reef (Australia); lode or vein (England). A more or less vertical deposit of ore formed after the rock in which it occurs. (2) A bed of alluvial pay dirt or an auriferous gutter. (3) The distance to which earth is hauled or wheeled. der.A seam of coal too small to be worked profitably, but often being a guide to larger seams lying in known proximity to it. Leat. A small water ditch. Leavings (Cornish). Hal vans. Ledge. See Lead. Leg. A wooden prop supporting one end of a collar. Leg Piece. An upright log placed against the side of a drive to support the cap piece. Lenador (Mexican). One that cuts, carries, or furnishes wood for com- bustible. Level A road or gangway running parallel or nearly so with the strike of the seam. Ley (Mexican). Law. As applied in mining matters, it means the propor- tion of precious or other metals contained in any mineral substance or metallic alloy. Lid, A cap piece used in timbering. 596 LIF GLOSSARY. LUM Lift. (I) The vertical height traveled by a cage in a shaft. (2) The lift of a pump is theoretical height from the level of the water in the sump to the point of discharge. (3) The distance between the first level and the surface, or between two levels. (4) The levels of a shaft or slope. Lifting Guards. Fencing placed around the mouth of a shaft, which is lifted out of the way by the ascending cage. Lignite. A. coal of a woody character containing about 66^ carbon and having a brown streak. Limadura (Mexican). Filings. The mercurial globules seen when a piece of argentiferous mud from a patio is washed in a spoon or saucer for an assay. Lime Cartridge. A charge or measured quantity of compressed dry caustic lime made up into a cartridge and used instead of gunpowder for breaking down coal. Water is applied to the cartridge, and the expan- sion breaks down the coal without producing a flame. Lime Coal. Small coal suitable for lime burning. Lines. Plumb-lines, not less than two in number, hung from hooks driven in wooden plugs. A line drawn through the centers of the two strings or wires, as the case may be, represents the bearing or course to be driven on. Lining. The planks arranged against frame-sets. Linnets (Derbyshire). Oxidized lead ores. Linternilla (Mexican). The drum of a Horse Whim. Lip Screen. A small screen or screen bars, placed at the draw hole of a coal pocket to take out the fine coal. Lis (Mexican). The flouring of mercury. Little Giant. The name given to a special sort of hydraulic nozzle used for sluicing purposes. Live Quartz. A variety of quartz usually associated with mineral. Lixiviating. See Leaching. Llaves (Mexican). Horizontal cross-beams in a shaft, or the upright pieces that sustain the roof beams in a drift or tunnel. Loaded Track. Track used for loaded cars. Loader. One that fills the mine cars at the working places. Loam. Any natural mixture of sand and clay that is neither distinctly sandy nor clayey. Location. The first approximate staking out or survey of a mining claim, in distinction from a Patent Survey, or a Patented Claim. Location Survey. See Location. Lode (Cornish). Strictly a fissure in the country rock filled with mineral; usually applied to metalliferous lodes. In general miners' usage, a lode, vein, or ledge is a tabular deposit of valuable minerals between definite boundaries. Whether it be a fissure formation or not is not always known, and does not affect the legal title under the United States federal and local statutes and customs relative to lodes. But it must not be a placer, i.e., it must consist of quartz or other rock in place, and bearing valuable mineral. Lodestone, or Lode. (1) Magnetic iron ore. ,(2) Stone found in veins or lodes. Logs. Portions of trunks of trees cut to lengths and built up so as to raise the mouth or collar of a shaft from the surface, in order to give the requisite space for the dumping of mullock and ore. Long-Pittar Work. A system of working coal seams in three separate oper- tions: (1) large pillars are left; (2) a number of parallel headings are driven through the block; and (3) the ribs or narrow pillars are worked away in both directions. Long Tom. A wooden sluice about 24 ft. long, 2 ft. wide, and 1 ft. high, for washing auriferous gravel. Long Ton. 2,240 Ib. LongwaU.A system of working a seam of coal in which the whole seam is taken out and no pillars left, excepting the shaft pillars, and sometimes the main-road pillars. Loob (Cornish). Sludge from tin dressing. Loose End. (I) A portion of a seam worked on two sides. (2) A portion that projects in the shape of a wedge between previous workings. Low Grade. Not rich in mineral. Lumber. Timber cut to the various sizes and shapes for carpenters' purposes. Lumbreras (Mexican). Ventilating shafts in a mine or other underground work. LVM GLOSSARY. MER 597 Lump Coal. (I) All coal (anthracite only) larger than broken coal, or, when steamboat coal is made, lumps larger than this size. (2) In soft coal, all coal passing over the nut-coal screen. Lute. An adhesive clay used either to protect any iron vessel from too strong a heat or for securing air- and gas-tight joints. Lye (English). A siding or turnout. Machote (Mexican). A stake or permanent bench mark fixed in an under- ground working, from which the length and progress thereof is measured. Macizo (Spanish). Unworked lode. Magistral (Spanish). Roasted copper pyrites, copper sulphate, etc., used to reduce silver ores. Magnetic Needle. Needle used in surveying. Magnetic North. The direction indicated by the north end of the magnetic needle. Magnetic Meridian. The line or great circle in which the magnetic needle sets at any given place. Main Road. The principal haulage road of a mine from which the several crossroads lead to the working face. Main Sod (English). See Pump Hod. Main Rope. In. tail-rope haulage, the rope that draws the loaded cars out. Makings (North of England). Small coal produced in kirving. Fines. Malacate (Mexican). A Horse Whim; now extended to any hoisting machine used in mines. Mamposteria (Mexican). Mason work. Manager. An official who has the control and supervision of a mine, both under and above ground. Man Engine. An apparatus consisting of one or two reciprocating rods, to which suitable stages are attached, used for lowering and raising men in shafts. Manga (Spanish). Canvas bag for straining amalgam. Manhole. (I) A refuge hole constructed in the side of a gangway, tunnel, or slope. (2) A hole in cylindrical boilers through wnich a man can get into the boiler to examine and repair it. Mano (Mexican). A grinding stone of an arrastre, etc. Mantas (Mexican). Jute or nenequen, etc., sacks in which ore or waste is carried. Manteo (Mexican). The act of hoisting ore or waste from a mine. Manto (Mexican). A blanket vein. Manway. A small passage used as a traveling way for the miner, and also often used as an airway or chute, or both. Maquilla (Spanish). A custom mill. Maquilar (Mexican). To work ore for its owner on shares or for a money payment. Marco (Mexican). A weight of 8 oz. Marl. Clay containing calcareous matter. Marlinespike.A sharp pointed and gradually tapered round iron, used in splicing ropes. Marmajas (Spanish). Concentrated sulphides. Marrow. A partner. Marsaut Lamp A type of safety lamp whose chief characteristic is the multiple-gauze chimneys. Marsh Gas. CH^ often used synonymously with Firedamp (see page 348). Match. (1) A charge of gunpowder put into a paper several inches long, and used for igniting explosives. (2) The touch end of a squib. Matte. A compound of iron and other metals, chiefly copper, with sulphur, formed during smelting. Mattock. A kind of pick with broad ends for digging. Maul. A driver's hammer. Maundril. A pick with two shanks and points, used for getting coal, etc. Mazo (Mexican). A stamp. Mear (Derbyshire). 32 yd. along the vein. Measures. Strata . Mecha (Mexican). A wick for a lamp or candle; a torch. Merced (Mexican). A gift, grant, or concession. Meridian. A north and south line, either true or approximate. 598 MET GLOSSARY. Mou Metal. (1) In coal mining, indurated clay or slate. (2) An element that forms a base by combining with oxygen that is solid at ordinary tem- perature (with exception of quicksilver), opaque (except in the thinnest possible films), has a metallic luster, and is a good conductor of heat . ,Jt _.^__ thenon . called n _ Metal reverberatory furnaces. Metal Ordinario. Common ore". Metal Pepena.The best class of selected ore. Metlapil (Mexican). See Mano. Mill. Works for crushing and amalgamating gold and silver ores. Mill Cinder. The slag from the puddling furnace of a rolling mill. Mill Hole. An. auxiliary shaft connecting a stope or other excavation with the level below. Mill Run. The test of a given quantity of ore by actual treatment in a mill. Mine. Any excavation made for the extraction of minerals. Miner. One who mines. Mineral. Any constituent of the earth's crust that has a definite com- position. Mineral Oil. Petroleum obtained from the earth, and its distillates. Minero (Mexican). A mine owner; a mining captain; an underground boss. Mine Road. Any mine track used for general haulage. Mine Run. The entire unscreened output of a mine. Minero Mayor (Mexican). The head mining captain. A mining workman is called Operario. Miners' Dial. An instrument used in surveying underground workings. Miners' Inch. A measure of water varying in different districts, being the quantity of water that passes through a slit 1 in. high, of a certain width under a given head (see page 136). Miner's Right. An annual permit from the Government to occupy and work mineral land. Mining. In. its broad sense, it embraces all that is concerned with the extraction of minerals and their complete utilization. Mining Engineer. A man having knowledge and experience in the many departments of mining. Mining Retreating. A process of mining by which the vein is untouched until after all the gangways, etc. are driven, when the mineral extraction begins at the boundary and progresses toward the shaft. Mistress (North of England). A miner's lamp. Mock Lead (Cornish). Zinc blende. Mogrollo (Mexican). Same as Metal de Cebo. Moil. A short length of steel rod tapered to a point, used for cutting hitches, etc. Molonque (Mexican). A rich specimen of which one-half or more is native silver. Monitor. See Gunboat. Monkey. The hammer or ram of a pile driver. Monkey Drift. A small drift driven in for prospecting purposes, or a crosscut driven to an airway above the gangway. Monkey Gangway A small gangway parallel with the main gangway. Monkey Rolls. The smaller rolls in an anthracite breaker. Monkey Shaft. A shaft rising from a lower to a higher level. MonoclinaL Applied to an area in which the rocks all dip in the same direction. Mop. Some material surrounding a drill in the form of a disk, to prevent water from splashing up. Mortar.-^-The vessel in which ore is placed to be pulverized by a pestle. Mortise. A hole cut in one piece of timber, etc. to receive the tenon that projects from another piece. Mote (Moat). A straw filled with gunpowder, for igniting a shot. Mother Gate. The main road of a district in longwall working. Mother Lode (Main Lode). The principal vein of any district. Motive Column. The length of a column of air whose weight is equal to the difference in weight of like columns of air in downcast and upcast shafts. The ventilating pressure in furnace ventilation is measured by the differ- ence of the weights of the air columns in the two shafts. Mouth. The top of a shaft or slope, or the entrance to a drift or tunnel. MOY GLOSSARY. OPE 599 Moyle.An iron with a sharp steel point, for driving into clefts when levering off rock. Mackle Soft clay overlying or underlying coal. Mucks (Staffordshire). Bad earthy coal. Muescas (Mexican). Notches in a stick; mortises; notches cut in a round or square beam, for the purpose of using it as a ladder. Mueseler Lamp. A type of safety lamp invented and used in the collieries of Belgium. Its chief characteristic is the inner sheet-iron chimney for increasing the draft of the lamp. Muffle. A thin clay oven heated from the outside. Muller.The upper grinding iron or rubbing shoe of amalgamating pans, etc. Mullock. Country rock and worthless minerals taken from a mine. Mundic. Iron pyrites. Naked Light. A candle or any form cf lamp that is not a safety lamp. Narrow Work.(\} All work for which a price per yard of length driven is paid, and which, therefore, must be measured. (2) Headings, chutes, crosscuts, gangways, etc. Natas (Mexican). Same as Escoria or Grasa. Native Metal. A metal found naturally in that state. Natural Ventilation Ventilation of a mine without either furnace or other artificial means; the heat imparted to the air by the strata, men, animals, and lights in the mine, causing it to now in one direction, or to ascend. Neck. A cylindrical body of rock differing from the country around it. Needle (I) A sharp-pointed metal rod with which a small hole is made through, the stemming to the cartridge in blasting operations. (2) A hitch cut in the side rock to receive the end of a timber. Negritto (Mexican). Black sulphide of silver. Nick. To cut or shear coal after holing. Nicking. (I) A vertical cutting or shearing up one side of a face of coal. (2) The chipping of the coal along the rib of an entry or room which is usually the first indications of a squeeze. Night Shift. The set of men that work during the night. Nip. When the roof and floor of a coal seam come close together, pinching the coal between them. Nip Out. The disappearance of a coal seam by the thickening of the adjoin- ing strata, which takes its place. mtro.A corrupted abbreviation for nitroglycerine or dynamite. Nittings Refuse of good ore. Nodular. Blistered or kidney-shaped ore. Nodules. Concretions that are frequently found to enclose organic remains. Nogs. Logs of wood piled one on another to support the roof. See Chock. Nook. The corner of a working place made by the face with one side. Noria (Spanish). An endless chain of buckets. Nozzle. The front nose piece of bellows of a blast pipe for a furnace, or of a water pipe. Nugget. A natural lump of gold or other metal, applied to any size above 2 to 3 dwt. Nut Coal. A contraction of the term chestnut coal. Nuts. Small lumps of coal that will pass through a screen or bars, the spaces between which vary in width from i to 2 in. Ocote (Mexican). Pitch pine. Odd Work. Work other than that done by contract, such as repairing roads, constructing stoppings, dams, etc. Offtake. The raised portion of an upcast shaft above the surface, for carrying off smoke and steam, etc., produced by the furnaces and engines under- ground. Oil Shale. Shale containing such a proportion of hydrocarbons as to be capable of yielding mineral oil on slow distillation. Oil Smellers. Men that profess to be able to indicate where petroleum oil is to be found. Old Man. Old workings in a mine. Oolitic. A structure peculiar to certain rocks, resembling the roe of a fish. Open Cast. Workings having no roof. 600 OPE GLOSSARY. PAN Open Cutting. (I) An excavation made on the surface for the purpose of get- ting a face wherein a tunnel can be driven. (2) Any surface excavation. Openings, An Opening. Any excavation on a coal or ore bed, or to reach the same; a mine. Openwork. An open cut. Operario (Mexican). A working miner. Operator. The individual or company actually working a colliery. Ore. A mineral of sufficient value (as to quality and quantity), to be mined with profit. Ores. Minerals or mineral masses from which metals or metallic combina- tions can be extracted on a large scale in an economic manner. Ore Shoot A large and usually rich aggregation of mineral in a vein. Distinguished from pay streak in that it is a more or less vertical zone or chimney of rich vein matter extending from wall to wall, and having a definite width laterally. Oro (Spanish). Gold. Oroche (Spanish). (1) Retorted bullion. (2) (Mexican) Bullion containing gold and silver. Outburst. A blower. A sudden emission of large quantities of occluded gas. Outbye.Iu the direction of the shaft or slope bottom, or toward the outside. Outcrop. The portion of a vein or bed, or any stratum appearing at the sur- face, or occurring immediately below the soil or diluvial drift. Outcropping. See Cropping Oat. Outlet. A passage furnishing an outlet for air, for the miners, for water, or for the mineral mined. Output. The product of a mine sent to market, or the total product of a mine. Outset. The walling of shafts built up above the original level of the ground. Outstroke Rent. The rent that the owner of a royalty receives on coal brought into his royalty from adjacent properties. Outtake. The passage by which the ventilating current is taken out of the mine; the upcast. Overburden. The covering of rock, earth, etc. overlying a mineral deposit that must be removed before effective work can be performed. Overcast. A passage through which the ventilating current is conveyed over a gangway or airway. Overhand Stoping. The ordinary method of stoping upwards. Overlap Fault. A fault in which the shifted strata double back over them- selves. Overman. One who has charge of the workings while the men are in the mine. He takes his orders from the Underviewer. Overwind To hoist the cage into or over the top of the head-frame. Oyamel (Mexican). White pine. Pack. A rough wall or block of coal or stone built up to support the roof. Packing. The material placed in stuffingboxes, etc. to prevent leaks. Pack Wall. A wall of stone or rubbish built on either side of a mine road, to carry the roof and keep the sides up. Pacos (Spanish). Ferrugin9us silver ores. Paddock. (I) An excavation made for procuring wash dirt in shallow ground. (2) A place built near the mouth of a shaft where ore is stored. Paint Gold. The very finest films of gold coating other minerals. Paleozoic. The oldest series of rocks in which fossils of animals occur. Paler o (Mexican). A mine carpenter. Palm.K piece of stout leather fitting the palm of the hand, and secured by a loop to the thumb; this has a flat indented plate for forcing the needle. Palm Needle. A straight triangular-sectioned needle, used for sewing canvas. Palo (Mexican). A stick; a piece of timber. Pan. A thin sheet-iron dish 16 in. across the top, and 10 in. at the bottom, used for panning gold. Panel. (I) A large rectangular block or pillar of coal measuring, say, 130 by 100 yd. (2) A group of breasts or rooms separated from the other workings by large pillars. Panel Working. A system of working coal seams in which the colliery is divided up into large squares or panels, isolated or surrounded by solid ribs of coal, in each of which a separate set of breasts and pillars is worked, and the ventilation is kept distinct, that is, every panel has its own circulation, the air of one not passing into the adjoining one, but being carried direct to the main return airway. PAN GLOSSARY. Pic 601 Panino (Mexican). The peculiar appearance, form, or manner in which the metalliierous minerals present themselves in any given district or mine. Panning, or Panning Off. Separating gold or tin from its accompanying minerals by washing off the latter in a pan. Parcionero (Mexican). A partner in a mining contract. Parrot Coal. A kind of coal that splits or cracks with a chattering noise when on the fire. Partido ( Mexican) .The division of ores between partners. Working a mine by partido is when the miners agree with the owners to take a certain part of the ores in place of wages. Usually, the mine owner provides candles, powder, and steel, and keeps the drills sharpened, and receives, in payment of royalty and supplies, two-thirds or more of the ore taken out. This contract is renewed weekly or monthly, etc., and the propor- tion of ore retained by the miners is more or less, according to the richness of the stopes where they work. This is a cheap way of getting ore as far as labor is concerned. But the miners must be constantly watched; otherwise they will leave the mine in bad state. The proportion of ore assigned to the miners is generally bought from them by the mine owner himself, for various reasons. Parting. (1) Any thin interstratified bed of earthy material. (2) A side track or turnout in a haulage road. Pasilla (Spanish). Dry silver amalgam. Pass. (1) A convenient hole for throwing down ore to a lower level. (2) A passage left in old workings for men to travel in from one level to another. Pass-By. A siding in which cars pass one another underground. A turnout. Pass- Into. When one mineral gradually passes into another without any sudden change. Patent Fuel. Small coal mixed with 8 to 10$ of pitch or tar, and compressed by machinery into bricks. Patented Claim. A claim to which a patent right has been secured from the government, by compliance with the laws relating to such claims. Patent Survey. An accurate survey of a claim by a deputized surveyor as required by law in order to secure a patent right to the claim. Pavement. The floor. Patio (Mexican). Any paved enclosure more or less surrounded by build- ings. An ore-sorting yard. A floor or yard where argentiferous mud is treated by amalgamation. Pay. Profitable ore. Pay Dirt. That portion of an alluvial deposit that contains gold in payable quantities. Pay Out. To slacken or let out rope. Pay Rock Mineralized rock. Pay Streak. Mineralized part of rock. Peach Stone (Cornish). Chlorite schist. Pea Coal. A small size of anthracite coal (see page 434). Peas. Small coal about i to $ in. cube. Peat. The decomposed Dartly carbonized organic matter of bogs, swamps, etc. Pebble 'Jack. Zinc blende in small crystals or pebble-like forms is not attached to rock, but is found in clay openings in the rock. Pee (Derbyshire). A fragment of lead ore. Pella, or Plata Pella (Mexican). Silver amalgam. Penstock. See Forebay. Pent House. A wooden covering for the protection of sinkers working in a pit bottom. Pentice.A few pieces of timber laid as a roof over men's heads, to screen them when working in dangerous places, e.g., at the bottom of shafts. Pepenado (Spanish). Dressed ore. Pepenar (Mexican). To sort ore. Percussion Table. A kind of jolting table used in separating very fine ores from slimes. Pestle. A hard rod for pounding minerals, etc. Peter Out. To " peter out " is to thin out, or gradually decrease in thickness. Petlanque (Mexican). Ruby silver. Petrifaction. Organic remams converted into stone. Pick (1) A tool for cutting and holing coal. (2) To dress the sides or face of an excavation with a pick. 602 Pic GLOSSARY. PLA Picker. (I) A small tool used to pull up the wick of a miner's lamp. (2) A person who picks the slate from the coal in an anthracite-coal breaker. Picking Chute. A chute in an anthracite breaker along which boys are stationed to pick the slate from coal. Picking Table. (I) A flat or slightly inclined platform on which anthracite coal is run to be picked free from slate. (2) A sorting table. Pico (Mexican). A striking or sledge hammer. Picture. A. screen to keep off falling water from men at work. Piedras de Mano (Mexican). Hand specimens. Pig. A piece of lead or iron cast into a long iron mold. Pigsty Timbering. Hollow pillows built up of logs of wood laid crosswise for supporting heavy weights. Pike. A pick. Pilar (Mexican). A pillar of rock or ore left to sustain some portion of the mine. Pilch (Cornish). Portion of lode worked by tributers. Pileta (Mexican). (1) A sump. (2) The basin or pot where melted metal is collected. Piling. Long pieces of timber driven into soft ground for the purpose of securing a solid base on which to build any superstructure. Pillar. (I) A solid block of coal, etc. varying in area from a few square yards to several acres. (2) Sometimes applied to a single timber support. Pillar-and-Room.A system of working coal by which solid blocks of coal are left on either side of the rooms, entries, etc. to support the roof until the rooms are driven up, after which they are drawn out. Pittar-and-StalLSeeBreast-and-Pillar. Pillar Roads. Working roads or inclines in pillars having a range of long- wall faces on either side. Pillion (Cornish). Metal remaining in slag. Pino, (Mexican). Same as Pella. Pinch. A contraction in the vein. Pinch Out. When a lode runs out to nothing. Pinta (Mexican). The color, weight, grain, etc. of ores, whereby it is pos- sible to form some idea of their richness in the various metals. Pipe. An elongated body of mineral. Also the name given to the fossil trunks of trees found in coal veins. Pipe Clay. A soft white clay. Piped Air. Air carried into the working place by pipes or brattices. Piping. Undercutting and washing away gravel before the water nozzle. Pit. (1) A shaft. (2) The underground portion of a colliery, including all workings. (3) A gravel pit. Pit Bank. The raised ground or platform where the coal is sorted and screened at the surface. Pit Bottom. The portion of a mine immediately around the bottom of a shaft or slope. See Shaft Bottom. Pitch. (I) Rise of a seam. (2) Grade of an incline. (3) Inclination. Pit Coal. Generally signifies the bituminous varieties of coal. Pit Frame. See Head-Frame. Pit Headman. The man who has charge at the top of the shaft or slope. Pitman. A miner; also, one who looks after the pumps, etc. Pit Prop. A piece of timber used as a temporary support for the roof. Pit Rails. Mine rails for underground roads. Pit Room. The extent of underground workings in use or available for use. Pit's Eye. Pit bottom or entrance into a shaft. Pit Top. The mouth of a shaft or slope. Place. The portion of coal face allotted to a hewer is spoken of as his "working place," or simply "place." Placer. A surface accumulation of mineral in the wash of streams. Placer Mining Surface mining for gold where there is but little depth of alluvial. Plan. (1) The system on which a colliery is worked as Longwall, Pillar- and-Breast, etc. (2) A map or plan of the colliery showing outside improvements and underground workings. (3) (Mexican) The very lowest working in a mine. Trabojar de Plan. To work to gain depth. Plancha (Mexican). A pig of lead, etc. A plate, thick sheet, or mass of any metal. PLA GLOSSARY. POP 603 Planchera (Mexican). 'A mold of sand, earth, or iron, to form pigs of lead. Plane. A main road, either level or inclined, along which coal is conveyed by engine power or gravity. Plane Table. A simple surveying instrument by means of which one can plot on the field. Planilla (Mexican). An inclined plane of mason work, wood, etc., on which tailings are spread out, to be concentrated by jets of water, skilfully applied. Planillero (Mexican). A workman who devotes himself to concentrating tailings, etc. on the Planillas; always paid by weight, measure, or con- centrates produced. Plank Dam. A water-tight stopping fixed in a heading constructed of timber placed across the passage, one upon another, sidewise, and tightly wedged. Plank Tubbing. Shaft lining of planks driven down vertically behind wooden cribs all around the shaft, all joints being tightly wedged, to keep back the water. Plant. The shafts or slope, tunnels, engine houses, railways, machinery, workshops, etc. of a colliery or other mine. Plat, or Map. A map of the surface and underground workings, or of either, to draw such a map from survey. Plata ( Spanish ) .Silver. Plata Blanca (Mexican). Native silver. Plata Cornea Amarillia (Spanish). lody rite. Plata Cornea Blanca (Spanish). Cerargy rite. Plata Cornea Verde (Spanish). Embolite. Plata Mixta (Spanish). Gold and silver alloy. Plata Negra (Spanish). Argentite. Plata Pasta (Spanish). Spongy silver bars after retorting. Plata Piha (Spanish). Silver after retorting. Plata Verde (Spanish). Bromyrite. Plate (North of England). Scaly shale in limestone beds. Plates. Metal rails 4 ft. long. Plenum. A mode of ventilating a mine or a heading by forcing fresh air into it. Plomada (Mexican). A plumb-line or plumb-bob. Plomb d'Oeuvre (French). Dressed galena. Plomillos (Mexican). Shots of lead found in slags. Plom,o (Spanish). Lead, galena. Plugging. When drift water forces its way through the puddle clay into the shaft, holes are bored through the slabs near the leakage point, and plugs of clay forced into them until the leakage is stopped. Pta&.-Vertical. Plummet. (1) A heavy weight attached to a string or fine copper wire used for determining the verticality of shaft timbering. (2) A plumb-bob for setting a surveying instrument over a point. Plunger. The solid ram of a force pump working in the plunger case. Plunger Case. The pump cylinder or barrel in which the plunger works. Plush Copper. Chalcotrichite. Plwm (Welsh). Lead. Poblar (Mexican). To set men at work in a mine. Pocket. (1) A thickening out of a seam of coal or other mineral over a small area. (2) A hopper-shaped receptacle from which coal or ore is loaded into cars or boats. Podar (Cornish). Copper pyrites. Pole Tools. Drilling tools used in drilling in the old fashion, with rods, now superseded by the rope-drilling method. Polroz (Cornish). Waterwheel pit. Poling. Refining metal, when in a molten condition, by stirring it up with a green pole of wood. Pott Pick. A pick having the longer end pointed and the shorter end ham- mer-shaped. Polvillos (Spanish). Rich ores or concentrates. Polvoulla (Spanish). Black silver. Poppet Heads. The pulley frame or hoisting gear over a shaft. Poppet (Puppet). (I) A pulley frame or the head-gear over a shaft. (2) A valve that lifts bodily from its seat instead of being hinged. 604 Pos GLOSSARY. PUN Post. (1) Any upright timber; applied particularly to the timbers used for propping. See Prop. (2) Local term for sandstone. Post stone may be "strong," "framey," "short," or "broken." Post-and-Stall.A system of working coal much the same as Pillar-and-Stall. Post Tertiary. Strata younger than the Tertiary formation. Pot Bottom. A large boulder in the roof slate, having the appearance of the rounded bottom of a pot, and which easily becomes detached. Pot Growan (Cornish). Decomposed granite. Pot Hole. A circular hole in the rock caused by the action of stones whirled around by the water when the strata was covered by water. They are generally filled with sand and drift. Power Drill. A rock drill employing steam, air, or electricity as a motor. Prian (Cornish). Soft white clay. Pricker. (1) A thin brass rod for making a hole in the stemming when blasting, for the insertion of a fuse. (2) A piece of bent wire by which the size of the flame in a safety lamp is regulated without removing the top of the lamp. Prill (1) An extra-rich stone of ore. (2) A bead of metal. Prong (English). The forked end of the bucket-pump rods for attachment to the traveling valve and seat. Prop. A wooden or cast-iron temporary support for the roof. Propping. The timbering of a mine. Prospect. The name given to underground workings whose value has not yet been made manifest. A prospect is to a mine what mineral is to ore. Prospect Hole. Any shaft or drift hole put down for the purpose of prospect- ing the ground. Prospect Tunnel or Entry. A tunnel or entry driven through barren measures or a fault to ascertain the character of strata beyond. Prospecting. Examining a tract of country in search of minerals. Prospector. One engaged in searching for minerals. Protector Lamp. A safety lamp whose flame cannot be exposed to the out- ward atmosphere, as the action of opening the lamp extinguishes the light. Prove. (I) To ascertain, by boring, driving, etc., the position and character of a coal seam, a fault, etc. (2) To examine a mine in search of fire- damp, etc., known as " proving the pit." Proving Hole. (1) A bore hole driven for prospecting purposes. (2) A small heading driven in to find a bed or vein lost by a dislocation of the strata, or to prove the quality of the mineral in advance of the other workings. Pudding Machine. A circular machine for washing pay dirt. Pudding Rock. Conglomerate. Puddle. (1) Earth well rammed into a trench, etc., to prevent leaking. (2) A process for converting cast iron into wrought iron. Pueble (Mexican). The actual working of a mine; the aggregation of persons employed therein. Puertas (Mexican). Massive barren rocks, or " horses," occurring in a vein. Pug Mill. A mill for preparing clay for bricks, pottery, etc. Pulley. (I) The wheel over which a winding rope passes at the top of the head -gear. (2) Small wooden cylinders over which a winding rope is carried on the floor or sides of a plane. Pulleying. Overwinding or drawing up a cage into the pulley frame. Pulp. Crushed ore, wet or dry. Pump. Any mechanism for raising water. Pump Bob. See Bob. Pump Ring. A flat iron ring that, when lapped with tarred baize or engine shag, secures the joints of water columns. Pump .Rods. Heavy timbers by which the motion of the engine is trans- mitted to the pump. In Cornish and bull pumps, the weight of the rods makes the effective (pumping) stroke, the engine merely lifting the rods on the up stroke. Pump Slope. A slope used for pumping machinery. Pump Station. An enlargement made in the shaft, slope, or gangway, to receive the pump. Pump Tree. -Cast-iron pipes, generally 9 ft. long, of which the column or set is formed. Punch-and-Thirl.A kind of pillar-and-stall system of working. PUN GLOSSARY. REE 605 Punch Prop. A short timber prop set on the top of a crown tree, or used in holding, as a sprag. Putty Stones. Soft pieces of decomposed rock found in placer deposits. Pyran (Cornish). See Prian. Pyrites. Sulphide of iron. Pyrometer. An instrument for measuring high degrees of heat. Qua] ado (Spanish). Dull lead ore. Quarry. (I) An open surface excavation for working valuable rocks or minerals. (2) An underground excavation for obtaining stone for stowage or pack walls. Quartz Bucket. A bucket for hoisting quartz. Quaternary. Post-tertiary period. Quemadero (Mexican). A burning place; a retorting furnace for silver or gold amalgam. Quemados (Mexican). Burnt stuff. Any dark cinder-like mineral encoun- tered in a vein or mineral deposit, generally manganiferous. Queme (Mexican). A roast of ore; the process of roasting ore. Quick (Adjective). Soft, running ground; an ore or pay streak is said to be quickening when the associated minerals indicate richer mineral ahead. Quick (Noun). (1) Productive. (2) Mercury. Quicksand. Soft watery strata easily moved, or readily yielding to pressure. Quicksilver. Mercury . Quillato (Spanish). Carat. Quitapepena (Mexican). A watchman that searches the miners as they come out at the mouth of a mine. Rabban (Cornish). Yellow dry gossan. Rabbling. Stirring up a charge of ore in a reverberatory furnace with specially designed iron rods. Race. A channel for conducting water to or from the place where it per- forms work. The former is termed the headrace, and the latter the tailrace. Rack (Cornish). A stationary buddle. Raff. The coarse ore after crushing by Cornish rolls. Raffain (Cornish). Poor ore. Raff Wheel. A. revolving wheel with side buckets for elevating the raff. Rafter Timbering. That in which the timbers appear like roof rafters. Rag Burning (Cornish). The first roasting of tin-witts. Ragging (Cornish). Rough cobbing. Rag Wheel. Sprocket wheel. A wheel with teeth or pins that catch into the links of chains. Rails. The iron or steel portion of the tramway or railroad. Rake (Cornish). -(1) A vein. (2) (Derbyshire) Fissure vein crossing strata. Ram. (I) The plunger of a pump. (2) A device for raising water. Ramal (Mexican). A branch vein. Ramalear (Mexican). To branch off into various divisions. Ramble. Stone of little coherence above a seam that falls readily on the removal of the coal. See Following Stone. Ranee. A pillar of coal. Rapper. A lever with a hammer attached at one end, which signals by striking a plate of metal, when the signaling wire to which it is attached is pulled. Rash. A term used to designate the bottom of a mine when soft and slaty. Rastrillo (Mexican). A rake; a stirrer for moving ore in a furnace. Rastron (Mexican). A Chilian mill. Raw Ore. Not roasted or calcined. Reacher.A slim prop reaching from one wall to the other. Reamer. An enlarging tool. Reaming. Enlarging the diameter of a bore hole. Receiving Pit. A shallow pit for containing material run into it. Red-Ash Coal.Co&l that produces a reddish ash, when burnt. Red Rob (Cornish). Red slaty rock. Reduced. When a metal is freed from its chemical associate it is said to be reduced to the metallic state. Reduction Works. Works for reducing metals from their ores. Reef. (I) A vein of quartz. (2) Bed rock of alluvial claims. Reef Drive, In alluvial mines-, drives made in the country rock or reef. 606 REF GLOSSARY. Riv Refining. The freeing of metals from impurities. Refractory. Rebellious ore, not easily treated by ordinary processes. Refuge Hole. A. place formed in the side of an underground plane in which a mail can take refuge during the passing of a train, or when shots are fired. Regulator. A. door in a mine, the opening or shutting of which regulates the supply of ventilation to a district of the mine. Regulus.See Matte. Relampago, or Relampaguear (Mexican). The brightening of the silver button during cupellation. Reliz (Spanish). Wall of lode. Rendir (Mexican). Is when all the silver has been amalgamated in a heap of argentiferous mud on a patio. Rendrock.A variety of dynamite. Repairman. A workman whose duty it is to repair tracks, doors, brattices, or to reset timbers, etc., under the direction of the foreman. Repaso-Repasar (Mexican). The art of mixing up the mud heaps in the patio process of amalgamation by treading them over with horses or mules. Repos Adero (Mexican). The bottom of a crucible or pot in an upright smelting furnace. Rescatadores (Mexican). Ore buyers. Reserve. Mineral already opened up by shafts, winzes, levels, etc., which may be broken at short notice for any emergency. Reservoir. An artificially built, dammed, or excavated place for holding a reserve of water, Respaldos (Mexican). The walls enclosing a vein. Rcspaldo Alto. The hanging wall. Respaldo Bajo. The foot-wall. Rests, Keeps, Wings. Supports on which a cage rests when the loaded car is being taken off and the empty one put on. Resue, See Stripping. Retort. (I) A vessel with a long neck, used for distilling the quicksilver from amalgam. (2) The vessel used in distilling zinc. Return. The air-course along which the vitiated air of a .mine is returned or conducted back to the upcast shaft. Return Air. The air that has been passed through the workings. Reverberatory. A class of furnaces in which the flame from the fire-grate is made to beat down on the charge in the body of the furnace. Reversed Fault. See Overlap Fault. Rib. The side of a pillar. Rib-and-Pillar.A system of working similar to Pillar-and-Stall. Ribbon. A line of bedding or a thin bed appearing on the cleavage surface and sometimes of a different color. Rick. Open heap in which coal is coked. Ridding. Clearing away fallen stone and debris. Riddle. An oblong frame holding iron bars parallel to each other, used for sifting material that is thrown against it. Ride, Riding. To be conveyed on a cage or mine car. Rider. (1) A guide frame for steadying a sinking bucket. (2) Boys that ride on trips on mechanical haulage roads. (3) A thin seam of coal overlying a thicker one. Riffle, or Ripple. Crosspieces placed on the bottom of a sluice to save gold: or grooves cut across inclined tables. Right Shore. The right shore of a river is on the right hand when descend- ing the river. Rill. The coarse ore at the periphery of a pile. Rim Rock. Bed. rock forming a boundary to gravel deposit. Ring. (1) A complete circle of tubbing plates placed round a circular shaft. (2) Troughs placed in shafts to catch the falling water, and so arranged as to convey it to a certain point. Ripping. Removing stone from its natural position above the seam. Riscos (Mexican). Sharp and precipitous rocks; amorphous quartz found in veins or outcrops. Rise. The inclination of the strata, when looking up the pitch. Rise Workings. Underground workings carried on to the rise or high side of the shaft. River Mining. Working beds of existing rivers by deflecting their course or by dredging. ROA GLOSSARY. SAF 607 Road. (I) Any underground passageway or gallery. (2) The iron rails, etc. of underground roads. Roasting. Heating ores at a temperature sufficient to cause a chemical change, but not enough to smelt them. Rob. To cut away or reduce the size of pillars of coal. Robbing. The taking of mineral from pillars. Robbing an Entry. See Drawing an Entry. Rock A. mixture of different minerals in varying proportions. Rock Breaker A. machine for reducing ore in size by crunching it between powerful jaws. Rock Chute. See Slate Chute. Rock Drill. A rock-boring machine worked by hand, compressed air, steam, or electrical power. Rocker. See Cradle. Rock Fault. A replacement of a coal seam over greater or less area, by some other rock, usually sandstone. Rodding. The operation of fixing or repairing wooden eye guides in shafts. Roll. An inequality in the roof or floor of a mine. Roller. A small steel, iron, or wooden w r heel or cylinder upon which the hauling rope is carried just above the floor. Rolleyway.A main haulage road. Rolling Ground. When the surface is much varied by many small hills and valleys. Rolls. Cast-iron cylinders, either plain or fitted with steel teeth, used to break coal and other materials into various sizes. Roof. The top of any subterranean passage. -Room. Synonymous with Breast. Room-and-Rance.A system of working coal similar to Pillar-and-Stall. Rope Roll. The drum of a winding engine. Rosiclara (Spanish). Ruby silver ore. Roughs (Cornish). Second quality tin sands. Round Coal. Coed in large lumps, either hand-picked, or, after passing over screens, to take out the small. Royalty. The price paid per ton to the owner of mineral land by the lessee. Rubbing Surface. The total area of a given length of airway; that is, the area of top, bottom, and sides added together, or the perimeter multi- plied by the length. Rubble. Coarse pieces of rock. Rumbo (Mexican). The course or direction of a vein. Run. (1) The sliding and crushing of pillars of coal. (2) The length of a lease or tract on the strike of the seam. Run Coal. Soft bituminous coal. Rung, Rundle, or Round. A step or cross-bar of a ladder. Runner. A man or boy whose duty it is to run mine cars by gravity from working places to the gangway. . Running Lijt. A sinking set of pumps constructed to lengthen or shorten at will, by means of a sliding or telescoping wind bore. Rush. An old-fashioned way of exploding blasts by filling a hollow stalk with slow powder and then igniting it. Rush Gold. Gold: coated with oxide of iron or manganese. Rush Together. See Caved In. Rusty. Stained by iron oxide. Saca (Mexican). A bagful of ore. A mine is said to be debuena saca when it has large quantities of ore easy to get out. Saddle. An anticlinal, a hogback. Saddleback. A depression in the strata. See Roll. Saddle Reef. A reef having the form of an inverted V. Safety Cage. A cage fitted with an apparatus for arresting its motion in the shaft in case the rope breaks. Safety Car. See Barney. Safety Catches. Appliances fitted to cages, to make them safety cages. Safety Door. A strongly constructed door, hinged to the roof, and always kept open and hung near to the main door, for immediate use when main door is damaged by an explosion or otherwise. Safety Fuse. A cord with slow-burning powder in the center for exploding charged blast holes, 608 SAP GLOSSARY. SEG Safety Lamp. A miner's lamp in which the flame is protected in such a manner that an explosive mixture of air and firedamp can be detected by the mixture burning inside the gauze. Sag. A depression, e. g., in ropes, ranges of mountains, etc. Sagre, or Seggar.A local term for fireclay, often forming the floor (or thill) of coal seams. Salting. (1) Changing the value of the ore in a mine or of ore samples before they have been assayed, so that the assay will show much higher values than it should. (2) Sprinkling salt on the floors of underground passages in very dry mines, in order to lay the dust. Sampler. (1) An instrument or apparatus for taking samples. (2) One whose duty it is to select the samples for an assay, or to prepare the mineral to be assayed, by grinding and sampling. Sampling Works. Works for sampling and determining the values obtained in ores; where ores are bought and sold. Samson Post. An upright supporting the working beam that communicates oscillatory motion to pump or drill rod. Sand Bag. A bag filled with sand for preventing a washout by obstructing the flow. Sand Pump. A sludger; a cylinder provided with a stem (or other) valve, lowered into a drill hole to remove the pulverized rock. Scaffolding. Incrustations on the inside of a blast furnace. Scale. (1) A small portion of the ventilating current in a mine passing through a certain size of aperture. (2) The rate of wages to be paid, which varies under certain contingencies. Scale Door. See Regulator. Scallop. To hew coal without kirving or nicking or shot firing. Schist. Crystalline or metamorphic rocks having a slaty structure. Schute.See Chute. Scissors Fault. A fault of dislocation, in which two beds are thrown so as to cross each other. Scoop. A large-sized shovel with a scoop-shaped blade. Scoria. Ashes. Scorifier.A small dish used in assaying. Scovan (Cornish). A tin lode showing no gossan at surface. Scove (Cornish). Purest tin ore. Scramming. Cleaning up small bodies or patches of ore left in the ordinary process of mining. Scraper. (I) A tool for cleaning the dust out of the bore hole. (2) A mechanical contrivance used at colleries to scrape the culm or slack along a trough to the place of deposit. Scrapper. A local name given to parties that pick up the ore left on dumps. Screen. (I) A mechanical apparatus for sizing materials. (2) A cloth brat- tice or curtain hung across a road in a mine, to direct the ventilation. Serin (Derbyshire). A small vein. Scrowl (Cornish). Loose ore where a vein is crossed. Sculping Fracturing the slate along the grain, i. e., across the cleavage. Scupper Nails. Nails with broad heads, for nailing down canvas, etc. Sea Coal. That which is transported by sea. Sealing. Shutting off all air from a mine or a part of a mine by stoppings. Seam. (1) Synonymous with Bed, Vein, etc. (2) (Cornish) A horse load of ore. Seam-Out. A term applied to a shot or blast that has simply blown out a softer stratum of the deposit in which it was placed, without dislodging the other strata or layers of the seam. Second Outlet (Second Opening). A passageway out of a mine, for use in case of accident to the main outlet. Seconds. The second-class ore of a mine that requires dressing. Second Working. The operation of getting or working out the pillars formed by the first working. Section. (1) A vertical or horizontal exposure of strata. (2) A drawing or sketch representing the rock strata as cut by a vertical or a horizontal plane. Sedimentary Rocks. Rocks formed from deposits of sediment by wind or water. Seedbag.A water-tight packing of flaxseed around the tube of a drill hole, to prevent the influx into the hole of water from above. Segregations. Detached portions of veins in place. SEL GLOSSARY. SHO 609 Self-Acting Plane. An inclined plane upon which the weight or force of gravity acting on the full cars is sufficient to overcome the resistance of the empties; in other words, the full car, running down, pulls the other car up. Self -Detaching Hook. A self-acting hook for setting free a hoisting rope in case of overwinding. Self-Feeders. Automatic appliances for feeding ore-dressing machines. Selvage. The clay seam on the walls of veins; gouge. Separation Doors. The main doors at or near the shaft or slope bottom, which separate the intake from the return airways. Separation Valve. A massive cast-iron plate suspended from the roof of a return airway through which all the return air of a separate district flows, allowing the air to always flow past or underneath it; but in the event of an explosion of gas, the force of the blast closes it against its frame or seating, and prevents a communication with other districts. The blast being over, the weight of the valve allows it to return to its normal position. Set. To fix in place a prop or sprag. Set Hammer. The flat-faced hammer held on hot iron by a blacksmith when shaping or smoothing a surface by aid of his striker's sledge. Set of Timber. The timbers which compose any framing, whether used in a shaft, slope, level, or gangway. Thus, the four pieces forming a single course in the curbing of a shaft, or the three or four pieces forming the legs and collar, and sometimes the sill of an entry framing are together called a set of timber, or timber set. Shackle. A U-shaped link in a chain closed by a pin; when the latter is with- drawn the chain is severed at that point. Shadd (Cornish). Rounded fragments of ore overlying a vein. Shaft. A vertical or highly inclined pit or hole made through strata, through which the product of the mine is hoisted, and through which the ventila- tion is passed either into or out of the mine. A shaft sunk from one seam to another is called a "blind shaft." Shaft Pillar. Solid, material left unworked beneath buildings and around the shaft, to support them against subsidence. Shaking Table. An inclined table for concentrating fine grains of ore, which is rapidly shaken by a short motion Shale. (1) Strictly speaking, all argillaceous strata that split up or peel off in thin laminae. (2) A laminated and stratified sedimentary deposit of clay, often impregnated with bituminous matter. Shank. The body portion of any tool, up from its cutting edge or bit. Shearing. Cutting a vertical groove in a coal face or breast. The cutting of a "fast end" of coal. Shear Legs. A high wooden frame placed over an engine or pumping shaft fitted with small pulleys and rope for lifting heavy weights. Shears, or Sheers (English). Two tall poles, with their feet some distance apart and their tops fastened together, for supporting hoisting tackle. Shear Zone. Hogback. Sheave. A wheel with a grooved circumference over which a rope is turned either for the transmission of power or for winding or hauling. Sheel Pump. See Sludger. Sheets. Coarse cloth curtains or screens for directing the ventilating current underground. Shelly A name applied to coal that has been so crushed and fractured that it easily breaks up into small pieces. The term is also applied to a lami- nated roof that sounds hollow and breaks into thin layers of slate or shale. Shet (Staffordshire). Fallen roof of coal mine. Sheth. An old term denoting a district of about eight or nine adjacent bords. Thus, a " sheth of bords," or a " sheth of pillars." Shift. (I) The number of hours worked without change. (2) A gang or force of workmen employed at one time upon any work, as the day shift, or the night shift. Shoad (Cornish). See Shadd. Shoading ( Cornish) .Prospecting. Shoe. (1) A steel or iron guide piece fixed to the ends or sides of cages, to fit or run on the conductors. (2) The upper working face of a stamp or grinding pan. (3) The lower capping of any post or pile, to protect its end while driving. (4) A wooden or sheet-iron frame or muff arranged 610 SHO GLOSSARY. SIN at the bottom of a shaft while sinking through quicksand, to prevent the inflow of sand while inserting the shaft lining. Shoot, Chute, Shute.(l) A run of rich material in a vein. (2) An inclined or vertical trough or pipe for conveying materials from a higher to a lower level. Shoot. To break rock or coal by means of explosives. Shooting. Blasting in a mine. Shore (English). A studdle or thrusting stay. Shore Up. To stay, prop up, or support by braces. Shot (I) A charge or blast. (2) The firing of a blast. (3) Injured by a blast. Shot-Firer.See Shot Lighter. Shot Hole. The bore hole in which an explosive substance is placed for blasting. Shot Lighter, or Shot Firer.A man specially appointed by the manager of the mine to fire off every shot in a certain district, if, after he has examined the immediate neighborhood of the shot, he finds it free from gas, and otherwise safe. Shotty Gold. Granular pieces like shot. Show. When the flame of a safety lamp becomes elongated or unsteady, owing to the presence of firedamp in the air, it is said to show. Showing. The first appearance of float, indicating the approach to an out- cropping vein or seam. Blossom. Shroud. A housing or jacket. Shute.See Chute, Shoot, and Schute. Shutter. (I) A movable sliding door, fitted within the outer casing of a Guibal or other closed fan, for regulating the size of the opening from the fan, to suit the ventilation and economical working of the machine. (2) A slide covering the opening in a door or brattice, and forming a regulator for the proportionate division of the air-current between two or more districts of a mine. Sickening. A coating of impurities on quicksilver that retards amalgama- tion or the coalescence of the globules of quicksilver. Siddle. Inclination. Side. (I) The more or less vertical face or wall of coal or goaf forming one side of an underground working place. (2) Rib. (3) A district. Side Chain. A chain hooked on to the sides of cars running on an incline or along a gangway, to keep the cars together in case the coupling breaks. Sidelong Reef. An overhanging wall of bed rock in alluvial formations running parallel with the course of the gutter; generally only on one side of it. Siding. A short piece of track parallel to the main track, to serve as a passing place. Siding Over. A short road driven in a pillar in a headwise direction. Sight. -(1) A bearing or angle taken with a compass or transit when making a survey. (2) Any established point of a survey. Sights. Bohs or weighted strings hung from two or more established points in the roof of a room or entry, to give direction to the men driving the entry or room. Sitt. (1) The floor piece of a timber set, or that on which the track rests; the base of any framing or structure. (2) The floor of a seam. Silver. (1) A certain white ductile and valuable metal. (2) Short for quick- silver. Sing. The noise made by a feeder of gas issuing from the coal. Singing Coal. Coal from which gas is issuing with a hissing sound. Singing Lamp. A safety lamp, which, when placed in an atmosphere of explosive gas, gives out a peculiar sound or note, the strength of the note varying in proportion to the percentage of firedamp present. Single-Entry System. A system of opening a mine by driving a single entry only, in place of a pair of entries. The air-current returns along the face of the rooms, which must be kept open. Single-Intake Fan. A ventilating fan that takes or receives its air upon one side only. Single-Rope Haulage. A system of underground haulage in which a single rope is used, the empty trip running in by gravity. This is engine-plane haulage. Sink. To excavate a shaft or slope; to bore or put down a bore hole. SIN GLOSSARY. SLI 611 Sinker. A man who works at the bottom of a shaft or face of a slope during the course of sinking. Sinker Bar.lu rope drilling, a heavy bar attached above the jars, to give force to the up stroke, so as to dislodge the bit in the hole. Sinking. The process of excavating a shaft or slope or boring a hole. Siphon. A simple, effective, and economical mode of conveying water over a hill whose height is not greater than what the atmospheric pressure will raise the water. Its form is that of an iron pipe, bent like an inverted U; the vertical height between the surface of the water in the upper basin and the top of the hill is called the lift of the siphon; while the vertical height between the surfaces of the water in the upper and lower basins is called the fall of the siphon. Sizing. To sort minerals into sizes. Skew Back. The beveled stone from which an arch springs, and upon which it rests. Skids. Slides upon which heavy bodies are slid from place to place. Skimpings (Cornish). The poorest ore skimmed off the jigger. Skip. (1) A mine car. (2) A car for hoisting out of a slope. (3) A thin slice taken off from a breast or pillar or rib along its entire length or part of its length. Skirting. Road opened up or driven next a fall of stone, or an old fallen place. Skit (Cornish). A pump. Slab. Split pieces of timber from 2 in. to 3 in. thick, 4 ft. to 6 ft. long, and 7 in. to 14 in. wide, placed behind sets or frames of timber in shafts or levels. Slack. (1) Fine coal that will pass through the smallest sized screen. The fine coal and dust resulting from the handling of coal, and the disinte- gration of soft coal. (2) The process by which soft coal disintegrates when exposed to the air and weather. Slag. The liquid refuse from a smelting operation, which floats on top of the metal. Slant. (1) An underground roadway driven at an angle betvyeen the full rise or dip of the seam and the strike or level. (2) Any inclined road in a seam. Slant Chutes. Chutes driven diagonally across a pillar, to connect a breast manway with a man way chute. Slate. (1) A hardened clay having a peculiar cleavage. (2) About coal mines, slate is any shale accompanying the coal, also sometimes applied to bony coal. Slate Picker. (1) A man or boy that picks the slate or bony coal from anthracite coal. (2) A mechanical contrivance for separating slate and coal. Slate Chute. (1) A chute for conveying slate or bony coal to a pocket from which it is loaded into " dumpers." (2) A chute driven through slate. Sleek (Derbyshire). Mud in a mine. Sled. A drag used to convey coal along the face to the road head where it is loaded, or to the chute. Sledge. A heavy double-handed hammer. Sleeper (English). The foundation pieces or cross-ties on which rails rest. Sleeping Table (Cornish). A buddle. Sleeve. A hollow cylinder fitting over two pieces, to hold them together. Slickensides. Polished surfaces of vein walls. Slide. Loose deposit covering the outcrop of a seam. Slides. See Guides. Sliding Scale. A mode of regulating the wages paid workingmen by taking as a basis for calculation the market price of coal, the wages rising and falling with the state of trade. Sliding Wind Bore (English). The bottom pipe or suction piece of a sinking set of pumps having a lining made to slide like a telescope within it, to give length without altering the adjustment of the whole column of pipes. Slime, Sludge. (I) The pulp or fine mud from a mill or from a drill hole. (2) Silt containing a very fine ore, which passes off in the water from the jigs. Slings. Pieces of ropes or chains to be put around stones, etc. for raising them. Slip. (1) A fault. (2) A smooth joint or crack where the strata have moved upon each other. 612 SLI GLOSSARY. SPI Slip Cleavage. Microscopic folding and fracture accompanied by slippage; quarrymen's " false cleavage." Slit. A short heading put through to connect two other headings. Slitter. See Pick. Slope. A plane or inclined roadway, usually driven in the seam from the surface. A rock slope is a slope driven across the strata, to connect two seams; or a slope opening driven from the surface, to reach a seam below that does not outcrop at an accessible point. Sludge. See Slime. Sludger, Sludge Pump. A cylinder having an upward opening valve at the bottom, which is lowered into a bore hole, to pump out the sludge or fine rock resulting from drillings. Sluice. (1) A long channel in rock or built of timber, with checks to catch gold. (2) Any overflow channel. Sluice Box. A trough with ripples or false bottom for catching gold. Sluice Head, or Head (Australia and New Zealand). A supply of 1 cu. ft. of water per second, regardless of the head, pressure, or size of orifice. Sluicing. Ground sluicing is working gravel by excavating with pick and shovel, and washing the debris in trenches with water not under pressure. Slurry (North of Wales). Half-smelted ore. Small. See Slack. Smeddum. Lead-ore dust. Smelting. Method of extracting a precious metal from, its ores. Smift, Snift.A bit of touch paper, touch wood, etc. attached by a bit of clay or grease to the outside end of the train of gunpowder when blasting. Smittem. Fine gravel-like ore, occurring free in mud openings, or derived from the breaking of the ore in blasting. Smut (Staffordshire). Soft, bad coal. Snore, Snore Piece. The hole in the lower part of a sinking or Cornish pump, through which water enters. Soapstone.A term incorrectly applied by the miner to any soft, unctuous rock. Socabon (Mexican). A mining tunnel; an adit. Socavon a kilo dc veta. A drift tunnel. Socavon crucero.A crosscut tunnel or adit. Socket. (I) The innermost end of a shot hole, not blown away after firing. (2) A wrought-iron contrivance by means of which a 'wire rope is securely attached to a chain or block. Sole, Sole Plate. A piece of timber set underneath a prop. Sollar.A wooden platform fixed in a shaft, for the ladders to rest on. Sondear (Mexican). To bore for prospecting purposes. Sondeo (Mexican). A boring for prospecting purposes. Soplete (Mexican). A blowpipe. Ensaye al Soplete. A blowpipe assay. Sorting. Separating valuable from worthless material. Sounding. (1) Knocking on a roof to see whether it is sound or safe to work under. (2) Rapping on a pillar so that a person on the other side of it may be signaled to, or to enable him to estimate its width. Sow. (I) A tool used for sharpening drills. (2) Iron deposits at the bottom of furnaces. Spall. To break up rocks with a large hammer, for hand sorting. Spalls. The chips' and other waste material cut from a block of stone in process of dressing. Spar. A name given to certain white quartz-like minerals, e. g., calcspar, feldspar, fluorspar. Spears. Pump-rods. Specimen. A picked piece of mineral. Speiss. A basic arsenide or antlmonide of iron, often containing nickel. cobalt, lead, bismuth, copper, etc., having a metallic luster of high specific, gravity and a strong tendency toward crystallization. Spelter. The commercial name for zinc. Spent Shot. A blast hole that has been fired, but has not done its work. Spew. The extension of mineral matter on the surface, past the ordinary limits of the lode. Spiders. See Drum Rings. Spiegeleisen. Manganiferous white cast iron. Spiking Curbs. A light ring of wood to which planks are spiked when plank tubbing is used. SPI GLOSSARY. STA 613 Spiles (Cornish). A temporary lagging driven ahead on levels in loose ground. Snort pieces of planking sharpened flatways, and used for driving into watery strata as sheath piling, to assist in checking the flow; used much in sinking through quicksands. Spiling. A process of timbering through soft ground. Spiral Drum. See Conical Drum. Splint, or Splent.A laminated, coarse, inferior, dull-looking, hard coal, pro- ducing much white ash, intermediate between cannel and bituminous coal. Split. (1) To divide an air-current into two or more separate currents. (2) Any division or branch of the ventilating current. (3) The workings ventilated by that branch. (4) Any member of a coal bed split by thick partings into two or more seams. (5) A bench separated by a consider- able interval from the other benches of a coal bed. Spoil. Debris from a coal mine. Spoon. A slender iron rod with a cup-shaped projection at right angles to the rod, used for scraping drillings out of a bore hole. Spout. A short underground passage connecting a main road with an air- course. Sprag. (1) A short wooden prop set in a slanting position for keeping up the coal during the operation of holing. (2) A short round piece of hard wood, pointed at both ends, to act as a brake when placed between the spokes of mine-car wheels. (3) The horizontal member of a square set of timber running longitudinally with the deposit. Spragger. One who attends to the spragging of cars. Sprag Road. A mine road having such a sharp grade that sprags are needed to control the speed of the car. Spreader. A timber stretched across a shaft or stope. Spring Beams. Two short parallel timber beams, built with a Cornish pump- ing engine house, nearly on a level with the engine beam, for catching the beam, etc., and preventing a smash in case of a breakdown. Spring Latch. The latch or tongue of an automatic switch, operated by a spring pole at the side of the track. Spring Pole. An elastic wooden pole from which boring rods are suspended. Used also to operate a spring latch. Sprocket Wheel (English). Rag wheel. A wheel with teeth or pins which catch in the links of a chain. Spud, Spaa. A horseshoe nail with a hole in the head, for driving into the mine timbers, or into a wooden plug fitted into the roof, to mark a sur- veying station. Spur. (1) A short ridge or offsetting pointed branch from a main ridge or mountain. (2) A short branch or feeder from the main lode of a vein. Square Set. A variety of timbering for large excavations. Squat (Cornish). Tin ore mixed with spar. Squeeze. See Creep. Squib. A straw, rush, paper, or quill tube filled with a priming of gun- powder, with a slow match on one end. Stage. A platform on which mine cars stand. Staging. A temporary flooring or scaffold, or platform. Stage Pumping. Draining a mine by means of two or more pumps placed at different levels, each of which raises the water to the next pump above, or to the surface. Stage Working. A system of working minerals by removing the strata above the beds, after which the various beds are removed in steps or stages. Stalactites. Icicle-shaped formations of mineral matter depending from roof strata. Stalagmites. Accumulations of mineral matter that form on the floor, caused by the continual dripping of water impregnated with mineral matter. Stall. A narrow breast, or chamber. Stall Gate. A road along which the mineral worked in a stall is conveyed to the main road. Stamp Mill, Stomps. Machine for crushing ore. Stanchion. A vertical prop or strut. Standage. Pump reservoir. Standing. Not at work, not going forwards, idle. Standing Gas. A body of firedamp known to exist in a mine, but not in cir- culation; sometimes fenced off. Standing Sett (English). A fixed lift of pumps in a sinking set. 614 STA <.! LOSS Alt)'. STO Stannary. Tin works. Staple. (1) A shallow pit within a mine. (2) An underground shaft. Starter. A. man who ascends a chute to the battery and starts the coal to running. Starved (English). When a pump is choked at the brass holes. Station. A plat or convenient resting place in a shaft or level. Stave. A. ladder step. Stay (English). Props, struts, or ties for keeping anything in its place. Steamboat Coal. In anthracite only, coal small enough to pass through bars set 6 to 8 in. apart, but too large to pass through bars from 3i to 5 in. Comparatively few collieries make steamboat coal except to fill special contracts or orders. Steam Coal. A hard, free-burning, non-caking coal. Steam Jet. A system of ventilating a mine by means of a number of jets of steam, at high pressure, kept constantly blowing off from a series of pipes in the bottom of the upcast shaft. Steel Mill. An. apparatus for obtaining light in a fiery mine. It consisted of a revolving steel wheel, to which a piece of flint was held, to produce sparking. Steel Needle. An instrument used in preparing blasting holes, before the safety fuse was invented. Steening, or Steining.The brick or stone lining of a shaft. Stemmer.A copper or wooden bar used for stemming. Stemming. (1) Fine shale or dirt put into a shot hole after the powder, and rammed hard. (2) Tamping a shot. Step (English). (1) The cavity in a piece for receiving the pivot of an upright shaft, or the end of an upright piece. (2) The shearing in a coal face. Stint. The amount of work to be done by a man in a specified time. Stobb.A long steel wedge used in bringing down coal after it has been holed. Stockwork.A rock run through with a number of small veins close together, the whole of which has to be worked when mining such deposits. Stomp. A short wooden plug fixed in the roof of a level, to serve as a bench mark for surveys. Stone Coal. Anthracite; also other hard varieties of coal. Stone Head. A heading or gangway driven in stone. A tunnel. Stone Tubbing. Water-tight stone walling of a shaft cemented at the back. Stook.A pillar of coal about 4 yd. square, being the last portion of a full- sized pillar to be worked away in bord-and-pillar workings. Stook-and-Feather.A wedge for breaking down coal, worked by hydraulic power, the pressure being applied at the extreme inner end of the drilled hole. Stoop. A pillar of coal. Stoop-and-Room.A system of working coal very similar to pillar-and-stall. Stop. Any cleat or beam to check the descent of a cage, car, pump rods, etc. Stope. (1) To excavate mineral in a series of steps. (2) A place in a mine that is worked by sloping. Stoping. Working out ore between two levels or on the surface, by stopes or steps. Stoping Overhand. Mining a stope upwards, the fliglit of steps being inverted. Stoping Underhand. Mining a stope downwards in such a series that it presents the appearance of a flight of steps. Stopping. An air-tight wall built across any passageway in a mine. Stove Coal. In anthracite only; two sizes of stove coal are made, large and small: large stove, known as No. 3, passes through a 2i" to "2" mesh and over a If" to H" mesh; small stove, known as No. 4, passes through a If" to If" mesh and over a 1|" to V mesh. Only one size of stove coal is now usually made. It passes through a 2" square mesh and over 1|" square mesh. Stove Up, or Stoved. Upset. When a rod of iron heated at one end is ham- mered endwise the diameter of that end is enlarged, and it is said to be upset. Stow. To pack away rubbish into goaves or old workings. Stowce. (1) Windlass. (2) Landmarks. Stowing. The d6bris of a vein thrown back of a miner and which supports the roof or hanging wall of the excavation. STR GLOSSARY. Swi 615 Straight Ends and Walls. A system of working coal somewhat similar to bord-and -pillar. Straight ends are headings from 4 ft. 6 in. to 6 ft. in width. Walls are pillars 30 ft. wide. Straight Work. A system of getting coal by headings or narrow work. Stroke. A slightly inclined table for separating heavier minerals from lighter ones. Stratification. Arrangement in layers. Stratum (plural, strata). A layer or bed of rocks, or other deposit. Streak. The color of the mark made when a mineral is scratched against a white surface. Strett. The system of getting coal by headings or narrow work. See Bord-and- Pitta r . Strike (of a seam or vein). The intersection of an inclined seam or a vein with a horizontal plane. A level course in the seam. The direction of strike is always at right angles to the direction of the dip of the seam. Strike Joints. Joints or cleavages that are parallel to the strike of the seam. Striking Deal. Planks fixed in a sloping direction just within the mouth of a shaft, to guide the tub to the surface. Stringer (English). Any longitudinal timber or beam. Stringpump.A system of pumping whereby the motion of the engine is transmitted to the pump by timbers or stringers bolted together. String Rods. A. line of surface rods connected rigidly for the transmission of power; used for operating small pumps in adjoining shafts from a central station. Strip. (I) To remove the overlying strata of a bed or vein. (2) Mining a deposit by first taking off the overlying material. Strut ( English). A prop to sustain compression, whether vertical or inclined. Struve Ventilator. A pneumatic ventilating apparatus consisting of two vessel-like gas holders, which are moved up and down in a tank of water. By this means, the air is sucked out of the mine as required. Studdle.A piece of squared timber placed vertically between two sets of timber in a shaft. Stutt. A post for supporting the wall or roof in a mine; a prop timber. Stump. The pillar between the gangway and each room turned off the gang- way. Sometimes the entry pillars are called stumps. Stumping. A kind of pillar-and-stall plan of getting coal. Stup. Powdered coke or coal mixed with clay. Sturt. A tribute bargain profitable to the miner. Stuttle, or Sprag. The horizontal member of a square set of timber running longitudinally with the deposit. Rtythe. Carbonic-acid gas (blackdamp). Sucker Rod. The pump rod of an oil or artesian well. Suction Pump (English). A pump wherein, by the movement of the piston, water is drawn up into the vacuum caused. Sulphur. (I) One of the elements. (2) Iron pyrites. Sulphuret.See Sulphide. Sulphide. A combination of sulphur and a base. Sump, or Sumpt.A catch basin into which the drainage of a mine flows and from which it is pumped to the surface. Surface Deposits. Those that are exposed and can be mined from the surface. Swab Stick. A short wooden rod, bruised into a kind of stumpy brush at one end, for cleaning out a drill hole. Swatty, or Swelly.A trough, or syncline, in a coal seam. Swamp. A depression or natural hollow in a seam. A basin. Sweeping Table. A stationary buddle. Sweet. Free from deleterious gases. Sweet Roast. To roast dead or completely. Swing. The arc or curve described by the point of an instrument, such as a pick or hammer, when being used. Swinging Plate. Amalgamated copper plates hung in sluices, to catch float gold. Switch. (I) The movable tongue or rail by which a train is diverted from one track to another. (2) The junction of two tracks. (3) A movable arm for changing the course of an electrical current. Switchboard. A board where several electrical wires terminate, and where, by means of switches, connection may be established between any of these wires and the main wire. Swither.A crevice branching from a main-lead lode. 616 SYN GLOSS AR Y. TEP Synclinal Axis. The line or course of a syneline. Syneline. The point or axis of a basin toward which the strata upon either side dip. An inverted anticline. A basin. Tackle (English). (1) Ropes, chain, detaching hooks, cages, and all other apparatus for raising coal or ore in shafts. (2) Any rope for hoisting, as a tackle rope, block and tackle, etc. Tahona (Mexican). An arrastre moved by water-power. Tahonero. The man in charge of the tahona. Tail-Back. When the firedamp ignites and the flame is elongated or creeps backwards against the current of air, it is said to tail-back. Tailing. The blossom; the outcrop or smut. Tailings. The detritus from reduction or gold-washing machinery. Tail-Pipe. The suction pipe of a pump. Tailrace. The channel along which water flows after it has done its work. Tail-Rope. (1) In a tail-rope system of haulage, the rope that is used to draw the empties back into the mine. (2) A wire rope attached beneath cages, as a balance. Tail- Rope System of Haulage. A haulage system in which the full trip is drawn out by the main rope, and the empty trip is drawn in by the tail- rope, these ropes being attached to the opposite ends of the trip (see page 400). Tail-Sheave. The sheave at the inbye end of any haulage system. See Turn Pulley. Take the Air. (1) To measure the ventilating current. (2) Applied to a ventilating fan as working well, or working poorly. Taladro (Mexican) .A drill for mechanical or mining purposes. Taladrar. To bore or drill. Tatty. (1) A mark or number placed by the miner on every car of coal sent out of his place, usually a tin ticket. By counting these, a tally is made of all the cars of coal he sends out. (2) Any numbering, or counting, or memorandum, as a tally sheet. Tamp. To fill a bore hole, after inserting the charge, with some substance which is rammed hard as it is put into the hole. Vertical holes are often tamped with water, when blasting with dynamite. Tamping. The process of stemming or filling a bore hole. Tamping Bar. A. copper-tipped bar, for ramming the tamping or stem- ming. Tanates (Mexican). Leather, hide, or jute bags, to carry ore or waste rock within or out of a mine. Tanatero. A laborer or bag carrier. Tap. (1) To cut or bore into old workings, for the purpose of liberating accu- mulations of gas or water. (2) To pierce or open any gas or water feeder. (3) To win coal in a new district. Tapextle (Mexican). A working platform or stage built up in a stope or any- where in a mine; a landing place between two flights of ladders. Teem. To pour or tip. Teeming Trough. A trough into which the water from a mine is pumped. Telegraph. A sheet-iron trough-shaped chute, for conveying coal or slate from the screens to the pockets, or boilers. Tellurides. Ores of the precious metals (chiefly gold) containing tellurium. Temesquitale (Mexican). The earthy part of ground-up ore. Temper. (1) To change the hardness of metals by first heating and then plunging them into water, oil, etc. (2) To mix mortar, or to prepare clay for bricks, etc. Tempering. The act of reheating and properly cooling a bar of metal to any desired degree of hardness. Temper Screw. In rope drilling, a screw for gradually lowering the clamped (upper) end of the rope as the hole is deepened. Tenon. A projecting tongue fitting into a corresponding cavity called a mortise. Tentadura (Mexican). An assay made in a horn spoon, an earthen saucer, or in a wide and shallow vessel of any kind, to ascertain the amount of amalgam present in a sample of argentiferous mud from an amalgama- ting patio. Any assay made by washing so as to concentrate the metallic portions of any mineral, and to cause the earthy portions to be floated off. Tepetate (Mexican). Any rock or earth found in a mine, which does not contain the metal sought for. TEQ GLOSS AH V. TUA 617 Tequio (Mexican). A task set for a drillman or for any laborer in a mine, to be regarded as a day's work. Terrace. A. raised level bank, such as river terraces, lake terraces, etc. Terrero (Mexican). The dump of a mine. Test. (1) A trial of an engine, fan, or other appliance or substance. (2) An iron framework that is filled with bone ash for cupeling on a large scale. Theodolite. An instrument used in surveying, for taking both vertical and horizontal angular measurements. An engineer's large transit, with attachments. Thill. See Floor. Thimble. (I) A short piece of tube slid over another piece, to strengthen a joint, etc. (2) An iron ring with a groove around it on the outside, used as an eye when a rope is doubled about it. Thirl. See Crosscut. Through-and-Through.A system of getting bituminous coal, without regard to the size of the lump. Throw. (I) A fault of dislocation. (2) The vertical distance between the two ends of a faulted bed of coal. Thrown. Faulted; broken by a fault. Thrust. Creep or squeeze due to excessive weight, hard floor, and too small pillars. Thurl (Staffordshire). To cut through from one working into another. Ticketing. English periodical markets for the sale of ores. Tie-Back. (1) A beam serving a purpose similar to a fend-off beam, but fixed at the opposite side of the shaft or inclined road. (2) The wire ropes or stayrods which are sometimes used on the side of the tower opposite the hoisting engine, in place of or to reenforce the engine braces. Tierras (Spanish). Earth impregnated with mercury ore. Tierras de Labor (Mexican). Dirt from a stope, mixed with particles of ore. Tierras de Llunque (Mexican). Chips made in breaking and sorting ore. Tiff. Calcite or carbonate of lime. Timber. (1) Props, bars, collars, legs, laggings, etc. (2) To set or place timber in a mine or shaft. Timber er, Timberman. A man who sets timber. Time. (1) Hours of work performed by workmen. (2) To count the strokes of a pump or revolutions of ah engine or fan. Tin-Can Safety Lamp. A. Davy lamp placed inside a tin can or cylinder having a glass in front, air holes near the bottom, and open-topped, making the lamp safer in a rapid current of air. Tin- Witts (Cornish). Product of first dressing of tin ores, containing, also, wolfram and sulphides. Tip. A dump. See Tipper, or Tipple. Tipper, or Tipple. An apparatus for emptying cars of coal or ore, by turning them upside down, and then bringing them back to original position, with a minimum of manual labor. Tipple. The dump trestle and tracks at the mouth of a shaft or slope, where the output of a mine is dumped, screened, and loaded. Tiro (Mexican). A mining shaft. Tiro Vertical. A vertical shaft. Token. (I) A mutually understood mark placed upon a bucket of ore when it is hoisted or lowered into a shaft, to acquaint the lander or filler of some important matter. (2) A piece of leather or metal stamped with the hewer's or putter's number or distinctive mark, and fastened to the tub he is filling or putting. Ton. A measure of weight. Long ton is 2,240 lb.; short ton is 2,000 lb.; metric ton is 1,000 kilograms = 2,204.6 lb. Top. (I) See Roof . (2) Top of a shaft; surface over a mine. Topit.A kind of brace head screwed to the top of boring rods, when with- drawing them from the hole. Tarta (Mexican). A pie or cake; the heaps of argentiferous mud that are treated in the patio process of amalgamation. Tossing. Shaking powdered ore in water, to effect separation of heavy and light particles. Tovera (Mexican). The tuyere of a smelting furnace. Track. Railways or tramways. Tracking. Wooden rails. Train Boy. A boy that rides on a trip, to attend to rope attachments, signal in case of derailment of cars. etc. Trip rider. 618 TRA GLOSSARY. TI14. Current estimates, 212. motors, 157. Curtains, 394. Curves for mine roads, 411. Railroad, 78. on slopes, Vertical, 416. Cylinder, 33. Cylinders, Contents of, 6. in a pump. Ratio of, 160. of a hoisting engine, To find size of, 397. To find contents of. in U. S. gal- lons or bushels, 5. Cylindrical boiler, Maximum work of, 178. boilers, Economy of, 188. drums, 394. drum, To find period of winding, 397. rings, 34. Dams, 154. Debris. 156. Earth, 156. in mines, 133. Masonry, 156. Stone, 155. Wing, 156. Danish measures of length, 3. Darcy's formulas (hydraulic), 148. Davy lamp, 356. Debris dams, 156. Decimals, 16. Decimals of a foot for each & inch, 3. Declination, Magnetic, 39. of Polaris, 46. Deflected angle, 45. Deflections in p o w e r - transmission ropes, Table of, 122. Density of a gas, 344. Departures, 537. Deposits over 8 ft. thick, 318. Depth of shafts, Calculation of, 340. of suction, 162. Derangement of ventilating current, 359. Detaching hooks, 398. Detection of small percentages of gas, 356. Detonation, 331. Diagram for reporting on mineral lands, 252. Diameter of holes (blasting), 330. Diamond drill, 243. weight, 12. Dies for stamps, 429. Differential pulley, 94. Diffusion of gases, 346, 348. Dip and strike from bore-hole records. 250. workings, Ventilation of, 382. Direct-current circuits, 210. dynamos, 215. motors, 220. Direction of face, 284. Directions for blasting by electricity, 332. Discharge, Coefficient of (water), 135. gates (dams), 154. through V notch. 138. INDEX. 627 Disintegrating rolls, 423. Disk fans, 385. Distance, Errors in, 77. from center to center of breasts, Table, 287. Distribution of air in mine ventila- tion, 373. Ditches, 142. Banks of, 143. Capacity of, 143. Grades of, 143. Velocity in, 142. Division of air-current, Proportional, 375. D., L. & W. telephone system, 234. Dodge crushers, 419. Domestic coals, 173. Door regulator, 375, 377. regulator, Size of opening for, 377. Doors, 393. Double-chute battery, 309. cylindrical drums, 394. entry, 284. Draft, 190. Drainage in shaft sinking, 263. Drawbar pull of electric locomotives, 407. Drawing pillars, 289. Dredge (centrifugal puinp), 164. Dredging, 279. Dressing of ores, 418. Drift of drill holes, 243. Drill, Diamond, 243. holes, 243. holes, Arrangement of, 335. records, 244, 250. Drilling, 242, 330. Driving the gangway, 264. Dron's formula for shaft pillars, 285. Drop for stamps, 428. Drums, Conical, 394. Double-cylindrical, 394. for wire rope, 123. Dry measure (U. S.), 5. Dunn's table of size of pillars, 286. Duplex pumps, 158. Dust briquets, 448. Effect of, 360. Duty of anthracite screens, 434. of miners' inch, 137. of stamps. 430. Dynamite. Thawing, 329. Dynamos, 215. Alternating-current, 224. Compound- wound, 219. Series-wound, 219. Shunt-wound, 219. Earth Augers, 242. dams, 156. Economizers, 185. Effect of altitude on air compression. 195. Efficiency, Manometrical, 390. Mechanical, 390. of water-power, 156. Electric blasting, 332. Electric circuit, 205. exploder, 332. haulage, 406. haulage plants, Conductors for, 214. haulage problem, 407. locomotives, Drawbar pull of, 407. locomotives, Hauling capacity of, 408. power, 204. pumps, 162. resistance, Estimation of, 209. signaling, 229-235. units, 203. wiring, 207. Electricity, 203. Electromotive force, 203, 218. Elements, 341. in ventilation, 363. of mechanics, 91. Table of, 342. Elevating capacity of buckets, 446. Elevation of rails for mine roads, 412. Elevations, Barometric, 340. Elevators, Water, 164. Ellipse, 32. End cleats, 284. on, 285. plates, 270. Endless-rope haulage. 401. Engine drivers, Rules for, 191. planes, 399. Engines, Sinking, 263. Steam, 190. Entries, Number of, 284. Equal settling factors, Table of, 439. settling particles, 439. shadows, 47. splits of air, 374. Equations, Chemical, 341. Equilibrium of liquids, 130. Equivalent orifice, 367. Errors, 76. in arc, 76. in distance, 77. in measurement, 77. in surveying, 66, 76. Eschka's method of analysis for sul- phur, 174. Establishing a meridian with solar attachment, 47. Estimates of current, 212. Evolution, 19, 545. Excitation of dynamos, 218. Exhaust fans, 386. Expansion of gases, 344. Exploder, Electric, 332. Exploring workings, 361. Explosions, Exploring workings after 361. in boilers, 179. Explosive conditions in mines, 359. Explosives, 329. Pressures developed by, 334. Relative strengths of various brands of, 330. Values of, 335. I Eytelwein's formulas (hydraulic), 148 628 INDEX. Face Cleats, 284. Direction of, 284. on, 285. Factor of a mine, Potential, 367. Factors, Conversion (hydraulic), 141. Fahrenheit to centigrade, 366. Fan construction, Principles of, 391. tests, 392. ventilation, 373, 385. Fans, Ventilating, 386. Fastenings for wire rope, 126. Feeders of gas, 352. Feed-pumps, 161, 186. Feedwater for boilers, 186. Field excitation of dynamos, 218. magnet, 216. notes for outside compass survey, Filling methods, 319. Finger bars, 432. Firedamp, 351. Fires, Gob, 291. Firing a boiler, 186. blasts, 331. by detonation, 331. Fixed carbon in coal, 171, 174. Flash signals, 234. Flat deposits, 318. Flat ropes, 119, 394. Flights, Capacity of, 446. Flow of water in channels, 142, 144. in rivers, 145. through flumes, 146. through orifices, 135. through pipes, 147, 150. Flumes, 145, 443. Flow of water through, 146. Grade of, 145. Flushing of culm, 314. Foaming (boilers), 186. Forced draft, 190. Force fans, 386. Forces, Composition of, 95. Foreign coins, Values of, 11. Forepoling, 260, 270. Form of roll teeth, 422. Forms of mine timbering, 267. Formulas for air splitting, 378. for inclined planes, 399. in ventilation, 370. Foster's formula for shaft pillars, 286. Foundations (dams), 154. Fractions, 15. Common, 15. Decimal, 16. Table of equivalent decimal, 16. Fragmental deposits, Mining of, 278. Free-burning coals, 170. gold per ton of ore, Value of, 241. Freezing process, 260. Friction, 95. coefficients for air in mines, 367. coefficients for various materials, 95, 96. in knees and bends, 153. of air in pipes, 201. of mine cars, 96. of water in pipes. 151. Friction pull on endless rope, 402. Frictional resistance of shafting, 96. Frozen ground, Mining of, 322. Frustums, 34. Fuel dust briquets, 448. Fuels, 166. Composition of, 169. Furnace stack, 385. Construction of ventilating, 383. ventilation, 373. ventilation, Air columns in, 384. Fuse boxes, 224. Fuses, 224. Fusible plugs, 186. Galvanic Action Around Boilers, 187. Gangway driving, 264. timbers, 268. Gas coals, 173. feeders, 352. Testing for, 354. Outbursts of, 352, 360. Gases, Chemistry of, 341. Diffusion of, 346, 348. enclosed in the pores of coal, 353. found in mines, 348. Pressure of, 345. Properties of, 344. Transpiration of, 346, 348. Gate for jig, 438. Gates crusher. Table of, 422. Gauge cocks. 186. of mine tracks, 411. Pressure. 185. Water, 365. Wire, 207, 208. Gauging by weirs, 138. water, 136. Gay-Lussac's law, 195, 345. Gears, Train of, 92. Gems and precious stones, Prospect- ing for, 241. General mathematical principles, 14. remarks on surveying, 49. Geological maps, Construction of, 249, periods, 237. Geometrical problems, 25. progression, 21. Geometry, 24. Geordy lamp, 356. George's creek method of mining, 297. Gilpin county stamps, 428. Glossary of mining terms, 565. Gob fires, 291. Gold 'coins, 10. mine, Opening of, 258. Gonda type of cell, 230. Gophering, 321. Gould's formulas (hydraulic), 148. Grade of mine road, 410. Gradient, Hydraulic, 147. Graham's law, 346. Gravity planes. 398. Specific, 107. specific, Table of, 108. stamps, 427. ; Gray lamp, 358. INDEX. 629 Grizzlies, 431. Guibal ventilator, 388. Guides, 398. Gyratory crushers, 420. Half on, 285. Hammer crushers, 423. Handling of material, 443. Hard coal, 169, 313. Hardness of coal, 171. Haulage, 398. by compressed air, 403. Cost of, 409. Electric, 214, 406. Motor, 402. problems, 399, 407. road signals, 235. rope, 122, 400. Speed of, 408. Hauling capacity of electric locomo- tives, 408. Ha wksley's formula (hydraulic), 148. Head-bars, 431. block, 268. frames, 275, 397. frames, Sinking. 262. gears, 275. . sheaves, 397. Headboard, 268. Heating surface of a boiler, 177. values of American coals, 168. Heberle gate, 438. High explosives, 329. Hill, E., 198. Hints for mining small seams, 313. to beginners in surveving, 80. Hoisting, 394. engine cylinders, 397. engine, To find size of, 396. problems, 396. ropes, Starting strain on, 126. ropes, Stress in, 123. Hooks, Detaching, 398. Horizontal distances, 50, 87, 537. distances, Stadia table of, 87. Horsepower for box regulators, 377. for bucket elevators, 445. for door regulators, 377. necessary to compress air, 406. of air-currents, 363. of boilers, 177. of coal conveyor, 445. of engine, 190. of manila ropes, 126. of stamps, 430. of a stream, 157. required to raise water, 161. Hughes' s formula for shaft pillars, Hydraulic classifiers, 434. gradient, 147. placer mining, 278. Hydraulics, 135. Hydrocarbons. 349. Hydrogen disulphide H.^S, 350. Sulphuretted, 350. Hydrostatics, 130. I Beams, Safe Loads for, 104. Illuminating power of safety lamps, 359. Impulse wheels, 158. Incandescent lamps, 213. Inch, Miners', 136. Inclined plane, 93. plane, Stress in hoisting ropes on, 123. roads, Calculation of power for, 402. roads, Haulage on, 398. shafts, Surveying, 73. Included angle, 45. Incrustation and scale, 182. Indiana method of mining, 298. Individual angle, 45. Induction motors, 227. Inertia, Angle of, 398. Influence of furnace stack on venti- lation, 385. of seasons on ventilation, 382. Injector, 186. Area of nozzle of, 187. Delivery in gallons per hour of, 187. Inside surveys, 56, 67. Inspection of boilers, 181. Insulated wires, 212. Interstitial currents, 439. factors, 440. Involution, 19, 545. Iowa method of mining, 299. Iron beams, 103. for track, 117. pipe, Weight of, 113. supports, 272. Weight of flat, 115. Weight of wrought, 114, Irregular mining deposits, 321. Isogonic chart, 40. Isothermal compression, 195, 198. Jaw Crushers, 419. Jeffrey-Robinson coal washer, 436. Jigs, 437. Joints in mine timbering, 267. Kind-Chaudron Method of Sinking, 262. Knees in pipes, 153. Koepe system of hoisting, 395. Lamp Tests for Gas, 354. Lamps, Arc, 214. Incandescent, 213. Safety, 355. Testing, 355. Lancashire boiler, 177. Landings, Timbering of, 272. Large deposits over 8 ft. thick, Min- ing, 318. Latches, 413. Latitude, 50, 537. with Burt's solar, 48. Launders, 443. 630 INDEX. Law of settling particles, 439. Laws in regard to air splitting, 373. in regard to quantity of air, 363. of volume, 341. Leaching methods of mining, 32. Lead, Weight of, 111, 113, 114, 115. Leclanch< cell, 229. Lehigh region, Costs of mining in, 323. Length, Measures of, 2. of steep pitch on inclined plane, 399. Leveling, 53. Trigonometric, 56. Level notes, 55, 62. roads, Haulage on, 398. timbers, 268. Levels (gangways), 316, in metal mines, 264. Levers, 91. Lid, 268. Life of shoes and dies, 429. of wire rope, 123. Lignite, 170. Line shafting, 110. Liquid measure (U. S.), 5. Liquids, Compressibility of, 133. Load for wire rope, 125. that a hoisting engine will start, To find, 396. Locating errors, 76. special work, 77. Locks for lamps, 358. Locomotive haulage, 402. Logarithmic functions, Table of, 492. Logarithms, 22, 473. of numbers, Table, 473. of trigonometric functions, Table of, 492. Log washer, 436. Long-hole process of shaft sinking, 262. horn, 285. section, 64. splice, 128. Longitudinal back stoping with fill- ing, 319. Longwall method, 281, 302. Modifications of, 302. Timbering, 283. Loss in transmitting air, 198. of blood, 449. of head in pipe by friction, 151. of heat from steam pipes, 184. of pressure of air in pipes, 202. Low explosives, 329. Lubricants for different purposes, 102. Lubrication, 100. Machine Mining, 336. Magnetic prospecting, 248. variation, 39. Malleable-iron buckets, 446. Manila ropes, Power transmitted by, 126. Manometrical efficiency, 390. Mapping, 74. Maps, Geological, 249. Mariotte's law, 345. Marsaut lamp, 358. Marsh gas, 348. Masonry, Bearing value of, 107. dams, 156. supports, 272. Material, Handling of, 443. Mathematical signs, 14. Mathematics, 14. Measurement, Error in, 77. of temperature, 366. of ventilating currents, 364. Measures of area, 4. American, 4. British, 4. Metric, 4. Measures of Length, 2. American, 2. Austrian, 3. British, 2. Chinese, 4. Danish, 3. Metric, 3. Norwegian, 3. Prussian, 3. Russian, 3. Swedish, 4. Measures of volume, 3. American, 5. British, 5. Metric, 5. Mechanical efficiency, 390. mixture, 341. ventilators, 385. Mechanics, 91. Mensuration, 28. of solids, 33. of surfaces, 28. Mercurial barometer, 339. Mercury and air columns, 347. column corresponding to water column, 340. Meridians, 46. Merivale's formula for shaft pillars, 285. Mesh for shaking screens, 433. of revolving screens for anthra- cite, 434. Size of, 433. Metal linings for shafts, 260. Methods and appliances in mine ven- tilation, 381. Methods of mining, 277. Alabama, 297. anthracite, 305. Blossburg, 298. Brown's, 306. California, 300. Clearfield, 295. Colorado, 302. Connellsville, 293. George's creek, 297. Indiana, 298. Iowa, 299. mineral deposits, 316. Newcastle, Colo., 302. Pittsburg, 295. IXDEX. 631 Methods of Mining, Reynoldsville, 295. Tesla, Cal., 300. West Virginia, 296. Williams', 312. Methods of surveying, 67. Metric conversion tables, 7-10. measures of area, 4. measures of length, 3. measures of volume, 5. system, 1, 2, 3, 9, 10. weight, 2. Mil, 207. Milling system, 278. Mine-car friction tests, 98. cars, Friction of, 96. corps, 66. dams, 133. explosions, 361. gases, 348. gases, Table of, 349. Opening a, 257. plan, Arrangement of, 381. resistances, 364, 366. roads, 410. sampling, 174. telephones, 233. timber and timbering, 265. tracks, 410. Mineral available in a prospect, 251. deposits,' Methods of mining, 316. lands, Report on, 252. Miners' inch, 136. Mining terms, Glossary of, 565. Mixture, Mechanical, 341. Moisture in coal, 171, 174. Molecule, 341. Money, Tables of, 10. Morris, W. H., 127. Motor haulage, 402. Motors, 214, 215. Current (water), 157. Induction, 227. Regulation of speed of, 222. Synchronous, 226. Movable bars, 432. pulley, 94. Mueseler lamp, 358. Multiphase alternators, 225. Murphy ventilator, 389. Nails, Sizes, Etc. of, 114. Nasmyth fan, 387. Natural division of air-currents, 374. functions, Tables of, 453. gas, Prospecting for, 249. splitting, Calculation of, 374. ventilation, 381. Needling, 268. Neville's formula (hydraulic), 148. Newcastle, Colorado, method of mining, 302. Nitrogen, 348. Non-conductors, Relative values of, 185. Norwegian measures of length, 3. Notes (survey). 60. Notes, Compass field, 44. for outside compass survey, 44. Level, 55, 62. on mapping, 74. Side, 60, 61. Stope-book, 62. Transit, 60. Nozzle, Injector, 187. Number of cars in a trip on a self- acting incline, 399. Nuts, Weight of, 116. Occluded Gases, 352. Occurrence of gases in mines, 351. Ohm's law, 204. Oils for safety lamps, 356. Lubricating, 100, 102. Open channels, 142. work, 277. Opening a mine, 257. in box regulators, 376. Order of drop of stamps, 428. Ore deposits, 238. dressing, 418. Handling of, 443. Orifice, Equivalent, 367. Oscillating bars, 432. Outbursts of gas, 352, 360. Outside surveys, 67. Overcasts. 393. Overhand stoping, 304, 317. Overshot wheels, 158. Oxygen, 348. Packing for Pumps, 159. Pack walls, 283. Paint, 59. Pamely's formula for shaft pillars, 286. Panel system, 283. Parallel circuits, 206. Parallelograms, 28. Parallelepiped, 33. Peele, Robert, 194. Percentage, 20. Percussion drills, 242. Period of winding on a cylindrical drum, To find, 397. Permitted explosives, 329. Petroleum, Fuel value of, 167. Prospecting for, 249. Pick machines, 336. Pillar timber, 268. and chamber, 280. and stall, 281, 292. drawing, 289. Pillars, 285. Weight on, at different depths, 287. Wooden, 105. Pins, 43. Pipes, Flow through, 147, 150. Friction in, 151. Pressure of water in, 132. Thickness of, 133. used for compressed-air haulage, Table of, 406. Piston speed of pumps. 101. 632 INDEX. Pitch at which anthracite will run, Table of, 443. distance, 51. Pitching work surveys, 68. Pittsburg method of mining, 295. Placer deposits, Prospecting for, 240. mining, 278. Plane trigonometry, 34. Planes, Engine, 399. Gravity, 398. Plates, metal, Weight of, 112. Platform bars, 431. Plats, Timbering of, 272. Plenum system of ventilation, 386. Plotting, 49. by coordinates, 51 . Plow-steel rope, 120. Plugs, 186. Plumb-bob, 44. Plumbing of shafts, 69. Pneumatic method of shaft sinking 260. stamps, 430. Pockets of gas, 352. Poetsch-Sooy smith process (freezing method), 260. Polaris observation. 46. Polygons, 30. Post and breast cap, 268. Potential factor of a mine, 367. Pound calorie, 168. Power, Electrical, 204. for hoisting, 395. in mine ventilation, 367. of air-currents, 363. of a hoisting engine, To find, 396. of an explosive, 334. of waterfall, 157. pumps, 162. required for inclined roads, 402. stamps, 431. Water, 156. Practical examples in the solution of triangles, 35. splitting of air-currents, 373. Precious stones, Prospecting for, 241. Preliminary work, 257. Preparation of anthracite, Diagram of, 442. of coal and ore, 418. Preservation of timber, 265. . Pressure. Absolute, 345. as affecting explosive conditions. 361. developed by explosives, 334. for box regulators, 376. gauge, 185. of anthracite coal against walls, 445. of bituminous coal against walls, 444. of gases, 345. of liquids on surfaces, 130. of occluded gases, 352. of steam at different tempera- tures, 188. of water in pipes, 132. on heading, 130. Pressure of water on plane surface, 132. Prices per ton of coal at mines, Table, 327. Primary splits, 374. Prism, 33. Prismoidal formula, 34. Problem in compressed-air haulage, 404. Problems in geometrical construc- tion, 25. in haulage, 399. in hoisting, 396. I Progression, Arithmetical, 20. Geometrical, 21. Properties of copper wire, 208. of materials, 107. Proportion, or Rule of Three, 18. Proportional division of the air-cur- rent, 375. Props, Undersetting of, 276, 277. Wooden, 105. Prospecting, 235. for bitumen, 249. for natural gas, 249. for petroleum, 249.. Magnetic, 248. Prussian measures of length, 3. Pulley, 94. Pulleys and belting, 193. Pulverizers, 423. Pump machinery, 158. memoranda, 163. packing, 159. valves. 162. Pumps, 158. Air-lift, 164. Centrifugal, 164. Cornish, 158. Electrical, 162. . for acid waters, 165. Power, 162. Simple and duplex, 158. Sinking, 165. Vacuum, 164. Push button, 234. Pyramid, 33. Quadrant, 34. Quantity of air required by State Laws, 363. for dilution of mine gases, 363. for ventilation, 362. to produce necessary velocity at face, 363. Radial Roller Mills, 426. Radii of curves, 79. ! Rail bending for mine roads, 412. elevation for mine roads. 412. Railroad curves, 78. Rails for mine roads, 411. per mile of track, 117. i Raises, 316. Rapid firing of boilers, 187. method of splicing a wire rope, 127. - ; Rate of diffusion, 346. r>33 Rating of compressors, 195. Ratio of steam and water cylinders in pump, 160. Reaumur to Fahrenheit, 366. Reciprocals, 545. Recoil 9f an explosion, 361. Reduction of inches to decimals of a foot, 2. Regular polygon, 30. Regulation of motors for speed, 222. Regulators, 375. Relation of power, pressure, and ve- locity, 364. Relative volume of gases, 343. Relighting stations, 359. Removal of sulphur from coal, 441. Repair of boiler coverings, 187. Repairs to boilers, 180. Reporting on mineral lands, 252. Requirements of law as to splitting, 373. Reservoirs, 154. Resistance, Electric, 203. Estimation of (electric). 209. in electric lines, 206. of soils to erosion, 143. Mine, 364. Return-call system, 232. Revolving screen mesh for anthracite, 433, 434. Reynoldsville method of mining, 295. Right-angled V notch, 137. Rings, 34. Rise workings, Ventilation of, 382. Rivers, Flow of water in, 145. Roads, Haulage on inclined, 398. Level, 398. Mine, 410. Rock-chute mining, 310. drills, 263. Handling of, 443. Roller mills, 426. Rollers, 412. Rolling friction, Coefficient of, 398. Roll-jaw crushers, 420. Rolls, 421. Amount crushed by, 424. Crushing, 423. Speeds of, 424. Teeth of, 422. Roof pressure, 280. Control of, 284. Room-and-pillar, 280. modifications of, 291. openings, 281. pillars, 286. Rooming with filling, 319. Rope haulage, 122, 400. Ropes, 118. fastenings, 126. Flat, 394. Manila, 126. Rotary crushers, 420, 422. Roughness, Coefficient of, 144. Rule of Three, 18. Rules for engine drivers, 191. Running of coal, 312. Russian measures of length, 3. Safe Loads for Cast-Iron Columns, 106. Safe loads for I beams, 104. Safety catches, 398. explosives, 329. lamp oils, 356. lamps, 355, 356. lamps, Locks for, 358. lamps, Illuminating power of, 359. valves, 185. Sampling available mineral, 251. of coal, 173. Scaife trough washer, 437. Scale, Removal of, from boilers, 181. Scalp wounds, 451. Schiele ventilator, 388. Schmidt's law of faults, 239. Screens, 431, 432. Screw, 93. Diameter and number of, 113. Seam blasting, 331. Seasons, Influence of, 382. Secant, 35, 454. Secondary splits, 374. Sederholm, E. T., 125. Semianthracite coal, 169. Semibituminous coal, 169. Series-circuits, 205. parallel method of regulation, 222. wound dynamos, 219. Settling boxes, 435. particles, Law of, 439. Shaft bottoms, Steel, 276. bottom tracks, 416. pillars, 285. plumbing, 69. sinking, Drainage for, 263. sinking, Ventilation, 263. timbering, 270. Shafting, Frictional resistance of, 96. Strength of, 110. Shafts, 259. Calculation of depth of, 340. Compartments of, 259. Form of, 259. Methods of sinking, 259. Size of, 259. Surface tracks at, 417. Table of depths of, etc., 261. Shaking screens, 432. Shanty, 268. Shearing machines, 337. Sheaves for wire rope, 123. Shoes for stamps, 429. Short horn, 285. Shots in close workings, 361. Shunt-wound dynamos, 219. Side notes, 60, 61. Signal for haulage roads, 235. Signaling, Electric, 229-235. Silver coins, 10. Similar airways, 372. Simple bell circuit, 230. Sine, 34, 453. Sines. Natural, Table of, 453. Single-chute battery, 309. entry, 284. phase alternators, 225. wire method of slope surveying, 74. 634 TXDEX. Sinking a shaft, 259. Cost of, 263. engines, 263. head-frames, 262. pumps, 165. Slope, 263. Speed of, 263. Siphons, 149. Size of engine for engine-plane haul- age, 399. of hoisting engine, To find, 39(5. of mesh for screens, 433. of opening for door regulator, 377. of opening in box regulator, 376. of pillars, 285. of timber, 267. Sizes of anthracite, percentages of each, 323, 326. coal, 173, 434. Sizing apparatus, 431. Slack, 167. Slicing method, 319. Slightly inclined deposits, 318. Slope bottoms, 413. level, 44. sinking, 263. surveying, 73. tracks, 413. Surface tracks at, 417. Small percentages of gas, 356. seams, mining of, 313. Soft coal, 169. Soils, Resistance of, to erosion, 143. Solar attachment, 47. Sole, 268. Space required to store coins, 11. Special forms of supports, 272. mining methods, 322. work, 77. Specific gravity, 107. of coal, 171. of gases, 344. of various substances, Table of, 108, 109. volume, 341. Speed of crushing rolls, 426. of drilling, 244. of haulage, 408. of revolving screens, 434. of rolls, 423. of sinking, 263. of stamps, 429. of water through pump passages, 160. regulation of motors, 222. Sphere, 33. Spikes, Railroad, 117. Sizes, etc., 114. Spiling, 270. Spillways, 155. Spitzkasten, 435. Spitzlutten, 435. Splices per mile of track, 117. Splicing a wire rope, 127. Splint coal, 170. Splitting formulas, 378. of air-currents, 373. Spontaneous combustion, 291. Sprags, 270. Square feet to acres, 4. root, 19, 545. roots, Table of, 545. sets, 270. set system, 321. work, 318. Squares, Table of, 545. Sq nibbing, 330. Stack, Furnace, 385. Stadia measurements, 81. table, 86. Stamps, 427. heads, 429. Pneumatic, 430. Power, 431. Speed of, 429. Steam, 431. Standard steel buckets, Weights and capacities of, 446. Starting strain on hoisting rope, 126. Stationary screen jigs, 437. screens, 431. Stations, Distinguishing, 59. Establishment of, 57. Kinds of, 57. Marking, 58. Relighting, 359. Timbering of, 272. Steam, 175. engine, 190. pipe coverings, 183. pressure at different tempera- tures, 188. shovel mines. 278. stamps, 431. Steaming coals, 171. Steel beams, 103. shaft bottoms, 276. supports, 272. tape, 43. Stems for stamps, 429. Stinkdamp, 350. Stone dams, 155. Stope books, 62. Stoping, 316. Overhand, 304. with filling, 319. Stoppings, 393. Storage, Coal, 291. Stowing, 283. Stream horsepower, 157. Strength of anthracite, 289. of electric current, 203. of materials, 102. of metals, 115. of roof, 280. of shafting, 110. of wire ropes, 119. Stress in hoisting ropes, 123. Strike from bore-hole records. 250. Stulls, 268. Stuttles, 270. Suction, 162. in jigging, 440. Sulphureted hydrogen, 350. Sulphur in coal, 171, 174. Removal of, from coal, 441. INDEX. 635 Sump, 264. Supplement of angle, 34. Surface tracks for shafts and slopes, 417. Surveying, 38. drill holes, 243. methods, 67. Underground, 56, 67. Susquehanna Coal Co. (friction of mine cars), 98. Swedish measures of length, 4. Switches, 413. Symbols, Chemical, 341. Synchronous motors, 226. Systems of working coal, 280. Table, Coal Dealers' Computing, 452. Tables of Barrier Pillars, 288. batteries, 231. circles, 545. circumferences and areas of cir- cles, ^ to 100, 561. combustibles, 166. elements, 342. hydraulic, 135-154. logarithms of numbers, 473. logarithms of trigonometric func- tions, 492. mine gases, 349. natural sines and cosines, 453. natural tangents and cotangents, 464. rail elevations, 412. reciprocals, 545. squares, cubes, square roots, cube roots, circumferences and areas, 545-560. Stadia, 88. strength of materials, 102-106. traverse (latitudes and depar- tures), 537. well-known shafts, 261. ( For tables not enumerated above see the various subjects.) Tail-rope haulage, 400. Tamping, 331. Tangent, 35, 453. Tangents, Natural, Table of, 464. Tappets for stamps, 429. Teeth for rolls, 422. Telephones in mines, 233. Telpherage, 278. Temperature, Absolute, 344, 345. Measurement of, 366. Tension on hauling rope, Calculation of, 401. Tertiary splits, 374. Tesla, Cal., method of mining, 300. Test of mine-car frictions, 98. Testing for gas by lamp flame, 354. lamps, 355. Tests, Boiler, 188. Fan, 392. of compressive strength of an- thracite, 290. Thawing dynamite, 329. Theory of air compression, 194. jigging, 439. Theory of stadia measurements, 81. Thermal unit, 168. Thermometer readings, Conversion of, 366. Thermometers, 366*. Thickness of boiler iron, 187. pipe, 133. Thin seams, Mining, 313. Three-phase alternators, 226. Thurston, table of lubricants, 102. Ties for mine roads, 410. Timber, Crushing load of, 105. Gangway, 268. joints, 267. Level, 268. measure, 12. Placing of, 266. Preservation of, 265. Size of, 267. Timbering, 265. Forms of, 267. longwall face, 284. Tools for sinking, 263. Torque, 220. Track iron, 117. Tracks for shaft bottoms, 416. Mine, 410. Tractive efforts of compressed-air locomotives, 404. Train of gears, 92. Transformers. 228. Transit, 40. adjustment, 41. notes, 60. surveying, 45. Transmission of air in pipes, 196, 198. Electric, 210. pressure through water, 132. Rope, 122. Transpiration of gases, 346, 348. Transporting a wounded person, 450. Transverse rooming with filling, 319. Trapeziums, 30. Trapezoids, 30. Traverse tables, 537. Traversing a survey, 51. Treatment of injured persons, 449. persons overcome by gas, 451 . Tremain stamp, 431. Trestles, 274. Triangles, 28, 35. Trigonometric leveling, 56. Trigonometry, 34. Triple entry, 284. Trommels, 433. Trough washer, 437. Troy weight, 1. { True north from Polaris, 46. with the Burt solar, 48. T-square method of plumbing shafts, 73. Tunnels, 265. Flow of water through, 147. i Turbines, 158. Turnouts, 413. , Two-phase alternators, 226. 636 INDEX. Undercasts, MS. Undercutting, 283. Underground prospecting, 239. supports, 267. . surveying, 56, 67. Underhand stoping, 316. Undersetting of props, 267, 276, 277. Undershot wheels, 157. Unequal splits of air, 374. Units of electricity, 203. of resistance, Electric, 203. of work, Electric, 205. Unloading coal, Cost of, 447. Useful horsepower during winding, To find, 397. Use of compass, 39. Vacuum Pumps, 164. Vacuum system of ventilation, 386. Value of a fuel, 166. Values of explosives, 335. Valves, Pump, 162. Safety, 185. Variation, Barometric, 339. of ventilation elements, 372. To turn off the, 39. Velocity, Coefficient of (water), 135. of air-current, 364. of a water jet, 135. of water through pump passages, 160. Ventilating currents, Measurements of, 364. Ventilation elements, 363. elements, Variation of, 372. formulas, 370. in shaft sinking, 263. methods and appliances, 381. of Mines, 337. of rise and dip workings, 382. Ventilators, Mechanical, 385. Verniers, Reading, 39. Versed sine, 35. Vertical angle, 51. curves on slopes, 416. distances. 50, 87, 537. distances, stadia table, 87. V Notch, 137. Volatile combustible matter of coal, 171, 174. Volume and absolute pressure, 345. and absolute temperature, Rela- tion of, 345. Atomic, 341. Measures of, 5. Specific, 341. Waddle Ventilator, 387. Wall plates, 270. Wardle's formula for shaft pillars. 285. Washers, Ore and coal, 436. Weight of, 116. Waste gates, 146. ways, 155. Water, 'Battery, 430. buckets, 164. column corresponding to any mercury column, 340. Water elevators, 164. now through orifices, 135. gauge. 186, 365. Gauging, 136. level, 186. memoranda, 163. power, 156. raised by single-acting lift pump, 162. ' weight of, 107, 130. Waterproof push button, 234. Waterwheels, 157. See Wheels. Watt-hour, 205. Weather-proof wire, 212. Wedge, 93. Weight, Apothecaries', 1. Atomic, 344. Avoirdupois, 2. Metric, 2. Troy, 1. W r eight of atmosphere, 337. boltheads, nuts, and washers, 116. bolts, 116. castings, 111. chains, 130. coal, 170. flat wrought iron, 115. gases, 344. iron pipe, 113. materials, 102. plates of steel, wrought iron, etc., 112. standard steel buckets, 446. water, 107, 130. wire ropes, 119. wrought iron, 114. Weight on pillars at different depths, Table of, 287. Weights and measures, 7. W r eir discharge, 140. Weirs, 138. Well drilling, Cost of, 242. West Virginia method of mining, 296. West Vulcan telephone system, 234. Wheel and axle, 92. Wheels, Water, 157. Breast, 157. Impulse, 158. Overshot, 158. Turbines, 158. Undershot, 157. Whitedamp, 349. Whiting system of hoisting, 395. Williams' method of mining, 312. Wing dams, 156. Winslow, Arthur, 81. Winzes, 316. Wire gauge, 207. nails, 114. Wire rope, 118. fastenings, 126. Life of, 123. Size of drums for, 123. splicing, 127. Weight and strength of, 119. Wire, Weather-proof, 212. INDEX. 637 Wiring, Bell, 230. Electric, 207. Wolf lamp, 358. Wood, Crushing load of, 105. fuel, Value of, 166. screws, 113. Wooden beams, 102. Constants for, 103. Wooden dams, 154. Working load for wire rope, 125. Methods of, 277. Wrought iron, Flat, 115. Wyoming region, Costs of mining in 325. Zinc, Weight of, 111. The Pulsometer Steam Pump. Recent Important q\ Improvements ..... in OVER 20.000 IN USE. ffi ** The Simplest Cheapest Most Efficient MostDurame w^ Pump FOR SHALL W MINES, GOAL AND ORE ft WASHING, DIP DRAINAGE, CONTRACTORS' USE ..... Catalogue Free. The Pulsometer Steam Pump Co., 135 Greenwich St., NEW YORK CITY. jjj AMERICAN SAFETY LAMP AND MINE SUPPLY COMPANY, 1321 to 1325 Capouse Ave., SCRANTON, PA. Largest Manufacturers of Miners' Safety Lamps IN AMERICA. SAFETY LAMPS OF ALL TYPES, EVERY LAMP TESTED BEFORE SHIPMENT, AND GUARANTEED PERFECT. SEAMLESS ALUMINUM HEAD LAMPS Cast in One Piece. STEEL OR BRASS HOOKS AS DESIRED. Grease Cups, Pneumatic Signal Gongs, Mine Whistles, Brass or Aluminum Castings, General Mine Supplies. B SEND FOR CATALOGUE. ESTABLISHED 1862. THE LUNKENHE1MER CO. MAIN OFFICES AND WORKS: CINCINNATI, OHIO, U. S. A. BRANCHES: NEW YORK : 26 Cortlandt St. LONDON : 35 Great Dover St n Originators, Sole Makers and Patentees of the Celebrated LUNKENHEIMER U Superior Brass and Iron Engineering Ap- pliances for Steam, Water, Gas, Air, Oils, Etc. Valves, Whistles, Cocks, Injectors, Lubricators, Oil and Grease Cups, Etc. All goods rigidly tested and inspected, and warranted as represented. Endorsed and liber- ally used by intelligent steam users in every land. The only goods of their class made, haying an international reputation for superior merit. Provide against substitution by "specifying lyUNKENHEiMER " make, and see that our name is on every article. None genuine without it. Investigation and comparison invited, and sat- isfaction guaranteed. Write for Catalogue. EXPOSITION UNIVERSELLE, Paris, 19003 Medals. If this page is printed well, the above will be a perfect reproduction of our IMPROVED TAIL ROPE HAULAGE ENGINES. Concisely stated they ' are equipped with steam brake convenient levers extra big bearings strong shafts best designed drums. They are perfect in adjustment and run noiselessly. MONONGAHELA MANUFACTURING CO., Manufacturers of General Mining Machinery, Hoisting Engines, vScreens, Fans, Etc. MONONGAHELA, PA. PAUL S. REEVES & SON, PHILADELPHIA, PA. Manufacturers of "Special" Phosphor Bronze RESISTS THE ACTION OF MINE WATER. Used in all pumps of the principal operators in the Anthracite and Bituminous coal regions. Reeves "TUBAL" Bronze MARK STRONG AS STEEL. Brass, Phosphor Bronze, and Manganese Bronze Castings FOR BEARINGS AND ALL OTHER PURPOSES. BABBITT METALS. Write for Prices. Everything ... For the ... ARTIST, ARCHITECT, ENGINEER, SURVEYOR. " If we have'nt it, no one has." CATALOGUES ON APPLICATION. THE WM. E. STIEREN CO., 544 Smithfield St., 406-408 Sixth Ave. Importers and Manufacturers, P1TTSBURG, PA. WM. STEWART, President. B. W. COOPER, Vice-Pres. . , nd Gen. Manage . L. A. CHESLEY, Se a&er. ic'y-Treas. The Danville Foundry^Machine Co. ENGINEERS. FOUNDERS. MACHINISTS. HELL TELEPHONE; Works, 14.' NEW TELEPHONE; ?g Danville, III. \A/ Hoisting Engines, Haulage Engines, Automatic Cages, Ordinary Cages, Ventilating Fans, Mine Cars, Car Wheels, Car Irons, Box Car Loaders, Screens, General Supplies and Foundry Work. Pat. Our Experience extends over a period of twenty years, and includes many of the largest plants of the United States, and British North America. Estimates cheerfully furnished, and personal examination made when required. WRITE US BEFORE PLACING YOUR ORDER. FIVE-GALLON CYLINDER LUBRICATOR. operate. Lubricators ENSURE PERFECT LUBRICATION Of Cylinders of all kinds of Steam Engines. They are economical of oil, reliable under all conditions, will not choke or clog, operate per- fectly in any temperature, and will not chill or freeze while steam is turned on, easily at- tached, convenient to fill and ONE FIVE-GALLON LUBRICATOR can be placed wherever conve- nient in the engine room and will lubricate all the cylinders on that steam line. Write us if you would like to try one. LACKAWANNA CYLINDER LUBRICATOR. Lackawanna Lubricator and Manufacturing Company, .WILMINGTON, DEL. ESTABLISHED 1855. THE FINCH MFG. COMPANY, SCRANTON, PA. DESIGNERS AND MANUFACTURERS OF MINING MACHINERY FOR ALL PURPOSES. Let us know what you need and we will furnish estimates. For forty-five years THE FINCH SHOPS have been noted as producers of efficient, durable, up-to-date MINING MACHINERY at moderate prices. HOISTING AND= HAULAGE MACHINERY A SPECIALTY. INSTRUCTION BY f IN . Coal and Metal Mining. ^ ^ /^ ^ Circulars and references on application. THE INTERNATIONAL CORRESPONDENCE SCHOOLS, Scranton, Pennsylvania. H. S. BEAGLE. GEO. WISE. The Beagle Hame Works, FREELAMD, PA. HAMES,~GOLLARS, and HARNESS . . FOJ* Mining, Lumbering, and Teaming. Write for Prices *>s>s>^^s*^^^^s>^^s^s*s^^^s^~*s^^^s*s^s*^^ MANGANESE STEELS IS HARD AND TOUGH. BEST METAL FOR Roll Shells, Stamp Shoes and Dies, Crusher Plates and Side Liners, Toggles and Toggle J Bearings, Gyratory Cones and Concaves, Mine Car Wheels, Coal Crushing Rolls, Etc -TAYLOR IRON AND STEEL COMPANY,- HIGH BRIDGE, NEW JERSEY. Sole Licensees in America under the Hadfield System and Patents. ULMER & HOFF, 224 Ghamplain St., CLEVELAND, OHIO. Sole Makers of THE NEW DAVIS SOLAR TRANSIT, and " LUCAS" CHAIN TAPES. Manufacturers of Strictly High Grade Engineering, Mining, and SURVEYING INSTRUMENTS. Special attention given to repairs. Send business car.l for price list. Cameron Mining Pumps for Station and Sinking are recognized in mining camps the world over as the stand- ard of excellence and the guarantor of security in operation. As " Imitation is the Sincerest Flattery " do not permit your- self to be cajoled into buying any pirated design, but get the ORIGINAL with its later and patented improvements. Our new catalogue, with full information, will be sent to you on application. The A. S. Cameron Steam Pump Works, Foot of East 23rd St., N. Y. City, I). S. A. GENERAL ELECTRIC COMPANY'S Electric Mining Apparatus, Vfc vfc Mine Locomotives ; Hoists for shafts, slopes, and rope haulage systems ; Coke Larry Equipments ; Piston or Centrifugal Pumps ; Motors for elevators, conveyors, car hoists, excavators, gold dredges ; and Sullivan Coal Cut- ters and Diamond Drills equipped with GE Motors. Estimates Given on Long Distance Power Transmission and Equipment. GENERAL OFFICE: - - SCHENECTADY, N. Y. Sales Offices in All Large Cities. "'If ite' J) \4i iif Hit Hit Hit Hii Of Hit Hit ESTABLISHED I860. Phillips Mine Supply Co. MANUFACTURERS OF Mine and Coke Works ...Equipment... South 23rd and Mary Sts., PITTSBURG, PA., U. S. A. Pat'd Waste-Packed Wheel. Simplest arid Most Effective Self-Oiling Wheel Made. Mine Gars, Gar Dumps, Gar Couplings, Coke Scrapers, Larry Wagons, Drums, Screens, Weigh Baskets, Screen Bars, Etc. | CONTRACTS FOR TIPPLE EQUIPMENT COMPLETE. | Our Patent Gross-Over Dumps Are Used EXCLUSIVELY by the Largest Concerns in the Country. LET US SUBMIT PLANS AND ESTIMATES. Get the Best Writ'e for prices and particulars ot THE BEST HAND DRILL MADE. The LeGrand Mine Drill Co. 193 Barney St., WILKES-BAKRH, PA. FOR PRICES ON Coal Tipples, Mine Cars, Larries, Drums, Etc., Etc. Address The Niles Mine and Mill Supply Co., NILES, OHIO. Chemistry, Qualitative and = Quantitative Analysis. A course of study by mail for Chemists, Assayers, and their assistants ; also employers in blast furnace works, iron and steel mills THE INTERNATIONAL CORRESPONDENCE SCHOOLS, SCRANTON, PA. ESTABLISHED 1881. MINES ^ MINERALS An Illustrated Mining and Metallurgical Journal MINE OWNERS, MANAGERS, SUPERINTENDENTS, FOREMEN, MINING ENGINEERS, MILL SUPERINTENDENTS, MINING STUDENTS. "The Most Progressive Mining Journal." Its merit as a practical periodical for all classes engaged in mining has won for it a Larger circulation than any other Mining Periodical. It is not a stock-jobbing organ, neither does it boom questionable mining schemes or regions. It is a practical mining journal for practical mining men. SUBSCRIPTION PRICE, $2.00 PER YEAR. United States, Canada, and Mexico. FOREIGN, $3.00. Send for Free Sample Copy. MINES AND MINERALS, Cable Address, " Retsof, Scranton." Scranton, Pa., U. S. A. A. Leschen & Sons Rope Co. SOLE MANUFACTURERS Patent Flattened Strand (TRADE MARK REGISTERED.) This is not a new brand of Rope. It has been on the Market for years. ALSO ALL KINDS OF Round Strand Wire Rope. SAFETY DETACHING HOOKS, ....ALSO.... Leschen's Patent Aerial Wire Rope Tramway 920-922 North First St. 47-49 South Canal St. - ST. LOUIS, MO. CHICAGO, ILL. THE TECHNICAL SUPPLY Co., SGRANTON, PA. Mining and Scientific Books, Surveying Instruments, Drawing Instruments and Supplies, Mining Instruments, Fine Mechanical Tools. SUPPLIES FOR STUDENTS OF THE INTERNATIONAL CORRESPONDENCE SCHOOLS, OF SCRANTON, PA., A SPECIALTY. Any of the following catalogues (always up to date) will be sent FREE on application : Practical Books Relating to ARCHITECTURE AND THE BUILD- ING TRADES. Practical Books Relating to CIVIL ENGINEERING. Practical Books Relating to ELECTRICITY AND ELECTRICAL ENGINEERING. Practical Books Relating to MECHANICAL AND STEAM ENGI- NEERING. Practical Books Relating to MINING. Practical Books Relating to ASSAYING. Practical Books Relating to CHEMISTRY. Special Catalogues of Drawing, Engineering, and Mining Instruments and Fine Tools. THE WATT MINING CAR WHEEL Co., BARNESVILLE, OHIO. Write us for prices. OUR SPECIALTIES : Mine Gars, Ore Gars, Gar Wheels and Axles. . SPECIAL OFFER. On bona fide application of mine superintendents or mine owners we will mail free our enlarged 1900 illustrated catalogue, describing STEAM AND COMPRESSED AIR LOCO- MOTIVES. Our system of air haulage is the safest, most efficient, and economical. Address, H. K. PORTER COMPANY, 547 Wood Street, PITTSBURG, PA. ERECTED FOR CORRESPONDENCE INSTRUCTION, IN 1898. COURSES BY MAIL IN ALL BRANCHES OF ENGINEERING. CIRCULARS ON APPLICATION. COURSES IN MECHANICAL ENGINEERING, CIVIL ENGINEERING, CHEMISTRY, COAL AND METAL MINING. THE INTERNATIONAL CORRESPONDENCE SCHOOLS, SCRANTON, PA. I Don't Get I ! Your Wires Crossed 1 I I 5 But you will unless you specify i t | THETVI PD Double Crimped | t I " I I LClX Wire Cloth ::::::: 51 * 2 The only make with the wires J |J thoroughly crimped both ways. U THE WIRES CANNOT SHIFT. PUTS ALL WIRES TO THE S ^ WEAR. IT HAS AN EVEN SURFACE. | o. q o. Q n, a a, n. B a, s, a i s a Q D, a i, a a, a a, a s, s a, R "] ^. G o, a o, Q t D D, a a, a ig a o 7, q i, S3, Q BL 81 , O O, O 0, O, E ! n. G n, q E. H s, a o, q a. q_ a" q r 1. B > n D , Q , E @ , B Q. Q G~, fi Q, ? b E], n D a a, B a, C3 a, a a', B ca, a r | THE W. S. TYLER COMPANY, ^ Cleveland, Ohio, U. S. A., > MANUFACTURERS OF if IRON, STEEL, BRASS, COPPER, AND PHOSPHOR | BRONZE WIRE CLOTH. We can make Extra Heavy Grades. Write for Pr s S ples and I t I J. & J. B. MILHOLLAND !S f COMPANY, - ! I - * _Wirc | ^ rfcru> * Manufacturers of VT1JE IXUUK, t Haulage % AND HOISTING ENGINES. +b Steel and Iron Wire Rope .... 1^1 | 'OFFICE AND WORKS: $ 714 Fifth Avenue, - - PITTSBURGH, PENNA. 3f & ^ 9??9?? ROPE HAULAGE ENGINES. > Jft HOISTING ENGINES. STEEly AND IRON WIRE ROPE. ^ +, GUM IvIN.ED SHEAVES. ROPE I^INED SHEAVES. |Jj INCLINED PI^ANE MACHINERY. PI.AIN IRON SHEAVES. COAI, CRUSHERS. WOOD ROGERS AND SIDE SHEAVES. STEAM ENGINES 10 TO 500 HORSE POWER. STEAM OR WATER POWER PLANTS. J| TAIl^ ROPE HAUtAGES. ENDLESS ROPE HAULAGES. NARROW GAUGE I.OCOMOTIVES. 2 SHAFTING AND PUIyl^EYS. SECOND HAND ENGINES. Jj AI.I, KINDS OF BOILERS. AI^I^ KINDS OF REPAIRING DONE. ^ KSTAJ'.MSHKI) lH6< . JAMES L NORRIS, Member of the Patent f.mc Association, Counselor in Patent Causes, SOLICITOR OF AMERICAN < AND FOREIGN PATENTS. ... IN ACTIVE PRACTICE THE UNIVERSITY OF CALIFORNIA LIBRARY Hardsocg Mfg. Co., Ottumwa, la. What Cheer Drill and Miners' Tool Co., What Cheer, la. The Carter Mfg. Co., Louisville, Ky. Anthony Wayne Mfg. Co., Fort Wayne, Ind. Athol Machine Co., Athol, Mass. Arlington Mfg. Co., New York. The Colliery Engineer Co., Scranton, Pa. Seneca Glass Co., Morgantown, W. Va. Metallic Cap Mfg. Co., New York. Gary Safe Co., Buffalo, N. Y. Columbia Carriage Co., Hamilton, O. .Buckeye Iron and Brass Works, Day- ton, O. Jackson & Sharp Co. .Wilmington, Del. Forked Deer Tobacco Works, Paducah, Ky. Keating Implement and Machine Co., Dallas, Texas.